ZSPMV(3)       LAPACK routine of NEC Numeric Library Collection       ZSPMV(3)



NAME
       ZSPMV

SYNOPSIS
       SUBROUTINE ZSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)



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.




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

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

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

           BETA      (input)
                     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         (input/output)
                     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      (input)
                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.
                      Unchanged on exit.



LAPACK routine                  31 October 2017                       ZSPMV(3)