////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 1998-2022 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// 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
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include <istream>
#include <ostream>

#include "quit.h"
#include "lo-ieee.h"
#include "lo-lapack-proto.h"
#include "lo-mappers.h"
#include "dRowVector.h"
#include "oct-locbuf.h"

#include "dDiagMatrix.h"
#include "CSparse.h"
#include "boolSparse.h"
#include "dSparse.h"
#include "oct-spparms.h"
#include "sparse-lu.h"
#include "MatrixType.h"
#include "oct-sparse.h"
#include "sparse-util.h"
#include "sparse-chol.h"
#include "sparse-qr.h"

#include "Sparse-op-defs.h"

#include "Sparse-diag-op-defs.h"

#include "Sparse-perm-op-defs.h"

// Define whether to use a basic QR solver or one that uses a Dulmange
// Mendelsohn factorization to separate the problem into under-determined,
// well-determined and over-determined parts and solves them separately
#if ! defined (USE_QRSOLVE)
#  include "sparse-dmsolve.h"
#endif

SparseMatrix::SparseMatrix (const SparseBoolMatrix& a)
  : MSparse<double> (a.rows (), a.cols (), a.nnz ())
{
  octave_idx_type nc = cols ();
  octave_idx_type nz = a.nnz ();

  for (octave_idx_type i = 0; i < nc + 1; i++)
    cidx (i) = a.cidx (i);

  for (octave_idx_type i = 0; i < nz; i++)
    {
      data (i) = a.data (i);
      ridx (i) = a.ridx (i);
    }
}

SparseMatrix::SparseMatrix (const DiagMatrix& a)
  : MSparse<double> (a.rows (), a.cols (), a.length ())
{
  octave_idx_type j = 0;
  octave_idx_type l = a.length ();
  for (octave_idx_type i = 0; i < l; i++)
    {
      cidx (i) = j;
      if (a(i, i) != 0.0)
        {
          data (j) = a(i, i);
          ridx (j) = i;
          j++;
        }
    }
  for (octave_idx_type i = l; i <= a.cols (); i++)
    cidx (i) = j;
}

bool
SparseMatrix::operator == (const SparseMatrix& a) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nz = nnz ();
  octave_idx_type nr_a = a.rows ();
  octave_idx_type nc_a = a.cols ();
  octave_idx_type nz_a = a.nnz ();

  if (nr != nr_a || nc != nc_a || nz != nz_a)
    return false;

  for (octave_idx_type i = 0; i < nc + 1; i++)
    if (cidx (i) != a.cidx (i))
      return false;

  for (octave_idx_type i = 0; i < nz; i++)
    if (data (i) != a.data (i) || ridx (i) != a.ridx (i))
      return false;

  return true;
}

bool
SparseMatrix::operator != (const SparseMatrix& a) const
{
  return !(*this == a);
}

bool
SparseMatrix::issymmetric (void) const
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr == nc && nr > 0)
    {
      for (octave_idx_type j = 0; j < nc; j++)
        {
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              octave_idx_type ri = ridx (i);

              if (ri != j)
                {
                  bool found = false;

                  for (octave_idx_type k = cidx (ri); k < cidx (ri+1); k++)
                    {
                      if (ridx (k) == j)
                        {
                          if (data (i) == data (k))
                            found = true;
                          break;
                        }
                    }

                  if (! found)
                    return false;
                }
            }
        }

      return true;
    }

  return false;
}

SparseMatrix&
SparseMatrix::insert (const SparseMatrix& a,
                      octave_idx_type r, octave_idx_type c)
{
  MSparse<double>::insert (a, r, c);
  return *this;
}

SparseMatrix&
SparseMatrix::insert (const SparseMatrix& a, const Array<octave_idx_type>& indx)
{
  MSparse<double>::insert (a, indx);
  return *this;
}

SparseMatrix
SparseMatrix::max (int dim) const
{
  Array<octave_idx_type> dummy_idx;
  return max (dummy_idx, dim);
}

SparseMatrix
SparseMatrix::max (Array<octave_idx_type>& idx_arg, int dim) const
{
  SparseMatrix result;
  dim_vector dv = dims ();
  octave_idx_type nr = dv(0);
  octave_idx_type nc = dv(1);

  if (dim >= dv.ndims ())
    {
      idx_arg.resize (dim_vector (nr, nc), 0);
      return *this;
    }

  if (dim < 0)
    dim = dv.first_non_singleton ();

  if (dim == 0)
    {
      idx_arg.resize (dim_vector (nr == 0 ? 0 : 1, nc), 0);

      if (nr == 0 || nc == 0 || dim >= dv.ndims ())
        return SparseMatrix (nr == 0 ? 0 : 1, nc);

      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          double tmp_max = octave::numeric_limits<double>::NaN ();
          octave_idx_type idx_j = 0;
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              if (ridx (i) != idx_j)
                break;
              else
                idx_j++;
            }

          if (idx_j != nr)
            tmp_max = 0.;

          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              double tmp = data (i);

              if (octave::math::isnan (tmp))
                continue;
              else if (octave::math::isnan (tmp_max) || tmp > tmp_max)
                {
                  idx_j = ridx (i);
                  tmp_max = tmp;
                }

            }

          idx_arg.elem (j) = (octave::math::isnan (tmp_max) ? 0 : idx_j);
          if (tmp_max != 0.)
            nel++;
        }

      result = SparseMatrix (1, nc, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          double tmp = elem (idx_arg(j), j);
          if (tmp != 0.)
            {
              result.xdata (ii) = tmp;
              result.xridx (ii++) = 0;
            }
          result.xcidx (j+1) = ii;

        }
    }
  else
    {
      idx_arg.resize (dim_vector (nr, nc == 0 ? 0 : 1), 0);

      if (nr == 0 || nc == 0 || dim >= dv.ndims ())
        return SparseMatrix (nr, nc == 0 ? 0 : 1);

      OCTAVE_LOCAL_BUFFER (octave_idx_type, found, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        found[i] = 0;

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
          if (found[ridx (i)] == -j)
            found[ridx (i)] = -j - 1;

      for (octave_idx_type i = 0; i < nr; i++)
        if (found[i] > -nc && found[i] < 0)
          idx_arg.elem (i) = -found[i];

      for (octave_idx_type j = 0; j < nc; j++)
        {
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              octave_idx_type ir = ridx (i);
              octave_idx_type ix = idx_arg.elem (ir);
              double tmp = data (i);

              if (octave::math::isnan (tmp))
                continue;
              else if (ix == -1 || tmp > elem (ir, ix))
                idx_arg.elem (ir) = j;
            }
        }

      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nr; j++)
        if (idx_arg.elem (j) == -1 || elem (j, idx_arg.elem (j)) != 0.)
          nel++;

      result = SparseMatrix (nr, 1, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      result.xcidx (1) = nel;
      for (octave_idx_type j = 0; j < nr; j++)
        {
          if (idx_arg(j) == -1)
            {
              idx_arg(j) = 0;
              result.xdata (ii) = octave::numeric_limits<double>::NaN ();
              result.xridx (ii++) = j;
            }
          else
            {
              double tmp = elem (j, idx_arg(j));
              if (tmp != 0.)
                {
                  result.xdata (ii) = tmp;
                  result.xridx (ii++) = j;
                }
            }
        }
    }

  return result;
}

SparseMatrix
SparseMatrix::min (int dim) const
{
  Array<octave_idx_type> dummy_idx;
  return min (dummy_idx, dim);
}

SparseMatrix
SparseMatrix::min (Array<octave_idx_type>& idx_arg, int dim) const
{
  SparseMatrix result;
  dim_vector dv = dims ();
  octave_idx_type nr = dv(0);
  octave_idx_type nc = dv(1);

  if (dim >= dv.ndims ())
    {
      idx_arg.resize (dim_vector (nr, nc), 0);
      return *this;
    }

  if (dim < 0)
    dim = dv.first_non_singleton ();

  if (dim == 0)
    {
      idx_arg.resize (dim_vector (nr == 0 ? 0 : 1, nc), 0);

      if (nr == 0 || nc == 0 || dim >= dv.ndims ())
        return SparseMatrix (nr == 0 ? 0 : 1, nc);

      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          double tmp_min = octave::numeric_limits<double>::NaN ();
          octave_idx_type idx_j = 0;
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              if (ridx (i) != idx_j)
                break;
              else
                idx_j++;
            }

          if (idx_j != nr)
            tmp_min = 0.;

          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              double tmp = data (i);

              if (octave::math::isnan (tmp))
                continue;
              else if (octave::math::isnan (tmp_min) || tmp < tmp_min)
                {
                  idx_j = ridx (i);
                  tmp_min = tmp;
                }

            }

          idx_arg.elem (j) = (octave::math::isnan (tmp_min) ? 0 : idx_j);
          if (tmp_min != 0.)
            nel++;
        }

      result = SparseMatrix (1, nc, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          double tmp = elem (idx_arg(j), j);
          if (tmp != 0.)
            {
              result.xdata (ii) = tmp;
              result.xridx (ii++) = 0;
            }
          result.xcidx (j+1) = ii;

        }
    }
  else
    {
      idx_arg.resize (dim_vector (nr, nc == 0 ? 0 : 1), 0);

      if (nr == 0 || nc == 0 || dim >= dv.ndims ())
        return SparseMatrix (nr, nc == 0 ? 0 : 1);

      OCTAVE_LOCAL_BUFFER (octave_idx_type, found, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        found[i] = 0;

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
          if (found[ridx (i)] == -j)
            found[ridx (i)] = -j - 1;

      for (octave_idx_type i = 0; i < nr; i++)
        if (found[i] > -nc && found[i] < 0)
          idx_arg.elem (i) = -found[i];

      for (octave_idx_type j = 0; j < nc; j++)
        {
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            {
              octave_idx_type ir = ridx (i);
              octave_idx_type ix = idx_arg.elem (ir);
              double tmp = data (i);

              if (octave::math::isnan (tmp))
                continue;
              else if (ix == -1 || tmp < elem (ir, ix))
                idx_arg.elem (ir) = j;
            }
        }

      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nr; j++)
        if (idx_arg.elem (j) == -1 || elem (j, idx_arg.elem (j)) != 0.)
          nel++;

      result = SparseMatrix (nr, 1, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      result.xcidx (1) = nel;
      for (octave_idx_type j = 0; j < nr; j++)
        {
          if (idx_arg(j) == -1)
            {
              idx_arg(j) = 0;
              result.xdata (ii) = octave::numeric_limits<double>::NaN ();
              result.xridx (ii++) = j;
            }
          else
            {
              double tmp = elem (j, idx_arg(j));
              if (tmp != 0.)
                {
                  result.xdata (ii) = tmp;
                  result.xridx (ii++) = j;
                }
            }
        }
    }

  return result;
}

/*

%!assert (max (max (speye (65536))), sparse (1))
%!assert (min (min (speye (65536))), sparse (0))
%!assert (size (max (sparse (8, 0), [], 1)), [1, 0])
%!assert (size (max (sparse (8, 0), [], 2)), [8, 0])
%!assert (size (max (sparse (0, 8), [], 1)), [0, 8])
%!assert (size (max (sparse (0, 8), [], 2)), [0, 1])
%!assert (size (min (sparse (8, 0), [], 1)), [1, 0])
%!assert (size (min (sparse (8, 0), [], 2)), [8, 0])
%!assert (size (min (sparse (0, 8), [], 1)), [0, 8])
%!assert (size (min (sparse (0, 8), [], 2)), [0, 1])

*/

RowVector
SparseMatrix::row (octave_idx_type i) const
{
  octave_idx_type nc = columns ();
  RowVector retval (nc, 0);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type k = cidx (j); k < cidx (j+1); k++)
      {
        if (ridx (k) == i)
          {
            retval(j) = data (k);
            break;
          }
      }

  return retval;
}

ColumnVector
SparseMatrix::column (octave_idx_type i) const
{
  octave_idx_type nr = rows ();
  ColumnVector retval (nr, 0);

  for (octave_idx_type k = cidx (i); k < cidx (i+1); k++)
    retval(ridx (k)) = data (k);

  return retval;
}

SparseMatrix
SparseMatrix::concat (const SparseMatrix& rb,
                      const Array<octave_idx_type>& ra_idx)
{
  // Don't use numel to avoid all possibility of an overflow
  if (rb.rows () > 0 && rb.cols () > 0)
    insert (rb, ra_idx(0), ra_idx(1));
  return *this;
}

SparseComplexMatrix
SparseMatrix::concat (const SparseComplexMatrix& rb,
                      const Array<octave_idx_type>& ra_idx)
{
  SparseComplexMatrix retval (*this);
  if (rb.rows () > 0 && rb.cols () > 0)
    retval.insert (rb, ra_idx(0), ra_idx(1));
  return retval;
}

