Dongarra, J, A. Lumsdaine, R. Pozo, K. Remington. (1994). A sparse matrix library in C++ for high performance architectures. Proceedings of the Second Object Oriented Numerics Conference, 214-218.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....version of SparseRowMatrix. Both store the complete matrix, but SymSparseRowMatrix can use the same algorithm for mult and multTranspose, eliminating the more expensive multiplication that is required for multTranspose. Instances of matrix 46 classes have also be implemented with SparseLib [30], and could also use other matrix packages. The mult and multTranspose operations both take an optional beginning and end row argument. This allows the matrix multiplication to be divided among processors in a parallel implementation. The discussion of the SolveMatrix module displays how these ....

....highly tuned vector vector dot product. ffl Utility functions for computing min and max of two or three variables. ffl A tuned tri diagonal matrix solver. ffl Other tuned matrix and vector operations. Other numerical libraries have also been used with SCIRun, including LAPACK [12] SparseLib [30], and portions of Diffpack [69] 6.6 Chapter Summary We presented an overview of the low level libraries used in SCIRun. A replacement for malloc is used to overcome difficulties with the previous implementations in a complex multithreaded environment. A multitasking library is used to simplify ....

DONGARRA, J., LUMSDAINE, A., POZO, R., AND REMINGTON, K. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Object Oriented Numerics Conference (1994), pp. 214--218.

....has increased over the last several years. For example, the designers of LAPACK [1] have provided a C interface (see [6] The interface is based on a collection of vector and matrix classes; these classes have evolved over the past few years through several related packages: Sparselib [4], IML [5] and MV [20] due to Pozo and his collaborators. Currently a package called Template Numerical Toolkit (TNT) 21] is being designed as a successor to these packages. The work culminating in TNT is very closely related to ours in motivation. Quoting from [4] 4 . code involving ....

....packages: Sparselib [4] IML [5] and MV [20] due to Pozo and his collaborators. Currently a package called Template Numerical Toolkit (TNT) 21] is being designed as a successor to these packages. The work culminating in TNT is very closely related to ours in motivation. Quoting from [4]: 4 . code involving sparse matrices tends to be very complicated, and not easily portable, because the details of the underlying data formats are invariably entangled within the application code. To address these difficulties, it is essential to develop codes which are as data format ....

J. Dongarra, A. Lumsdaine, X. Niu, R. Pozo, and K. REMINGTON. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Annual Object-Oriented Numerics Conference, pages 214--218, 1994.

....In addition, the use of expression templates was pioneered in Blitz . CHAPTER 3. RELATED WORK 16 Library OO ET Op Generative Template Numeric Toolkit (TNT) 47] X X C Scientific Library (SL ) 20] X X Generative Matrix Computation Library (GMCL) 16] X X X LAPACK [25] X Sparslib [26] X GNU Scientific Software Library (GNUSSL) 46] X Newmat [19] X X Table 3.1. Summary of C Libraries for Linear Algebra 3.4 Generic Programming and Software Engineering As already mentioned, the design of the MTL draws heavily from the Standard Template Library [52, 3] which popularized the ....

....such a large group of iterative methods in short time (4 man months) CHAPTER 7. ITERATIVE TEMPLATE LIBRARY (ITL) 85 7. 3 ITL Performance This section compares the performance of the ITL with IML [24] one of the few other comprehensive iterative method packages (which uses SparseLib [26] for the sparse basic linear algebra) Six matrices from the Harwell Boeing collection are used. Computation time (in seconds) per iteration is plotted in Figure 7.4 for each of the following methods: CGS, BICG, BICGSTAB, QMR and TFQMR (which only exists in ITL) The ILU (without fill in) ....

J. J. Dongarra, A. Lumsdaine, R. Pozo, and K. A. Remington. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Annual Object-Oriented Numerics Conference, pages 214--218, 1994.

....number of platforms. Existing sparse matrix collections like the Harwell Boeing suite [8] are important tools for designers of numerical algorithms and partitioning algorithms. And existing software libraries that support sparse matrix computations are useful tools for application programmers [2, 7, 11]. However, to date the designers of parallel systems have not had access to a set of public domain sparse matrix kernels that are simple, realistic, and portable. Towards that end, we introduce the Spark98 kernels, a set of 10 SMVP kernels for shared memory and message passing systems. 1 We ....

DONGARRA, J., LUMSDAINE, A., POZO, R., AND REMINGTON, K. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Object Oriented Numerics Conference (1994), pp. 214--218.

