LAPACK Linear Equation RoutinesΒΆ

LAPACK Linear Equation routines are used for factoring a matrix, solving a system of linear equations, solving linear least squares problems, and inverting a matrix. The following table lists the LAPACK Linear Equation routine groups.

Routines

Scratchpad Size Routines

Description

geqrf

geqrf_scratchpad_size

Computes the QR factorization of a general m-by-n matrix.

gerqf

gerqf_scratchpad_size

Computes the RQ factorization of a general m-by-n matrix.

getrf

getrf_scratchpad_size

Computes the LU factorization of a general m-by-n matrix.

getri

getri_scratchpad_size

Computes the inverse of an LU-factored general matrix.

getrs

getrs_scratchpad_size

Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.

hetrf

hetrf_scratchpad_size

Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.

orgqr

orgqr_scratchpad_size

Generates the real orthogonal matrix \(Q\) of the QR factorization formed by geqrf.

ormqr

ormqr_scratchpad_size

Multiplies a real matrix by the orthogonal matrix \(Q\) of the QR factorization formed by geqrf.

ormrq

ormrq_scratchpad_size

Multiplies a real matrix by the orthogonal matrix \(Q\) of the RQ factorization formed by gerqf.

potrf

potrf_scratchpad_size

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.

potri

potri_scratchpad_size

Computes the inverse of a Cholesky-factored symmetric (Hermitian) positive-definite matrix.

potrs

potrs_scratchpad_size

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix, with multiple right-hand sides.

sytrf

sytrf_scratchpad_size

Computes the Bunch-Kaufman factorization of a symmetric matrix.

trtrs

trtrs_scratchpad_size

Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides.

ungqr

ungqr_scratchpad_size

Generates the complex unitary matrix \(Q\) of the QR factorization formed by geqrf.

unmqr

unmqr_scratchpad_size

Multiplies a complex matrix by the unitary matrix \(Q\) of the QR factorization formed by geqrf.

unmrq

unmrq_scratchpad_size

Multiplies a complex matrix by the unitary matrix \(Q\) of the RQ factorization formed by gerqf.