SparseMatrix
real (const SparseComplexMatrix& a)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();
  octave_idx_type nz = a.nnz ();
  SparseMatrix r (nr, nc, nz);

  for (octave_idx_type i = 0; i < nc +1; i++)
    r.cidx (i) = a.cidx (i);

  for (octave_idx_type i = 0; i < nz; i++)
    {
      r.data (i) = std::real (a.data (i));
      r.ridx (i) = a.ridx (i);
    }

  r.maybe_compress (true);
  return r;
}

SparseMatrix
imag (const SparseComplexMatrix& a)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();
  octave_idx_type nz = a.nnz ();
  SparseMatrix r (nr, nc, nz);

  for (octave_idx_type i = 0; i < nc +1; i++)
    r.cidx (i) = a.cidx (i);

  for (octave_idx_type i = 0; i < nz; i++)
    {
      r.data (i) = std::imag (a.data (i));
      r.ridx (i) = a.ridx (i);
    }

  r.maybe_compress (true);
  return r;
}

/*

%!assert (nnz (real (sparse ([1i,1]))), 1)
%!assert (nnz (real (sparse ([1i,1]))), 1)

*/

SparseMatrix
SparseMatrix::inverse (void) const
{
  octave_idx_type info;
  double rcond;
  MatrixType mattype (*this);
  return inverse (mattype, info, rcond, 0, 0);
}

SparseMatrix
SparseMatrix::inverse (MatrixType& mattype) const
{
  octave_idx_type info;
  double rcond;
  return inverse (mattype, info, rcond, 0, 0);
}

SparseMatrix
SparseMatrix::inverse (MatrixType& mattype, octave_idx_type& info) const
{
  double rcond;
  return inverse (mattype, info, rcond, 0, 0);
}

SparseMatrix
SparseMatrix::dinverse (MatrixType& mattype, octave_idx_type& info,
                        double& rcond, const bool,
                        const bool calccond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  info = 0;

  if (nr == 0 || nc == 0 || nr != nc)
    (*current_liboctave_error_handler) ("inverse requires square matrix");

  // Print spparms("spumoni") info if requested
  int typ = mattype.type ();
  mattype.info ();

  if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal)
    (*current_liboctave_error_handler) ("incorrect matrix type");

  if (typ == MatrixType::Permuted_Diagonal)
    retval = transpose ();
  else
    retval = *this;

  // Force make_unique to be called
  double *v = retval.data ();

  if (calccond)
    {
      double dmax = 0.;
      double dmin = octave::numeric_limits<double>::Inf ();
      for (octave_idx_type i = 0; i < nr; i++)
        {
          double tmp = fabs (v[i]);
          if (tmp > dmax)
            dmax = tmp;
          if (tmp < dmin)
            dmin = tmp;
        }
      rcond = dmin / dmax;
    }

  for (octave_idx_type i = 0; i < nr; i++)
    v[i] = 1.0 / v[i];

  return retval;
}

SparseMatrix
SparseMatrix::tinverse (MatrixType& mattype, octave_idx_type& info,
                        double& rcond, const bool,
                        const bool calccond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  info = 0;

  if (nr == 0 || nc == 0 || nr != nc)
    (*current_liboctave_error_handler) ("inverse requires square matrix");

  // Print spparms("spumoni") info if requested
  int typ = mattype.type ();
  mattype.info ();

  if (typ != MatrixType::Upper && typ != MatrixType::Permuted_Upper
      && typ != MatrixType::Lower && typ != MatrixType::Permuted_Lower)
    (*current_liboctave_error_handler) ("incorrect matrix type");

  double anorm = 0.;
  double ainvnorm = 0.;

  if (calccond)
    {
      // Calculate the 1-norm of matrix for rcond calculation
      for (octave_idx_type j = 0; j < nr; j++)
        {
          double atmp = 0.;
          for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
            atmp += fabs (data (i));
          if (atmp > anorm)
            anorm = atmp;
        }
    }

  if (typ == MatrixType::Upper || typ == MatrixType::Lower)
    {
      octave_idx_type nz = nnz ();
      octave_idx_type cx = 0;
      octave_idx_type nz2 = nz;
      retval = SparseMatrix (nr, nc, nz2);

      for (octave_idx_type i = 0; i < nr; i++)
        {
          octave_quit ();
          // place the 1 in the identity position
          octave_idx_type cx_colstart = cx;

          if (cx == nz2)
            {
              nz2 *= 2;
              retval.change_capacity (nz2);
            }

          retval.xcidx (i) = cx;
          retval.xridx (cx) = i;
          retval.xdata (cx) = 1.0;
          cx++;

          // iterate across columns of input matrix
          for (octave_idx_type j = i+1; j < nr; j++)
            {
              double v = 0.;
              // iterate to calculate sum
              octave_idx_type colXp = retval.xcidx (i);
              octave_idx_type colUp = cidx (j);
              octave_idx_type rpX, rpU;

              if (cidx (j) == cidx (j+1))
                (*current_liboctave_error_handler) ("division by zero");

              do
                {
                  octave_quit ();
                  rpX = retval.xridx (colXp);
                  rpU = ridx (colUp);

                  if (rpX < rpU)
                    colXp++;
                  else if (rpX > rpU)
                    colUp++;
                  else
                    {
                      v -= retval.xdata (colXp) * data (colUp);
                      colXp++;
                      colUp++;
                    }
                }
              while (rpX < j && rpU < j && colXp < cx && colUp < nz);

              // get A(m,m)
              if (typ == MatrixType::Upper)
                colUp = cidx (j+1) - 1;
              else
                colUp = cidx (j);
              double pivot = data (colUp);
              if (pivot == 0. || ridx (colUp) != j)
                (*current_liboctave_error_handler) ("division by zero");

              if (v != 0.)
                {
                  if (cx == nz2)
                    {
                      nz2 *= 2;
                      retval.change_capacity (nz2);
                    }

                  retval.xridx (cx) = j;
                  retval.xdata (cx) = v / pivot;
                  cx++;
                }
            }

          // get A(m,m)
          octave_idx_type colUp;
          if (typ == MatrixType::Upper)
            colUp = cidx (i+1) - 1;
          else
            colUp = cidx (i);
          double pivot = data (colUp);
          if (pivot == 0. || ridx (colUp) != i)
            (*current_liboctave_error_handler) ("division by zero");

          if (pivot != 1.0)
            for (octave_idx_type j = cx_colstart; j < cx; j++)
              retval.xdata (j) /= pivot;
        }
      retval.xcidx (nr) = cx;
      retval.maybe_compress ();
    }
  else
    {
      octave_idx_type nz = nnz ();
      octave_idx_type cx = 0;
      octave_idx_type nz2 = nz;
      retval = SparseMatrix (nr, nc, nz2);

      OCTAVE_LOCAL_BUFFER (double, work, nr);
      OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nr);

      octave_idx_type *perm = mattype.triangular_perm ();
      if (typ == MatrixType::Permuted_Upper)
        {
          for (octave_idx_type i = 0; i < nr; i++)
            rperm[perm[i]] = i;
        }
      else
        {
          for (octave_idx_type i = 0; i < nr; i++)
            rperm[i] = perm[i];
          for (octave_idx_type i = 0; i < nr; i++)
            perm[rperm[i]] = i;
        }

      for (octave_idx_type i = 0; i < nr; i++)
        {
          octave_quit ();
          octave_idx_type iidx = rperm[i];

          for (octave_idx_type j = 0; j < nr; j++)
            work[j] = 0.;

          // place the 1 in the identity position
          work[iidx] = 1.0;

          // iterate across columns of input matrix
          for (octave_idx_type j = iidx+1; j < nr; j++)
            {
              double v = 0.;
              octave_idx_type jidx = perm[j];
              // iterate to calculate sum
              for (octave_idx_type k = cidx (jidx);
                   k < cidx (jidx+1); k++)
                {
                  octave_quit ();
                  v -= work[ridx (k)] * data (k);
                }

              // get A(m,m)
              double pivot;
              if (typ == MatrixType::Permuted_Upper)
                pivot = data (cidx (jidx+1) - 1);
              else
                pivot = data (cidx (jidx));
              if (pivot == 0.)
                (*current_liboctave_error_handler) ("division by zero");

              work[j] = v / pivot;
            }

          // get A(m,m)
          octave_idx_type colUp;
          if (typ == MatrixType::Permuted_Upper)
            colUp = cidx (perm[iidx]+1) - 1;
          else
            colUp = cidx (perm[iidx]);

          double pivot = data (colUp);
          if (pivot == 0.)
            (*current_liboctave_error_handler) ("division by zero");

          octave_idx_type new_cx = cx;
          for (octave_idx_type j = iidx; j < nr; j++)
            if (work[j] != 0.0)
              {
                new_cx++;
                if (pivot != 1.0)
                  work[j] /= pivot;
              }

          if (cx < new_cx)
            {
              nz2 = (2*nz2 < new_cx ? new_cx : 2*nz2);
              retval.change_capacity (nz2);
            }

          retval.xcidx (i) = cx;
          for (octave_idx_type j = iidx; j < nr; j++)
            if (work[j] != 0.)
              {
                retval.xridx (cx) = j;
                retval.xdata (cx++) = work[j];
              }
        }

      retval.xcidx (nr) = cx;
      retval.maybe_compress ();
    }

  if (calccond)
    {
      // Calculate the 1-norm of inverse matrix for rcond calculation
      for (octave_idx_type j = 0; j < nr; j++)
        {
          double atmp = 0.;
          for (octave_idx_type i = retval.cidx (j);
               i < retval.cidx (j+1); i++)
            atmp += fabs (retval.data (i));
          if (atmp > ainvnorm)
            ainvnorm = atmp;
        }

      rcond = 1. / ainvnorm / anorm;
    }

  return retval;
}

SparseMatrix
SparseMatrix::inverse (MatrixType& mattype, octave_idx_type& info,
                       double& rcond, bool, bool calc_cond) const
{
  if (nnz () == 0)
    {
      (*current_liboctave_error_handler)
        ("inverse of the null matrix not defined");
    }

  int typ = mattype.type (false);
  SparseMatrix ret;

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal)
    ret = dinverse (mattype, info, rcond, true, calc_cond);
  else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    ret = tinverse (mattype, info, rcond, true, calc_cond).transpose ();
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    {
      MatrixType newtype = mattype.transpose ();
      ret = transpose ().tinverse (newtype, info, rcond, true, calc_cond);
    }
  else
    {
      if (mattype.ishermitian ())
        {
          MatrixType tmp_typ (MatrixType::Upper);
          octave::math::sparse_chol<SparseMatrix> fact (*this, info, false);
          rcond = fact.rcond ();
          if (info == 0)
            {
              double rcond2;
              SparseMatrix Q = fact.Q ();
              SparseMatrix InvL = fact.L ().transpose ().tinverse (tmp_typ,
                                  info, rcond2, true, false);
              ret = Q * InvL.transpose () * InvL * Q.transpose ();
            }
          else
            {
              // Matrix is either singular or not positive definite
              mattype.mark_as_unsymmetric ();
            }
        }

      if (! mattype.ishermitian ())
        {
          octave_idx_type n = rows ();
          ColumnVector Qinit(n);
          for (octave_idx_type i = 0; i < n; i++)
            Qinit(i) = i;

          MatrixType tmp_typ (MatrixType::Upper);
          octave::math::sparse_lu<SparseMatrix> fact (*this,
                                                      Qinit, Matrix (),
                                                      false, false);
          rcond = fact.rcond ();
          if (rcond == 0.0)
            {
              // Return all Inf matrix with sparsity pattern of input.
              octave_idx_type nz = nnz ();
              ret = SparseMatrix (rows (), cols (), nz);
              std::fill (ret.xdata (), ret.xdata () + nz,
                         octave::numeric_limits<double>::Inf ());
              std::copy_n (ridx (), nz, ret.xridx ());
              std::copy_n (cidx (), cols () + 1, ret.xcidx ());

              return ret;
            }

          double rcond2;
          SparseMatrix InvL = fact.L ().transpose ().tinverse (tmp_typ,
                              info, rcond2, true, false);
          SparseMatrix InvU = fact.U ().tinverse (tmp_typ, info, rcond2,
                                                  true, false).transpose ();
          ret = fact.Pc ().transpose () * InvU * InvL * fact.Pr ();
        }
    }

  return ret;
}

DET
SparseMatrix::determinant (void) const
{
  octave_idx_type info;
  double rcond;
  return determinant (info, rcond, 0);
}

DET
SparseMatrix::determinant (octave_idx_type& info) const
{
  double rcond;
  return determinant (info, rcond, 0);
}

DET
SparseMatrix::determinant (octave_idx_type& err, double& rcond, bool) const
{
  DET retval;

#if defined (HAVE_UMFPACK)

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  if (nr == 0 || nc == 0 || nr != nc)
    {
      retval = DET (1.0);
    }
  else
    {
      err = 0;

