Purpose
=======

DGEMV performs one of the 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
==========

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 - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION.
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 - DOUBLE PRECISION 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.