1DSPR2(1)                         BLAS routine                         DSPR2(1)
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NAME

6       DSPR2 - the symmetric rank 2 operation   A := alpha*x*y' + alpha*y*x' +
7       A,
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SYNOPSIS

10       SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
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12           DOUBLE                                      PRECISION ALPHA
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14           INTEGER                                     INCX,INCY,N
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16           CHARACTER                                   UPLO
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18           DOUBLE                                      PRECISION
19                                                       AP(*),X(*),Y(*)
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PURPOSE

22       DSPR2  performs the symmetric rank 2 operation
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24       where alpha is a scalar, x and y are n element vectors and A is an n by
25       n symmetric matrix, supplied in packed form.
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ARGUMENTS

29       UPLO   - CHARACTER*1.
30              On entry, UPLO specifies whether the upper or  lower  triangular
31              part  of the matrix A is supplied in the packed array AP as fol‐
32              lows:
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34              UPLO = 'U' or 'u'   The upper triangular part of A  is  supplied
35              in AP.
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37              UPLO  =  'L' or 'l'   The lower triangular part of A is supplied
38              in AP.
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40              Unchanged on exit.
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42       N      - INTEGER.
43              On entry, N specifies the order of the matrix A.  N must  be  at
44              least zero.  Unchanged on exit.
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46       ALPHA  - DOUBLE PRECISION.
47              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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49       X      - DOUBLE PRECISION array of dimension at least
50              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
51              array X must contain the n element vector x.  Unchanged on exit.
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53       INCX   - INTEGER.
54              On entry, INCX specifies the increment for the  elements  of  X.
55              INCX must not be zero.  Unchanged on exit.
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57       Y      - DOUBLE PRECISION array of dimension at least
58              (  1  +  ( n - 1 )*abs( INCY ) ).  Before entry, the incremented
59              array Y must contain the n element vector y.  Unchanged on exit.
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61       INCY   - INTEGER.
62              On entry, INCY specifies the increment for the  elements  of  Y.
63              INCY must not be zero.  Unchanged on exit.
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65       AP     - DOUBLE PRECISION array of DIMENSION at least
66              (  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u',
67              the array AP must contain the upper triangular part of the  sym‐
68              metric matrix packed sequentially, column by column, so that AP(
69              1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a(  1,  2  )
70              and  a( 2, 2 ) respectively, and so on. On exit, the array AP is
71              overwritten by the upper triangular part of the updated  matrix.
72              Before  entry  with UPLO = 'L' or 'l', the array AP must contain
73              the lower triangular part of the symmetric matrix packed sequen‐
74              tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
75              AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )  respec‐
76              tively,  and  so on. On exit, the array AP is overwritten by the
77              lower triangular part of the updated matrix.
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79              Level 2 Blas routine.
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81              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
82              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
83              Central Office.  Richard Hanson, Sandia National Labs.
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87BLAS routine                     November 2006                        DSPR2(1)