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ScaLAPACK and BLACS

Introduction

ScaLAPACK (Scalable Linear Algebra PACKage) is a library of high-performance linear algebra routines for distributed-memory message passing computers. ScaLAPACK has routines for systems of linear equations, linear least squares problems, eigenvalue calculation, and singular value decomposition. ScaLAPACK can also handle many associated computations such as matrix factorization or estimating condition numbers. Dense and band matrices are supported, but not general sparse matrices. Similar functionality is provided for both real and complex matrices.

As in LAPACK, the ScaLAPACK routines are based on block-partitioned algorithms, in order to minimize data movement. The fundamental building block of the ScaLAPACK library is a distributed memory version of the Level 1, 2, and 3 BLAS, called PBLAS (Parallel BLAS). The PBLAS are, in turn, built on the BLAS for computation on a single node, and on BLACS for communication across nodes. PBLAS is an integral part of the ScaLAPACK library.

BLACS (Basic Linear Algebra Communication Subprograms) are a message-passing library designed for linear algebra. The computational model consists of a one- or two-dimensional process grid, where each process stores pieces of the matrices and vectors. The BLACS include synchronous send/receive routines to communicate a matrix or submatrix from one process to another, to broadcast submatrices to many processes, or to compute global data reductions (sums, maxima and minima). There are also routines to construct, change, or query the process grid. Since several ScaLAPACK algorithms require broadcasts or reductions among different subsets of processes, the BLACS permit a process to be a member of several overlapping or disjoint process grids, each one labeled by a context. In MPI this is called a communicator. The BLACS provide facilities for safe inter-operation of system contexts and BLACS contexts.

How to use ScaLAPACK and BLACS

• The ScaLAPACK, PBLAS and BLACS Routine Lists contain one-line summaries for subprograms in ScaLAPACK, PBLAS, and BLACS, respectively.
• For additional user interface information, see the ScaLAPACK User's Guide [1] and the ScaLAPACK, PBLAS and BLACS Quick References [2][3][4].
• Compiling and Linking tells how to compile and link with the ScaLAPACK and BLACS library.

ScaLAPACK Routine List

Simple Driver and Divide and Conquer Driver Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
P?DBSV PSDBSV PDDBSV PCDBSV PZDBSV	S D C Z	Solves a general banded system of linear equations AX=B with no pivoting.
P?DTSV PSDTSV PDDTSV PCDTSV PZDTSV	S D C Z	Solves a general tridiagonal system of linear equations AX=B with no pivoting.
P?GBSV PSGBSV PDGBSV PCGBSV PZGBSV	S D C Z	Solves a general banded system of linear equations AX=B.
P?GELS PSGELS PDGELS PCGELS PZGELS	S D C Z	Solves over-determined or under-determined linear systems involving a matrix of full rank.
P?GESV PSGESV PDGESV PCGESV PZGESV	S D C Z	Solves a general system of linear equations AX=B.
P?GESVD PSGESVD PDGESVD PCGESVD PZGESVD	S D C Z	Computes the singular value decomposition of a general matrix, optionally computing the left and/or right singular vectors.
P?PBSV PSPBSV PDPBSV PCPBSV PZPBSV	S D C Z	Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B.
P?POSV PSPOSV PDPOSV PCPOSV PZPOSV	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B.
P?PTSV PSPTSV PDPTSV PCPTSV PZPTSV	S D C Z	Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B.
P?SYEV PSSYEV PDSYEV	S D	Computes selected eigenvalues and eigenvectors of a symmetric matrix.
P?SYEVD PSSYEVD PDSYEVD	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
P?HEEV PCHEEV PZHEEV	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix.
P?HEEVD PCHEEVD PZHEEVD	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
P?HSEQR PSHSEQR PDHSEQR	S D	Computes the eigenvalues of an upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z*T*ZT, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors.

