--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libinterp/corefcn/__ilu__.cc	Fri Feb 27 19:44:28 2015 -0500
@@ -0,0 +1,1108 @@
+/*
+
+Copyright (C) 2014-2015 Eduardo Ramos Fernández <eduradical951@gmail.com>
+Copyright (C) 2013-2015 Kai T. Ohlhus <k.ohlhus@gmail.com>
+
+This file is part of Octave.
+
+Octave is free software; you can redistribute it and/or modify it
+under the terms of the GNU General Public License as published by the
+Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+Octave is distributed in the hope that it will be useful, but WITHOUT
+ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with Octave; see the file COPYING.  If not, see
+<http://www.gnu.org/licenses/>.
+
+*/
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "oct-locbuf.h"
+
+#include "defun.h"
+#include "error.h"
+#include "parse.h"
+
+// That function implements the IKJ and JKI variants of Gaussian elimination to
+// perform the ILUTP decomposition.  The behaviour is controlled by milu
+// parameter.  If milu = ['off'|'col'] the JKI version is performed taking
+// advantage of CCS format of the input matrix.  If milu = 'row' the input
+// matrix has to be transposed to obtain the equivalent CRS structure so we can
+// work efficiently with rows.  In this case IKJ version is used.
+template <typename octave_matrix_t, typename T>
+void ilu_0 (octave_matrix_t& sm, const std::string milu = "off")
+{
+
+  const octave_idx_type n = sm.cols ();
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, iw, n);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, uptr, n);
+  octave_idx_type j1, j2, jrow, jw, i, k, jj;
+  T tl, r;
+
+  enum {OFF, ROW, COL};
+  char opt;
+  if (milu == "row")
+    {
+      opt = ROW;
+      sm = sm.transpose ();
+    }
+  else if (milu == "col")
+    opt = COL;
+  else
+    opt = OFF;
+
+  octave_idx_type* cidx = sm.cidx ();
+  octave_idx_type* ridx = sm.ridx ();
+  T* data = sm.data ();
+  for (i = 0; i < n; i++)
+    iw[i] = -1;
+  for (k = 0; k < n; k++)
+    {
+      j1 = cidx[k];
+      j2 = cidx[k+1] - 1;
+      octave_idx_type j;
+      for (j = j1; j <= j2; j++)
+        {
+          iw[ridx[j]] = j;
+        }
+      r = 0;
+      j = j1;
+      jrow = ridx[j];
+      while ((jrow < k) && (j <= j2))
+        {
+          if (opt == ROW)
+            {
+              tl = data[j] / data[uptr[jrow]];
+              data[j] = tl;
+            }
+          for (jj = uptr[jrow] + 1; jj < cidx[jrow+1]; jj++)
+            {
+              jw = iw[ridx[jj]];
+              if (jw != -1)
+                if (opt == ROW)
+                  data[jw] -= tl * data[jj];
+                else
+                  data[jw] -= data[j] * data[jj];
+
+              else
+                // That is for the milu='row'
+                if (opt == ROW)
+                  r += tl * data[jj];
+                else if (opt == COL)
+                  r += data[j] * data[jj];
+            }
+          j++;
+          jrow = ridx[j];
+        }
+      uptr[k] = j;
+      if (opt != OFF)
+        data[uptr[k]] -= r;
+      if (opt != ROW)
+        for (jj = uptr[k] + 1; jj < cidx[k+1]; jj++)
+          data[jj] /=  data[uptr[k]];
+      if (k != jrow)
+        {
+          error ("ilu: A has a zero on the diagonal");
+          break;
+        }
+
+      if (data[j] == T(0))
+        {
+          error ("ilu: encountered a pivot equal to 0");
+          break;
+        }
+      for (i = j1; i <= j2; i++)
+        iw[ridx[i]] = -1;
+    }
+  if (opt == ROW)
+    sm = sm.transpose ();
+}
+
+DEFUN (__ilu0__, args, nargout,
+       "-*- texinfo -*-\n\
+@deftypefn  {Built-in Function} {[@var{L}, @var{U}] =} __ilu0__ (@var{A})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __ilu0__ (@var{A}, @var{milu})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} __ilu0__ (@var{A}, @dots{})\n\
+Undocumented internal function.\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+
+  int nargin = args.length ();
+  std::string milu;
+
+  if (nargout > 2 || nargin < 1 || nargin > 2)
+    {
+      print_usage ();
+      return retval;
+    }
+
+  // In ILU0 algorithm the zero-pattern of the input matrix is preserved so
+  // it's structure does not change during the algorithm.  The same input
+  // matrix is used to build the output matrix due to that fact.
