Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Sparse matrix-vector multiplication on network-on-chip

NASA Astrophysics Data System (ADS)

Sun, C.-C.; Götze, J.; Jheng, H.-Y.; Ruan, S.-J.

2010-12-01

In this paper, we present an idea for performing matrix-vector multiplication by using Network-on-Chip (NoC) architecture. In traditional IC design on-chip communications have been designed with dedicated point-to-point interconnections. Therefore, regular local data transfer is the major concept of many parallel implementations. However, when dealing with the parallel implementation of sparse matrix-vector multiplication (SMVM), which is the main step of all iterative algorithms for solving systems of linear equation, the required data transfers depend on the sparsity structure of the matrix and can be extremely irregular. Using the NoC architecture makes it possible to deal with arbitrary structure of the data transfers; i.e. with the irregular structure of the sparse matrices. So far, we have already implemented the proposed SMVM-NoC architecture with the size 4×4 and 5×5 in IEEE 754 single float point precision using FPGA.

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

Simon, Horst D.; Kremenetsky, Mark D.; Richardson, John; Lasinski, T. A. (Technical Monitor)

1994-01-01

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Communications oriented programming of parallel iterative solutions of sparse linear systems

NASA Technical Reports Server (NTRS)

Patrick, M. L.; Pratt, T. W.

1986-01-01

Parallel algorithms are developed for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions is determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. Three different parallel algorithms for solving the same class of problems are presented, and their effectiveness is analyzed from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

Optimal parallel solution of sparse triangular systems

NASA Technical Reports Server (NTRS)

Alvarado, Fernando L.; Schreiber, Robert

1990-01-01

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Methods for design and evaluation of integrated hardware-software systems for concurrent computation

NASA Technical Reports Server (NTRS)

Pratt, T. W.

1985-01-01

Research activities and publications are briefly summarized. The major tasks reviewed are: (1) VAX implementation of the PISCES parallel programming environment; (2) Apollo workstation network implementation of the PISCES environment; (3) FLEX implementation of the PISCES environment; (4) sparse matrix iterative solver in PSICES Fortran; (5) image processing application of PISCES; and (6) a formal model of concurrent computation being developed.

Parallel computation of multigroup reactivity coefficient using iterative method

NASA Astrophysics Data System (ADS)

Susmikanti, Mike; Dewayatna, Winter

2013-09-01

One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium.

Optimization and validation of accelerated golden-angle radial sparse MRI reconstruction with self-calibrating GRAPPA operator gridding.

PubMed

Benkert, Thomas; Tian, Ye; Huang, Chenchan; DiBella, Edward V R; Chandarana, Hersh; Feng, Li

2018-07-01

Golden-angle radial sparse parallel (GRASP) MRI reconstruction requires gridding and regridding to transform data between radial and Cartesian k-space. These operations are repeatedly performed in each iteration, which makes the reconstruction computationally demanding. This work aimed to accelerate GRASP reconstruction using self-calibrating GRAPPA operator gridding (GROG) and to validate its performance in clinical imaging. GROG is an alternative gridding approach based on parallel imaging, in which k-space data acquired on a non-Cartesian grid are shifted onto a Cartesian k-space grid using information from multicoil arrays. For iterative non-Cartesian image reconstruction, GROG is performed only once as a preprocessing step. Therefore, the subsequent iterative reconstruction can be performed directly in Cartesian space, which significantly reduces computational burden. Here, a framework combining GROG with GRASP (GROG-GRASP) is first optimized and then compared with standard GRASP reconstruction in 22 prostate patients. GROG-GRASP achieved approximately 4.2-fold reduction in reconstruction time compared with GRASP (∼333 min versus ∼78 min) while maintaining image quality (structural similarity index ≈ 0.97 and root mean square error ≈ 0.007). Visual image quality assessment by two experienced radiologists did not show significant differences between the two reconstruction schemes. With a graphics processing unit implementation, image reconstruction time can be further reduced to approximately 14 min. The GRASP reconstruction can be substantially accelerated using GROG. This framework is promising toward broader clinical application of GRASP and other iterative non-Cartesian reconstruction methods. Magn Reson Med 80:286-293, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation

PubMed Central

Zhang, Jie; Fan, Shangang; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki

2017-01-01

Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation.

PubMed

Li, Yunyi; Zhang, Jie; Fan, Shangang; Yang, Jie; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki; Gui, Guan

2017-12-15

Both L 1/2 and L 2/3 are two typical non-convex regularizations of L p (0

Exploiting Data Sparsity in Parallel Matrix Powers Computations

DTIC Science & Technology

2013-05-03

2013 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour...matrices of the form A = D+USV H, where D is sparse and USV H has low rank but may be dense. Matrices of this form arise in many practical applications...methods numerical partial di erential equation solvers, and preconditioned iterative methods. If A has this form , our algorithm enables a communication

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization.

PubMed

Xu, Peng; Tian, Yin; Lei, Xu; Hu, Xiao; Yao, Dezhong

2008-12-01

How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.

Parallelization of the preconditioned IDR solver for modern multicore computer systems

NASA Astrophysics Data System (ADS)

Bessonov, O. A.; Fedoseyev, A. I.

2012-10-01

This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).

Highly undersampled contrast-enhanced MRA with iterative reconstruction: Integration in a clinical setting.

PubMed

Stalder, Aurelien F; Schmidt, Michaela; Quick, Harald H; Schlamann, Marc; Maderwald, Stefan; Schmitt, Peter; Wang, Qiu; Nadar, Mariappan S; Zenge, Michael O

2015-12-01

To integrate, optimize, and evaluate a three-dimensional (3D) contrast-enhanced sparse MRA technique with iterative reconstruction on a standard clinical MR system. Data were acquired using a highly undersampled Cartesian spiral phyllotaxis sampling pattern and reconstructed directly on the MR system with an iterative SENSE technique. Undersampling, regularization, and number of iterations of the reconstruction were optimized and validated based on phantom experiments and patient data. Sparse MRA of the whole head (field of view: 265 × 232 × 179 mm(3) ) was investigated in 10 patient examinations. High-quality images with 30-fold undersampling, resulting in 0.7 mm isotropic resolution within 10 s acquisition, were obtained. After optimization of the regularization factor and of the number of iterations of the reconstruction, it was possible to reconstruct images with excellent quality within six minutes per 3D volume. Initial results of sparse contrast-enhanced MRA (CEMRA) in 10 patients demonstrated high-quality whole-head first-pass MRA for both the arterial and venous contrast phases. While sparse MRI techniques have not yet reached clinical routine, this study demonstrates the technical feasibility of high-quality sparse CEMRA of the whole head in a clinical setting. Sparse CEMRA has the potential to become a viable alternative where conventional CEMRA is too slow or does not provide sufficient spatial resolution. © 2014 Wiley Periodicals, Inc.

Sparse magnetic resonance imaging reconstruction using the bregman iteration

NASA Astrophysics Data System (ADS)

Lee, Dong-Hoon; Hong, Cheol-Pyo; Lee, Man-Woo

2013-01-01

Magnetic resonance imaging (MRI) reconstruction needs many samples that are sequentially sampled by using phase encoding gradients in a MRI system. It is directly connected to the scan time for the MRI system and takes a long time. Therefore, many researchers have studied ways to reduce the scan time, especially, compressed sensing (CS), which is used for sparse images and reconstruction for fewer sampling datasets when the k-space is not fully sampled. Recently, an iterative technique based on the bregman method was developed for denoising. The bregman iteration method improves on total variation (TV) regularization by gradually recovering the fine-scale structures that are usually lost in TV regularization. In this study, we studied sparse sampling image reconstruction using the bregman iteration for a low-field MRI system to improve its temporal resolution and to validate its usefulness. The image was obtained with a 0.32 T MRI scanner (Magfinder II, SCIMEDIX, Korea) with a phantom and an in-vivo human brain in a head coil. We applied random k-space sampling, and we determined the sampling ratios by using half the fully sampled k-space. The bregman iteration was used to generate the final images based on the reduced data. We also calculated the root-mean-square-error (RMSE) values from error images that were obtained using various numbers of bregman iterations. Our reconstructed images using the bregman iteration for sparse sampling images showed good results compared with the original images. Moreover, the RMSE values showed that the sparse reconstructed phantom and the human images converged to the original images. We confirmed the feasibility of sparse sampling image reconstruction methods using the bregman iteration with a low-field MRI system and obtained good results. Although our results used half the sampling ratio, this method will be helpful in increasing the temporal resolution at low-field MRI systems.

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2002-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

NASA Astrophysics Data System (ADS)

Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo

2016-11-01

We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.

Representation-Independent Iteration of Sparse Data Arrays

NASA Technical Reports Server (NTRS)

James, Mark

2007-01-01

An approach is defined that describes a method of iterating over massively large arrays containing sparse data using an approach that is implementation independent of how the contents of the sparse arrays are laid out in memory. What is unique and important here is the decoupling of the iteration over the sparse set of array elements from how they are internally represented in memory. This enables this approach to be backward compatible with existing schemes for representing sparse arrays as well as new approaches. What is novel here is a new approach for efficiently iterating over sparse arrays that is independent of the underlying memory layout representation of the array. A functional interface is defined for implementing sparse arrays in any modern programming language with a particular focus for the Chapel programming language. Examples are provided that show the translation of a loop that computes a matrix vector product into this representation for both the distributed and not-distributed cases. This work is directly applicable to NASA and its High Productivity Computing Systems (HPCS) program that JPL and our current program are engaged in. The goal of this program is to create powerful, scalable, and economically viable high-powered computer systems suitable for use in national security and industry by 2010. This is important to NASA for its computationally intensive requirements for analyzing and understanding the volumes of science data from our returned missions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

A communication-avoiding, hybrid-parallel, rank-revealing orthogonalization method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoemmen, Mark

2010-11-01

Orthogonalization consumes much of the run time of many iterative methods for solving sparse linear systems and eigenvalue problems. Commonly used algorithms, such as variants of Gram-Schmidt or Householder QR, have performance dominated by communication. Here, 'communication' includes both data movement between the CPU and memory, and messages between processors in parallel. Our Tall Skinny QR (TSQR) family of algorithms requires asymptotically fewer messages between processors and data movement between CPU and memory than typical orthogonalization methods, yet achieves the same accuracy as Householder QR factorization. Furthermore, in block orthogonalizations, TSQR is faster and more accurate than existing approaches formore » orthogonalizing the vectors within each block ('normalization'). TSQR's rank-revealing capability also makes it useful for detecting deflation in block iterative methods, for which existing approaches sacrifice performance, accuracy, or both. We have implemented a version of TSQR that exploits both distributed-memory and shared-memory parallelism, and supports real and complex arithmetic. Our implementation is optimized for the case of orthogonalizing a small number (5-20) of very long vectors. The shared-memory parallel component uses Intel's Threading Building Blocks, though its modular design supports other shared-memory programming models as well, including computation on the GPU. Our implementation achieves speedups of 2 times or more over competing orthogonalizations. It is available now in the development branch of the Trilinos software package, and will be included in the 10.8 release.« less

Laplace-domain waveform modeling and inversion for the 3D acoustic-elastic coupled media

NASA Astrophysics Data System (ADS)

Shin, Jungkyun; Shin, Changsoo; Calandra, Henri

2016-06-01

Laplace-domain waveform inversion reconstructs long-wavelength subsurface models by using the zero-frequency component of damped seismic signals. Despite the computational advantages of Laplace-domain waveform inversion over conventional frequency-domain waveform inversion, an acoustic assumption and an iterative matrix solver have been used to invert 3D marine datasets to mitigate the intensive computing cost. In this study, we develop a Laplace-domain waveform modeling and inversion algorithm for 3D acoustic-elastic coupled media by using a parallel sparse direct solver library (MUltifrontal Massively Parallel Solver, MUMPS). We precisely simulate a real marine environment by coupling the 3D acoustic and elastic wave equations with the proper boundary condition at the fluid-solid interface. In addition, we can extract the elastic properties of the Earth below the sea bottom from the recorded acoustic pressure datasets. As a matrix solver, the parallel sparse direct solver is used to factorize the non-symmetric impedance matrix in a distributed memory architecture and rapidly solve the wave field for a number of shots by using the lower and upper matrix factors. Using both synthetic datasets and real datasets obtained by a 3D wide azimuth survey, the long-wavelength component of the P-wave and S-wave velocity models is reconstructed and the proposed modeling and inversion algorithm are verified. A cluster of 80 CPU cores is used for this study.

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

LDRD final report on massively-parallel linear programming : the parPCx system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parekh, Ojas; Phillips, Cynthia Ann; Boman, Erik Gunnar

2005-02-01

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce fast, stable serial LP solvers. Previous parallel codes run on shared-memory systems and have little or no distribution of the constraint matrix. We have seen no reports of general LP solver runsmore » on large numbers of processors. Our parallel LP code is based on an efficient serial implementation of Mehrotra's interior-point predictor-corrector algorithm (PCx). The computational core of this algorithm is the assembly and solution of a sparse linear system. We have substantially rewritten the PCx code and based it on Trilinos, the parallel linear algebra library developed at Sandia. Our interior-point method can use either direct or iterative solvers for the linear system. To achieve a good parallel data distribution of the constraint matrix, we use a (pre-release) version of a hypergraph partitioner from the Zoltan partitioning library. We describe the design and implementation of our new LP solver called parPCx and give preliminary computational results. We summarize a number of issues related to efficient parallel solution of LPs with interior-point methods including data distribution, numerical stability, and solving the core linear system using both direct and iterative methods. We describe a number of applications of LP specific to US Department of Energy mission areas and we summarize our efforts to integrate parPCx (and parallel LP solvers in general) into Sandia's massively-parallel integer programming solver PICO (Parallel Interger and Combinatorial Optimizer). We conclude with directions for long-term future algorithmic research and for near-term development that could improve the performance of parPCx.« less

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

DOE PAGES

Banerjee, Amartya S.; Lin, Lin; Hu, Wei; ...

2016-10-21

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) canmore » be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.« less

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles.

PubMed

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-08-13

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well.

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Use of general purpose graphics processing units with MODFLOW

USGS Publications Warehouse

Hughes, Joseph D.; White, Jeremy T.

2013-01-01

To evaluate the use of general-purpose graphics processing units (GPGPUs) to improve the performance of MODFLOW, an unstructured preconditioned conjugate gradient (UPCG) solver has been developed. The UPCG solver uses a compressed sparse row storage scheme and includes Jacobi, zero fill-in incomplete, and modified-incomplete lower-upper (LU) factorization, and generalized least-squares polynomial preconditioners. The UPCG solver also includes options for sequential and parallel solution on the central processing unit (CPU) using OpenMP. For simulations utilizing the GPGPU, all basic linear algebra operations are performed on the GPGPU; memory copies between the central processing unit CPU and GPCPU occur prior to the first iteration of the UPCG solver and after satisfying head and flow criteria or exceeding a maximum number of iterations. The efficiency of the UPCG solver for GPGPU and CPU solutions is benchmarked using simulations of a synthetic, heterogeneous unconfined aquifer with tens of thousands to millions of active grid cells. Testing indicates GPGPU speedups on the order of 2 to 8, relative to the standard MODFLOW preconditioned conjugate gradient (PCG) solver, can be achieved when (1) memory copies between the CPU and GPGPU are optimized, (2) the percentage of time performing memory copies between the CPU and GPGPU is small relative to the calculation time, (3) high-performance GPGPU cards are utilized, and (4) CPU-GPGPU combinations are used to execute sequential operations that are difficult to parallelize. Furthermore, UPCG solver testing indicates GPGPU speedups exceed parallel CPU speedups achieved using OpenMP on multicore CPUs for preconditioners that can be easily parallelized.

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods.

PubMed

Schmidt, Johannes F M; Santelli, Claudio; Kozerke, Sebastian

2016-01-01

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles

PubMed Central

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-01-01

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well. PMID:26287194

Low-rank Atlas Image Analyses in the Presence of Pathologies

PubMed Central

Liu, Xiaoxiao; Niethammer, Marc; Kwitt, Roland; Singh, Nikhil; McCormick, Matt; Aylward, Stephen

2015-01-01

We present a common framework, for registering images to an atlas and for forming an unbiased atlas, that tolerates the presence of pathologies such as tumors and traumatic brain injury lesions. This common framework is particularly useful when a sufficient number of protocol-matched scans from healthy subjects cannot be easily acquired for atlas formation and when the pathologies in a patient cause large appearance changes. Our framework combines a low-rank-plus-sparse image decomposition technique with an iterative, diffeomorphic, group-wise image registration method. At each iteration of image registration, the decomposition technique estimates a “healthy” version of each image as its low-rank component and estimates the pathologies in each image as its sparse component. The healthy version of each image is used for the next iteration of image registration. The low-rank and sparse estimates are refined as the image registrations iteratively improve. When that framework is applied to image-to-atlas registration, the low-rank image is registered to a pre-defined atlas, to establish correspondence that is independent of the pathologies in the sparse component of each image. Ultimately, image-to-atlas registrations can be used to define spatial priors for tissue segmentation and to map information across subjects. When that framework is applied to unbiased atlas formation, at each iteration, the average of the low-rank images from the patients is used as the atlas image for the next iteration, until convergence. Since each iteration’s atlas is comprised of low-rank components, it provides a population-consistent, pathology-free appearance. Evaluations of the proposed methodology are presented using synthetic data as well as simulated and clinical tumor MRI images from the brain tumor segmentation (BRATS) challenge from MICCAI 2012. PMID:26111390

Convergence Speed of a Dynamical System for Sparse Recovery

NASA Astrophysics Data System (ADS)

Balavoine, Aurele; Rozell, Christopher J.; Romberg, Justin

2013-09-01

This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to underdetermined systems of linear equations and come with strong performance guarantees. The LCA under study differs from the typical L1 solver in that it operates in continuous time: instead of being specified by discrete iterations, it evolves according to a system of nonlinear ordinary differential equations. The LCA is constructed from simple components, giving it the potential to be implemented as a large-scale analog circuit. The goal of this paper is to give guarantees on the convergence time of the LCA system. To do so, we analyze how the LCA evolves as it is recovering a sparse signal from underdetermined measurements. We show that under appropriate conditions on the measurement matrix and the problem parameters, the path the LCA follows can be described as a sequence of linear differential equations, each with a small number of active variables. This allows us to relate the convergence time of the system to the restricted isometry constant of the matrix. Interesting parallels to sparse-recovery digital solvers emerge from this study. Our analysis covers both the noisy and noiseless settings and is supported by simulation results.

Accelerated Path-following Iterative Shrinkage Thresholding Algorithm with Application to Semiparametric Graph Estimation

PubMed Central

Zhao, Tuo; Liu, Han

2016-01-01

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, i.e., APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results which do not exist in the existing literature. Thorough numerical results are provided to back up our theory. PMID:28133430

Parallel computation safety analysis irradiation targets fission product molybdenum in neutronic aspect using the successive over-relaxation algorithm

NASA Astrophysics Data System (ADS)

Susmikanti, Mike; Dewayatna, Winter; Sulistyo, Yos

2014-09-01

One of the research activities in support of commercial radioisotope production program is a safety research on target FPM (Fission Product Molybdenum) irradiation. FPM targets form a tube made of stainless steel which contains nuclear-grade high-enrichment uranium. The FPM irradiation tube is intended to obtain fission products. Fission materials such as Mo99 used widely the form of kits in the medical world. The neutronics problem is solved using first-order perturbation theory derived from the diffusion equation for four groups. In contrast, Mo isotopes have longer half-lives, about 3 days (66 hours), so the delivery of radioisotopes to consumer centers and storage is possible though still limited. The production of this isotope potentially gives significant economic value. The criticality and flux in multigroup diffusion model was calculated for various irradiation positions and uranium contents. This model involves complex computation, with large and sparse matrix system. Several parallel algorithms have been developed for the sparse and large matrix solution. In this paper, a successive over-relaxation (SOR) algorithm was implemented for the calculation of reactivity coefficients which can be done in parallel. Previous works performed reactivity calculations serially with Gauss-Seidel iteratives. The parallel method can be used to solve multigroup diffusion equation system and calculate the criticality and reactivity coefficients. In this research a computer code was developed to exploit parallel processing to perform reactivity calculations which were to be used in safety analysis. The parallel processing in the multicore computer system allows the calculation to be performed more quickly. This code was applied for the safety limits calculation of irradiated FPM targets containing highly enriched uranium. The results of calculations neutron show that for uranium contents of 1.7676 g and 6.1866 g (× 106 cm-1) in a tube, their delta reactivities are the still within safety limits; however, for 7.9542 g and 8.838 g (× 106 cm-1) the limits were exceeded.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

View-interpolation of sparsely sampled sinogram using convolutional neural network

NASA Astrophysics Data System (ADS)

Lee, Hoyeon; Lee, Jongha; Cho, Suengryong

2017-02-01

Spare-view sampling and its associated iterative image reconstruction in computed tomography have actively investigated. Sparse-view CT technique is a viable option to low-dose CT, particularly in cone-beam CT (CBCT) applications, with advanced iterative image reconstructions with varying degrees of image artifacts. One of the artifacts that may occur in sparse-view CT is the streak artifact in the reconstructed images. Another approach has been investigated for sparse-view CT imaging by use of the interpolation methods to fill in the missing view data and that reconstructs the image by an analytic reconstruction algorithm. In this study, we developed an interpolation method using convolutional neural network (CNN), which is one of the widely used deep-learning methods, to find missing projection data and compared its performances with the other interpolation techniques.

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement

PubMed Central

Hao, Yansong; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-01-01

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency. PMID:29597280

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement.

PubMed

Ren, Bangyue; Hao, Yansong; Wang, Huaqing; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-03-28

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

Parallel pivoting combined with parallel reduction

NASA Technical Reports Server (NTRS)

Alaghband, Gita

1987-01-01

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

X-ray computed tomography using curvelet sparse regularization.

PubMed

Wieczorek, Matthias; Frikel, Jürgen; Vogel, Jakob; Eggl, Elena; Kopp, Felix; Noël, Peter B; Pfeiffer, Franz; Demaret, Laurent; Lasser, Tobias

2015-04-01

Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.

NASA Technical Reports Server (NTRS)

Reddy, C. J.

2000-01-01

PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.

Parallel solution of sparse one-dimensional dynamic programming problems

NASA Technical Reports Server (NTRS)

Nicol, David M.

1989-01-01

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Effective channel estimation and efficient symbol detection for multi-input multi-output underwater acoustic communications

NASA Astrophysics Data System (ADS)

Ling, Jun

Achieving reliable underwater acoustic communications (UAC) has long been recognized as a challenging problem owing to the scarce bandwidth available and the reverberant spread in both time and frequency domains. To pursue high data rates, we consider a multi-input multi-output (MIMO) UAC system, and our focus is placed on two main issues regarding a MIMO UAC system: (1) channel estimation, which involves the design of the training sequences and the development of a reliable channel estimation algorithm, and (2) symbol detection, which requires interference cancelation schemes due to simultaneous transmission from multiple transducers. To enhance channel estimation performance, we present a cyclic approach for designing training sequences with good auto- and cross-correlation properties, and a channel estimation algorithm called the iterative adaptive approach (IAA). Sparse channel estimates can be obtained by combining IAA with the Bayesian information criterion (BIC). Moreover, we present sparse learning via iterative minimization (SLIM) and demonstrate that SLIM gives similar performance to IAA but at a much lower computational cost. Furthermore, an extension of the SLIM algorithm is introduced to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). Regarding symbol detection, a linear minimum mean-squared error based detection scheme, called RELAX-BLAST, which is a combination of vertical Bell Labs layered space-time (V-BLAST) algorithm and the cyclic principle of the RELAX algorithm, is presented and it is shown that RELAX-BLAST outperforms V-BLAST. We show that RELAX-BLAST can be implemented efficiently by making use of the conjugate gradient method and diagonalization properties of circulant matrices. This fast implementation approach requires only simple fast Fourier transform operations and facilitates parallel implementations. The effectiveness of the proposed MIMO schemes is verified by both computer simulations and experimental results obtained by analyzing the measurements acquired in multiple in-water experiments.

Storage of sparse files using parallel log-structured file system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, John M.; Faibish, Sorin; Grider, Gary

A sparse file is stored without holes by storing a data portion of the sparse file using a parallel log-structured file system; and generating an index entry for the data portion, the index entry comprising a logical offset, physical offset and length of the data portion. The holes can be restored to the sparse file upon a reading of the sparse file. The data portion can be stored at a logical end of the sparse file. Additional storage efficiency can optionally be achieved by (i) detecting a write pattern for a plurality of the data portions and generating a singlemore » patterned index entry for the plurality of the patterned data portions; and/or (ii) storing the patterned index entries for a plurality of the sparse files in a single directory, wherein each entry in the single directory comprises an identifier of a corresponding sparse file.« less

A distributed-memory approximation algorithm for maximum weight perfect bipartite matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azad, Ariful; Buluc, Aydin; Li, Xiaoye S.

We design and implement an efficient parallel approximation algorithm for the problem of maximum weight perfect matching in bipartite graphs, i.e. the problem of finding a set of non-adjacent edges that covers all vertices and has maximum weight. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated by finding good pivots in scalable sparse direct solvers before factorization where sequential implementations of maximum weight perfect matching algorithms, such as those available in MC64, are widely used due to the lack of scalable alternatives. To overcome this limitation, we proposemore » a fully parallel distributed memory algorithm that first generates a perfect matching and then searches for weightaugmenting cycles of length four in parallel and iteratively augments the matching with a vertex disjoint set of such cycles. For most practical problems the weights of the perfect matchings generated by our algorithm are very close to the optimum. An efficient implementation of the algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer and can solve instances that are too large to be handled by a single node using the sequential algorithm.« less

FPGA implementation of sparse matrix algorithm for information retrieval

NASA Astrophysics Data System (ADS)

Bojanic, Slobodan; Jevtic, Ruzica; Nieto-Taladriz, Octavio

2005-06-01

Information text data retrieval requires a tremendous amount of processing time because of the size of the data and the complexity of information retrieval algorithms. In this paper the solution to this problem is proposed via hardware supported information retrieval algorithms. Reconfigurable computing may adopt frequent hardware modifications through its tailorable hardware and exploits parallelism for a given application through reconfigurable and flexible hardware units. The degree of the parallelism can be tuned for data. In this work we implemented standard BLAS (basic linear algebra subprogram) sparse matrix algorithm named Compressed Sparse Row (CSR) that is showed to be more efficient in terms of storage space requirement and query-processing timing over the other sparse matrix algorithms for information retrieval application. Although inverted index algorithm is treated as the de facto standard for information retrieval for years, an alternative approach to store the index of text collection in a sparse matrix structure gains more attention. This approach performs query processing using sparse matrix-vector multiplication and due to parallelization achieves a substantial efficiency over the sequential inverted index. The parallel implementations of information retrieval kernel are presented in this work targeting the Virtex II Field Programmable Gate Arrays (FPGAs) board from Xilinx. A recent development in scientific applications is the use of FPGA to achieve high performance results. Computational results are compared to implementations on other platforms. The design achieves a high level of parallelism for the overall function while retaining highly optimised hardware within processing unit.

Fast implementation for compressive recovery of highly accelerated cardiac cine MRI using the balanced sparse model.

PubMed

Ting, Samuel T; Ahmad, Rizwan; Jin, Ning; Craft, Jason; Serafim da Silveira, Juliana; Xue, Hui; Simonetti, Orlando P

2017-04-01

Sparsity-promoting regularizers can enable stable recovery of highly undersampled magnetic resonance imaging (MRI), promising to improve the clinical utility of challenging applications. However, lengthy computation time limits the clinical use of these methods, especially for dynamic MRI with its large corpus of spatiotemporal data. Here, we present a holistic framework that utilizes the balanced sparse model for compressive sensing and parallel computing to reduce the computation time of cardiac MRI recovery methods. We propose a fast, iterative soft-thresholding method to solve the resulting ℓ1-regularized least squares problem. In addition, our approach utilizes a parallel computing environment that is fully integrated with the MRI acquisition software. The methodology is applied to two formulations of the multichannel MRI problem: image-based recovery and k-space-based recovery. Using measured MRI data, we show that, for a 224 × 144 image series with 48 frames, the proposed k-space-based approach achieves a mean reconstruction time of 2.35 min, a 24-fold improvement compared a reconstruction time of 55.5 min for the nonlinear conjugate gradient method, and the proposed image-based approach achieves a mean reconstruction time of 13.8 s. Our approach can be utilized to achieve fast reconstruction of large MRI datasets, thereby increasing the clinical utility of reconstruction techniques based on compressed sensing. Magn Reson Med 77:1505-1515, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE PAGES

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel; ...

2017-06-01

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

DOE PAGES

Ballard, Grey; Druinsky, Alex; Knight, Nicholas; ...

2015-01-01

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computationmore » to improve application-specific algorithms for multiplying sparse matrices.« less

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

PubMed

Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

2016-12-13

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

A performance study of sparse Cholesky factorization on INTEL iPSC/860

NASA Technical Reports Server (NTRS)

Zubair, M.; Ghose, M.

1992-01-01

The problem of Cholesky factorization of a sparse matrix has been very well investigated on sequential machines. A number of efficient codes exist for factorizing large unstructured sparse matrices. However, there is a lack of such efficient codes on parallel machines in general, and distributed machines in particular. Some of the issues that are critical to the implementation of sparse Cholesky factorization on a distributed memory parallel machine are ordering, partitioning and mapping, load balancing, and ordering of various tasks within a processor. Here, we focus on the effect of various partitioning schemes on the performance of sparse Cholesky factorization on the Intel iPSC/860. Also, a new partitioning heuristic for structured as well as unstructured sparse matrices is proposed, and its performance is compared with other schemes.

Highly parallel sparse Cholesky factorization

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Schreiber, Robert

1990-01-01

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

An iterative method for systems of nonlinear hyperbolic equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1989-01-01

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

Efficient diagonalization of the sparse matrices produced within the framework of the UK R-matrix molecular codes

NASA Astrophysics Data System (ADS)

Galiatsatos, P. G.; Tennyson, J.

2012-11-01

The most time consuming step within the framework of the UK R-matrix molecular codes is that of the diagonalization of the inner region Hamiltonian matrix (IRHM). Here we present the method that we follow to speed up this step. We use shared memory machines (SMM), distributed memory machines (DMM), the OpenMP directive based parallel language, the MPI function based parallel language, the sparse matrix diagonalizers ARPACK and PARPACK, a variation for real symmetric matrices of the official coordinate sparse matrix format and finally a parallel sparse matrix-vector product (PSMV). The efficient application of the previous techniques rely on two important facts: the sparsity of the matrix is large enough (more than 98%) and in order to get back converged results we need a small only part of the matrix spectrum.

Impact of view reduction in CT on radiation dose for patients

NASA Astrophysics Data System (ADS)

Parcero, E.; Flores, L.; Sánchez, M. G.; Vidal, V.; Verdú, G.

