LAPACK Functions

This page contains the comprehensive function list of the CULAPACK linear algebra routines available in CULA and their LAPACK equivalents. For more details on specific routines, please see the CULA API Reference Manual available online and available for download.

Linear Equation Routines

CULA contains the following LAPACK function equivalents from the linear equations family of computational routines:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
General	Solves a general system of linear equations AX=B.	SGESV	CGESV	DGESV	ZGESV
	Solves a general system of linear equations AX=B with iterative refinement.	-	-	DSGESV	ZCGESV
	Computes an LU factorization of a general matrix, using partial pivoting with row interchanges.	SGETRF	CGETRF	DGETRF	ZGETRF
	Computes the inverse of a general matrix, using the LU factorization.	SGETRI	CGETRI	DGETRI	ZGETRI
	Solves a general system of linear equations AX=B, ATX=B, or AHX=B, using the LU factorization.	SGETRS	CGETRS	DGETRS	ZGETRS
Positive Definite	Solves a symmetric positive definite system of linear equations AX=B.	SPOSV	CPOSV	DPOSV	ZPOSV
	Computes the Cholesky factorization of a symmetric positive definite matrix.	SPOTRF	CPOTRF	DPOTRF	ZPOTRF
	Solves a symmetric positive definite system of linear equations AX=B, using the Cholesky factorization.	SPOTRS	CPOTRS	DPOTRS	ZPOTRS
Triangular	Solves a triangular system of linear equations AX=B, ATX=B, or AHX=B.	STRTRS	CTRTRS	DTRTRS	ZTRTRS
	Computes the inverse of a triangular matrix.	STRTRI	CTRTRI	DTRTRI	ZTRTRI

Orthogonal Factorizations

CULA contains the following LAPACK function equivalents from the orthogonal factorization family of computational routines:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
General, QR	Computes a QR factorization of a general rectangular matrix.	SGEQRF	CGEQRF	DGEQRF	ZGEQRF
	Generates all or part of the orthogonal matrix Q from a QR factorization.	SORGQR	CUNGQR	DORGQR	ZUNGQR
	Multiplies a general matrix by the orthogonal matrix from a QR factorization.	SORMQR	CUNMQR	DORMQR	ZUNMQR
General, LQ	Computes a LQ factorization of a general rectangular matrix.	SGELQF	CGELQF	DGELQF	ZGELQF
	Generates all or part of the orthogonal matrix Q from a LQ factorization.	SORLQR	CUNGLQ	DORGLQ	ZUNGLQ
	Multiplies a general matrix by the orthogonal matrix from a LQ factorization.	SORMLQ	CUNMLQ	DORMLQ	ZUNMLQ
General, RQ	Computes a RQ factorization of a general rectangular matrix.	SGERQF	CGERQF	DGERQF	ZGERQF
	Computes a generalized RQ factorization of a pair of matrices.	SGGRQF	CGGRQG	DGGRQF	ZGGRQF
	Generates all or part of the orthogonal matrix Q from a RQ factorization.	SORRQR	CUNGRQ	DORGRQ	ZUNGRQ
	Multiplies a general matrix by the orthogonal matrix from a RQ factorization.	SORMRQ	CUNMRQ	DORMRQ	ZUNMRQ
General, QL	Computes a QL factorization of a general rectangular matrix.	SGEQLF	CGEQLF	DGEQLF	ZGEQLF
	Generates all or part of the orthogonal matrix Q from a QL factorization.	SORQLR	CUNGQL	DORGQL	ZUNGQL
	Multiplies a general matrix by the orthogonal matrix from a QL factorization.	SORMQL	CUNMQL	DORMQL	ZUNMQL

Least Squares Routines

CULA contains the following LAPACK function equivalents from the least squares solver family of computational routines:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
General	Computes the least squares solution to an over-determined system of linear equations, AX=B, ATX=B, or AHX=B, or the minimum norm solution of an under-determined system, where A is a general rectangular matrix of full rank, using a QR or LQ factorization.	SGELS	CGELS	DGELS	ZGELS
	Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization.	SGGLSE	CGGLSE	DGGLSE	ZGGLSE

Symmetric Eigenvalue Routines

CULA contains the following LAPACK function equivalents from the symmetric Eigenproblem family of computational routines. Please note that the complex Eigenproblem routines will be added in a future release of CULA:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
Symmetric	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix	SSYEV	CHEEV	DSYEV	ZHEEV
	Computes selected eigenvalues and eigenvectors of a symmetric matrix.	SSYEVX	CHEEVX	DSYEVX	ZHEEVX
	Reduces a real symmetric matrix to tridiagonal form with Successive Bandwidth Reduction approach.	SSYRDB	CHERDB	DSYRDB	ZHERDB
Tridiagonal	Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection.	SSTEBZ	-	DSTEBZ	-
	Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm.	SSTEQR	CSTEQR	DSTEQR	ZSTEQR

Non-Symmetric Eigenvalue Routines

CULA contains the following LAPACK function equivalents from the non-symmetric Eigenproblem family of computational routines:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
General	Computes the eigenvalues and left and right eigenvectors of a general matrix.	SGEEV	CGEEV	DGEEV	ZGEEV
	Reduces a general matrix to upper Hessenberg form by an orthogonal similarity transformation.	SGEHRD	CGEHRD	DGEHRD	ZGEHRD
	Generates the orthogonal transformation matrix from a reduction to Hessenberg form.	SORGHR	CUNGHR	DORGHR	ZUNGHR

Singular Value Decomposition Routines

CULA contains the following LAPACK function equivalents from the Singular Value Decomposition family of computational routines:

		Single Precision		Double Precision
Type	Description	Real	Complex	Real	Complex
General	Computes the singular value decomposition (SVD) of a general rectangular matrix.	SGESVD	CGESVD	DGESVD	ZGESVD
	Reduces a general rectangular matrix to real bidiagonal form by an orthogonal transformation.	SGEBRD	CGEBRD	DGEBRD	ZGEBRD
	Generates the orthogonal transformation matrices from a reduction to bidiagonal form.	SORGBR	CUNGBR	DORGBR	ZORGBR
Bidiagonal	Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using the bidiagonal QR algorithm.	SBDSQR	CBDSQR	DBDSQR	ZBDSQR