Expert Driver and RRR Driver Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
P?GESVX PSGESVX PDGESVX PCGESVX PZGESVX	S D C Z	Solves a general system of linear equations AX=B.
P?POSVX PSPOSVX PDPOSVX PCPOSVX PZPOSVX	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B.
P?SYEVX PSSYEVX PDSYEVX	S D	Computes selected eigenvalues and eigenvectors of a symmetric matrix.
P?SYEVR PSSYEVR PDSYEVR	S D	Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A distributed in 2D blockcyclic format by calling the recommended sequence of ScaLAPACK routines.
P?SYGVX PSSYGVX PDSYGVX	S D	Computes selected eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem.
P?HEEVX PCHEEVX PZHEEVX	C Z	Computes selected eigenvalues and eigenvectors of a Hermitian matrix.
P?HEEVR PCHEEVR PZHEEVR	C Z	Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A distributed in 2D blockcyclic format by calling the recommended sequence of ScaLAPACK routines.
P?HEGVX PCHEGVX PZHEGVX	C Z	Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem.

Computational Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
P?DBTRF PSDBTRF PDDBTRF PCDBTRF PZDBTRF	S D C Z	Computes an LU factorization of a general band matrix with no pivoting.
P?DBTRS PSDBTRS PDDBTRS PCDBTRS PZDBTRS	S D C Z	Solves a general banded system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?DBTRF.
P?DBTRSV PSDBTRSV PDDBTRSV PCDBTRSV PZDBTRSV	S D C Z	Solves a banded triangular system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?DBTRF.
P?DTTRF PSDTTRF PDDTTRF PCDTTRF PZDTTRF	S D C Z	Computes an LU factorization of a general tridiagonal matrix with no pivoting.
P?DTTRS PSDTTRS PDDTTRS PCDTTRS PZDTTRS	S D C Z	Solves a general tridiagonal system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?DTTRF.
P?DTTRSV PSDTTRSV PDDTTRSV PCDTTRSV PZDTTRSV	S D C Z	Solves a tridiagonal triangular system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?DTTRF.
P?GBTRF PSGBTRF PDGBTRF PCGBTRF PZGBTRF	S D C Z	Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges.
P?GBTRS PSGBTRS PDGBTRS PCGBTRS PZGBTRS	S D C Z	Solves a general banded system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?GBTRF.
P?GEBRD PSGEBRD PDGEBRD PCGEBRD PZGEBRD	S D C Z	Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/unitary transformation.
P?GECON PSGECON PDGECON PCGECON PZGECON	S D C Z	Estimates the reciprocal of the condition number of a general matrix.
P?GEEQU PSGEEQU PDGEEQU PCGEEQU PZGEEQU	S D C Z	Computes row and column scalings to equilibrate a general rectangular matrix and reduce its condition number.
P?GEHRD PSGEHRD PDGEHRD PCGEHRD PZGEHRD	S D C Z	Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation.
P?GELQF PSGELQF PDGELQF PCGELQF PZGELQF	S D C Z	Computes an LQ factorization of a general rectangular matrix.
P?GEQLF PSGEQLF PDGEQLF PCGEQLF PZGEQLF	S D C Z	Computes a QL factorization of a general rectangular matrix.
P?GEQPF PSGEQPF PDGEQPF PCGEQPF PZGEQPF	S D C Z	Computes a QR factorization with column pivoting of a general rectangular matrix.
P?GEQRF PSGEQRF PDGEQRF PCGEQRF PZGEQRF	S D C Z	Computes a QR factorization of a general rectangular matrix.
P?GERFS PSGERFS PDGERFS PCGERFS PZGERFS	S D C Z	Improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions.
P?GERQF PSGERQF PDGERQF PCGERQF PZGERQF	S D C Z	Computes an RQ factorization of a general rectangular matrix.
P?GETRF PSGETRF PDGETRF PCGETRF PZGETRF	S D C Z	Computes an LU factorization of a general matrix, using partial pivoting with row interchanges.
