SPOCO(3F)

NAME
     SPOCO   - SPOCO factors a real symmetric positive definite matrix and
     estimates the condition of the matrix.

     If  RCOND  is not needed, SPOFA is slightly faster.  To solve  A*X = B ,
     follow SPOCO by SPOSL.  To compute  INVERSE(A)*C , follow SPOCO by SPOSL.
     To compute  DETERMINANT(A) , follow SPOCO by SPODI.  To compute
     INVERSE(A) , follow SPOCO by SPODI.


SYNOPSYS
      SUBROUTINE SPOCO(A,LDA,N,RCOND,Z,INFO)

DESCRIPTION
     On Entry

     A REAL(LDA, N)
        the symmetric matrix to be factored.  Only the
        diagonal and upper triangle are used.

     LDA INTEGER
        the leading dimension of the array  A .

     N INTEGER
        the order of the matrix  A .  On Return

     A an upper triangular matrix  R  so that  A = TRANS(R)*R
        where  TRANS(R)  is the transpose.
        The strict lower triangle is unaltered.
        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 close to a singular matrix, 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.  LINPACK.  This version dated
     08/14/78 .  Cleve Moler, University of New Mexico, Argonne National Lab.
     Subroutines and Functions LINPACK SPOFA BLAS SAXPY,SDOT,SSCAL,SASUM
     Fortran ABS,AMAX1,REAL,SIGN