# NAG Library Chapter Contents

## F07 (lapacklin)Linear Equations (LAPACK)

F07 (lapacklin) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

 RoutineName Mark ofIntroduction Purpose f07aaf (dgesv) Example Text Example Data 21 dgesv nagf_lapacklin_dgesv Computes the solution to a real system of linear equations f07abf (dgesvx) Example Text Example Data 21 dgesvx nagf_lapacklin_dgesvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a real system of linear equations f07acf (dsgesv) Example Text Example Data 22 dsgesv nagf_lapacklin_dsgesv Computes the solution to a real system of linear equations using mixed precision arithmetic f07adf (dgetrf) Example Text Example Data 15 dgetrf nagf_lapacklin_dgetrf $LU$ factorization of real $m$ by $n$ matrix f07aef (dgetrs) Example Text Example Data 15 dgetrs nagf_lapacklin_dgetrs Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by f07adf (dgetrf) f07aff (dgeequ) Example Text Example Data 22 dgeequ nagf_lapacklin_dgeequ Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number f07agf (dgecon) Example Text Example Data 15 dgecon nagf_lapacklin_dgecon Estimate condition number of real matrix, matrix already factorized by f07adf (dgetrf) f07ahf (dgerfs) Example Text Example Data 15 dgerfs nagf_lapacklin_dgerfs Refined solution with error bounds of real system of linear equations, multiple right-hand sides f07ajf (dgetri) Example Text Example Data 15 dgetri nagf_lapacklin_dgetri Inverse of real matrix, matrix already factorized by f07adf (dgetrf) f07anf (zgesv) Example Text Example Data 21 zgesv nagf_lapacklin_zgesv Computes the solution to a complex system of linear equations f07apf (zgesvx) Example Text Example Data 21 zgesvx nagf_lapacklin_zgesvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations f07aqf (zcgesv) Example Text Example Data 22 zcgesv nagf_lapacklin_zcgesv Computes the solution to a complex system of linear equations using mixed precision arithmetic f07arf (zgetrf) Example Text Example Data 15 zgetrf nagf_lapacklin_zgetrf $LU$ factorization of complex $m$ by $n$ matrix f07asf (zgetrs) Example Text Example Data 15 zgetrs nagf_lapacklin_zgetrs Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by f07arf (zgetrf) f07atf (zgeequ) Example Text Example Data 22 zgeequ nagf_lapacklin_zgeequ Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number f07auf (zgecon) Example Text Example Data 15 zgecon nagf_lapacklin_zgecon Estimate condition number of complex matrix, matrix already factorized by f07arf (zgetrf) f07avf (zgerfs) Example Text Example Data 15 zgerfs nagf_lapacklin_zgerfs Refined solution with error bounds of complex system of linear equations, multiple right-hand sides f07awf (zgetri) Example Text Example Data 15 zgetri nagf_lapacklin_zgetri Inverse of complex matrix, matrix already factorized by f07arf (zgetrf) f07baf (dgbsv) Example Text Example Data 21 dgbsv nagf_lapacklin_dgbsv Computes the solution to a real banded system of linear equations f07bbf (dgbsvx) Example Text Example Data 21 dgbsvx nagf_lapacklin_dgbsvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations f07bdf (dgbtrf) Example Text Example Data 15 dgbtrf nagf_lapacklin_dgbtrf $LU$ factorization of real $m$ by $n$ band matrix f07bef (dgbtrs) Example Text Example Data 15 dgbtrs nagf_lapacklin_dgbtrs Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by f07bdf (dgbtrf) f07bff (dgbequ) Example Text Example Data 22 dgbequ nagf_lapacklin_dgbequ Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number f07bgf (dgbcon) Example Text Example Data 15 dgbcon nagf_lapacklin_dgbcon Estimate condition number of real band matrix, matrix already factorized by f07bdf (dgbtrf) f07bhf (dgbrfs) Example Text Example Data 15 dgbrfs nagf_lapacklin_dgbrfs Refined solution with error bounds of real band system of linear equations, multiple right-hand sides f07bnf (zgbsv) Example Text Example Data 21 zgbsv nagf_lapacklin_zgbsv Computes the solution