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zsymv

 NAME
      ZSYMV - perform the matrix-vector operation   y := alpha*A*x
      + beta*y,

 SYNOPSIS
      SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
                        INCY )

          CHARACTER     UPLO

          INTEGER       INCX, INCY, LDA, N

          COMPLEX*16    ALPHA, BETA

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

 PURPOSE
      ZSYMV  performs the matrix-vector  operation

      where alpha and beta are scalars, x and y are n element vec-
      tors and A is an n by n symmetric matrix.

 ARGUMENTS
      UPLO   - CHARACTER*1
             On entry, UPLO specifies whether the upper or lower
             triangular part of the array A is to be referenced as
             follows:

             UPLO = 'U' or 'u'   Only the upper triangular part of
             A is to be referenced.

             UPLO = 'L' or 'l'   Only the lower triangular part of
             A is to be referenced.

             Unchanged on exit.

      N      - INTEGER
             On entry, N specifies the order 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, dimension( LDA, N )
             Before entry with  UPLO = 'U' or 'u', the leading n
             by n upper triangular part of the array A must con-
             tain the upper triangular part of the symmetric
             matrix and the strictly lower triangular part of A is
             not referenced.  Before entry with UPLO = 'L' or 'l',
             the leading n by n lower triangular part of the array

             A must contain the lower triangular part of the sym-
             metric matrix and the strictly upper triangular part
             of A is not referenced.  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, N ).  Unchanged on exit.

      X      - COMPLEX*16 array, dimension at least
             ( 1 + ( N - 1 )*abs( INCX ) ).  Before entry, the
             incremented array X must contain the N- element vec-
             tor 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*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, dimension at least
             ( 1 + ( N - 1 )*abs( INCY ) ).  Before entry, the
             incremented array Y must contain the n element 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.