      // Setup the control parameters
      Matrix Control (UMFPACK_CONTROL, 1);
      double *control = Control.fortran_vec ();
      UMFPACK_DNAME (defaults) (control);

      double tmp = octave::sparse_params::get_key ("spumoni");
      if (! octave::math::isnan (tmp))
        Control (UMFPACK_PRL) = tmp;

      tmp = octave::sparse_params::get_key ("piv_tol");
      if (! octave::math::isnan (tmp))
        {
          Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp;
          Control (UMFPACK_PIVOT_TOLERANCE) = tmp;
        }

      // Set whether we are allowed to modify Q or not
      tmp = octave::sparse_params::get_key ("autoamd");
      if (! octave::math::isnan (tmp))
        Control (UMFPACK_FIXQ) = tmp;

      // Turn-off UMFPACK scaling for LU
      Control (UMFPACK_SCALE) = UMFPACK_SCALE_NONE;

      UMFPACK_DNAME (report_control) (control);

      const octave_idx_type *Ap = cidx ();
      const octave_idx_type *Ai = ridx ();
      const double *Ax = data ();

      UMFPACK_DNAME (report_matrix) (nr, nc,
                                     octave::to_suitesparse_intptr (Ap),
                                     octave::to_suitesparse_intptr (Ai),
                                     Ax, 1, control);

      void *Symbolic;
      Matrix Info (1, UMFPACK_INFO);
      double *info = Info.fortran_vec ();
      int status = UMFPACK_DNAME (qsymbolic) (nr, nc,
                                              octave::to_suitesparse_intptr (Ap),
                                              octave::to_suitesparse_intptr (Ai),
                                              Ax, nullptr, &Symbolic, control, info);

      if (status < 0)
        {
          UMFPACK_DNAME (report_status) (control, status);
          UMFPACK_DNAME (report_info) (control, info);

          UMFPACK_DNAME (free_symbolic) (&Symbolic);

          (*current_liboctave_error_handler)
            ("SparseMatrix::determinant symbolic factorization failed");
        }
      else
        {
          UMFPACK_DNAME (report_symbolic) (Symbolic, control);

          void *Numeric;
          status = UMFPACK_DNAME (numeric) (octave::to_suitesparse_intptr (Ap),
                                            octave::to_suitesparse_intptr (Ai),
                                            Ax, Symbolic,
                                            &Numeric, control, info);
          UMFPACK_DNAME (free_symbolic) (&Symbolic);

          rcond = Info (UMFPACK_RCOND);

          if (status < 0)
            {
              UMFPACK_DNAME (report_status) (control, status);
              UMFPACK_DNAME (report_info) (control, info);

              UMFPACK_DNAME (free_numeric) (&Numeric);
              (*current_liboctave_error_handler)
                ("SparseMatrix::determinant numeric factorization failed");
            }
          else
            {
              UMFPACK_DNAME (report_numeric) (Numeric, control);

              double c10, e10;

              status = UMFPACK_DNAME (get_determinant) (&c10, &e10, Numeric,
                                                        info);

              if (status < 0)
                {
                  UMFPACK_DNAME (report_status) (control, status);
                  UMFPACK_DNAME (report_info) (control, info);

                  (*current_liboctave_error_handler)
                    ("SparseMatrix::determinant error calculating determinant");
                }
              else
                retval = DET (c10, e10, 10);

              UMFPACK_DNAME (free_numeric) (&Numeric);
            }
        }
    }

#else

  octave_unused_parameter (err);
  octave_unused_parameter (rcond);

  (*current_liboctave_error_handler)
    ("support for UMFPACK was unavailable or disabled "
     "when liboctave was built");

#endif

  return retval;
}

Matrix
SparseMatrix::dsolve (MatrixType& mattype, const Matrix& b,
                      octave_idx_type& err,
                      double& rcond, solve_singularity_handler,
                      bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc < nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      retval.resize (nc, b.cols (), 0.);
      if (typ == MatrixType::Diagonal)
        for (octave_idx_type j = 0; j < b.cols (); j++)
          for (octave_idx_type i = 0; i < nm; i++)
            retval(i, j) = b(i, j) / data (i);
      else
        for (octave_idx_type j = 0; j < b.cols (); j++)
          for (octave_idx_type k = 0; k < nc; k++)
            for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
              retval(k, j) = b(ridx (i), j) / data (i);

      if (calc_cond)
        {
          double dmax = 0.;
          double dmin = octave::numeric_limits<double>::Inf ();
          for (octave_idx_type i = 0; i < nm; i++)
            {
              double tmp = fabs (data (i));
              if (tmp > dmax)
                dmax = tmp;
              if (tmp < dmin)
                dmin = tmp;
            }
          rcond = dmin / dmax;
        }
      else
        rcond = 1.;
    }

  return retval;
}

SparseMatrix
SparseMatrix::dsolve (MatrixType& mattype, const SparseMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler, bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc < nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseMatrix (nc, b_nc, b_nz);

      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      if (typ == MatrixType::Diagonal)
        for (octave_idx_type j = 0; j < b_nc; j++)
          {
            for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
              {
                if (b.ridx (i) >= nm)
                  break;
                retval.xridx (ii) = b.ridx (i);
                retval.xdata (ii++) = b.data (i) / data (b.ridx (i));
              }
            retval.xcidx (j+1) = ii;
          }
      else
        for (octave_idx_type j = 0; j < b_nc; j++)
          {
            for (octave_idx_type l = 0; l < nc; l++)
              for (octave_idx_type i = cidx (l); i < cidx (l+1); i++)
                {
                  bool found = false;
                  octave_idx_type k;
                  for (k = b.cidx (j); k < b.cidx (j+1); k++)
                    if (ridx (i) == b.ridx (k))
                      {
                        found = true;
                        break;
                      }
                  if (found)
                    {
                      retval.xridx (ii) = l;
                      retval.xdata (ii++) = b.data (k) / data (i);
                    }
                }
            retval.xcidx (j+1) = ii;
          }

      if (calc_cond)
        {
          double dmax = 0.;
          double dmin = octave::numeric_limits<double>::Inf ();
          for (octave_idx_type i = 0; i < nm; i++)
            {
              double tmp = fabs (data (i));
              if (tmp > dmax)
                dmax = tmp;
              if (tmp < dmin)
                dmin = tmp;
            }
          rcond = dmin / dmax;
        }
      else
        rcond = 1.;
    }

  return retval;
}

ComplexMatrix
SparseMatrix::dsolve (MatrixType& mattype, const ComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler, bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc < nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      retval.resize (nc, b.cols (), 0);
      if (typ == MatrixType::Diagonal)
        for (octave_idx_type j = 0; j < b.cols (); j++)
          for (octave_idx_type i = 0; i < nm; i++)
            retval(i, j) = b(i, j) / data (i);
      else
        for (octave_idx_type j = 0; j < b.cols (); j++)
          for (octave_idx_type k = 0; k < nc; k++)
            for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
              retval(k, j) = b(ridx (i), j) / data (i);

      if (calc_cond)
        {
          double dmax = 0.;
          double dmin = octave::numeric_limits<double>::Inf ();
          for (octave_idx_type i = 0; i < nm; i++)
            {
              double tmp = fabs (data (i));
              if (tmp > dmax)
                dmax = tmp;
              if (tmp < dmin)
                dmin = tmp;
            }
          rcond = dmin / dmax;
        }
      else
        rcond = 1.;
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::dsolve (MatrixType& mattype, const SparseComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler, bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc < nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Diagonal && typ != MatrixType::Permuted_Diagonal)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseComplexMatrix (nc, b_nc, b_nz);

      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      if (typ == MatrixType::Diagonal)
        for (octave_idx_type j = 0; j < b.cols (); j++)
          {
            for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
              {
                if (b.ridx (i) >= nm)
                  break;
                retval.xridx (ii) = b.ridx (i);
                retval.xdata (ii++) = b.data (i) / data (b.ridx (i));
              }
            retval.xcidx (j+1) = ii;
          }
      else
        for (octave_idx_type j = 0; j < b.cols (); j++)
          {
            for (octave_idx_type l = 0; l < nc; l++)
              for (octave_idx_type i = cidx (l); i < cidx (l+1); i++)
                {
                  bool found = false;
                  octave_idx_type k;
                  for (k = b.cidx (j); k < b.cidx (j+1); k++)
                    if (ridx (i) == b.ridx (k))
                      {
                        found = true;
                        break;
                      }
                  if (found)
                    {
                      retval.xridx (ii) = l;
                      retval.xdata (ii++) = b.data (k) / data (i);
                    }
                }
            retval.xcidx (j+1) = ii;
          }

      if (calc_cond)
        {
          double dmax = 0.;
          double dmin = octave::numeric_limits<double>::Inf ();
          for (octave_idx_type i = 0; i < nm; i++)
            {
              double tmp = fabs (data (i));
              if (tmp > dmax)
                dmax = tmp;
              if (tmp < dmin)
                dmin = tmp;
            }
          rcond = dmin / dmax;
        }
      else
        rcond = 1.;
    }

  return retval;
}

Matrix
SparseMatrix::utsolve (MatrixType& mattype, const Matrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      octave_idx_type b_nc = b.cols ();
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      if (typ == MatrixType::Permuted_Upper)
        {
          retval.resize (nc, b_nc);
          octave_idx_type *perm = mattype.triangular_perm ();
          OCTAVE_LOCAL_BUFFER (double, work, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                work[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                work[i] = 0.;

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  octave_idx_type kidx = perm[k];

                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (kidx+1)-1) != k
                          || data (cidx (kidx+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (kidx+1)-1);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (kidx);
                           i < cidx (kidx+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (perm[i], j) = work[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      octave_idx_type iidx = perm[k];

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (iidx+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (iidx);
                               i < cidx (iidx+1)-1; i++)
                            {
                              octave_idx_type idx2 = ridx (i);
                              work[idx2] = work[idx2] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (double, work, nm);
          retval.resize (nc, b_nc);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                work[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                work[i] = 0.;

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (k+1)-1) != k
                          || data (cidx (k+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (k+1)-1);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (i, j) = work[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

SparseMatrix
SparseMatrix::utsolve (MatrixType& mattype, const SparseMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseMatrix (nc, b_nc, b_nz);
      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      octave_idx_type x_nz = b_nz;

      if (typ == MatrixType::Permuted_Upper)
        {
          octave_idx_type *perm = mattype.triangular_perm ();
          OCTAVE_LOCAL_BUFFER (double, work, nm);

          OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            rperm[perm[i]] = i;

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                work[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  octave_idx_type kidx = perm[k];

                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (kidx+1)-1) != k
                          || data (cidx (kidx+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (kidx+1)-1);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (kidx);
                           i < cidx (kidx+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (work[rperm[i]] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = work[rperm[i]];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      octave_idx_type iidx = perm[k];

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (iidx+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (iidx);
                               i < cidx (iidx+1)-1; i++)
                            {
                              octave_idx_type idx2 = ridx (i);
                              work[idx2] = work[idx2] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (double, work, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                work[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (k+1)-1) != k
                          || data (cidx (k+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (k+1)-1);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = work[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1)-1; i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }
  return retval;
}

ComplexMatrix
SparseMatrix::utsolve (MatrixType& mattype, const ComplexMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      octave_idx_type b_nc = b.cols ();
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      if (typ == MatrixType::Permuted_Upper)
        {
          retval.resize (nc, b_nc);
          octave_idx_type *perm = mattype.triangular_perm ();
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                cwork[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                cwork[i] = 0.;

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  octave_idx_type kidx = perm[k];

                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (kidx+1)-1) != k
                          || data (cidx (kidx+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (kidx+1)-1);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (kidx);
                           i < cidx (kidx+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (perm[i], j) = cwork[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      octave_idx_type iidx = perm[k];

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (iidx+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (iidx);
                               i < cidx (iidx+1)-1; i++)
                            {
                              octave_idx_type idx2 = ridx (i);
                              work[idx2] = work[idx2] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);
          retval.resize (nc, b_nc);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                cwork[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                cwork[i] = 0.;

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (k+1)-1) != k
                          || data (cidx (k+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (k+1)-1);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp  * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (i, j) = cwork[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1)-1; i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::utsolve (MatrixType& mattype, const SparseComplexMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseComplexMatrix (nc, b_nc, b_nz);
      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      octave_idx_type x_nz = b_nz;

      if (typ == MatrixType::Permuted_Upper)
        {
          octave_idx_type *perm = mattype.triangular_perm ();
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);

          OCTAVE_LOCAL_BUFFER (octave_idx_type, rperm, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            rperm[perm[i]] = i;

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                cwork[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                cwork[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  octave_idx_type kidx = perm[k];

