NAME

       zspmv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
           ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric
           packed matrix

Function/Subroutine Documentation

   subroutine zspmv (character UPLO, integer N, complex*16 ALPHA, complex*16, dimension( * ) AP,
       complex*16, dimension( * ) X, integer INCX, complex*16 BETA, complex*16, dimension( * ) Y,
       integer INCY)
       ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric
       packed matrix

       Purpose:

            ZSPMV  performs the matrix-vector operation

               y := alpha*A*x + beta*y,

            where alpha and beta are scalars, x and y are n element vectors and
            A is an n by n symmetric matrix, supplied in packed form.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                      On entry, UPLO specifies whether the upper or lower
                      triangular part of the matrix A is supplied in the packed
                      array AP as follows:

                         UPLO = 'U' or 'u'   The upper triangular part of A is
                                             supplied in AP.

                         UPLO = 'L' or 'l'   The lower triangular part of A is
                                             supplied in AP.

                      Unchanged on exit.

           N

                     N is INTEGER
                      On entry, N specifies the order of the matrix A.
                      N must be at least zero.
                      Unchanged on exit.

           ALPHA

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

           AP

                     AP is COMPLEX*16 array, dimension at least
                      ( ( N*( N + 1 ) )/2 ).
                      Before entry, with UPLO = 'U' or 'u', the array AP must
                      contain the upper triangular part of the symmetric matrix
                      packed sequentially, column by column, so that AP( 1 )
                      contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
                      and a( 2, 2 ) respectively, and so on.
                      Before entry, with UPLO = 'L' or 'l', the array AP must
                      contain the lower triangular part of the symmetric matrix
                      packed sequentially, column by column, so that AP( 1 )
                      contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
                      and a( 3, 1 ) respectively, and so on.
                      Unchanged on exit.

           X

                     X is COMPLEX*16 array, dimension at least
                      ( 1 + ( N - 1 )*abs( INCX ) ).
                      Before entry, the incremented array X must contain the N-
                      element vector x.
                      Unchanged on exit.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.
                      Unchanged on exit.

           BETA

                     BETA is 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

                     Y is 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

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.
                      Unchanged on exit.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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