to a complex banded system of linear equations f07bpf (zgbsvx) Example Text Example Data 21 zgbsvx nagf_lapacklin_zgbsvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations f07brf (zgbtrf) Example Text Example Data 15 zgbtrf nagf_lapacklin_zgbtrf $LU$ factorization of complex $m$ by $n$ band matrix f07bsf (zgbtrs) Example Text Example Data 15 zgbtrs nagf_lapacklin_zgbtrs Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by f07brf (zgbtrf) f07btf (zgbequ) Example Text Example Data 22 zgbequ nagf_lapacklin_zgbequ Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number f07buf (zgbcon) Example Text Example Data 15 zgbcon nagf_lapacklin_zgbcon Estimate condition number of complex band matrix, matrix already factorized by f07brf (zgbtrf) f07bvf (zgbrfs) Example Text Example Data 15 zgbrfs nagf_lapacklin_zgbrfs Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides f07caf (dgtsv) Example Text Example Data 21 dgtsv nagf_lapacklin_dgtsv Computes the solution to a real tridiagonal system of linear equations f07cbf (dgtsvx) Example Text Example Data 21 dgtsvx nagf_lapacklin_dgtsvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations f07cdf (dgttrf) Example Text Example Data 22 dgttrf nagf_lapacklin_dgttrf $LU$ factorization of real tridiagonal matrix f07cef (dgttrs) Example Text Example Data 22 dgttrs nagf_lapacklin_dgttrs Solves a real tridiagonal system of linear equations using the $LU$ factorization computed by f07cdf (dgttrf) f07cgf (dgtcon) Example Text Example Data 22 dgtcon nagf_lapacklin_dgtcon Estimates the reciprocal of the condition number of a real tridiagonal matrix using the $LU$ factorization computed by f07cdf (dgttrf) f07chf (dgtrfs) Example Text Example Data 22 dgtrfs nagf_lapacklin_dgtrfs Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides f07cnf (zgtsv) Example Text Example Data 21 zgtsv nagf_lapacklin_zgtsv Computes the solution to a complex tridiagonal system of linear equations f07cpf (zgtsvx) Example Text Example Data 21 zgtsvx nagf_lapacklin_zgtsvx Uses the $LU$ factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations f07crf (zgttrf) Example Text Example Data 22 zgttrf nagf_lapacklin_zgttrf $LU$ factorization of complex tridiagonal matrix f07csf (zgttrs) Example Text Example Data 22 zgttrs nagf_lapacklin_zgttrs Solves a complex tridiagonal system of linear equations using the $LU$ factorization computed by f07cdf (dgttrf) f07cuf (zgtcon) Example Text Example Data 22 zgtcon nagf_lapacklin_zgtcon Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the $LU$ factorization computed by f07cdf (dgttrf) f07cvf (zgtrfs) Example Text Example Data 22 zgtrfs nagf_lapacklin_zgtrfs Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides f07faf (dposv) Example Text Example Data 21 dposv nagf_lapacklin_dposv Computes the solution to a real symmetric positive definite system of linear equations f07fbf (dposvx) Example Text Example Data 21 dposvx nagf_lapacklin_dposvx Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations f07fcf (dsposv) Example Text Example Data 23 dsposv nagf_lapacklin_dsposv Computes the solution to a real symmetric positive definite system of linear equations using mixed precision arithmetic f07fdf (dpotrf) Example Text Example Data 15 dpotrf nagf_lapacklin_dpotrf Cholesky factorization of real symmetric positive definite matrix f07fef (dpotrs) Example Text Example Data 15 dpotrs nagf_lapacklin_dpotrs Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by f07fdf (dpotrf) f07fff (dpoequ) Example Text Example Data 22 dpoequ nagf_lapacklin_dpoequ Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number f07fgf (dpocon) Example Text Example Data 15 dpocon nagf_lapacklin_dpocon Estimate condition number of real symmetric positive definite matrix, matrix already factorized by f07fdf (dpotrf) f07fhf (dporfs) Example Text Example Data 15 dporfs nagf_lapacklin_dporfs Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides