Function List

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
General Banded Computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. SGBTRF CGBTRF DGBTRF ZGBTRF
Positive Definite Banded Computes the Cholesky factorization of a real symmetric positive definite band matrix A. SPBTRF CPBTRF DPBTRF ZPBTRF

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
Computes a QR factorization of a general rectangular matrix, avoiding denorms. SGEQRFP CGEQRFP DGEQRFP ZGEQRFP
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:

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

Auxiliary Routines

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

Single Precision
Double Precision
Type
Description
Real
Complex
Real
Complex
General Copies all or part of a two-dimensional matrix to another matrix. SLACPY CLACPY DLACPY ZLACPY
Converts a matrix to a higher or lower precision. SLAG2D CLAG2Z DLAG2S ZLAG2D
Applies a block reflector to a matrix. SLARFB CLARFB DLARFB ZLARFB
Generates an elementary reflector. SLARFG CLARFG DLARFG ZLARFG
Generates a vector of plane rotations. SLARGV CLARGV DLARGV ZLARGV
Applies a vector of plane rotations to a sequence of vectors. SLARTV CLARTV DLARTV ZLARTV
Multiplies a matrix by a scalar. SLASCL CLASCL DLASCL ZLASCL
Initialized a matrix with one value on the diagonal and another value on the off-diagonals. SLASET CLASET DLASET ZLASET
Applies a sequence of plane rotations to a matrix. SLASR CLASR DLASR ZLASR
Symmetric Applies a vector of plane rotations to a sequence of matrices. SLAR2V CLAR2V DLAR2V ZLAR2V
Triangular Converts a triangular matrix to a higher or lower precision. SLAT2D CLAT2Z DLAT2S ZLAT2D

Unique Auxiliary Routines

CULA contains the following unique auxiliary routines:

Single Precision
Double Precision
Type
Description
Real
Complex
Real
Complex
General Conjugates each individual element in a matrix. - CGECONJUGATE - ZGECONJUGATE
Checks for NaN in matrix. SGENANCHECK CGENANCHECK DGENANCHECK ZGENANCHECK
Performs an out-of-place transpose from one matrix into another. SGETRANSPOSE CGETRANSPOSE DGETRANSPOSE ZGETRANSPOSE
Performs an out-of-place transpose from one matrix into another, additionally conjugating the off-diagonal elements. - CGETRANSPOSE_
CONJUGATE
- ZGETRANSPOSE_
CONJUGATE
Performs an in-place transpose of a matrix. SGETRANSPOSE CGETRANSPOSE DGETRANSPOSE ZGETRANSPOSE
Performs an in-place transpose of a matrix, additionally conjugating the off-diagonal elements. - CGETRANSPOSE_
CONJUGATE_
INPLACE
- ZGETRANSPOSE_
CONJUGATE_
INPLACE
Triangular Conjugates each individual element in a triangular matrix. - CTRCONJUGATE - ZTRCONJUGATE