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2nd Introduction to the Matrix package

Published on Jan 1, 2016
Martin Mächler16
Estimated H-index: 16
,
Douglas M. Bates32
Estimated H-index: 32
Abstract
Linear algebra is at the core of many areas of statistical computing and from its inception the S language has supported numerical linear algebra via a matrix data type and several functions and operators, such as %*%, qr, chol, and solve. However, these data types and functions do not provide direct access to all of the facilities for efficient manipulation of dense matrices, as provided by the Lapack subroutines, and they do not provide for manipulation of sparse matrices. The Matrix package provides a set of S4 classes for dense and sparse matrices that extend the basic matrix data type. Methods for a wide variety of functions and operators applied to objects from these classes provide efficient access to BLAS (Basic Linear Algebra Subroutines), Lapack (dense matrix), CHOLMOD including AMD and COLAMD and Csparse (sparse matrix) routines. One notable characteristic of the package is that whenever a matrix is factored, the factorization is stored as part of the original matrix so that further operations on the matrix can reuse this factorization.
  • References (5)
  • Citations (2)
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References5
Newest
SparseM provides some basic R functionality for linear algebra with sparse matrices. Use of the package is illustrated by a family of linear model fitting functions that implement least squares methods for problems with sparse design matrices. Significant performance improvements in memory utilization and computational speed are possible for applications involving large sparse matrices.
53 CitationsSource
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Last. D. SaltzH-Index: 1
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Abstract This paper describes the automatically tuned linear algebra software (ATLAS) project, as well as the fundamental principles that underly it. ATLAS is an instantiation of a new paradigm in high performance library production and maintenance, which we term automated empirical optimization of software (AEOS); this style of library management has been created in order to allow software to keep pace with the incredible rate of hardware advancement inherent in Moore's Law. ATLAS is the applic...
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#1Ed AndersonH-Index: 1
Preface to the third edition Preface to the secondedition Part 1. Guide. 1. Essentials 2. Contents of LAPACK 3. Performance of LAPACK 4. Accuracy and Stability 5. Documentation and Software Conventions 6. Installing LAPACK Routines 7. Troubleshooting Appendix A. Index of Driver and Computational Routines Appendix B. Index of Auxiliary Routines Appendix C. Quick Reference Guide to the BLAS Appendix D. Converting from LINPACK or EISPACK Appendix E. LAPACK Working Notes Part 2. Specifications of Ro...
1,432 Citations
#1Jack DongarraH-Index: 101
#2Cleve B. MolerH-Index: 26
Last. G. W. StewartH-Index: 41
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General matrices Band matrices Positive definite matrices Positive definite band matrices Symmetric Indefinite Matrices Triangular matrices Tridiagonal matrices The Cholesky decomposition The QR decomposition Updating QR and Cholesky decompositions The singular value decomposition References Basic linear algebra subprograms Timing data Program listings BLA Listings.
860 Citations
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