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, 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 ele-
ments 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)
