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 matrixvector 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 nonzero, 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 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.