Function List
Nonsymmetric Eigenproblems  Singular Value Decomposition
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, A^{T}X=B, or A^{H}X=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, A^{T}X=B, or A^{H}X=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 mbyn 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 overdetermined system of linear equations, AX=B, A^{T}X=B, or A^{H}X=B, or the minimum norm solution of an underdetermined 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 
NonSymmetric Eigenvalue Routines
CULA contains the following LAPACK function equivalents from the nonsymmetric 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 twodimensional 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 offdiagonals.  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 outofplace transpose from one matrix into another.  SGETRANSPOSE 
CGETRANSPOSE 
DGETRANSPOSE 
ZGETRANSPOSE 

Performs an outofplace transpose from one matrix into another, additionally conjugating the offdiagonal elements.   
CGETRANSPOSE_ 
 
ZGETRANSPOSE_ 

Performs an inplace transpose of a matrix.  SGETRANSPOSE 
CGETRANSPOSE 
DGETRANSPOSE 
ZGETRANSPOSE 

Performs an inplace transpose of a matrix, additionally conjugating the offdiagonal elements.   
CGETRANSPOSE_ 
 
ZGETRANSPOSE_ 

Triangular  Conjugates each individual element in a triangular matrix.   
CTRCONJUGATE 
 
ZTRCONJUGATE 