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       LAPACK-3 - computes the solution to a real system of linear equations  A * X = B,



           INTEGER        INFO, ITER, LDA, LDB, LDX, N, NRHS

           INTEGER        IPIV( * )

           REAL           SWORK( * )

           DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ), X( LDX, * )


       DSGESV computes the solution to a real system of linear equations
          A * X = B,
        where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
        DSGESV first attempts to factorize the matrix in SINGLE PRECISION
        and use this factorization within an iterative refinement procedure
        to produce a solution with DOUBLE PRECISION normwise backward error
        quality (see below). If the approach fails the method switches to a
        DOUBLE PRECISION factorization and solve.
        The iterative refinement is not going to be a winning strategy if
        the ratio SINGLE PRECISION performance over DOUBLE PRECISION
        performance is too small. A reasonable strategy should take the
        number of right-hand sides and the size of the matrix into account.
        This might be done with a call to ILAENV in the future. Up to now, we
        always try iterative refinement.
        The iterative refinement process is stopped if
            ITER > ITERMAX
        or for all the RHS we have:
            o ITER is the number of the current iteration in the iterative
              refinement process
            o RNRM is the infinity-norm of the residual
            o XNRM is the infinity-norm of the solution
            o ANRM is the infinity-operator-norm of the matrix A
            o EPS is the machine epsilon returned by DLAMCH('Epsilon')
        The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00


        N       (input) INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

        NRHS    (input) INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrix B.  NRHS >= 0.

        A       (input/output) DOUBLE PRECISION array,
                dimension (LDA,N)
                On entry, the N-by-N coefficient matrix A.
                On exit, if iterative refinement has been successfully used
                (INFO.EQ.0 and ITER.GE.0, see description below), then A is
                unchanged, if double precision factorization has been used
                (INFO.EQ.0 and ITER.LT.0, see description below), then the
                array A contains the factors L and U from the factorization
                A = P*L*U; the unit diagonal elements of L are not stored.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        IPIV    (output) INTEGER array, dimension (N)
                The pivot indices that define the permutation matrix P;
                row i of the matrix was interchanged with row IPIV(i).
                Corresponds either to the single precision factorization
                (if INFO.EQ.0 and ITER.GE.0) or the double precision
                factorization (if INFO.EQ.0 and ITER.LT.0).

        B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
                The N-by-NRHS right hand side matrix B.

        LDB     (input) INTEGER
                The leading dimension of the array B.  LDB >= max(1,N).

        X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
                If INFO = 0, the N-by-NRHS solution matrix X.

        LDX     (input) INTEGER
                The leading dimension of the array X.  LDX >= max(1,N).

        WORK    (workspace) DOUBLE PRECISION array, dimension (N,NRHS)
                This array is used to hold the residual vectors.

        SWORK   (workspace) REAL array, dimension (N*(N+NRHS))
                This array is used to use the single precision matrix and the
                right-hand sides or solutions in single precision.

        ITER    (output) INTEGER
                < 0: iterative refinement has failed, double precision
                factorization has been performed
                -1 : the routine fell back to full precision for
                implementation- or machine-specific reasons
                -2 : narrowing the precision induced an overflow,
                the routine fell back to full precision
                -3 : failure of SGETRF
                -31: stop the iterative refinement after the 30th
                > 0: iterative refinement has been sucessfully used.
                Returns the number of iterations

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i, U(i,i) computed in DOUBLE PRECISION is
                exactly zero.  The factorization has been completed,
                but the factor U is exactly singular, so the solution
                could not be computed.

 LAPACK PROTOTYPE driver routine (version 3.April 2011                            DSGESV(3lapack)