P?GETRI PSGETRI PDGETRI PCGETRI PZGETRI	S D C Z	Computes the inverse of a general matrix, using the LU factorization computed by P?GETRF.
P?GETRS PSGETRS PDGETRS PCGETRS PZGETRS	S D C Z	Solves a general system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by P?GETRF.
P?GGQRF PSGGQRF PDGGQRF PCGGQRF PZGGQRF	S D C Z	Computes a generalized QR factorization.
P?GGRQF PSGGRQF PDGGRQF PCGGRQF PZGGRQF	S D C Z	Computes a generalized RQ factorization.
P?LAHQR PSLAHQR PDLAHQR PCLAHQR PZLAHQR	S D C Z	Computes the Schur decomposition and/or eigenvalues of a matrix already in Hessenberg form.
P?ORGLQ PSORGLQ PDORGLQ	S D	Generates all or part of the orthogonal matrix Q from an LQ factorization determined by PSGELQF.
P?ORGQL PSORGQL PDORGQL	S D	Generates all or part of the orthogonal matrix Q from a QL factorization determined by PSGEQLF.
P?ORGQR PSORGQR PDORGQR	S D	Generates all or part of the orthogonal matrix Q from a QR factorization determined by PSGEQRF.
P?ORGRQ PSORGRQ PDORGRQ	S D	Generates all or part of the orthogonal matrix Q from an RQ factorization determined by PSGERQF.
P?ORMBR PSORMBR PDORMBR	S D	Multiplies a general matrix by one of the orthogonal transformation matrices from a reduction to bidiagonal form determined by PSGEBRD.
P?ORMHR PSORMHR PDORMHR	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to Hessenberg form determined by PSGEHRD.
P?ORMLQ PSORMLQ PDORMLQ	S D	Multiplies a general matrix by the orthogonal matrix from an LQ factorization determined by PSGELQF.
P?ORMQL PSORMQL PDORMQL	S D	Multiplies a general matrix by the orthogonal matrix from a QL factorization determined by PSGEQLF.
P?ORMQR PSORMQR PDORMQR	S D	Multiplies a general matrix by the orthogonal matrix from a QR factorization determined by PSGEQRF.
P?ORMRQ PSORMRQ PDORMRQ	S D	Multiplies a general matrix by the orthogonal matrix from an RQ factorization determined by PSGERQF.
P?ORMRZ PSORMRZ PDORMRZ	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to upper triangular form determined by PSTZRZF.
P?ORMTR PSORMTR PDORMTR	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form determined by PSSYTRD.
P?PBTRF PSPBTRF PDPBTRF PCPBTRF PZPBTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite banded matrix.
P?PBTRS PSPBTRS PDPBTRS PCPBTRS PZPBTRS	S D C Z	Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B, using the Cholesky factorization computed by P?PBTRF.
P?PBTRSV PSPBTRSV PDPBTRSV PCPBTRSV PZPBTRSV	S D C Z	Solves a banded triangular system of linear equations AX=B, using the Cholesky factorization computed by P?PBTRF.
P?POCON PSPOCON PDPOCON PCPOCON PZPOCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite distributed matrix.
P?POEQU PSPOEQU PDPOEQU PCPOEQU PZPOEQU	S D C Z	Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix and reduce its condition number.
P?PORFS PSPORFS PDPORFS PCPORFS PZPORFS	S D C Z	Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations AX=B, and provides forward and backward error bounds for the solution.
P?POTRF PSPOTRF PDPOTRF PCPOTRF PZPOTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix.
P?POTRI PSPOTRI PDPOTRI PCPOTRI PZPOTRI	S D C Z	Computes the inverse of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by P?POTRF.
P?POTRS PSPOTRS PDPOTRS PCPOTRS PZPOTRS	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, using the Cholesky factorization computed by P?POTRF.
P?PTTRF PSPTTRF PDPTTRF PCPTTRF PZPTTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite tridiagonal matrix.