2017-08-01

Iterative methods have become a hot topic of research in computed tomography (CT) imaging because of their capacity to resolve the reconstruction problem from a limited number of projections. This allows the reduction of radiation exposure on patients during the data acquisition. The reconstruction time and the high radiation dose imposed on patients are the two major drawbacks in CT. To solve them effectively we adapted the method for sparse linear equations and sparse least squares (LSQR) with soft threshold filtering (STF) and the fast iterative shrinkage-thresholding algorithm (FISTA) to computed tomography reconstruction. The feasibility of the proposed methods is demonstrated numerically.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

WE-G-18A-04: 3D Dictionary Learning Based Statistical Iterative Reconstruction for Low-Dose Cone Beam CT Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, T; UT Southwestern Medical Center, Dallas, TX; Yan, H

2014-06-15

Purpose: To develop a 3D dictionary learning based statistical reconstruction algorithm on graphic processing units (GPU), to improve the quality of low-dose cone beam CT (CBCT) imaging with high efficiency. Methods: A 3D dictionary containing 256 small volumes (atoms) of 3x3x3 voxels was trained from a high quality volume image. During reconstruction, we utilized a Cholesky decomposition based orthogonal matching pursuit algorithm to find a sparse representation on this dictionary basis of each patch in the reconstructed image, in order to regularize the image quality. To accelerate the time-consuming sparse coding in the 3D case, we implemented our algorithm inmore » a parallel fashion by taking advantage of the tremendous computational power of GPU. Evaluations are performed based on a head-neck patient case. FDK reconstruction with full dataset of 364 projections is used as the reference. We compared the proposed 3D dictionary learning based method with a tight frame (TF) based one using a subset data of 121 projections. The image qualities under different resolutions in z-direction, with or without statistical weighting are also studied. Results: Compared to the TF-based CBCT reconstruction, our experiments indicated that 3D dictionary learning based CBCT reconstruction is able to recover finer structures, to remove more streaking artifacts, and is less susceptible to blocky artifacts. It is also observed that statistical reconstruction approach is sensitive to inconsistency between the forward and backward projection operations in parallel computing. Using high a spatial resolution along z direction helps improving the algorithm robustness. Conclusion: 3D dictionary learning based CBCT reconstruction algorithm is able to sense the structural information while suppressing noise, and hence to achieve high quality reconstruction. The GPU realization of the whole algorithm offers a significant efficiency enhancement, making this algorithm more feasible for potential clinical application. A high zresolution is preferred to stabilize statistical iterative reconstruction. This work was supported in part by NIH(1R01CA154747-01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011), China Scholarship Council.« less

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Single-agent parallel window search

NASA Technical Reports Server (NTRS)

Powley, Curt; Korf, Richard E.

1991-01-01

Parallel window search is applied to single-agent problems by having different processes simultaneously perform iterations of Iterative-Deepening-A(asterisk) (IDA-asterisk) on the same problem but with different cost thresholds. This approach is limited by the time to perform the goal iteration. To overcome this disadvantage, the authors consider node ordering. They discuss how global node ordering by minimum h among nodes with equal f = g + h values can reduce the time complexity of serial IDA-asterisk by reducing the time to perform the iterations prior to the goal iteration. Finally, the two ideas of parallel window search and node ordering are combined to eliminate the weaknesses of each approach while retaining the strengths. The resulting approach, called simply parallel window search, can be used to find a near-optimal solution quickly, improve the solution until it is optimal, and then finally guarantee optimality, depending on the amount of time available.

Optimizing convergence rates of alternating minimization reconstruction algorithms for real-time explosive detection applications

NASA Astrophysics Data System (ADS)

Bosch, Carl; Degirmenci, Soysal; Barlow, Jason; Mesika, Assaf; Politte, David G.; O'Sullivan, Joseph A.

2016-05-01

X-ray computed tomography reconstruction for medical, security and industrial applications has evolved through 40 years of experience with rotating gantry scanners using analytic reconstruction techniques such as filtered back projection (FBP). In parallel, research into statistical iterative reconstruction algorithms has evolved to apply to sparse view scanners in nuclear medicine, low data rate scanners in Positron Emission Tomography (PET) [5, 7, 10] and more recently to reduce exposure to ionizing radiation in conventional X-ray CT scanners. Multiple approaches to statistical iterative reconstruction have been developed based primarily on variations of expectation maximization (EM) algorithms. The primary benefit of EM algorithms is the guarantee of convergence that is maintained when iterative corrections are made within the limits of convergent algorithms. The primary disadvantage, however is that strict adherence to correction limits of convergent algorithms extends the number of iterations and ultimate timeline to complete a 3D volumetric reconstruction. Researchers have studied methods to accelerate convergence through more aggressive corrections [1], ordered subsets [1, 3, 4, 9] and spatially variant image updates. In this paper we describe the development of an AM reconstruction algorithm with accelerated convergence for use in a real-time explosive detection application for aviation security. By judiciously applying multiple acceleration techniques and advanced GPU processing architectures, we are able to perform 3D reconstruction of scanned passenger baggage at a rate of 75 slices per second. Analysis of the results on stream of commerce passenger bags demonstrates accelerated convergence by factors of 8 to 15, when comparing images from accelerated and strictly convergent algorithms.

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

Shedding New Light on Exploding Stars: Terascale Simulations of Nuetrino-Dreiven Supernovas and Their Nucleosynthesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis C. Smolarski, S.J.

Project Abstract This project was a continuation of work begun under a subcontract issued off of TSI-DOE Grant 1528746, awarded to the University of Illinois Urbana-Champaign. Dr. Anthony Mezzacappa is the Principal Investigator on the Illinois award. A separate award was issued to Santa Clara University to continue the collaboration during the time period May 2003 ? 2004. Smolarski continued to work on preconditioner technology and its interface with various iterative methods. He worked primarily with F. Dough Swesty (SUNY-Stony Brook) in continuing software development started in the 2002-03 academic year. Special attention was paid to the development and testingmore » of difference sparse approximate inverse preconditioners and their use in the solution of linear systems arising from radiation transport equations. The target was a high performance platform on which efficient implementation is a critical component of the overall effort. Smolarski also focused on the integration of the adaptive iterative algorithm, Chebycode, developed by Tom Manteuffel and Steve Ashby and adapted by Ryan Szypowski for parallel platforms, into the radiation transport code being developed at SUNY-Stony Brook.« less

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators.

PubMed

Zhao, Jing; Zong, Haili

2018-01-01

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

DOE PAGES

Zhao, Qiang; Du, Qizhen; Gong, Xufei; ...

2018-04-06

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Qiang; Du, Qizhen; Gong, Xufei

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less

Ontology Sparse Vector Learning Algorithm for Ontology Similarity Measuring and Ontology Mapping via ADAL Technology

NASA Astrophysics Data System (ADS)

Gao, Wei; Zhu, Linli; Wang, Kaiyun

2015-12-01

Ontology, a model of knowledge representation and storage, has had extensive applications in pharmaceutics, social science, chemistry and biology. In the age of “big data”, the constructed concepts are often represented as higher-dimensional data by scholars, and thus the sparse learning techniques are introduced into ontology algorithms. In this paper, based on the alternating direction augmented Lagrangian method, we present an ontology optimization algorithm for ontological sparse vector learning, and a fast version of such ontology technologies. The optimal sparse vector is obtained by an iterative procedure, and the ontology function is then obtained from the sparse vector. Four simulation experiments show that our ontological sparse vector learning model has a higher precision ratio on plant ontology, humanoid robotics ontology, biology ontology and physics education ontology data for similarity measuring and ontology mapping applications.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

An Assessment of Iterative Reconstruction Methods for Sparse Ultrasound Imaging

PubMed Central

Valente, Solivan A.; Zibetti, Marcelo V. W.; Pipa, Daniel R.; Maia, Joaquim M.; Schneider, Fabio K.

2017-01-01

Ultrasonic image reconstruction using inverse problems has recently appeared as an alternative to enhance ultrasound imaging over beamforming methods. This approach depends on the accuracy of the acquisition model used to represent transducers, reflectivity, and medium physics. Iterative methods, well known in general sparse signal reconstruction, are also suited for imaging. In this paper, a discrete acquisition model is assessed by solving a linear system of equations by an ℓ1-regularized least-squares minimization, where the solution sparsity may be adjusted as desired. The paper surveys 11 variants of four well-known algorithms for sparse reconstruction, and assesses their optimization parameters with the goal of finding the best approach for iterative ultrasound imaging. The strategy for the model evaluation consists of using two distinct datasets. We first generate data from a synthetic phantom that mimics real targets inside a professional ultrasound phantom device. This dataset is contaminated with Gaussian noise with an estimated SNR, and all methods are assessed by their resulting images and performances. The model and methods are then assessed with real data collected by a research ultrasound platform when scanning the same phantom device, and results are compared with beamforming. A distinct real dataset is finally used to further validate the proposed modeling. Although high computational effort is required by iterative methods, results show that the discrete model may lead to images closer to ground-truth than traditional beamforming. However, computing capabilities of current platforms need to evolve before frame rates currently delivered by ultrasound equipments are achievable. PMID:28282862

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Long-range multi-carrier acoustic communications in shallow water based on iterative sparse channel estimation.

PubMed

Kang, Taehyuk; Song, H C; Hodgkiss, W S; Soo Kim, Jea

2010-12-01

Long-range orthogonal frequency division multiplexing (OFDM) acoustic communications is demonstrated using data from the Kauai Acomms MURI 2008 (KAM08) experiment carried out in about 106 m deep shallow water west of Kauai, HI, in June 2008. The source bandwidth was 8 kHz (12-20 kHz), and the data were received by a 16-element vertical array at a distance of 8 km. Iterative sparse channel estimation is applied in conjunction with low-density parity-check decoding. In addition, the impact of diversity combining in a highly inhomogeneous underwater environment is investigated. Error-free transmission using 16-quadtrative amplitude modulation is achieved at a data rate of 10 kb/s.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Layout optimization with algebraic multigrid methods

NASA Technical Reports Server (NTRS)

Regler, Hans; Ruede, Ulrich

1993-01-01

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

A new scheduling algorithm for parallel sparse LU factorization with static pivoting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grigori, Laura; Li, Xiaoye S.

2002-08-20

In this paper we present a static scheduling algorithm for parallel sparse LU factorization with static pivoting. The algorithm is divided into mapping and scheduling phases, using the symmetric pruned graphs of L' and U to represent dependencies. The scheduling algorithm is designed for driving the parallel execution of the factorization on a distributed-memory architecture. Experimental results and comparisons with SuperLU{_}DIST are reported after applying this algorithm on real world application matrices on an IBM SP RS/6000 distributed memory machine.

Efficient parallel simulation of CO2 geologic sequestration insaline aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Keni; Doughty, Christine; Wu, Yu-Shu

2007-01-01

An efficient parallel simulator for large-scale, long-termCO2 geologic sequestration in saline aquifers has been developed. Theparallel simulator is a three-dimensional, fully implicit model thatsolves large, sparse linear systems arising from discretization of thepartial differential equations for mass and energy balance in porous andfractured media. The simulator is based on the ECO2N module of the TOUGH2code and inherits all the process capabilities of the single-CPU TOUGH2code, including a comprehensive description of the thermodynamics andthermophysical properties of H2O-NaCl- CO2 mixtures, modeling singleand/or two-phase isothermal or non-isothermal flow processes, two-phasemixtures, fluid phases appearing or disappearing, as well as saltprecipitation or dissolution. The newmore » parallel simulator uses MPI forparallel implementation, the METIS software package for simulation domainpartitioning, and the iterative parallel linear solver package Aztec forsolving linear equations by multiple processors. In addition, theparallel simulator has been implemented with an efficient communicationscheme. Test examples show that a linear or super-linear speedup can beobtained on Linux clusters as well as on supercomputers. Because of thesignificant improvement in both simulation time and memory requirement,the new simulator provides a powerful tool for tackling larger scale andmore complex problems than can be solved by single-CPU codes. Ahigh-resolution simulation example is presented that models buoyantconvection, induced by a small increase in brine density caused bydissolution of CO2.« less

A general parallel sparse-blocked matrix multiply for linear scaling SCF theory

NASA Astrophysics Data System (ADS)

Challacombe, Matt

2000-06-01

A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.

Twostep-by-twostep PIRK-type PC methods with continuous output formulas

NASA Astrophysics Data System (ADS)

Cong, Nguyen Huu; Xuan, Le Ngoc

2008-11-01

This paper deals with parallel predictor-corrector (PC) iteration methods based on collocation Runge-Kutta (RK) corrector methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of first-order differential equations. At nth step, the continuous output formulas are used not only for predicting the stage values in the PC iteration methods but also for calculating the step values at (n+2)th step. In this case, the integration processes can be proceeded twostep-by-twostep. The resulting twostep-by-twostep (TBT) parallel-iterated RK-type (PIRK-type) methods with continuous output formulas (twostep-by-twostep PIRKC methods or TBTPIRKC methods) give us a faster integration process. Fixed stepsize applications of these TBTPIRKC methods to a few widely-used test problems reveal that the new PC methods are much more efficient when compared with the well-known parallel-iterated RK methods (PIRK methods), parallel-iterated RK-type PC methods with continuous output formulas (PIRKC methods) and sequential explicit RK codes DOPRI5 and DOP853 available from the literature.

Learning to read aloud: A neural network approach using sparse distributed memory

NASA Technical Reports Server (NTRS)

Joglekar, Umesh Dwarkanath

1989-01-01

An attempt to solve a problem of text-to-phoneme mapping is described which does not appear amenable to solution by use of standard algorithmic procedures. Experiments based on a model of distributed processing are also described. This model (sparse distributed memory (SDM)) can be used in an iterative supervised learning mode to solve the problem. Additional improvements aimed at obtaining better performance are suggested.

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, W. R.; Nguyen, D. T.; Reddy, C. J.; Vatsa, V. N.; Tang, W. H.

2001-01-01

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Sinogram-based adaptive iterative reconstruction for sparse view x-ray computed tomography

NASA Astrophysics Data System (ADS)

Trinca, D.; Zhong, Y.; Wang, Y.-Z.; Mamyrbayev, T.; Libin, E.

2016-10-01

With the availability of more powerful computing processors, iterative reconstruction algorithms have recently been successfully implemented as an approach to achieving significant dose reduction in X-ray CT. In this paper, we propose an adaptive iterative reconstruction algorithm for X-ray CT, that is shown to provide results comparable to those obtained by proprietary algorithms, both in terms of reconstruction accuracy and execution time. The proposed algorithm is thus provided for free to the scientific community, for regular use, and for possible further optimization.

Automatic Management of Parallel and Distributed System Resources

NASA Technical Reports Server (NTRS)

Yan, Jerry; Ngai, Tin Fook; Lundstrom, Stephen F.

1990-01-01

Viewgraphs on automatic management of parallel and distributed system resources are presented. Topics covered include: parallel applications; intelligent management of multiprocessing systems; performance evaluation of parallel architecture; dynamic concurrent programs; compiler-directed system approach; lattice gaseous cellular automata; and sparse matrix Cholesky factorization.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

B. Hendrickson; T.G. Kolda

1998-09-01

A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

Limited-memory trust-region methods for sparse relaxation

NASA Astrophysics Data System (ADS)

Adhikari, Lasith; DeGuchy, Omar; Erway, Jennifer B.; Lockhart, Shelby; Marcia, Roummel F.

2017-08-01

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and applying a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving computational time.

Solving very large, sparse linear systems on mesh-connected parallel computers

NASA Technical Reports Server (NTRS)

Opsahl, Torstein; Reif, John

1987-01-01

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

Towards the low-dose characterization of beam sensitive nanostructures via implementation of sparse image acquisition in scanning transmission electron microscopy

NASA Astrophysics Data System (ADS)

Hwang, Sunghwan; Han, Chang Wan; Venkatakrishnan, Singanallur V.; Bouman, Charles A.; Ortalan, Volkan

2017-04-01

Scanning transmission electron microscopy (STEM) has been successfully utilized to investigate atomic structure and chemistry of materials with atomic resolution. However, STEM’s focused electron probe with a high current density causes the electron beam damages including radiolysis and knock-on damage when the focused probe is exposed onto the electron-beam sensitive materials. Therefore, it is highly desirable to decrease the electron dose used in STEM for the investigation of biological/organic molecules, soft materials and nanomaterials in general. With the recent emergence of novel sparse signal processing theories, such as compressive sensing and model-based iterative reconstruction, possibilities of operating STEM under a sparse acquisition scheme to reduce the electron dose have been opened up. In this paper, we report our recent approach to implement a sparse acquisition in STEM mode executed by a random sparse-scan and a signal processing algorithm called model-based iterative reconstruction (MBIR). In this method, a small portion, such as 5% of randomly chosen unit sampling areas (i.e. electron probe positions), which corresponds to pixels of a STEM image, within the region of interest (ROI) of the specimen are scanned with an electron probe to obtain a sparse image. Sparse images are then reconstructed using the MBIR inpainting algorithm to produce an image of the specimen at the original resolution that is consistent with an image obtained using conventional scanning methods. Experimental results for down to 5% sampling show consistency with the full STEM image acquired by the conventional scanning method. Although, practical limitations of the conventional STEM instruments, such as internal delays of the STEM control electronics and the continuous electron gun emission, currently hinder to achieve the full potential of the sparse acquisition STEM in realizing the low dose imaging condition required for the investigation of beam-sensitive materials, the results obtained in our experiments demonstrate the sparse acquisition STEM imaging is potentially capable of reducing the electron dose by at least 20 times expanding the frontiers of our characterization capabilities for investigation of biological/organic molecules, polymers, soft materials and nanostructures in general.

From the Rendering Equation to Stratified Light Transport Inversion

DTIC Science & Technology

2010-12-09

iteratively. These approaches relate closely to the radiosity method for diffuse global illumination in forward rendering (Hanrahan et al, 1991; Gortler et...currently simply use sparse matrices to represent T, we are also interested in exploring connections with hierar- chical and wavelet radiosity as in...Seidel iterative methods used in radiosity . 2.4 Inverse Light Transport Previous work on inverse rendering has considered inversion of the direct

Advancing Underwater Acoustic Communication for Autonomous Distributed Networks via Sparse Channel Sensing, Coding, and Navigation Support

DTIC Science & Technology

2012-09-30

Estimation Methods for Underwater OFDM 5) Two Iterative Receivers for Distributed MIMO - OFDM with Large Doppler Deviations. 6) Asynchronous Multiuser...multi-input multi-output ( MIMO ) OFDM is also pursued, where it is shown that the proposed hybrid initialization enables drastically improved receiver...are investigated. 5) Two Iterative Receivers for Distributed MIMO - OFDM with Large Doppler Deviations. This work studies a distributed system with

Iteration and superposition encryption scheme for image sequences based on multi-dimensional keys

NASA Astrophysics Data System (ADS)

Han, Chao; Shen, Yuzhen; Ma, Wenlin

2017-12-01

An iteration and superposition encryption scheme for image sequences based on multi-dimensional keys is proposed for high security, big capacity and low noise information transmission. Multiple images to be encrypted are transformed into phase-only images with the iterative algorithm and then are encrypted by different random phase, respectively. The encrypted phase-only images are performed by inverse Fourier transform, respectively, thus new object functions are generated. The new functions are located in different blocks and padded zero for a sparse distribution, then they propagate to a specific region at different distances by angular spectrum diffraction, respectively and are superposed in order to form a single image. The single image is multiplied with a random phase in the frequency domain and then the phase part of the frequency spectrums is truncated and the amplitude information is reserved. The random phase, propagation distances, truncated phase information in frequency domain are employed as multiple dimensional keys. The iteration processing and sparse distribution greatly reduce the crosstalk among the multiple encryption images. The superposition of image sequences greatly improves the capacity of encrypted information. Several numerical experiments based on a designed optical system demonstrate that the proposed scheme can enhance encrypted information capacity and make image transmission at a highly desired security level.

Learning Efficient Sparse and Low Rank Models.

PubMed

Sprechmann, P; Bronstein, A M; Sapiro, G

2015-09-01

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speed-up compared to the exact optimization algorithms.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chao; Pouransari, Hadi; Rajamanickam, Sivasankaran

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by everymore » processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.« less

Supercomputing on massively parallel bit-serial architectures

NASA Technical Reports Server (NTRS)

Iobst, Ken

1985-01-01

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Effects of sparse sampling in combination with iterative reconstruction on quantitative bone microstructure assessment

NASA Astrophysics Data System (ADS)

Mei, Kai; Kopp, Felix K.; Fehringer, Andreas; Pfeiffer, Franz; Rummeny, Ernst J.; Kirschke, Jan S.; Noël, Peter B.; Baum, Thomas

2017-03-01

The trabecular bone microstructure is a key to the early diagnosis and advanced therapy monitoring of osteoporosis. Regularly measuring bone microstructure with conventional multi-detector computer tomography (MDCT) would expose patients with a relatively high radiation dose. One possible solution to reduce exposure to patients is sampling fewer projection angles. This approach can be supported by advanced reconstruction algorithms, with their ability to achieve better image quality under reduced projection angles or high levels of noise. In this work, we investigated the performance of iterative reconstruction from sparse sampled projection data on trabecular bone microstructure in in-vivo MDCT scans of human spines. The computed MDCT images were evaluated by calculating bone microstructure parameters. We demonstrated that bone microstructure parameters were still computationally distinguishable when half or less of the radiation dose was employed.

Acceleration of GPU-based Krylov solvers via data transfer reduction

DOE PAGES

Anzt, Hartwig; Tomov, Stanimire; Luszczek, Piotr; ...

2015-04-08

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphicsmore » processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.« less

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering.

PubMed

Sicat, Ronell; Krüger, Jens; Möller, Torsten; Hadwiger, Markus

2014-12-01

This paper presents a new multi-resolution volume representation called sparse pdf volumes, which enables consistent multi-resolution volume rendering based on probability density functions (pdfs) of voxel neighborhoods. These pdfs are defined in the 4D domain jointly comprising the 3D volume and its 1D intensity range. Crucially, the computation of sparse pdf volumes exploits data coherence in 4D, resulting in a sparse representation with surprisingly low storage requirements. At run time, we dynamically apply transfer functions to the pdfs using simple and fast convolutions. Whereas standard low-pass filtering and down-sampling incur visible differences between resolution levels, the use of pdfs facilitates consistent results independent of the resolution level used. We describe the efficient out-of-core computation of large-scale sparse pdf volumes, using a novel iterative simplification procedure of a mixture of 4D Gaussians. Finally, our data structure is optimized to facilitate interactive multi-resolution volume rendering on GPUs.

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

NASA Astrophysics Data System (ADS)

Vitello, Peter; Fried, Laurence E.; Pudliner, Brian; McAbee, Tom

2004-07-01

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamic calculations, CHEETAH uses parallel communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH coupled to an ALE hydrocode. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George Widgery

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented onmore » both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.« less

Sparse distributed memory overview

NASA Technical Reports Server (NTRS)

Raugh, Mike

1990-01-01

The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.

Automatic correction of intensity nonuniformity from sparseness of gradient distribution in medical images.

PubMed

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P; Gee, James C

2009-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities.

Automatic Correction of Intensity Nonuniformity from Sparseness of Gradient Distribution in Medical Images

PubMed Central

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P.; Gee, James C.

2013-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities. PMID:20426191

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

AZTEC: A parallel iterative package for the solving linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1996-12-31

We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

Accessing sparse arrays in parallel memories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, U.; Gajski, D.; Kuck, D.

The concept of dense and sparse execution of arrays is introduced. Arrays themselves can be stored in a dense or sparse manner in a parallel memory with m memory modules. The paper proposes hardware for speeding up the execution of array operations of the form c(c/sub 0/+ci)=a(a/sub 0/+ai) op b(b/sub 0/+bi), where a/sub 0/, a, b/sub 0/, b, c/sub 0/, c are integer constants and i is an index variable. The hardware handles 'sparse execution', in which the operation op is not executed for every value of i. The hardware also makes provision for 'sparse storage', in which memory spacemore » is not provided for every array element. It is shown how to access array elements of the above form without conflict in an efficient way. The efficiency is obtained by using some specialised units which are basically smart memories with priority detection, one's counting or associative searching. Generalisation to multidimensional arrays is shown possible under restrictions defined in the paper. 12 references.« less

Computational efficiency improvements for image colorization

NASA Astrophysics Data System (ADS)

Yu, Chao; Sharma, Gaurav; Aly, Hussein

2013-03-01

We propose an efficient algorithm for colorization of greyscale images. As in prior work, colorization is posed as an optimization problem: a user specifies the color for a few scribbles drawn on the greyscale image and the color image is obtained by propagating color information from the scribbles to surrounding regions, while maximizing the local smoothness of colors. In this formulation, colorization is obtained by solving a large sparse linear system, which normally requires substantial computation and memory resources. Our algorithm improves the computational performance through three innovations over prior colorization implementations. First, the linear system is solved iteratively without explicitly constructing the sparse matrix, which significantly reduces the required memory. Second, we formulate each iteration in terms of integral images obtained by dynamic programming, reducing repetitive computation. Third, we use a coarseto- fine framework, where a lower resolution subsampled image is first colorized and this low resolution color image is upsampled to initialize the colorization process for the fine level. The improvements we develop provide significant speedup and memory savings compared to the conventional approach of solving the linear system directly using off-the-shelf sparse solvers, and allow us to colorize images with typical sizes encountered in realistic applications on typical commodity computing platforms.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strout, Michelle

Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programsmore » through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.« less

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Liver segmentation from CT images using a sparse priori statistical shape model (SP-SSM).

PubMed

Wang, Xuehu; Zheng, Yongchang; Gan, Lan; Wang, Xuan; Sang, Xinting; Kong, Xiangfeng; Zhao, Jie

2017-01-01

This study proposes a new liver segmentation method based on a sparse a priori statistical shape model (SP-SSM). First, mark points are selected in the liver a priori model and the original image. Then, the a priori shape and its mark points are used to obtain a dictionary for the liver boundary information. Second, the sparse coefficient is calculated based on the correspondence between mark points in the original image and those in the a priori model, and then the sparse statistical model is established by combining the sparse coefficients and the dictionary. Finally, the intensity energy and boundary energy models are built based on the intensity information and the specific boundary information of the original image. Then, the sparse matching constraint model is established based on the sparse coding theory. These models jointly drive the iterative deformation of the sparse statistical model to approximate and accurately extract the liver boundaries. This method can solve the problems of deformation model initialization and a priori method accuracy using the sparse dictionary. The SP-SSM can achieve a mean overlap error of 4.8% and a mean volume difference of 1.8%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 0.8 mm and 1.4 mm, respectively.

Matching pursuit parallel decomposition of seismic data

NASA Astrophysics Data System (ADS)

Li, Chuanhui; Zhang, Fanchang

2017-07-01

In order to improve the computation speed of matching pursuit decomposition of seismic data, a matching pursuit parallel algorithm is designed in this paper. We pick a fixed number of envelope peaks from the current signal in every iteration according to the number of compute nodes and assign them to the compute nodes on average to search the optimal Morlet wavelets in parallel. With the help of parallel computer systems and Message Passing Interface, the parallel algorithm gives full play to the advantages of parallel computing to significantly improve the computation speed of the matching pursuit decomposition and also has good expandability. Besides, searching only one optimal Morlet wavelet by every compute node in every iteration is the most efficient implementation.

Coupled Modeling of Hydrodynamics and Sound in Coastal Ocean for Renewable Ocean Energy Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Jung, Ki Won; Yang, Zhaoqing

An underwater sound model was developed to simulate sound propagation from marine and hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite difference methods were developed to solve the 3D Helmholtz equation for sound propagation in the coastal environment. A 3D sparse matrix solver with complex coefficients was formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method was applied to solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model was then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generatedmore » by human activities, such as construction of OSW turbines or tidal stream turbine operations, in a range-dependent setting. As a proof of concept, initial validation of the solver is presented for two coastal wedge problems. This sound model can be useful for evaluating impacts on marine mammals due to deployment of MHK devices and OSW energy platforms.« less

HO2 rovibrational eigenvalue studies for nonzero angular momentum

NASA Astrophysics Data System (ADS)

Wu, Xudong T.; Hayes, Edward F.

1997-08-01

An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO2 molecule for nonzero angular momentum values, J=1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J=3. The algorithm uses a direct product discrete variable representation (DVR) basis and the implicitly restarted Lanczos method (IRLM) of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix—it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

Solving lattice QCD systems of equations using mixed precision solvers on GPUs

NASA Astrophysics Data System (ADS)

Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.

2010-09-01

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Greedy Algorithms for Nonnegativity-Constrained Simultaneous Sparse Recovery

PubMed Central

Kim, Daeun; Haldar, Justin P.

2016-01-01

This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure. PMID:26973368

Efficient convolutional sparse coding

DOEpatents

Wohlberg, Brendt

2017-06-20

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

Sparse-View Ultrasound Diffraction Tomography Using Compressed Sensing with Nonuniform FFT

PubMed Central

2014-01-01

Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT). In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed. PMID:24868241

Organizing Compression of Hyperspectral Imagery to Allow Efficient Parallel Decompression

NASA Technical Reports Server (NTRS)

Klimesh, Matthew A.; Kiely, Aaron B.

2014-01-01

family of schemes has been devised for organizing the output of an algorithm for predictive data compression of hyperspectral imagery so as to allow efficient parallelization in both the compressor and decompressor. In these schemes, the compressor performs a number of iterations, during each of which a portion of the data is compressed via parallel threads operating on independent portions of the data. The general idea is that for each iteration it is predetermined how much compressed data will be produced from each thread.

Joint Sparse Recovery With Semisupervised MUSIC

NASA Astrophysics Data System (ADS)

Wen, Zaidao; Hou, Biao; Jiao, Licheng

2017-05-01

Discrete multiple signal classification (MUSIC) with its low computational cost and mild condition requirement becomes a significant noniterative algorithm for joint sparse recovery (JSR). However, it fails in rank defective problem caused by coherent or limited amount of multiple measurement vectors (MMVs). In this letter, we provide a novel sight to address this problem by interpreting JSR as a binary classification problem with respect to atoms. Meanwhile, MUSIC essentially constructs a supervised classifier based on the labeled MMVs so that its performance will heavily depend on the quality and quantity of these training samples. From this viewpoint, we develop a semisupervised MUSIC (SS-MUSIC) in the spirit of machine learning, which declares that the insufficient supervised information in the training samples can be compensated from those unlabeled atoms. Instead of constructing a classifier in a fully supervised manner, we iteratively refine a semisupervised classifier by exploiting the labeled MMVs and some reliable unlabeled atoms simultaneously. Through this way, the required conditions and iterations can be greatly relaxed and reduced. Numerical experimental results demonstrate that SS-MUSIC can achieve much better recovery performances than other MUSIC extended algorithms as well as some typical greedy algorithms for JSR in terms of iterations and recovery probability.

Investigation of wall-bounded turbulence over sparsely distributed roughness

NASA Astrophysics Data System (ADS)

Placidi, Marco; Ganapathisubramani, Bharath

2011-11-01

The effects of sparsely distributed roughness elements on the structure of a turbulent boundary layer are examined by performing a series of Particle Image Velocimetry (PIV) experiments in a wind tunnel. From the literature, the best way to characterise a rough wall, especially one where the density of roughness elements is sparse, is unclear. In this study, rough surfaces consisting of sparsely and uniformly distributed LEGO® blocks are used. Five different patterns are adopted in order to examine the effects of frontal solidity (λf, frontal area of the roughness elements per unit wall-parallel area), plan solidity (λp, plan area of roughness elements per unit wall-parallel area) and the geometry of the roughness element (square and cylindrical elements), on the turbulence structure. The Karman number, Reτ , has been matched, at the value of approximately 2300, in order to compare across the different cases. In the talk, we will present detailed analysis of mean and rms velocity profiles, Reynolds stresses and quadrant decomposition.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Fast l₁-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime.

PubMed

Murphy, Mark; Alley, Marcus; Demmel, James; Keutzer, Kurt; Vasanawala, Shreyas; Lustig, Michael

2012-06-01

We present l₁-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative self-consistent parallel imaging (SPIRiT). Like many iterative magnetic resonance imaging reconstructions, l₁-SPIRiT's image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing l₁-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of l₁-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT spoiled gradient echo (SPGR) sequence with up to 8× acceleration via Poisson-disc undersampling in the two phase-encoded directions.

