dspr2

NAME

dspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A

SYNOPSIS 

  SUBROUTINE DSPR2( UPLO, N, ALPHA, X, INCX, Y, INCY, A)
  CHARACTER * 1 UPLO
  INTEGER N, INCX, INCY
  DOUBLE PRECISION ALPHA
  DOUBLE PRECISION X(*), Y(*), A(*)
 
  SUBROUTINE DSPR2_64( UPLO, N, ALPHA, X, INCX, Y, INCY, A)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INCX, INCY
  DOUBLE PRECISION ALPHA
  DOUBLE PRECISION X(*), Y(*), A(*)

F95 INTERFACE 

  SUBROUTINE SPR2( UPLO, [N], ALPHA, X, [INCX], Y, [INCY], A)
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, INCX, INCY
  REAL(8) :: ALPHA
  REAL(8), DIMENSION(:) :: X, Y, A
 
  SUBROUTINE SPR2_64( UPLO, [N], ALPHA, X, [INCX], Y, [INCY], A)
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, INCX, INCY
  REAL(8) :: ALPHA
  REAL(8), DIMENSION(:) :: X, Y, A

C INTERFACE

#include <sunperf.h>

void dspr2(char uplo, int n, double alpha, double *x, int incx, double *y, int incy, double *a);

void dspr2_64(char uplo, long n, double alpha, double *x, long incx, double *y, long incy, double *a);

PURPOSE

dspr2 performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

ARGUMENTS

* UPLO (input)
On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array A as follows:

UPLO = 'U' or 'u' The upper triangular part of A is supplied in A.

UPLO = 'L' or 'l' The lower triangular part of A is supplied in A.

Unchanged on exit.

* N (input)
On entry, N specifies the order of the matrix A. N >= 0. Unchanged on exit.

* ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

* X (input)
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit.

* INCX (input)
On entry, INCX specifies the increment for the elements of X. INCX <> 0. Unchanged on exit.

* Y (input)
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit.

* INCY (input)
On entry, INCY specifies the increment for the elements of Y. INCY <> 0. Unchanged on exit.

* A (input/output)
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array A must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array A must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array A is overwritten by the lower triangular part of the updated matrix.