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:
     RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
 where
     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
 respectively.

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

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

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

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

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

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

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

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

          SWORK is 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 is 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
                    iterations
          > 0: iterative refinement has been sucessfully used.
               Returns the number of iterations

          INFO is 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.