Optimized LAPACK Functions

Feature	Function Family	Data Type	Description
Matrix factorization	?getrf	s, d, c, z	Computes the LU factorization of the matrix, allowing row interchanges.
	?geqrf	s, d, c, z	Matrix QR factorization
	?potrf	s, d, c, z	Cholesky factorization of real symmetric or conjugate symmetric positive definite matrices.
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
Linear equation systems solving	?gesv	s, d, c, z	The system of linear equations is solved by the result of LU factorization.
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.
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 rows, 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.
	?he(sy)trd	s, d, c, z	Transforms a symmetric or Hermitian matrix to symmetric tridiagonal form T by means of similarity transformation.

Parent topic: Function Syntax