f07fjf (dpotri) Example Text Example Data 15 dpotri nagf_lapacklin_dpotri Inverse of real symmetric positive definite matrix, matrix already factorized by f07fdf (dpotrf) f07fnf (zposv) Example Text Example Data 21 zposv nagf_lapacklin_zposv Computes the solution to a complex Hermitian positive definite system of linear equations f07fpf (zposvx) Example Text Example Data 21 zposvx nagf_lapacklin_zposvx Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite system of linear equations f07fqf (zcposv) Example Text Example Data 23 zcposv nagf_lapacklin_zcposv Computes the solution to a complex Hermitian positive definite system of linear equations using mixed precision arithmetic f07frf (zpotrf) Example Text Example Data 15 zpotrf nagf_lapacklin_zpotrf Cholesky factorization of complex Hermitian positive definite matrix f07fsf (zpotrs) Example Text Example Data 15 zpotrs nagf_lapacklin_zpotrs Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by f07frf (zpotrf) f07ftf (zpoequ) Example Text Example Data 22 zpoequ nagf_lapacklin_zpoequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number f07fuf (zpocon) Example Text Example Data 15 zpocon nagf_lapacklin_zpocon Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by f07frf (zpotrf) f07fvf (zporfs) Example Text Example Data 15 zporfs nagf_lapacklin_zporfs Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides f07fwf (zpotri) Example Text Example Data 15 zpotri nagf_lapacklin_zpotri Inverse of complex Hermitian positive definite matrix, matrix already factorized by f07frf (zpotrf) f07gaf (dppsv) Example Text Example Data 21 dppsv nagf_lapacklin_dppsv Computes the solution to a real symmetric positive definite system of linear equations, packed storage f07gbf (dppsvx) Example Text Example Data 21 dppsvx nagf_lapacklin_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 f07gdf (dpptrf) Example Text Example Data 15 dpptrf nagf_lapacklin_dpptrf Cholesky factorization of real symmetric positive definite matrix, packed storage f07gef (dpptrs) Example Text Example Data 15 dpptrs nagf_lapacklin_dpptrs Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by f07gdf (dpptrf), packed storage f07gff (dppequ) Example Text Example Data 22 dppequ nagf_lapacklin_dppequ Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage f07ggf (dppcon) Example Text Example Data 15 dppcon nagf_lapacklin_dppcon Estimate condition number of real symmetric positive definite matrix, matrix already factorized by f07gdf (dpptrf), packed storage f07ghf (dpprfs) Example Text Example Data 15 dpprfs nagf_lapacklin_dpprfs Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage f07gjf (dpptri) Example Text Example Data 15 dpptri nagf_lapacklin_dpptri Inverse of real symmetric positive definite matrix, matrix already factorized by f07gdf (dpptrf), packed storage f07gnf (zppsv) Example Text Example Data 21 zppsv nagf_lapacklin_zppsv Computes the solution to a complex Hermitian positive definite system of linear equations, packed storage f07gpf (zppsvx) Example Text Example Data 21 zppsvx nagf_lapacklin_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 f07grf (zpptrf) Example Text Example Data 15 zpptrf nagf_lapacklin_zpptrf Cholesky factorization of complex Hermitian positive definite matrix, packed storage f07gsf (zpptrs) Example Text Example Data 15 zpptrs nagf_lapacklin_zpptrs Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, matrix already factorized by f07grf (zpptrf), packed storage f07gtf (zppequ) Example Text Example Data 22 zppequ nagf_lapacklin_zppequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number, packed storage f07guf (zppcon) Example Text Example Data 15 zppcon nagf_lapacklin_zppcon Estimate condition number of complex Hermitian positive definite matrix, matrix already factorized by f07grf (zpptrf), packed storage f07gvf (zpprfs) Example Text Example Data 15 zpprfs nagf_lapacklin_zpprfs Refined solution with error bounds