 SGEMV(3) perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,

## SYNOPSIS

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( * )

## PURPOSE

SGEMV performs one of the matrix-vector operations

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

## PARAMETERS

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

Level 2 Blas routine.

-- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.