+  octave_value_list param_list;
+  if (! args(0).is_complex_type ())
+    {
+      SparseMatrix sm = args(0).sparse_matrix_value ();
+      ilu_0 <SparseMatrix, double> (sm, milu);
+      if (!error_state)
+        {
+          param_list.append (sm);
+          retval(1) = feval ("triu", param_list)(0).sparse_matrix_value ();
+          SparseMatrix eye =
+            feval ("speye", octave_value_list (
+                     octave_value (sm.cols ())))(0).sparse_matrix_value ();
+          param_list.append (-1);
+          retval(0) = eye +
+                      feval ("tril", param_list)(0).sparse_matrix_value ();
+        }
+    }
+  else
+    {
+      SparseComplexMatrix sm = args(0).sparse_complex_matrix_value ();
+      ilu_0 <SparseComplexMatrix, Complex> (sm, milu);
+      if (! error_state)
+        {
+          param_list.append (sm);
+          retval(1) =
+            feval ("triu", param_list)(0).sparse_complex_matrix_value ();
+          SparseComplexMatrix eye =
+            feval ("speye", octave_value_list (
+                     octave_value (sm.cols ())))(0).sparse_complex_matrix_value ();
+          param_list.append (-1);
+          retval(0) =
+            eye + feval ("tril", param_list)(0).sparse_complex_matrix_value ();
+        }
+    }
+
+  return retval;
+}
+
+template <typename octave_matrix_t, typename T>
+void ilu_crout (octave_matrix_t& sm_l, octave_matrix_t& sm_u,
+                octave_matrix_t& L, octave_matrix_t& U, T* cols_norm,
+                T* rows_norm, const T droptol = 0,
+                const std::string milu = "off")
+{
+
+  // Map the strings into chars for faster comparing inside loops
+  char opt;
+  enum {OFF, ROW, COL};
+  if (milu == "row")
+    opt = ROW;
+  else if (milu == "col")
+    opt = COL;
+  else
+    opt = OFF;
+
+  octave_idx_type jrow, i, j, k, jj, total_len_l, total_len_u, max_len_u,
+                  max_len_l, w_len_u, w_len_l, cols_list_len, rows_list_len;
+
+  const octave_idx_type n = sm_u.cols ();
+  sm_u = sm_u.transpose ();
+
+  max_len_u = sm_u.nnz ();
+  max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n;
+  max_len_l = sm_l.nnz ();
+  max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n;
+  // Extract pointers to the arrays for faster access inside loops
+  octave_idx_type* cidx_in_u = sm_u.cidx ();
+  octave_idx_type* ridx_in_u = sm_u.ridx ();
+  T* data_in_u = sm_u.data ();
+  octave_idx_type* cidx_in_l = sm_l.cidx ();
+  octave_idx_type* ridx_in_l = sm_l.ridx ();
+  T* data_in_l = sm_l.data ();
+
+  // L output arrays
+  Array <octave_idx_type> ridx_out_l (dim_vector (max_len_l, 1));
+  octave_idx_type* ridx_l = ridx_out_l.fortran_vec ();
+  Array <T> data_out_l (dim_vector (max_len_l, 1));
+  T* data_l = data_out_l.fortran_vec ();
+
+  // U output arrays
+  Array <octave_idx_type> ridx_out_u (dim_vector (max_len_u, 1));
+  octave_idx_type* ridx_u = ridx_out_u.fortran_vec ();
+  Array <T> data_out_u (dim_vector (max_len_u, 1));
+  T* data_u = data_out_u.fortran_vec ();
+
+  // Working arrays
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, cidx_l, n + 1);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, cidx_u, n + 1);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, cols_list, n);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, rows_list, n);
+  OCTAVE_LOCAL_BUFFER (T, w_data_l, n);
+  OCTAVE_LOCAL_BUFFER (T, w_data_u, n);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, Ufirst, n);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, Lfirst, n);
+  OCTAVE_LOCAL_BUFFER (T, cr_sum, n);
+
+  T zero = T (0);
+
+  cidx_u[0] = cidx_in_u[0];
+  cidx_l[0] = cidx_in_l[0];
+  for (i = 0; i < n; i++)
+    {
+      w_data_u[i] = zero;
+      w_data_l[i] = zero;
+      cr_sum[i] = zero;
+    }
+
+  total_len_u = 0;
+  total_len_l = 0;
+  cols_list_len = 0;
+  rows_list_len = 0;
+
+  for (k = 0; k < n; k++)
+    {
+      // Load the working column and working row
+      for (i = cidx_in_l[k]; i < cidx_in_l[k+1]; i++)
+        w_data_l[ridx_in_l[i]] = data_in_l[i];
+
+      for (i = cidx_in_u[k]; i < cidx_in_u[k+1]; i++)
+        w_data_u[ridx_in_u[i]] = data_in_u[i];
+
+      // Update U working row
+      for (j = 0; j < rows_list_len; j++)
+        {
+          if ((Ufirst[rows_list[j]] != -1))