                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (kidx+1)-1) != k
                          || data (cidx (kidx+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (kidx+1)-1);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (kidx);
                           i < cidx (kidx+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[rperm[i]] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = cwork[rperm[i]];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      octave_idx_type iidx = perm[k];

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (iidx+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (iidx);
                               i < cidx (iidx+1)-1; i++)
                            {
                              octave_idx_type idx2 = ridx (i);
                              work[idx2] = work[idx2] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                cwork[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                cwork[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = nc-1; k >= 0; k--)
                {
                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (k+1)-1) != k
                          || data (cidx (k+1)-1) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (k+1)-1);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1)-1; i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = cwork[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k >= 0; k--)
                    {
                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k+1)-1);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1)-1; i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = 0; i < j+1; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

Matrix
SparseMatrix::ltsolve (MatrixType& mattype, const Matrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      octave_idx_type b_nc = b.cols ();
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      if (typ == MatrixType::Permuted_Lower)
        {
          retval.resize (nc, b_nc);
          OCTAVE_LOCAL_BUFFER (double, work, nm);
          octave_idx_type *perm = mattype.triangular_perm ();

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              if (nc > nr)
                for (octave_idx_type i = 0; i < nm; i++)
                  work[i] = 0.;
              for (octave_idx_type i = 0; i < nr; i++)
                work[perm[i]] = b(i, j);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (work[k] != 0.)
                    {
                      octave_idx_type minr = nr;
                      octave_idx_type mini = 0;

                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        if (perm[ridx (i)] < minr)
                          {
                            minr = perm[ridx (i)];
                            mini = i;
                          }

                      if (minr != k || data (mini) == 0)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (mini);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        {
                          if (i == mini)
                            continue;

                          octave_idx_type iidx = perm[ridx (i)];
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval(i, j) = work[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = 0; k < nc; k++)
                    {
                      if (work[k] != 0.)
                        {
                          octave_idx_type minr = nr;
                          octave_idx_type mini = 0;

                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            if (perm[ridx (i)] < minr)
                              {
                                minr = perm[ridx (i)];
                                mini = i;
                              }

                          double tmp = work[k] / data (mini);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            {
                              if (i == mini)
                                continue;

                              octave_idx_type iidx = perm[ridx (i)];
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }

                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (double, work, nm);
          retval.resize (nc, b_nc, 0.);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                work[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                work[i] = 0.;
              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (k)) != k || data (cidx (k)) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (k));
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k)+1;
                           i < cidx (k+1); i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (i, j) = work[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k < nc; k++)
                    {

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k));
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k)+1;
                               i < cidx (k+1); i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

SparseMatrix
SparseMatrix::ltsolve (MatrixType& mattype, const SparseMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseMatrix (nc, b_nc, b_nz);
      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      octave_idx_type x_nz = b_nz;

      if (typ == MatrixType::Permuted_Lower)
        {
          OCTAVE_LOCAL_BUFFER (double, work, nm);
          octave_idx_type *perm = mattype.triangular_perm ();

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                work[perm[b.ridx (i)]] = b.data (i);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (work[k] != 0.)
                    {
                      octave_idx_type minr = nr;
                      octave_idx_type mini = 0;

                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        if (perm[ridx (i)] < minr)
                          {
                            minr = perm[ridx (i)];
                            mini = i;
                          }

                      if (minr != k || data (mini) == 0)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (mini);
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        {
                          if (i == mini)
                            continue;

                          octave_idx_type iidx = perm[ridx (i)];
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = work[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = 0; k < nc; k++)
                    {
                      if (work[k] != 0.)
                        {
                          octave_idx_type minr = nr;
                          octave_idx_type mini = 0;

                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            if (perm[ridx (i)] < minr)
                              {
                                minr = perm[ridx (i)];
                                mini = i;
                              }

                          double tmp = work[k] / data (mini);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            {
                              if (i == mini)
                                continue;

                              octave_idx_type iidx = perm[ridx (i)];
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }

                  double atmp = 0;
                  for (octave_idx_type i = j; i < nr; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (double, work, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                work[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (work[k] != 0.)
                    {
                      if (ridx (cidx (k)) != k || data (cidx (k)) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      double tmp = work[k] / data (cidx (k));
                      work[k] = tmp;
                      for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          work[iidx] = work[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (work[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = work[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k < nc; k++)
                    {

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k));
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k)+1;
                               i < cidx (k+1); i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

ComplexMatrix
SparseMatrix::ltsolve (MatrixType& mattype, const ComplexMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      octave_idx_type b_nc = b.cols ();
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      if (typ == MatrixType::Permuted_Lower)
        {
          retval.resize (nc, b_nc);
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);
          octave_idx_type *perm = mattype.triangular_perm ();

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                cwork[i] = 0.;
              for (octave_idx_type i = 0; i < nr; i++)
                cwork[perm[i]] = b(i, j);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (cwork[k] != 0.)
                    {
                      octave_idx_type minr = nr;
                      octave_idx_type mini = 0;

                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        if (perm[ridx (i)] < minr)
                          {
                            minr = perm[ridx (i)];
                            mini = i;
                          }

                      if (minr != k || data (mini) == 0)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (mini);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        {
                          if (i == mini)
                            continue;

                          octave_idx_type iidx = perm[ridx (i)];
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval(i, j) = cwork[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = 0; k < nc; k++)
                    {
                      if (work[k] != 0.)
                        {
                          octave_idx_type minr = nr;
                          octave_idx_type mini = 0;

                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            if (perm[ridx (i)] < minr)
                              {
                                minr = perm[ridx (i)];
                                mini = i;
                              }

                          double tmp = work[k] / data (mini);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            {
                              if (i == mini)
                                continue;

                              octave_idx_type iidx = perm[ridx (i)];
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }

                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);
          retval.resize (nc, b_nc, 0.);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nr; i++)
                cwork[i] = b(i, j);
              for (octave_idx_type i = nr; i < nc; i++)
                cwork[i] = 0.;

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (k)) != k || data (cidx (k)) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (k));
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              for (octave_idx_type i = 0; i < nc; i++)
                retval.xelem (i, j) = cwork[i];
            }

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k < nc; k++)
                    {

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k));
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k)+1;
                               i < cidx (k+1); i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::ltsolve (MatrixType& mattype, const SparseComplexMatrix& b,
                       octave_idx_type& err, double& rcond,
                       solve_singularity_handler sing_handler,
                       bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nm = (nc > nr ? nc : nr);
  err = 0;

  if (nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || nc == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower)
        (*current_liboctave_error_handler) ("incorrect matrix type");

      double anorm = 0.;
      double ainvnorm = 0.;
      rcond = 1.;

      if (calc_cond)
        {
          // Calculate the 1-norm of matrix for rcond calculation
          for (octave_idx_type j = 0; j < nc; j++)
            {
              double atmp = 0.;
              for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                atmp += fabs (data (i));
              if (atmp > anorm)
                anorm = atmp;
            }
        }

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nz = b.nnz ();
      retval = SparseComplexMatrix (nc, b_nc, b_nz);
      retval.xcidx (0) = 0;
      octave_idx_type ii = 0;
      octave_idx_type x_nz = b_nz;

      if (typ == MatrixType::Permuted_Lower)
        {
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);
          octave_idx_type *perm = mattype.triangular_perm ();

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                cwork[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                cwork[perm[b.ridx (i)]] = b.data (i);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (cwork[k] != 0.)
                    {
                      octave_idx_type minr = nr;
                      octave_idx_type mini = 0;

                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        if (perm[ridx (i)] < minr)
                          {
                            minr = perm[ridx (i)];
                            mini = i;
                          }

                      if (minr != k || data (mini) == 0)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (mini);
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k); i < cidx (k+1); i++)
                        {
                          if (i == mini)
                            continue;

                          octave_idx_type iidx = perm[ridx (i)];
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = cwork[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = 0; k < nc; k++)
                    {
                      if (work[k] != 0.)
                        {
                          octave_idx_type minr = nr;
                          octave_idx_type mini = 0;

                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            if (perm[ridx (i)] < minr)
                              {
                                minr = perm[ridx (i)];
                                mini = i;
                              }

                          double tmp = work[k] / data (mini);
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k);
                               i < cidx (k+1); i++)
                            {
                              if (i == mini)
                                continue;

                              octave_idx_type iidx = perm[ridx (i)];
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }

                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (Complex, cwork, nm);

          for (octave_idx_type j = 0; j < b_nc; j++)
            {
              for (octave_idx_type i = 0; i < nm; i++)
                cwork[i] = 0.;
              for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                cwork[b.ridx (i)] = b.data (i);

              for (octave_idx_type k = 0; k < nc; k++)
                {
                  if (cwork[k] != 0.)
                    {
                      if (ridx (cidx (k)) != k || data (cidx (k)) == 0.)
                        {
                          err = -2;
                          goto triangular_error;
                        }

                      Complex tmp = cwork[k] / data (cidx (k));
                      cwork[k] = tmp;
                      for (octave_idx_type i = cidx (k)+1; i < cidx (k+1); i++)
                        {
                          octave_idx_type iidx = ridx (i);
                          cwork[iidx] = cwork[iidx] - tmp * data (i);
                        }
                    }
                }

              // Count nonzeros in work vector and adjust space in
              // retval if needed
              octave_idx_type new_nnz = 0;
              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  new_nnz++;

              if (ii + new_nnz > x_nz)
                {
                  // Resize the sparse matrix
                  octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                  retval.change_capacity (sz);
                  x_nz = sz;
                }

              for (octave_idx_type i = 0; i < nc; i++)
                if (cwork[i] != 0.)
                  {
                    retval.xridx (ii) = i;
                    retval.xdata (ii++) = cwork[i];
                  }
              retval.xcidx (j+1) = ii;
            }

          retval.maybe_compress ();

          if (calc_cond)
            {
              // Calculation of 1-norm of inv(*this)
              OCTAVE_LOCAL_BUFFER (double, work, nm);
              for (octave_idx_type i = 0; i < nm; i++)
                work[i] = 0.;

              for (octave_idx_type j = 0; j < nr; j++)
                {
                  work[j] = 1.;

                  for (octave_idx_type k = j; k < nc; k++)
                    {

                      if (work[k] != 0.)
                        {
                          double tmp = work[k] / data (cidx (k));
                          work[k] = tmp;
                          for (octave_idx_type i = cidx (k)+1;
                               i < cidx (k+1); i++)
                            {
                              octave_idx_type iidx = ridx (i);
                              work[iidx] = work[iidx] - tmp * data (i);
                            }
                        }
                    }
                  double atmp = 0;
                  for (octave_idx_type i = j; i < nc; i++)
                    {
                      atmp += fabs (work[i]);
                      work[i] = 0.;
                    }
                  if (atmp > ainvnorm)
                    ainvnorm = atmp;
                }
              rcond = 1. / ainvnorm / anorm;
            }
        }

    triangular_error:
      if (err != 0)
        {
          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }

      volatile double rcond_plus_one = rcond + 1.0;

      if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          err = -2;

          if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
          else
            octave::warn_singular_matrix (rcond);
        }
    }

  return retval;
}

Matrix
SparseMatrix::trisolve (MatrixType& mattype, const Matrix& b,
                        octave_idx_type& err, double& rcond,
                        solve_singularity_handler sing_handler,
                        bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else if (calc_cond)
    (*current_liboctave_error_handler)
      ("calculation of condition number not implemented");
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Tridiagonal_Hermitian)
        {
          OCTAVE_LOCAL_BUFFER (double, D, nr);
          OCTAVE_LOCAL_BUFFER (double, DL, nr - 1);

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii);
                  ii += 2;
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT b_nr = octave::to_f77_int (b.rows ());
          F77_INT b_nc = octave::to_f77_int (b.cols ());

          retval = b;
          double *result = retval.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dptsv, DPTSV, (tmp_nr, b_nc, D, DL, result,
                                   b_nr, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              err = 0;
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Tridiagonal;
            }
          else
            rcond = 1.;
        }

      if (typ == MatrixType::Tridiagonal)
        {
          OCTAVE_LOCAL_BUFFER (double, DU, nr - 1);
          OCTAVE_LOCAL_BUFFER (double, D, nr);
          OCTAVE_LOCAL_BUFFER (double, DL, nr - 1);