Fast ℓ1-SPIRiT Compressed Sensing Parallel Imaging MRI: Scalable Parallel Implementation and Clinically Feasible Runtime

PubMed Central

Murphy, Mark; Alley, Marcus; Demmel, James; Keutzer, Kurt; Vasanawala, Shreyas; Lustig, Michael

2012-01-01

We present ℓ1-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the Wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative Self-Consistent Parallel Imaging (SPIRiT). Like many iterative MRI reconstructions, ℓ1-SPIRiT’s image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing ℓ1-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of ℓ1-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT Spoiled Gradient Echo (SPGR) sequence with up to 8× acceleration via poisson-disc undersampling in the two phase-encoded directions. PMID:22345529

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering

PubMed Central

Sicat, Ronell; Krüger, Jens; Möller, Torsten; Hadwiger, Markus

2015-01-01

This paper presents a new multi-resolution volume representation called sparse pdf volumes, which enables consistent multi-resolution volume rendering based on probability density functions (pdfs) of voxel neighborhoods. These pdfs are defined in the 4D domain jointly comprising the 3D volume and its 1D intensity range. Crucially, the computation of sparse pdf volumes exploits data coherence in 4D, resulting in a sparse representation with surprisingly low storage requirements. At run time, we dynamically apply transfer functions to the pdfs using simple and fast convolutions. Whereas standard low-pass filtering and down-sampling incur visible differences between resolution levels, the use of pdfs facilitates consistent results independent of the resolution level used. We describe the efficient out-of-core computation of large-scale sparse pdf volumes, using a novel iterative simplification procedure of a mixture of 4D Gaussians. Finally, our data structure is optimized to facilitate interactive multi-resolution volume rendering on GPUs. PMID:26146475

Numerical Aspects of Nonhydrostatic Implementations Applied to a Parallel Finite Element Tsunami Model

NASA Astrophysics Data System (ADS)

Fuchs, A.; Androsov, A.; Harig, S.; Hiller, W.; Rakowsky, N.

2012-04-01

Based on the jeopardy of devastating tsunamis and the unpredictability of such events, tsunami modelling as part of warning systems is still a contemporary topic. The tsunami group of Alfred Wegener Institute developed the simulation tool TsunAWI as contribution to the Early Warning System in Indonesia. Although the precomputed scenarios for this purpose qualify for satisfying deliverables, the study of further improvements continues. While TsunAWI is governed by the Shallow Water Equations, an extension of the model is based on a nonhydrostatic approach. At the arrival of a tsunami wave in coastal regions with rough bathymetry, the term containing the nonhydrostatic part of pressure, that is neglected in the original hydrostatic model, gains in importance. In consideration of this term, a better approximation of the wave is expected. Differences of hydrostatic and nonhydrostatic model results are contrasted in the standard benchmark problem of a solitary wave runup on a plane beach. The observation data provided by Titov and Synolakis (1995) serves as reference. The nonhydrostatic approach implies a set of equations that are similar to the Shallow Water Equations, so the variation of the code can be implemented on top. However, this additional routines cause a lot of issues you have to cope with. So far the computations of the model were purely explicit. In the nonhydrostatic version the determination of an additional unknown and the solution of a large sparse system of linear equations is necessary. The latter constitutes the lion's share of computing time and memory requirement. Since the corresponding matrix is only symmetric in structure and not in values, an iterative Krylov Subspace Method is used, in particular the restarted Generalized Minimal Residual Algorithm GMRES(m). With regard to optimization, we present a comparison of several combinations of sequential and parallel preconditioning techniques respective number of iterations and setup/application time. Since the used software package pARMS 3.2, that provides solving and preconditioning techniques, works via MPI parallelism, in an auxiliary branch we adapted TsunAWI and switched from OpenMP to MPI with attached importance to internal partition management.

Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

NASA Astrophysics Data System (ADS)

Zerr, Robert Joseph

2011-12-01

The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of thousands of processors. The PGS method does outperform SI DSA for the periodic heterogeneous layers (PHL) configuration problems. Although this demonstrates a relative strength/weakness between the two methods, the practicality of these problems is much less, further limiting instances where it would be beneficial to select ITMM over SI DSA. The results strongly indicate a need for a robust, stable, and efficient acceleration method (or preconditioner for PGMRES). The spatial multigrid (SMG) method is currently incomplete in that it does not work for all cases considered and does not effectively improve the convergence rate for all values of scattering ratio c or cell dimension h. Nevertheless, it does display the desired trend for highly scattering, optically thin problems. That is, it tends to lower the rate of growth of number of iterations with increasing number of processes, P, while not increasing the number of additional operations per iteration to the extent that the total execution time of the rapidly converging accelerated iterations exceeds that of the slower unaccelerated iterations. A predictive parallel performance model has been developed for the PBJ method. Timing tests were performed such that trend lines could be fitted to the data for the different components and used to estimate the execution times. Applied to the weak scaling results, the model notably underestimates construction time, but combined with a slight overestimation in iterative solution time, the model predicts total execution time very well for large P. It also does a decent job with the strong scaling results, closely predicting the construction time and time per iteration, especially as P increases. Although not shown to be competitive up to 1,024 processing elements with the current state of the art, the parallelized ITMM exhibits promising scaling trends. Ultimately, compared to the KBA method, the parallelized ITMM may be found to be a very attractive option for transport calculations spatially decomposed over several tens of thousands of processes. Acceleration/preconditioning of the parallelized ITMM once developed will improve the convergence rate and improve its competitiveness. (Abstract shortened by UMI.)

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Feature Clustering for Accelerating Parallel Coordinate Descent

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scherrer, Chad; Tewari, Ambuj; Halappanavar, Mahantesh

2012-12-06

We demonstrate an approach for accelerating calculation of the regularization path for L1 sparse logistic regression problems. We show the benefit of feature clustering as a preconditioning step for parallel block-greedy coordinate descent algorithms.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1991-01-01

Run-time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run-time, wavefronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing, and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run-time reordering of loop indexes can have a significant impact on performance.

Exploiting parallel computing with limited program changes using a network of microcomputers

NASA Technical Reports Server (NTRS)

Rogers, J. L., Jr.; Sobieszczanski-Sobieski, J.

1985-01-01

Network computing and multiprocessor computers are two discernible trends in parallel processing. The computational behavior of an iterative distributed process in which some subtasks are completed later than others because of an imbalance in computational requirements is of significant interest. The effects of asynchronus processing was studied. A small existing program was converted to perform finite element analysis by distributing substructure analysis over a network of four Apple IIe microcomputers connected to a shared disk, simulating a parallel computer. The substructure analysis uses an iterative, fully stressed, structural resizing procedure. A framework of beams divided into three substructures is used as the finite element model. The effects of asynchronous processing on the convergence of the design variables are determined by not resizing particular substructures on various iterations.

Sparse representation-based image restoration via nonlocal supervised coding

NASA Astrophysics Data System (ADS)

Li, Ao; Chen, Deyun; Sun, Guanglu; Lin, Kezheng

2016-10-01

Sparse representation (SR) and nonlocal technique (NLT) have shown great potential in low-level image processing. However, due to the degradation of the observed image, SR and NLT may not be accurate enough to obtain a faithful restoration results when they are used independently. To improve the performance, in this paper, a nonlocal supervised coding strategy-based NLT for image restoration is proposed. The novel method has three main contributions. First, to exploit the useful nonlocal patches, a nonnegative sparse representation is introduced, whose coefficients can be utilized as the supervised weights among patches. Second, a novel objective function is proposed, which integrated the supervised weights learning and the nonlocal sparse coding to guarantee a more promising solution. Finally, to make the minimization tractable and convergence, a numerical scheme based on iterative shrinkage thresholding is developed to solve the above underdetermined inverse problem. The extensive experiments validate the effectiveness of the proposed method.

Embedded sparse representation of fMRI data via group-wise dictionary optimization

NASA Astrophysics Data System (ADS)

Zhu, Dajiang; Lin, Binbin; Faskowitz, Joshua; Ye, Jieping; Thompson, Paul M.

2016-03-01

Sparse learning enables dimension reduction and efficient modeling of high dimensional signals and images, but it may need to be tailored to best suit specific applications and datasets. Here we used sparse learning to efficiently represent functional magnetic resonance imaging (fMRI) data from the human brain. We propose a novel embedded sparse representation (ESR), to identify the most consistent dictionary atoms across different brain datasets via an iterative group-wise dictionary optimization procedure. In this framework, we introduced additional criteria to make the learned dictionary atoms more consistent across different subjects. We successfully identified four common dictionary atoms that follow the external task stimuli with very high accuracy. After projecting the corresponding coefficient vectors back into the 3-D brain volume space, the spatial patterns are also consistent with traditional fMRI analysis results. Our framework reveals common features of brain activation in a population, as a new, efficient fMRI analysis method.

An iterative reduced field-of-view reconstruction for periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) MRI.

PubMed

Lin, Jyh-Miin; Patterson, Andrew J; Chang, Hing-Chiu; Gillard, Jonathan H; Graves, Martin J

2015-10-01

To propose a new reduced field-of-view (rFOV) strategy for iterative reconstructions in a clinical environment. Iterative reconstructions can incorporate regularization terms to improve the image quality of periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) MRI. However, the large amount of calculations required for full FOV iterative reconstructions has posed a huge computational challenge for clinical usage. By subdividing the entire problem into smaller rFOVs, the iterative reconstruction can be accelerated on a desktop with a single graphic processing unit (GPU). This rFOV strategy divides the iterative reconstruction into blocks, based on the block-diagonal dominant structure. A near real-time reconstruction system was developed for the clinical MR unit, and parallel computing was implemented using the object-oriented model. In addition, the Toeplitz method was implemented on the GPU to reduce the time required for full interpolation. Using the data acquired from the PROPELLER MRI, the reconstructed images were then saved in the digital imaging and communications in medicine format. The proposed rFOV reconstruction reduced the gridding time by 97%, as the total iteration time was 3 s even with multiple processes running. A phantom study showed that the structure similarity index for rFOV reconstruction was statistically superior to conventional density compensation (p < 0.001). In vivo study validated the increased signal-to-noise ratio, which is over four times higher than with density compensation. Image sharpness index was improved using the regularized reconstruction implemented. The rFOV strategy permits near real-time iterative reconstruction to improve the image quality of PROPELLER images. Substantial improvements in image quality metrics were validated in the experiments. The concept of rFOV reconstruction may potentially be applied to other kinds of iterative reconstructions for shortened reconstruction duration.

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« less

A Distributed Learning Method for ℓ1-Regularized Kernel Machine over Wireless Sensor Networks

PubMed Central

Ji, Xinrong; Hou, Cuiqin; Hou, Yibin; Gao, Fang; Wang, Shulong

2016-01-01

In wireless sensor networks, centralized learning methods have very high communication costs and energy consumption. These are caused by the need to transmit scattered training examples from various sensor nodes to the central fusion center where a classifier or a regression machine is trained. To reduce the communication cost, a distributed learning method for a kernel machine that incorporates ℓ1 norm regularization (ℓ1-regularized) is investigated, and a novel distributed learning algorithm for the ℓ1-regularized kernel minimum mean squared error (KMSE) machine is proposed. The proposed algorithm relies on in-network processing and a collaboration that transmits the sparse model only between single-hop neighboring nodes. This paper evaluates the proposed algorithm with respect to the prediction accuracy, the sparse rate of model, the communication cost and the number of iterations on synthetic and real datasets. The simulation results show that the proposed algorithm can obtain approximately the same prediction accuracy as that obtained by the batch learning method. Moreover, it is significantly superior in terms of the sparse rate of model and communication cost, and it can converge with fewer iterations. Finally, an experiment conducted on a wireless sensor network (WSN) test platform further shows the advantages of the proposed algorithm with respect to communication cost. PMID:27376298

Vectorized and multitasked solution of the few-group neutron diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

An efficient parallel algorithm: Poststack and prestack Kirchhoff 3D depth migration using flexi-depth iterations

NASA Astrophysics Data System (ADS)

Rastogi, Richa; Srivastava, Abhishek; Khonde, Kiran; Sirasala, Kirannmayi M.; Londhe, Ashutosh; Chavhan, Hitesh

2015-07-01

This paper presents an efficient parallel 3D Kirchhoff depth migration algorithm suitable for current class of multicore architecture. The fundamental Kirchhoff depth migration algorithm exhibits inherent parallelism however, when it comes to 3D data migration, as the data size increases the resource requirement of the algorithm also increases. This challenges its practical implementation even on current generation high performance computing systems. Therefore a smart parallelization approach is essential to handle 3D data for migration. The most compute intensive part of Kirchhoff depth migration algorithm is the calculation of traveltime tables due to its resource requirements such as memory/storage and I/O. In the current research work, we target this area and develop a competent parallel algorithm for post and prestack 3D Kirchhoff depth migration, using hybrid MPI+OpenMP programming techniques. We introduce a concept of flexi-depth iterations while depth migrating data in parallel imaging space, using optimized traveltime table computations. This concept provides flexibility to the algorithm by migrating data in a number of depth iterations, which depends upon the available node memory and the size of data to be migrated during runtime. Furthermore, it minimizes the requirements of storage, I/O and inter-node communication, thus making it advantageous over the conventional parallelization approaches. The developed parallel algorithm is demonstrated and analysed on Yuva II, a PARAM series of supercomputers. Optimization, performance and scalability experiment results along with the migration outcome show the effectiveness of the parallel algorithm.

Using parallel banded linear system solvers in generalized eigenvalue problems

NASA Technical Reports Server (NTRS)

Zhang, Hong; Moss, William F.

1993-01-01

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

Parallel solution of the symmetric tridiagonal eigenproblem. Research report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-10-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method ismore » the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Parallel solution of the symmetric tridiagonal eigenproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-01-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accuratemore » approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Small-Tip-Angle Spokes Pulse Design Using Interleaved Greedy and Local Optimization Methods

PubMed Central

Grissom, William A.; Khalighi, Mohammad-Mehdi; Sacolick, Laura I.; Rutt, Brian K.; Vogel, Mika W.

2013-01-01

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent-based) optimization of the transverse-plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation-based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off-resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off-resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single- and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods. PMID:22392822

Parallel iterative solution for h and p approximations of the shallow water equations

USGS Publications Warehouse

Barragy, E.J.; Walters, R.A.

1998-01-01

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

ILUBCG2-11: Solution of 11-banded nonsymmetric linear equation systems by a preconditioned biconjugate gradient routine

NASA Astrophysics Data System (ADS)

Chen, Y.-M.; Koniges, A. E.; Anderson, D. V.

1989-10-01

The biconjugate gradient method (BCG) provides an attractive alternative to the usual conjugate gradient algorithms for the solution of sparse systems of linear equations with nonsymmetric and indefinite matrix operators. A preconditioned algorithm is given, whose form resembles the incomplete L-U conjugate gradient scheme (ILUCG2) previously presented. Although the BCG scheme requires the storage of two additional vectors, it converges in a significantly lesser number of iterations (often half), while the number of calculations per iteration remains essentially the same.

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.

PubMed

He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie

2010-11-22

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Performance Models for the Spike Banded Linear System Solver

DOE PAGES

Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...

2011-01-01

With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated on diverse heterogeneous multiclusters – platforms for which performance prediction is particularly challenging. Finally, we provide predict the scalability of the Spike algorithm using up to 65,536 cores with our model. In this paper we extend the results presented in the Ninth International Symposium on Parallel and Distributed Computing.« less

Iterative approach of dual regression with a sparse prior enhances the performance of independent component analysis for group functional magnetic resonance imaging (fMRI) data.

PubMed

Kim, Yong-Hwan; Kim, Junghoe; Lee, Jong-Hwan

2012-12-01

This study proposes an iterative dual-regression (DR) approach with sparse prior regularization to better estimate an individual's neuronal activation using the results of an independent component analysis (ICA) method applied to a temporally concatenated group of functional magnetic resonance imaging (fMRI) data (i.e., Tc-GICA method). An ordinary DR approach estimates the spatial patterns (SPs) of neuronal activation and corresponding time courses (TCs) specific to each individual's fMRI data with two steps involving least-squares (LS) solutions. Our proposed approach employs iterative LS solutions to refine both the individual SPs and TCs with an additional a priori assumption of sparseness in the SPs (i.e., minimally overlapping SPs) based on L(1)-norm minimization. To quantitatively evaluate the performance of this approach, semi-artificial fMRI data were created from resting-state fMRI data with the following considerations: (1) an artificially designed spatial layout of neuronal activation patterns with varying overlap sizes across subjects and (2) a BOLD time series (TS) with variable parameters such as onset time, duration, and maximum BOLD levels. To systematically control the spatial layout variability of neuronal activation patterns across the "subjects" (n=12), the degree of spatial overlap across all subjects was varied from a minimum of 1 voxel (i.e., 0.5-voxel cubic radius) to a maximum of 81 voxels (i.e., 2.5-voxel radius) across the task-related SPs with a size of 100 voxels for both the block-based and event-related task paradigms. In addition, several levels of maximum percentage BOLD intensity (i.e., 0.5, 1.0, 2.0, and 3.0%) were used for each degree of spatial overlap size. From the results, the estimated individual SPs of neuronal activation obtained from the proposed iterative DR approach with a sparse prior showed an enhanced true positive rate and reduced false positive rate compared to the ordinary DR approach. The estimated TCs of the task-related SPs from our proposed approach showed greater temporal correlation coefficients with a reference hemodynamic response function than those of the ordinary DR approach. Moreover, the efficacy of the proposed DR approach was also successfully demonstrated by the results of real fMRI data acquired from left-/right-hand clenching tasks in both block-based and event-related task paradigms. Copyright © 2012 Elsevier Inc. All rights reserved.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1990-01-01

Run time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases, where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run time, wave fronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run time reordering of loop indices can have a significant impact on performance. Furthermore, the overheads associated with this type of reordering are amortized when the loop is executed several times with the same dependency structure.

MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX

NASA Astrophysics Data System (ADS)

Krotkiewski, Marcin; Dabrowski, Marcin

2013-04-01

The need for computational performance is common in scientific applications, and in particular in numerical simulations, where high resolution models require efficient processing of large amounts of data. Especially in the context of geological problems the need to increase the model resolution to resolve physical and geometrical complexities seems to have no limits. Alas, the performance of new generations of CPUs does not improve any longer by simply increasing clock speeds. Current industrial trends are to increase the number of computational cores. As a result, parallel implementations are required in order to fully utilize the potential of new processors, and to study more complex models. We target simulations on small to medium scale shared memory computers: laptops and desktop PCs with ~8 CPU cores and up to tens of GB of memory to high-end servers with ~50 CPU cores and hundereds of GB of memory. In this setting MATLAB is often the environment of choice for scientists that want to implement their own models with little effort. It is a useful general purpose mathematical software package, but due to its versatility some of its functionality is not as efficient as it could be. In particular, the challanges of modern multi-core architectures are not fully addressed. We have developed MILAMIN 2 - an efficient FEM modeling environment written in native MATLAB. Amongst others, MILAMIN provides functions to define model geometry, generate and convert structured and unstructured meshes (also through interfaces to external mesh generators), compute element and system matrices, apply boundary conditions, solve the system of linear equations, address non-linear and transient problems, and perform post-processing. MILAMIN strives to combine the ease of code development and the computational efficiency. Where possible, the code is optimized and/or parallelized within the MATLAB framework. Native MATLAB is augmented with the MUTILS library - a set of MEX functions that implement the computationally intensive, performance critical parts of the code, which we have identified to be bottlenecks. Here, we discuss the functionality and performance of the MUTILS library. Currently, it includes: 1. time and memory efficient assembly of sparse matrices for FEM simulations 2. parallel sparse matrix - vector product with optimizations speficic to symmetric matrices and multiple degrees of freedom per node 3. parallel point in triangle location and point in tetrahedron location for unstructured, adaptive 2D and 3D meshes (useful for 'marker in cell' type of methods) 4. parallel FEM interpolation for 2D and 3D meshes of elements of different types and orders, and for different number of degrees of freedom per node 5. a stand-alone, MEX implementation of the Conjugate Gradients iterative solver 6. interface to METIS graph partitioning and a fast implementation of RCM reordering

GPU-accelerated algorithms for compressed signals recovery with application to astronomical imagery deblurring

NASA Astrophysics Data System (ADS)

Fiandrotti, Attilio; Fosson, Sophie M.; Ravazzi, Chiara; Magli, Enrico

2018-04-01

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain.

Solving Boltzmann and Fokker-Planck Equations Using Sparse Representation

DTIC Science & Technology

2011-05-31

material science. We have com- puted the electronic structure of 2D quantum dot system, and compared the efficiency with the benchmark software OCTOPUS . For...one self-consistent iteration step with 512 electrons, OCTOPUS costs 1091 sec, and selected inversion costs 9.76 sec. The algorithm exhibits

Defining and Characterizing Ecosystem Services for Education: A Delphi Study

ERIC Educational Resources Information Center

Ruppert, John; Duncan, Ravit Golan

2017-01-01

Recent advancements in science have led to an increasingly sophisticated understanding of the many ways in which humans benefit from environmental systems. These benefits, termed Ecosystem Services, are sparsely characterized in education literature, but were included in the most recent iteration of US national science standards: the Next…

A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging

PubMed Central

Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2017-01-01

This paper presents a sparse superresolution approach for high cross-range resolution imaging of forward-looking scanning radar based on the Bayesian criterion. First, a novel forward-looking signal model is established as the product of the measurement matrix and the cross-range target distribution, which is more accurate than the conventional convolution model. Then, based on the Bayesian criterion, the widely-used sparse regularization is considered as the penalty term to recover the target distribution. The derivation of the cost function is described, and finally, an iterative expression for minimizing this function is presented. Alternatively, this paper discusses how to estimate the single parameter of Gaussian noise. With the advantage of a more accurate model, the proposed sparse Bayesian approach enjoys a lower model error. Meanwhile, when compared with the conventional superresolution methods, the proposed approach shows high cross-range resolution and small location error. The superresolution results for the simulated point target, scene data, and real measured data are presented to demonstrate the superior performance of the proposed approach. PMID:28604583

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Systematic sparse matrix error control for linear scaling electronic structure calculations.

PubMed

Rubensson, Emanuel H; Sałek, Paweł

2005-11-30

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. Copyright 2005 Wiley Periodicals, Inc.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Visual recognition and inference using dynamic overcomplete sparse learning.

PubMed

Murray, Joseph F; Kreutz-Delgado, Kenneth

2007-09-01

We present a hierarchical architecture and learning algorithm for visual recognition and other visual inference tasks such as imagination, reconstruction of occluded images, and expectation-driven segmentation. Using properties of biological vision for guidance, we posit a stochastic generative world model and from it develop a simplified world model (SWM) based on a tractable variational approximation that is designed to enforce sparse coding. Recent developments in computational methods for learning overcomplete representations (Lewicki & Sejnowski, 2000; Teh, Welling, Osindero, & Hinton, 2003) suggest that overcompleteness can be useful for visual tasks, and we use an overcomplete dictionary learning algorithm (Kreutz-Delgado, et al., 2003) as a preprocessing stage to produce accurate, sparse codings of images. Inference is performed by constructing a dynamic multilayer network with feedforward, feedback, and lateral connections, which is trained to approximate the SWM. Learning is done with a variant of the back-propagation-through-time algorithm, which encourages convergence to desired states within a fixed number of iterations. Vision tasks require large networks, and to make learning efficient, we take advantage of the sparsity of each layer to update only a small subset of elements in a large weight matrix at each iteration. Experiments on a set of rotated objects demonstrate various types of visual inference and show that increasing the degree of overcompleteness improves recognition performance in difficult scenes with occluded objects in clutter.

Image segmentation by iterative parallel region growing with application to data compression and image analysis

NASA Technical Reports Server (NTRS)

Tilton, James C.

1988-01-01

Image segmentation can be a key step in data compression and image analysis. However, the segmentation results produced by most previous approaches to region growing are suspect because they depend on the order in which portions of the image are processed. An iterative parallel segmentation algorithm avoids this problem by performing globally best merges first. Such a segmentation approach, and two implementations of the approach on NASA's Massively Parallel Processor (MPP) are described. Application of the segmentation approach to data compression and image analysis is then described, and results of such application are given for a LANDSAT Thematic Mapper image.

Parallelizing flow-accumulation calculations on graphics processing units—From iterative DEM preprocessing algorithm to recursive multiple-flow-direction algorithm

NASA Astrophysics Data System (ADS)

Qin, Cheng-Zhi; Zhan, Lijun

2012-06-01

As one of the important tasks in digital terrain analysis, the calculation of flow accumulations from gridded digital elevation models (DEMs) usually involves two steps in a real application: (1) using an iterative DEM preprocessing algorithm to remove the depressions and flat areas commonly contained in real DEMs, and (2) using a recursive flow-direction algorithm to calculate the flow accumulation for every cell in the DEM. Because both algorithms are computationally intensive, quick calculation of the flow accumulations from a DEM (especially for a large area) presents a practical challenge to personal computer (PC) users. In recent years, rapid increases in hardware capacity of the graphics processing units (GPUs) provided in modern PCs have made it possible to meet this challenge in a PC environment. Parallel computing on GPUs using a compute-unified-device-architecture (CUDA) programming model has been explored to speed up the execution of the single-flow-direction algorithm (SFD). However, the parallel implementation on a GPU of the multiple-flow-direction (MFD) algorithm, which generally performs better than the SFD algorithm, has not been reported. Moreover, GPU-based parallelization of the DEM preprocessing step in the flow-accumulation calculations has not been addressed. This paper proposes a parallel approach to calculate flow accumulations (including both iterative DEM preprocessing and a recursive MFD algorithm) on a CUDA-compatible GPU. For the parallelization of an MFD algorithm (MFD-md), two different parallelization strategies using a GPU are explored. The first parallelization strategy, which has been used in the existing parallel SFD algorithm on GPU, has the problem of computing redundancy. Therefore, we designed a parallelization strategy based on graph theory. The application results show that the proposed parallel approach to calculate flow accumulations on a GPU performs much faster than either sequential algorithms or other parallel GPU-based algorithms based on existing parallelization strategies.

Analog system for computing sparse codes

DOEpatents

Rozell, Christopher John; Johnson, Don Herrick; Baraniuk, Richard Gordon; Olshausen, Bruno A.; Ortman, Robert Lowell

2010-08-24

A parallel dynamical system for computing sparse representations of data, i.e., where the data can be fully represented in terms of a small number of non-zero code elements, and for reconstructing compressively sensed images. The system is based on the principles of thresholding and local competition that solves a family of sparse approximation problems corresponding to various sparsity metrics. The system utilizes Locally Competitive Algorithms (LCAs), nodes in a population continually compete with neighboring units using (usually one-way) lateral inhibition to calculate coefficients representing an input in an over complete dictionary.

Accelerated dynamic cardiac MRI exploiting sparse-Kalman-smoother self-calibration and reconstruction (k  -  t SPARKS)

NASA Astrophysics Data System (ADS)

Park, Suhyung; Park, Jaeseok

2015-05-01

Accelerated dynamic MRI, which exploits spatiotemporal redundancies in k  -  t space and coil dimension, has been widely used to reduce the number of signal encoding and thus increase imaging efficiency with minimal loss of image quality. Nonetheless, particularly in cardiac MRI it still suffers from artifacts and amplified noise in the presence of time-drifting coil sensitivity due to relative motion between coil and subject (e.g. free breathing). Furthermore, a substantial number of additional calibrating signals is to be acquired to warrant accurate calibration of coil sensitivity. In this work, we propose a novel, accelerated dynamic cardiac MRI with sparse-Kalman-smoother self-calibration and reconstruction (k  -  t SPARKS), which is robust to time-varying coil sensitivity even with a small number of calibrating signals. The proposed k  -  t SPARKS incorporates Kalman-smoother self-calibration in k  -  t space and sparse signal recovery in x  -   f space into a single optimization problem, leading to iterative, joint estimation of time-varying convolution kernels and missing signals in k  -  t space. In the Kalman-smoother calibration, motion-induced uncertainties over the entire time frames were included in modeling state transition while a coil-dependent noise statistic in describing measurement process. The sparse signal recovery iteratively alternates with the self-calibration to tackle the ill-conditioning problem potentially resulting from insufficient calibrating signals. Simulations and experiments were performed using both the proposed and conventional methods for comparison, revealing that the proposed k  -  t SPARKS yields higher signal-to-error ratio and superior temporal fidelity in both breath-hold and free-breathing cardiac applications over all reduction factors.

Accelerated dynamic cardiac MRI exploiting sparse-Kalman-smoother self-calibration and reconstruction (k  -  t SPARKS).

PubMed

Park, Suhyung; Park, Jaeseok

2015-05-07

Accelerated dynamic MRI, which exploits spatiotemporal redundancies in k  -  t space and coil dimension, has been widely used to reduce the number of signal encoding and thus increase imaging efficiency with minimal loss of image quality. Nonetheless, particularly in cardiac MRI it still suffers from artifacts and amplified noise in the presence of time-drifting coil sensitivity due to relative motion between coil and subject (e.g. free breathing). Furthermore, a substantial number of additional calibrating signals is to be acquired to warrant accurate calibration of coil sensitivity. In this work, we propose a novel, accelerated dynamic cardiac MRI with sparse-Kalman-smoother self-calibration and reconstruction (k  -  t SPARKS), which is robust to time-varying coil sensitivity even with a small number of calibrating signals. The proposed k  -  t SPARKS incorporates Kalman-smoother self-calibration in k  -  t space and sparse signal recovery in x  -   f space into a single optimization problem, leading to iterative, joint estimation of time-varying convolution kernels and missing signals in k  -  t space. In the Kalman-smoother calibration, motion-induced uncertainties over the entire time frames were included in modeling state transition while a coil-dependent noise statistic in describing measurement process. The sparse signal recovery iteratively alternates with the self-calibration to tackle the ill-conditioning problem potentially resulting from insufficient calibrating signals. Simulations and experiments were performed using both the proposed and conventional methods for comparison, revealing that the proposed k  -  t SPARKS yields higher signal-to-error ratio and superior temporal fidelity in both breath-hold and free-breathing cardiac applications over all reduction factors.

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

NASA Technical Reports Server (NTRS)

Venter, Gerhard; Sobieszczanski-Sobieski, Jaroslaw

2005-01-01

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Data preprocessing for determining outer/inner parallelization in the nested loop problem using OpenMP

NASA Astrophysics Data System (ADS)

Handhika, T.; Bustamam, A.; Ernastuti, Kerami, D.

2017-07-01

Multi-thread programming using OpenMP on the shared-memory architecture with hyperthreading technology allows the resource to be accessed by multiple processors simultaneously. Each processor can execute more than one thread for a certain period of time. However, its speedup depends on the ability of the processor to execute threads in limited quantities, especially the sequential algorithm which contains a nested loop. The number of the outer loop iterations is greater than the maximum number of threads that can be executed by a processor. The thread distribution technique that had been found previously only be applied by the high-level programmer. This paper generates a parallelization procedure for low-level programmer in dealing with 2-level nested loop problems with the maximum number of threads that can be executed by a processor is smaller than the number of the outer loop iterations. Data preprocessing which is related to the number of the outer loop and the inner loop iterations, the computational time required to execute each iteration and the maximum number of threads that can be executed by a processor are used as a strategy to determine which parallel region that will produce optimal speedup.

Efficient Iterative Methods Applied to the Solution of Transonic Flows

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Chronopoulos, Anthony T.

1996-02-01

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton's method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GMRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton-GMRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems.

A Parallel Numerical Algorithm To Solve Linear Systems Of Equations Emerging From 3D Radiative Transfer

NASA Astrophysics Data System (ADS)

Wichert, Viktoria; Arkenberg, Mario; Hauschildt, Peter H.

