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	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.