LAPACK Linear Equation Computational Routines

Table "Computational Routines for Systems of Equations with Real Matrices" lists the LAPACK computational routines (FORTRAN 77 and Fortran 95 interfaces) for factorizing, equilibrating, and inverting real matrices, estimating their condition numbers, solving systems of equations with real matrices, refining the solution, and estimating its error. Table "Computational Routines for Systems of Equations with Complex Matrices" lists similar routines for complex matrices. Respective routine names in the Fortran 95 interface are without the first symbol (see Routine Naming Conventions).

Computational Routines for Systems of Equations with Real Matrices
Matrix type, storage scheme	Factorize matrix	Equilibrate matrix	Solve system	Condition number	Estimate error	Invert matrix
general	?getrf	?geequ, ?geequb	?getrs	?gecon	?gerfs, ?gerfsx	?getri
general band	?gbtrf	?gbequ, ?gbequb	?gbtrs	?gbcon	?gbrfs, ?gbrfsx
general tridiagonal	?gttrf		?gttrs	?gtcon	?gtrfs
diagonally dominant tridiagonal	?dttrfb		?dttrsb
symmetric positive-definite	?potrf	?poequ, ?poequb	?potrs	?pocon	?porfs, ?porfsx	?potri
symmetric positive-definite, packed storage	?pptrf	?ppequ	?pptrs	?ppcon	?pprfs	?pptri
symmetric positive-definite, RFP storage	?pftrf		?pftrs			?pftri
symmetric positive-definite, band	?pbtrf	?pbequ	?pbtrs	?pbcon	?pbrfs
symmetric positive-definite, tridiagonal	?pttrf		?pttrs	?ptcon	?ptrfs
symmetric indefinite	?sytrf ?sytrf_rook ?sytrf_rk ?sytrf_aa	?syequb	?sytrs ?sytrs_rook ?sytrs2 ?sytrs3 ?sytrs_aa	?sycon ?sycon_rook ?sycon_3	?syrfs, ?syrfsx	?sytri ?sytri_rook ?sytri2 ?sytri2x ?sytri_3
symmetric indefinite, packed storage	?sptrf mkl_?spffrt2, mkl_?spffrtx		?sptrs	?spcon	?sprfs	?sptri
triangular			?trtrs	?trcon	?trrfs	?trtri
triangular, packed storage			?tptrs	?tpcon	?tprfs	?tptri
triangular, RFP storage						?tftri
triangular band			?tbtrs	?tbcon	?tbrfs

In the table above, ? denotes s (single precision) or d (double precision) for the FORTRAN 77 interface.

Computational Routines for Systems of Equations with Complex Matrices
Matrix type, storage scheme	Factorize matrix	Equilibrate matrix	Solve system	Condition number	Estimate error	Invert matrix
general	?getrf	?geequ, ?geequb	?getrs	?gecon	?gerfs, ?gerfsx	?getri
general band	?gbtrf	?gbequ, ?gbequb	?gbtrs	?gbcon	?gbrfs, ?gbrfsx
general tridiagonal	?gttrf		?gttrs	?gtcon	?gtrfs
Hermitian positive-definite	?potrf	?poequ, ?poequb	?potrs	?pocon	?porfs, ?porfsx	?potri
Hermitian positive-definite, packed storage	?pptrf	?ppequ	?pptrs	?ppcon	?pprfs	?pptri
Hermitian positive-definite, RFP storage	?pftrf		?pftrs			?pftri
Hermitian positive-definite, band	?pbtrf	?pbequ	?pbtrs	?pbcon	?pbrfs
Hermitian positive-definite, tridiagonal	?pttrf		?pttrs	?ptcon	?ptrfs
Hermitian indefinite	?hetrf ?hetrf_rook ?hetrf_rk ?hetrf_aa	?heequb	?hetrs ?hetrs_rook ?hetrs2 ?hetrs_3 ?hetrs_aa	?hecon ?hecon_rook ?hecon_3	?herfs, ?herfsx	?hetri ?hetri_rook ?hetri2 ?hetri2x ?hetri_3
symmetric indefinite	?sytrf ?sytrf_rook ?sytrf_rk	?syequb	?sytrs ?sytrs_rook ?sytrs2 ?sytrs3	?sycon ?sycon_rook ?sycon_3	?syrfs, ?syrfsx	?sytri ?sytri_rook ?sytri2 ?sytri2x ?sytri_3
Hermitian indefinite, packed storage	?hptrf		?hptrs	?hpcon	?hprfs	?hptri
symmetric indefinite, packed storage	?sptrf mkl_?spffrt2, mkl_?spffrtx		?sptrs	?spcon	?sprfs	?sptri
triangular			?trtrs	?trcon	?trrfs	?trtri
triangular, packed storage			?tptrs	?tpcon	?tprfs	?tptri
triangular, RFP storage						?tftri
triangular band			?tbtrs	?tbcon	?tbrfs

In the table above, ? stands for c (single precision complex) or z (double precision complex) for FORTRAN 77 interface.