+            for (jj = Ufirst[rows_list[j]]; jj < cidx_u[rows_list[j]+1]; jj++)
+              {
+                jrow = ridx_u[jj];
+                w_data_u[jrow] -= data_u[jj] * data_l[Lfirst[rows_list[j]]];
+              }
+        }
+      // Update L working column
+      for (j = 0; j < cols_list_len; j++)
+        {
+          if (Lfirst[cols_list[j]] != -1)
+            for (jj = Lfirst[cols_list[j]]; jj < cidx_l[cols_list[j]+1]; jj++)
+              {
+                jrow = ridx_l[jj];
+                w_data_l[jrow] -= data_l[jj] * data_u[Ufirst[cols_list[j]]];
+              }
+        }
+
+      if ((max_len_u - total_len_u) < n)
+        {
+          max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n;
+          data_out_u.resize (dim_vector (max_len_u, 1));
+          data_u = data_out_u.fortran_vec ();
+          ridx_out_u.resize (dim_vector (max_len_u, 1));
+          ridx_u = ridx_out_u.fortran_vec ();
+        }
+
+      if ((max_len_l - total_len_l) < n)
+        {
+          max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n;
+          data_out_l.resize (dim_vector (max_len_l, 1));
+          data_l = data_out_l.fortran_vec ();
+          ridx_out_l.resize (dim_vector (max_len_l, 1));
+          ridx_l = ridx_out_l.fortran_vec ();
+        }
+
+      // Expand the working row into the U output data structures
+      w_len_l = 0;
+      data_u[total_len_u] = w_data_u[k];
+      ridx_u[total_len_u] = k;
+      w_len_u = 1;
+      for (i = k + 1; i < n; i++)
+        {
+          if (w_data_u[i] != zero)
+            {
+              if (std::abs (w_data_u[i]) < (droptol * rows_norm[k]))
+                {
+                  if (opt == ROW)
+                    cr_sum[k] += w_data_u[i];
+                  else if (opt == COL)
+                    cr_sum[i] += w_data_u[i];
+                }
+              else
+                {
+                  data_u[total_len_u + w_len_u] = w_data_u[i];
+                  ridx_u[total_len_u + w_len_u] = i;
+                  w_len_u++;
+                }
+            }
+
+          // Expand the working column into the L output data structures
+          if (w_data_l[i] != zero)
+            {
+              if (std::abs (w_data_l[i]) < (droptol * cols_norm[k]))
+                {
+                  if (opt == COL)
+                    cr_sum[k] += w_data_l[i];
+                  else if (opt == ROW)
+                    cr_sum[i] += w_data_l[i];
+                }
+              else
+                {
+                  data_l[total_len_l + w_len_l] = w_data_l[i];
+                  ridx_l[total_len_l + w_len_l] = i;
+                  w_len_l++;
+                }
+            }
+          w_data_u[i] = zero;
+          w_data_l[i] = zero;
+        }
+
+      // Compensate row and column sums --> milu option
+      if (opt == COL || opt == ROW)
+        data_u[total_len_u] += cr_sum[k];
+
+      // Check if the pivot is zero
+      if (data_u[total_len_u] == zero)
+        {
+          error ("ilu: encountered a pivot equal to 0");
+          break;
+        }
+
+      // Scale the elements in L by the pivot
+      for (i = total_len_l ; i < (total_len_l + w_len_l); i++)
+        data_l[i] /= data_u[total_len_u];
+
+
+      total_len_u += w_len_u;
+      total_len_l += w_len_l;
+      // Check if there are too many elements to be indexed with
+      // octave_idx_type type due to fill-in during the process.
+      if (total_len_l < 0 || total_len_u < 0)
+        {
+          error ("ilu: integer overflow.  Too many fill-in elements in L or U");
+          break;
+        }
+      cidx_u[k+1] = cidx_u[k] - cidx_u[0] + w_len_u;
+      cidx_l[k+1] = cidx_l[k] - cidx_l[0] + w_len_l;
+
+      // The tricky part of the algorithm.  The arrays pointing to the first
+      // working element of each column in the next iteration (Lfirst) or
+      // the first working element of each row (Ufirst) are updated.  Also the
+      // arrays working as lists cols_list and rows_list are filled with
+      // indices pointing to Ufirst and Lfirst respectively.
+      // TODO: Maybe the -1 indicating in Ufirst and Lfirst, that no elements
+      // have to be considered in a certain column or row in next iteration,
+      // can be removed.  It feels safer to me using such an indicator.
