DSPCO(3F)

NAME
     DSPCO   - DSPCO factors a double precision symmetric matrix stored in
     packed form by elimination with symmetric pivoting and estimates the
     condition of the matrix.

     IF  RCOND  is not needed, DSPFA is slightly faster.  To solve  A*X = B ,
     follow DSPCO by DSPSL.  To compute  INVERSE(A)*C , follow DSPCO by DSPSL.
     To compute  INVERSE(A) , follow DSPCO by DSPDI.  To compute
     DETERMINANT(A) , follow DSPCO by DSPDI.  To compute  INERTIA(A), follow
     DSPCO by DSPDI.


SYNOPSYS
      SUBROUTINE DSPCO(AP,N,KPVT,RCOND,Z)

DESCRIPTION
     On Entry

     AP DOUBLE PRECISION (N*(N+1)/2)
        the packed form of a symmetric matrix  A .  The
        columns of the upper triangle are stored sequentially
        in a one-dimensional array of length  N*(N+1)/2 .
        See comments below for details.

     N INTEGER
        the order of the matrix  A .  Output

     AP a block diagonal matrix and the multipliers which
        were used to obtain it stored in packed form.
        The factorization can be written  A = U*D*TRANS(U)
        where  U  is a product of permutation and unit
        upper triangular matrices , TRANS(U) is the
        transpose of  U , and  D  is block diagonal
        with 1 by 1 and 2 by 2 blocks.

     KPVT INTEGER(N)
        an integer vector of pivot indices.

     RCOND DOUBLE PRECISION
        an estimate of the reciprocal condition of  A .
        For the system  A*X = B , relative perturbations
        in  A  and  B  of size  EPSILON  may cause
        relative perturbations in  X  of size  EPSILON/RCOND .
        If  RCOND  is so small that the logical expression
        1.0 + RCOND .EQ. 1.0
        is true, then  A  may be singular to working
        precision.  In particular,  RCOND  is zero  if
        exact singularity is detected or the estimate
        underflows.

     Z DOUBLE PRECISION(N)
        a work vector whose contents are usually unimportant.
        If  A  is close to a singular matrix, then  Z  is
        an approximate null vector in the sense that
        NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .  Packed Storage The following
     program segment will pack the upper triangle of a symmetric matrix.
        K = 0
        DO 20 J = 1, N
        DO 10 I = 1, J
        K = K + 1
        AP(K) = A(I,J)
        10    CONTINUE
        20 CONTINUE LINPACK.  This version dated 08/14/78 .  Cleve Moler,
     University of New Mexico, Argonne National Lab.  Subroutines and
     Functions LINPACK DSPFA BLAS DAXPY,DDOT,DSCAL,DASUM Fortran
     DABS,DMAX1,IABS,DSIGN