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Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format

Published: 01 March 2007 Publication History

Abstract

We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into n(n + 1)/2 real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage (n2 variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs.

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Software for Fortran 95 subroutines for Cholesky factorization in block hybrid format

References

[1]
Andersen, B., Gunnels, J., Gustavson, F., Reid, J., and Waśniewski, J. 2005. A fully portable high performance minimal storage hybrid format Cholesky algorithm. ACM Trans. Math. Softw. 31, 201--227.
[2]
Dongarra, J., Du Croz, J., Duff, I. S., and Hammarling, S. 1990. A set of level 3 Basic Linear Algebra Subprograms. ACM Trans. Math. Soft. 16, 1 (Mar.), 1--17.

Cited By

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  • (2013)Level-3 Cholesky Factorization Routines Improve Performance of Many Cholesky AlgorithmsACM Transactions on Mathematical Software10.1145/2427023.242702639:2(1-10)Online publication date: 1-Feb-2013
  • (2011)New level-3 BLAS kernels for cholesky factorizationProceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I10.1007/978-3-642-31464-3_7(60-69)Online publication date: 11-Sep-2011
  • (2010)Rectangular full packed format for cholesky's algorithmACM Transactions on Mathematical Software10.1145/1731022.173102837:2(1-21)Online publication date: 23-Apr-2010
  • Show More Cited By

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Published In

cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 33, Issue 1
March 2007
134 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/1206040
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 2007
Published in TOMS Volume 33, Issue 1

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Author Tags

  1. BLAS
  2. Cholesky factorization and solution
  3. Real symmetric matrices
  4. linear systems of equations
  5. novel packed matrix data structures
  6. positive definite matrices
  7. recursive algorithms

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Cited By

View all
  • (2013)Level-3 Cholesky Factorization Routines Improve Performance of Many Cholesky AlgorithmsACM Transactions on Mathematical Software10.1145/2427023.242702639:2(1-10)Online publication date: 1-Feb-2013
  • (2011)New level-3 BLAS kernels for cholesky factorizationProceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I10.1007/978-3-642-31464-3_7(60-69)Online publication date: 11-Sep-2011
  • (2010)Rectangular full packed format for cholesky's algorithmACM Transactions on Mathematical Software10.1145/1731022.173102837:2(1-21)Online publication date: 23-Apr-2010
  • (2008)Application of Rectangular Full Packed and Blocked Hybrid Matrix Formats in Semidefinite Programming for Sensor Network LocalizationParallel Processing and Applied Mathematics10.1007/978-3-540-68111-3_68(649-658)Online publication date: 2008
  • (2007)Application of rectangular full packed and blocked hybrid matrix formats in semidefinite programming for sensor network localizationProceedings of the 7th international conference on Parallel processing and applied mathematics10.5555/1786194.1786269(649-658)Online publication date: 9-Sep-2007

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