of complex Hermitian positive definite system of linear equations, multiple right-hand sides, packed storage f07gwf (zpptri) Example Text Example Data 15 zpptri nagf_lapacklin_zpptri Inverse of complex Hermitian positive definite matrix, matrix already factorized by f07grf (zpptrf), packed storage f07haf (dpbsv) Example Text Example Data 21 dpbsv nagf_lapacklin_dpbsv Computes the solution to a real symmetric positive definite banded system of linear equations f07hbf (dpbsvx) Example Text Example Data 21 dpbsvx nagf_lapacklin_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 f07hdf (dpbtrf) Example Text Example Data 15 dpbtrf nagf_lapacklin_dpbtrf Cholesky factorization of real symmetric positive definite band matrix f07hef (dpbtrs) Example Text Example Data 15 dpbtrs nagf_lapacklin_dpbtrs Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hdf (dpbtrf) f07hff (dpbequ) Example Text Example Data 22 dpbequ nagf_lapacklin_dpbequ Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number f07hgf (dpbcon) Example Text Example Data 15 dpbcon nagf_lapacklin_dpbcon Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by f07hdf (dpbtrf) f07hhf (dpbrfs) Example Text Example Data 15 dpbrfs nagf_lapacklin_dpbrfs Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides f07hnf (zpbsv) Example Text Example Data 21 zpbsv nagf_lapacklin_zpbsv Computes the solution to a complex Hermitian positive definite banded system of linear equations f07hpf (zpbsvx) Example Text Example Data 21 zpbsvx nagf_lapacklin_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 f07hrf (zpbtrf) Example Text Example Data 15 zpbtrf nagf_lapacklin_zpbtrf Cholesky factorization of complex Hermitian positive definite band matrix f07hsf (zpbtrs) Example Text Example Data 15 zpbtrs nagf_lapacklin_zpbtrs Solution of complex Hermitian positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hrf (zpbtrf) f07htf (zpbequ) Example Text Example Data 22 zpbequ nagf_lapacklin_zpbequ Computes row and column scalings intended to equilibrate a complex Hermitian positive definite banded matrix and reduce its condition number f07huf (zpbcon) Example Text Example Data 15 zpbcon nagf_lapacklin_zpbcon Estimate condition number of complex Hermitian positive definite band matrix, matrix already factorized by f07hrf (zpbtrf) f07hvf (zpbrfs) Example Text Example Data 15 zpbrfs nagf_lapacklin_zpbrfs Refined solution with error bounds of complex Hermitian positive definite band system of linear equations, multiple right-hand sides f07jaf (dptsv) Example Text Example Data 21 dptsv nagf_lapacklin_dptsv Computes the solution to a real symmetric positive definite tridiagonal system of linear equations f07jbf (dptsvx) Example Text Example Data 21 dptsvx nagf_lapacklin_dptsvx Uses the ${\mathrm{LDL}}^{\mathrm{T}}$ factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations f07jdf (dpttrf) Example Text Example Data 22 dpttrf nagf_lapacklin_dpttrf Computes the ${\mathrm{LDL}}^{\mathrm{T}}$ factorization of a real symmetric positive definite tridiagonal matrix f07jef (dpttrs) Example Text Example Data 22 dpttrs nagf_lapacklin_dpttrs Solves a real symmetric positive definite tridiagonal system using the ${\mathrm{LDL}}^{\mathrm{T}}$ factorization computed by f07jdf (dpttrf) f07jgf (dptcon) Example Text Example Data 22 dptcon nagf_lapacklin_dptcon Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the ${\mathrm{LDL}}^{\mathrm{T}}$ factorization computed by f07jdf (dpttrf) f07jhf (dptrfs) Example Text Example Data 22 dptrfs nagf_lapacklin_dptrfs Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides f07jnf (zptsv) Example Text Example Data 21 zptsv nagf_lapacklin_zptsv Computes the solution to a complex Hermitian positive definite tridiagonal system of linear equations f07jpf (zptsvx) Example Text Example Data 21 zptsvx nagf_lapacklin_zptsvx Uses the ${\mathrm{LDL}}^{\mathrm{T}}$ factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive definite tridiagonal system of linear equations f07jrf (zpttrf) Example Text Example Data 22 zpttrf nagf_lapacklin_zpttrf Computes the ${\mathrm{LDL}}^{\mathrm{H}}$ factorization of a complex Hermitian positive definite tridiagonal matrix f07jsf (zpttrs) Example Text Example Data 22 zpttrs nagf_lapacklin_zpttrs Solves a complex Hermitian positive definite tridiagonal system using the ${\mathrm{LDL}}^{\mathrm{H}}$ factorization computed by f07jrf (zpttrf) f07juf (zptcon) Example Text Example Data 22 zptcon nagf_lapacklin_zptcon Computes the reciprocal of the condition number of a complex Hermitian positive definite tridiagonal system using the ${\mathrm{LDL}}^{\mathrm{H}}$ factorization computed by f07jrf (zpttrf) f07jvf (zptrfs) Example Text Example Data 22 zptrfs nagf_lapacklin_zptrfs Refined solution with error bounds of complex Hermitian positive definite tridiagonal system of linear equations, multiple right-hand sides f07kdf (dpstrf) Example Text Example Data 23 dpstrf nagf_lapacklin_dpstrf Cholesky factorization, with complete pivoting, of a real, symmetric, positive semidefinite matrix f07krf (zpstrf) Example Text Example Data 23 zpstrf nagf_lapacklin_zpstrf Cholesky factorization of complex Hermitian positive semidefinite matrix f07maf (dsysv) Example Text Example Data 21 dsysv nagf_lapacklin_dsysv Computes the solution to a real symmetric system of linear equations f07mbf (dsysvx) Example Text Example Data 21 dsysvx nagf_lapacklin_dsysvx Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations f07mdf (dsytrf) Example Text Example Data 15 dsytrf nagf_lapacklin_dsytrf Bunch–Kaufman factorization of real symmetric indefinite matrix f07mef (dsytrs) Example Text Example Data 15 dsytrs nagf_lapacklin_dsytrs Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mdf (dsytrf) f07mgf (dsycon) Example Text Example Data 15 dsycon nagf_lapacklin_dsycon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07mdf (dsytrf) f07mhf (dsyrfs) Example Text Example Data 15 dsyrfs nagf_lapacklin_dsyrfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides f07mjf (dsytri) Example Text Example Data 15 dsytri nagf_lapacklin_dsytri Inverse of real symmetric indefinite matrix, matrix already factorized by f07mdf (dsytrf) f07mnf (zhesv) Example Text Example Data 21 zhesv nagf_lapacklin_zhesv Computes the solution to a complex Hermitian system of linear equations f07mpf (zhesvx) Example Text Example Data 21 zhesvx nagf_lapacklin_zhesvx Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations f07mrf (zhetrf) Example Text Example Data 15 zhetrf nagf_lapacklin_zhetrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix f07msf (zhetrs) Example Text Example Data 15 zhetrs nagf_lapacklin_zhetrs Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mrf (zhetrf) f07muf (zhecon) Example Text Example Data 15 zhecon nagf_lapacklin_zhecon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07mrf (zhetrf) f07mvf (zherfs) Example Text Example Data 15 zherfs nagf_lapacklin_zherfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides f07mwf (zhetri) Example Text Example Data 15 zhetri nagf_lapacklin_zhetri Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07mrf (zhetrf) f07nnf (zsysv) Example Text Example Data 21 zsysv nagf_lapacklin_zsysv Computes the solution to a complex symmetric system of linear equations f07npf (zsysvx) Example Text Example Data 21 zsysvx nagf_lapacklin_zsysvx Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations f07nrf (zsytrf) Example Text Example Data 15 zsytrf nagf_lapacklin_zsytrf Bunch–Kaufman factorization of complex symmetric matrix f07nsf (zsytrs) Example Text Example Data 15 zsytrs nagf_lapacklin_zsytrs Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07nrf (zsytrf) f07nuf (zsycon) Example Text Example Data 15 zsycon nagf_lapacklin_zsycon Estimate condition number of complex symmetric matrix, matrix already factorized by f07nrf (zsytrf) f07nvf (zsyrfs) Example Text Example Data 15 zsyrfs nagf_lapacklin_zsyrfs Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides f07nwf (zsytri) Example Text Example Data 15 zsytri nagf_lapacklin_zsytri Inverse of complex symmetric matrix, matrix already factorized by f07nrf (zsytrf) f07paf (dspsv) Example Text Example Data 21 dspsv nagf_lapacklin_dspsv Computes the solution to a real symmetric system of linear equations, packed storage f07pbf (dspsvx) Example Text Example Data 21 dspsvx nagf_lapacklin_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 f07pdf (dsptrf) Example Text Example Data 15 dsptrf nagf_lapacklin_dsptrf Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage f07pef (dsptrs) Example Text Example Data 15 dsptrs nagf_lapacklin_dsptrs Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07pdf (dsptrf), packed storage f07pgf (dspcon) Example Text Example Data 15 dspcon nagf_lapacklin_dspcon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07pdf (dsptrf), packed storage f07phf (dsprfs) Example Text Example Data 15 dsprfs nagf_lapacklin_dsprfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage f07pjf (dsptri) Example Text Example Data 15 dsptri nagf_lapacklin_dsptri Inverse of real symmetric indefinite matrix, matrix already factorized by f07pdf (dsptrf), packed storage f07pnf (zhpsv) Example Text Example Data 21 zhpsv nagf_lapacklin_zhpsv Computes the solution to a complex Hermitian system of linear equations, packed storage f07ppf (zhpsvx) Example Text Example Data 21 zhpsvx nagf_lapacklin_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 f07prf (zhptrf) Example Text Example Data 15 zhptrf nagf_lapacklin_zhptrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage f07psf (zhptrs) Example Text Example Data 15 zhptrs nagf_lapacklin_zhptrs Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07prf (zhptrf), packed storage f07puf (zhpcon) Example Text Example Data 15 zhpcon nagf_lapacklin_zhpcon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07prf (zhptrf), packed storage f07pvf (zhprfs) Example Text Example Data 15 zhprfs nagf_lapacklin_zhprfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage f07pwf (zhptri) Example Text Example Data 15 zhptri nagf_lapacklin_zhptri Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07prf (zhptrf), packed storage f07qnf (zspsv) Example Text Example Data 21 zspsv nagf_lapacklin_zspsv Computes the solution to a complex symmetric system of linear equations, packed storage f07qpf (zspsvx) Example Text Example Data 21 zspsvx nagf_lapacklin_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 f07qrf (zsptrf) Example Text Example Data 15 zsptrf nagf_lapacklin_zsptrf Bunch–Kaufman factorization of complex symmetric matrix, packed storage f07qsf (zsptrs) Example Text Example Data 15 zsptrs nagf_lapacklin_zsptrs Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07qrf (zsptrf), packed storage f07quf (zspcon) Example Text Example Data 15 zspcon nagf_lapacklin_zspcon Estimate condition number of complex symmetric matrix, matrix already factorized by f07qrf (zsptrf), packed storage f07qvf (zsprfs) Example Text Example Data 15 zsprfs nagf_lapacklin_zsprfs Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage f07qwf (zsptri) Example Text Example Data 15 zsptri nagf_lapacklin_zsptri Inverse of complex symmetric matrix, matrix already factorized by f07qrf (zsptrf), packed storage f07tef (dtrtrs) Example Text Example Data 15 dtrtrs nagf_lapacklin_dtrtrs Solution of real triangular system of linear equations, multiple right-hand sides f07tgf (dtrcon) Example Text Example Data 15 dtrcon nagf_lapacklin_dtrcon Estimate condition number of real triangular matrix f07thf (dtrrfs) Example Text Example Data 15 dtrrfs nagf_lapacklin_dtrrfs Error bounds for solution of real triangular system of linear equations, multiple right-hand sides f07tjf (dtrtri) Example Text Example Data 15 dtrtri nagf_lapacklin_dtrtri Inverse of real triangular