SPPCO(3F)

NAME
     SPPCO   - SPPCO factors a real symmetric positive definite matrix stored
     in packed form and estimates the condition of the matrix.

     If  RCOND  is not needed, SPPFA is slightly faster.  To solve  A*X = B ,
     follow SPPCO by SPPSL.  To compute  INVERSE(A)*C , follow SPPCO by SPPSL.
     To compute  DETERMINANT(A) , follow SPPCO by SPPDI.  To compute
     INVERSE(A) , follow SPPCO by SPPDI.


SYNOPSYS
      SUBROUTINE SPPCO(AP,N,RCOND,Z,INFO)

DESCRIPTION
     On Entry

     AP REAL (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 .  On Return

     AP an upper triangular matrix  R , stored in packed
        form, so that  A = TRANS(R)*R .
        If  INFO .NE. 0 , the factorization is not complete.

     RCOND REAL
        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.  If INFO .NE. 0 , RCOND is unchanged.

     Z REAL(N)
        a work vector whose contents are usually unimportant.
        If  A  is singular to working precision, then  Z  is
        an approximate null vector in the sense that
        NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
        If  INFO .NE. 0 , Z  is unchanged.

     INFO INTEGER
        = 0  for normal return.
        = K  signals an error condition.  The leading minor
        of order  K  is not positive definite.  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 SPPFA BLAS SAXPY,SDOT,SSCAL,SASUM Fortran
     ABS,AMAX1,REAL,SIGN