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii++);
                  DU[j] = data (ii++);
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                  DU[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                    else if (ridx (i) == j - 1)
                      DU[j-1] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT b_nr = octave::to_f77_int (b.rows ());
          F77_INT b_nc = octave::to_f77_int (b.cols ());

          retval = b;
          double *result = retval.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dgtsv, DGTSV, (tmp_nr, b_nc, DL, D, DU, result,
                                   b_nr, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              rcond = 0.;
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            rcond = 1.;
        }
      else if (typ != MatrixType::Tridiagonal_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseMatrix
SparseMatrix::trisolve (MatrixType& mattype, const SparseMatrix& b,
                        octave_idx_type& err, double& rcond,
                        solve_singularity_handler sing_handler,
                        bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else if (calc_cond)
    (*current_liboctave_error_handler)
      ("calculation of condition number not implemented");
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      // Note can't treat symmetric case as there is no dpttrf function
      if (typ == MatrixType::Tridiagonal
          || typ == MatrixType::Tridiagonal_Hermitian)
        {
          OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2);
          OCTAVE_LOCAL_BUFFER (double, DU, nr - 1);
          OCTAVE_LOCAL_BUFFER (double, D, nr);
          OCTAVE_LOCAL_BUFFER (double, DL, nr - 1);
          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii++);
                  DU[j] = data (ii++);
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                  DU[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                    else if (ridx (i) == j - 1)
                      DU[j-1] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          F77_XFCN (dgttrf, DGTTRF, (tmp_nr, DL, D, DU, DU2, pipvt, tmp_err));

          if (err != 0)
            {
              rcond = 0.0;
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              rcond = 1.0;
              char job = 'N';
              volatile octave_idx_type x_nz = b.nnz ();
              octave_idx_type b_nc = b.cols ();
              retval = SparseMatrix (nr, b_nc, x_nz);
              retval.xcidx (0) = 0;
              volatile octave_idx_type ii = 0;

              OCTAVE_LOCAL_BUFFER (double, work, nr);

              for (volatile octave_idx_type j = 0; j < b_nc; j++)
                {
                  for (octave_idx_type i = 0; i < nr; i++)
                    work[i] = 0.;
                  for (octave_idx_type i = b.cidx (j); i < b.cidx (j+1); i++)
                    work[b.ridx (i)] = b.data (i);

                  F77_INT b_nr = octave::to_f77_int (b.rows ());

                  F77_XFCN (dgttrs, DGTTRS,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, 1, DL, D, DU, DU2, pipvt,
                             work, b_nr, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  // Count nonzeros in work vector and adjust
                  // space in retval if needed
                  octave_idx_type new_nnz = 0;
                  for (octave_idx_type i = 0; i < nr; i++)
                    if (work[i] != 0.)
                      new_nnz++;

                  if (ii + new_nnz > x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                      retval.change_capacity (sz);
                      x_nz = sz;
                    }

                  for (octave_idx_type i = 0; i < nr; i++)
                    if (work[i] != 0.)
                      {
                        retval.xridx (ii) = i;
                        retval.xdata (ii++) = work[i];
                      }
                  retval.xcidx (j+1) = ii;
                }

              retval.maybe_compress ();
            }
        }
      else if (typ != MatrixType::Tridiagonal_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

ComplexMatrix
SparseMatrix::trisolve (MatrixType& mattype, const ComplexMatrix& b,
                        octave_idx_type& err, double& rcond,
                        solve_singularity_handler sing_handler,
                        bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else if (calc_cond)
    (*current_liboctave_error_handler)
      ("calculation of condition number not implemented");
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Tridiagonal_Hermitian)
        {
          OCTAVE_LOCAL_BUFFER (double, D, nr);
          OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1);

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii);
                  ii += 2;
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT b_nr = octave::to_f77_int (b.rows ());
          F77_INT b_nc = octave::to_f77_int (b.cols ());

          rcond = 1.;

          retval = b;
          Complex *result = retval.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (zptsv, ZPTSV, (tmp_nr, b_nc, D, F77_DBLE_CMPLX_ARG (DL),
                                   F77_DBLE_CMPLX_ARG (result),
                                   b_nr, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              err = 0;
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Tridiagonal;
            }
        }

      if (typ == MatrixType::Tridiagonal)
        {
          OCTAVE_LOCAL_BUFFER (Complex, DU, nr - 1);
          OCTAVE_LOCAL_BUFFER (Complex, D, nr);
          OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1);

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii++);
                  DU[j] = data (ii++);
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                  DU[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                    else if (ridx (i) == j - 1)
                      DU[j-1] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT b_nr = octave::to_f77_int (b.rows ());
          F77_INT b_nc = octave::to_f77_int (b.cols ());

          rcond = 1.;

          retval = b;
          Complex *result = retval.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (zgtsv, ZGTSV, (tmp_nr, b_nc, F77_DBLE_CMPLX_ARG (DL),
                                   F77_DBLE_CMPLX_ARG (D),
                                   F77_DBLE_CMPLX_ARG (DU),
                                   F77_DBLE_CMPLX_ARG (result),
                                   b_nr, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              rcond = 0.;
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
        }
      else if (typ != MatrixType::Tridiagonal_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::trisolve (MatrixType& mattype, const SparseComplexMatrix& b,
                        octave_idx_type& err, double& rcond,
                        solve_singularity_handler sing_handler,
                        bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else if (calc_cond)
    (*current_liboctave_error_handler)
      ("calculation of condition number not implemented");
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattype.type ();
      mattype.info ();

      // Note can't treat symmetric case as there is no dpttrf function
      if (typ == MatrixType::Tridiagonal
          || typ == MatrixType::Tridiagonal_Hermitian)
        {
          OCTAVE_LOCAL_BUFFER (double, DU2, nr - 2);
          OCTAVE_LOCAL_BUFFER (double, DU, nr - 1);
          OCTAVE_LOCAL_BUFFER (double, D, nr);
          OCTAVE_LOCAL_BUFFER (double, DL, nr - 1);
          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          if (mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < nc-1; j++)
                {
                  D[j] = data (ii++);
                  DL[j] = data (ii++);
                  DU[j] = data (ii++);
                }
              D[nc-1] = data (ii);
            }
          else
            {
              D[0] = 0.;
              for (octave_idx_type i = 0; i < nr - 1; i++)
                {
                  D[i+1] = 0.;
                  DL[i] = 0.;
                  DU[i] = 0.;
                }

              for (octave_idx_type j = 0; j < nc; j++)
                for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                  {
                    if (ridx (i) == j)
                      D[j] = data (i);
                    else if (ridx (i) == j + 1)
                      DL[j] = data (i);
                    else if (ridx (i) == j - 1)
                      DU[j-1] = data (i);
                  }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          F77_XFCN (dgttrf, DGTTRF, (tmp_nr, DL, D, DU, DU2, pipvt, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              rcond = 0.0;
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              rcond = 1.;
              char job = 'N';
              F77_INT b_nr = octave::to_f77_int (b.rows ());
              octave_idx_type b_nc = b.cols ();
              OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Bz, b_nr);

              // Take a first guess that the number of nonzero terms
              // will be as many as in b
              volatile octave_idx_type x_nz = b.nnz ();
              volatile octave_idx_type ii = 0;
              retval = SparseComplexMatrix (b_nr, b_nc, x_nz);

              retval.xcidx (0) = 0;
              for (volatile octave_idx_type j = 0; j < b_nc; j++)
                {

                  for (F77_INT i = 0; i < b_nr; i++)
                    {
                      Complex c = b(i, j);
                      Bx[i] = c.real ();
                      Bz[i] = c.imag ();
                    }

                  F77_XFCN (dgttrs, DGTTRS,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, 1, DL, D, DU, DU2, pipvt,
                             Bx, b_nr, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    {
                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }

                  F77_XFCN (dgttrs, DGTTRS,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, 1, DL, D, DU, DU2, pipvt,
                             Bz, b_nr, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    {
                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }

                  // Count nonzeros in work vector and adjust
                  // space in retval if needed
                  octave_idx_type new_nnz = 0;
                  for (octave_idx_type i = 0; i < nr; i++)
                    if (Bx[i] != 0. || Bz[i] != 0.)
                      new_nnz++;

                  if (ii + new_nnz > x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                      retval.change_capacity (sz);
                      x_nz = sz;
                    }

                  for (octave_idx_type i = 0; i < nr; i++)
                    if (Bx[i] != 0. || Bz[i] != 0.)
                      {
                        retval.xridx (ii) = i;
                        retval.xdata (ii++) = Complex (Bx[i], Bz[i]);
                      }

                  retval.xcidx (j+1) = ii;
                }

              retval.maybe_compress ();
            }
        }
      else if (typ != MatrixType::Tridiagonal_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

Matrix
SparseMatrix::bsolve (MatrixType& mattype, const Matrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Banded_Hermitian)
        {
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_lower + 1;
          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              {
                octave_idx_type ri = ridx (i);
                if (ri >= j)
                  m_band(ri - j, j) = data (i);
              }

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            anorm = m_band.abs ().sum ().row (0).max ();

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          char job = 'L';
          F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                                     tmp_nr, n_lower, tmp_data, ldm, tmp_err
                                     F77_CHAR_ARG_LEN (1)));

          err = tmp_err;

          if (err != 0)
            {
              // Matrix is not positive definite!! Fall through to
              // unsymmetric banded solver.
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Banded;
              rcond = 0.0;
              err = 0;
            }
          else
            {
              if (calc_cond)
                {
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_XFCN (dpbcon, DPBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, tmp_data, ldm,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  retval = b;
                  double *result = retval.fortran_vec ();

                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  F77_INT b_nc = octave::to_f77_int (b.cols ());

                  F77_XFCN (dpbtrs, DPBTRS,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, b_nc, tmp_data,
                             ldm, result, b_nr, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    {
                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");
                      err = -1;
                    }
                }
            }
        }

      if (typ == MatrixType::Banded)
        {
          // Create the storage for the banded form of the sparse matrix
          F77_INT n_upper = octave::to_f77_int (mattype.nupper ());
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_upper + 2 * n_lower + 1;

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              m_band(ridx (i) - j + n_lower + n_upper, j) = data (i);

          // Calculate the norm of the matrix, for later use.
          double anorm = 0.0;
          if (calc_cond)
            {
              for (octave_idx_type j = 0; j < nr; j++)
                {
                  double atmp = 0.;
                  for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                    atmp += fabs (data (i));
                  if (atmp > anorm)
                    anorm = atmp;
                }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper,
                                     tmp_data, ldm, pipvt, tmp_err));

          err = tmp_err;

          // Throw away extra info LAPACK gives so as to not
          // change output.
          if (err != 0)
            {
              err = -2;
              rcond = 0.0;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              if (calc_cond)
                {
                  char job = '1';
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_INT tmp_nc = octave::to_f77_int (nc);

                  F77_XFCN (dgbcon, DGBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  retval = b;
                  double *result = retval.fortran_vec ();

                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  F77_INT b_nc = octave::to_f77_int (b.cols ());

                  char job = 'N';
                  F77_XFCN (dgbtrs, DGBTRS,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, n_upper, b_nc, tmp_data,
                             ldm, pipvt, result, b_nr, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;
                }
            }
        }
      else if (typ != MatrixType::Banded_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseMatrix
SparseMatrix::bsolve (MatrixType& mattype, const SparseMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Banded_Hermitian)
        {
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = octave::to_f77_int (n_lower + 1);

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              {
                octave_idx_type ri = ridx (i);
                if (ri >= j)
                  m_band(ri - j, j) = data (i);
              }

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            anorm = m_band.abs ().sum ().row (0).max ();

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          char job = 'L';
          F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                                     tmp_nr, n_lower, tmp_data, ldm, tmp_err
                                     F77_CHAR_ARG_LEN (1)));

          err = tmp_err;

          if (err != 0)
            {
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Banded;
              rcond = 0.0;
              err = 0;
            }
          else
            {
              if (calc_cond)
                {
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_XFCN (dpbcon, DPBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, tmp_data, ldm,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  octave_idx_type b_nc = b.cols ();
                  OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);

                  // Take a first guess that the number of nonzero terms
                  // will be as many as in b
                  volatile octave_idx_type x_nz = b.nnz ();
                  volatile octave_idx_type ii = 0;
                  retval = SparseMatrix (b_nr, b_nc, x_nz);

                  retval.xcidx (0) = 0;
                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {
                      for (F77_INT i = 0; i < b_nr; i++)
                        Bx[i] = b.elem (i, j);

                      F77_XFCN (dpbtrs, DPBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, 1, tmp_data,
                                 ldm, Bx, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      if (err != 0)
                        {
                          // FIXME: Should this be a warning?
                          (*current_liboctave_error_handler)
                            ("SparseMatrix::solve solve failed");
                          err = -1;
                          break;
                        }

                      for (F77_INT i = 0; i < b_nr; i++)
                        {
                          double tmp = Bx[i];
                          if (tmp != 0.0)
                            {
                              if (ii == x_nz)
                                {
                                  // Resize the sparse matrix
                                  octave_idx_type sz;
                                  sz = (static_cast<double> (b_nc) - j) / b_nc
                                       * x_nz;
                                  sz = x_nz + (sz > 100 ? sz : 100);
                                  retval.change_capacity (sz);
                                  x_nz = sz;
                                }
                              retval.xdata (ii) = tmp;
                              retval.xridx (ii++) = i;
                            }
                        }
                      retval.xcidx (j+1) = ii;
                    }

                  retval.maybe_compress ();
                }
            }
        }

      if (typ == MatrixType::Banded)
        {
          // Create the storage for the banded form of the sparse matrix
          F77_INT n_upper = octave::to_f77_int (mattype.nupper ());
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = octave::to_f77_int (n_upper + 2 * n_lower + 1);

