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	Computes the LU factorization of general tridiagonal matrix A.
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 the 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.
Matrix inversion	?getri	s, d, c, z	Computes the inverse matrix based on the ?getrf result.
Matrix inversion	?potri	s, d, c, z	Computes the inverse matrix based on the ?potrf result.
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 a system of linear equations with a tridiagonal matrix A * X = B, A^T * X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.
Eigenvalue problem solving	?sy(he)evd	s, d, c, z	Computes the eigenvalues and eigenvectors of a real symmetric or Hermitian matrix. The eigenvectors are computed using a division and conquer algorithm.
Eigenvalue problem solving	?sy(he)ev	s, d, c, z	Computes the eigenvalues and eigenvectors of a real symmetric or Hermitian matrix.
Others	?(or,un)glq	s, d, c, z	Generates a real or complex matrix Q with orthogonal 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 orthogonal 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 orthogonal 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 orthogonal columns, where H for calculating Q is obtained by calling ?geqlf.
	?(or,un)mlq	s, d, c, z	Calculates $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?gelqf. Q^* can be Q^T or Q^H.
	?(or,un)mqr	s, d, c, z	Calculates $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?geqrf. Q^* can be Q^T or Q^H.
	?(or,un)mql	s, d, c, z	Calculates $\text{[math]}$ or $\text{[math]}$ , where Q is returned by ?geqlf. Q^* can be Q^T or Q^H.
	?(or,un)mrq	s, d, c, z	Calculates $\text{[math]}$ 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 form T by means of similarity transformation.
	?sy(he)trd_2stage	s, d, c, z	Transforms a symmetric matrix to symmetric tridiagonal. 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.

Parent topic: Function Syntax