NAME
SSPR - perform the symmetric rank 1 operation A := alpha*x*x’ + A,
SYNOPSIS
SUBROUTINE SSPR ( UPLO, N, ALPHA, X, INCX, AP )
REAL ALPHA
INTEGER INCX, N
CHARACTER*1 UPLO
REAL AP( * ), X( * )
PURPOSE
SSPR performs the symmetric rank 1 operation
where alpha is a real scalar, x is an n element vector and A is an n by
n symmetric matrix, supplied in packed form.
PARAMETERS
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 - REAL .
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X - REAL array of 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 elements of X.
INCX must not be zero. Unchanged on exit.
AP - REAL array of 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.
Level 2 Blas routine.
-- Written on 22-October-1986. Jack Dongarra, Argonne National
Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag
Central Office. Richard Hanson, Sandia National Labs.