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (octave_idx_type j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              m_band(ridx (i) - j + n_lower + n_upper, j) = data (i);

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            {
              anorm = 0.0;
              for (octave_idx_type j = 0; j < nr; j++)
                {
                  double atmp = 0.0;
                  for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                    atmp += fabs (data (i));
                  if (atmp > anorm)
                    anorm = atmp;
                }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper,
                                     tmp_data, ldm, pipvt, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              err = -2;
              rcond = 0.0;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              if (calc_cond)
                {
                  char job = '1';
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_INT tmp_nc = octave::to_f77_int (nc);

                  F77_XFCN (dgbcon, DGBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  char job = 'N';
                  volatile octave_idx_type x_nz = b.nnz ();
                  octave_idx_type b_nc = b.cols ();
                  retval = SparseMatrix (nr, b_nc, x_nz);
                  retval.xcidx (0) = 0;
                  volatile octave_idx_type ii = 0;

                  OCTAVE_LOCAL_BUFFER (double, work, nr);

                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {
                      for (octave_idx_type i = 0; i < nr; i++)
                        work[i] = 0.;
                      for (octave_idx_type i = b.cidx (j);
                           i < b.cidx (j+1); i++)
                        work[b.ridx (i)] = b.data (i);

                      F77_INT b_nr = octave::to_f77_int (b.rows ());

                      F77_XFCN (dgbtrs, DGBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, n_upper, 1, tmp_data,
                                 ldm, pipvt, work, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      // Count nonzeros in work vector and adjust
                      // space in retval if needed
                      octave_idx_type new_nnz = 0;
                      for (octave_idx_type i = 0; i < nr; i++)
                        if (work[i] != 0.)
                          new_nnz++;

                      if (ii + new_nnz > x_nz)
                        {
                          // Resize the sparse matrix
                          octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                          retval.change_capacity (sz);
                          x_nz = sz;
                        }

                      for (octave_idx_type i = 0; i < nr; i++)
                        if (work[i] != 0.)
                          {
                            retval.xridx (ii) = i;
                            retval.xdata (ii++) = work[i];
                          }
                      retval.xcidx (j+1) = ii;
                    }

                  retval.maybe_compress ();
                }
            }
        }
      else if (typ != MatrixType::Banded_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

ComplexMatrix
SparseMatrix::bsolve (MatrixType& mattype, const ComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Banded_Hermitian)
        {
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_lower + 1;

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              {
                octave_idx_type ri = ridx (i);
                if (ri >= j)
                  m_band(ri - j, j) = data (i);
              }

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            anorm = m_band.abs ().sum ().row (0).max ();

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          char job = 'L';
          F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                                     tmp_nr, n_lower, tmp_data, ldm, tmp_err
                                     F77_CHAR_ARG_LEN (1)));

          err = tmp_err;

          if (err != 0)
            {
              // Matrix is not positive definite!! Fall through to
              // unsymmetric banded solver.
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Banded;
              rcond = 0.0;
              err = 0;
            }
          else
            {
              if (calc_cond)
                {
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_XFCN (dpbcon, DPBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, tmp_data, ldm,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  octave_idx_type b_nc = b.cols ();

                  OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
                  OCTAVE_LOCAL_BUFFER (double, Bz, b_nr);

                  retval.resize (b_nr, b_nc);

                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {
                      for (F77_INT i = 0; i < b_nr; i++)
                        {
                          Complex c = b(i, j);
                          Bx[i] = c.real ();
                          Bz[i] = c.imag ();
                        }

                      F77_XFCN (dpbtrs, DPBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, 1, tmp_data,
                                 ldm, Bx, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      if (err != 0)
                        {
                          // FIXME: Should this be a warning?
                          (*current_liboctave_error_handler)
                            ("SparseMatrix::solve solve failed");
                          err = -1;
                          break;
                        }

                      F77_XFCN (dpbtrs, DPBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, 1, tmp_data,
                                 ldm, Bz, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      if (err != 0)
                        {
                          // FIXME: Should this be a warning?
                          (*current_liboctave_error_handler)
                            ("SparseMatrix::solve solve failed");
                          err = -1;
                          break;
                        }

                      for (octave_idx_type i = 0; i < b_nr; i++)
                        retval(i, j) = Complex (Bx[i], Bz[i]);
                    }
                }
            }
        }

      if (typ == MatrixType::Banded)
        {
          // Create the storage for the banded form of the sparse matrix
          F77_INT n_upper = octave::to_f77_int (mattype.nupper ());
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_upper + 2 * n_lower + 1;

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              m_band(ridx (i) - j + n_lower + n_upper, j) = data (i);

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            {
              anorm = 0.0;
              for (octave_idx_type j = 0; j < nr; j++)
                {
                  double atmp = 0.0;
                  for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                    atmp += fabs (data (i));
                  if (atmp > anorm)
                    anorm = atmp;
                }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper,
                                     tmp_data, ldm, pipvt, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              err = -2;
              rcond = 0.0;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              if (calc_cond)
                {
                  char job = '1';
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_INT tmp_nc = octave::to_f77_int (nc);

                  F77_XFCN (dgbcon, DGBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  char job = 'N';
                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  octave_idx_type b_nc = b.cols ();
                  retval.resize (nr, b_nc);

                  OCTAVE_LOCAL_BUFFER (double, Bz, nr);
                  OCTAVE_LOCAL_BUFFER (double, Bx, nr);

                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {
                      for (octave_idx_type i = 0; i < nr; i++)
                        {
                          Complex c = b(i, j);
                          Bx[i] = c.real ();
                          Bz[i] = c.imag ();
                        }

                      F77_XFCN (dgbtrs, DGBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, n_upper, 1, tmp_data,
                                 ldm, pipvt, Bx, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      F77_XFCN (dgbtrs, DGBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, n_upper, 1, tmp_data,
                                 ldm, pipvt, Bz, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      for (octave_idx_type i = 0; i < nr; i++)
                        retval(i, j) = Complex (Bx[i], Bz[i]);
                    }
                }
            }
        }
      else if (typ != MatrixType::Banded_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::bsolve (MatrixType& mattype, const SparseComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Banded_Hermitian)
        {
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_lower + 1;

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              {
                octave_idx_type ri = ridx (i);
                if (ri >= j)
                  m_band(ri - j, j) = data (i);
              }

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            anorm = m_band.abs ().sum ().row (0).max ();

          F77_INT tmp_nr = octave::to_f77_int (nr);

          F77_INT tmp_err = 0;

          char job = 'L';
          F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                                     tmp_nr, n_lower, tmp_data, ldm, tmp_err
                                     F77_CHAR_ARG_LEN (1)));

          err = tmp_err;

          if (err != 0)
            {
              // Matrix is not positive definite!! Fall through to
              // unsymmetric banded solver.
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Banded;

              rcond = 0.0;
              err = 0;
            }
          else
            {
              if (calc_cond)
                {
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_XFCN (dpbcon, DPBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nr, n_lower, tmp_data, ldm,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  octave_idx_type b_nc = b.cols ();
                  OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
                  OCTAVE_LOCAL_BUFFER (double, Bz, b_nr);

                  // Take a first guess that the number of nonzero terms
                  // will be as many as in b
                  volatile octave_idx_type x_nz = b.nnz ();
                  volatile octave_idx_type ii = 0;
                  retval = SparseComplexMatrix (b_nr, b_nc, x_nz);

                  retval.xcidx (0) = 0;
                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {

                      for (F77_INT i = 0; i < b_nr; i++)
                        {
                          Complex c = b(i, j);
                          Bx[i] = c.real ();
                          Bz[i] = c.imag ();
                        }

                      F77_XFCN (dpbtrs, DPBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, 1, tmp_data,
                                 ldm, Bx, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      if (err != 0)
                        {
                          // FIXME: Should this be a warning?
                          (*current_liboctave_error_handler)
                            ("SparseMatrix::solve solve failed");
                          err = -1;
                          break;
                        }

                      F77_XFCN (dpbtrs, DPBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, 1, tmp_data,
                                 ldm, Bz, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      if (err != 0)
                        {
                          // FIXME: Should this be a warning?
                          (*current_liboctave_error_handler)
                            ("SparseMatrix::solve solve failed");

                          err = -1;
                          break;
                        }

                      // Count nonzeros in work vector and adjust
                      // space in retval if needed
                      octave_idx_type new_nnz = 0;
                      for (octave_idx_type i = 0; i < nr; i++)
                        if (Bx[i] != 0. || Bz[i] != 0.)
                          new_nnz++;

                      if (ii + new_nnz > x_nz)
                        {
                          // Resize the sparse matrix
                          octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                          retval.change_capacity (sz);
                          x_nz = sz;
                        }

                      for (octave_idx_type i = 0; i < nr; i++)
                        if (Bx[i] != 0. || Bz[i] != 0.)
                          {
                            retval.xridx (ii) = i;
                            retval.xdata (ii++) = Complex (Bx[i], Bz[i]);
                          }

                      retval.xcidx (j+1) = ii;
                    }

                  retval.maybe_compress ();
                }
            }
        }

      if (typ == MatrixType::Banded)
        {
          // Create the storage for the banded form of the sparse matrix
          F77_INT n_upper = octave::to_f77_int (mattype.nupper ());
          F77_INT n_lower = octave::to_f77_int (mattype.nlower ());
          F77_INT ldm = n_upper + 2 * n_lower + 1;

          Matrix m_band (ldm, nc);
          double *tmp_data = m_band.fortran_vec ();

          if (! mattype.is_dense ())
            {
              octave_idx_type ii = 0;

              for (F77_INT j = 0; j < ldm; j++)
                for (octave_idx_type i = 0; i < nc; i++)
                  tmp_data[ii++] = 0.;
            }

          for (octave_idx_type j = 0; j < nc; j++)
            for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
              m_band(ridx (i) - j + n_lower + n_upper, j) = data (i);

          // Calculate the norm of the matrix, for later use.
          double anorm;
          if (calc_cond)
            {
              anorm = 0.0;
              for (octave_idx_type j = 0; j < nr; j++)
                {
                  double atmp = 0.0;
                  for (octave_idx_type i = cidx (j); i < cidx (j+1); i++)
                    atmp += fabs (data (i));
                  if (atmp > anorm)
                    anorm = atmp;
                }
            }

          F77_INT tmp_nr = octave::to_f77_int (nr);

          Array<F77_INT> ipvt (dim_vector (nr, 1));
          F77_INT *pipvt = ipvt.fortran_vec ();

          F77_INT tmp_err = 0;

          F77_XFCN (dgbtrf, DGBTRF, (tmp_nr, tmp_nr, n_lower, n_upper,
                                     tmp_data, ldm, pipvt, tmp_err));

          err = tmp_err;

          if (err != 0)
            {
              err = -2;
              rcond = 0.0;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                octave::warn_singular_matrix ();
            }
          else
            {
              if (calc_cond)
                {
                  char job = '1';
                  Array<double> z (dim_vector (3 * nr, 1));
                  double *pz = z.fortran_vec ();
                  Array<F77_INT> iz (dim_vector (nr, 1));
                  F77_INT *piz = iz.fortran_vec ();

                  F77_INT tmp_nc = octave::to_f77_int (nc);

                  F77_XFCN (dgbcon, DGBCON,
                            (F77_CONST_CHAR_ARG2 (&job, 1),
                             tmp_nc, n_lower, n_upper, tmp_data, ldm, pipvt,
                             anorm, rcond, pz, piz, tmp_err
                             F77_CHAR_ARG_LEN (1)));

                  err = tmp_err;

                  if (err != 0)
                    err = -2;

                  volatile double rcond_plus_one = rcond + 1.0;

                  if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                    {
                      err = -2;

                      if (sing_handler)
                        {
                          sing_handler (rcond);
                          mattype.mark_as_rectangular ();
                        }
                      else
                        octave::warn_singular_matrix (rcond);
                    }
                }
              else
                rcond = 1.;

              if (err == 0)
                {
                  char job = 'N';
                  volatile octave_idx_type x_nz = b.nnz ();
                  F77_INT b_nr = octave::to_f77_int (b.rows ());
                  octave_idx_type b_nc = b.cols ();
                  retval = SparseComplexMatrix (nr, b_nc, x_nz);
                  retval.xcidx (0) = 0;
                  volatile octave_idx_type ii = 0;

