CSPR(3F)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.
Page 1
CSPR(3F)CSPR(3F)
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.
Page 2