P?PTTRS PSPTTRS PDPTTRS PCPTTRS PZPTTRS	S D C Z	Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B, using the Cholesky factorization computed by P?PTTRF.
P?PTTRSV PSPTTRSV PDPTTRSV PCPTTRSV PZPTTRSV	S D C Z	Solves a tridiagonal triangular system of linear equations AX=B, using the Cholesky factorization computed by P?PTTRF.
P?STEBZ PSSTEBZ PDSTEBZ	S D	Computes the eigenvalues of a symmetric/Hermitian tridiagonal matrix by bisection.
P?STEDC PSSTEDC PDSTEDC	S D	Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer algorithm.
P?STEIN PSSTEIN PDSTEIN PCSTEIN PZSTEIN	S D C Z	Computes the eigenvectors of a symmetric/Hermitian tridiagonal matrix using inverse iteration.
P?SYGST PSSYGST PDSYGST	S D	Reduces a symmetric-definite generalized eigenproblem to standard form.
P?SYTRD PSSYTRD PDSYTRD	S D	Reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.
P?TRCON PSTRCON PDTRCON PCTRCON PZTRCON	S D C Z	Estimates the reciprocal of the condition number of a triangular matrix.
P?TRRFS PSTRRFS PDTRRFS PCTRRFS PZTRRFS	S D C Z	Provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix.
P?TRTRI PSTRTRI PDTRTRI PCTRTRI PZTRTRI	S D C Z	Computes the inverse of a triangular matrix.
P?TRTRS PSTRTRS PDTRTRS PCTRTRS PZTRTRS	S D C Z	Solves a triangular system of linear equations AX=B, ATX=B or AHX=B.
P?TZRZF PSTZRZF PDTZRZF PCTZRZF PZTZRZF	S D C Z	Reduces an upper trapezoidal matrix to upper triangular form by means of orthogonal transformations.
P?HEGST PCHEGST PZHEGST	C Z	Reduces a Hermitian-definite generalized eigenproblem to standard form.
P?HETRD PCHETRD PZHETRD	C Z	Reduces a Hermitian matrix to Hermitian tridiagonal form by a unitary similarity transformation.
P?UNGLQ PCUNGLQ PZUNGLQ	C Z	Generates all or part of the unitary matrix Q from an LQ factorization determined by PCGELQF.
P?UNGQL PCUNGQL PZUNGQL	C Z	Generates all or part of the unitary matrix Q from a QL factorization determined by PCGEQLF.
P?UNGQR PCUNGQR PZUNGQR	C Z	Generates all or part of the unitary matrix Q from a QR factorization determined by PCGEQRF.
P?UNGRQ PCUNGRQ PZUNGRQ	C Z	Generates all or part of the unitary matrix Q from an RQ factorization determined by PCGERQF.
P?UNMBR PCUNMBR PZUNMBR	C Z	Multiplies a general matrix by one of the unitary transformation matrices from a reduction to bidiagonal form determined by PCGEBRD.
P?UNMHR PCUNMHR PZUNMHR	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to Hessenberg form determined by PCGEHRD.
P?UNMLQ PCUNMLQ PZUNMLQ	C Z	Multiplies a general matrix by the unitary matrix from an LQ factorization determined by PCGELQF.
P?UNMQL PCUNMQL PZUNMQL	C Z	Multiplies a general matrix by the unitary matrix from a QL factorization determined by PCGEQLF.
P?UNMQR PCUNMQR PZUNMQR	C Z	Multiplies a general matrix by the unitary matrix from a QR factorization determined by PCGEQRF.
P?UNMRQ PCUNMRQ PZUNMRQ	C Z	Multiplies a general matrix by the unitary matrix from an RQ factorization determined by PCGERQF.
P?UNMRZ PCUNMRZ PZUNMRZ	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to upper triangular form determined by PCTZRZF.
P?UNMTR PCUNMTR PZUNMTR	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by PCHETRD.
B?LAAPP BSLAAPP BDLAAPP	S D	Computes B = QT * A or B = A * Q, where A is an M-by-N matrix and Q is an orthogonal matrix represented by the parameters in the arrays ITRAF and DTRAF as described in BDTREXC.
B?LAEXC BSLAEXC BDLAEXC	S D	Swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation.
