SUBROUTINE DSPCO(AP,N,KPVT,RCOND,Z)
C***BEGIN PROLOGUE  DSPCO
C***DATE WRITTEN   780814   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2B1A
C***KEYWORDS  CONDITION,DOUBLE PRECISION,FACTOR,LINEAR ALGEBRA,LINPACK,
C             MATRIX,PACKED,SYMMETRIC
C***AUTHOR  MOLER, C. B., (U. OF NEW MEXICO)
C***PURPOSE  Factors a d.p. SYMMETRIC matrix stored in packed form by
C            elimination with symmetric pivoting and estimates the
C            condition of the matrix.
C***DESCRIPTION
C
C     DSPCO factors a double precision symmetric matrix stored in
C     packed form by elimination with symmetric pivoting and estimates
C     the condition of the matrix.
C
C     IF  RCOND  is not needed, DSPFA is slightly faster.
C     To solve  A*X = B , follow DSPCO by DSPSL.
C     To compute  INVERSE(A)*C , follow DSPCO by DSPSL.
C     To compute  INVERSE(A) , follow DSPCO by DSPDI.
C     To compute  DETERMINANT(A) , follow DSPCO by DSPDI.
C     To compute  INERTIA(A), follow DSPCO 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        RCOND   DOUBLE PRECISION
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       DOUBLE PRECISION(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     LINPACK.  This version dated 08/14/78 .
C     Cleve Moler, University of New Mexico, Argonne National Lab.
C
C     Subroutines and Functions
C
C     LINPACK DSPFA
C     BLAS DAXPY,DDOT,DSCAL,DASUM
C     Fortran DABS,DMAX1,IABS,DSIGN
C***REFERENCES  DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C                 *LINPACK USERS  GUIDE*, SIAM, 1979.
C***ROUTINES CALLED  DASUM,DAXPY,DDOT,DSCAL,DSPFA
C***END PROLOGUE  DSPCO