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 ele
ments of X. INCX must not be zero. Unchanged on
exit.
( ( 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 tri
angular 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 tri
angular 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.
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