6.23 F07 Linear Equations

f07 - Linear Equations (LAPACK)

f07 Chapter Introduction

Routine Name Mark of Introduction Purpose
f07aac 23 nag_dgesv
Computes the solution to a real system of linear equations
f07abc 23 nag_dgesvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real system of linear equations
f07acc 23 nag_dsgesv
Computes the solution to a real system of linear equations using mixed precision arithmetic
f07adc 7 nag_dgetrf
LU factorization of real m by n matrix
f07aec 7 nag_dgetrs
Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by nag_dgetrf (f07adc)
f07afc 23 nag_dgeequ
Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number
f07agc 7 nag_dgecon
Estimate condition number of real matrix, matrix already factorized by nag_dgetrf (f07adc)
f07ahc 7 nag_dgerfs
Refined solution with error bounds of real system of linear equations, multiple right-hand sides
f07ajc 7 nag_dgetri
Inverse of real matrix, matrix already factorized by nag_dgetrf (f07adc)
f07anc 23 nag_zgesv
Computes the solution to a complex system of linear equations
f07apc 23 nag_zgesvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations
f07aqc 23 nag_zcgesv
Computes the solution to a complex system of linear equations using mixed precision arithmetic
f07arc 7 nag_zgetrf
LU factorization of complex m by n matrix
f07asc 7 nag_zgetrs
Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by nag_zgetrf (f07arc)
f07atc 23 nag_zgeequ
Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number
f07auc 7 nag_zgecon
Estimate condition number of complex matrix, matrix already factorized by nag_zgetrf (f07arc)
f07avc 7 nag_zgerfs
Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
f07awc 7 nag_zgetri
Inverse of complex matrix, matrix already factorized by nag_zgetrf (f07arc)
f07bac 23 nag_dgbsv
Computes the solution to a real banded system of linear equations
f07bbc 23 nag_dgbsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations
f07bdc 7 nag_dgbtrf
LU factorization of real m by n band matrix
f07bec 7 nag_dgbtrs
Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by nag_dgbtrf (f07bdc)
f07bfc 23 nag_dgbequ
Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number
f07bgc 7 nag_dgbcon
Estimate condition number of real band matrix, matrix already factorized by nag_dgbtrf (f07bdc)
f07bhc 7 nag_dgbrfs
Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
f07bnc 23 nag_zgbsv
Computes the solution to a complex banded system of linear equations
f07bpc 23 nag_zgbsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations
f07brc 7 nag_zgbtrf
LU factorization of complex m by n band matrix
f07bsc 7 nag_zgbtrs
Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by nag_zgbtrf (f07brc)
f07btc 23 nag_zgbequ
Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number
f07buc 7 nag_zgbcon
Estimate condition number of complex band matrix, matrix already factorized by nag_zgbtrf (f07brc)
f07bvc 7 nag_zgbrfs
Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
f07cac 23 nag_dgtsv
Computes the solution to a real tridiagonal system of linear equations
f07cbc 23 nag_dgtsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations
f07cdc 23 nag_dgttrf
LU factorization of real tridiagonal matrix
f07cec 23 nag_dgttrs
Solves a real tridiagonal system of linear equations using the LU factorization computed by nag_dgttrf (f07cdc)
f07cgc 23 nag_dgtcon
Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by nag_dgttrf (f07cdc)
f07chc 23 nag_dgtrfs
Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides
f07cnc 23 nag_zgtsv
Computes the solution to a complex tridiagonal system of linear equations
f07cpc 23 nag_zgtsvx
Uses the LU factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations
f07crc 23 nag_zgttrf
LU factorization of complex tridiagonal matrix
f07csc 23 nag_zgttrs
Solves a complex tridiagonal system of linear equations using the LU factorization computed by nag_dgttrf (f07cdc)
f07cuc 23 nag_zgtcon
Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by nag_dgttrf (f07cdc)