B?TREXC BSTREXC BDTREXC	S D	Reorders the real Schur factorization of a real matrix A = Q*T*QT, so that the diagonal block of T with row index IFST is moved to row ILST.
?LAQR6 SLAQR6 DLAQR6	S D	Performs a single small-bulge multi-shift QR sweep, moving the chain of bulges from top to bottom in the submatrix H(KTOP:KBOT,KTOP:KBOT), collecting the transformations in the matrix HV *or* accumulating the transformations in the matrix Z (see below).
?LAR1VA SLAR1VA DLAR1VA	S D	Computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix LDLT - σI.
?LARRB2 SLARRB2 DLARRB2	S D	Does "limited" bisection to refine the eigenvalues of LDLT, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy.
?LARRD2 SLARRD2 DLARRD2	S D	Computes the eigenvalues of a symmetric tridiagonal matrix T to limited initial accuracy.
?LARRE2 SLARRE2 DLARRE2	S D	To find the desired eigenvalues of a given real symmetric tridiagonal matrix T, DLARRE2 sets, via DLARRA, "small" off-diagonal elements to zero.
?LARRE2A SLARRE2A DLARRE2A	S D	To find the desired eigenvalues of a given real symmetric tridiagonal matrix T, DLARRE2 sets any "small" off-diagonal elements to zero, and for each unreduced block T_i.
?LARRF2 SLARRF2 DLARRF2	S D	Finds a new relatively robust representation LDLT - SIGMA I = L(+) D(+) L(+)T such that at least one of the eigenvalues of L(+) D(+) L(+)T is relatively isolated.
?LARRV2 SLARRV2 DLARRV2	S D	Computes the eigenvectors of the tridiagonal matrix T = LDLT given L, D and APPROXIMATIONS to the eigenvalues of LDLT.
?STEGR2 SSTEGR2 DSTEGR2	S D	Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T.
?STEGR2A SSTEGR2A DSTEGR2A	S D	DSTEGR2A computes selected eigenvalues and initial representations needed for eigenvector computations in DSTEGR2B.
?STEGR2B SSTEGR2B DSTEGR2B	S D	Computes the selected eigenvalues and eigenvectors of the real symmetric tridiagonal matrix in parallel on multiple processors.
P?GEBAL PSGEBAL PDGEBAL	S D	Balances a general real matrix A.
P?LAMVE PSLAMVE PDLAMVE	S D	Copies all or part of a distributed matrix A to another distributed matrix B.
P?LAQR0 PSLAQR0 PDLAQR0	S D	Computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z*T*ZT, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors.
P?LAQR1 PSLAQR1 PDLAQR1	S D	Find the Schur decomposition and or eigenvalues of a matrix already in Hessenberg form from cols ILO to IHI.
P?LAQR2 PSLAQR2 PDLAQR2	S D	Accepts as input an upper Hessenberg matrix A and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix.
P?LAQR3 PSLAQR3 PDLAQR3	S D	Accepts as input an upper Hessenberg matrix H and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix.
P?LAQR4 PSLAQR4 PDLAQR4	S D	Find the Schur decomposition and or eigenvalues of a matrix already in Hessenberg form from cols ILO to IHI.
P?LAQR5 PSLAQR5 PDLAQR5	S D	Performs a single small-bulge multi-shift QR sweep by chasing separated groups of bulges along the main block diagonal of H.
P?ROT PSROT PDROT	S D	Applies a planar rotation defined by CS and SN to the two distributed vectors sub(X) and sub(Y).
P?TRORD PSTRORD PDTRORD	S D	Reorders the real Schur factorization of a real matrix A = Q*T*QT, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.
P?TRSEN PSTRSEN PDTRSEN	S D	Reorders the real Schur factorization of a real matrix A = Q*T*QT, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.
PILAENVX		Choose problem-dependent parameters for the local environment.
PILAVER		Return the ScaLAPACK version.
PIPARMQ		Sets problem and machine dependent parameters useful for PxHSEQR and its subroutines.

