# dspr.f

          SUBROUTINE DSPR (UPLO, N, ALPHA, X, INCX, AP)
    C***BEGIN PROLOGUE  DSPR
    C***PURPOSE  Perform the symmetric rank 1 operation.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B4
    C***TYPE      DOUBLE PRECISION (DSPR-D)
    C***KEYWORDS  LEVEL 2 BLAS, LINEAR ALGEBRA
    C***AUTHOR  Dongarra, J. J., (ANL)
    C           Du Croz, J., (NAG)
    C           Hammarling, S., (NAG)
    C           Hanson, R. J., (SNLA)
    C***DESCRIPTION
    C
    C  DSPR    performs the symmetric rank 1 operation
    C
    C     A := alpha*x*x' + A,
    C
    C  where alpha is a real scalar, x is an n element vector and A is an
    C  n by n symmetric matrix, supplied in packed form.
    C
    C  Parameters
    C  ==========
    C
    C  UPLO   - CHARACTER*1.
    C           On entry, UPLO specifies whether the upper or lower
    C           triangular part of the matrix A is supplied in the packed
    C           array AP as follows:
    C
    C              UPLO = 'U' or 'u'   The upper triangular part of A is
    C                                  supplied in AP.
    C
    C              UPLO = 'L' or 'l'   The lower triangular part of A is
    C                                  supplied in AP.
    C
    C           Unchanged on exit.
    C
    C  N      - INTEGER.
    C           On entry, N specifies the order of the matrix A.
    C           N must be at least zero.
    C           Unchanged on exit.
    C
    C  ALPHA  - DOUBLE PRECISION.
    C           On entry, ALPHA specifies the scalar alpha.
    C           Unchanged on exit.
    C
    C  X      - DOUBLE PRECISION array of dimension at least
    C           ( 1 + ( n - 1)*abs( INCX)).
    C           Before entry, the incremented array X must contain the n
    C           element vector x.
    C           Unchanged on exit.
    C
    C  INCX   - INTEGER.
    C           On entry, INCX specifies the increment for the elements of
    C           X. INCX must not be zero.
    C           Unchanged on exit.
    C
    C  AP     - DOUBLE PRECISION array of DIMENSION at least
    C           ( ( n*( n + 1 ) )/2 ).
    C           Before entry with  UPLO = 'U' or 'u', the array AP must
    C           contain the upper triangular part of the symmetric matrix
    C           packed sequentially, column by column, so that AP( 1 )
    C           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    C           and a( 2, 2 ) respectively, and so on. On exit, the array
    C           AP is overwritten by the upper triangular part of the
    C           updated matrix.
    C           Before entry with UPLO = 'L' or 'l', the array AP must
    C           contain the lower triangular part of the symmetric matrix
    C           packed sequentially, column by column, so that AP( 1 )
    C           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    C           and a( 3, 1 ) respectively, and so on. On exit, the array
    C           AP is overwritten by the lower triangular part of the
    C           updated matrix.
    C
    C***REFERENCES  Dongarra, J. J., Du Croz, J., Hammarling, S., and
    C                 Hanson, R. J.  An extended set of Fortran basic linear
    C                 algebra subprograms.  ACM TOMS, Vol. 14, No. 1,
    C                 pp. 1-17, March 1988.
    C***ROUTINES CALLED  LSAME, XERBLA
    C***REVISION HISTORY  (YYMMDD)
    C   861022  DATE WRITTEN
    C   910605  Modified to meet SLATEC prologue standards.  Only comment
    C           lines were modified.  (BKS)
    C***END PROLOGUE  DSPR