f07cvc 23 nag_zgtrfs
Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides
f07fac 23 nag_dposv
Computes the solution to a real symmetric positive definite system of linear equations
f07fbc 23 nag_dposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations
f07fdc 7 nag_dpotrf
Cholesky factorization of real symmetric positive-definite matrix
f07fec 7 nag_dpotrs
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by nag_dpotrf (f07fdc)
f07ffc 23 nag_dpoequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number
f07fgc 7 nag_dpocon
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by nag_dpotrf (f07fdc)
f07fhc 7 nag_dporfs
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
f07fjc 7 nag_dpotri
Inverse of real symmetric positive-definite matrix, matrix already factorized by nag_dpotrf (f07fdc)
f07fnc 23 nag_zposv
Computes the solution to a complex Hermitian positive definite system of linear equations
f07fpc 23 nag_zposvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations
f07frc 7 nag_zpotrf
Cholesky factorization of complex Hermitian positive-definite matrix
f07fsc 7 nag_zpotrs
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by nag_zpotrf (f07frc)
f07ftc 23 nag_zpoequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number
f07fuc 7 nag_zpocon
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by nag_zpotrf (f07frc)
f07fvc 7 nag_zporfs
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
f07fwc 7 nag_zpotri
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by nag_zpotrf (f07frc)
f07gac 23 nag_dppsv
Computes the solution to a real symmetric positive definite system of linear equations, packed storage
f07gbc 23 nag_dppsvx
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
f07gdc 7 nag_dpptrf
Cholesky factorization of real symmetric positive-definite matrix, packed storage
f07gec 7 nag_dpptrs
Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by nag_dpptrf (f07gdc), packed storage
f07gfc 23 nag_dppequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage
f07ggc 7 nag_dppcon
Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by nag_dpptrf (f07gdc), packed storage
f07ghc 7 nag_dpprfs
Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gjc 7 nag_dpptri
Inverse of real symmetric positive-definite matrix, matrix already factorized by nag_dpptrf (f07gdc), packed storage
f07gnc 23 nag_zppsv
Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage
f07gpc 23 nag_zppsvx
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
f07grc 7 nag_zpptrf
Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
f07gsc 7 nag_zpptrs
Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by nag_zpptrf (f07grc), packed storage
f07gtc 23 nag_zppequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage
f07guc 7 nag_zppcon
Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by nag_zpptrf (f07grc), packed storage
f07gvc 7 nag_zpprfs
Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gwc 7 nag_zpptri
Inverse of complex Hermitian positive-definite matrix, matrix already factorized by nag_zpptrf (f07grc), packed storage
f07hac 23 nag_dpbsv
Computes the solution to a real symmetric positive definite banded system of linear equations
f07hbc 23 nag_dpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations
f07hdc 7 nag_dpbtrf
Cholesky factorization of real symmetric positive-definite band matrix
f07hec 7 nag_dpbtrs
Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by nag_dpbtrf (f07hdc)
f07hfc 23 nag_dpbequ
Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number
f07hgc 7 nag_dpbcon
Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by nag_dpbtrf (f07hdc)
f07hhc 7 nag_dpbrfs
Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
f07hnc 23 nag_zpbsv
Computes the solution to a complex Hermitian positive definite banded system of linear equations
f07hpc 23 nag_zpbsvx
Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite banded system of linear equations
f07hrc 7 nag_zpbtrf
Cholesky factorization of complex Hermitian positive-definite band matrix