Auxiliary Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Prefixes	Routine†
S D C Z	?DBTF2 SDBTF2 DDBTF2 CDBTF2 ZDBTF2 ?DBTRF SDBTRF DDBTRF CDBTRF ZDBTRF ?DTTRF SDTTRF DDTTRF CDTTRF ZDTTRF ?DTTRSV SDTTRSV DDTTRSV CDTTRSV ZDTTRSV ?LAMSH SLAMSH DLAMSH CLAMSH ZLAMSH ?LAREF SLAREF DLAREF CLAREF ZLAREF ?PTTRSV SPTTRSV DPTTRSV CPTTRSV ZPTTRSV ?STEQR2 SSTEQR2 DSTEQR2 CSTEQR2 ZSTEQR2 ?TRMVT STRMVT DTRMVT CTRMVT ZTRMVT P?GEBD2 PSGEBD2 PDGEBD2 PCGEBD2 PZGEBD2 P?GEHD2 PSGEHD2 PDGEHD2 PCGEHD2 PZGEHD2 P?GELQ2 PSGELQ2 PDGELQ2 PCGELQ2 PZGELQ2 P?GEQL2 PSGEQL2 PDGEQL2 PCGEQL2 PZGEQL2 P?GEQR2 PSGEQR2 PDGEQR2 PCGEQR2 PZGEQR2 P?GERQ2 PSGERQ2 PDGERQ2 PCGERQ2 PZGERQ2 P?GETF2 PSGETF2 PDGETF2 PCGETF2 PZGETF2 P?LABRD PSLABRD PDLABRD PCLABRD PZLABRD P?LACON PSLACON PDLACON PCLACON PZLACON P?LACONSB PSLACONSB PDLACONSB PCLACONSB PZLACONSB P?LACP2 PSLACP2 PDLACP2 PCLACP2 PZLACP2 P?LACP3 PSLACP3 PDLACP3 PCLACP3 PZLACP3 P?LACPY PSLACPY PDLACPY PCLACPY PZLACPY P?LAEVSWP PSLAEVSWP PDLAEVSWP PCLAEVSWP PZLAEVSWP P?LAHRD PSLAHRD PDLAHRD PCLAHRD PZLAHRD P?LAMR1D PSLAMR1D PDLAMR1D PCLAMR1D PZLAMR1D P?LANGE PSLANGE PDLANGE PCLANGE PZLANGE P?LANHS PSLANHS PDLANHS PCLANHS PZLANHS P?LANSY PSLANSY PDLANSY PCLANSY PZLANSY P?LANTR PSLANTR PDLANTR PCLANTR PZLANTR P?LAPIV PSLAPIV PDLAPIV PCLAPIV PZLAPIV P?LAPV2 PSLAPV2 PDLAPV2 PCLAPV2 PZLAPV2 P?LAQGE PSLAQGE PDLAQGE PCLAQGE PZLAQGE P?LAQSY PSLAQSY PDLAQSY PCLAQSY PZLAQSY P?LARF PSLARF PDLARF PCLARF PZLARF P?LARFB PSLARFB PDLARFB PCLARFB PZLARFB P?LARFG PSLARFG PDLARFG PCLARFG PZLARFG P?LARFT PSLARFT PDLARFT PCLARFT PZLARFT P?LARZ PSLARZ PDLARZ PCLARZ PZLARZ P?LARZB PSLARZB PDLARZB PCLARZB PZLARZB P?LARZT PSLARZT PDLARZT PCLARZT PZLARZT P?LASCL PSLASCL PDLASCL PCLASCL PZLASCL P?LASE2 PSLASE2 PDLASE2 PCLASE2 PZLASE2 P?LASET PSLASET PDLASET PCLASET PZLASET P?LASMSUB PSLASMSUB PDLASMSUB