cspr(3F)

NAME
     CSPR - perform the symmetric rank 1 operation   A := alpha*x*conjg( x' )
     + A,

SYNOPSIS
     SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP )

         CHARACTER    UPLO

         INTEGER      INCX, N

         COMPLEX      ALPHA

         COMPLEX      AP( * ), X( * )

PURPOSE
     CSPR    performs the symmetric rank 1 operation

     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.


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
            On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

     X      - COMPLEX 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.
     AP     - COMPLEX 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.