LAPACK Linear Equation Computational Routines

Table "Computational Routines for Systems of Equations with Real Matrices" lists the LAPACK computational routines 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.

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_rk

?sytrf_aa

?syequb

?sytrs

?sytrs2

?sytrs3

?sytrs_aa

?sycon

?sycon_3

?syrfs,

?syrfsx

?sytri

?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

 

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_rk

?hetrf_aa

?heequb

?hetrs

?hetrs2

?hetrs_3

?hetrs_aa

?hecon

?hecon_3

?herfs,

?herfsx

?hetri

?hetri2

?hetri2x

?hetri_3

symmetric indefinite

?sytrf

?sytrf_rk

?syequb

?sytrs

?sytrs2

?sytrs3

?sycon

?sycon_3

?syrfs,

?syrfsx

?sytri

?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

 

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