
CSPR(l) ) CSPR(l)
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 A := alpha*x*conjg( x' ) + 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.
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, col
umn 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.
LAPACK version 3.0 15 June 2000 CSPR(l) 