+      if (k < (n - 1))
+        {
+          if (w_len_u > 0)
+            Ufirst[k] = cidx_u[k];
+          else
+            Ufirst[k] = -1;
+          if (w_len_l > 0)
+            Lfirst[k] = cidx_l[k];
+          else
+            Lfirst[k] = -1;
+          cols_list_len = 0;
+          rows_list_len = 0;
+          for (i = 0; i <= k; i++)
+            {
+              if (Ufirst[i] != -1)
+                {
+                  jj = ridx_u[Ufirst[i]];
+                  if (jj < (k + 1))
+                    {
+                      if (Ufirst[i] < (cidx_u[i+1]))
+                        {
+                          Ufirst[i]++;
+                          if (Ufirst[i] == cidx_u[i+1])
+                            Ufirst[i] = -1;
+                          else
+                            jj = ridx_u[Ufirst[i]];
+                        }
+                    }
+                  if (jj == (k + 1))
+                    {
+                      cols_list[cols_list_len] = i;
+                      cols_list_len++;
+                    }
+                }
+
+              if (Lfirst[i] != -1)
+                {
+                  jj = ridx_l[Lfirst[i]];
+                  if (jj < (k + 1))
+                    if (Lfirst[i] < (cidx_l[i+1]))
+                      {
+                        Lfirst[i]++;
+                        if (Lfirst[i] == cidx_l[i+1])
+                          Lfirst[i] = -1;
+                        else
+                          jj = ridx_l[Lfirst[i]];
+                      }
+                  if (jj == (k + 1))
+                    {
+                      rows_list[rows_list_len] = i;
+                      rows_list_len++;
+                    }
+                }
+            }
+        }
+    }
+
+  if (! error_state)
+    {
+      // Build the output matrices
+      L = octave_matrix_t (n, n, total_len_l);
+      U = octave_matrix_t (n, n, total_len_u);
+      for (i = 0; i <= n; i++)
+        L.cidx (i) = cidx_l[i];
+      for (i = 0; i < total_len_l; i++)
+        {
+          L.ridx (i) = ridx_l[i];
+          L.data (i) = data_l[i];
+        }
+      for (i = 0; i <= n; i++)
+        U.cidx (i) = cidx_u[i];
+      for (i = 0; i < total_len_u; i++)
+        {
+          U.ridx (i) = ridx_u[i];
+          U.data (i) = data_u[i];
+        }
+      U = U.transpose ();
+    }
+}
+
+DEFUN (__iluc__, args, nargout,
+       "-*- texinfo -*-\n\
+@deftypefn  {Built-in Function} {[@var{L}, @var{U}] =} __iluc__ (@var{A})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __iluc__ (@var{A}, @var{droptol}) \n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __iluc__ (@var{A}, @var{droptol}, @var{milu})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} __iluc__ (@var{A}, @dots{})\n\
+Undocumented internal function.\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+  int nargin = args.length ();
+  std::string milu = "off";
+  double droptol = 0;
+
+  if (nargout != 2 || nargin < 1 || nargin > 3)
+    {
+      print_usage ();
+      return retval;
+    }
+
+  // Don't repeat input validation of arguments done in ilu.m
+  if (nargin >= 2)
+    droptol = args(1).double_value ();
+
+  if (nargin == 3)
+    milu = args(2).string_value ();
+
+  octave_value_list param_list;
+  if (! args(0).is_complex_type ())
+    {
+      Array<double> cols_norm, rows_norm;
+      param_list.append (args(0).sparse_matrix_value ());
+      SparseMatrix sm_u = feval ("triu", param_list)(0).sparse_matrix_value ();
+      param_list.append (-1);
+      SparseMatrix sm_l = feval ("tril", param_list)(0).sparse_matrix_value ();
+      param_list(1) = "rows";
+      rows_norm = feval ("norm", param_list)(0).vector_value ();
+      param_list(1) = "cols";
+      cols_norm = feval ("norm", param_list)(0).vector_value ();
+      param_list.clear ();
+      SparseMatrix U;
+      SparseMatrix L;
+      ilu_crout <SparseMatrix, double> (sm_l, sm_u, L, U,
+                                        cols_norm.fortran_vec (),
+                                        rows_norm.fortran_vec (),
+                                        droptol, milu);
+      if (! error_state)
+        {
+          param_list.append (octave_value (L.cols ()));
+          SparseMatrix eye =
+            feval ("speye", param_list)(0).sparse_matrix_value ();
+          retval(1) = U;
+          retval(0) = L + eye;
+        }
+    }
+  else
+    {
+      Array<Complex> cols_norm, rows_norm;
+      param_list.append (args(0).sparse_complex_matrix_value ());
+      SparseComplexMatrix sm_u =
+        feval("triu", param_list)(0).sparse_complex_matrix_value ();
+      param_list.append (-1);
+      SparseComplexMatrix sm_l =
+        feval("tril", param_list)(0).sparse_complex_matrix_value ();
+      param_list(1) = "rows";
+      rows_norm = feval ("norm", param_list)(0).complex_vector_value ();
+      param_list(1) = "cols";
+      cols_norm = feval ("norm", param_list)(0).complex_vector_value ();
+      param_list.clear ();
+      SparseComplexMatrix U;
+      SparseComplexMatrix L;
+      ilu_crout < SparseComplexMatrix, Complex >
+                (sm_l, sm_u, L, U, cols_norm.fortran_vec () ,
+                 rows_norm.fortran_vec (), Complex (droptol), milu);
+      if (! error_state)
+        {
+          param_list.append (octave_value (L.cols ()));
+          SparseComplexMatrix eye =
+            feval ("speye", param_list)(0).sparse_complex_matrix_value ();
+          retval(1) = U;
+          retval(0) = L + eye;
+        }
+    }
+
+  return retval;
+}
+
+// That function implements the IKJ and JKI variants of gaussian elimination
+// to perform the ILUTP decomposition.  The behaviour is controlled by milu
+// parameter.  If milu = ['off'|'col'] the JKI version is performed taking
+// advantage of CCS format of the input matrix.  Row pivoting is performed.