.... 3 L 2 L 1 d d d 0 1 L 1 L 2 ) 0 1 L 1 ( 0 1 = ETH Zurich, CS Technical Report #282, Institute of Scientific Computing, January 9, 1998 7 In order to solve the system of linear equations we either use a conjugate gradient solver with an incomplete Cholesky preconditioning [6, 7] or a LU decomposition [16] for the indefinite matrices arising from totally incompressible materials. 4 RESULTS The implementation offers a great choice of possible simulation types. We can interpolate to a lower or higher degree, choose between compressible and incompressible media, and ....

J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington. "A sparse matrix library in c++ for high performance architectures." In Proceedings of the Second Object Oriented Numerics Conference, pages 214--218, 1994.

....omit the details of these simple calculations. The boundary conditions of the uncontrolled system and system (2.1) 2.5) are handled similarly. The resulting sparse linear system is solved using the preconditioned BiConjugate Gradient Stabilized method implemented in a C templated library ( 1] [7]) The computation was performed on a 300MHz, 130Mb memory Sun SPARC Workstation and, due to the small time step, it required several hours to reach one time unit with the numerical solution. As an example, we consider the (KdVB) equation (3.4) with parameters ffl 0 = 1, ffi 0 = 10, p = 100 ....

J. Dongarra, A. Lumsdaine, R. Pozo and K. Remington, "A sparse matrix library in C++ for high performance architectures," Proceedings of the Second Object Oriented Numerics Conference, pp. 214-218, 1994.

....In the first stage of SCIRun, we have concentrated on integrating the computational components that we have used to solve our own computational problems. We have recently expanded focus and are now in the process of integrating popular libraries and tools, such as Diffpack [10, 11] SparseLib [12], and PETSc [13, 14] into the SCIRun environment. 6 S.G. Parker, D.W. Weinstein, C.R. Johnson 1.2.3 SCIRun the Development Environment Perhaps the most powerful facet of SCIRun is the ability to use it in the development phases of a simulation. SCIRun augments the development environment by ....

....A few other surfaces are provided such as cylinders, spheres, and points (a degenerate surface) 1.4.4 The Matrix Class Matrices: We implement a base class called Matrix, which defines multiply and transpose multiply abstract methods. Instances of this class may be implemented with SparseLib [12], or other sparse matrix packages. SCIRun also implements a compressed row storage matrix which has been highly tuned for the architectures which we use most often. The discussion of the SolveMatrix module will display how these abstract interfaces are used to implement the conjugate gradient ....

J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Object Oriented Numerics Conference, pages 214--218, 1994.

....E. Chow and M. A. Heroux BPKIT is available at http: www.cs.umn.edu chow bpkit.html. Other C efforts in the numerical solution of linear equations include LAPACK [Dongarra et al. 1993] for dense systems, and Diffpack [Bruaset and Langtangen 1997] ISIS [Clay 1997] SparseLib and IML [Dongarra et al. 1994] for sparse systems. It is also possible to use an object oriented style in other languages [Eijkhout 1996; Machiels and Deville 1997; Smith et al. 1995] In Section 2, we discuss various issues that arise when designing interfaces for block preconditioning and for preconditioned iterative methods ....

Dongarra, J. J., Lumsdaine, A., Niu, X., Pozo, R., and Remington, K. 1994. A sparse matrix library in C++ for high performance architectures. In Proc. Object Oriented Numerics Conference (Sun River, OR, 1994).

....comparisons. The calculation of the local stiffness matrices is done analytically when assembling the global matrix. The corresponding code was generated by Maple. In order to solve the system of linear equations we either use a conjugate gradient solver with incomplete Cholesky preconditioning [6, 7] or an LU decomposition [16] for the indefinite matrices arising from totally incompressible materials. 4. Results The implementation offers a great choice of possible simulation types. We can interpolate to a lower or higher degree, choose between compressible and incompressible media, and ....

J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington. "A sparse matrix library in c++ for high performance architectures. " In Proceedings of the Second Object Oriented Numerics Conference, pages 214--218, 1994.

....heat equation with unit spatial dimension and T = 64 for the temporal dimension. The problem is discretized with 64 spatial points and 32 temporal points and is solved using backward Euler. The experimental code for CCG was written in C , using the CG module from the IML class library [2]. Although IML was developed for solving linear systems of equations, by using it with a waveform class and by overloading the appropriate operators, the same CG code was able to be used for both linear algebra problems and waveform problems. Figure 5.1 compares the convergence rates of WR, ....

