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NAME

       ZGEMV  - 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 ZGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

           COMPLEX*16   ALPHA, BETA

           INTEGER      INCX, INCY, LDA, M, N

           CHARACTER*1  TRANS

           COMPLEX*16   A( LDA, * ), X( * ), Y( * )

PURPOSE

       ZGEMV  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*16      .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on  exit.

       A      - COMPLEX*16       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*16       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*16      .
              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*16       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.