PCLASMSUB PZLASMSUB P?LASSQ PSLASSQ PDLASSQ PCLASSQ PZLASSQ P?LASWP PSLASWP PDLASWP PCLASWP PZLASWP P?LATRA PSLATRA PDLATRA PCLATRA PZLATRA P?LATRD PSLATRD PDLATRD PCLATRD PZLATRD P?LATRS PSLATRS PDLATRS PCLATRS PZLATRS P?LATRZ PSLATRZ PDLATRZ PCLATRZ PZLATRZ P?LAUU2 PSLAUU2 PDLAUU2 PCLAUU2 PZLAUU2 P?LAUUM PSLAUUM PDLAUUM PCLAUUM PZLAUUM P?LAWIL PSLAWIL PDLAWIL PCLAWIL PZLAWIL P?POTF2 PSPOTF2 PDPOTF2 PCPOTF2 PZPOTF2 P?TRTI2 PSTRTI2 PDTRTI2 PCTRTI2 PZTRTI2
S D CS ZD	P?RSCL PSRSCL PDRSCL PCSRSCL PZDRSCL
S D	?LAPST SLAPST DLAPST ?LASORTE SLASORTE DLASORTE ?LASRT2 SLASRT2 DLASRT2 ?STEIN2 SSTEIN2 DSTEIN2 P?LABAD PSLABAD PDLABAD P?LAED0 PSLAED0 PDLAED0 P?LAED1 PSLAED1 PDLAED1 P?LAED2 PSLAED2 PDLAED2 P?LAED3 PSLAED3 PDLAED3 P?LAEDZ PSLAEDZ PDLAEDZ P?LAMCH PSLAMCH PDLAMCH P?LARED1D PSLARED1D PDLARED1D P?LARED2D PSLARED2D PDLARED2D P?LASRT PSLASRT PDLASRT P?ORG2L PSORG2L PDORG2L P?ORG2R PSORG2R PDORG2R P?ORGL2 PSORGL2 PDORGL2 P?ORGR2 PSORGR2 PDORGR2 P?ORM2L PSORM2L PDORM2L P?ORM2R PSORM2R PDORM2R P?ORML2 PSORML2 PDORML2 P?ORMR2 PSORMR2 PDORMR2 P?ORMR3 PSORMR3 PDORMR3 P?SYGS2 PSSYGS2 PDSYGS2 P?SYNGST PSSYNGST PDSYNGST P?SYNTRD PSSYNTRD PDSYNTRD P?SYTD2 PSSYTD2 PDSYTD2 P?SYTTRD PSSYTTRD PDSYTTRD
C Z	?LAHQR2 CLAHQR2 ZLAHQR2 ?LANV2 CLANV2 ZLANV2 P?HEGS2 PCHEGS2 PZHEGS2 P?HENGST PCHENGST PZHENGST P?HENTRD PCHENTRD PZHENTRD P?HETD2 PCHETD2 PZHETD2 P?HETTRD PCHETTRD PZHETTRD P?LACGV PCLACGV PZLACGV P?LANHE PCLANHE PZLANHE P?LARFC PCLARFC PZLARFC P?LARZC PCLARZC PZLARZC P?LATTRS PCLATTRS PZLATTRS P?MAX1 PCMAX1 PZMAX1 P?TREVC PCTREVC PZTREVC P?UNG2L PCUNG2L PZUNG2L P?UNG2R PCUNG2R PZUNG2R P?UNGL2 PCUNGL2 PZUNGL2 P?UNGR2 PCUNGR2 PZUNGR2 P?UNM2L PCUNM2L PZUNM2L P?UNM2R PCUNM2R PZUNM2R P?UNML2 PCUNML2 PZUNML2 P?UNMR2 PCUNMR2 PZUNMR2 P?UNMR3 PCUNMR3 PZUNMR3
SC DZ	P?SUM1 PSCSUM1 PDZSUM1
n/a	PJLAENV PMPCOL PMPIM2

