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## NAME

```       CGEMV  - perform one of the matrix-vector operations   y := alpha*A*x +
beta*y, or y := alpha*A’*x + beta*y, or   y := alpha*conjg(  A’  )*x  +
beta*y,

```

## SYNOPSIS

```       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( * )

```

## PURPOSE

```       CGEMV  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*conjg( 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  - COMPLEX         .
On entry, ALPHA specifies the scalar alpha.  Unchanged on  exit.

A      - COMPLEX          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      - COMPLEX          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   - COMPLEX         .
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      - COMPLEX          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.
```