Optimized LAPACK Functions

This section describes all function families in the optimized LAPACK.

**Table 1** Optimized LAPACK functions
Feature	Function Family	Data Type	Description
Matrix factorization	?getrf	s, d, c, z	Matrix LU factorization, allowing row interchanges.
	?geqrf	s, d, c, z	Matrix QR factorization.
	?gerqf	s, d, c, z	Matrix RQ factorization.
	?geqlf	s, d, c, z	Matrix QL factorization.
	?gelqf	s, d, c, z	Matrix LQ factorization.
	?potrf	s, d, c, z	Cholesky factorization of a real symmetric or conjugate symmetric positive definite matrix.
	?pttrf	s, d, c, z	LDL^* or U*DU factorization of a real (conjugate) symmetric positive definite tridiagonal matrix A.
	?gttrf	s, d, c, z	LU factorization of general tridiagonal matrix A.
	?sptrf	s, d, c, z	LDL^* or U*DU factorization of a packed symmetric matrix.
	?hptrf	c, z	LDL^* or U*DU factorization of a packed Hermite matrix.
	?pptrf	s, d, c, z	LL^T or UTU factorization of a symmetric positive definite matrix in packed storage.
Linear equation systems solving	?ppsv	s, d, c, z	Cholesky factorization of a positive definite matrix in packed storage with real symmetry or conjugate symmetry.
	?gesv	s, d, c, z	Solves the system of linear equations using the result of LU factorization.
	?ptsv	s, d, c, z	Solves a system of linear equations, in which the coefficient matrix A is a real (conjugate) symmetric positive definite tridiagonal matrix.
	?gtsv	s, d, c, z	Solves the system of linear equations A X = B*, where A is a general tridiagonal coefficient matrix.
	?posv	s, d, c, z	Solves the system of linear equations A X = B*, where A is a real or conjugate symmetric positive definite coefficient matrix.
Matrix inversion	?getri	s, d, c, z	Computes the inverse matrix based on the ?getrf result.
	?potri	s, d, c, z	Computes the inverse matrix based on the ?potrf result.
	?pptri	s, d, c, z	Computes the inverse matrix based on the ?pptrf result.
	?trtri	s, d, c, z	Computes the inverse matrix of an upper/lower triangular matrix.
Back substitution solution	?pttrs	s, d, c, z	Solves the tridiagonal equation AX = B, where the coefficient matrix A is the ?pttrf factorization result.
	?ptts2	s, d, c, z	Solves the tridiagonal equation AX = B, where the coefficient matrix A is the ?pttrf factorization result.
	?gttrs	s, d, c, z	Solves the tridiagonal equation A X = B, A^T X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.
	?gtts2	s, d, c, z	Solves the tridiagonal equation A X = B, A^T X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.
	?trtrs	s, d, c, z	Solves the trigonometric equation A X = B* or A^T * X = B.
	?getrs	s, d, c, z	Solves the general linear equation AX = B, where the coefficient matrix A is the ?getrf factorization result.
	?pptrs	s, d, c, z	Solves packed symmetric positive definite linear equation AX = B, where the coefficient matrix A is the ?pptrf factorization result.
Eigenvalue problem solving	?(sy/he)evd	s, d, c, z	Computes the eigenvalues and eigenvectors of a real symmetric (Hermitian) matrix. The eigenvectors are computed using a divide and conquer algorithm.
	?(sy/he)ev	s, d, c, z	Computes the eigenvalues and eigenvectors of a real symmetric (Hermitian) matrix.
	?steqr	s, d, c, z	Computes the eigenvalues and eigenvectors of a symmetric tridiagonal matrix through QL or QR factorization.
	?stedc	s, d, c, z	Computes the eigenvalues of a symmetric (Hermitian) tridiagonal matrix through the Divide-and-Conquer algorithm.
	?sy(he)evx	s, d, c, z	Computes eigenvalues and (optional) eigenvectors of a symmetric (Hermitian) matrix within a specified range.