2016-10-01

Highly resolved state-of-the-art 3D atmosphere simulations will remain computationally extremely expensive for years to come. In addition to the need for more computing power, rethinking coding practices is necessary. We take a dual approach by introducing especially adapted, parallel numerical methods and correspondingly parallelizing critical code passages. In the following, we present our respective work on PHOENIX/3D. With new parallel numerical algorithms, there is a big opportunity for improvement when iteratively solving the system of equations emerging from the operator splitting of the radiative transfer equation J = ΛS. The narrow-banded approximate Λ-operator Λ* , which is used in PHOENIX/3D, occurs in each iteration step. By implementing a numerical algorithm which takes advantage of its characteristic traits, the parallel code's efficiency is further increased and a speed-up in computational time can be achieved.

Multidisciplinary systems optimization by linear decomposition

NASA Technical Reports Server (NTRS)

Sobieski, J.

1984-01-01

In a typical design process major decisions are made sequentially. An illustrated example is given for an aircraft design in which the aerodynamic shape is usually decided first, then the airframe is sized for strength and so forth. An analogous sequence could be laid out for any other major industrial product, for instance, a ship. The loops in the discipline boxes symbolize iterative design improvements carried out within the confines of a single engineering discipline, or subsystem. The loops spanning several boxes depict multidisciplinary design improvement iterations. Omitted for graphical simplicity is parallelism of the disciplinary subtasks. The parallelism is important in order to develop a broad workfront necessary to shorten the design time. If all the intradisciplinary and interdisciplinary iterations were carried out to convergence, the process could yield a numerically optimal design. However, it usually stops short of that because of time and money limitations. This is especially true for the interdisciplinary iterations.

Split Bregman's optimization method for image construction in compressive sensing

NASA Astrophysics Data System (ADS)

Skinner, D.; Foo, S.; Meyer-Bäse, A.

2014-05-01

The theory of compressive sampling (CS) was reintroduced by Candes, Romberg and Tao, and D. Donoho in 2006. Using a priori knowledge that a signal is sparse, it has been mathematically proven that CS can defY Nyquist sampling theorem. Theoretically, reconstruction of a CS image relies on the minimization and optimization techniques to solve this complex almost NP-complete problem. There are many paths to consider when compressing and reconstructing an image but these methods have remained untested and unclear on natural images, such as underwater sonar images. The goal of this research is to perfectly reconstruct the original sonar image from a sparse signal while maintaining pertinent information, such as mine-like object, in Side-scan sonar (SSS) images. Goldstein and Osher have shown how to use an iterative method to reconstruct the original image through a method called Split Bregman's iteration. This method "decouples" the energies using portions of the energy from both the !1 and !2 norm. Once the energies are split, Bregman iteration is used to solve the unconstrained optimization problem by recursively solving the problems simultaneously. The faster these two steps or energies can be solved then the faster the overall method becomes. While the majority of CS research is still focused on the medical field, this paper will demonstrate the effectiveness of the Split Bregman's methods on sonar images.

Performance issues for iterative solvers in device simulation

NASA Technical Reports Server (NTRS)

Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai

1994-01-01

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Enhancing sparsity of Hermite polynomial expansions by iterative rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiu; Lei, Huan; Baker, Nathan A.

2016-02-01

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Massive parallelization of a 3D finite difference electromagnetic forward solution using domain decomposition methods on multiple CUDA enabled GPUs

NASA Astrophysics Data System (ADS)

Schultz, A.

2010-12-01

3D forward solvers lie at the core of inverse formulations used to image the variation of electrical conductivity within the Earth's interior. This property is associated with variations in temperature, composition, phase, presence of volatiles, and in specific settings, the presence of groundwater, geothermal resources, oil/gas or minerals. The high cost of 3D solutions has been a stumbling block to wider adoption of 3D methods. Parallel algorithms for modeling frequency domain 3D EM problems have not achieved wide scale adoption, with emphasis on fairly coarse grained parallelism using MPI and similar approaches. The communications bandwidth as well as the latency required to send and receive network communication packets is a limiting factor in implementing fine grained parallel strategies, inhibiting wide adoption of these algorithms. Leading Graphics Processor Unit (GPU) companies now produce GPUs with hundreds of GPU processor cores per die. The footprint, in silicon, of the GPU's restricted instruction set is much smaller than the general purpose instruction set required of a CPU. Consequently, the density of processor cores on a GPU can be much greater than on a CPU. GPUs also have local memory, registers and high speed communication with host CPUs, usually through PCIe type interconnects. The extremely low cost and high computational power of GPUs provides the EM geophysics community with an opportunity to achieve fine grained (i.e. massive) parallelization of codes on low cost hardware. The current generation of GPUs (e.g. NVidia Fermi) provides 3 billion transistors per chip die, with nearly 500 processor cores and up to 6 GB of fast (DDR5) GPU memory. This latest generation of GPU supports fast hardware double precision (64 bit) floating point operations of the type required for frequency domain EM forward solutions. Each Fermi GPU board can sustain nearly 1 TFLOP in double precision, and multiple boards can be installed in the host computer system. We describe our ongoing efforts to achieve massive parallelization on a novel hybrid GPU testbed machine currently configured with 12 Intel Westmere Xeon CPU cores (or 24 parallel computational threads) with 96 GB DDR3 system memory, 4 GPU subsystems which in aggregate contain 960 NVidia Tesla GPU cores with 16 GB dedicated DDR3 GPU memory, and a second interleved bank of 4 GPU subsystems containing in aggregate 1792 NVidia Fermi GPU cores with 12 GB dedicated DDR5 GPU memory. We are applying domain decomposition methods to a modified version of Weiss' (2001) 3D frequency domain full physics EM finite difference code, an open source GPL licensed f90 code available for download from www.OpenEM.org. This will be the core of a new hybrid 3D inversion that parallelizes frequencies across CPUs and individual forward solutions across GPUs. We describe progress made in modifying the code to use direct solvers in GPU cores dedicated to each small subdomain, iteratively improving the solution by matching adjacent subdomain boundary solutions, rather than iterative Krylov space sparse solvers as currently applied to the whole domain.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

DOE PAGES

Azad, Ariful; Ballard, Grey; Buluc, Aydin; ...

2016-11-08

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achievingmore » significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.« less

Total recall in distributive associative memories

NASA Technical Reports Server (NTRS)

Danforth, Douglas G.

1991-01-01

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifacts.

PubMed

Meng, Yuguang; Lei, Hao

2010-06-01

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. (c) 2010 Wiley-Liss, Inc.

Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm

NASA Astrophysics Data System (ADS)

Backes, Werner; Wetzel, Susanne

In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multi-threaded algorithm is the first to provide an efficient, parallel implementation of the Schorr-Euchner algorithm for today’s multi-processor, multi-core computer architectures. Experiments with sparse and dense lattice bases show a speed-up factor of about 1.8 for the 2-thread and about factor 3.2 for the 4-thread version of our new parallel lattice basis reduction algorithm in comparison to the traditional non-parallel algorithm.

Sparse-view proton computed tomography using modulated proton beams.

PubMed

Lee, Jiseoc; Kim, Changhwan; Min, Byungjun; Kwak, Jungwon; Park, Seyjoon; Lee, Se Byeong; Park, Sungyong; Cho, Seungryong

2015-02-01

Proton imaging that uses a modulated proton beam and an intensity detector allows a relatively fast image acquisition compared to the imaging approach based on a trajectory tracking detector. In addition, it requires a relatively simple implementation in a conventional proton therapy equipment. The model of geometric straight ray assumed in conventional computed tomography (CT) image reconstruction is however challenged by multiple-Coulomb scattering and energy straggling in the proton imaging. Radiation dose to the patient is another important issue that has to be taken care of for practical applications. In this work, the authors have investigated iterative image reconstructions after a deconvolution of the sparsely view-sampled data to address these issues in proton CT. Proton projection images were acquired using the modulated proton beams and the EBT2 film as an intensity detector. Four electron-density cylinders representing normal soft tissues and bone were used as imaged object and scanned at 40 views that are equally separated over 360°. Digitized film images were converted to water-equivalent thickness by use of an empirically derived conversion curve. For improving the image quality, a deconvolution-based image deblurring with an empirically acquired point spread function was employed. They have implemented iterative image reconstruction algorithms such as adaptive steepest descent-projection onto convex sets (ASD-POCS), superiorization method-projection onto convex sets (SM-POCS), superiorization method-expectation maximization (SM-EM), and expectation maximization-total variation minimization (EM-TV). Performance of the four image reconstruction algorithms was analyzed and compared quantitatively via contrast-to-noise ratio (CNR) and root-mean-square-error (RMSE). Objects of higher electron density have been reconstructed more accurately than those of lower density objects. The bone, for example, has been reconstructed within 1% error. EM-based algorithms produced an increased image noise and RMSE as the iteration reaches about 20, while the POCS-based algorithms showed a monotonic convergence with iterations. The ASD-POCS algorithm outperformed the others in terms of CNR, RMSE, and the accuracy of the reconstructed relative stopping power in the region of lung and soft tissues. The four iterative algorithms, i.e., ASD-POCS, SM-POCS, SM-EM, and EM-TV, have been developed and applied for proton CT image reconstruction. Although it still seems that the images need to be improved for practical applications to the treatment planning, proton CT imaging by use of the modulated beams in sparse-view sampling has demonstrated its feasibility.

Analysis and Design of ITER 1 MV Core Snubber

NASA Astrophysics Data System (ADS)

Wang, Haitian; Li, Ge

2012-11-01

The core snubber, as a passive protection device, can suppress arc current and absorb stored energy in stray capacitance during the electrical breakdown in accelerating electrodes of ITER NBI. In order to design the core snubber of ITER, the control parameters of the arc peak current have been firstly analyzed by the Fink-Baker-Owren (FBO) method, which are used for designing the DIIID 100 kV snubber. The B-H curve can be derived from the measured voltage and current waveforms, and the hysteresis loss of the core snubber can be derived using the revised parallelogram method. The core snubber can be a simplified representation as an equivalent parallel resistance and inductance, which has been neglected by the FBO method. A simulation code including the parallel equivalent resistance and inductance has been set up. The simulation and experiments result in dramatically large arc shorting currents due to the parallel inductance effect. The case shows that the core snubber utilizing the FBO method gives more compact design.

Towards a Better Distributed Framework for Learning Big Data

DTIC Science & Technology

2017-06-14

UNLIMITED: PB Public Release 13. SUPPLEMENTARY NOTES 14. ABSTRACT This work aimed at solving issues in distributed machine learning. The PI’s team proposed...communication load. Finally, the team proposed the parallel least-squares policy iteration (parallel LSPI) to parallelize a reinforcement policy learning. 15

FPGA architecture and implementation of sparse matrix vector multiplication for the finite element method

NASA Astrophysics Data System (ADS)

Elkurdi, Yousef; Fernández, David; Souleimanov, Evgueni; Giannacopoulos, Dennis; Gross, Warren J.

2008-04-01

The Finite Element Method (FEM) is a computationally intensive scientific and engineering analysis tool that has diverse applications ranging from structural engineering to electromagnetic simulation. The trends in floating-point performance are moving in favor of Field-Programmable Gate Arrays (FPGAs), hence increasing interest has grown in the scientific community to exploit this technology. We present an architecture and implementation of an FPGA-based sparse matrix-vector multiplier (SMVM) for use in the iterative solution of large, sparse systems of equations arising from FEM applications. FEM matrices display specific sparsity patterns that can be exploited to improve the efficiency of hardware designs. Our architecture exploits FEM matrix sparsity structure to achieve a balance between performance and hardware resource requirements by relying on external SDRAM for data storage while utilizing the FPGAs computational resources in a stream-through systolic approach. The architecture is based on a pipelined linear array of processing elements (PEs) coupled with a hardware-oriented matrix striping algorithm and a partitioning scheme which enables it to process arbitrarily big matrices without changing the number of PEs in the architecture. Therefore, this architecture is only limited by the amount of external RAM available to the FPGA. The implemented SMVM-pipeline prototype contains 8 PEs and is clocked at 110 MHz obtaining a peak performance of 1.76 GFLOPS. For 8 GB/s of memory bandwidth typical of recent FPGA systems, this architecture can achieve 1.5 GFLOPS sustained performance. Using multiple instances of the pipeline, linear scaling of the peak and sustained performance can be achieved. Our stream-through architecture provides the added advantage of enabling an iterative implementation of the SMVM computation required by iterative solution techniques such as the conjugate gradient method, avoiding initialization time due to data loading and setup inside the FPGA internal memory.

Parallel/Vector Integration Methods for Dynamical Astronomy

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

1999-01-01

This paper reviews three recent works on the numerical methods to integrate ordinary differential equations (ODE), which are specially designed for parallel, vector, and/or multi-processor-unit(PU) computers. The first is the Picard-Chebyshev method (Fukushima, 1997a). It obtains a global solution of ODE in the form of Chebyshev polynomial of large (> 1000) degree by applying the Picard iteration repeatedly. The iteration converges for smooth problems and/or perturbed dynamics. The method runs around 100-1000 times faster in the vector mode than in the scalar mode of a certain computer with vector processors (Fukushima, 1997b). The second is a parallelization of a symplectic integrator (Saha et al., 1997). It regards the implicit midpoint rules covering thousands of timesteps as large-scale nonlinear equations and solves them by the fixed-point iteration. The method is applicable to Hamiltonian systems and is expected to lead an acceleration factor of around 50 in parallel computers with more than 1000 PUs. The last is a parallelization of the extrapolation method (Ito and Fukushima, 1997). It performs trial integrations in parallel. Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3.5 by using several PUs. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators (Makino and Aarseth, 1992), (Hut et al., 1995) or the implicit symmetric multistep methods (Fukushima, 1998), (Fukushima, 1999).

A high-capacity model for one shot association learning in the brain

PubMed Central

Einarsson, Hafsteinn; Lengler, Johannes; Steger, Angelika

2014-01-01

We present a high-capacity model for one-shot association learning (hetero-associative memory) in sparse networks. We assume that basic patterns are pre-learned in networks and associations between two patterns are presented only once and have to be learned immediately. The model is a combination of an Amit-Fusi like network sparsely connected to a Willshaw type network. The learning procedure is palimpsest and comes from earlier work on one-shot pattern learning. However, in our setup we can enhance the capacity of the network by iterative retrieval. This yields a model for sparse brain-like networks in which populations of a few thousand neurons are capable of learning hundreds of associations even if they are presented only once. The analysis of the model is based on a novel result by Janson et al. on bootstrap percolation in random graphs. PMID:25426060

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

A high-capacity model for one shot association learning in the brain.

PubMed

Einarsson, Hafsteinn; Lengler, Johannes; Steger, Angelika

2014-01-01

We present a high-capacity model for one-shot association learning (hetero-associative memory) in sparse networks. We assume that basic patterns are pre-learned in networks and associations between two patterns are presented only once and have to be learned immediately. The model is a combination of an Amit-Fusi like network sparsely connected to a Willshaw type network. The learning procedure is palimpsest and comes from earlier work on one-shot pattern learning. However, in our setup we can enhance the capacity of the network by iterative retrieval. This yields a model for sparse brain-like networks in which populations of a few thousand neurons are capable of learning hundreds of associations even if they are presented only once. The analysis of the model is based on a novel result by Janson et al. on bootstrap percolation in random graphs.

Efficient iterative methods applied to the solution of transonic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wissink, A.M.; Lyrintzis, A.S.; Chronopoulos, A.T.

1996-02-01

We investigate the use of an inexact Newton`s method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton`s method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GIVIRES method. The preconditionermore » is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton- GIVIRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems. 38 refs., 14 figs., 7 tabs.« less

Block iterative restoration of astronomical images with the massively parallel processor

NASA Technical Reports Server (NTRS)

Heap, Sara R.; Lindler, Don J.

1987-01-01

A method is described for algebraic image restoration capable of treating astronomical images. For a typical 500 x 500 image, direct algebraic restoration would require the solution of a 250,000 x 250,000 linear system. The block iterative approach is used to reduce the problem to solving 4900 121 x 121 linear systems. The algorithm was implemented on the Goddard Massively Parallel Processor, which can solve a 121 x 121 system in approximately 0.06 seconds. Examples are shown of the results for various astronomical images.

Perceptually controlled doping for audio source separation

NASA Astrophysics Data System (ADS)

Mahé, Gaël; Nadalin, Everton Z.; Suyama, Ricardo; Romano, João MT

2014-12-01

The separation of an underdetermined audio mixture can be performed through sparse component analysis (SCA) that relies however on the strong hypothesis that source signals are sparse in some domain. To overcome this difficulty in the case where the original sources are available before the mixing process, the informed source separation (ISS) embeds in the mixture a watermark, which information can help a further separation. Though powerful, this technique is generally specific to a particular mixing setup and may be compromised by an additional bitrate compression stage. Thus, instead of watermarking, we propose a `doping' method that makes the time-frequency representation of each source more sparse, while preserving its audio quality. This method is based on an iterative decrease of the distance between the distribution of the signal and a target sparse distribution, under a perceptual constraint. We aim to show that the proposed approach is robust to audio coding and that the use of the sparsified signals improves the source separation, in comparison with the original sources. In this work, the analysis is made only in instantaneous mixtures and focused on voice sources.

Multi-objective based spectral unmixing for hyperspectral images

NASA Astrophysics Data System (ADS)

Xu, Xia; Shi, Zhenwei

2017-02-01

Sparse hyperspectral unmixing assumes that each observed pixel can be expressed by a linear combination of several pure spectra in a priori library. Sparse unmixing is challenging, since it is usually transformed to a NP-hard l0 norm based optimization problem. Existing methods usually utilize a relaxation to the original l0 norm. However, the relaxation may bring in sensitive weighted parameters and additional calculation error. In this paper, we propose a novel multi-objective based algorithm to solve the sparse unmixing problem without any relaxation. We transform sparse unmixing to a multi-objective optimization problem, which contains two correlative objectives: minimizing the reconstruction error and controlling the endmember sparsity. To improve the efficiency of multi-objective optimization, a population-based randomly flipping strategy is designed. Moreover, we theoretically prove that the proposed method is able to recover a guaranteed approximate solution from the spectral library within limited iterations. The proposed method can directly deal with l0 norm via binary coding for the spectral signatures in the library. Experiments on both synthetic and real hyperspectral datasets demonstrate the effectiveness of the proposed method.

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Yupeng, E-mail: yupeng@ualberta.ca; Deutsch, Clayton V.

2012-06-15

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells.more » In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.« less

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deveci, Mehmet; Trott, Christian Robert; Rajamanickam, Sivasankaran

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Integrating Concept Mapping into Information Systems Education for Meaningful Learning and Assessment

ERIC Educational Resources Information Center

Wei, Wei; Yue, Kwok-Bun

2017-01-01

Concept map (CM) is a theoretically sound yet easy to learn tool and can be effectively used to represent knowledge. Even though many disciplines have adopted CM as a teaching and learning tool to improve learning effectiveness, its application in IS curriculum is sparse. Meaningful learning happens when one iteratively integrates new concepts and…

Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram

2013-04-09

A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithmmore » is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.« less

Using sparsity information for iterative phase retrieval in x-ray propagation imaging.

PubMed

Pein, A; Loock, S; Plonka, G; Salditt, T

2016-04-18

For iterative phase retrieval algorithms in near field x-ray propagation imaging experiments with a single distance measurement, it is indispensable to have a strong constraint based on a priori information about the specimen; for example, information about the specimen's support. Recently, Loock and Plonka proposed to use the a priori information that the exit wave is sparsely represented in a certain directional representation system, a so-called shearlet system. In this work, we extend this approach to complex-valued signals by applying the new shearlet constraint to amplitude and phase separately. Further, we demonstrate its applicability to experimental data.

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

NASA Technical Reports Server (NTRS)

Zhang, Jun; Ge, Lixin; Kouatchou, Jules

2000-01-01

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

Parallel Reconstruction Using Null Operations (PRUNO)

PubMed Central

Zhang, Jian; Liu, Chunlei; Moseley, Michael E.

2011-01-01

A novel iterative k-space data-driven technique, namely Parallel Reconstruction Using Null Operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using Singular Value Decomposition (SVD). And an iterative conjugate- gradient approach is proposed to efficiently solve missing k-space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUO reconstruction, ultra high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with 8 coils and only a few autocalibration signal (ACS) lines. PMID:21604290

Xyce

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomquist, Heidi K.; Fixel, Deborah A.; Fett, David Brian

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.

On nonlinear finite element analysis in single-, multi- and parallel-processors

NASA Technical Reports Server (NTRS)

Utku, S.; Melosh, R.; Islam, M.; Salama, M.

1982-01-01

Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

An M-step preconditioned conjugate gradient method for parallel computation

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.

Parallel Implementation of 3-D Iterative Reconstruction With Intra-Thread Update for the jPET-D4

NASA Astrophysics Data System (ADS)

Lam, Chih Fung; Yamaya, Taiga; Obi, Takashi; Yoshida, Eiji; Inadama, Naoko; Shibuya, Kengo; Nishikido, Fumihiko; Murayama, Hideo

2009-02-01

One way to speed-up iterative image reconstruction is by parallel computing with a computer cluster. However, as the number of computing threads increases, parallel efficiency decreases due to network transfer delay. In this paper, we proposed a method to reduce data transfer between computing threads by introducing an intra-thread update. The update factor is collected from each slave thread and a global image is updated as usual in the first K sub-iteration. In the rest of the sub-iterations, the global image is only updated at an interval which is controlled by a parameter L. In between that interval, the intra-thread update is carried out whereby an image update is performed in each slave thread locally. We investigated combinations of K and L parameters based on parallel implementation of RAMLA for the jPET-D4 scanner. Our evaluation used four workstations with a total of 16 slave threads. Each slave thread calculated a different set of LORs which are divided according to ring difference numbers. We assessed image quality of the proposed method with a hotspot simulation phantom. The figure of merit was the full-width-half-maximum of hotspots and the background normalized standard deviation. At an optimum K and L setting, we did not find significant change in the output images. We also applied the proposed method to a Hoffman phantom experiment and found the difference due to intra-thread update was negligible. With the intra-thread update, computation time could be reduced by about 23%.

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation.

PubMed

Grossi, Giuliano; Lanzarotti, Raffaella; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD's robustness and wide applicability.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

New Bandwidth Efficient Parallel Concatenated Coding Schemes

NASA Technical Reports Server (NTRS)

Denedetto, S.; Divsalar, D.; Montorsi, G.; Pollara, F.

1996-01-01

We propose a new solution to parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2 bits/sec/Hz with 8PSK and 16QAM signal constellations.

Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Alaghband, Gita; Jordan, Harry F.

1989-01-01

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor (Kowalik, 1985) are presented and analyzed.

A feasibility study for compressed sensing combined phase contrast MR angiography reconstruction

NASA Astrophysics Data System (ADS)

Lee, Dong-Hoon; Hong, Cheol-Pyo; Lee, Man-Woo; Han, Bong-Soo

2012-02-01

Phase contrast magnetic resonance angiography (PC MRA) is a technique for flow velocity measurement and vessels visualization, simultaneously. The PC MRA takes long scan time because each flow encoding gradients which are composed bipolar gradient type need to reconstruct the angiography image. Moreover, it takes more image acquisition time when we use the PC MRA at the low-tesla MRI system. In this study, we studied and evaluation of feasibility for CS MRI reconstruction combined PC MRA which data acquired by low-tesla MRI system. We used non-linear reconstruction algorithm which named Bregman iteration for CS image reconstruction and validate the usefulness of CS combined PC MRA reconstruction technique. The results of CS reconstructed PC MRA images provide similar level of image quality between fully sampled reconstruction data and sparse sampled reconstruction using CS technique. Although our results used half of sampling ratio and do not used specification hardware device or performance which are improving the temporal resolution of MR image acquisition such as parallel imaging reconstruction using phased array coil or non-cartesian trajectory, we think that CS combined PC MRA technique will be helpful to increase the temporal resolution and at low-tesla MRI system.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Real-Time Data Streaming and Storing Structure for the LHD's Fusion Plasma Experiments

NASA Astrophysics Data System (ADS)

Nakanishi, Hideya; Ohsuna, Masaki; Kojima, Mamoru; Imazu, Setsuo; Nonomura, Miki; Emoto, Masahiko; Yoshida, Masanobu; Iwata, Chie; Ida, Katsumi

2016-02-01

The LHD data acquisition and archiving system, i.e., LABCOM system, has been fully equipped with high-speed real-time acquisition, streaming, and storage capabilities. To deal with more than 100 MB/s continuously generated data at each data acquisition (DAQ) node, DAQ tasks have been implemented as multitasking and multithreaded ones in which the shared memory plays the most important role for inter-process fast and massive data handling. By introducing a 10-second time chunk named “subshot,” endless data streams can be stored into a consecutive series of fixed length data blocks so that they will soon become readable by other processes even while the write process is continuing. Real-time device and environmental monitoring are also implemented in the same way with further sparse resampling. The central data storage has been separated into two layers to be capable of receiving multiple 100 MB/s inflows in parallel. For the frontend layer, high-speed SSD arrays are used as the GlusterFS distributed filesystem which can provide max. 2 GB/s throughput. Those design optimizations would be informative for implementing the next-generation data archiving system in big physics, such as ITER.

Fast, Accurate and Shift-Varying Line Projections for Iterative Reconstruction Using the GPU

PubMed Central

Pratx, Guillem; Chinn, Garry; Olcott, Peter D.; Levin, Craig S.

2013-01-01

List-mode processing provides an efficient way to deal with sparse projections in iterative image reconstruction for emission tomography. An issue often reported is the tremendous amount of computation required by such algorithm. Each recorded event requires several back- and forward line projections. We investigated the use of the programmable graphics processing unit (GPU) to accelerate the line-projection operations and implement fully-3D list-mode ordered-subsets expectation-maximization for positron emission tomography (PET). We designed a reconstruction approach that incorporates resolution kernels, which model the spatially-varying physical processes associated with photon emission, transport and detection. Our development is particularly suitable for applications where the projection data is sparse, such as high-resolution, dynamic, and time-of-flight PET reconstruction. The GPU approach runs more than 50 times faster than an equivalent CPU implementation while image quality and accuracy are virtually identical. This paper describes in details how the GPU can be used to accelerate the line projection operations, even when the lines-of-response have arbitrary endpoint locations and shift-varying resolution kernels are used. A quantitative evaluation is included to validate the correctness of this new approach. PMID:19244015

Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms.

PubMed

Liu, Li; Lin, Weikai; Jin, Mingwu

2015-01-01

In this paper, we propose two reconstruction algorithms for sparse-view X-ray computed tomography (CT). Treating the reconstruction problems as data fidelity constrained total variation (TV) minimization, both algorithms adapt the alternate two-stage strategy: projection onto convex sets (POCS) for data fidelity and non-negativity constraints and steepest descent for TV minimization. The novelty of this work is to determine iterative parameters automatically from data, thus avoiding tedious manual parameter tuning. In TV minimization, the step sizes of steepest descent are adaptively adjusted according to the difference from POCS update in either the projection domain or the image domain, while the step size of algebraic reconstruction technique (ART) in POCS is determined based on the data noise level. In addition, projection errors are used to compare with the error bound to decide whether to perform ART so as to reduce computational costs. The performance of the proposed methods is studied and evaluated using both simulated and physical phantom data. Our methods with automatic parameter tuning achieve similar, if not better, reconstruction performance compared to a representative two-stage algorithm. Copyright © 2014 Elsevier Ltd. All rights reserved.

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

NDetermin: Inferring Nondeterministic Sequential Specifications for Parallelism Correctness

DTIC Science & Technology

2011-12-16

other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a...Lab affiliates National Instruments, NEC, Nokia , NVIDIA, and Samsung. NDetermin: Inferring Nondeterministic Sequential Specifications for Parallelism...concurrently update x, some of these CAS’s will fail and those parallel loop iterations will recompute their updates to x and try again. Consider the parallel

Learning control system design based on 2-D theory - An application to parallel link manipulator

NASA Technical Reports Server (NTRS)

Geng, Z.; Carroll, R. L.; Lee, J. D.; Haynes, L. H.

1990-01-01

An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Soft-output decoding algorithms in iterative decoding of turbo codes

NASA Technical Reports Server (NTRS)

Benedetto, S.; Montorsi, G.; Divsalar, D.; Pollara, F.

1996-01-01

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Curvelet-based compressive sensing for InSAR raw data

NASA Astrophysics Data System (ADS)

Costa, Marcello G.; da Silva Pinho, Marcelo; Fernandes, David

2015-10-01

The aim of this work is to evaluate the compression performance of SAR raw data for interferometry applications collected by airborne from BRADAR (Brazilian SAR System operating in X and P bands) using the new approach based on compressive sensing (CS) to achieve an effective recovery with a good phase preserving. For this framework is desirable a real-time capability, where the collected data can be compressed to reduce onboard storage and bandwidth required for transmission. In the CS theory, a sparse unknown signals can be recovered from a small number of random or pseudo-random measurements by sparsity-promoting nonlinear recovery algorithms. Therefore, the original signal can be significantly reduced. To achieve the sparse representation of SAR signal, was done a curvelet transform. The curvelets constitute a directional frame, which allows an optimal sparse representation of objects with discontinuities along smooth curves as observed in raw data and provides an advanced denoising optimization. For the tests were made available a scene of 8192 x 2048 samples in range and azimuth in X-band with 2 m of resolution. The sparse representation was compressed using low dimension measurements matrices in each curvelet subband. Thus, an iterative CS reconstruction method based on IST (iterative soft/shrinkage threshold) was adjusted to recover the curvelets coefficients and then the original signal. To evaluate the compression performance were computed the compression ratio (CR), signal to noise ratio (SNR), and because the interferometry applications require more reconstruction accuracy the phase parameters like the standard deviation of the phase (PSD) and the mean phase error (MPE) were also computed. Moreover, in the image domain, a single-look complex image was generated to evaluate the compression effects. All results were computed in terms of sparsity analysis to provides an efficient compression and quality recovering appropriated for inSAR applications, therefore, providing a feasibility for compressive sensing application.

Visual Tracking Based on Extreme Learning Machine and Sparse Representation

PubMed Central

Wang, Baoxian; Tang, Linbo; Yang, Jinglin; Zhao, Baojun; Wang, Shuigen

2015-01-01

The existing sparse representation-based visual trackers mostly suffer from both being time consuming and having poor robustness problems. To address these issues, a novel tracking method is presented via combining sparse representation and an emerging learning technique, namely extreme learning machine (ELM). Specifically, visual tracking can be divided into two consecutive processes. Firstly, ELM is utilized to find the optimal separate hyperplane between the target observations and background ones. Thus, the trained ELM classification function is able to remove most of the candidate samples related to background contents efficiently, thereby reducing the total computational cost of the following sparse representation. Secondly, to further combine ELM and sparse representation, the resultant confidence values (i.e., probabilities to be a target) of samples on the ELM classification function are used to construct a new manifold learning constraint term of the sparse representation framework, which tends to achieve robuster results. Moreover, the accelerated proximal gradient method is used for deriving the optimal solution (in matrix form) of the constrained sparse tracking model. Additionally, the matrix form solution allows the candidate samples to be calculated in parallel, thereby leading to a higher efficiency. Experiments demonstrate the effectiveness of the proposed tracker. PMID:26506359

A sparse matrix algorithm on the Boolean vector machine

NASA Technical Reports Server (NTRS)

Wagner, Robert A.; Patrick, Merrell L.

1988-01-01

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Comparison of multihardware parallel implementations for a phase unwrapping algorithm

NASA Astrophysics Data System (ADS)

Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

2018-04-01

Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss-Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O (Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix-vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

Visual Tracking via Sparse and Local Linear Coding.

PubMed

Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan

2015-11-01

The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes.

An efficient dictionary learning algorithm and its application to 3-D medical image denoising.

