Chapter Introduction (pdf version)
NAG Library Manual

F07 – Linear Equations (LAPACK)

F07 Chapter Introduction
Routine
Name
Mark of
Introduction

Purpose
F07AAF
Example Text
Example Data
21 Computes the solution to a real system of linear equations
F07ABF
Example Text
Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
F07ADF
Example Text
Example Data
15 LU factorization of real m by n matrix
F07AEF
Example Text
Example Data
15 Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF)
F07AFF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
F07AGF
Example Text
Example Data
15 Estimate condition number of real matrix, matrix already factorized by F07ADF (DGETRF)
F07AHF
Example Text
Example Data
15 Refined solution with error bounds of real system of linear equations, multiple right-hand sides
F07AJF
Example Text
Example Data
15 Inverse of real matrix, matrix already factorized by F07ADF (DGETRF)
F07ANF
Example Text
Example Data
21 Computes the solution to a complex system of linear equations
F07APF
Example Text
Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
F07ARF
Example Text
Example Data
15 LU factorization of complex m by n matrix
F07ASF
Example Text
Example Data
15 Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF)
F07ATF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
F07AUF
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Example Data
15 Estimate condition number of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07AVF
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Example Data
15 Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
F07AWF
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Example Data
15 Inverse of complex matrix, matrix already factorized by F07ARF (ZGETRF)
F07BAF
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Example Data
21 Computes the solution to a real banded system of linear equations
F07BBF
Example Text
Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
F07BDF
Example Text
Example Data
15 LU factorization of real m by n band matrix
F07BEF
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Example Data
15 Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF)
F07BFF
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Example Data
21 Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
F07BGF
Example Text
Example Data
15 Estimate condition number of real band matrix, matrix already factorized by F07BDF (DGBTRF)
F07BHF
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Example Data
15 Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
F07BNF
Example Text
Example Data
21 Computes the solution to a complex banded system of linear equations
F07BPF
Example Text
Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
F07BRF
Example Text
Example Data
15 LU factorization of complex m by n band matrix
F07BSF
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Example Data
15 Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF)
F07BTF
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Example Data
21 Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
F07BUF
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Example Data
15 Estimate condition number of complex band matrix, matrix already factorized by F07BRF (ZGBTRF)
F07BVF
Example Text
Example Data
15 Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
F07CAF
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Example Data
21 Computes the solution to a real tridiagonal system of linear equations
F07CBF
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Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
F07CDF
Example Text
Example Data
21 LU factorization of real tridiagonal matrix
F07CEF
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Example Data
21 Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF)
F07CGF
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Example Data
21 Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF)
F07CHF
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Example Data
21 Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
F07CNF
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Example Data
21 Computes the solution to a complex tridiagonal system of linear equations
F07CPF
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Example Data
21 Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
F07CRF
Example Text
Example Data
21 LU factorization of complex tridiagonal matrix
F07CSF
Example Text
Example Data
21 Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF)
F07CUF
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Example Data
21 Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF)
F07CVF
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Example Data
21 Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
F07FAF
Example Text
Example Data
21 Computes the solution to a real symmetric positive-definite system of linear equations
F07FBF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations
F07FDF
Example Text
Example Data
15 Cholesky factorization of real symmetric positive-definite matrix
F07FEF
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Example Data
15 Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF)
F07FFF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number
F07FGF
Example Text
Example Data
15 Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FHF
Example Text
Example Data
15 Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
F07FJF
Example Text
Example Data
15 Inverse of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF)
F07FNF
Example Text
Example Data
21 Computes the solution to a complex Hermitian positive-definite system of linear equations
F07FPF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations
F07FRF
Example Text
Example Data
15 Cholesky factorization of complex Hermitian positive-definite matrix
F07FSF
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Example Data
15 Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF)
F07FTF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number
F07FUF
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Example Data
15 Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07FVF
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Example Data
15 Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
F07FWF
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Example Data
15 Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF)
F07GAF
Example Text
Example Data
21 Computes the solution to a real symmetric positive-definite system of linear equations, packed storage
F07GBF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations, packed storage
F07GDF
Example Text
Example Data
15 Cholesky factorization of real symmetric positive-definite matrix, packed storage
F07GEF
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Example Data
15 Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GFF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number, packed storage
F07GGF
Example Text
Example Data
15 Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GHF
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Example Data
15 Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GJF
Example Text
Example Data
15 Inverse of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage
F07GNF
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Example Data
21 Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage
F07GPF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations, packed storage
F07GRF
Example Text
Example Data
15 Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
F07GSF
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Example Data
15 Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GTF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number, packed storage
F07GUF
Example Text
Example Data
15 Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07GVF
Example Text
Example Data
15 Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
F07GWF
Example Text
Example Data
15 Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage
F07HAF
Example Text
Example Data
21 Computes the solution to a real symmetric positive-definite banded system of linear equations
F07HBF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite banded system of linear equations
F07HDF
Example Text
Example Data
15 Cholesky factorization of real symmetric positive-definite band matrix
F07HEF
Example Text
Example Data
15 Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (DPBTRF)
F07HFF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a real symmetric positive-definite banded matrix and reduce its condition number