PBLAS Routine List

^† ?  indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

	Name†	Prefixes	Description
Level 1	P?SWAP	S D C Z	Swap vectors
	P?SCAL	S D C Z CS ZD	Scale vector
	P?COPY	S D C Z	Copy vector
	P?AXPY	S D C Z	Vector scale and add
	P?DOT	S D	Dot product, real
	P?DOTU	C Z	Dot product, complex
	P?DOTC	C Z	Dot product, complex, conjugate first vector
	P?NRM2	S D SC DZ	Euclidean norm
	P?ASUM	S D SC DZ	Sum absolute values
	PI?AMAX	S D C Z	Index of maximum absolute value
Level 2	P?GEMV	S D C Z	General matrix-vector multiplication
	P?HEMV	C Z	Hermitian matrix-vector multiplication
	P?SYMV	S D C Z	Symmetric matrix-vector multiplication
	P?TRMV	S D C Z	Triangular matrix-vector multiplication
	P?TRSV	S D C Z	Triangular solve
	P?GER	S D	General rank-1 update, real
	P?GERU	C Z	General rank-1 update, complex
	P?GERC	C Z	General rank-1 update, complex, second vector conjugate
	P?HER	C Z	Hermitian rank-1 update
	P?HER2	C Z	Hermitian rank-2 update
	P?SYR	S D	Symmetric rank-1 update
	P?SYR2	S D	Symmetric rank-2 update
Level 3	P?GEMM	S D C Z	General matrix-matrix multiplication
	P?SYMM	S D C Z	Symmetric matrix-matrix multiplication
	P?HEMM	C Z	Hermitian matrix-matrix multiplication
	P?SYRK	S D C Z	Symmetric rank-k update
	P?HERK	C Z	Hermitian rank-k update
	P?SYR2K	S D C Z	Symmetric rank-2k update
	P?HER2K	C Z	Hermitian rank-2k update
	P?TRAN	S D	Matrix transpose, real
	P?TRANU	C Z	Matrix transpose, complex
	P?TRANC	C Z	Matrix transpose, complex, conjugate
	P?TRMM	S D C Z	Triangular matrix-matrix multiply
	P?TRSM	S D C Z	Triangular solve

BLACS Routine List

^† ? indicates prefix which must be filled with a combination of:
s = REAL(kind=4), d = REAL(kind=8), c = COMPLEX(kind=4), z = COMPLEX(kind=8), i = INTEGER

	Name†	Prefixes	Description
Initialization	blacs_pinfo		Get initial system information that is required before BLACS is set up
	blacs_setup		Functionally equivalent to blas_pinfo
	blacs_get		Returns values BLACS is using for internal defaults
	blacs_set		Sets BLACS internal defaults
	blacs_gridinit		Assigns processors to BLACS process grid
	blacs_gridmap		Assigns processors to BLACS process grid in arbitrary manner
Destruction	blacs_freebuff		Releases BLACS buffer
	blacs_gridexit		Frees a BLACS context
	blacs_abort		Aborts all BLACS processes
	blacs_exit		Frees all BLACS contexts and allocated memory
Sending	?gesd2d	s d c z i	General send 2-d
	?gebs2d	s d c z i	General broadcast send 2-d
	?trsd2d	s d c z i	Trapezoidal send 2-d
	?trbs2d	s d c z i	Trapezoidal broadcast send 2-d
Receiving	?gerv2d	s d c z i	General receive
	?gebr2d	s d c z i	General broadcast receive
	?trrv2d	s d c z i	Trapezoidal receive
	?trbr2d	s d c z i	Trapezoidal broadcast receive
Combine	?gamx2d	s d c z i	General element-wise absolute value maximum
	?gamn2d	s d c z i	General element-wise absolute value minimum
	?gsum2d	s d c z i	General element-wise summation
Information and Miscellaneous	blacs_gridinfo		Returns information on BLACS grid
	blacs_pnum		Returns system process number
	blacs_pcoord		Returns rows and columns in the BLACS process grid
	blacs_barrier		Holds up execution of all processes till all processes call this routine
Non-Standard	dcputime00		Returns CPU seconds since arbitrary starting point
	dwalltime00		Returns wall clock seconds since arbitrary starting point
	ksendid		Returns BLACS message ID
	krecvid		Returns BLACS message ID for receive
	kbsid		Returns BLACS message ID for source
	kbrid		Returns BLACS message ID for destination in broadcast

External Links

1. ScaLAPACK User's Guide
2. ScaLAPACK Quick Reference (downloading a PostScript format file)
3. PBLAS Quick Reference
4. BLACS Quick Reference
5. A hardcopy ScaLAPACK User's Guide may be ordered from SIAM.

Version Information

• This manual page version: 2.2.0-180823