DSPR(3)         BLAS routine of NEC Numeric Library Collection         DSPR(3)



NAME
       DSPR - perform the symmetric rank 1 operation   A := alpha*x*x' + A

SYNOPSIS
       SUBROUTINE DSPR ( UPLO, N, ALPHA, X, INCX, AP )

           DOUBLE      PRECISION ALPHA

           INTEGER     INCX, N

           CHARACTER*1 UPLO

           DOUBLE      PRECISION AP( * ), X( * )

PURPOSE
       DSPR    performs the symmetric rank 1 operation

          A := alpha*x*x' + A

       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 fol-
              lows:

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

       X      - DOUBLE PRECISION 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     - DOUBLE PRECISION 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  sym-
              metric 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 sequen-
              tially,  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.

              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.



BLAS routine                    16 October 1992                        DSPR(3)