+// If milu = 'row' the input matrix has to be transposed to obtain the
+// equivalent CRS structure so we can work efficiently with rows.  In that
+// case IKJ version is used and column pivoting is performed.
+
+template <typename octave_matrix_t, typename T>
+void ilu_tp (octave_matrix_t& sm, octave_matrix_t& L, octave_matrix_t& U,
+             octave_idx_type nnz_u, octave_idx_type nnz_l, T* cols_norm,
+             Array <octave_idx_type>& perm_vec, const T droptol = T(0),
+             const T thresh = T(0), const  std::string milu = "off",
+             const double udiag = 0)
+{
+  char opt;
+  enum {OFF, ROW, COL};
+  if (milu == "row")
+    opt = ROW;
+  else if (milu == "col")
+    opt = COL;
+  else
+    opt = OFF;
+
+  const octave_idx_type n = sm.cols ();
+
+  // That is necessary for the JKI (milu = "row") variant.
+  if (opt == ROW)
+    sm = sm.transpose();
+
+  // Extract pointers to the arrays for faster access inside loops
+  octave_idx_type* cidx_in = sm.cidx ();
+  octave_idx_type* ridx_in = sm.ridx ();
+  T* data_in = sm.data ();
+  octave_idx_type jrow, i, j, k, jj, c, total_len_l, total_len_u, p_perm,
+                  max_ind, max_len_l, max_len_u;
+  T zero = T(0);
+
+  T tl = zero, aux, maximum;
+
+  max_len_u = nnz_u;
+  max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n;
+  max_len_l = nnz_l;
+  max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n;
+
+  Array <octave_idx_type> cidx_out_l (dim_vector (n + 1, 1));
+  octave_idx_type* cidx_l = cidx_out_l.fortran_vec ();
+  Array <octave_idx_type> ridx_out_l (dim_vector (max_len_l, 1));
+  octave_idx_type* ridx_l = ridx_out_l.fortran_vec ();
+  Array <T> data_out_l (dim_vector (max_len_l ,1));
+  T* data_l = data_out_l.fortran_vec ();
+  // Data for U
+  Array <octave_idx_type> cidx_out_u (dim_vector (n + 1, 1));
+  octave_idx_type* cidx_u = cidx_out_u.fortran_vec ();
+  Array <octave_idx_type> ridx_out_u (dim_vector (max_len_u, 1));
+  octave_idx_type* ridx_u = ridx_out_u.fortran_vec ();
+  Array <T> data_out_u (dim_vector (max_len_u, 1));
+  T* data_u = data_out_u.fortran_vec();
+
+  // Working arrays and permutation arrays
+  octave_idx_type w_len_u, w_len_l;
+  T total_sum, partial_col_sum = zero, partial_row_sum = zero;
+  std::set <octave_idx_type> iw_l;
+  std::set <octave_idx_type> iw_u;
+  std::set <octave_idx_type>::iterator it, it2;
+  OCTAVE_LOCAL_BUFFER (T, w_data, n);
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, iperm, n);
+  octave_idx_type* perm = perm_vec.fortran_vec ();
+  OCTAVE_LOCAL_BUFFER (octave_idx_type, uptr, n);
+
+
+  cidx_l[0] = cidx_in[0];
+  cidx_u[0] = cidx_in[0];
+  for (i = 0; i < n; i++)
+    {
+      w_data[i] = 0;
+      perm[i] = i;
+      iperm[i] = i;
+    }
+  total_len_u = 0;
+  total_len_l = 0;
+
+  for (k = 0; k < n; k++)
+    {
+
+      for (j = cidx_in[k]; j < cidx_in[k+1]; j++)
+        {
+          p_perm = iperm[ridx_in[j]];
+          w_data[iperm[ridx_in[j]]] = data_in[j];
+          if (p_perm > k)
+            iw_l.insert (ridx_in[j]);
+          else
+            iw_u.insert (p_perm);
+        }
+
+      it = iw_u.begin ();
+      jrow = *it;
+      total_sum = zero;
+      while ((jrow < k) && (it != iw_u.end ()))
+        {
+          if (opt == COL)
+            partial_col_sum = w_data[jrow];
+          if (w_data[jrow] != zero)
+            {
+              if (opt == ROW)
+                {
+                  partial_row_sum = w_data[jrow];
+                  tl = w_data[jrow] / data_u[uptr[jrow]];
+                }
+              for (jj = cidx_l[jrow]; jj < cidx_l[jrow+1]; jj++)
+                {
+                  p_perm = iperm[ridx_l[jj]];
+                  aux = w_data[p_perm];
+                  if (opt == ROW)
+                    {
+                      w_data[p_perm] -= tl * data_l[jj];
+                      partial_row_sum += tl * data_l[jj];
