ScaLAPACK Routines

In this appendix, we review the subroutine naming scheme for ScaLAPACK and indicate by means of a table which subroutines are included in this release. We also list the driver routines.

Each subroutine name in ScaLAPACK, which has an LAPACK equivalent, is simply the LAPACK name prepended by a P. All names consist of seven characters in the form PTXXYYY. The second letter, T, indicates the matrix data type as follows:

S 		 REAL 


D 		 DOUBLE PRECISION 


C 		 COMPLEX 


Z 		 COMPLEX*16 (if available)

The next two letters, XX, indicate the type of matrix. Most of these two-letter codes apply to both real and complex routines; a few apply specifically to one or the other, as indicated below:

DB 		  general band (diagonally-dominant like) 


DT 		  general tridiagonal (diagonally-dominant like) 


GB 		  general band 


GE 		  general (i.e. unsymmetric, in some cases rectangular) 


GG 		  general matrices, generalized problem (i.e. a pair of general matrices)


HE 		  (complex) Hermitian 


OR 		  (real) orthogonal 


PB 		  symmetric or Hermitian positive definite band 


PO 		  symmetric or Hermitian positive definite 


PT 		  symmetric or Hermitian positive definite tridiagonal 


ST 		  symmetric tridiagonal 


SY 		  symmetric 


TR 		  triangular (or in some cases quasi-triangular)


TZ 		  trapezoidal 


UN 		  (complex) unitary 

The last three characters, YYY, indicate the computation done by a particular subroutine. Included in this release are subroutines to perform the following computations:

BRD 		  reduce to bidiagonal form by orthogonal transformations 


CON 		  estimate condition number


EBZ 		  compute selected eigenvalues by bisection 


EDC 		  compute eigenvectors using divide and conquer 


EIN 		  compute selected eigenvectors by inverse iteration 


EQU 		  equilibrate a matrix to reduce its condition number 


EVC 		  compute the eigenvectors from the Schur factorization 


GBR 		  generate the orthogonal/unitary matrix from PxGEBRD 


GHR 		  generate the orthogonal/unitary matrix from PxGEHRD 


GLQ 		  generate the orthogonal/unitary matrix from PxGELQF 


GQL 		  generate the orthogonal/unitary matrix from PxGEQLF 


GQR 		  generate the orthogonal/unitary matrix from PxGEQRF 


GRQ 		  generate the orthogonal/unitary matrix from PxGERQF 


GST 		  reduce a symmetric-definite generalized eigenvalue problem to standard form 


HRD 		  reduce to upper Hessenberg form by orthogonal transformations 


LQF 		  compute an LQ factorization without pivoting 


MBR 		  multiply by the orthogonal/unitary matrix from PxGEBRD 


MHR 		  multiply by the orthogonal/unitary matrix from PxGEHRD 


MLQ 		  multiply by the orthogonal/unitary matrix from PxGELQF 


MQL 		  multiply by the orthogonal/unitary matrix from PxGEQLF 


MQR 		  multiply by the orthogonal/unitary matrix from PxGEQRF 


MRQ 		  multiply by the orthogonal/unitary matrix from PxGERQF 


MRZ 		  multiply by the orthogonal/unitary matrix from PxTZRZF 


MTR 		  multiply by the orthogonal/unitary matrix from PxxxTRD 


QLF 		  compute a QL factorization without pivoting 


QPF 		  compute a QR factorization with column pivoting


QRF 		  compute a QR factorization without pivoting 


RFS 		  refine initial solution returned by TRS routines 


RQF 		  compute an RQ factorization without pivoting 


RZF 		  compute an RZ factorization without pivoting 


TRD 		  reduce a symmetric matrix to real symmetric tridiagonal form 


TRF 		  compute a triangular factorization (LU, Cholesky, etc.) 


TRI 		  compute inverse (based on triangular factorization)


TRS 		  solve systems of linear equations (based on triangular factorization)

Given these definitions, the following table indicates the ScaLAPACK subroutines for the solution of systems of linear equations:

HE

UN

GE

GG

DB

GB

DT

GT

PO

PB

PT

SY

TR

TZ

OR

TRF

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

TRS

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

RFS

$\times$

$\times$

$\times$

TRI

$\times$

$\times$

$\times$

CON

$\times$

$\times$

$\times$

EQU

$\times$

$\times$

QPF

$\times$

QRF

$\times$

$\times$

RZF

$\times$

GQR

$\times$

MQR

$\times$

- also RQ, QL, and LQ

- also RQ, RZ, QL, and LQ

The following table indicates the ScaLAPACK subroutines for finding eigenvalues and eigenvectors or singular values and singular vectors:

							HE
	GE	GG	HS	HG	TR	TG	SY	ST	PT	BD
HRD	$\times$
TRD							$\times$
BRD	$\times$
EQZ
EIN								$\times$
EBZ								$\times$
EDC								$\times$
EVC					$\times$			$\times$
GST							$\times$

Orthogonal/unitary transformation routines have also been provided for the reductions that use elementary transformations.

	UN
	OR
GHR	$\times$
GTR	$\times$
GBR	$\times$
MHR	$\times$
MTR	$\times$
MBR	$\times$

In addition, a number of driver routines are provided with this release. The naming convention for the driver routines is the same as for the LAPACK routines, but the last 3 characters YYY have the following meanings (note an `X' in the last character position indicates a more expert driver):

SV 		 factor the matrix and solve a system of equations 


SVX 		 equilibrate, factor, solve, compute error bounds and do iterative refinement, and 


estimate the condition number 


LS 		 solve over- or underdetermined linear system using orthogonal factorizations 


EV 		 compute all eigenvalues and/or eigenvectors 


EVD 		 compute all eigenvalues and, optionally, eigenvectors (using divide and conquer algorithm) 


EVX 		 compute selected eigenvalues and eigenvectors 


GVX 		 compute selected generalized eigenvalues and/or generalized eigenvectors 


SVD 		 compute the SVD and/or singular vectors

The driver routines provided in ScaLAPACK are indicated by the following table:

HE

HB

GE

GG

DB

GB

DT

GT

PO

PB

PT

SY

SB

ST

SV

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

$\times$

SVX

$\times$

$\times$

LS

$\times$

EV

$\times$

EVD

$\times$

EVX

$\times$

GVX

$\times$

SVD

$\times$