zspr.f(3)

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 (character UPLO, integer N, complex*16 ALPHA, complex*16, dimension( * ) X, integer INCX, complex*16, dimension( * ) AP)

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.

Definition at line 131 of file zspr.f.

Author

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