PubMed

Li, Shutao; Fang, Leyuan; Yin, Haitao

2012-02-01

In this paper, we propose an efficient dictionary learning algorithm for sparse representation of given data and suggest a way to apply this algorithm to 3-D medical image denoising. Our learning approach is composed of two main parts: sparse coding and dictionary updating. On the sparse coding stage, an efficient algorithm named multiple clusters pursuit (MCP) is proposed. The MCP first applies a dictionary structuring strategy to cluster the atoms with high coherence together, and then employs a multiple-selection strategy to select several competitive atoms at each iteration. These two strategies can greatly reduce the computation complexity of the MCP and assist it to obtain better sparse solution. On the dictionary updating stage, the alternating optimization that efficiently approximates the singular value decomposition is introduced. Furthermore, in the 3-D medical image denoising application, a joint 3-D operation is proposed for taking the learning capabilities of the presented algorithm to simultaneously capture the correlations within each slice and correlations across the nearby slices, thereby obtaining better denoising results. The experiments on both synthetically generated data and real 3-D medical images demonstrate that the proposed approach has superior performance compared to some well-known methods. © 2011 IEEE

Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction

NASA Astrophysics Data System (ADS)

Niu, Shanzhou; Yu, Gaohang; Ma, Jianhua; Wang, Jing

2018-02-01

Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.

WE-EF-207-07: Dual Energy CT with One Full Scan and a Second Sparse-View Scan Using Structure Preserving Iterative Reconstruction (SPIR)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, T; Zhu, L

Purpose: Conventional dual energy CT (DECT) reconstructs CT and basis material images from two full-size projection datasets with different energy spectra. To relax the data requirement, we propose an iterative DECT reconstruction algorithm using one full scan and a second sparse-view scan by utilizing redundant structural information of the same object acquired at two different energies. Methods: We first reconstruct a full-scan CT image using filtered-backprojection (FBP) algorithm. The material similarities of each pixel with other pixels are calculated by an exponential function about pixel value differences. We assume that the material similarities of pixels remains in the second CTmore » scan, although pixel values may vary. An iterative method is designed to reconstruct the second CT image from reduced projections. Under the data fidelity constraint, the algorithm minimizes the L2 norm of the difference between pixel value and its estimation, which is the average of other pixel values weighted by their similarities. The proposed algorithm, referred to as structure preserving iterative reconstruction (SPIR), is evaluated on physical phantoms. Results: On the Catphan600 phantom, SPIR-based DECT method with a second 10-view scan reduces the noise standard deviation of a full-scan FBP CT reconstruction by a factor of 4 with well-maintained spatial resolution, while iterative reconstruction using total-variation regularization (TVR) degrades the spatial resolution at the same noise level. The proposed method achieves less than 1% measurement difference on electron density map compared with the conventional two-full-scan DECT. On an anthropomorphic pediatric phantom, our method successfully reconstructs the complicated vertebra structures and decomposes bone and soft tissue. Conclusion: We develop an effective method to reduce the number of views and therefore data acquisition in DECT. We show that SPIR-based DECT using one full scan and a second 10-view scan can provide high-quality DECT images and accurate electron density maps as conventional two-full-scan DECT.« less

A Fast and Accurate Sparse Continuous Signal Reconstruction by Homotopy DCD with Non-Convex Regularization

PubMed Central

Wang, Tianyun; Lu, Xinfei; Yu, Xiaofei; Xi, Zhendong; Chen, Weidong

2014-01-01

In recent years, various applications regarding sparse continuous signal recovery such as source localization, radar imaging, communication channel estimation, etc., have been addressed from the perspective of compressive sensing (CS) theory. However, there are two major defects that need to be tackled when considering any practical utilization. The first issue is off-grid problem caused by the basis mismatch between arbitrary located unknowns and the pre-specified dictionary, which would make conventional CS reconstruction methods degrade considerably. The second important issue is the urgent demand for low-complexity algorithms, especially when faced with the requirement of real-time implementation. In this paper, to deal with these two problems, we have presented three fast and accurate sparse reconstruction algorithms, termed as HR-DCD, Hlog-DCD and Hlp-DCD, which are based on homotopy, dichotomous coordinate descent (DCD) iterations and non-convex regularizations, by combining with the grid refinement technique. Experimental results are provided to demonstrate the effectiveness of the proposed algorithms and related analysis. PMID:24675758

A linear recurrent kernel online learning algorithm with sparse updates.

PubMed

Fan, Haijin; Song, Qing

2014-02-01

In this paper, we propose a recurrent kernel algorithm with selectively sparse updates for online learning. The algorithm introduces a linear recurrent term in the estimation of the current output. This makes the past information reusable for updating of the algorithm in the form of a recurrent gradient term. To ensure that the reuse of this recurrent gradient indeed accelerates the convergence speed, a novel hybrid recurrent training is proposed to switch on or off learning the recurrent information according to the magnitude of the current training error. Furthermore, the algorithm includes a data-dependent adaptive learning rate which can provide guaranteed system weight convergence at each training iteration. The learning rate is set as zero when the training violates the derived convergence conditions, which makes the algorithm updating process sparse. Theoretical analyses of the weight convergence are presented and experimental results show the good performance of the proposed algorithm in terms of convergence speed and estimation accuracy. Copyright © 2013 Elsevier Ltd. All rights reserved.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

NASA Astrophysics Data System (ADS)

Shao, Meiyue; Aktulga, H. Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P.

2018-01-01

We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. We also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Low photon count based digital holography for quadratic phase cryptography.

PubMed

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

2017-07-15

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Photoacoustic image reconstruction via deep learning

NASA Astrophysics Data System (ADS)

Antholzer, Stephan; Haltmeier, Markus; Nuster, Robert; Schwab, Johannes

2018-02-01

Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction algorithms which allow to include prior knowledge such as smoothness, total variation (TV) or sparsity constraints. These algorithms tend to be time consuming as the forward and adjoint problems have to be solved repeatedly. Further, iterative algorithms have additional drawbacks. For example, the reconstruction quality strongly depends on a-priori model assumptions about the objects to be recovered, which are often not strictly satisfied in practical applications. To overcome these issues, in this paper, we develop direct and efficient reconstruction algorithms based on deep learning. As opposed to iterative algorithms, we apply a convolutional neural network, whose parameters are trained before the reconstruction process based on a set of training data. For actual image reconstruction, a single evaluation of the trained network yields the desired result. Our presented numerical results (using two different network architectures) demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative reconstruction methods.

Solution of a tridiagonal system of equations on the finite element machine

NASA Technical Reports Server (NTRS)

Bostic, S. W.

1984-01-01

Two parallel algorithms for the solution of tridiagonal systems of equations were implemented on the Finite Element Machine. The Accelerated Parallel Gauss method, an iterative method, and the Buneman algorithm, a direct method, are discussed and execution statistics are presented.

Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

NASA Astrophysics Data System (ADS)

Marx, Alain; Lütjens, Hinrich

2017-03-01

A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Parallel fast multipole boundary element method applied to computational homogenization

NASA Astrophysics Data System (ADS)

Ptaszny, Jacek

2018-01-01

In the present work, a fast multipole boundary element method (FMBEM) and a parallel computer code for 3D elasticity problem is developed and applied to the computational homogenization of a solid containing spherical voids. The system of equation is solved by using the GMRES iterative solver. The boundary of the body is dicretized by using the quadrilateral serendipity elements with an adaptive numerical integration. Operations related to a single GMRES iteration, performed by traversing the corresponding tree structure upwards and downwards, are parallelized by using the OpenMP standard. The assignment of tasks to threads is based on the assumption that the tree nodes at which the moment transformations are initialized can be partitioned into disjoint sets of equal or approximately equal size and assigned to the threads. The achieved speedup as a function of number of threads is examined.

The Battlefield Environment Division Modeling Framework (BMF). Part 1: Optimizing the Atmospheric Boundary Layer Environment Model for Cluster Computing

DTIC Science & Technology

2014-02-01

idle waiting for the wavefront to reach it. To overcome this, Reeve et al. (2001) 3 developed a scheme in analogy to the red-black Gauss - Seidel iterative ...understandable procedure calls. Parallelization of the SIMPLE iterative scheme with SIP used a red-black scheme similar to the red-black Gauss - Seidel ...scheme, the SIMPLE method, for pressure-velocity coupling. The result is a slowing convergence of the outer iterations . The red-black scheme excites a 2

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

Notes on implementation of sparsely distributed memory

NASA Technical Reports Server (NTRS)

Keeler, J. D.; Denning, P. J.

1986-01-01

The Sparsely Distributed Memory (SDM) developed by Kanerva is an unconventional memory design with very interesting and desirable properties. The memory works in a manner that is closely related to modern theories of human memory. The SDM model is discussed in terms of its implementation in hardware. Two appendices discuss the unconventional approaches of the SDM: Appendix A treats a resistive circuit for fast, parallel address decoding; and Appendix B treats a systolic array for high throughput read and write operations.

Kanerva's sparse distributed memory with multiple hamming thresholds

NASA Technical Reports Server (NTRS)

Pohja, Seppo; Kaski, Kimmo

1992-01-01

If the stored input patterns of Kanerva's Sparse Distributed Memory (SDM) are highly correlated, utilization of the storage capacity is very low compared to the case of uniformly distributed random input patterns. We consider a variation of SDM that has a better storage capacity utilization for correlated input patterns. This approach uses a separate selection threshold for each physical storage address or hard location. The selection of the hard locations for reading or writing can be done in parallel of which SDM implementations can benefit.

Development of parallel algorithms for electrical power management in space applications

NASA Technical Reports Server (NTRS)

Berry, Frederick C.

1989-01-01

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

Improved parallel data partitioning by nested dissection with applications to information retrieval.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Michael M.; Chevalier, Cedric; Boman, Erik Gunnar

The computational work in many information retrieval and analysis algorithms is based on sparse linear algebra. Sparse matrix-vector multiplication is a common kernel in many of these computations. Thus, an important related combinatorial problem in parallel computing is how to distribute the matrix and the vectors among processors so as to minimize the communication cost. We focus on minimizing the total communication volume while keeping the computation balanced across processes. In [1], the first two authors presented a new 2D partitioning method, the nested dissection partitioning algorithm. In this paper, we improve on that algorithm and show that it ismore » a good option for data partitioning in information retrieval. We also show partitioning time can be substantially reduced by using the SCOTCH software, and quality improves in some cases, too.« less

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation

PubMed Central

Grossi, Giuliano; Lin, Jianyi

2017-01-01

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD’s robustness and wide applicability. PMID:28103283

Comparing implementations of penalized weighted least-squares sinogram restoration.

PubMed

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-11-01

A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation. Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitello, P; Fried, L E; Pudliner, B

2003-07-14

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values, called the ''cache'' is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamicmore » calculations, CHEETAH uses MPI communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.« less

Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deveci, Mehmet; Rajamanickam, Sivasankaran; Trott, Christian Robert

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scienti c computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1986-01-01

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations.

Sparse representation of multi parametric DCE-MRI features using K-SVD for classifying gene expression based breast cancer recurrence risk

NASA Astrophysics Data System (ADS)

Mahrooghy, Majid; Ashraf, Ahmed B.; Daye, Dania; Mies, Carolyn; Rosen, Mark; Feldman, Michael; Kontos, Despina

2014-03-01

We evaluate the prognostic value of sparse representation-based features by applying the K-SVD algorithm on multiparametric kinetic, textural, and morphologic features in breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). K-SVD is an iterative dimensionality reduction method that optimally reduces the initial feature space by updating the dictionary columns jointly with the sparse representation coefficients. Therefore, by using K-SVD, we not only provide sparse representation of the features and condense the information in a few coefficients but also we reduce the dimensionality. The extracted K-SVD features are evaluated by a machine learning algorithm including a logistic regression classifier for the task of classifying high versus low breast cancer recurrence risk as determined by a validated gene expression assay. The features are evaluated using ROC curve analysis and leave one-out cross validation for different sparse representation and dimensionality reduction numbers. Optimal sparse representation is obtained when the number of dictionary elements is 4 (K=4) and maximum non-zero coefficients is 2 (L=2). We compare K-SVD with ANOVA based feature selection for the same prognostic features. The ROC results show that the AUC of the K-SVD based (K=4, L=2), the ANOVA based, and the original features (i.e., no dimensionality reduction) are 0.78, 0.71. and 0.68, respectively. From the results, it can be inferred that by using sparse representation of the originally extracted multi-parametric, high-dimensional data, we can condense the information on a few coefficients with the highest predictive value. In addition, the dimensionality reduction introduced by K-SVD can prevent models from over-fitting.

Impact of the implementation of MPI point-to-point communications on the performance of two general sparse solvers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amestoy, Patrick R.; Duff, Iain S.; L'Excellent, Jean-Yves

2001-10-10

We examine the mechanics of the send and receive mechanism of MPI and in particular how we can implement message passing in a robust way so that our performance is not significantly affected by changes to the MPI system. This leads us to using the Isend/Irecv protocol which will entail sometimes significant algorithmic changes. We discuss this within the context of two different algorithms for sparse Gaussian elimination that we have parallelized. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. Both algorithms are difficult to parallelize on distributed memory machines. Our initial strategiesmore » were based on simple MPI point-to-point communication primitives. With such approaches, the parallel performance of both codes are very sensitive to the MPI implementation, the way MPI internal buffers are used in particular. We then modified our codes to use more sophisticated nonblocking versions of MPI communication. This significantly improved the performance robustness (independent of the MPI buffering mechanism) and scalability, but at the cost of increased code complexity.« less

Hierarchical Parallelism in Finite Difference Analysis of Heat Conduction

NASA Technical Reports Server (NTRS)

Padovan, Joseph; Krishna, Lala; Gute, Douglas

1997-01-01

Based on the concept of hierarchical parallelism, this research effort resulted in highly efficient parallel solution strategies for very large scale heat conduction problems. Overall, the method of hierarchical parallelism involves the partitioning of thermal models into several substructured levels wherein an optimal balance into various associated bandwidths is achieved. The details are described in this report. Overall, the report is organized into two parts. Part 1 describes the parallel modelling methodology and associated multilevel direct, iterative and mixed solution schemes. Part 2 establishes both the formal and computational properties of the scheme.

Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.

PubMed

Okimoto, Gordon; Zeinalzadeh, Ashkan; Wenska, Tom; Loomis, Michael; Nation, James B; Fabre, Tiphaine; Tiirikainen, Maarit; Hernandez, Brenda; Chan, Owen; Wong, Linda; Kwee, Sandi

2016-01-01

Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1. The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation. We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology. Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.

Bit error rate tester using fast parallel generation of linear recurring sequences

DOEpatents

Pierson, Lyndon G.; Witzke, Edward L.; Maestas, Joseph H.

2003-05-06

A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permits the receiver to synchronize to the transmitted pattern within 2n bits.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data

NASA Astrophysics Data System (ADS)

Humphries, T.; Winn, J.; Faridani, A.

2017-08-01

Recent work in CT image reconstruction has seen increasing interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed heuristic which provides an automatic procedure to ‘superiorize’ an iterative image reconstruction algorithm with respect to a chosen objective function, such as TV. Under certain conditions, the superiorized algorithm is guaranteed to find a solution that is as satisfactory as any found by the original algorithm with respect to satisfying the constraints of the problem; this solution is also expected to be superior with respect to the chosen objective. Most work on superiorization has used reconstruction algorithms which assume a linear measurement model, which in the case of CT corresponds to data generated from a monoenergetic x-ray beam. Many CT systems generate x-rays from a polyenergetic spectrum, however, in which the measured data represent an integral of object attenuation over all energies in the spectrum. This inconsistency with the linear model produces the well-known beam hardening artifacts, which impair analysis of CT images. In this work we superiorize an iterative algorithm for reconstruction from polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply the superiorized algorithm in numerical phantom experiments modeling both sparse-view and limited-angle scenarios. In our experiments, the superiorized algorithm successfully finds solutions which are as constraints-compatible as those found by the original algorithm, with significantly reduced TV and ATV values. The superiorized algorithm thus produces images with greatly reduced sparse-view and limited angle artifacts, which are also largely free of the beam hardening artifacts that would be present if a superiorized version of a monoenergetic algorithm were used.

A Subspace Pursuit–based Iterative Greedy Hierarchical Solution to the Neuromagnetic Inverse Problem

PubMed Central

Babadi, Behtash; Obregon-Henao, Gabriel; Lamus, Camilo; Hämäläinen, Matti S.; Brown, Emery N.; Purdon, Patrick L.

2013-01-01

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness. PMID:24055554

Adapting high-level language programs for parallel processing using data flow

NASA Technical Reports Server (NTRS)

Standley, Hilda M.

1988-01-01

EASY-FLOW, a very high-level data flow language, is introduced for the purpose of adapting programs written in a conventional high-level language to a parallel environment. The level of parallelism provided is of the large-grained variety in which parallel activities take place between subprograms or processes. A program written in EASY-FLOW is a set of subprogram calls as units, structured by iteration, branching, and distribution constructs. A data flow graph may be deduced from an EASY-FLOW program.

ML 3.0 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

Computational Issues in Damping Identification for Large Scale Problems

NASA Technical Reports Server (NTRS)

Pilkey, Deborah L.; Roe, Kevin P.; Inman, Daniel J.

1997-01-01

Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm. Tests were performed using the IBM-SP2 at NASA Ames Research Center. The least squares method tested incurs high communication costs, which reduces the benefit of high performance computing. This method's memory requirement grows at a very rapid rate meaning that larger problems can quickly exceed available computer memory. The iterative method's memory requirement grows at a much slower pace and is able to handle problems with 500+ degrees of freedom on a single processor. This method benefits from parallelization, and significant speedup can he seen for problems of 100+ degrees-of-freedom.

jInv: A Modular and Scalable Framework for Electromagnetic Inverse Problems

NASA Astrophysics Data System (ADS)

Belliveau, P. T.; Haber, E.

2016-12-01

Inversion is a key tool in the interpretation of geophysical electromagnetic (EM) data. Three-dimensional (3D) EM inversion is very computationally expensive and practical software for inverting large 3D EM surveys must be able to take advantage of high performance computing (HPC) resources. It has traditionally been difficult to achieve those goals in a high level dynamic programming environment that allows rapid development and testing of new algorithms, which is important in a research setting. With those goals in mind, we have developed jInv, a framework for PDE constrained parameter estimation problems. jInv provides optimization and regularization routines, a framework for user defined forward problems, and interfaces to several direct and iterative solvers for sparse linear systems. The forward modeling framework provides finite volume discretizations of differential operators on rectangular tensor product meshes and tetrahedral unstructured meshes that can be used to easily construct forward modeling and sensitivity routines for forward problems described by partial differential equations. jInv is written in the emerging programming language Julia. Julia is a dynamic language targeted at the computational science community with a focus on high performance and native support for parallel programming. We have developed frequency and time-domain EM forward modeling and sensitivity routines for jInv. We will illustrate its capabilities and performance with two synthetic time-domain EM inversion examples. First, in airborne surveys, which use many sources, we achieve distributed memory parallelism by decoupling the forward and inverse meshes and performing forward modeling for each source on small, locally refined meshes. Secondly, we invert grounded source time-domain data from a gradient array style induced polarization survey using a novel time-stepping technique that allows us to compute data from different time-steps in parallel. These examples both show that it is possible to invert large scale 3D time-domain EM datasets within a modular, extensible framework written in a high-level, easy to use programming language.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Parallel processing of real-time dynamic systems simulation on OSCAR (Optimally SCheduled Advanced multiprocessoR)

NASA Technical Reports Server (NTRS)

Kasahara, Hironori; Honda, Hiroki; Narita, Seinosuke

1989-01-01

Parallel processing of real-time dynamic systems simulation on a multiprocessor system named OSCAR is presented. In the simulation of dynamic systems, generally, the same calculation are repeated every time step. However, we cannot apply to Do-all or the Do-across techniques for parallel processing of the simulation since there exist data dependencies from the end of an iteration to the beginning of the next iteration and furthermore data-input and data-output are required every sampling time period. Therefore, parallelism inside the calculation required for a single time step, or a large basic block which consists of arithmetic assignment statements, must be used. In the proposed method, near fine grain tasks, each of which consists of one or more floating point operations, are generated to extract the parallelism from the calculation and assigned to processors by using optimal static scheduling at compile time in order to reduce large run time overhead caused by the use of near fine grain tasks. The practicality of the scheme is demonstrated on OSCAR (Optimally SCheduled Advanced multiprocessoR) which has been developed to extract advantageous features of static scheduling algorithms to the maximum extent.

Parallel heuristics for scalable community detection

DOE PAGES

Lu, Hao; Halappanavar, Mahantesh; Kalyanaraman, Ananth

2015-08-14

Community detection has become a fundamental operation in numerous graph-theoretic applications. Despite its potential for application, there is only limited support for community detection on large-scale parallel computers, largely owing to the irregular and inherently sequential nature of the underlying heuristics. In this paper, we present parallelization heuristics for fast community detection using the Louvain method as the serial template. The Louvain method is an iterative heuristic for modularity optimization. Originally developed in 2008, the method has become increasingly popular owing to its ability to detect high modularity community partitions in a fast and memory-efficient manner. However, the method ismore » also inherently sequential, thereby limiting its scalability. Here, we observe certain key properties of this method that present challenges for its parallelization, and consequently propose heuristics that are designed to break the sequential barrier. For evaluation purposes, we implemented our heuristics using OpenMP multithreading, and tested them over real world graphs derived from multiple application domains. Compared to the serial Louvain implementation, our parallel implementation is able to produce community outputs with a higher modularity for most of the inputs tested, in comparable number or fewer iterations, while providing real speedups of up to 16x using 32 threads.« less

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald.

PubMed

Lagardère, Louis; Lipparini, Filippo; Polack, Étienne; Stamm, Benjamin; Cancès, Éric; Schnieders, Michael; Ren, Pengyu; Maday, Yvon; Piquemal, Jean-Philip

2014-02-28

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald

PubMed Central

Lagardère, Louis; Lipparini, Filippo; Polack, Étienne; Stamm, Benjamin; Cancès, Éric; Schnieders, Michael; Ren, Pengyu; Maday, Yvon; Piquemal, Jean-Philip

2015-01-01

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations. PMID:26512230

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE PAGES

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao; ...

2017-09-14

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

Iterative load-balancing method with multigrid level relaxation for particle simulation with short-range interactions

NASA Astrophysics Data System (ADS)

Furuichi, Mikito; Nishiura, Daisuke

2017-10-01

We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

Performance Analysis of Iterative Channel Estimation and Multiuser Detection in Multipath DS-CDMA Channels

NASA Astrophysics Data System (ADS)

Li, Husheng; Betz, Sharon M.; Poor, H. Vincent

2007-05-01

This paper examines the performance of decision feedback based iterative channel estimation and multiuser detection in channel coded aperiodic DS-CDMA systems operating over multipath fading channels. First, explicit expressions describing the performance of channel estimation and parallel interference cancellation based multiuser detection are developed. These results are then combined to characterize the evolution of the performance of a system that iterates among channel estimation, multiuser detection and channel decoding. Sufficient conditions for convergence of this system to a unique fixed point are developed.

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

Joint image restoration and location in visual navigation system

NASA Astrophysics Data System (ADS)

Wu, Yuefeng; Sang, Nong; Lin, Wei; Shao, Yuanjie

2018-02-01

Image location methods are the key technologies of visual navigation, most previous image location methods simply assume the ideal inputs without taking into account the real-world degradations (e.g. low resolution and blur). In view of such degradations, the conventional image location methods first perform image restoration and then match the restored image on the reference image. However, the defective output of the image restoration can affect the result of localization, by dealing with the restoration and location separately. In this paper, we present a joint image restoration and location (JRL) method, which utilizes the sparse representation prior to handle the challenging problem of low-quality image location. The sparse representation prior states that the degraded input image, if correctly restored, will have a good sparse representation in terms of the dictionary constructed from the reference image. By iteratively solving the image restoration in pursuit of the sparest representation, our method can achieve simultaneous restoration and location. Based on such a sparse representation prior, we demonstrate that the image restoration task and the location task can benefit greatly from each other. Extensive experiments on real scene images with Gaussian blur are carried out and our joint model outperforms the conventional methods of treating the two tasks independently.

Sparsity-promoting orthogonal dictionary updating for image reconstruction from highly undersampled magnetic resonance data.

PubMed

Huang, Jinhong; Guo, Li; Feng, Qianjin; Chen, Wufan; Feng, Yanqiu

2015-07-21

Image reconstruction from undersampled k-space data accelerates magnetic resonance imaging (MRI) by exploiting image sparseness in certain transform domains. Employing image patch representation over a learned dictionary has the advantage of being adaptive to local image structures and thus can better sparsify images than using fixed transforms (e.g. wavelets and total variations). Dictionary learning methods have recently been introduced to MRI reconstruction, and these methods demonstrate significantly reduced reconstruction errors compared to sparse MRI reconstruction using fixed transforms. However, the synthesis sparse coding problem in dictionary learning is NP-hard and computationally expensive. In this paper, we present a novel sparsity-promoting orthogonal dictionary updating method for efficient image reconstruction from highly undersampled MRI data. The orthogonality imposed on the learned dictionary enables the minimization problem in the reconstruction to be solved by an efficient optimization algorithm which alternately updates representation coefficients, orthogonal dictionary, and missing k-space data. Moreover, both sparsity level and sparse representation contribution using updated dictionaries gradually increase during iterations to recover more details, assuming the progressively improved quality of the dictionary. Simulation and real data experimental results both demonstrate that the proposed method is approximately 10 to 100 times faster than the K-SVD-based dictionary learning MRI method and simultaneously improves reconstruction accuracy.

Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

NASA Astrophysics Data System (ADS)

Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

2017-12-01

This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

Low-dose CT reconstruction via L1 dictionary learning regularization using iteratively reweighted least-squares.

PubMed

Zhang, Cheng; Zhang, Tao; Li, Ming; Peng, Chengtao; Liu, Zhaobang; Zheng, Jian

2016-06-18

In order to reduce the radiation dose of CT (computed tomography), compressed sensing theory has been a hot topic since it provides the possibility of a high quality recovery from the sparse sampling data. Recently, the algorithm based on DL (dictionary learning) was developed to deal with the sparse CT reconstruction problem. However, the existing DL algorithm focuses on the minimization problem with the L2-norm regularization term, which leads to reconstruction quality deteriorating while the sampling rate declines further. Therefore, it is essential to improve the DL method to meet the demand of more dose reduction. In this paper, we replaced the L2-norm regularization term with the L1-norm one. It is expected that the proposed L1-DL method could alleviate the over-smoothing effect of the L2-minimization and reserve more image details. The proposed algorithm solves the L1-minimization problem by a weighting strategy, solving the new weighted L2-minimization problem based on IRLS (iteratively reweighted least squares). Through the numerical simulation, the proposed algorithm is compared with the existing DL method (adaptive dictionary based statistical iterative reconstruction, ADSIR) and other two typical compressed sensing algorithms. It is revealed that the proposed algorithm is more accurate than the other algorithms especially when further reducing the sampling rate or increasing the noise. The proposed L1-DL algorithm can utilize more prior information of image sparsity than ADSIR. By transforming the L2-norm regularization term of ADSIR with the L1-norm one and solving the L1-minimization problem by IRLS strategy, L1-DL could reconstruct the image more exactly.

Performance and capacity analysis of Poisson photon-counting based Iter-PIC OCDMA systems.

PubMed

Li, Lingbin; Zhou, Xiaolin; Zhang, Rong; Zhang, Dingchen; Hanzo, Lajos

2013-11-04

In this paper, an iterative parallel interference cancellation (Iter-PIC) technique is developed for optical code-division multiple-access (OCDMA) systems relying on shot-noise limited Poisson photon-counting reception. The novel semi-analytical tool of extrinsic information transfer (EXIT) charts is used for analysing both the bit error rate (BER) performance as well as the channel capacity of these systems and the results are verified by Monte Carlo simulations. The proposed Iter-PIC OCDMA system is capable of achieving two orders of magnitude BER improvements and a 0.1 nats of capacity improvement over the conventional chip-level OCDMA systems at a coding rate of 1/10.

SparseCT: interrupted-beam acquisition and sparse reconstruction for radiation dose reduction

NASA Astrophysics Data System (ADS)

Koesters, Thomas; Knoll, Florian; Sodickson, Aaron; Sodickson, Daniel K.; Otazo, Ricardo

2017-03-01

State-of-the-art low-dose CT methods reduce the x-ray tube current and use iterative reconstruction methods to denoise the resulting images. However, due to compromises between denoising and image quality, only moderate dose reductions up to 30-40% are accepted in clinical practice. An alternative approach is to reduce the number of x-ray projections and use compressed sensing to reconstruct the full-tube-current undersampled data. This idea was recognized in the early days of compressed sensing and proposals for CT dose reduction appeared soon afterwards. However, no practical means of undersampling has yet been demonstrated in the challenging environment of a rapidly rotating CT gantry. In this work, we propose a moving multislit collimator as a practical incoherent undersampling scheme for compressed sensing CT and evaluate its application for radiation dose reduction. The proposed collimator is composed of narrow slits and moves linearly along the slice dimension (z), to interrupt the incident beam in different slices for each x-ray tube angle (θ). The reduced projection dataset is then reconstructed using a sparse approach, where 3D image gradients are employed to enforce sparsity. The effects of the collimator slits on the beam profile were measured and represented as a continuous slice profile. SparseCT was tested using retrospective undersampling and compared against commercial current-reduction techniques on phantoms and in vivo studies. Initial results suggest that SparseCT may enable higher performance than current-reduction, particularly for high dose reduction factors.

Sparse image reconstruction for molecular imaging.

PubMed

Ting, Michael; Raich, Raviv; Hero, Alfred O

2009-06-01

The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.

Filtered gradient reconstruction algorithm for compressive spectral imaging

NASA Astrophysics Data System (ADS)

Mejia, Yuri; Arguello, Henry

2017-04-01

Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual ΦTy, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Blind motion image deblurring using nonconvex higher-order total variation model

NASA Astrophysics Data System (ADS)

Li, Weihong; Chen, Rui; Xu, Shangwen; Gong, Weiguo

2016-09-01

We propose a nonconvex higher-order total variation (TV) method for blind motion image deblurring. First, we introduce a nonconvex higher-order TV differential operator to define a new model of the blind motion image deblurring, which can effectively eliminate the staircase effect of the deblurred image; meanwhile, we employ an image sparse prior to improve the edge recovery quality. Second, to improve the accuracy of the estimated motion blur kernel, we use L1 norm and H1 norm as the blur kernel regularization term, considering the sparsity and smoothing of the motion blur kernel. Third, because it is difficult to solve the numerically computational complexity problem of the proposed model owing to the intrinsic nonconvexity, we propose a binary iterative strategy, which incorporates a reweighted minimization approximating scheme in the outer iteration, and a split Bregman algorithm in the inner iteration. And we also discuss the convergence of the proposed binary iterative strategy. Last, we conduct extensive experiments on both synthetic and real-world degraded images. The results demonstrate that the proposed method outperforms the previous representative methods in both quality of visual perception and quantitative measurement.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Xuanhua; Luo, Xuan; Liang, Junling

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weightmore » asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.« less

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Design of a MIMD neural network processor

NASA Astrophysics Data System (ADS)

Saeks, Richard E.; Priddy, Kevin L.; Pap, Robert M.; Stowell, S.

1994-03-01

The Accurate Automation Corporation (AAC) neural network processor (NNP) module is a fully programmable multiple instruction multiple data (MIMD) parallel processor optimized for the implementation of neural networks. The AAC NNP design fully exploits the intrinsic sparseness of neural network topologies. Moreover, by using a MIMD parallel processing architecture one can update multiple neurons in parallel with efficiency approaching 100 percent as the size of the network increases. Each AAC NNP module has 8 K neurons and 32 K interconnections and is capable of 140,000,000 connections per second with an eight processor array capable of over one billion connections per second.

Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

DOE PAGES

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas; ...

2016-01-06

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

Computing row and column counts for sparse QR and LU factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilbert, John R.; Li, Xiaoye S.; Ng, Esmond G.

2001-01-01

We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and theremore » is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.« less

A three-dimensional wide-angle BPM for optical waveguide structures.

PubMed

Ma, Changbao; Van Keuren, Edward

2007-01-22

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra's scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

Towards an Automated Classification of Transient Events in Synoptic Sky Surveys

NASA Technical Reports Server (NTRS)

Djorgovski, S. G.; Donalek, C.; Mahabal, A. A.; Moghaddam, B.; Turmon, M.; Graham, M. J.; Drake, A. J.; Sharma, N.; Chen, Y.

2011-01-01

We describe the development of a system for an automated, iterative, real-time classification of transient events discovered in synoptic sky surveys. The system under development incorporates a number of Machine Learning techniques, mostly using Bayesian approaches, due to the sparse nature, heterogeneity, and variable incompleteness of the available data. The classifications are improved iteratively as the new measurements are obtained. One novel featrue is the development of an automated follow-up recommendation engine, that suggest those measruements that would be the most advantageous in terms of resolving classification ambiguities and/or characterization of the astrophysically most interesting objects, given a set of available follow-up assets and their cost funcations. This illustrates the symbiotic relationship of astronomy and applied computer science through the emerging disciplne of AstroInformatics.

Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-02-01

Multi-conjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.

A three-dimensional wide-angle BPM for optical waveguide structures

NASA Astrophysics Data System (ADS)

Ma, Changbao; van Keuren, Edward

2007-01-01

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra’s scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

Parallel programming of gradient-based iterative image reconstruction schemes for optical tomography.

PubMed

Hielscher, Andreas H; Bartel, Sebastian

2004-02-01

Optical tomography (OT) is a fast developing novel imaging modality that uses near-infrared (NIR) light to obtain cross-sectional views of optical properties inside the human body. A major challenge remains the time-consuming, computational-intensive image reconstruction problem that converts NIR transmission measurements into cross-sectional images. To increase the speed of iterative image reconstruction schemes that are commonly applied for OT, we have developed and implemented several parallel algorithms on a cluster of workstations. Static process distribution as well as dynamic load balancing schemes suitable for heterogeneous clusters and varying machine performances are introduced and tested. The resulting algorithms are shown to accelerate the reconstruction process to various degrees, substantially reducing the computation times for clinically relevant problems.

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE PAGES

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; ...

2016-11-07

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Dissipation, Voltage Profile and Levy Dragon in a Special Ladder Network

ERIC Educational Resources Information Center

Ucak, C.

2009-01-01

A ladder network constructed by an elementary two-terminal network consisting of a parallel resistor-inductor block in series with a parallel resistor-capacitor block sometimes is said to have a non-dispersive dissipative response. This special ladder network is created iteratively by replacing the elementary two-terminal network in place of the…

Parallel Computing Strategies for Irregular Algorithms

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid; Shan, Hongzhang; Biegel, Bryan (Technical Monitor)

2002-01-01

Parallel computing promises several orders of magnitude increase in our ability to solve realistic computationally-intensive problems, but relies on their efficient mapping and execution on large-scale multiprocessor architectures. Unfortunately, many important applications are irregular and dynamic in nature, making their effective parallel implementation a daunting task. Moreover, with the proliferation of parallel architectures and programming paradigms, the typical scientist is faced with a plethora of questions that must be answered in order to obtain an acceptable parallel implementation of the solution algorithm. In this paper, we consider three representative irregular applications: unstructured remeshing, sparse matrix computations, and N-body problems, and parallelize them using various popular programming paradigms on a wide spectrum of computer platforms ranging from state-of-the-art supercomputers to PC clusters. We present the underlying problems, the solution algorithms, and the parallel implementation strategies. Smart load-balancing, partitioning, and ordering techniques are used to enhance parallel performance. Overall results demonstrate the complexity of efficiently parallelizing irregular algorithms.

Tuning iteration space slicing based tiled multi-core code implementing Nussinov's RNA folding.

PubMed

Palkowski, Marek; Bielecki, Wlodzimierz

2018-01-15

RNA folding is an ongoing compute-intensive task of bioinformatics. Parallelization and improving code locality for this kind of algorithms is one of the most relevant areas in computational biology. Fortunately, RNA secondary structure approaches, such as Nussinov's recurrence, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. This allows us to apply powerful polyhedral compilation techniques based on the transitive closure of dependence graphs to generate parallel tiled code implementing Nussinov's RNA folding. Such techniques are within the iteration space slicing framework - the transitive dependences are applied to the statement instances of interest to produce valid tiles. The main problem at generating parallel tiled code is defining a proper tile size and tile dimension which impact parallelism degree and code locality. To choose the best tile size and tile dimension, we first construct parallel parametric tiled code (parameters are variables defining tile size). With this purpose, we first generate two nonparametric tiled codes with different fixed tile sizes but with the same code structure and then derive a general affine model, which describes all integer factors available in expressions of those codes. Using this model and known integer factors present in the mentioned expressions (they define the left-hand side of the model), we find unknown integers in this model for each integer factor available in the same fixed tiled code position and replace in this code expressions, including integer factors, with those including parameters. Then we use this parallel parametric tiled code to implement the well-known tile size selection (TSS) technique, which allows us to discover in a given search space the best tile size and tile dimension maximizing target code performance. For a given search space, the presented approach allows us to choose the best tile size and tile dimension in parallel tiled code implementing Nussinov's RNA folding. Experimental results, received on modern Intel multi-core processors, demonstrate that this code outperforms known closely related implementations when the length of RNA strands is bigger than 2500.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES*

PubMed Central

Fu, Zhisong; Jeong, Won-Ki; Pan, Yongsheng; Kirby, Robert M.; Whitaker, Ross T.

2012-01-01

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton–Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512–2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers. PMID:22641200

Myria: Scalable Analytics as a Service

NASA Astrophysics Data System (ADS)

Howe, B.; Halperin, D.; Whitaker, A.

2014-12-01

At the UW eScience Institute, we're working to empower non-experts, especially in the sciences, to write and use data-parallel algorithms. To this end, we are building Myria, a web-based platform for scalable analytics and data-parallel programming. Myria's internal model of computation is the relational algebra extended with iteration, such that every program is inherently data-parallel, just as every query in a database is inherently data-parallel. But unlike databases, iteration is a first class concept, allowing us to express machine learning tasks, graph traversal tasks, and more. Programs can be expressed in a number of languages and can be executed on a number of execution environments, but we emphasize a particular language called MyriaL that supports both imperative and declarative styles and a particular execution engine called MyriaX that uses an in-memory column-oriented representation and asynchronous iteration. We deliver Myria over the web as a service, providing an editor, performance analysis tools, and catalog browsing features in a single environment. We find that this web-based "delivery vector" is critical in reaching non-experts: they are insulated from irrelevant effort technical work associated with installation, configuration, and resource management. The MyriaX backend, one of several execution runtimes we support, is a main-memory, column-oriented, RDBMS-on-the-worker system that supports cyclic data flows as a first-class citizen and has been shown to outperform competitive systems on 100-machine cluster sizes. I will describe the Myria system, give a demo, and present some new results in large-scale oceanographic microbiology.

Comparing implementations of penalized weighted least-squares sinogram restoration

PubMed Central

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-01-01

Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. Results: All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors’ previous penalized-likelihood implementation. Conclusions: Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes. PMID:21158306

The multigrid preconditioned conjugate gradient method

NASA Technical Reports Server (NTRS)

Tatebe, Osamu

1993-01-01

A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

Signal processing using sparse derivatives with applications to chromatograms and ECG

NASA Astrophysics Data System (ADS)

Ning, Xiaoran

In this thesis, we investigate the sparsity exist in the derivative domain. Particularly, we focus on the type of signals which posses up to Mth (M > 0) order sparse derivatives. Efforts are put on formulating proper penalty functions and optimization problems to capture properties related to sparse derivatives, searching for fast, computationally efficient solvers. Also the effectiveness of these algorithms are applied to two real world applications. In the first application, we provide an algorithm which jointly addresses the problems of chromatogram baseline correction and noise reduction. The series of chromatogram peaks are modeled as sparse with sparse derivatives, and the baseline is modeled as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is also utilized with symmetric penalty functions. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. Promising result is obtained. In the second application, a novel Electrocardiography (ECG) enhancement algorithm is designed also based on sparse derivatives. In the real medical environment, ECG signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. By solving the proposed convex l1 optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. At the end, the algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109452 anotations), resulting a sensitivity of Se = 99.87%$ and a positive prediction of +P = 99.88%.

2-D Ultrasound Sparse Arrays Multidepth Radiation Optimization Using Simulated Annealing and Spiral-Array Inspired Energy Functions.

PubMed

Roux, Emmanuel; Ramalli, Alessandro; Tortoli, Piero; Cachard, Christian; Robini, Marc C; Liebgott, Herve

2016-12-01

Full matrix arrays are excellent tools for 3-D ultrasound imaging, but the required number of active elements is too high to be individually controlled by an equal number of scanner channels. The number of active elements is significantly reduced by the sparse array techniques, but the position of the remaining elements must be carefully optimized. This issue is faced here by introducing novel energy functions in the simulated annealing (SA) algorithm. At each iteration step of the optimization process, one element is freely translated and the associated radiated pattern is simulated. To control the pressure field behavior at multiple depths, three energy functions inspired by the pressure field radiated by a Blackman-tapered spiral array are introduced. Such energy functions aim at limiting the main lobe width while lowering the side lobe and grating lobe levels at multiple depths. Numerical optimization results illustrate the influence of the number of iterations, pressure measurement points, and depths, as well as the influence of the energy function definition on the optimized layout. It is also shown that performance close to or even better than the one provided by a spiral array, here assumed as reference, may be obtained. The finite-time convergence properties of SA allow the duration of the optimization process to be set in advance.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Dual energy CT with one full scan and a second sparse-view scan using structure preserving iterative reconstruction (SPIR)

NASA Astrophysics Data System (ADS)

Wang, Tonghe; Zhu, Lei

2016-09-01

Conventional dual-energy CT (DECT) reconstruction requires two full-size projection datasets with two different energy spectra. In this study, we propose an iterative algorithm to enable a new data acquisition scheme which requires one full scan and a second sparse-view scan for potential reduction in imaging dose and engineering cost of DECT. A bilateral filter is calculated as a similarity matrix from the first full-scan CT image to quantify the similarity between any two pixels, which is assumed unchanged on a second CT image since DECT scans are performed on the same object. The second CT image from reduced projections is reconstructed by an iterative algorithm which updates the image by minimizing the total variation of the difference between the image and its filtered image by the similarity matrix under data fidelity constraint. As the redundant structural information of the two CT images is contained in the similarity matrix for CT reconstruction, we refer to the algorithm as structure preserving iterative reconstruction (SPIR). The proposed method is evaluated on both digital and physical phantoms, and is compared with the filtered-backprojection (FBP) method, the conventional total-variation-regularization-based algorithm (TVR) and prior-image-constrained-compressed-sensing (PICCS). SPIR with a second 10-view scan reduces the image noise STD by a factor of one order of magnitude with same spatial resolution as full-view FBP image. SPIR substantially improves over TVR on the reconstruction accuracy of a 10-view scan by decreasing the reconstruction error from 6.18% to 1.33%, and outperforms TVR at 50 and 20-view scans on spatial resolution with a higher frequency at the modulation transfer function value of 10% by an average factor of 4. Compared with the 20-view scan PICCS result, the SPIR image has 7 times lower noise STD with similar spatial resolution. The electron density map obtained from the SPIR-based DECT images with a second 10-view scan has an average error of less than 1%.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Solving large sparse eigenvalue problems on supercomputers

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef

1988-01-01

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.

Performance Implications of Synchronization Support for Parallel FORTRAN Programs

DTIC Science & Technology

1991-06-17

applications we used in this study are BDNA and FLO52. BDNA is a molecular dy- I namics simulator for biomolecules in water and it uses ordinary...parallelism structures and loop granularity. In the BDNA program, most of the parallel loops are not nested and the iterations are 200-1000 instructions long...are of concern. The BDNA curve in Figure 21 shows that for this program only 17% of all 32 I I 100 BDNA -4 FLO52 -I 80 3 CumuilatQe percentage of3

A highly parallel multigrid-like method for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Tuminaro, Ray S.

1989-01-01

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Track monitoring from the dynamic response of a passing train: A sparse approach

NASA Astrophysics Data System (ADS)

Lederman, George; Chen, Siheng; Garrett, James H.; Kovačević, Jelena; Noh, Hae Young; Bielak, Jacobo

2017-06-01

Collecting vibration data from revenue service trains could be a low-cost way to more frequently monitor railroad tracks, yet operational variability makes robust analysis a challenge. We propose a novel analysis technique for track monitoring that exploits the sparsity inherent in train-vibration data. This sparsity is based on the observation that large vertical train vibrations typically involve the excitation of the train's fundamental mode due to track joints, switchgear, or other discrete hardware. Rather than try to model the entire rail profile, in this study we examine a sparse approach to solving an inverse problem where (1) the roughness is constrained to a discrete and limited set of "bumps"; and (2) the train system is idealized as a simple damped oscillator that models the train's vibration in the fundamental mode. We use an expectation maximization (EM) approach to iteratively solve for the track profile and the train system properties, using orthogonal matching pursuit (OMP) to find the sparse approximation within each step. By enforcing sparsity, the inverse problem is well posed and the train's position can be found relative to the sparse bumps, thus reducing the uncertainty in the GPS data. We validate the sparse approach on two sections of track monitored from an operational train over a 16 month period of time, one where track changes did not occur during this period and another where changes did occur. We show that this approach can not only detect when track changes occur, but also offers insight into the type of such changes.

Shape prior modeling using sparse representation and online dictionary learning.

PubMed

Zhang, Shaoting; Zhan, Yiqiang; Zhou, Yan; Uzunbas, Mustafa; Metaxas, Dimitris N

2012-01-01

The recently proposed sparse shape composition (SSC) opens a new avenue for shape prior modeling. Instead of assuming any parametric model of shape statistics, SSC incorporates shape priors on-the-fly by approximating a shape instance (usually derived from appearance cues) by a sparse combination of shapes in a training repository. Theoretically, one can increase the modeling capability of SSC by including as many training shapes in the repository. However, this strategy confronts two limitations in practice. First, since SSC involves an iterative sparse optimization at run-time, the more shape instances contained in the repository, the less run-time efficiency SSC has. Therefore, a compact and informative shape dictionary is preferred to a large shape repository. Second, in medical imaging applications, training shapes seldom come in one batch. It is very time consuming and sometimes infeasible to reconstruct the shape dictionary every time new training shapes appear. In this paper, we propose an online learning method to address these two limitations. Our method starts from constructing an initial shape dictionary using the K-SVD algorithm. When new training shapes come, instead of re-constructing the dictionary from the ground up, we update the existing one using a block-coordinates descent approach. Using the dynamically updated dictionary, sparse shape composition can be gracefully scaled up to model shape priors from a large number of training shapes without sacrificing run-time efficiency. Our method is validated on lung localization in X-Ray and cardiac segmentation in MRI time series. Compared to the original SSC, it shows comparable performance while being significantly more efficient.

Dictionary Learning Algorithms for Sparse Representation

PubMed Central

Kreutz-Delgado, Kenneth; Murray, Joseph F.; Rao, Bhaskar D.; Engan, Kjersti; Lee, Te-Won; Sejnowski, Terrence J.

2010-01-01

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial “25 words or less”), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an over-complete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error). PMID:12590811

Parallel transformation of K-SVD solar image denoising algorithm

NASA Astrophysics Data System (ADS)

Liang, Youwen; Tian, Yu; Li, Mei

2017-02-01

The images obtained by observing the sun through a large telescope always suffered with noise due to the low SNR. K-SVD denoising algorithm can effectively remove Gauss white noise. Training dictionaries for sparse representations is a time consuming task, due to the large size of the data involved and to the complexity of the training algorithms. In this paper, an OpenMP parallel programming language is proposed to transform the serial algorithm to the parallel version. Data parallelism model is used to transform the algorithm. Not one atom but multiple atoms updated simultaneously is the biggest change. The denoising effect and acceleration performance are tested after completion of the parallel algorithm. Speedup of the program is 13.563 in condition of using 16 cores. This parallel version can fully utilize the multi-core CPU hardware resources, greatly reduce running time and easily to transplant in multi-core platform.

Optimization of sparse matrix-vector multiplication on emerging multicore platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2007-01-01

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD dual-core and Intel quad-core designs, the heterogeneous STI Cell, as well as the first scientificmore » study of the highly multithreaded Sun Niagara2. We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural tradeoffs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

Array signal recovery algorithm for a single-RF-channel DBF array

NASA Astrophysics Data System (ADS)

Zhang, Duo; Wu, Wen; Fang, Da Gang

2016-12-01

An array signal recovery algorithm based on sparse signal reconstruction theory is proposed for a single-RF-channel digital beamforming (DBF) array. A single-RF-channel antenna array is a low-cost antenna array in which signals are obtained from all antenna elements by only one microwave digital receiver. The spatially parallel array signals are converted into time-sequence signals, which are then sampled by the system. The proposed algorithm uses these time-sequence samples to recover the original parallel array signals by exploiting the second-order sparse structure of the array signals. Additionally, an optimization method based on the artificial bee colony (ABC) algorithm is proposed to improve the reconstruction performance. Using the proposed algorithm, the motion compensation problem for the single-RF-channel DBF array can be solved effectively, and the angle and Doppler information for the target can be simultaneously estimated. The effectiveness of the proposed algorithms is demonstrated by the results of numerical simulations.

Multiprocessor sparse L/U decomposition with controlled fill-in

NASA Technical Reports Server (NTRS)

Alaghband, G.; Jordan, H. F.

1985-01-01

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

The fusion code XGC: Enabling kinetic study of multi-scale edge turbulent transport in ITER [Book Chapter

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, Eduardo; Abbott, Stephen; Koskela, Tuomas

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning for balancing computational work in pushing particlesmore » and in grid related work, scalable and accurate discretization algorithms for non-linear Coulomb collisions, and communication-avoiding subcycling technology for pushing particles on both CPUs and GPUs are also utilized to dramatically improve the scalability and time-to-solution, hence enabling the difficult kinetic ITER edge simulation on a present-day leadership class computer.« less

Varying face occlusion detection and iterative recovery for face recognition

NASA Astrophysics Data System (ADS)

Wang, Meng; Hu, Zhengping; Sun, Zhe; Zhao, Shuhuan; Sun, Mei

2017-05-01

In most sparse representation methods for face recognition (FR), occlusion problems were usually solved via removing the occlusion part of both query samples and training samples to perform the recognition process. This practice ignores the global feature of facial image and may lead to unsatisfactory results due to the limitation of local features. Considering the aforementioned drawback, we propose a method called varying occlusion detection and iterative recovery for FR. The main contributions of our method are as follows: (1) to detect an accurate occlusion area of facial images, an image processing and intersection-based clustering combination method is used for occlusion FR; (2) according to an accurate occlusion map, the new integrated facial images are recovered iteratively and put into a recognition process; and (3) the effectiveness on recognition accuracy of our method is verified by comparing it with three typical occlusion map detection methods. Experiments show that the proposed method has a highly accurate detection and recovery performance and that it outperforms several similar state-of-the-art methods against partial contiguous occlusion.

Iterative Correction Scheme Based on Discrete Cosine Transform and L1 Regularization for Fluorescence Molecular Tomography With Background Fluorescence.

PubMed

Zhang, Jiulou; Shi, Junwei; Guang, Huizhi; Zuo, Simin; Liu, Fei; Bai, Jing; Luo, Jianwen

2016-06-01

High-intensity background fluorescence is generally encountered in fluorescence molecular tomography (FMT), because of the accumulation of fluorescent probes in nontarget tissues or the existence of autofluorescence in biological tissues. The reconstruction results are affected or even distorted by the background fluorescence, especially when the distribution of fluorescent targets is relatively sparse. The purpose of this paper is to reduce the negative effect of background fluorescence on FMT reconstruction. After each iteration of the Tikhonov regularization algorithm, 3-D discrete cosine transform is adopted to filter the intermediate results. And then, a sparsity constraint step based on L1 regularization is applied to restrain the energy of the objective function. Phantom experiments with different fluorescence intensities of homogeneous and heterogeneous background are carried out to validate the performance of the proposed scheme. The results show that the reconstruction quality can be improved with the proposed iterative correction scheme. The influence of background fluorescence in FMT can be reduced effectively because of the filtering of the intermediate results, the detail preservation, and noise suppression of L1 regularization.

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

NASA Astrophysics Data System (ADS)

Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

2013-04-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

Optimization of image quality and acquisition time for lab-based X-ray microtomography using an iterative reconstruction algorithm

NASA Astrophysics Data System (ADS)

Lin, Qingyang; Andrew, Matthew; Thompson, William; Blunt, Martin J.; Bijeljic, Branko

2018-05-01

Non-invasive laboratory-based X-ray microtomography has been widely applied in many industrial and research disciplines. However, the main barrier to the use of laboratory systems compared to a synchrotron beamline is its much longer image acquisition time (hours per scan compared to seconds to minutes at a synchrotron), which results in limited application for dynamic in situ processes. Therefore, the majority of existing laboratory X-ray microtomography is limited to static imaging; relatively fast imaging (tens of minutes per scan) can only be achieved by sacrificing imaging quality, e.g. reducing exposure time or number of projections. To alleviate this barrier, we introduce an optimized implementation of a well-known iterative reconstruction algorithm that allows users to reconstruct tomographic images with reasonable image quality, but requires lower X-ray signal counts and fewer projections than conventional methods. Quantitative analysis and comparison between the iterative and the conventional filtered back-projection reconstruction algorithm was performed using a sandstone rock sample with and without liquid phases in the pore space. Overall, by implementing the iterative reconstruction algorithm, the required image acquisition time for samples such as this, with sparse object structure, can be reduced by a factor of up to 4 without measurable loss of sharpness or signal to noise ratio.

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

PubMed

Cheng, Wenlong; Zhao, Mingbo; Xiong, Naixue; Chui, Kwok Tai

2017-07-15

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l ₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating l p -norm and Schatten p -norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Visual tracking based on the sparse representation of the PCA subspace

NASA Astrophysics Data System (ADS)

Chen, Dian-bing; Zhu, Ming; Wang, Hui-li

2017-09-01

We construct a collaborative model of the sparse representation and the subspace representation. First, we represent the tracking target in the principle component analysis (PCA) subspace, and then we employ an L 1 regularization to restrict the sparsity of the residual term, an L 2 regularization term to restrict the sparsity of the representation coefficients, and an L 2 norm to restrict the distance between the reconstruction and the target. Then we implement the algorithm in the particle filter framework. Furthermore, an iterative method is presented to get the global minimum of the residual and the coefficients. Finally, an alternative template update scheme is adopted to avoid the tracking drift which is caused by the inaccurate update. In the experiment, we test the algorithm on 9 sequences, and compare the results with 5 state-of-art methods. According to the results, we can conclude that our algorithm is more robust than the other methods.

NITPICK: peak identification for mass spectrometry data

PubMed Central

Renard, Bernhard Y; Kirchner, Marc; Steen , Hanno; Steen, Judith AJ; Hamprecht , Fred A

2008-01-01

Background The reliable extraction of features from mass spectra is a fundamental step in the automated analysis of proteomic mass spectrometry (MS) experiments. Results This contribution proposes a sparse template regression approach to peak picking called NITPICK. NITPICK is a Non-greedy, Iterative Template-based peak PICKer that deconvolves complex overlapping isotope distributions in multicomponent mass spectra. NITPICK is based on fractional averagine, a novel extension to Senko's well-known averagine model, and on a modified version of sparse, non-negative least angle regression, for which a suitable, statistically motivated early stopping criterion has been derived. The strength of NITPICK is the deconvolution of overlapping mixture mass spectra. Conclusion Extensive comparative evaluation has been carried out and results are provided for simulated and real-world data sets. NITPICK outperforms pepex, to date the only alternate, publicly available, non-greedy feature extraction routine. NITPICK is available as software package for the R programming language and can be downloaded from . PMID:18755032

An Online Dictionary Learning-Based Compressive Data Gathering Algorithm in Wireless Sensor Networks

PubMed Central

Wang, Donghao; Wan, Jiangwen; Chen, Junying; Zhang, Qiang

2016-01-01

To adapt to sense signals of enormous diversities and dynamics, and to decrease the reconstruction errors caused by ambient noise, a novel online dictionary learning method-based compressive data gathering (ODL-CDG) algorithm is proposed. The proposed dictionary is learned from a two-stage iterative procedure, alternately changing between a sparse coding step and a dictionary update step. The self-coherence of the learned dictionary is introduced as a penalty term during the dictionary update procedure. The dictionary is also constrained with sparse structure. It’s theoretically demonstrated that the sensing matrix satisfies the restricted isometry property (RIP) with high probability. In addition, the lower bound of necessary number of measurements for compressive sensing (CS) reconstruction is given. Simulation results show that the proposed ODL-CDG algorithm can enhance the recovery accuracy in the presence of noise, and reduce the energy consumption in comparison with other dictionary based data gathering methods. PMID:27669250

An Online Dictionary Learning-Based Compressive Data Gathering Algorithm in Wireless Sensor Networks.

PubMed

Wang, Donghao; Wan, Jiangwen; Chen, Junying; Zhang, Qiang

2016-09-22

To adapt to sense signals of enormous diversities and dynamics, and to decrease the reconstruction errors caused by ambient noise, a novel online dictionary learning method-based compressive data gathering (ODL-CDG) algorithm is proposed. The proposed dictionary is learned from a two-stage iterative procedure, alternately changing between a sparse coding step and a dictionary update step. The self-coherence of the learned dictionary is introduced as a penalty term during the dictionary update procedure. The dictionary is also constrained with sparse structure. It's theoretically demonstrated that the sensing matrix satisfies the restricted isometry property (RIP) with high probability. In addition, the lower bound of necessary number of measurements for compressive sensing (CS) reconstruction is given. Simulation results show that the proposed ODL-CDG algorithm can enhance the recovery accuracy in the presence of noise, and reduce the energy consumption in comparison with other dictionary based data gathering methods.

3D Reconstruction of human bones based on dictionary learning.

PubMed

Zhang, Binkai; Wang, Xiang; Liang, Xiao; Zheng, Jinjin

2017-11-01

An effective method for reconstructing a 3D model of human bones from computed tomography (CT) image data based on dictionary learning is proposed. In this study, the dictionary comprises the vertices of triangular meshes, and the sparse coefficient matrix indicates the connectivity information. For better reconstruction performance, we proposed a balance coefficient between the approximation and regularisation terms and a method for optimisation. Moreover, we applied a local updating strategy and a mesh-optimisation method to update the dictionary and the sparse matrix, respectively. The two updating steps are iterated alternately until the objective function converges. Thus, a reconstructed mesh could be obtained with high accuracy and regularisation. The experimental results show that the proposed method has the potential to obtain high precision and high-quality triangular meshes for rapid prototyping, medical diagnosis, and tissue engineering. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Joint Probabilistic Reasoning About Coreference and Relations of Univeral Schema

DTIC Science & Technology

2017-10-01

containing Barack and Michelle Obama state that they are married. A variety of one - shot and iterative methods have addressed the alignment problem [25...speed. Most of the computation time for these linear models is spent on the dot-product between the sparse features of an example and the weights...of the model. In some cases , it is clear that the use of all of these features is excessive and the example can be correctly classified without such

Statistical Mechanics of Combinatorial Auctions

NASA Astrophysics Data System (ADS)

Galla, Tobias; Leone, Michele; Marsili, Matteo; Sellitto, Mauro; Weigt, Martin; Zecchina, Riccardo

2006-09-01

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, A.; Davis, A.; University of Wisconsin-Madison, Madison, WI 53706

CCFE perform Monte-Carlo transport simulations on large and complex tokamak models such as ITER. Such simulations are challenging since streaming and deep penetration effects are equally important. In order to make such simulations tractable, both variance reduction (VR) techniques and parallel computing are used. It has been found that the application of VR techniques in such models significantly reduces the efficiency of parallel computation due to 'long histories'. VR in MCNP can be accomplished using energy-dependent weight windows. The weight window represents an 'average behaviour' of particles, and large deviations in the arriving weight of a particle give rise tomore » extreme amounts of splitting being performed and a long history. When running on parallel clusters, a long history can have a detrimental effect on the parallel efficiency - if one process is computing the long history, the other CPUs complete their batch of histories and wait idle. Furthermore some long histories have been found to be effectively intractable. To combat this effect, CCFE has developed an adaptation of MCNP which dynamically adjusts the WW where a large weight deviation is encountered. The method effectively 'de-optimises' the WW, reducing the VR performance but this is offset by a significant increase in parallel efficiency. Testing with a simple geometry has shown the method does not bias the result. This 'long history method' has enabled CCFE to significantly improve the performance of MCNP calculations for ITER on parallel clusters, and will be beneficial for any geometry combining streaming and deep penetration effects. (authors)« less

Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications

PubMed Central

Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian

2016-01-01

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406

A Modified Sparse Representation Method for Facial Expression Recognition.

PubMed

Wang, Wei; Xu, LiHong

2016-01-01

In this paper, we carry on research on a facial expression recognition method, which is based on modified sparse representation recognition (MSRR) method. On the first stage, we use Haar-like+LPP to extract feature and reduce dimension. On the second stage, we adopt LC-K-SVD (Label Consistent K-SVD) method to train the dictionary, instead of adopting directly the dictionary from samples, and add block dictionary training into the training process. On the third stage, stOMP (stagewise orthogonal matching pursuit) method is used to speed up the convergence of OMP (orthogonal matching pursuit). Besides, a dynamic regularization factor is added to iteration process to suppress noises and enhance accuracy. We verify the proposed method from the aspect of training samples, dimension, feature extraction and dimension reduction methods and noises in self-built database and Japan's JAFFE and CMU's CK database. Further, we compare this sparse method with classic SVM and RVM and analyze the recognition effect and time efficiency. The result of simulation experiment has shown that the coefficient of MSRR method contains classifying information, which is capable of improving the computing speed and achieving a satisfying recognition result.

Sparse signals recovered by non-convex penalty in quasi-linear systems.

PubMed

Cui, Angang; Li, Haiyang; Wen, Meng; Peng, Jigen

2018-01-01

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the [Formula: see text]-norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function [Formula: see text] in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem [Formula: see text] for all [Formula: see text]. With the change of parameter [Formula: see text], our algorithm could get a promising result, which is one of the advantages for our algorithm compared with some state-of-art algorithms. Numerical experiments show that our method performs much better than some state-of-the-art methods.

FDD Massive MIMO Channel Estimation With Arbitrary 2D-Array Geometry

NASA Astrophysics Data System (ADS)

Dai, Jisheng; Liu, An; Lau, Vincent K. N.

2018-05-01

This paper addresses the problem of downlink channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the cdownlink channel. However, there are at least two shortcomings of these DFT-based methods: 1) they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs, and 2) they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary 2D-array antenna geometry, and propose an efficient sparse Bayesian learning (SBL) approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization-minimization (MM) algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplink-aided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance.

