NAME

       zspr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zspr (UPLO, N, ALPHA, X, INCX, AP)
           ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Function/Subroutine Documentation

   subroutine zspr (characterUPLO, integerN, complex*16ALPHA, complex*16, dimension( * )X,
       integerINCX, complex*16, dimension( * )AP)
       ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

       Purpose:

            ZSPR    performs the symmetric rank 1 operation

               A := alpha*x*x**H + A,

            where alpha is a complex scalar, x is an n element vector 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.

           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.

           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. On exit, the array
                      AP is overwritten by the upper triangular part of the
                      updated matrix.
                      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. On exit, the array
                      AP is overwritten by the lower triangular part of the
                      updated matrix.
                      Note that the imaginary parts of the diagonal elements need
                      not be set, they are assumed to be zero, and on exit they
                      are set to zero.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 133 of file zspr.f.

Author

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