f07hsc 7 nag_zpbtrs
Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by nag_zpbtrf (f07hrc)


f07htc 23 nag_zpbequ
Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number


f07huc 7 nag_zpbcon
Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by nag_zpbtrf (f07hrc)
f07hvc 7 nag_zpbrfs
Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides


f07jac 23 nag_dptsv
Computes the solution to a real symmetric positive definite tridiagonal system of linear equations
f07jbc 23 nag_dptsvx
Uses the LDLT factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations
f07jdc 23 nag_dpttrf
Computes the LDLT factorization of a real symmetric positive definite tridiagonal matrix
f07jec 23 nag_dpttrs
Solves a real symmetric positive definite tridiagonal system using the LDLT factorization computed by nag_dpttrf (f07jdc)
f07jgc 23 nag_dptcon
Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the LDLT factorization computed by nag_dpttrf (f07jdc)
f07jhc 23 nag_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
f07jnc 23 nag_zptsv
Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations
f07jpc 23 nag_zptsvx
Uses the LDLT factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations
f07jrc 23 nag_zpttrf
Computes the LDLH factorization of a complex Hermitian positive definite tridiagonal matrix
f07jsc 23 nag_zpttrs
Solves a complex Hermitian positive definite tridiagonal system using the LDLH factorization computed by nag_zpttrf (f07jrc)
f07juc 23 nag_zptcon
Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the LDLH factorization computed by nag_zpttrf (f07jrc)
f07jvc 23 nag_zptrfs
Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides
f07kdc 25 nag_dpstrf
Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix
f07krc 25 nag_zpstrf
Cholesky factorization of complex Hermitian positive semidefinite matrix
f07mac 23 nag_dsysv
Computes the solution to a real symmetric system of linear equations
f07mbc 23 nag_dsysvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations
f07mdc 7 nag_dsytrf
Bunch-Kaufman factorization of real symmetric indefinite matrix
f07mec 7 nag_dsytrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by nag_dsytrf (f07mdc)
f07mgc 7 nag_dsycon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by nag_dsytrf (f07mdc)
f07mhc 7 nag_dsyrfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
f07mjc 7 nag_dsytri
Inverse of real symmetric indefinite matrix, matrix already factorized by nag_dsytrf (f07mdc)
f07mnc 23 nag_zhesv
Computes the solution to a complex Hermitian system of linear equations
f07mpc 23 nag_zhesvx
Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations
f07mrc 7 nag_zhetrf
Bunch-Kaufman factorization of complex Hermitian indefinite matrix
f07msc 7 nag_zhetrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by nag_zhetrf (f07mrc)
f07muc 7 nag_zhecon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by nag_zhetrf (f07mrc)
f07mvc 7 nag_zherfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
f07mwc 7 nag_zhetri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by nag_zhetrf (f07mrc)
f07nnc 23 nag_zsysv
Computes the solution to a complex symmetric system of linear equations
f07npc 23 nag_zsysvx
Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations
f07nrc 7 nag_zsytrf
Bunch-Kaufman factorization of complex symmetric matrix
f07nsc 7 nag_zsytrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by nag_zsytrf (f07nrc)
f07nuc 7 nag_zsycon
Estimate condition number of complex symmetric matrix, matrix already factorized by nag_zsytrf (f07nrc)
f07nvc 7 nag_zsyrfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
f07nwc 7 nag_zsytri
Inverse of complex symmetric matrix, matrix already factorized by nag_zsytrf (f07nrc)
f07pac 23 nag_dspsv
Computes the solution to a real symmetric system of linear equations, packed storage
f07pbc 23 nag_dspsvx
Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage. Error bounds and a condition estimate are also computed.