                  OCTAVE_LOCAL_BUFFER (double, Bx, nr);
                  OCTAVE_LOCAL_BUFFER (double, Bz, nr);

                  for (volatile octave_idx_type j = 0; j < b_nc; j++)
                    {
                      for (octave_idx_type i = 0; i < nr; i++)
                        {
                          Bx[i] = 0.;
                          Bz[i] = 0.;
                        }
                      for (octave_idx_type i = b.cidx (j);
                           i < b.cidx (j+1); i++)
                        {
                          Complex c = b.data (i);
                          Bx[b.ridx (i)] = c.real ();
                          Bz[b.ridx (i)] = c.imag ();
                        }

                      F77_XFCN (dgbtrs, DGBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, n_upper, 1, tmp_data,
                                 ldm, pipvt, Bx, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      F77_XFCN (dgbtrs, DGBTRS,
                                (F77_CONST_CHAR_ARG2 (&job, 1),
                                 tmp_nr, n_lower, n_upper, 1, tmp_data,
                                 ldm, pipvt, Bz, b_nr, tmp_err
                                 F77_CHAR_ARG_LEN (1)));

                      err = tmp_err;

                      // Count nonzeros in work vector and adjust
                      // space in retval if needed
                      octave_idx_type new_nnz = 0;
                      for (octave_idx_type i = 0; i < nr; i++)
                        if (Bx[i] != 0. || Bz[i] != 0.)
                          new_nnz++;

                      if (ii + new_nnz > x_nz)
                        {
                          // Resize the sparse matrix
                          octave_idx_type sz = new_nnz * (b_nc - j) + x_nz;
                          retval.change_capacity (sz);
                          x_nz = sz;
                        }

                      for (octave_idx_type i = 0; i < nr; i++)
                        if (Bx[i] != 0. || Bz[i] != 0.)
                          {
                            retval.xridx (ii) = i;
                            retval.xdata (ii++) = Complex (Bx[i], Bz[i]);
                          }
                      retval.xcidx (j+1) = ii;
                    }

                  retval.maybe_compress ();
                }
            }
        }
      else if (typ != MatrixType::Banded_Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

void *
SparseMatrix::factorize (octave_idx_type& err, double& rcond, Matrix& Control,
                         Matrix& Info, solve_singularity_handler sing_handler,
                         bool calc_cond) const
{
  // The return values
  void *Numeric = nullptr;
  err = 0;

#if defined (HAVE_UMFPACK)

  // Setup the control parameters
  Control = Matrix (UMFPACK_CONTROL, 1);
  double *control = Control.fortran_vec ();
  UMFPACK_DNAME (defaults) (control);

  double tmp = octave::sparse_params::get_key ("spumoni");
  if (! octave::math::isnan (tmp))
    Control (UMFPACK_PRL) = tmp;
  tmp = octave::sparse_params::get_key ("piv_tol");
  if (! octave::math::isnan (tmp))
    {
      Control (UMFPACK_SYM_PIVOT_TOLERANCE) = tmp;
      Control (UMFPACK_PIVOT_TOLERANCE) = tmp;
    }

  // Set whether we are allowed to modify Q or not
  tmp = octave::sparse_params::get_key ("autoamd");
  if (! octave::math::isnan (tmp))
    Control (UMFPACK_FIXQ) = tmp;

  UMFPACK_DNAME (report_control) (control);

  const octave_idx_type *Ap = cidx ();
  const octave_idx_type *Ai = ridx ();
  const double *Ax = data ();
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  UMFPACK_DNAME (report_matrix) (nr, nc,
                                 octave::to_suitesparse_intptr (Ap),
                                 octave::to_suitesparse_intptr (Ai),
                                 Ax, 1, control);

  void *Symbolic;
  Info = Matrix (1, UMFPACK_INFO);
  double *info = Info.fortran_vec ();
  int status = UMFPACK_DNAME (qsymbolic) (nr, nc,
                                          octave::to_suitesparse_intptr (Ap),
                                          octave::to_suitesparse_intptr (Ai),
                                          Ax, nullptr, &Symbolic, control, info);

  if (status < 0)
    {
      UMFPACK_DNAME (report_status) (control, status);
      UMFPACK_DNAME (report_info) (control, info);

      UMFPACK_DNAME (free_symbolic) (&Symbolic);

      // FIXME: Should this be a warning?
      (*current_liboctave_error_handler)
        ("SparseMatrix::solve symbolic factorization failed");
      err = -1;
    }
  else
    {
      UMFPACK_DNAME (report_symbolic) (Symbolic, control);

      status = UMFPACK_DNAME (numeric) (octave::to_suitesparse_intptr (Ap),
                                        octave::to_suitesparse_intptr (Ai),
                                        Ax, Symbolic, &Numeric, control, info);
      UMFPACK_DNAME (free_symbolic) (&Symbolic);

      if (calc_cond)
        rcond = Info (UMFPACK_RCOND);
      else
        rcond = 1.;
      volatile double rcond_plus_one = rcond + 1.0;

      if (status == UMFPACK_WARNING_singular_matrix
          || rcond_plus_one == 1.0 || octave::math::isnan (rcond))
        {
          UMFPACK_DNAME (report_numeric) (Numeric, control);

          err = -2;

          if (sing_handler)
            sing_handler (rcond);
          else
            octave::warn_singular_matrix (rcond);
        }
      else if (status < 0)
        {
          UMFPACK_DNAME (report_status) (control, status);
          UMFPACK_DNAME (report_info) (control, info);

          // FIXME: Should this be a warning?
          (*current_liboctave_error_handler)
            ("SparseMatrix::solve numeric factorization failed");

          err = -1;
        }
      else
        {
          UMFPACK_DNAME (report_numeric) (Numeric, control);
        }
    }

  if (err != 0)
    UMFPACK_DNAME (free_numeric) (&Numeric);

#else

  octave_unused_parameter (rcond);
  octave_unused_parameter (Control);
  octave_unused_parameter (Info);
  octave_unused_parameter (sing_handler);
  octave_unused_parameter (calc_cond);

  (*current_liboctave_error_handler)
    ("support for UMFPACK was unavailable or disabled "
     "when liboctave was built");

#endif

  return Numeric;
}

Matrix
SparseMatrix::fsolve (MatrixType& mattype, const Matrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  Matrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = Matrix (nc, b.cols (), 0.0);
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Hermitian)
        {
#if defined (HAVE_CHOLMOD)
          cholmod_common Common;
          cholmod_common *cm = &Common;

          // Setup initial parameters
          CHOLMOD_NAME(start) (cm);
          cm->prefer_zomplex = false;

          double spu = octave::sparse_params::get_key ("spumoni");
          if (spu == 0.)
            {
              cm->print = -1;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr);
            }
          else
            {
              cm->print = static_cast<int> (spu) + 2;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint);
            }

          cm->error_handler = &SparseCholError;
          SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex);
          SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);

          cm->final_ll = true;

          cholmod_sparse Astore;
          cholmod_sparse *A = &Astore;
          A->nrow = nr;
          A->ncol = nc;

          A->p = cidx ();
          A->i = ridx ();
          A->nzmax = nnz ();
          A->packed = true;
          A->sorted = true;
          A->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          A->itype = CHOLMOD_LONG;
#else
          A->itype = CHOLMOD_INT;
#endif
          A->dtype = CHOLMOD_DOUBLE;
          A->stype = 1;
          A->xtype = CHOLMOD_REAL;

          A->x = data ();

          cholmod_dense Bstore;
          cholmod_dense *B = &Bstore;
          B->nrow = b.rows ();
          B->ncol = b.cols ();
          B->d = B->nrow;
          B->nzmax = B->nrow * B->ncol;
          B->dtype = CHOLMOD_DOUBLE;
          B->xtype = CHOLMOD_REAL;

          B->x = const_cast<double *> (b.data ());

          cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm);
          CHOLMOD_NAME(factorize) (A, L, cm);
          if (calc_cond)
            rcond = CHOLMOD_NAME(rcond)(L, cm);
          else
            rcond = 1.0;

          if (rcond == 0.0)
            {
              // Either its indefinite or singular.  Try UMFPACK
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Full;
            }
          else
            {
              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                    {
                      sing_handler (rcond);
                      mattype.mark_as_rectangular ();
                    }
                  else
                    octave::warn_singular_matrix (rcond);

                  return retval;
                }

              cholmod_dense *X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm);

              retval.resize (b.rows (), b.cols ());
              for (octave_idx_type j = 0; j < b.cols (); j++)
                {
                  octave_idx_type jr = j * b.rows ();
                  for (octave_idx_type i = 0; i < b.rows (); i++)
                    retval.xelem (i, j) = static_cast<double *>(X->x)[jr + i];
                }

              CHOLMOD_NAME(free_dense) (&X, cm);
              CHOLMOD_NAME(free_factor) (&L, cm);
              CHOLMOD_NAME(finish) (cm);
              static char blank_name[] = " ";
              CHOLMOD_NAME(print_common) (blank_name, cm);
            }
#else
          (*current_liboctave_warning_with_id_handler)
            ("Octave:missing-dependency",
             "support for CHOLMOD was unavailable or disabled "
             "when liboctave was built");

          mattype.mark_as_unsymmetric ();
          typ = MatrixType::Full;
#endif
        }

      if (typ == MatrixType::Full)
        {
#if defined (HAVE_UMFPACK)
          Matrix Control, Info;
          void *Numeric
            = factorize (err, rcond, Control, Info, sing_handler, calc_cond);

          if (err == 0)
            {
              // one iterative refinement instead of the default two in UMFPACK
              Control (UMFPACK_IRSTEP) = 1;
              const double *Bx = b.data ();
              retval.resize (b.rows (), b.cols ());
              double *result = retval.fortran_vec ();
              octave_idx_type b_nr = b.rows ();
              octave_idx_type b_nc = b.cols ();
              int status = 0;
              double *control = Control.fortran_vec ();
              double *info = Info.fortran_vec ();
              const octave_idx_type *Ap = cidx ();
              const octave_idx_type *Ai = ridx ();
              const double *Ax = data ();

              for (octave_idx_type j = 0, iidx = 0; j < b_nc; j++, iidx += b_nr)
                {
                  status = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                  octave::to_suitesparse_intptr (Ap),
                                                  octave::to_suitesparse_intptr (Ai),
                                                  Ax, &result[iidx], &Bx[iidx],
                                                  Numeric, control, info);
                  if (status < 0)
                    {
                      UMFPACK_DNAME (report_status) (control, status);

                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }
                }

              UMFPACK_DNAME (report_info) (control, info);

              UMFPACK_DNAME (free_numeric) (&Numeric);
            }
          else
            mattype.mark_as_rectangular ();

#else
          octave_unused_parameter (rcond);
          octave_unused_parameter (sing_handler);
          octave_unused_parameter (calc_cond);

          (*current_liboctave_error_handler)
            ("support for UMFPACK was unavailable or disabled "
             "when liboctave was built");
#endif
        }
      else if (typ != MatrixType::Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseMatrix
SparseMatrix::fsolve (MatrixType& mattype, const SparseMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  SparseMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Hermitian)
        {
#if defined (HAVE_CHOLMOD)
          cholmod_common Common;
          cholmod_common *cm = &Common;

          // Setup initial parameters
          CHOLMOD_NAME(start) (cm);
          cm->prefer_zomplex = false;

          double spu = octave::sparse_params::get_key ("spumoni");
          if (spu == 0.)
            {
              cm->print = -1;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr);
            }
          else
            {
              cm->print = static_cast<int> (spu) + 2;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint);
            }

          cm->error_handler = &SparseCholError;
          SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex);
          SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);

          cm->final_ll = true;

          cholmod_sparse Astore;
          cholmod_sparse *A = &Astore;
          A->nrow = nr;
          A->ncol = nc;

          A->p = cidx ();
          A->i = ridx ();
          A->nzmax = nnz ();
          A->packed = true;
          A->sorted = true;
          A->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          A->itype = CHOLMOD_LONG;
#else
          A->itype = CHOLMOD_INT;
#endif
          A->dtype = CHOLMOD_DOUBLE;
          A->stype = 1;
          A->xtype = CHOLMOD_REAL;

          A->x = data ();

          cholmod_sparse Bstore;
          cholmod_sparse *B = &Bstore;
          B->nrow = b.rows ();
          B->ncol = b.cols ();
          B->p = b.cidx ();
          B->i = b.ridx ();
          B->nzmax = b.nnz ();
          B->packed = true;
          B->sorted = true;
          B->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          B->itype = CHOLMOD_LONG;
#else
          B->itype = CHOLMOD_INT;
#endif
          B->dtype = CHOLMOD_DOUBLE;
          B->stype = 0;
          B->xtype = CHOLMOD_REAL;

