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

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

     CHARACTER UPLO

     INTEGER INCX, INCY, N

     COMPLEX*16 ALPHA, BETA

     COMPLEX*16 AP( * ), X( * ), Y( * )



     #include <sunperf.h>

     void zspmv(char *uplo, int *n, doublecomplex *zalpha,  doub-
               lecomplex  *zap,  doublecomplex  *zx,  int  *incx,
               doublecomplex  *zbeta,  doublecomplex   *zy,   int
               *incy) ;

PURPOSE
     ZSPMV  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, supplied in packed
     form.


ARGUMENTS
     UPLO      - 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         - 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.

     AP        - 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 sym-
               metric  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         - 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      - 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, 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
               elements  of  Y. INCY must not be zero.  Unchanged
               on exit.

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