SLATEC Routines --- DSPFA ---

*DECK DSPFA
      SUBROUTINE DSPFA (AP, N, KPVT, INFO)
C***BEGIN PROLOGUE  DSPFA
C***PURPOSE  Factor a real symmetric matrix stored in packed form by
C            elimination with symmetric pivoting.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2B1A
C***TYPE      DOUBLE PRECISION (SSPFA-S, DSPFA-D, CHPFA-C, CSPFA-C)
C***KEYWORDS  LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED,
C             SYMMETRIC
C***AUTHOR  Bunch, J., (UCSD)
C***DESCRIPTION
C
C     DSPFA factors a double precision symmetric matrix stored in
C     packed form by elimination with symmetric pivoting.
C
C     To solve  A*X = B , follow DSPFA by DSPSL.
C     To compute  INVERSE(A)*C , follow DSPFA by DSPSL.
C     To compute  DETERMINANT(A) , follow DSPFA by DSPDI.
C     To compute  INERTIA(A) , follow DSPFA by DSPDI.
C     To compute  INVERSE(A) , follow DSPFA by DSPDI.
C
C     On Entry
C
C        AP      DOUBLE PRECISION (N*(N+1)/2)
C                the packed form of a symmetric matrix  A .  The
C                columns of the upper triangle are stored sequentially
C                in a one-dimensional array of length  N*(N+1)/2 .
C                See comments below for details.
C
C        N       INTEGER
C                the order of the matrix  A .
C
C     Output
C
C        AP      a block diagonal matrix and the multipliers which
C                were used to obtain it stored in packed form.
C                The factorization can be written  A = U*D*TRANS(U)
C                where  U  is a product of permutation and unit
C                upper triangular matrices, TRANS(U) is the
C                transpose of  U , and  D  is block diagonal
C                with 1 by 1 and 2 by 2 blocks.
C
C        KPVT    INTEGER(N)
C                an integer vector of pivot indices.
C
C        INFO    INTEGER
C                = 0  normal value.
C                = K  if the K-th pivot block is singular.  This is
C                     not an error condition for this subroutine,
C                     but it does indicate that DSPSL or DSPDI may
C                     divide by zero if called.
C
C     Packed Storage
C
C          The following program segment will pack the upper
C          triangle of a symmetric matrix.
C
C                K = 0
C                DO 20 J = 1, N
C                   DO 10 I = 1, J
C                      K = K + 1
C                      AP(K)  = A(I,J)
C             10    CONTINUE
C             20 CONTINUE
C
C***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C                 Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED  DAXPY, DSWAP, IDAMAX
C***REVISION HISTORY  (YYMMDD)
C   780814  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891107  Modified routine equivalence list.  (WRB)
C   891107  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DSPFA