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SGEFA

       SUBROUTINE  SGEFA (A,LDA,N,IPVT,INFO)
 C$    (Factor Linear System)
 C$
 C$    SGEFA factors a real matrix by Gaussian elimination.
 C$
 C$    SGEFA is  usually called  by SGECO,  but it  can be  called
 C$    directly with  a saving  in time  if RCOND  is not  needed.
 C$    (Time for SGECO) = (1 + 9/N)*(time for SGEFA) .
 C$
 C$    On entry
 C$
 C$    A.........REAL(LDA, N)
 C$              The matrix to be factored.
 C$
 C$    LDA.......INTEGER
 C$              The leading dimension of the array A.
 C$
 C$    N.........INTEGER
 C$              The order of the matrix A.
 C$
 C$    On return
 C$
 C$    A.........An upper  triangular matrix  and the  multipliers
 C$              which were used to obtain it.  The  factorization
 C$              can be written A  = L*U where L  is a product  of
 C$              permutation and  unit lower  triangular  matrices
 C$              and U is upper triangular.
 C$
 C$    IPVT......INTEGER(N)
 C$              An integer vector of pivot indices.
 C$
 C$    INFO......INTEGER
 C$              = 0  Normal value.
 C$              = K  If  U(K,K) .EQ. 0.0.    This is not an error
 C$                   condition for this  subroutine, but it  does
 C$                   indicate that SGESL or SGEDI will divide  by
 C$                   zero if called.   Use RCOND in  SGECO for  a
 C$                   reliable indication of singularity.
 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$    BLAS SAXPY,SSCAL,ISAMAX
 C$
 C$    (03-APR-82)