	?sy(he)gv	s, d, c, z	Computes all the eigenvalues and (optional) eigenvectors of a generalized eigenvalue problem.
	?geev	s, d, c, z	Computes some eigenvalues and eigenvectors of a general matrix.
Singular value problem solving	?gesvd	s, d, c, z	Performs SVD factorization on a general matrix.
	?gebrd	s, d, c, z	Transforms a general matrix to a two-diagonal matrix.
	?bdsdc	s, d	Performs SVD factorization on a two-diagonal matrix through the Divide-and-Conquer algorithm.
	?gesdd	s, d, c, z	Performs SVD factorization on a general matrix through the Divide-and-Conquer algorithm.
	?bdsqr	s, d	Performs SVD factorization on a two-diagonal matrix.
Least squares solution	?gels	s, d, c, z	Use QR or LQ factorization to solve an overdetermined or underdetermined linear system with full rank matrix.
	?gelss	s, d, c, z	Computes the minimum-norm solution to a linear least squares problem using SVD.
	?gelsd	s, d, c, z	Computes the minimum-norm solution to a linear least squares problem using a divide and conquer method.
Others	?(or,un)glq	s, d, c, z	Generates a real or complex matrix Q with orthonormal rows, where H for calculating Q is obtained by calling ?gelqf.
	?(or,un)gqr	s, d, c, z	Generates a real or complex matrix Q with orthonormal rows, where H for calculating Q is obtained by calling ?geqrf.
	?(or,un)grq	s, d, c, z	Generates a real or complex matrix Q with orthonormal rows, where H for calculating Q is obtained by calling ?gerqf.
	?(or,un)gql	s, d, c, z	Generates a real or complex matrix Q with orthonormal columns, where H for calculating Q is obtained by calling ?geqlf.
	?(or,un)mlq	s, d, c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?gelqf. Q^* can be Q^T or Q^H.
	?(or,un)mqr	s, d, c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?geqrf. Q^* can be Q^T or Q^H.
	?(or,un)mql	s, d, c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?geqlf. Q^* can be Q^T or Q^H.
	?(or,un)mrq	s, d, c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?gerqf. Q^* can be Q^T or Q^H.
	?sy(he)trd	s, d, c, z	Transforms a symmetric or Hermitian matrix to symmetric tridiagonal matrix T by means of similarity transformation.
	?sy(he)trd_2stage	s, d, c, z	Transforms symmetric matrix A to symmetric tridiagonal matrix T. That is, A^T * A * Q = T, where Q is an orthogonal matrix.
	?lasr	s, d, c, z	Performs a plane rotation operation on matrix A.
	?(or,un)mbr	s, d, c, z	Computes QC, Q^TC, CQ, CQ^T, PC, P^TC, CP, or CP^T, where Q and P^T are orthogonal matrices computed by a call to GEBRD, that is, A=QBP^T.
	?(or,un)gtr	s, d, c, z	Generates an orthogonal matrix Q through reflector factors computed by a call to SYTRD.
	Kml?steqr2	s, d	Computes all eigenvalues and optional eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.
	KmlBlockBandedMatrixSolve	d	Solves a block-banded matrix with a block size of 5 and returns the matrix factorization result.
	KmlBlockBandedMatrixSubstitude	d	Performs back substitution on the factorization result of a block-banded matrix with a block size of 5.
Auxiliary functions	?laset	s, d, c, z	Initializes an mn matrix and sets the diagonal elements to beta* and the non-diagonal elements to alpha.
	?laswp	s, d, c, z	Perform a series of row exchange operations on a matrix.
	?lascl	s, d, c, z	Performs scalar operations on a matrix.
	?lange	s, d, c, z	Computes the norms of a matrix (including 1-norm, F-norm, and infinite norm).
	?lacpy	s, d, c, z	Copies all or some elements of matrix A to matrix B.
Mixed-precision solution of linear equation systems	?gesv	zc, ds	Uses mixed-precision methods to solve general linear equations.

Parent topic: Function Syntax