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( * )
#include <sunperf.h>
void cspr(char *uplo, int *n, complex *calpha, complex *cx,
int *incx, complex *ap) ;
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 ele-
ments need not be set, they are assumed to be
zero, and on exit they are set to zero.
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