J. Dongarra, A. Lumsdaine, X. Niu, R. Pozo, and K. Remington, A sparse matrix library in C++ for high performance architectures, in Proceedings Object Oriented Numerics Conference, Sun River, OR, 1994.

.... The misperception about abstraction springs from numerous examples of C libraries that provide a very nice user interface through polymorphism, operator overloading, and so forth so that the user can implement an algorithm or a library in a natural way (see, e.g. SparseLib and IML [8]) Such an approach will (by design) hide computational costs from the user and degrade performance. One approach to providing performance and abastraction is through the use of lazy evaluation (see, e.g. 2] but this approach can have other performance penalties as well as implementation ....

....x2.end( x3.begin( 0.0) 3 The Matrix Template Library MTL is by no means the first attempt to bring abstraction to scientific programming [3] nor is it the first attempt at a mathematical library in C . Other notable efforts include HPC [20] LAPACK [9] SparseLib IML [8], and the Template Numerical Toolkit [16] MTL is unique, however, in its general underlying philosophy (see below) and in its particular commitment to self contained high performance. Other libraries, if they are concerned about performance at all, attain high performance by making ....

J. Dongarra, A. Lumsdaine, X. Niu, R. Pozo, and K. Remington, A sparse matrix library in C++ for high performance architectures, in Proc. Object Oriented Numerics Conference, Sun River, OR, 1994.

....computation. Each driver routine typically calls a sequence of computational routines. Taken as a whole, the computational routines can perform a wider range of tasks than are covered by the driver routines. Currently, dense and band matrices are supported. General sparse matrices are handled in [7]. 2.1 Contents of LAPACK With over 1,000 subroutines in the original f77 LAPACK, not every routine is implemented in LAPACK . Instead, source code examples in the various major areas are provided, allowing users to easily extend the package for their particular needs. LAPACK provides source ....

J. J. Dongarra, A. Lumsdaine, Xinhiu Niu, Roldan Pozo, Karin Remington, A Sparse Matrix Library in C++ for High Performance Architectures, Proceedings of the Object Oriented Numerics Conference, Sunriver, Oregon, April 1994.

....or a particular matrix vector multiply, optimizations at these levels can happen with no change to the iterative method code. 7. 3 ITL Performance Here we present a performance comparison with the IML [10] one of the few other comprehensize iterative method packages (which uses SparseLib [8] for the sparse basic Generic Programming for Numerical Linear Algebra 9 Initial r (0) b Gamma Ax (0) for i = 1; 2; solve Mz (i Gamma1) r (i Gamma1) ae i Gamma1 = r (i Gamma1) T z (i Gamma1) if i = 1 p (1) z (0) else fi i Gamma1 = ae i Gamma1 =ae i Gamma2 p ....

J. J. Dongarra, A. Lumsdaine, R. Pozo, and K. A. Remington. A sparse matrix library in C++ for high performance architectures. In Proceedings of the Second Annual Object-Oriented Numerics Conference, pages 214--218, 1994.

....computation. Each driver routine typically calls a sequence of computational routines. Taken as a whole, the computational routines can perform a wider range of tasks than are covered by the driver routines. Currently, dense and band matrices are supported. General sparse matrices are handled in [7]. 2.1 Contents of LAPACK With over 1,000 subroutines in the original f77 LAPACK, not every routine is implemented in LAPACK . Instead, source code examples in the various major areas are provided, allowing users to easily extend the package for their particular needs. LAPACK provides source ....

J. J. Dongarra, A. Lumsdaine, Xinhiu Niu, Roldan Pozo, Karin Remington, A Sparse Matrix Library in C++ for High Performance Architectures, Proceedings of the Object Oriented Numerics Conference, Sunriver, Oregon, April 1994.

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Dongarra, J, A. Lumsdaine, R. Pozo, K. Remington. (1994). A sparse matrix library in C++ for high performance architectures. Proceedings of the Second Object Oriented Numerics Conference, 214-218.

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J. J. Dongarra, A. Lumsdaine, R. Pozo, K. A. Remington, A Sparse Matrix Library in C++ for High Performance Architectures, Proceedings of the Second Annual Object-Oriented Numerics Conference, 1994, pp. 214-218.

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-171. [2] J. Dongarra, A. Lumsdaine, R. Pozo, K. Remington, "A Sparse Matrix Library in C++ for High Performance Architectures," Proceedings of the Object Oriented Numerics Conference, 1994, pp.

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