# LAPACK Linear Equation Routines¶

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

Description

geqrf

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

gerqf

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

getrf

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

getri

Computes the inverse of an LU-factored general matrix.

getrs

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

hetrf

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

orgqr

Generates the real orthogonal matrix $$Q$$ of the QR factorization formed by geqrf.

ormqr

Multiplies a real matrix by the orthogonal matrix $$Q$$ of the QR factorization formed by geqrf.

ormrq

Multiplies a real matrix by the orthogonal matrix $$Q$$ of the RQ factorization formed by gerqf.

potrf

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

potri

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

potrs

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

sytrf

Computes the Bunch-Kaufman factorization of a symmetric matrix.

trtrs

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

ungqr

Generates the complex unitary matrix $$Q$$ of the QR factorization formed by geqrf.

unmqr

Multiplies a complex matrix by the unitary matrix $$Q$$ of the QR factorization formed by geqrf.
Multiplies a complex matrix by the unitary matrix $$Q$$ of the RQ factorization formed by gerqf.