NAME¶

ZSPR - performs the symmetric rank 1 operation A := alpha*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 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 (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*16

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

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.

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*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 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 elements need not be set, they are assumed to be zero, and on exit they are set to zero.