STRSV, DTRSV, CTRSV, or ZTRSV Subroutine

Base Operating System and Extensions Technical Reference, Volume 2

STRSV, DTRSV, CTRSV, or ZTRSV Subroutine

Purpose

Solves system of equations.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

SUBROUTINE STRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
REAL A(LDA,*), X(*)

SUBROUTINE DTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX) 
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
DOUBLE PRECISION A(LDA,*), X(*)

SUBROUTINE CTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)

SUBROUTINE ZTRSV(UPLO, TRANS, DIAG,
N, A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX*16 A(LDA,*), X(*)

Description

The STRSV, DTRSV, CTRSV, or ZTRSV subroutine solves one of the systems of equations:

A * x = b

A' * x = b

where b and x are N element vectors and A is an N by N unit, or non-unit, upper or lower triangular matrix.

Parameters

UPLO

On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

UPLO = 'U' or 'u'	A is an upper triangular matrix.
UPLO = 'L' or 'l'	A is a lower triangular matrix.

Unchanged on exit.

TRANS

On entry, TRANS specifies the equations to be solved as follows:

TRANS = 'N' or 'n'	A * x = b
TRANS = 'T' or 't'	A' * x = b
TRANS = 'C' or 'c'	A' * x = b

Unchanged on exit.

DIAG

On entry, DIAG specifies whether or not A is unit triangular as follows:

DIAG = 'U' or 'u'	A is assumed to be unit triangular.
DIAG = 'N' or 'n'	A is not assumed to be unit triangular.

Unchanged on exit.

On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.

An array of dimension ( LDA, N ); on entry with UPLO = 'U' or 'u', the leading N by N upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. On entry with UPLO = 'L' or 'l', the leading N by N lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. When DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity; unchanged on exit.

LDA

On entry, LDA specifies the first dimension of A as declared in the calling (sub) program; LDA must be at least max( 1, N ); unchanged on exit.

A vector of dimension at least (1 + (N-1) * abs(INCX) ); on entry, the incremented array X must contain the N element right-hand side vector b; on exit, X is overwritten with the solution vector x.

INCX

On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.

Implementation Specifics

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.