.TH ZSPR 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
ZSPR - the symmetric rank 1 operation A := alpha*x*conjg( x\(aq ) + A,
.SH SYNOPSIS
.TP 17
SUBROUTINE ZSPR(
UPLO, N, ALPHA, X, INCX, AP )
.TP 17
.ti +4
CHARACTER
UPLO
.TP 17
.ti +4
INTEGER
INCX, N
.TP 17
.ti +4
COMPLEX*16
ALPHA
.TP 17
.ti +4
COMPLEX*16
AP( * ), X( * )
.SH PURPOSE
ZSPR 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.
.br
.SH ARGUMENTS
.TP 9
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 = \(aqU\(aq or \(aqu\(aq The upper triangular part of A is
supplied in AP.
UPLO = \(aqL\(aq or \(aql\(aq The lower triangular part of A is
supplied in AP.
Unchanged on exit.
.TP 9
N (input) INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
.TP 9
ALPHA (input) COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
.TP 9
X (input) COMPLEX*16 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.
.TP 9
INCX (input) INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
.TP 9
AP (input/output) COMPLEX*16 array, dimension at least
( ( N*( N + 1 ) )/2 ).
Before entry, with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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.