f07pdc 7 nag_dsptrf
Bunch-Kaufman factorization of real symmetric indefinite matrix, packed storage
f07pec 7 nag_dsptrs
Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by nag_dsptrf (f07pdc), packed storage
f07pgc 7 nag_dspcon
Estimate condition number of real symmetric indefinite matrix, matrix already factorized by nag_dsptrf (f07pdc), packed storage
f07phc 7 nag_dsprfs
Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
f07pjc 7 nag_dsptri
Inverse of real symmetric indefinite matrix, matrix already factorized by nag_dsptrf (f07pdc), packed storage
f07pnc 23 nag_zhpsv
Computes the solution to a complex Hermitian system of linear equations, packed storage
f07ppc 23 nag_zhpsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, Hermitian, system of linear equations, error bounds and condition estimates. Packed storage
f07prc 7 nag_zhptrf
Bunch-Kaufman factorization of complex Hermitian indefinite matrix, packed storage
f07psc 7 nag_zhptrs
Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by nag_zhptrf (f07prc), packed storage
f07puc 7 nag_zhpcon
Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by nag_zhptrf (f07prc), packed storage
f07pvc 7 nag_zhprfs
Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
f07pwc 7 nag_zhptri
Inverse of complex Hermitian indefinite matrix, matrix already factorized by nag_zhptrf (f07prc), packed storage
f07qnc 23 nag_zspsv
Computes the solution to a complex symmetric system of linear equations, packed storage
f07qpc 23 nag_zspsvx
Uses the diagonal pivoting factorization to compute the solution to a complex, symmetric, system of linear equations, error bounds and condition estimates. Packed storage
f07qrc 7 nag_zsptrf
Bunch-Kaufman factorization of complex symmetric matrix, packed storage
f07qsc 7 nag_zsptrs
Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by nag_zsptrf (f07qrc), packed storage
f07quc 7 nag_zspcon
Estimate condition number of complex symmetric matrix, matrix already factorized by nag_zsptrf (f07qrc), packed storage
f07qvc 7 nag_zsprfs
Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
f07qwc 7 nag_zsptri
Inverse of complex symmetric matrix, matrix already factorized by nag_zsptrf (f07qrc), packed storage
f07tec 7 nag_dtrtrs
Solution of real triangular system of linear equations, multiple right-hand sides
f07tgc 7 nag_dtrcon
Estimate condition number of real triangular matrix
f07thc 7 nag_dtrrfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
f07tjc 7 nag_dtrtri
Inverse of real triangular matrix
f07tsc 7 nag_ztrtrs
Solution of complex triangular system of linear equations, multiple right-hand sides
f07tuc 7 nag_ztrcon
Estimate condition number of complex triangular matrix
f07tvc 7 nag_ztrrfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
f07twc 7 nag_ztrtri
Inverse of complex triangular matrix
f07uec 7 nag_dtptrs
Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ugc 7 nag_dtpcon
Estimate condition number of real triangular matrix, packed storage
f07uhc 7 nag_dtprfs
Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ujc 7 nag_dtptri
Inverse of real triangular matrix, packed storage
f07usc 7 nag_ztptrs
Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uuc 7 nag_ztpcon
Estimate condition number of complex triangular matrix, packed storage
f07uvc 7 nag_ztprfs
Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uwc 7 nag_ztptri
Inverse of complex triangular matrix, packed storage
f07vec 7 nag_dtbtrs
Solution of real band triangular system of linear equations, multiple right-hand sides
f07vgc 7 nag_dtbcon
Estimate condition number of real band triangular matrix
f07vhc 7 nag_dtbrfs
Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
f07vsc 7 nag_ztbtrs
Solution of complex band triangular system of linear equations, multiple right-hand sides
f07vuc 7 nag_ztbcon
Estimate condition number of complex band triangular matrix
f07vvc 7 nag_ztbrfs
Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
f07wdc 25 nag_dpftrf
Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format
f07wec 25 nag_dpftrs
Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_dpftrf (f07wdc), Rectangular Full Packed format
f07wjc 25 nag_dpftri
Inverse of real symmetric positive definite matrix, matrix already factorized by nag_dpftrf (f07wdc), Rectangular Full Packed format
f07wkc 25 nag_dtftri
Inverse of real triangular matrix, Rectangular Full Packed format
f07wrc 25 nag_zpftrf
Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format
f07wsc 25 nag_zpftrs
Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by nag_zpftrf (f07wrc), Rectangular Full Packed format
f07wwc 25 nag_zpftri
Inverse of complex Hermitian positive definite matrix, matrix already factorized by nag_zpftrf (f07wrc), Rectangular Full Packed format
f07wxc 25 nag_ztftri
Inverse of complex triangular matrix, Rectangular Full Packed format