SGEEV computes for an N-by-N real nonsymmetric matrix A, the
 eigenvalues and, optionally, the left and/or right eigenvectors.

 The right eigenvector v(j) of A satisfies
                  A * v(j) = lambda(j) * v(j)
 where lambda(j) is its eigenvalue.
 The left eigenvector u(j) of A satisfies
               u(j)**T * A = lambda(j) * u(j)**T
 where u(j)**T denotes the transpose of u(j).

 The computed eigenvectors are normalized to have Euclidean norm
 equal to 1 and largest component real.

          JOBVL is CHARACTER*1
          = 'N': left eigenvectors of A are not computed;
          = 'V': left eigenvectors of A are computed.

          JOBVR is CHARACTER*1
          = 'N': right eigenvectors of A are not computed;
          = 'V': right eigenvectors of A are computed.

          N is INTEGER
          The order of the matrix A. N >= 0.

          A is REAL array, dimension (LDA,N)
          On entry, the N-by-N matrix A.
          On exit, A has been overwritten.

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

          WR is REAL array, dimension (N)

          WI is REAL array, dimension (N)
          WR and WI contain the real and imaginary parts,
          respectively, of the computed eigenvalues.  Complex
          conjugate pairs of eigenvalues appear consecutively
          with the eigenvalue having the positive imaginary part
          first.

          VL is REAL array, dimension (LDVL,N)
          If JOBVL = 'V', the left eigenvectors u(j) are stored one
          after another in the columns of VL, in the same order
          as their eigenvalues.
          If JOBVL = 'N', VL is not referenced.
          If the j-th eigenvalue is real, then u(j) = VL(:,j),
          the j-th column of VL.
          If the j-th and (j+1)-st eigenvalues form a complex
          conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
          u(j+1) = VL(:,j) - i*VL(:,j+1).

          LDVL is INTEGER
          The leading dimension of the array VL.  LDVL >= 1; if
          JOBVL = 'V', LDVL >= N.

          VR is REAL array, dimension (LDVR,N)
          If JOBVR = 'V', the right eigenvectors v(j) are stored one
          after another in the columns of VR, in the same order
          as their eigenvalues.
          If JOBVR = 'N', VR is not referenced.
          If the j-th eigenvalue is real, then v(j) = VR(:,j),
          the j-th column of VR.
          If the j-th and (j+1)-st eigenvalues form a complex
          conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
          v(j+1) = VR(:,j) - i*VR(:,j+1).

          LDVR is INTEGER
          The leading dimension of the array VR.  LDVR >= 1; if
          JOBVR = 'V', LDVR >= N.

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,3*N), and
          if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.  For good
          performance, LWORK must generally be larger.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = i, the QR algorithm failed to compute all the
                eigenvalues, and no eigenvectors have been computed;
                elements i+1:N of WR and WI contain eigenvalues which
                have converged.