SGEMV, DGEMV, CGEMV, or ZGEMV Subroutine

Purpose

Performs matrix-vector operation with general matrices.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

SUBROUTINE SGEMV(TRANS, M, N, ALPHA, A, LDA, X,
INCX, BETA, Y, INCY)
REAL  ALPHA, BETA
INTEGER  INCX, INCY, LDA, M, N
CHARACTER*1  TRANS
REAL  A(LDA,*),  X(*),  Y(*)

SUBROUTINE DGEMV(TRANS, M, N, ALPHA, A, LDA, X,
INCX, BETA, Y, INCY)
DOUBLE PRECISION ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER*1 TRANS
DOUBLE PRECISION A(LDA,*), X(*), Y(*)
SUBROUTINE CGEMV(TRANS, M, N, ALPHA, A, LDA, X, 
INCX, BETA, Y, INCY)
COMPLEX ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER*1 TRANS
COMPLEX A(LDA,*), X(*), Y(*)
SUBROUTINE ZGEMV(TRANS, M, N, ALPHA, A, LDA, X,
INCX, BETA, Y, INCY)
COMPLEX*16 ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER*1 TRANS
COMPLEX*16 A(LDA,*), X(*), Y(*)

Description

The SGEMV, DGEMV, CGEMV, or ZGEMV subroutine performs one of the following matrix-vector operations:

y := alpha * A * x + beta * y

OR

y := alpha * A' * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

Parameters

Item Description
TRANS On entry, TRANS specifies the operation to be performed as follows:
TRANS = 'N' or 'n'
y := alpha * A * x + beta * y
TRANS = 'T' or 't'
y := alpha * A' * x + beta * y
TRANS = 'C' or 'c'
y := alpha * A' * x + beta * y

Unchanged on exit.
M On entry, M specifies the number of rows of the matrix A; M must be at least 0; unchanged on exit.
N On entry, N specifies the number of columns of the matrix A; N must be at least 0; unchanged on exit.
ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit.
A An array of dimension ( LDA, N ); on entry, the leading M by N part of the array A must contain the matrix of coefficients; 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, M ); unchanged on exit.
X A vector of dimension at least (1 + (N-1) * abs( INCX ) ) when TRANS = 'N' or 'n', otherwise, at least (1 + (M-1) * abs( INCX ) ); on entry, the incremented array X must contain the vector x; unchanged on exit.
INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.
BETA On entry, BETA specifies the scalar beta; when BETA is supplied as 0, Y need not be set on input; unchanged on exit.
Y A vector of dimension at least 1 + (M-1) * abs( INCY ) ) when TRANS = 'N' or 'n', otherwise at least (1 + (N-1) * abs( INCY ) ); on entry, with BETA nonzero, the incremented array Y must contain the vector y; on exit, Y is overwritten by the updated vector y.
INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit.