STRMV, DTRMV, CTRMV, or ZTRMV Subroutine

Purpose

Performs matrix-vector operations using a triangular matrix.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

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

SUBROUTINE DTRMV(UPLO, TRANS, DIAG, N,
A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
DOUBLE PRECISION A(LDA,*), X(*)
SUBROUTINE CTRMV(UPLO, TRANS, DIAG, N,
A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX A(LDA,*), X(*)
SUBROUTINE ZTRMV(UPLO, TRANS, DIAG, N,
A, LDA, X, INCX)
INTEGER INCX,LDA,N
CHARACTER*1 DIAG,TRANS,UPLO
COMPLEX*16 A(LDA,*),X(*)

Description

The STRMV, DTRMV, CTRMV, or ZTRMV subroutine performs one of the matrix-vector operations:

x := A * x

OR

x := A' * x

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

Parameters

Item Description
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 operation to be performed as follows:
TRANS = 'N' or 'n'
x := A * x
TRANS = 'T' or 't'
x := A' * x
TRANS = 'C' or 'c'
x := A' * x

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.
N On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.
A 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.
X A vector of dimension at least (1 + (N-1) * abs( INCX ) ). On entry, the incremented array X must contain the N element vector x; on exit, X is overwritten with the transformed vector x.
INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.