F07HGF
Example Text
Example Data
15 Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF (DPBTRF)
F07HHF
Example Text
Example Data
15 Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
F07HNF
Example Text
Example Data
21 Computes the solution to a complex Hermitian positive-definite banded system of linear equations
F07HPF
Example Text
Example Data
21 Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite banded system of linear equations
F07HRF
Example Text
Example Data
15 Cholesky factorization of complex Hermitian positive-definite band matrix
F07HSF
Example Text
Example Data
15 Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (ZPBTRF)
F07HTF
Example Text
Example Data
21 Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite banded matrix and reduce its condition number
F07HUF
Example Text
Example Data
15 Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF (ZPBTRF)
F07HVF
Example Text
Example Data
15 Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
F07JAF
Example Text
Example Data
21 Computes the solution to a real symmetric positive-definite tridiagonal system of linear equations
F07JBF
Example Text
Example Data
21 Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal system of linear equations
F07JDF
Example Text
Example Data
21 Computes the modified Cholesky factorization of a real symmetric positive-definite tridiagonal matrix
F07JEF
Example Text
Example Data
21 Solves a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF)
F07JGF
Example Text
Example Data
21 Computes the reciprocal of the condition number of a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF)
F07JHF
Example Text
Example Data
21 Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07JNF
Example Text
Example Data
21 Computes the solution to a complex Hermitian positive-definite tridiagonal system of linear equations
F07JPF
Example Text
Example Data
21 Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal system of linear equations
F07JRF
Example Text
Example Data
21 Computes the modified Cholesky factorization of a complex Hermitian positive-definite tridiagonal matrix
F07JSF
Example Text
Example Data
21 Solves a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF)
F07JUF
Example Text
Example Data
21 Computes the reciprocal of the condition number of a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF)
F07JVF
Example Text
Example Data
21 Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple right-hand sides
F07MAF
Example Text
Example Data
21 Computes the solution to a real symmetric system of linear equations
F07MBF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
F07MDF
Example Text
Example Data
15 Bunch–Kaufman factorization of real symmetric indefinite matrix
F07MEF
Example Text
Example Data
15 Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF (DSYTRF)
F07MGF
Example Text
Example Data
15 Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MHF
Example Text
Example Data
15 Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
F07MJF
Example Text
Example Data
15 Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF)
F07MNF
Example Text
Example Data
21 Computes the solution to a complex Hermitian system of linear equations
F07MPF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
F07MRF
Example Text
Example Data
15 Bunch–Kaufman factorization of complex Hermitian indefinite matrix
F07MSF
Example Text
Example Data
15 Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF (ZHETRF)
F07MUF
Example Text
Example Data
15 Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07MVF
Example Text
Example Data
15 Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
F07MWF
Example Text
Example Data
15 Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF)
F07NNF
Example Text
Example Data
21 Computes the solution to a complex symmetric system of linear equations
F07NPF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
F07NRF
Example Text
Example Data
15 Bunch–Kaufman factorization of complex symmetric matrix
F07NSF
Example Text
Example Data
15 Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF (ZSYTRF)
F07NUF
Example Text
Example Data
15 Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07NVF
Example Text
Example Data
15 Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
F07NWF
Example Text
Example Data
15 Inverse of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF)
F07PAF
Example Text
Example Data
21 Computes the solution to a real symmetric system of linear equations, packed storage
F07PBF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage
F07PDF
Example Text
Example Data
15 Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
F07PEF
Example Text
Example Data
15 Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PGF
Example Text
Example Data
15 Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PHF
Example Text
Example Data
15 Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
F07PJF
Example Text
Example Data
15 Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage
F07PNF
Example Text
Example Data
21 Computes the solution to a complex Hermitian system of linear equations, packed storage
F07PPF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage
F07PRF
Example Text
Example Data
15 Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
F07PSF
Example Text
Example Data
15 Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PUF
Example Text
Example Data
15 Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07PVF
Example Text
Example Data
15 Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
F07PWF
Example Text
Example Data
15 Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage
F07QNF
Example Text
Example Data
21 Computes the solution to a complex symmetric system of linear equations, packed storage
F07QPF
Example Text
Example Data
21 Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage
F07QRF
Example Text
Example Data
15 Bunch–Kaufman factorization of complex symmetric matrix, packed storage
F07QSF
Example Text
Example Data
15 Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QUF
Example Text
Example Data
15 Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07QVF
Example Text
Example Data
15 Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
F07QWF
Example Text
Example Data
15 Inverse of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage
F07TEF
Example Text
Example Data
15 Solution of real triangular system of linear equations, multiple right-hand sides
F07TGF
Example Text
Example Data
15 Estimate condition number of real triangular matrix
F07THF
Example Text
Example Data
15 Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
F07TJF
Example Text
Example Data
15 Inverse of real triangular matrix
F07TSF
Example Text
Example Data
15 Solution of complex triangular system of linear equations, multiple right-hand sides
F07TUF
Example Text
Example Data
15 Estimate condition number of complex triangular matrix
F07TVF
Example Text
Example Data
15 Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
F07TWF
Example Text
Example Data
15 Inverse of complex triangular matrix
F07UEF
Example Text
Example Data
15 Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UGF
Example Text
Example Data
15 Estimate condition number of real triangular matrix, packed storage
F07UHF
Example Text
Example Data
15 Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
F07UJF
Example Text
Example Data
15 Inverse of real triangular matrix, packed storage
F07USF
Example Text
Example Data
15 Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UUF
Example Text
Example Data
15 Estimate condition number of complex triangular matrix, packed storage
F07UVF
Example Text
Example Data
15 Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
F07UWF
Example Text
Example Data
15 Inverse of complex triangular matrix, packed storage
F07VEF
Example Text
Example Data
15 Solution of real band triangular system of linear equations, multiple right-hand sides
F07VGF
Example Text
Example Data
15 Estimate condition number of real band triangular matrix
F07VHF
Example Text
Example Data
15 Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
F07VSF
Example Text
Example Data
15 Solution of complex band triangular system of linear equations, multiple right-hand sides
F07VUF
Example Text
Example Data
15 Estimate condition number of complex band triangular matrix
F07VVF
Example Text
Example Data
15 Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides

Chapter Introduction (pdf version)
NAG Library Manual

The Numerical Algorithms Group Ltd, Oxford, UK. 2006