zspr(3)

NAME

ZSPR - perform the symmetric rank 1 operation A := al

pha*x*conjg( x' ) + A,

SYNOPSIS

SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
    CHARACTER    UPLO
    INTEGER      INCX, N
    COMPLEX*16   ALPHA
    COMPLEX*16   AP( * ), X( * )

PURPOSE

ZSPR performs the symmetric rank 1 operation A := al

pha*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*16

On entry, ALPHA specifies the scalar alpha. Un

changed on exit.

X - COMPLEX*16 array, dimension at least

( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the

incremented array X must contain the N- element vector x. Un

changed on exit.

INCX - INTEGER

On entry, INCX specifies the increment for the ele

ments of X. INCX must not be zero. Unchanged on exit.

AP - COMPLEX*16 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 ma

trix. 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 ) respec

tively, and so on. On exit, the array AP is overwritten by the

lower triangular part of the updated matrix. Note that the imag

inary parts of the diagonal elements need not be set, they are

assumed to be zero, and on exit they are set to zero.

LAPACK version 3.0 15 June 2000

ZSPR(3)