CSPR(1) LAPACK auxiliary routine (version 3.2) CSPR(1)NAME
CSPR - performs 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 com‐
plex scalar, x is an n element vector and A is an n by n symmetric
matrix, supplied in packed form.
ARGUMENTS
UPLO (input) 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 (input) INTEGER
On entry, N specifies the order of the matrix A. N must be at
least zero. Unchanged on exit.
ALPHA (input) COMPLEX
On entry, ALPHA specifies the scalar alpha. Unchanged on
exit.
X (input) 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 (input) INTEGER
On entry, INCX specifies the increment for the elements of X.
INCX must not be zero. Unchanged on exit.
AP (input/output) 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 symmet‐
ric 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 auxiliary routine (versioNovember 2008 CSPR(1)
