1DSPR(1)                          BLAS routine                          DSPR(1)
2
3
4

NAME

6       DSPR - performs the symmetric rank 1 operation   A := alpha*x*x' + A,
7

SYNOPSIS

9       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
10
11           DOUBLE                              PRECISION ALPHA
12
13           INTEGER                             INCX,N
14
15           CHARACTER                           UPLO
16
17           DOUBLE                              PRECISION AP(*),X(*)
18

PURPOSE

20       DSPR    performs the symmetric rank 1 operation
21
22       where alpha is a real scalar, x is an n element vector and A is an n by
23       n symmetric matrix, supplied in packed form.
24
25

ARGUMENTS

27       UPLO   - CHARACTER*1.
28              On entry, UPLO specifies whether the upper or  lower  triangular
29              part  of the matrix A is supplied in the packed array AP as fol‐
30              lows:
31
32              UPLO = 'U' or 'u'   The upper triangular part of A  is  supplied
33              in AP.
34
35              UPLO  =  'L' or 'l'   The lower triangular part of A is supplied
36              in AP.
37
38              Unchanged on exit.
39
40       N      - INTEGER.
41              On entry, N specifies the order of the matrix A.  N must  be  at
42              least zero.  Unchanged on exit.
43
44       ALPHA  - DOUBLE PRECISION.
45              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
46
47       X      - DOUBLE PRECISION array of dimension at least
48              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
49              array X must contain the n element vector x.  Unchanged on exit.
50
51       INCX   - INTEGER.
52              On entry, INCX specifies the increment for the  elements  of  X.
53              INCX must not be zero.  Unchanged on exit.
54
55       AP     - DOUBLE PRECISION array of DIMENSION at least
56              (  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u',
57              the array AP must contain the upper triangular part of the  sym‐
58              metric matrix packed sequentially, column by column, so that AP(
59              1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a(  1,  2  )
60              and  a( 2, 2 ) respectively, and so on. On exit, the array AP is
61              overwritten by the upper triangular part of the updated  matrix.
62              Before  entry  with UPLO = 'L' or 'l', the array AP must contain
63              the lower triangular part of the symmetric matrix packed sequen‐
64              tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
65              AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )  respec‐
66              tively,  and  so on. On exit, the array AP is overwritten by the
67              lower triangular part of the updated matrix.
68

FURTHER DETAILS

70       Level 2 Blas routine.
71
72       -- Written on 22-October-1986.
73          Jack Dongarra, Argonne National Lab.
74          Jeremy Du Croz, Nag Central Office.
75          Sven Hammarling, Nag Central Office.
76          Richard Hanson, Sandia National Labs.
77
78
79
80
81BLAS routine                     November 2008                         DSPR(1)
Impressum