+                    }
+                  else
+                    {
+                      tl = data_l[jj] * w_data[jrow];
+                      w_data[p_perm] -= tl;
+                      if (opt == COL)
+                        partial_col_sum += tl;
+                    }
+
+                  if ((aux == zero) && (w_data[p_perm] != zero))
+                    {
+                      if (p_perm > k)
+                        iw_l.insert (ridx_l[jj]);
+                      else
+                        iw_u.insert (p_perm);
+                    }
+                }
+
+              // Drop element from the U part in IKJ and L part in JKI
+              // variant (milu = [col|off])
+              if ((std::abs (w_data[jrow]) < (droptol * cols_norm[k]))
+                  && (w_data[jrow] != zero))
+                {
+                  if (opt == COL)
+                    total_sum += partial_col_sum;
+                  else if (opt == ROW)
+                    total_sum += partial_row_sum;
+                  w_data[jrow] = zero;
+                  it2 = it;
+                  it++;
+                  iw_u.erase (it2);
+                  jrow = *it;
+                  continue;
+                }
+              else
+                // This is the element scaled by the pivot
+                // in the actual iteration
+                if (opt == ROW)
+                  w_data[jrow] = tl;
+            }
+          jrow = *(++it);
+        }
+
+      // Search for the pivot and update iw_l and iw_u if the pivot is not the
+      // diagonal element
+      if ((thresh > zero) && (k < (n - 1)))
+        {
+          maximum = std::abs (w_data[k]) / thresh;
+          max_ind = perm[k];
+          for (it = iw_l.begin (); it != iw_l.end (); ++it)
+            {
+              p_perm = iperm[*it];
+              if (std::abs (w_data[p_perm]) > maximum)
+                {
+                  maximum = std::abs (w_data[p_perm]);
+                  max_ind = *it;
+                  it2 = it;
+                }
+            }
+          // If the pivot is not the diagonal element update all.
+          p_perm = iperm[max_ind];
+          if (max_ind != perm[k])
+            {
+              iw_l.erase (it2);
+              if (w_data[k] != zero)
+                iw_l.insert (perm[k]);
+              else
+                iw_u.insert (k);
+              // Swap data and update permutation vectors
+              aux = w_data[k];
+              iperm[perm[p_perm]] = k;
+              iperm[perm[k]] = p_perm;
+              c = perm[k];
+              perm[k] = perm[p_perm];
+              perm[p_perm] = c;
+              w_data[k] = w_data[p_perm];
+              w_data[p_perm] = aux;
+            }
+
+        }
+
+      // Drop elements in the L part in the IKJ and from the U part in the JKI
+      // version.
+      it = iw_l.begin ();
+      while (it != iw_l.end ())
+        {
+          p_perm = iperm[*it];
+          if (droptol > zero)
+            if (std::abs (w_data[p_perm]) < (droptol * cols_norm[k]))
+              {
+                if (opt != OFF)
+                  total_sum += w_data[p_perm];
+                w_data[p_perm] = zero;
+                it2 = it;
+                it++;
+                iw_l.erase (it2);
+                continue;
+              }
+
+          it++;
+        }
+
+      // If milu == [row|col] summation is preserved.
+      // Compensate diagonal element.
+      if (opt != OFF)
+        {
+          if ((total_sum > zero) && (w_data[k] == zero))
+            iw_u.insert (k);
+          w_data[k] += total_sum;
+        }
+
+
+
+      // Check if the pivot is zero and if udiag is active.
+      // NOTE: If the pivot == 0 and udiag is active, then if milu = [col|row]
+      //       will not preserve the row sum for that column/row.
