SGECO(3F)

NAME
     SGECO   - SGECO factors a real matrix by Gaussian elimination and
     estimates the condition of the matrix.

     If  RCOND  is not needed, SGEFA is slightly faster.  To solve  A*X = B ,
     follow SGECO by SGESL.  To compute  INVERSE(A)*C , follow SGECO by SGESL.
     To compute  DETERMINANT(A) , follow SGECO by SGEDI.  To compute
     INVERSE(A) , follow SGECO by SGEDI.


SYNOPSYS
      SUBROUTINE SGECO(A,LDA,N,IPVT,RCOND,Z)

DESCRIPTION
     On Entry

     A REAL(LDA, N)
        the matrix to be factored.

     LDA INTEGER
        the leading dimension of the array  A .

     N INTEGER
        the order of the matrix  A .  On Return

     A an upper triangular matrix and the multipliers
        which were used to obtain it.
        The factorization can be written  A = L*U , where
        L  is a product of permutation and unit lower
        triangular matrices and  U  is upper triangular.

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

     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.

     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) .  LINPACK.  This version dated
     08/14/78 .  Cleve Moler, University of New Mexico, Argonne National Lab.
     Subroutines and Functions LINPACK SGEFA BLAS SAXPY,SDOT,SSCAL,SASUM
     Fortran ABS,AMAX1,SIGN