A Modified Sparse Representation Method for Facial Expression Recognition

PubMed Central

Wang, Wei; Xu, LiHong

2016-01-01

In this paper, we carry on research on a facial expression recognition method, which is based on modified sparse representation recognition (MSRR) method. On the first stage, we use Haar-like+LPP to extract feature and reduce dimension. On the second stage, we adopt LC-K-SVD (Label Consistent K-SVD) method to train the dictionary, instead of adopting directly the dictionary from samples, and add block dictionary training into the training process. On the third stage, stOMP (stagewise orthogonal matching pursuit) method is used to speed up the convergence of OMP (orthogonal matching pursuit). Besides, a dynamic regularization factor is added to iteration process to suppress noises and enhance accuracy. We verify the proposed method from the aspect of training samples, dimension, feature extraction and dimension reduction methods and noises in self-built database and Japan's JAFFE and CMU's CK database. Further, we compare this sparse method with classic SVM and RVM and analyze the recognition effect and time efficiency. The result of simulation experiment has shown that the coefficient of MSRR method contains classifying information, which is capable of improving the computing speed and achieving a satisfying recognition result. PMID:26880878

Fast in-memory elastic full-waveform inversion using consumer-grade GPUs

NASA Astrophysics Data System (ADS)

Sivertsen Bergslid, Tore; Birger Raknes, Espen; Arntsen, Børge

2017-04-01

Full-waveform inversion (FWI) is a technique to estimate subsurface properties by using the recorded waveform produced by a seismic source and applying inverse theory. This is done through an iterative optimization procedure, where each iteration requires solving the wave equation many times, then trying to minimize the difference between the modeled and the measured seismic data. Having to model many of these seismic sources per iteration means that this is a highly computationally demanding procedure, which usually involves writing a lot of data to disk. We have written code that does forward modeling and inversion entirely in memory. A typical HPC cluster has many more CPUs than GPUs. Since FWI involves modeling many seismic sources per iteration, the obvious approach is to parallelize the code on a source-by-source basis, where each core of the CPU performs one modeling, and do all modelings simultaneously. With this approach, the GPU is already at a major disadvantage in pure numbers. Fortunately, GPUs can more than make up for this hardware disadvantage by performing each modeling much faster than a CPU. Another benefit of parallelizing each individual modeling is that it lets each modeling use a lot more RAM. If one node has 128 GB of RAM and 20 CPU cores, each modeling can use only 6.4 GB RAM if one is running the node at full capacity with source-by-source parallelization on the CPU. A parallelized per-source code using GPUs can use 64 GB RAM per modeling. Whenever a modeling uses more RAM than is available and has to start using regular disk space the runtime increases dramatically, due to slow file I/O. The extremely high computational speed of the GPUs combined with the large amount of RAM available for each modeling lets us do high frequency FWI for fairly large models very quickly. For a single modeling, our GPU code outperforms the single-threaded CPU-code by a factor of about 75. Successful inversions have been run on data with frequencies up to 40 Hz for a model of 2001 by 600 grid points with 5 m grid spacing and 5000 time steps, in less than 2.5 minutes per source. In practice, using 15 nodes (30 GPUs) to model 101 sources, each iteration took approximately 9 minutes. For reference, the same inversion run with our CPU code uses two hours per iteration. This was done using only a very simple wavefield interpolation technique, saving every second timestep. Using a more sophisticated checkpointing or wavefield reconstruction method would allow us to increase this model size significantly. Our results show that ordinary gaming GPUs are a viable alternative to the expensive professional GPUs often used today, when performing large scale modeling and inversion in geophysics.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

DOE PAGES

Zhang, Hong; Zapol, Peter; Dixon, David A.; ...

2015-11-17

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong; Zapol, Peter; Dixon, David A.

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Analysis, tuning and comparison of two general sparse solvers for distributed memory computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.

2000-06-30

We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differencesmore » in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.« less

Iterative nonlinear joint transform correlation for the detection of objects in cluttered scenes

NASA Astrophysics Data System (ADS)

Haist, Tobias; Tiziani, Hans J.

1999-03-01

An iterative correlation technique with digital image processing in the feedback loop for the detection of small objects in cluttered scenes is proposed. A scanning aperture is combined with the method in order to improve the immunity against noise and clutter. Multiple reference objects or different views of one object are processed in parallel. We demonstrate the method by detecting a noisy and distorted face in a crowd with a nonlinear joint transform correlator.

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, P; Mao, T; Gong, S

2016-06-15

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimizationmore » trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917).« less

Shading correction assisted iterative cone-beam CT reconstruction

NASA Astrophysics Data System (ADS)

Yang, Chunlin; Wu, Pengwei; Gong, Shutao; Wang, Jing; Lyu, Qihui; Tang, Xiangyang; Niu, Tianye

2017-11-01

Recent advances in total variation (TV) technology enable accurate CT image reconstruction from highly under-sampled and noisy projection data. The standard iterative reconstruction algorithms, which work well in conventional CT imaging, fail to perform as expected in cone beam CT (CBCT) applications, wherein the non-ideal physics issues, including scatter and beam hardening, are more severe. These physics issues result in large areas of shading artifacts and cause deterioration to the piecewise constant property assumed in reconstructed images. To overcome this obstacle, we incorporate a shading correction scheme into low-dose CBCT reconstruction and propose a clinically acceptable and stable three-dimensional iterative reconstruction method that is referred to as the shading correction assisted iterative reconstruction. In the proposed method, we modify the TV regularization term by adding a shading compensation image to the reconstructed image to compensate for the shading artifacts while leaving the data fidelity term intact. This compensation image is generated empirically, using image segmentation and low-pass filtering, and updated in the iterative process whenever necessary. When the compensation image is determined, the objective function is minimized using the fast iterative shrinkage-thresholding algorithm accelerated on a graphic processing unit. The proposed method is evaluated using CBCT projection data of the Catphan© 600 phantom and two pelvis patients. Compared with the iterative reconstruction without shading correction, the proposed method reduces the overall CT number error from around 200 HU to be around 25 HU and increases the spatial uniformity by a factor of 20 percent, given the same number of sparsely sampled projections. A clinically acceptable and stable iterative reconstruction algorithm for CBCT is proposed in this paper. Differing from the existing algorithms, this algorithm incorporates a shading correction scheme into the low-dose CBCT reconstruction and achieves more stable optimization path and more clinically acceptable reconstructed image. The method proposed by us does not rely on prior information and thus is practically attractive to the applications of low-dose CBCT imaging in the clinic.

New shape models of asteroids reconstructed from sparse-in-time photometry

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Vanco, Radim; Oszkiewicz, Dagmara Anna

2015-08-01

Asteroid physical parameters - the shape, the sidereal rotation period, and the spin axis orientation - can be reconstructed from the disk-integrated photometry either dense (classical lightcurves) or sparse in time by the lightcurve inversion method. We will review our recent progress in asteroid shape reconstruction from sparse photometry. The problem of finding a unique solution of the inverse problem is time consuming because the sidereal rotation period has to be found by scanning a wide interval of possible periods. This can be efficiently solved by splitting the period parameter space into small parts that are sent to computers of volunteers and processed in parallel. We will show how this approach of distributed computing works with currently available sparse photometry processed in the framework of project Asteroids@home. In particular, we will show the results based on the Lowell Photometric Database. The method produce reliable asteroid models with very low rate of false solutions and the pipelines and codes can be directly used also to other sources of sparse photometry - Gaia data, for example. We will present the distribution of spin axis of hundreds of asteroids, discuss the dependence of the spin obliquity on the size of an asteroid,and show examples of spin-axis distribution in asteroid families that confirm the Yarkovsky/YORP evolution scenario.

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION

PubMed Central

Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong

2015-01-01

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645

A parallel Jacobson-Oksman optimization algorithm. [parallel processing (computers)

NASA Technical Reports Server (NTRS)

Straeter, T. A.; Markos, A. T.

1975-01-01

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boman, Erik G.

This LDRD project was a campus exec fellowship to fund (in part) Donald Nguyen’s PhD research at UT-Austin. His work has focused on parallel programming models, and scheduling irregular algorithms on shared-memory systems using the Galois framework. Galois provides a simple but powerful way for users and applications to automatically obtain good parallel performance using certain supported data containers. The naïve user can write serial code, while advanced users can optimize performance by advanced features, such as specifying the scheduling policy. Galois was used to parallelize two sparse matrix reordering schemes: RCM and Sloan. Such reordering is important in high-performancemore » computing to obtain better data locality and thus reduce run times.« less

A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.

PubMed

Liang, Faming; Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively.

A Parallel Fast Sweeping Method for the Eikonal Equation

NASA Astrophysics Data System (ADS)

Baker, B.

2017-12-01

Recently, there has been an exciting emergence of probabilistic methods for travel time tomography. Unlike gradient-based optimization strategies, probabilistic tomographic methods are resistant to becoming trapped in a local minimum and provide a much better quantification of parameter resolution than, say, appealing to ray density or performing checkerboard reconstruction tests. The benefits associated with random sampling methods however are only realized by successive computation of predicted travel times in, potentially, strongly heterogeneous media. To this end this abstract is concerned with expediting the solution of the Eikonal equation. While many Eikonal solvers use a fast marching method, the proposed solver will use the iterative fast sweeping method because the eight fixed sweep orderings in each iteration are natural targets for parallelization. To reduce the number of iterations and grid points required the high-accuracy finite difference stencil of Nobel et al., 2014 is implemented. A directed acyclic graph (DAG) is created with a priori knowledge of the sweep ordering and finite different stencil. By performing a topological sort of the DAG sets of independent nodes are identified as candidates for concurrent updating. Additionally, the proposed solver will also address scalability during earthquake relocation, a necessary step in local and regional earthquake tomography and a barrier to extending probabilistic methods from active source to passive source applications, by introducing an asynchronous parallel forward solve phase for all receivers in the network. Synthetic examples using the SEG over-thrust model will be presented.

A Bootstrap Metropolis–Hastings Algorithm for Bayesian Analysis of Big Data

PubMed Central

Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively. PMID:29033469

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity.

PubMed

Dummer, Benjamin; Wieland, Stefan; Lindner, Benjamin

2014-01-01

A major source of random variability in cortical networks is the quasi-random arrival of presynaptic action potentials from many other cells. In network studies as well as in the study of the response properties of single cells embedded in a network, synaptic background input is often approximated by Poissonian spike trains. However, the output statistics of the cells is in most cases far from being Poisson. This is inconsistent with the assumption of similar spike-train statistics for pre- and postsynaptic cells in a recurrent network. Here we tackle this problem for the popular class of integrate-and-fire neurons and study a self-consistent statistics of input and output spectra of neural spike trains. Instead of actually using a large network, we use an iterative scheme, in which we simulate a single neuron over several generations. In each of these generations, the neuron is stimulated with surrogate stochastic input that has a similar statistics as the output of the previous generation. For the surrogate input, we employ two distinct approximations: (i) a superposition of renewal spike trains with the same interspike interval density as observed in the previous generation and (ii) a Gaussian current with a power spectrum proportional to that observed in the previous generation. For input parameters that correspond to balanced input in the network, both the renewal and the Gaussian iteration procedure converge quickly and yield comparable results for the self-consistent spike-train power spectrum. We compare our results to large-scale simulations of a random sparsely connected network of leaky integrate-and-fire neurons (Brunel, 2000) and show that in the asynchronous regime close to a state of balanced synaptic input from the network, our iterative schemes provide an excellent approximations to the autocorrelation of spike trains in the recurrent network.

Enhancing Scalability and Efficiency of the TOUGH2_MP for LinuxClusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Keni; Wu, Yu-Shu

2006-04-17

TOUGH2{_}MP, the parallel version TOUGH2 code, has been enhanced by implementing more efficient communication schemes. This enhancement is achieved through reducing the amount of small-size messages and the volume of large messages. The message exchange speed is further improved by using non-blocking communications for both linear and nonlinear iterations. In addition, we have modified the AZTEC parallel linear-equation solver to nonblocking communication. Through the improvement of code structuring and bug fixing, the new version code is now more stable, while demonstrating similar or even better nonlinear iteration converging speed than the original TOUGH2 code. As a result, the new versionmore » of TOUGH2{_}MP is improved significantly in its efficiency. In this paper, the scalability and efficiency of the parallel code are demonstrated by solving two large-scale problems. The testing results indicate that speedup of the code may depend on both problem size and complexity. In general, the code has excellent scalability in memory requirement as well as computing time.« less

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Compressive sensing using optimized sensing matrix for face verification

NASA Astrophysics Data System (ADS)

Oey, Endra; Jeffry; Wongso, Kelvin; Tommy

2017-12-01

Biometric appears as one of the solutions which is capable in solving problems that occurred in the usage of password in terms of data access, for example there is possibility in forgetting password and hard to recall various different passwords. With biometrics, physical characteristics of a person can be captured and used in the identification process. In this research, facial biometric is used in the verification process to determine whether the user has the authority to access the data or not. Facial biometric is chosen as its low cost implementation and generate quite accurate result for user identification. Face verification system which is adopted in this research is Compressive Sensing (CS) technique, in which aims to reduce dimension size as well as encrypt data in form of facial test image where the image is represented in sparse signals. Encrypted data can be reconstructed using Sparse Coding algorithm. Two types of Sparse Coding namely Orthogonal Matching Pursuit (OMP) and Iteratively Reweighted Least Squares -ℓp (IRLS-ℓp) will be used for comparison face verification system research. Reconstruction results of sparse signals are then used to find Euclidean norm with the sparse signal of user that has been previously saved in system to determine the validity of the facial test image. Results of system accuracy obtained in this research are 99% in IRLS with time response of face verification for 4.917 seconds and 96.33% in OMP with time response of face verification for 0.4046 seconds with non-optimized sensing matrix, while 99% in IRLS with time response of face verification for 13.4791 seconds and 98.33% for OMP with time response of face verification for 3.1571 seconds with optimized sensing matrix.

Accelerating scientific computations with mixed precision algorithms

NASA Astrophysics Data System (ADS)

Baboulin, Marc; Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Langou, Julie; Langou, Julien; Luszczek, Piotr; Tomov, Stanimire

2009-12-01

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented. Program summaryProgram title: ITER-REF Catalogue identifier: AECO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7211 No. of bytes in distributed program, including test data, etc.: 41 862 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: desktop, server Operating system: Unix/Linux RAM: 512 Mbytes Classification: 4.8 External routines: BLAS (optional) Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision. Running time: seconds/minutes

Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform.

PubMed

Tamhane, Ashish A; Anastasio, Mark A; Gui, Minzhi; Arfanakis, Konstantinos

2010-07-01

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI. Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding. (c) 2010 Wiley-Liss, Inc.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

Exploring the Ability of a Coarse-grained Potential to Describe the Stress-strain Response of Glassy Polystyrene

DTIC Science & Technology

2012-10-01

using the open-source code Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) (http://lammps.sandia.gov) (23). The commercial...parameters are proprietary and cannot be ported to the LAMMPS 4 simulation code. In our molecular dynamics simulations at the atomistic resolution, we...IBI iterative Boltzmann inversion LAMMPS Large-scale Atomic/Molecular Massively Parallel Simulator MAPS Materials Processes and Simulations MS

Real-Time, Multiple, Pan/Tilt/Zoom, Computer Vision Tracking, and 3D Position Estimating System for Unmanned Aerial System Metrology

DTIC Science & Technology

2013-10-18

of the enclosed tasks plus the last parallel task for a total of five parallel tasks for one iteration, i). for j = 1…N for i = 1… 8 Figure...drizzling juices culminating in a state of salivating desire to cut a piece and enjoy. On the other hand, the smell could be that of a pungent, unpleasant

Median prior constrained TV algorithm for sparse view low-dose CT reconstruction.

PubMed

Liu, Yi; Shangguan, Hong; Zhang, Quan; Zhu, Hongqing; Shu, Huazhong; Gui, Zhiguo

2015-05-01

It is known that lowering the X-ray tube current (mAs) or tube voltage (kVp) and simultaneously reducing the total number of X-ray views (sparse view) is an effective means to achieve low-dose in computed tomography (CT) scan. However, the associated image quality by the conventional filtered back-projection (FBP) usually degrades due to the excessive quantum noise. Although sparse-view CT reconstruction algorithm via total variation (TV), in the scanning protocol of reducing X-ray tube current, has been demonstrated to be able to result in significant radiation dose reduction while maintain image quality, noticeable patchy artifacts still exist in reconstructed images. In this study, to address the problem of patchy artifacts, we proposed a median prior constrained TV regularization to retain the image quality by introducing an auxiliary vector m in register with the object. Specifically, the approximate action of m is to draw, in each iteration, an object voxel toward its own local median, aiming to improve low-dose image quality with sparse-view projection measurements. Subsequently, an alternating optimization algorithm is adopted to optimize the associative objective function. We refer to the median prior constrained TV regularization as "TV_MP" for simplicity. Experimental results on digital phantoms and clinical phantom demonstrated that the proposed TV_MP with appropriate control parameters can not only ensure a higher signal to noise ratio (SNR) of the reconstructed image, but also its resolution compared with the original TV method. Copyright © 2015 Elsevier Ltd. All rights reserved.

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

LCAMP: Location Constrained Approximate Message Passing for Compressed Sensing MRI

PubMed Central

Sung, Kyunghyun; Daniel, Bruce L; Hargreaves, Brian A

2016-01-01

Iterative thresholding methods have been extensively studied as faster alternatives to convex optimization methods for solving large-sized problems in compressed sensing. A novel iterative thresholding method called LCAMP (Location Constrained Approximate Message Passing) is presented for reducing computational complexity and improving reconstruction accuracy when a nonzero location (or sparse support) constraint can be obtained from view shared images. LCAMP modifies the existing approximate message passing algorithm by replacing the thresholding stage with a location constraint, which avoids adjusting regularization parameters or thresholding levels. This work is first compared with other conventional reconstruction methods using random 1D signals and then applied to dynamic contrast-enhanced breast MRI to demonstrate the excellent reconstruction accuracy (less than 2% absolute difference) and low computation time (5 - 10 seconds using Matlab) with highly undersampled 3D data (244 × 128 × 48; overall reduction factor = 10). PMID:23042658

Methodes iteratives paralleles: Applications en neutronique et en mecanique des fluides

NASA Astrophysics Data System (ADS)

Qaddouri, Abdessamad

Dans cette these, le calcul parallele est applique successivement a la neutronique et a la mecanique des fluides. Dans chacune de ces deux applications, des methodes iteratives sont utilisees pour resoudre le systeme d'equations algebriques resultant de la discretisation des equations du probleme physique. Dans le probleme de neutronique, le calcul des matrices des probabilites de collision (PC) ainsi qu'un schema iteratif multigroupe utilisant une methode inverse de puissance sont parallelises. Dans le probleme de mecanique des fluides, un code d'elements finis utilisant un algorithme iteratif du type GMRES preconditionne est parallelise. Cette these est presentee sous forme de six articles suivis d'une conclusion. Les cinq premiers articles traitent des applications en neutronique, articles qui representent l'evolution de notre travail dans ce domaine. Cette evolution passe par un calcul parallele des matrices des PC et un algorithme multigroupe parallele teste sur un probleme unidimensionnel (article 1), puis par deux algorithmes paralleles l'un mutiregion l'autre multigroupe, testes sur des problemes bidimensionnels (articles 2--3). Ces deux premieres etapes sont suivies par l'application de deux techniques d'acceleration, le rebalancement neutronique et la minimisation du residu aux deux algorithmes paralleles (article 4). Finalement, on a mis en oeuvre l'algorithme multigroupe et le calcul parallele des matrices des PC sur un code de production DRAGON ou les tests sont plus realistes et peuvent etre tridimensionnels (article 5). Le sixieme article (article 6), consacre a l'application a la mecanique des fluides, traite la parallelisation d'un code d'elements finis FES ou le partitionneur de graphe METIS et la librairie PSPARSLIB sont utilises.

Generalizations of the Alternating Direction Method of Multipliers for Large-Scale and Distributed Optimization

DTIC Science & Technology

2014-05-01

exact one is solved later — as- signed as step 5 of Algorithm 2 — because at each iteration , the ADMM updates the variables in the Gauss - Seidel ...Jacobi ADMM (see Algo- rithm 5 below). Unlike the Gauss - Seidel ADMM, the Jacobi ADMM updates all the 70 blocks in parallel at every iteration : xk+1i...that extending ADMM straightforwardly from the classic Gauss - Seidel setting to the Jacobi setting, from two blocks to multiple blocks, will preserve

Inversion of potential field data using the finite element method on parallel computers

NASA Astrophysics Data System (ADS)

Gross, L.; Altinay, C.; Shaw, S.

2015-11-01

In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.

Scalable splitting algorithms for big-data interferometric imaging in the SKA era

NASA Astrophysics Data System (ADS)

Onose, Alexandru; Carrillo, Rafael E.; Repetti, Audrey; McEwen, Jason D.; Thiran, Jean-Philippe; Pesquet, Jean-Christophe; Wiaux, Yves

2016-11-01

In the context of next-generation radio telescopes, like the Square Kilometre Array (SKA), the efficient processing of large-scale data sets is extremely important. Convex optimization tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimization algorithmic structures able to solve the convex optimization tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy, with the CLEAN major-minor cycle, as running sophisticated CLEAN-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularization function, in particular, the well-studied ℓ1 priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomization, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our MATLAB code is available online on GitHub.

Performance evaluation of canny edge detection on a tiled multicore architecture

NASA Astrophysics Data System (ADS)

Brethorst, Andrew Z.; Desai, Nehal; Enright, Douglas P.; Scrofano, Ronald

2011-01-01

In the last few years, a variety of multicore architectures have been used to parallelize image processing applications. In this paper, we focus on assessing the parallel speed-ups of different Canny edge detection parallelization strategies on the Tile64, a tiled multicore architecture developed by the Tilera Corporation. Included in these strategies are different ways Canny edge detection can be parallelized, as well as differences in data management. The two parallelization strategies examined were loop-level parallelism and domain decomposition. Loop-level parallelism is achieved through the use of OpenMP,1 and it is capable of parallelization across the range of values over which a loop iterates. Domain decomposition is the process of breaking down an image into subimages, where each subimage is processed independently, in parallel. The results of the two strategies show that for the same number of threads, programmer implemented, domain decomposition exhibits higher speed-ups than the compiler managed, loop-level parallelism implemented with OpenMP.

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1996-01-01

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Optimization of Sparse Matrix-Vector Multiplication on Emerging Multicore Platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2008-10-16

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific-optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD quad-core, AMD dual-core, and Intel quad-core designs, the heterogeneous STI Cell, as well as one ofmore » the first scientific studies of the highly multithreaded Sun Victoria Falls (a Niagara2 SMP). We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural trade-offs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

DOE PAGES

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; ...

2016-10-27

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.

PubMed

Zelyak, O; Fallone, B G; St-Aubin, J

2017-12-14

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

NASA Astrophysics Data System (ADS)

Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-01-01

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Corrigendum to "Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy".

PubMed

Zelyak, Oleksandr; Fallone, B Gino; St-Aubin, Joel

2018-03-12

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation. © 2018 Institute of Physics and Engineering in Medicine.

Multiprocessor smalltalk: Implementation, performance, and analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pallas, J.I.

1990-01-01

Multiprocessor Smalltalk demonstrates the value of object-oriented programming on a multiprocessor. Its implementation and analysis shed light on three areas: concurrent programming in an object oriented language without special extensions, implementation techniques for adapting to multiprocessors, and performance factors in the resulting system. Adding parallelism to Smalltalk code is easy, because programs already use control abstractions like iterators. Smalltalk's basic control and concurrency primitives (lambda expressions, processes and semaphores) can be used to build parallel control abstractions, including parallel iterators, parallel objects, atomic objects, and futures. Language extensions for concurrency are not required. This implementation demonstrates that it is possiblemore » to build an efficient parallel object-oriented programming system and illustrates techniques for doing so. Three modification tools-serialization, replication, and reorganization-adapted the Berkeley Smalltalk interpreter to the Firefly multiprocessor. Multiprocessor Smalltalk's performance shows that the combination of multiprocessing and object-oriented programming can be effective: speedups (relative to the original serial version) exceed 2.0 for five processors on all the benchmarks; the median efficiency is 48%. Analysis shows both where performance is lost and how to improve and generalize the experimental results. Changes in the interpreter to support concurrency add at most 12% overhead; better access to per-process variables could eliminate much of that. Changes in the user code to express concurrency add as much as 70% overhead; this overhead could be reduced to 54% if blocks (lambda expressions) were reentrant. Performance is also lost when the program cannot keep all five processors busy.« less

Exploiting loop level parallelism in nonprocedural dataflow programs

NASA Technical Reports Server (NTRS)

Gokhale, Maya B.

1987-01-01

Discussed are how loop level parallelism is detected in a nonprocedural dataflow program, and how a procedural program with concurrent loops is scheduled. Also discussed is a program restructuring technique which may be applied to recursive equations so that concurrent loops may be generated for a seemingly iterative computation. A compiler which generates C code for the language described below has been implemented. The scheduling component of the compiler and the restructuring transformation are described.

Fault Tolerant Parallel Implementations of Iterative Algorithms for Optimal Control Problems

DTIC Science & Technology

1988-01-21

p/.V)] steps, but did not discuss any specific parallel implementation. Gajski [51 improved upon this result by performing the SIMD computation in...N = p2. our approach reduces to that of [51, except that Gajski presents the coefficient computation and partial solution phases as a single...8217>. the SIMD algo- rithm presented by Gajski [5] can be most efficiently mapped to a unidirec- tional ring network with broadcasting capability. Based

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1993-01-01

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

PubMed Central

LIU, Han; WANG, Lie; ZHAO, Tuo

2014-01-01

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators

NASA Astrophysics Data System (ADS)

Gonzalez, Juan; Núñez, Rafael C.

2009-07-01

We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.

PRIM: An Efficient Preconditioning Iterative Reweighted Least Squares Method for Parallel Brain MRI Reconstruction.

PubMed

Xu, Zheng; Wang, Sheng; Li, Yeqing; Zhu, Feiyun; Huang, Junzhou

2018-02-08

The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.

SPIRiT: Iterative Self-consistent Parallel Imaging Reconstruction from Arbitrary k-Space

PubMed Central

Lustig, Michael; Pauly, John M.

2010-01-01

A new approach to autocalibrating, coil-by-coil parallel imaging reconstruction is presented. It is a generalized reconstruction framework based on self consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k-space sampling patterns. The formulation can flexibly incorporate additional image priors such as off-resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k-space domain are presented. These are based on a projection over convex sets (POCS) and a conjugate gradient (CG) algorithms. Phantom and in-vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off-resonance correction and nonlinear ℓ1-wavelet regularization are also demonstrated. PMID:20665790

Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

NASA Astrophysics Data System (ADS)

Yang, Xiang; Mittal, Rajat

2017-03-01

In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

Aerodynamic optimization by simultaneously updating flow variables and design parameters

NASA Technical Reports Server (NTRS)

Rizk, M. H.

1990-01-01

The application of conventional optimization schemes to aerodynamic design problems leads to inner-outer iterative procedures that are very costly. An alternative approach is presented based on the idea of updating the flow variable iterative solutions and the design parameter iterative solutions simultaneously. Two schemes based on this idea are applied to problems of correcting wind tunnel wall interference and optimizing advanced propeller designs. The first of these schemes is applicable to a limited class of two-design-parameter problems with an equality constraint. It requires the computation of a single flow solution. The second scheme is suitable for application to general aerodynamic problems. It requires the computation of several flow solutions in parallel. In both schemes, the design parameters are updated as the iterative flow solutions evolve. Computations are performed to test the schemes' efficiency, accuracy, and sensitivity to variations in the computational parameters.

High-Resolution DCE-MRI of the Pituitary Gland Using Radial k-Space Acquisition with Compressed Sensing Reconstruction.

PubMed

Rossi Espagnet, M C; Bangiyev, L; Haber, M; Block, K T; Babb, J; Ruggiero, V; Boada, F; Gonen, O; Fatterpekar, G M

2015-08-01

The pituitary gland is located outside of the blood-brain barrier. Dynamic T1 weighted contrast enhanced sequence is considered to be the gold standard to evaluate this region. However, it does not allow assessment of intrinsic permeability properties of the gland. Our aim was to demonstrate the utility of radial volumetric interpolated brain examination with the golden-angle radial sparse parallel technique to evaluate permeability characteristics of the individual components (anterior and posterior gland and the median eminence) of the pituitary gland and areas of differential enhancement and to optimize the study acquisition time. A retrospective study was performed in 52 patients (group 1, 25 patients with normal pituitary glands; and group 2, 27 patients with a known diagnosis of microadenoma). Radial volumetric interpolated brain examination sequences with golden-angle radial sparse parallel technique were evaluated with an ROI-based method to obtain signal-time curves and permeability measures of individual normal structures within the pituitary gland and areas of differential enhancement. Statistical analyses were performed to assess differences in the permeability parameters of these individual regions and optimize the study acquisition time. Signal-time curves from the posterior pituitary gland and median eminence demonstrated a faster wash-in and time of maximum enhancement with a lower peak of enhancement compared with the anterior pituitary gland (P < .005). Time-optimization analysis demonstrated that 120 seconds is ideal for dynamic pituitary gland evaluation. In the absence of a clinical history, differences in the signal-time curves allow easy distinction between a simple cyst and a microadenoma. This retrospective study confirms the ability of the golden-angle radial sparse parallel technique to evaluate the permeability characteristics of the pituitary gland and establishes 120 seconds as the ideal acquisition time for dynamic pituitary gland imaging. © 2015 by American Journal of Neuroradiology.

High-Resolution DCE-MRI of the Pituitary Gland Using Radial k-Space Acquisition with Compressed Sensing Reconstruction

PubMed Central

Rossi Espagnet, M.C.; Bangiyev, L.; Haber, M.; Block, K.T.; Babb, J.; Ruggiero, V.; Boada, F.; Gonen, O.; Fatterpekar, G.M.

2015-01-01

BACKGROUNDANDPURPOSE The pituitary gland is located outside of the blood-brain barrier. Dynamic T1 weighted contrast enhanced sequence is considered to be the gold standard to evaluate this region. However, it does not allow assessment of intrinsic permeability properties of the gland. Our aim was to demonstrate the utility of radial volumetric interpolated brain examination with the golden-angle radial sparse parallel technique to evaluate permeability characteristics of the individual components (anterior and posterior gland and the median eminence) of the pituitary gland and areas of differential enhancement and to optimize the study acquisition time. MATERIALS AND METHODS A retrospective study was performed in 52 patients (group 1, 25 patients with normal pituitary glands; and group 2, 27 patients with a known diagnosis of microadenoma). Radial volumetric interpolated brain examination sequences with golden-angle radial sparse parallel technique were evaluated with an ROI-based method to obtain signal-time curves and permeability measures of individual normal structures within the pituitary gland and areas of differential enhancement. Statistical analyses were performed to assess differences in the permeability parameters of these individual regions and optimize the study acquisition time. RESULTS Signal-time curves from the posterior pituitary gland and median eminence demonstrated a faster wash-in and time of maximum enhancement with a lower peak of enhancement compared with the anterior pituitary gland (P < .005). Time-optimization analysis demonstrated that 120 seconds is ideal for dynamic pituitary gland evaluation. In the absence of a clinical history, differences in the signal-time curves allow easy distinction between a simple cyst and a microadenoma. CONCLUSIONS This retrospective study confirms the ability of the golden-angle radial sparse parallel technique to evaluate the permeability characteristics of the pituitary gland and establishes 120 seconds as the ideal acquisition time for dynamic pituitary gland imaging. PMID:25953760

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Parallel medicinal chemistry approaches to selective HDAC1/HDAC2 inhibitor (SHI-1:2) optimization.

