SLATEC Routines --- SSPCO ---

*DECK SSPCO
      SUBROUTINE SSPCO (AP, N, KPVT, RCOND, Z)
C***BEGIN PROLOGUE  SSPCO
C***PURPOSE  Factor a real symmetric matrix stored in packed form
C            by elimination with symmetric pivoting and estimate the
C            condition number of the matrix.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2B1A
C***TYPE      SINGLE PRECISION (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C)
C***KEYWORDS  CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
C             MATRIX FACTORIZATION, PACKED, SYMMETRIC
C***AUTHOR  Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C     SSPCO factors a real symmetric matrix stored in packed
C     form by elimination with symmetric pivoting and estimates
C     the condition of the matrix.
C
C     If  RCOND  is not needed, SSPFA is slightly faster.
C     To solve  A*X = B , follow SSPCO by SSPSL.
C     To compute  INVERSE(A)*C , follow SSPCO by SSPSL.
C     To compute  INVERSE(A) , follow SSPCO by SSPDI.
C     To compute  DETERMINANT(A) , follow SSPCO by SSPDI.
C     To compute  INERTIA(A), follow SSPCO by SSPDI.
C
C     On Entry
C
C        AP      REAL (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        RCOND   REAL
C                an estimate of the reciprocal condition of  A .
C                For the system  A*X = B , relative perturbations
C                in  A  and  B  of size  EPSILON  may cause
C                relative perturbations in  X  of size  EPSILON/RCOND .
C                If  RCOND  is so small that the logical expression
C                           1.0 + RCOND .EQ. 1.0
C                is true, then  A  may be singular to working
C                precision.  In particular,  RCOND  is zero  if
C                exact singularity is detected or the estimate
C                underflows.
C
C        Z       REAL(N)
C                a work vector whose contents are usually unimportant.
C                If  A  is close to a singular matrix, then  Z  is
C                an approximate null vector in the sense that
C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
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  SASUM, SAXPY, SDOT, SSCAL, SSPFA
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  SSPCO