matrix f07tsf (ztrtrs) Example Text Example Data 15 ztrtrs nagf_lapacklin_ztrtrs Solution of complex triangular system of linear equations, multiple right-hand sides f07tuf (ztrcon) Example Text Example Data 15 ztrcon nagf_lapacklin_ztrcon Estimate condition number of complex triangular matrix f07tvf (ztrrfs) Example Text Example Data 15 ztrrfs nagf_lapacklin_ztrrfs Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides f07twf (ztrtri) Example Text Example Data 15 ztrtri nagf_lapacklin_ztrtri Inverse of complex triangular matrix f07uef (dtptrs) Example Text Example Data 15 dtptrs nagf_lapacklin_dtptrs Solution of real triangular system of linear equations, multiple right-hand sides, packed storage f07ugf (dtpcon) Example Text Example Data 15 dtpcon nagf_lapacklin_dtpcon Estimate condition number of real triangular matrix, packed storage f07uhf (dtprfs) Example Text Example Data 15 dtprfs nagf_lapacklin_dtprfs Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage f07ujf (dtptri) Example Text Example Data 15 dtptri nagf_lapacklin_dtptri Inverse of real triangular matrix, packed storage f07usf (ztptrs) Example Text Example Data 15 ztptrs nagf_lapacklin_ztptrs Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage f07uuf (ztpcon) Example Text Example Data 15 ztpcon nagf_lapacklin_ztpcon Estimate condition number of complex triangular matrix, packed storage f07uvf (ztprfs) Example Text Example Data 15 ztprfs nagf_lapacklin_ztprfs Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage f07uwf (ztptri) Example Text Example Data 15 ztptri nagf_lapacklin_ztptri Inverse of complex triangular matrix, packed storage f07vef (dtbtrs) Example Text Example Data 15 dtbtrs nagf_lapacklin_dtbtrs Solution of real band triangular system of linear equations, multiple right-hand sides f07vgf (dtbcon) Example Text Example Data 15 dtbcon nagf_lapacklin_dtbcon Estimate condition number of real band triangular matrix f07vhf (dtbrfs) Example Text Example Data 15 dtbrfs nagf_lapacklin_dtbrfs Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides f07vsf (ztbtrs) Example Text Example Data 15 ztbtrs nagf_lapacklin_ztbtrs Solution of complex band triangular system of linear equations, multiple right-hand sides f07vuf (ztbcon) Example Text Example Data 15 ztbcon nagf_lapacklin_ztbcon Estimate condition number of complex band triangular matrix f07vvf (ztbrfs) Example Text Example Data 15 ztbrfs nagf_lapacklin_ztbrfs Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides f07wdf (dpftrf) Example Text Example Data 23 dpftrf nagf_lapacklin_dpftrf Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format f07wef (dpftrs) Example Text Example Data 23 dpftrs nagf_lapacklin_dpftrs Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by f07wdf (dpftrf), Rectangular Full Packed format f07wjf (dpftri) Example Text Example Data 23 dpftri nagf_lapacklin_dpftri Inverse of real symmetric positive definite matrix, matrix already factorized by f07wdf (dpftrf), Rectangular Full Packed format f07wkf (dtftri) Example Text Example Data 23 dtftri nagf_lapacklin_dtftri Inverse of real triangular matrix, Rectangular Full Packed format f07wrf (zpftrf) Example Text Example Data 23 zpftrf nagf_lapacklin_zpftrf Cholesky factorization of complex Hermitian positive definite matrix, Rectangular Full Packed format f07wsf (zpftrs) Example Text Example Data 23 zpftrs nagf_lapacklin_zpftrs Solution of complex Hermitian positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by f07wrf (zpftrf), Rectangular Full Packed format f07wwf (zpftri) Example Text Example Data 23 zpftri nagf_lapacklin_zpftri Inverse of complex Hermitian positive definite matrix, matrix already factorized by f07wrf (zpftrf), Rectangular Full Packed format f07wxf (ztftri) Example Text Example Data 23 ztftri nagf_lapacklin_ztftri Inverse of complex triangular matrix, Rectangular Full Packed format
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