PubMed

Kattar, Solomon D; Surdi, Laura M; Zabierek, Anna; Methot, Joey L; Middleton, Richard E; Hughes, Bethany; Szewczak, Alexander A; Dahlberg, William K; Kral, Astrid M; Ozerova, Nicole; Fleming, Judith C; Wang, Hongmei; Secrist, Paul; Harsch, Andreas; Hamill, Julie E; Cruz, Jonathan C; Kenific, Candia M; Chenard, Melissa; Miller, Thomas A; Berk, Scott C; Tempest, Paul

2009-02-15

The successful application of both solid and solution phase library synthesis, combined with tight integration into the medicinal chemistry effort, resulted in the efficient optimization of a novel structural series of selective HDAC1/HDAC2 inhibitors by the MRL-Boston Parallel Medicinal Chemistry group. An initial lead from a small parallel library was found to be potent and selective in biochemical assays. Advanced compounds were the culmination of iterative library design and possess excellent biochemical and cellular potency, as well as acceptable PK and efficacy in animal models.

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

Applications of compressed sensing image reconstruction to sparse view phase tomography

NASA Astrophysics Data System (ADS)

Ueda, Ryosuke; Kudo, Hiroyuki; Dong, Jian

2017-10-01

X-ray phase CT has a potential to give the higher contrast in soft tissue observations. To shorten the measure- ment time, sparse-view CT data acquisition has been attracting the attention. This paper applies two major compressed sensing (CS) approaches to image reconstruction in the x-ray sparse-view phase tomography. The first CS approach is the standard Total Variation (TV) regularization. The major drawbacks of TV regularization are a patchy artifact and loss in smooth intensity changes due to the piecewise constant nature of image model. The second CS method is a relatively new approach of CS which uses a nonlinear smoothing filter to design the regularization term. The nonlinear filter based CS is expected to reduce the major artifact in the TV regular- ization. The both cost functions can be minimized by the very fast iterative reconstruction method. However, in the past research activities, it is not clearly demonstrated how much image quality difference occurs between the TV regularization and the nonlinear filter based CS in x-ray phase CT applications. We clarify the issue by applying the two CS applications to the case of x-ray phase tomography. We provide results with numerically simulated data, which demonstrates that the nonlinear filter based CS outperforms the TV regularization in terms of textures and smooth intensity changes.

Fast iterative censoring CFAR algorithm for ship detection from SAR images

NASA Astrophysics Data System (ADS)

Gu, Dandan; Yue, Hui; Zhang, Yuan; Gao, Pengcheng

2017-11-01

Ship detection is one of the essential techniques for ship recognition from synthetic aperture radar (SAR) images. This paper presents a fast iterative detection procedure to eliminate the influence of target returns on the estimation of local sea clutter distributions for constant false alarm rate (CFAR) detectors. A fast block detector is first employed to extract potential target sub-images; and then, an iterative censoring CFAR algorithm is used to detect ship candidates from each target blocks adaptively and efficiently, where parallel detection is available, and statistical parameters of G0 distribution fitting local sea clutter well can be quickly estimated based on an integral image operator. Experimental results of TerraSAR-X images demonstrate the effectiveness of the proposed technique.

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie; Hernandez, Kevin; Probe, Austin; Junkins, John L.

2018-03-01

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require "shooting" but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2014-10-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Initial results of the code parallelization will be reported. Work is supported by the U.S. DOE SBIR program.

Exploiting Vector and Multicore Parallelsim for Recursive, Data- and Task-Parallel Programs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Bin; Krishnamoorthy, Sriram; Agrawal, Kunal

Modern hardware contains parallel execution resources that are well-suited for data-parallelism-vector units-and task parallelism-multicores. However, most work on parallel scheduling focuses on one type of hardware or the other. In this work, we present a scheduling framework that allows for a unified treatment of task- and data-parallelism. Our key insight is an abstraction, task blocks, that uniformly handles data-parallel iterations and task-parallel tasks, allowing them to be scheduled on vector units or executed independently as multicores. Our framework allows us to define schedulers that can dynamically select between executing task- blocks on vector units or multicores. We show that thesemore » schedulers are asymptotically optimal, and deliver the maximum amount of parallelism available in computation trees. To evaluate our schedulers, we develop program transformations that can convert mixed data- and task-parallel pro- grams into task block-based programs. Using a prototype instantiation of our scheduling framework, we show that, on an 8-core system, we can simultaneously exploit vector and multicore parallelism to achieve 14×-108× speedup over sequential baselines.« less

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

NITPICK: peak identification for mass spectrometry data.

PubMed

Renard, Bernhard Y; Kirchner, Marc; Steen, Hanno; Steen, Judith A J; Hamprecht, Fred A

2008-08-28

The reliable extraction of features from mass spectra is a fundamental step in the automated analysis of proteomic mass spectrometry (MS) experiments. This contribution proposes a sparse template regression approach to peak picking called NITPICK. NITPICK is a Non-greedy, Iterative Template-based peak PICKer that deconvolves complex overlapping isotope distributions in multicomponent mass spectra. NITPICK is based on fractional averaging, a novel extension to Senko's well-known averaging model, and on a modified version of sparse, non-negative least angle regression, for which a suitable, statistically motivated early stopping criterion has been derived. The strength of NITPICK is the deconvolution of overlapping mixture mass spectra. Extensive comparative evaluation has been carried out and results are provided for simulated and real-world data sets. NITPICK outperforms pepex, to date the only alternate, publicly available, non-greedy feature extraction routine. NITPICK is available as software package for the R programming language and can be downloaded from (http://hci.iwr.uni-heidelberg.de/mip/proteomics/).

Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures

DTIC Science & Technology

2008-10-01

42 3.4 Residual history of WSO banded preconditioner for problem 2D 54019 HIGHK . . . . . . . . . . . . . . . . . . . . . . . . . . 43...3.5 Residual history of WSO banded preconditioner for problem Appu 43 3.6 Residual history of WSO banded preconditioner for problem ASIC 680k...44 3.7 Residual history of WSO banded preconditioner for problem BUN- DLE1

Parallel AFSA algorithm accelerating based on MIC architecture

NASA Astrophysics Data System (ADS)

Zhou, Junhao; Xiao, Hong; Huang, Yifan; Li, Yongzhao; Xu, Yuanrui

2017-05-01

Analysis AFSA past for solving the traveling salesman problem, the algorithm efficiency is often a big problem, and the algorithm processing method, it does not fully responsive to the characteristics of the traveling salesman problem to deal with, and therefore proposes a parallel join improved AFSA process. The simulation with the current TSP known optimal solutions were analyzed, the results showed that the AFSA iterations improved less, on the MIC cards doubled operating efficiency, efficiency significantly.

Air Force Maui Optical and Supercomputing Site (AMOS) Application Briefs 2004

DTIC Science & Technology

2004-01-01

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection...17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 60 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT...SOR methods, the work in parallel matrix iterative methods is very relevant to the parallelization of a CA. The Moore neighborhood used in this work

Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

NASA Astrophysics Data System (ADS)

Chacon, L.; Finn, J. M.; Knoll, D. A.

2000-10-01

Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

BCYCLIC: A parallel block tridiagonal matrix cyclic solver

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; Perumalla, K. S.; Lynch, V. E.; Sanchez, R.

2010-09-01

A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.

Noniterative MAP reconstruction using sparse matrix representations.

PubMed

Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

2009-09-01

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

FPGA implementation of low complexity LDPC iterative decoder

NASA Astrophysics Data System (ADS)

Verma, Shivani; Sharma, Sanjay

2016-07-01

Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.

Drifts, currents, and power scrape-off width in SOLPS-ITER modeling of DIII-D

DOE PAGES

Meier, E. T.; Goldston, R. J.; Kaveeva, E. G.; ...

2016-12-27

The effects of drifts and associated flows and currents on the width of the parallel heat flux channel (λ q) in the tokamak scrape-off layer (SOL) are analyzed using the SOLPS-ITER 2D fluid transport code. Motivation is supplied by Goldston’s heuristic drift (HD) model for λ q, which yields the same approximately inverse poloidal magnetic field dependence seen in multi-machine regression. The analysis, focusing on a DIII-D H-mode discharge, reveals HD-like features, including comparable density and temperature fall-off lengths in the SOL, and up-down ion pressure asymmetry that allows net cross-separatrix ion magnetic drift flux to exceed net anomalous ionmore » flux. In experimentally relevant high-recycling cases, scans of both toroidal and poloidal magnetic field (B tor and B pol) are conducted, showing minimal λ q dependence on either component of the field. Insensitivity to B tor is expected, and suggests that SOLPS-ITER is effectively capturing some aspects of HD physics. Absence of λ q dependence on B pol, however, is inconsistent with both the HD model and experimental results. As a result, the inconsistency is attributed to strong variation in the parallel Mach number, which violates one of the premises of the HD model.« less

Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging

NASA Astrophysics Data System (ADS)

Wu, Ping; Liu, Kai; Zhang, Qian; Xue, Zhenwen; Li, Yongbao; Ning, Nannan; Yang, Xin; Li, Xingde; Tian, Jie

2012-12-01

Liver cancer is one of the most common malignant tumors worldwide. In order to enable the noninvasive detection of small liver tumors in mice, we present a parallel iterative shrinkage (PIS) algorithm for dual-modality tomography. It takes advantage of microcomputed tomography and multiview bioluminescence imaging, providing anatomical structure and bioluminescence intensity information to reconstruct the size and location of tumors. By incorporating prior knowledge of signal sparsity, we associate some mathematical strategies including specific smooth convex approximation, an iterative shrinkage operator, and affine subspace with the PIS method, which guarantees the accuracy, efficiency, and reliability for three-dimensional reconstruction. Then an in vivo experiment on the bead-implanted mouse has been performed to validate the feasibility of this method. The findings indicate that a tiny lesion less than 3 mm in diameter can be localized with a position bias no more than 1 mm the computational efficiency is one to three orders of magnitude faster than the existing algorithms; this approach is robust to the different regularization parameters and the lp norms. Finally, we have applied this algorithm to another in vivo experiment on an HCCLM3 orthotopic xenograft mouse model, which suggests the PIS method holds the promise for practical applications of whole-body cancer detection.

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam

In this paper, we introduce the Dynamic Load-balanced Tensor Contractions (DLTC), a domain-specific library for efficient task parallel execution of tensor contraction expressions, a class of computation encountered in quantum chemistry and physics. Our framework decomposes each contraction into smaller unit of tasks, represented by an abstraction referred to as iterators. We exploit an extra level of parallelism by having tasks across independent contractions executed concurrently through a dynamic load balancing run- time. We demonstrate the improved performance, scalability, and flexibility for the computation of tensor contraction expressions on parallel computers using examples from coupled cluster methods.

A GPU-paralleled implementation of an enhanced face recognition algorithm

NASA Astrophysics Data System (ADS)

Chen, Hao; Liu, Xiyang; Shao, Shuai; Zan, Jiguo

2013-03-01

Face recognition algorithm based on compressed sensing and sparse representation is hotly argued in these years. The scheme of this algorithm increases recognition rate as well as anti-noise capability. However, the computational cost is expensive and has become a main restricting factor for real world applications. In this paper, we introduce a GPU-accelerated hybrid variant of face recognition algorithm named parallel face recognition algorithm (pFRA). We describe here how to carry out parallel optimization design to take full advantage of many-core structure of a GPU. The pFRA is tested and compared with several other implementations under different data sample size. Finally, Our pFRA, implemented with NVIDIA GPU and Computer Unified Device Architecture (CUDA) programming model, achieves a significant speedup over the traditional CPU implementations.

Acceleration of linear stationary iterative processes in multiprocessor computers. II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romm, Ya.E.

1982-05-01

For pt.I, see Kibernetika, vol.18, no.1, p.47 (1982). For pt.I, see Cybernetics, vol.18, no.1, p.54 (1982). Considers a reduced system of linear algebraic equations x=ax+b, where a=(a/sub ij/) is a real n*n matrix; b is a real vector with common euclidean norm >>>. It is supposed that the existence and uniqueness of solution det (0-a) not equal to e is given, where e is a unit matrix. The linear iterative process converging to x x/sup (k+1)/=fx/sup (k)/, k=0, 1, 2, ..., where the operator f translates r/sup n/ into r/sup n/. In considering implementation of the iterative process (ip) inmore » a multiprocessor system, it is assumed that the number of processors is constant, and are various values of the latter investigated; it is assumed in addition, that the processors perform elementary binary arithmetic operations of addition and multiestimates only include the time of execution of arithmetic operations. With any paralleling of individual iteration, the execution time of the ip is proportional to the number of sequential steps k+1. The author sets the task of reducing the number of sequential steps in the ip so as to execute it in a time proportional to a value smaller than k+1. He also sets the goal of formulating a method of accelerated bit serial-parallel execution of each successive step of the ip, with, in the modification sought, a reduced number of steps in a time comparable to the operation time of logical elements. 6 references.« less

Reconstruction of coded aperture images

NASA Technical Reports Server (NTRS)

Bielefeld, Michael J.; Yin, Lo I.

1987-01-01

Balanced correlation method and the Maximum Entropy Method (MEM) were implemented to reconstruct a laboratory X-ray source as imaged by a Uniformly Redundant Array (URA) system. Although the MEM method has advantages over the balanced correlation method, it is computationally time consuming because of the iterative nature of its solution. Massively Parallel Processing, with its parallel array structure is ideally suited for such computations. These preliminary results indicate that it is possible to use the MEM method in future coded-aperture experiments with the help of the MPP.

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

NASA Technical Reports Server (NTRS)

Wigton, Larry

1996-01-01

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

Fast Solution in Sparse LDA for Binary Classification

NASA Technical Reports Server (NTRS)

Moghaddam, Baback

2010-01-01

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

PubMed

Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N

2015-10-13

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Agile parallel bioinformatics workflow management using Pwrake.

PubMed

Mishima, Hiroyuki; Sasaki, Kensaku; Tanaka, Masahiro; Tatebe, Osamu; Yoshiura, Koh-Ichiro

2011-09-08

In bioinformatics projects, scientific workflow systems are widely used to manage computational procedures. Full-featured workflow systems have been proposed to fulfil the demand for workflow management. However, such systems tend to be over-weighted for actual bioinformatics practices. We realize that quick deployment of cutting-edge software implementing advanced algorithms and data formats, and continuous adaptation to changes in computational resources and the environment are often prioritized in scientific workflow management. These features have a greater affinity with the agile software development method through iterative development phases after trial and error.Here, we show the application of a scientific workflow system Pwrake to bioinformatics workflows. Pwrake is a parallel workflow extension of Ruby's standard build tool Rake, the flexibility of which has been demonstrated in the astronomy domain. Therefore, we hypothesize that Pwrake also has advantages in actual bioinformatics workflows. We implemented the Pwrake workflows to process next generation sequencing data using the Genomic Analysis Toolkit (GATK) and Dindel. GATK and Dindel workflows are typical examples of sequential and parallel workflows, respectively. We found that in practice, actual scientific workflow development iterates over two phases, the workflow definition phase and the parameter adjustment phase. We introduced separate workflow definitions to help focus on each of the two developmental phases, as well as helper methods to simplify the descriptions. This approach increased iterative development efficiency. Moreover, we implemented combined workflows to demonstrate modularity of the GATK and Dindel workflows. Pwrake enables agile management of scientific workflows in the bioinformatics domain. The internal domain specific language design built on Ruby gives the flexibility of rakefiles for writing scientific workflows. Furthermore, readability and maintainability of rakefiles may facilitate sharing workflows among the scientific community. Workflows for GATK and Dindel are available at http://github.com/misshie/Workflows.

Agile parallel bioinformatics workflow management using Pwrake

PubMed Central

2011-01-01

Background In bioinformatics projects, scientific workflow systems are widely used to manage computational procedures. Full-featured workflow systems have been proposed to fulfil the demand for workflow management. However, such systems tend to be over-weighted for actual bioinformatics practices. We realize that quick deployment of cutting-edge software implementing advanced algorithms and data formats, and continuous adaptation to changes in computational resources and the environment are often prioritized in scientific workflow management. These features have a greater affinity with the agile software development method through iterative development phases after trial and error. Here, we show the application of a scientific workflow system Pwrake to bioinformatics workflows. Pwrake is a parallel workflow extension of Ruby's standard build tool Rake, the flexibility of which has been demonstrated in the astronomy domain. Therefore, we hypothesize that Pwrake also has advantages in actual bioinformatics workflows. Findings We implemented the Pwrake workflows to process next generation sequencing data using the Genomic Analysis Toolkit (GATK) and Dindel. GATK and Dindel workflows are typical examples of sequential and parallel workflows, respectively. We found that in practice, actual scientific workflow development iterates over two phases, the workflow definition phase and the parameter adjustment phase. We introduced separate workflow definitions to help focus on each of the two developmental phases, as well as helper methods to simplify the descriptions. This approach increased iterative development efficiency. Moreover, we implemented combined workflows to demonstrate modularity of the GATK and Dindel workflows. Conclusions Pwrake enables agile management of scientific workflows in the bioinformatics domain. The internal domain specific language design built on Ruby gives the flexibility of rakefiles for writing scientific workflows. Furthermore, readability and maintainability of rakefiles may facilitate sharing workflows among the scientific community. Workflows for GATK and Dindel are available at http://github.com/misshie/Workflows. PMID:21899774

Acoustical source reconstruction from non-synchronous sequential measurements by Fast Iterative Shrinkage Thresholding Algorithm

NASA Astrophysics Data System (ADS)

Yu, Liang; Antoni, Jerome; Leclere, Quentin; Jiang, Weikang

2017-11-01

Acoustical source reconstruction is a typical inverse problem, whose minimum frequency of reconstruction hinges on the size of the array and maximum frequency depends on the spacing distance between the microphones. For the sake of enlarging the frequency of reconstruction and reducing the cost of an acquisition system, Cyclic Projection (CP), a method of sequential measurements without reference, was recently investigated (JSV,2016,372:31-49). In this paper, the Propagation based Fast Iterative Shrinkage Thresholding Algorithm (Propagation-FISTA) is introduced, which improves CP in two aspects: (1) the number of acoustic sources is no longer needed and the only making assumption is that of a "weakly sparse" eigenvalue spectrum; (2) the construction of the spatial basis is much easier and adaptive to practical scenarios of acoustical measurements benefiting from the introduction of propagation based spatial basis. The proposed Propagation-FISTA is first investigated with different simulations and experimental setups and is next illustrated with an industrial case.

Single-snapshot DOA estimation by using Compressed Sensing

NASA Astrophysics Data System (ADS)

Fortunati, Stefano; Grasso, Raffaele; Gini, Fulvio; Greco, Maria S.; LePage, Kevin

2014-12-01

This paper deals with the problem of estimating the directions of arrival (DOA) of multiple source signals from a single observation vector of an array data. In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classical ℓ 1 minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smooth ℓ 0 minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phase Estimation, IAA-APES algorithms, are analyzed, and their statistical properties are investigated and compared with the classical Fourier beamformer (FB) in different simulated scenarios. We show that unlike the classical FB, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g., Capon and MUSIC) even in the single snapshot case. Particular attention is devoted to the super-resolution property. Theoretical arguments and simulation analysis provide evidence that a CS-based beamformer can achieve resolution beyond the classical Rayleigh limit. Finally, the theoretical findings are validated by processing a real sonar dataset.

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Sparse time-frequency decomposition based on dictionary adaptation.

PubMed

Hou, Thomas Y; Shi, Zuoqiang

2016-04-13

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions. © 2016 The Author(s).

Revisiting Parallel Cyclic Reduction and Parallel Prefix-Based Algorithms for Block Tridiagonal System of Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seal, Sudip K; Perumalla, Kalyan S; Hirshman, Steven Paul

2013-01-01

Simulations that require solutions of block tridiagonal systems of equations rely on fast parallel solvers for runtime efficiency. Leading parallel solvers that are highly effective for general systems of equations, dense or sparse, are limited in scalability when applied to block tridiagonal systems. This paper presents scalability results as well as detailed analyses of two parallel solvers that exploit the special structure of block tridiagonal matrices to deliver superior performance, often by orders of magnitude. A rigorous analysis of their relative parallel runtimes is shown to reveal the existence of a critical block size that separates the parameter space spannedmore » by the number of block rows, the block size and the processor count, into distinct regions that favor one or the other of the two solvers. Dependence of this critical block size on the above parameters as well as on machine-specific constants is established. These formal insights are supported by empirical results on up to 2,048 cores of a Cray XT4 system. To the best of our knowledge, this is the highest reported scalability for parallel block tridiagonal solvers to date.« less

A finite element formulation for scattering from electrically large 2-dimensional structures

NASA Technical Reports Server (NTRS)

Ross, Daniel C.; Volakis, John L.

1992-01-01

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

Generation of complementary sampled phase-only holograms.

PubMed

Tsang, P W M; Chow, Y T; Poon, T-C

2016-10-03

If an image is uniformly down-sampled into a sparse form and converted into a hologram, the phase component alone will be adequate to reconstruct the image. However, the appearance of the reconstructed image is degraded with numerous empty holes. In this paper, we present a low complexity and non-iterative solution to this problem. Briefly, two phase-only holograms are generated for an image, each based on a different down-sampling lattice. Subsequently, the holograms are displayed alternately at high frame rate. The reconstructed images of the 2 holograms will appear to be a single, densely sampled image with enhance visual quality.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Multilevel acceleration of scattering-source iterations with application to electron transport

DOE PAGES

Drumm, Clif; Fan, Wesley

2017-08-18

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates (S N) or spherical-harmonics (P N) solve to accelerate convergence of a high-order S N source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergencemore » of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.« less

Iterative Importance Sampling Algorithms for Parameter Estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray W; Morzfeld, Matthias; Day, Marcus S.

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicabilitymore » of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using 'coarse' MCMC runs or Gaussian mixture models.« less

Accelerated Brain DCE-MRI Using Iterative Reconstruction With Total Generalized Variation Penalty for Quantitative Pharmacokinetic Analysis: A Feasibility Study.

PubMed

Wang, Chunhao; Yin, Fang-Fang; Kirkpatrick, John P; Chang, Zheng

2017-08-01

To investigate the feasibility of using undersampled k-space data and an iterative image reconstruction method with total generalized variation penalty in the quantitative pharmacokinetic analysis for clinical brain dynamic contrast-enhanced magnetic resonance imaging. Eight brain dynamic contrast-enhanced magnetic resonance imaging scans were retrospectively studied. Two k-space sparse sampling strategies were designed to achieve a simulated image acquisition acceleration factor of 4. They are (1) a golden ratio-optimized 32-ray radial sampling profile and (2) a Cartesian-based random sampling profile with spatiotemporal-regularized sampling density constraints. The undersampled data were reconstructed to yield images using the investigated reconstruction technique. In quantitative pharmacokinetic analysis on a voxel-by-voxel basis, the rate constant K trans in the extended Tofts model and blood flow F B and blood volume V B from the 2-compartment exchange model were analyzed. Finally, the quantitative pharmacokinetic parameters calculated from the undersampled data were compared with the corresponding calculated values from the fully sampled data. To quantify each parameter's accuracy calculated using the undersampled data, error in volume mean, total relative error, and cross-correlation were calculated. The pharmacokinetic parameter maps generated from the undersampled data appeared comparable to the ones generated from the original full sampling data. Within the region of interest, most derived error in volume mean values in the region of interest was about 5% or lower, and the average error in volume mean of all parameter maps generated through either sampling strategy was about 3.54%. The average total relative error value of all parameter maps in region of interest was about 0.115, and the average cross-correlation of all parameter maps in region of interest was about 0.962. All investigated pharmacokinetic parameters had no significant differences between the result from original data and the reduced sampling data. With sparsely sampled k-space data in simulation of accelerated acquisition by a factor of 4, the investigated dynamic contrast-enhanced magnetic resonance imaging pharmacokinetic parameters can accurately estimate the total generalized variation-based iterative image reconstruction method for reliable clinical application.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Capabilities of Fully Parallelized MHD Stability Code MARS

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2016-10-01

Results of full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. Parallel version of MARS, named PMARS, has been recently developed at FAR-TECH. Parallelized MARS is an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, implemented in MARS. Parallelization of the code included parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse vector iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the MARS algorithm using parallel libraries and procedures. Parallelized MARS is capable of calculating eigenmodes with significantly increased spatial resolution: up to 5,000 adapted radial grid points with up to 500 poloidal harmonics. Such resolution is sufficient for simulation of kink, tearing and peeling-ballooning instabilities with physically relevant parameters. Work is supported by the U.S. DOE SBIR program.

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2015-11-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.

Real-Time Compressive Sensing MRI Reconstruction Using GPU Computing and Split Bregman Methods

PubMed Central

Smith, David S.; Gore, John C.; Yankeelov, Thomas E.; Welch, E. Brian

2012-01-01

Compressive sensing (CS) has been shown to enable dramatic acceleration of MRI acquisition in some applications. Being an iterative reconstruction technique, CS MRI reconstructions can be more time-consuming than traditional inverse Fourier reconstruction. We have accelerated our CS MRI reconstruction by factors of up to 27 by using a split Bregman solver combined with a graphics processing unit (GPU) computing platform. The increases in speed we find are similar to those we measure for matrix multiplication on this platform, suggesting that the split Bregman methods parallelize efficiently. We demonstrate that the combination of the rapid convergence of the split Bregman algorithm and the massively parallel strategy of GPU computing can enable real-time CS reconstruction of even acquisition data matrices of dimension 40962 or more, depending on available GPU VRAM. Reconstruction of two-dimensional data matrices of dimension 10242 and smaller took ~0.3 s or less, showing that this platform also provides very fast iterative reconstruction for small-to-moderate size images. PMID:22481908

Real-Time Compressive Sensing MRI Reconstruction Using GPU Computing and Split Bregman Methods.

PubMed

Smith, David S; Gore, John C; Yankeelov, Thomas E; Welch, E Brian

2012-01-01

Compressive sensing (CS) has been shown to enable dramatic acceleration of MRI acquisition in some applications. Being an iterative reconstruction technique, CS MRI reconstructions can be more time-consuming than traditional inverse Fourier reconstruction. We have accelerated our CS MRI reconstruction by factors of up to 27 by using a split Bregman solver combined with a graphics processing unit (GPU) computing platform. The increases in speed we find are similar to those we measure for matrix multiplication on this platform, suggesting that the split Bregman methods parallelize efficiently. We demonstrate that the combination of the rapid convergence of the split Bregman algorithm and the massively parallel strategy of GPU computing can enable real-time CS reconstruction of even acquisition data matrices of dimension 4096(2) or more, depending on available GPU VRAM. Reconstruction of two-dimensional data matrices of dimension 1024(2) and smaller took ~0.3 s or less, showing that this platform also provides very fast iterative reconstruction for small-to-moderate size images.

Segmentation of remotely sensed data using parallel region growing

NASA Technical Reports Server (NTRS)

Tilton, J. C.; Cox, S. C.

1983-01-01

The improved spatial resolution of the new earth resources satellites will increase the need for effective utilization of spatial information in machine processing of remotely sensed data. One promising technique is scene segmentation by region growing. Region growing can use spatial information in two ways: only spatially adjacent regions merge together, and merging criteria can be based on region-wide spatial features. A simple region growing approach is described in which the similarity criterion is based on region mean and variance (a simple spatial feature). An effective way to implement region growing for remote sensing is as an iterative parallel process on a large parallel processor. A straightforward parallel pixel-based implementation of the algorithm is explored and its efficiency is compared with sequential pixel-based, sequential region-based, and parallel region-based implementations. Experimental results from on aircraft scanner data set are presented, as is a discussioon of proposed improvements to the segmentation algorithm.

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

Non-Cartesian Parallel Imaging Reconstruction

PubMed Central

Wright, Katherine L.; Hamilton, Jesse I.; Griswold, Mark A.; Gulani, Vikas; Seiberlich, Nicole

2014-01-01

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be employed to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the non-homogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian GRAPPA, and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. PMID:24408499

Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

PubMed

Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

2017-01-01

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

DOE PAGES

Bicer, Tekin; Gursoy, Doga; Andrade, Vincent De; ...

2017-01-28

Here, synchrotron light source and detector technologies enable scientists to perform advanced experiments. These scientific instruments and experiments produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used data acquisition technique at light sources is Computed Tomography, which can generate tens of GB/s depending on x-ray range. A large-scale tomographic dataset, such as mouse brain, may require hours of computation time with a medium size workstation. In this paper, we present Trace, a data-intensive computing middleware we developed for implementation and parallelization of iterative tomographic reconstruction algorithms. Tracemore » provides fine-grained reconstruction of tomography datasets using both (thread level) shared memory and (process level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations we have done on the replicated reconstruction objects and evaluate them using a shale and a mouse brain sinogram. Our experimental evaluations show that the applied optimizations and parallelization techniques can provide 158x speedup (using 32 compute nodes) over single core configuration, which decreases the reconstruction time of a sinogram (with 4501 projections and 22400 detector resolution) from 12.5 hours to less than 5 minutes per iteration.« less

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bicer, Tekin; Gursoy, Doga; Andrade, Vincent De

Here, synchrotron light source and detector technologies enable scientists to perform advanced experiments. These scientific instruments and experiments produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used data acquisition technique at light sources is Computed Tomography, which can generate tens of GB/s depending on x-ray range. A large-scale tomographic dataset, such as mouse brain, may require hours of computation time with a medium size workstation. In this paper, we present Trace, a data-intensive computing middleware we developed for implementation and parallelization of iterative tomographic reconstruction algorithms. Tracemore » provides fine-grained reconstruction of tomography datasets using both (thread level) shared memory and (process level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations we have done on the replicated reconstruction objects and evaluate them using a shale and a mouse brain sinogram. Our experimental evaluations show that the applied optimizations and parallelization techniques can provide 158x speedup (using 32 compute nodes) over single core configuration, which decreases the reconstruction time of a sinogram (with 4501 projections and 22400 detector resolution) from 12.5 hours to less than 5 minutes per iteration.« less

Virtual fringe projection system with nonparallel illumination based on iteration

NASA Astrophysics Data System (ADS)

Zhou, Duo; Wang, Zhangying; Gao, Nan; Zhang, Zonghua; Jiang, Xiangqian

2017-06-01

Fringe projection profilometry has been widely applied in many fields. To set up an ideal measuring system, a virtual fringe projection technique has been studied to assist in the design of hardware configurations. However, existing virtual fringe projection systems use parallel illumination and have a fixed optical framework. This paper presents a virtual fringe projection system with nonparallel illumination. Using an iterative method to calculate intersection points between rays and reference planes or object surfaces, the proposed system can simulate projected fringe patterns and captured images. A new explicit calibration method has been presented to validate the precision of the system. Simulated results indicate that the proposed iterative method outperforms previous systems. Our virtual system can be applied to error analysis, algorithm optimization, and help operators to find ideal system parameter settings for actual measurements.

Variable aperture-based ptychographical iterative engine method

NASA Astrophysics Data System (ADS)

Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

2018-02-01

A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches.

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

PubMed Central

Lan, Ti-Yen; Wierman, Jennifer L.; Tate, Mark W.; Philipp, Hugh T.; Elser, Veit

2017-01-01

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such ‘sparse’ frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E, 80, 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources. PMID:28808431

MPF: A portable message passing facility for shared memory multiprocessors

NASA Technical Reports Server (NTRS)

Malony, Allen D.; Reed, Daniel A.; Mcguire, Patrick J.

1987-01-01

The design, implementation, and performance evaluation of a message passing facility (MPF) for shared memory multiprocessors are presented. The MPF is based on a message passing model conceptually similar to conversations. Participants (parallel processors) can enter or leave a conversation at any time. The message passing primitives for this model are implemented as a portable library of C function calls. The MPF is currently operational on a Sequent Balance 21000, and several parallel applications were developed and tested. Several simple benchmark programs are presented to establish interprocess communication performance for common patterns of interprocess communication. Finally, performance figures are presented for two parallel applications, linear systems solution, and iterative solution of partial differential equations.