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 per­
              formed 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

              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 ) ) oth­
              erwise.  Before entry, the incremented array X must
              contain the vector x.  Unchanged on exit.

       INCX   - INTEGER.
              On entry, INCX specifies the increment for the ele­
              ments 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 ) ) oth­
              erwise.   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 ele­
              ments 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.


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