+      if (w_data[k] == zero)
+        {
+          if (udiag == 1)
+            {
+              w_data[k] = droptol;
+              iw_u.insert (k);
+            }
+          else
+            {
+              error ("ilu: encountered a pivot equal to 0");
+              break;
+            }
+        }
+
+      // Scale the elements on the L part for IKJ version (milu = [col|off])
+      if (opt != ROW)
+        for (it = iw_l.begin (); it != iw_l.end (); ++it)
+          {
+            p_perm = iperm[*it];
+            w_data[p_perm] = w_data[p_perm] / w_data[k];
+          }
+
+
+      if ((max_len_u - total_len_u) < n)
+        {
+          max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n;
+          data_out_u.resize (dim_vector (max_len_u, 1));
+          data_u = data_out_u.fortran_vec ();
+          ridx_out_u.resize (dim_vector (max_len_u, 1));
+          ridx_u = ridx_out_u.fortran_vec ();
+        }
+
+      if ((max_len_l - total_len_l) < n)
+        {
+          max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n;
+          data_out_l.resize (dim_vector (max_len_l, 1));
+          data_l = data_out_l.fortran_vec ();
+          ridx_out_l.resize (dim_vector (max_len_l, 1));
+          ridx_l = ridx_out_l.fortran_vec ();
+        }
+
+      // Expand working vector into U.
+      w_len_u = 0;
+      for (it = iw_u.begin (); it != iw_u.end (); ++it)
+        {
+          if (w_data[*it] != zero)
+            {
+              data_u[total_len_u + w_len_u] = w_data[*it];
+              ridx_u[total_len_u + w_len_u] = *it;
+              w_len_u++;
+            }
+          w_data[*it] = 0;
+        }
+      // Expand working vector into L.
+      w_len_l = 0;
+      for (it = iw_l.begin (); it != iw_l.end (); ++it)
+        {
+          p_perm = iperm[*it];
+          if (w_data[p_perm] != zero)
+            {
+              data_l[total_len_l + w_len_l] = w_data[p_perm];
+              ridx_l[total_len_l + w_len_l] = *it;
+              w_len_l++;
+            }
+          w_data[p_perm] = 0;
+        }
+      total_len_u += w_len_u;
+      total_len_l += w_len_l;
+      // Check if there are too many elements to be indexed with
+      // octave_idx_type type due to fill-in during the process.
+      if (total_len_l < 0 || total_len_u < 0)
+        {
+          error ("ilu: Integer overflow.  Too many fill-in elements in L or U");
+          break;
+        }
+      if (opt == ROW)
+        uptr[k] = total_len_u - 1;
+      cidx_u[k+1] = cidx_u[k] - cidx_u[0] + w_len_u;
+      cidx_l[k+1] = cidx_l[k] - cidx_l[0] + w_len_l;
+
+      iw_l.clear ();
+      iw_u.clear ();
+    }
+
+  if (! error_state)
+    {
+      octave_matrix_t *L_ptr;
+      octave_matrix_t *U_ptr;
+      octave_matrix_t diag (n, n, n);
+
+      // L and U are interchanged if milu = 'row'.  It is a matter
+      // of nomenclature to re-use code with both IKJ and JKI
+      // versions of the algorithm.
+      if (opt == ROW)
+        {
+          L_ptr = &U;
+          U_ptr = &L;
+          L = octave_matrix_t (n, n, total_len_u - n);
+          U = octave_matrix_t (n, n, total_len_l);
+        }
+      else
+        {
+          L_ptr = &L;
+          U_ptr = &U;
+          L = octave_matrix_t (n, n, total_len_l);
+          U = octave_matrix_t (n, n, total_len_u);
+        }
+
+      for (i = 0; i <= n; i++)
+        {
+          L_ptr->cidx (i) = cidx_l[i];
+          U_ptr->cidx (i) = cidx_u[i];
+          if (opt == ROW)
+            U_ptr->cidx (i) -= i;
+        }
+
+      for (i = 0; i < n; i++)
+        {
+          if (opt == ROW)
+            diag.elem (i,i) = data_u[uptr[i]];
+          j = cidx_l[i];
+
+          while (j < cidx_l[i+1])
+            {
+              L_ptr->ridx (j) = ridx_l[j];
+              L_ptr->data (j) = data_l[j];
+              j++;
+            }
+          j = cidx_u[i];
+
+          while (j < cidx_u[i+1])
+            {
+              c = j;
+              if (opt == ROW)
+                {
+                  // The diagonal is removed from L if milu = 'row'.
+                  // That is because is convenient to have it inside
+                  // the L part to carry out the process.
+                  if (ridx_u[j] == i)
+                    {
+                      j++;
+                      continue;
+                    }
+                  else
+                    c -= i;
+                }
+              U_ptr->data (c) = data_u[j];
+              U_ptr->ridx (c) = ridx_u[j];
+              j++;
+            }
+        }
+
+      if (opt == ROW)
+        {
+          U = U.transpose ();
+          // The diagonal, conveniently permuted is added to U
+          U += diag.index (idx_vector::colon, perm_vec);
+          L = L.transpose ();
+        }
+    }
+}
+
+DEFUN (__ilutp__, args, nargout,
+       "-*- texinfo -*-\n\
+@deftypefn  {Built-in Function} {[@var{L}, @var{U}] =} __ilutp__ (@var{A})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh}, @var{milu})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh}, @var{milu}, @var{udiag})\n\
+@deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} __ilutp__ (@var{A}, @dots{})\n\
+Undocumented internal function.\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+
+  int nargin = args.length ();
+  std::string milu = "";
+  double droptol = 0, thresh = 1;
+  double udiag = 0;
+
+  if (nargout < 2 || nargout > 3 || nargin < 1 || nargin > 5)
+    {
+      print_usage ();
+      return retval;
+    }
+
+  // Don't repeat input validation of arguments done in ilu.m
+  if (nargin >= 2)
+    droptol = args(1).double_value ();
+
+  if (nargin >= 3)
+    thresh = args(2).double_value ();
+
+  if (nargin >= 4)
+    milu = args(3).string_value ();
+
+  if (nargin == 5)
+    udiag = args(4).double_value ();
+
+  octave_value_list param_list;
+  octave_idx_type nnz_u, nnz_l;
+  if (! args(0).is_complex_type ())
+    {
+      Array <double> rc_norm;
+      SparseMatrix sm = args(0).sparse_matrix_value ();
+      param_list.append (sm);
+      nnz_u =  (feval ("triu", param_list)(0).sparse_matrix_value ()).nnz ();
+      param_list.append (-1);
+      nnz_l =  (feval ("tril", param_list)(0).sparse_matrix_value ()).nnz ();
+      if (milu == "row")
+        param_list (1) = "rows";
+      else
+        param_list (1) = "cols";
+      rc_norm = feval ("norm", param_list)(0).vector_value ();
+      param_list.clear ();
+      Array <octave_idx_type> perm (dim_vector (sm.cols (), 1));
+      SparseMatrix U;
+      SparseMatrix L;
+      ilu_tp <SparseMatrix, double> (sm, L, U, nnz_u, nnz_l,
+                                     rc_norm.fortran_vec (),
+                                     perm, droptol, thresh, milu, udiag);
+      if (! error_state)
+        {
+          param_list.append (octave_value (L.cols ()));
+          SparseMatrix eye =
+            feval ("speye", param_list)(0).sparse_matrix_value ();
+          if (milu == "row")
+            {
+              if (nargout == 3)
+                {
+                  retval(2) = eye.index (idx_vector::colon, perm);
+                  retval(1) = U.index (idx_vector::colon, perm);
+                }
+              else if (nargout == 2)
+                retval(1) = U;
+              retval(0) = L + eye;
+            }
+          else
+            {
+              if (nargout == 3)
+                {
+                  retval(2) = eye.index (perm, idx_vector::colon);
+                  retval(1) = U;
+                  retval(0) = L.index (perm, idx_vector::colon) + eye;
+                }
+              else
+                {
+                  retval(1) = U;
+                  retval(0) = L + eye.index (perm, idx_vector::colon);
+                }
+            }
+        }
+    }
+  else
+    {
+      Array <Complex> rc_norm;
+      SparseComplexMatrix sm = args(0).sparse_complex_matrix_value ();
+      param_list.append (sm);
+      nnz_u =
+        feval ("triu", param_list)(0).sparse_complex_matrix_value ().nnz ();
+      param_list.append (-1);
+      nnz_l =
+        feval ("tril", param_list)(0).sparse_complex_matrix_value ().nnz ();
+      if (milu == "row")
+        param_list(1) = "rows";
+      else
+        param_list(1) = "cols";
+      rc_norm = feval ("norm", param_list)(0).complex_vector_value ();
+      Array <octave_idx_type> perm (dim_vector (sm.cols (), 1));
+      param_list.clear ();
+      SparseComplexMatrix U;
+      SparseComplexMatrix L;
+      ilu_tp < SparseComplexMatrix, Complex>
+              (sm, L, U, nnz_u, nnz_l, rc_norm.fortran_vec (), perm,
+               Complex (droptol), Complex (thresh), milu, udiag);
+
+      if (! error_state)
+        {
+          param_list.append (octave_value (L.cols ()));
+          SparseComplexMatrix eye =
+            feval ("speye", param_list)(0).sparse_complex_matrix_value ();
+          if (milu == "row")
+            {
+              if (nargout == 3)
+                {
+                  retval(2) = eye.index (idx_vector::colon, perm);
+                  retval(1) = U.index (idx_vector::colon, perm);
+                }
+              else if (nargout == 2)
+                retval(1) = U;
+              retval(0) = L + eye;
+            }
+          else
+            {
+              if (nargout == 3)
+                {
+                  retval(2) = eye.index (perm, idx_vector::colon);
+                  retval(1) = U;
+                  retval(0) = L.index (perm, idx_vector::colon) + eye;
+                }
+              else
+                {
+                  retval(1) = U;
+                  retval(0) = L + eye.index (perm, idx_vector::colon);
+                }
+            }
+        }
+    }
+
+  return retval;
+}
+
+/*
+## No test needed for internal helper function.
+%!assert (1)
+*/
+