          B->x = b.data ();

          cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm);
          CHOLMOD_NAME(factorize) (A, L, cm);
          if (calc_cond)
            rcond = CHOLMOD_NAME(rcond)(L, cm);
          else
            rcond = 1.;

          if (rcond == 0.0)
            {
              // Either its indefinite or singular.  Try UMFPACK
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Full;
            }
          else
            {
              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                    {
                      sing_handler (rcond);
                      mattype.mark_as_rectangular ();
                    }
                  else
                    octave::warn_singular_matrix (rcond);

                  return retval;
                }

              cholmod_sparse *X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm);

              retval = SparseMatrix (static_cast<octave_idx_type> (X->nrow),
                                     static_cast<octave_idx_type> (X->ncol),
                                     static_cast<octave_idx_type> (X->nzmax));
              for (octave_idx_type j = 0;
                   j <= static_cast<octave_idx_type> (X->ncol); j++)
                retval.xcidx (j) = static_cast<octave_idx_type *>(X->p)[j];
              for (octave_idx_type j = 0;
                   j < static_cast<octave_idx_type> (X->nzmax); j++)
                {
                  retval.xridx (j) = static_cast<octave_idx_type *>(X->i)[j];
                  retval.xdata (j) = static_cast<double *>(X->x)[j];
                }

              CHOLMOD_NAME(free_sparse) (&X, cm);
              CHOLMOD_NAME(free_factor) (&L, cm);
              CHOLMOD_NAME(finish) (cm);
              static char blank_name[] = " ";
              CHOLMOD_NAME(print_common) (blank_name, cm);
            }
#else
          (*current_liboctave_warning_with_id_handler)
            ("Octave:missing-dependency",
             "support for CHOLMOD was unavailable or disabled "
             "when liboctave was built");

          mattype.mark_as_unsymmetric ();
          typ = MatrixType::Full;
#endif
        }

      if (typ == MatrixType::Full)
        {
#if defined (HAVE_UMFPACK)
          Matrix Control, Info;
          void *Numeric = factorize (err, rcond, Control, Info,
                                     sing_handler, calc_cond);

          if (err == 0)
            {
              // one iterative refinement instead of the default two in UMFPACK
              Control (UMFPACK_IRSTEP) = 1;
              octave_idx_type b_nr = b.rows ();
              octave_idx_type b_nc = b.cols ();
              int status = 0;
              double *control = Control.fortran_vec ();
              double *info = Info.fortran_vec ();
              const octave_idx_type *Ap = cidx ();
              const octave_idx_type *Ai = ridx ();
              const double *Ax = data ();

              OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Xx, b_nr);

              // Take a first guess that the number of nonzero terms
              // will be as many as in b
              octave_idx_type x_nz = b.nnz ();
              octave_idx_type ii = 0;
              retval = SparseMatrix (b_nr, b_nc, x_nz);

              retval.xcidx (0) = 0;
              for (octave_idx_type j = 0; j < b_nc; j++)
                {

                  for (octave_idx_type i = 0; i < b_nr; i++)
                    Bx[i] = b.elem (i, j);

                  status = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                  octave::to_suitesparse_intptr (Ap),
                                                  octave::to_suitesparse_intptr (Ai),
                                                  Ax, Xx, Bx, Numeric,
                                                  control, info);
                  if (status < 0)
                    {
                      UMFPACK_DNAME (report_status) (control, status);

                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }

                  for (octave_idx_type i = 0; i < b_nr; i++)
                    {
                      double tmp = Xx[i];
                      if (tmp != 0.0)
                        {
                          if (ii == x_nz)
                            {
                              // Resize the sparse matrix
                              octave_idx_type sz;
                              sz = (static_cast<double> (b_nc) - j) / b_nc
                                   * x_nz;
                              sz = x_nz + (sz > 100 ? sz : 100);
                              retval.change_capacity (sz);
                              x_nz = sz;
                            }
                          retval.xdata (ii) = tmp;
                          retval.xridx (ii++) = i;
                        }
                    }
                  retval.xcidx (j+1) = ii;
                }

              retval.maybe_compress ();

              UMFPACK_DNAME (report_info) (control, info);

              UMFPACK_DNAME (free_numeric) (&Numeric);
            }
          else
            mattype.mark_as_rectangular ();

#else
          octave_unused_parameter (rcond);
          octave_unused_parameter (sing_handler);
          octave_unused_parameter (calc_cond);

          (*current_liboctave_error_handler)
            ("support for UMFPACK was unavailable or disabled "
             "when liboctave was built");
#endif
        }
      else if (typ != MatrixType::Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

ComplexMatrix
SparseMatrix::fsolve (MatrixType& mattype, const ComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  ComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0));
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Hermitian)
        {
#if defined (HAVE_CHOLMOD)
          cholmod_common Common;
          cholmod_common *cm = &Common;

          // Setup initial parameters
          CHOLMOD_NAME(start) (cm);
          cm->prefer_zomplex = false;

          double spu = octave::sparse_params::get_key ("spumoni");
          if (spu == 0.)
            {
              cm->print = -1;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr);
            }
          else
            {
              cm->print = static_cast<int> (spu) + 2;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint);
            }

          cm->error_handler = &SparseCholError;
          SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex);
          SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);

          cm->final_ll = true;

          cholmod_sparse Astore;
          cholmod_sparse *A = &Astore;
          A->nrow = nr;
          A->ncol = nc;

          A->p = cidx ();
          A->i = ridx ();
          A->nzmax = nnz ();
          A->packed = true;
          A->sorted = true;
          A->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          A->itype = CHOLMOD_LONG;
#else
          A->itype = CHOLMOD_INT;
#endif
          A->dtype = CHOLMOD_DOUBLE;
          A->stype = 1;
          A->xtype = CHOLMOD_REAL;

          A->x = data ();

          cholmod_dense Bstore;
          cholmod_dense *B = &Bstore;
          B->nrow = b.rows ();
          B->ncol = b.cols ();
          B->d = B->nrow;
          B->nzmax = B->nrow * B->ncol;
          B->dtype = CHOLMOD_DOUBLE;
          B->xtype = CHOLMOD_COMPLEX;

          B->x = const_cast<Complex *> (b.data ());

          cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm);
          CHOLMOD_NAME(factorize) (A, L, cm);
          if (calc_cond)
            rcond = CHOLMOD_NAME(rcond)(L, cm);
          else
            rcond = 1.0;

          if (rcond == 0.0)
            {
              // Either its indefinite or singular.  Try UMFPACK
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Full;
            }
          else
            {
              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                    {
                      sing_handler (rcond);
                      mattype.mark_as_rectangular ();
                    }
                  else
                    octave::warn_singular_matrix (rcond);

                  return retval;
                }

              cholmod_dense *X = CHOLMOD_NAME(solve) (CHOLMOD_A, L, B, cm);

              retval.resize (b.rows (), b.cols ());
              for (octave_idx_type j = 0; j < b.cols (); j++)
                {
                  octave_idx_type jr = j * b.rows ();
                  for (octave_idx_type i = 0; i < b.rows (); i++)
                    retval.xelem (i, j) = static_cast<Complex *>(X->x)[jr + i];
                }

              CHOLMOD_NAME(free_dense) (&X, cm);
              CHOLMOD_NAME(free_factor) (&L, cm);
              CHOLMOD_NAME(finish) (cm);
              static char blank_name[] = " ";
              CHOLMOD_NAME(print_common) (blank_name, cm);
            }
#else
          (*current_liboctave_warning_with_id_handler)
            ("Octave:missing-dependency",
             "support for CHOLMOD was unavailable or disabled "
             "when liboctave was built");

          mattype.mark_as_unsymmetric ();
          typ = MatrixType::Full;
#endif
        }

      if (typ == MatrixType::Full)
        {
#if defined (HAVE_UMFPACK)
          Matrix Control, Info;
          void *Numeric = factorize (err, rcond, Control, Info,
                                     sing_handler, calc_cond);

          if (err == 0)
            {
              // one iterative refinement instead of the default two in UMFPACK
              Control (UMFPACK_IRSTEP) = 1;
              octave_idx_type b_nr = b.rows ();
              octave_idx_type b_nc = b.cols ();
              int status = 0;
              double *control = Control.fortran_vec ();
              double *info = Info.fortran_vec ();
              const octave_idx_type *Ap = cidx ();
              const octave_idx_type *Ai = ridx ();
              const double *Ax = data ();

              OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Bz, b_nr);

              retval.resize (b_nr, b_nc);

              OCTAVE_LOCAL_BUFFER (double, Xx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Xz, b_nr);

              for (octave_idx_type j = 0; j < b_nc; j++)
                {
                  for (octave_idx_type i = 0; i < b_nr; i++)
                    {
                      Complex c = b(i, j);
                      Bx[i] = c.real ();
                      Bz[i] = c.imag ();
                    }

                  status = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                  octave::to_suitesparse_intptr (Ap),
                                                  octave::to_suitesparse_intptr (Ai),
                                                  Ax, Xx, Bx, Numeric,
                                                  control, info);
                  int status2 = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                       octave::to_suitesparse_intptr (Ap),
                                                       octave::to_suitesparse_intptr (Ai),
                                                       Ax, Xz, Bz,
                                                       Numeric, control, info);

                  if (status < 0 || status2 < 0)
                    {
                      UMFPACK_DNAME (report_status) (control, status);

                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }

                  for (octave_idx_type i = 0; i < b_nr; i++)
                    retval(i, j) = Complex (Xx[i], Xz[i]);
                }

              UMFPACK_DNAME (report_info) (control, info);

              UMFPACK_DNAME (free_numeric) (&Numeric);
            }
          else
            mattype.mark_as_rectangular ();

#else
          octave_unused_parameter (rcond);
          octave_unused_parameter (sing_handler);
          octave_unused_parameter (calc_cond);

          (*current_liboctave_error_handler)
            ("support for UMFPACK was unavailable or disabled "
             "when liboctave was built");
#endif
        }
      else if (typ != MatrixType::Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::fsolve (MatrixType& mattype, const SparseComplexMatrix& b,
                      octave_idx_type& err, double& rcond,
                      solve_singularity_handler sing_handler,
                      bool calc_cond) const
{
  SparseComplexMatrix retval;

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  err = 0;

  if (nr != nc || nr != b.rows ())
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch solution of linear equations");

  if (nr == 0 || b.cols () == 0)
    retval = SparseComplexMatrix (nc, b.cols ());
  else
    {
      // Print spparms("spumoni") info if requested
      volatile int typ = mattype.type ();
      mattype.info ();

      if (typ == MatrixType::Hermitian)
        {
#if defined (HAVE_CHOLMOD)
          cholmod_common Common;
          cholmod_common *cm = &Common;

          // Setup initial parameters
          CHOLMOD_NAME(start) (cm);
          cm->prefer_zomplex = false;

          double spu = octave::sparse_params::get_key ("spumoni");
          if (spu == 0.)
            {
              cm->print = -1;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr);
            }
          else
            {
              cm->print = static_cast<int> (spu) + 2;
              SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint);
            }

          cm->error_handler = &SparseCholError;
          SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex);
          SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot);

          cm->final_ll = true;

          cholmod_sparse Astore;
          cholmod_sparse *A = &Astore;
          A->nrow = nr;
          A->ncol = nc;

          A->p = cidx ();
          A->i = ridx ();
          A->nzmax = nnz ();
          A->packed = true;
          A->sorted = true;
          A->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          A->itype = CHOLMOD_LONG;
#else
          A->itype = CHOLMOD_INT;
#endif
          A->dtype = CHOLMOD_DOUBLE;
          A->stype = 1;
          A->xtype = CHOLMOD_REAL;

          A->x = data ();

          cholmod_sparse Bstore;
          cholmod_sparse *B = &Bstore;
          B->nrow = b.rows ();
          B->ncol = b.cols ();
          B->p = b.cidx ();
          B->i = b.ridx ();
          B->nzmax = b.nnz ();
          B->packed = true;
          B->sorted = true;
          B->nz = nullptr;
#if defined (OCTAVE_ENABLE_64)
          B->itype = CHOLMOD_LONG;
#else
          B->itype = CHOLMOD_INT;
#endif
          B->dtype = CHOLMOD_DOUBLE;
          B->stype = 0;
          B->xtype = CHOLMOD_COMPLEX;

          B->x = b.data ();

          cholmod_factor *L = CHOLMOD_NAME(analyze) (A, cm);
          CHOLMOD_NAME(factorize) (A, L, cm);
          if (calc_cond)
            rcond = CHOLMOD_NAME(rcond)(L, cm);
          else
            rcond = 1.0;

          if (rcond == 0.0)
            {
              // Either its indefinite or singular.  Try UMFPACK
              mattype.mark_as_unsymmetric ();
              typ = MatrixType::Full;
            }
          else
            {
              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || octave::math::isnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                    {
                      sing_handler (rcond);
                      mattype.mark_as_rectangular ();
                    }
                  else
                    octave::warn_singular_matrix (rcond);

                  return retval;
                }

              cholmod_sparse *X = CHOLMOD_NAME(spsolve) (CHOLMOD_A, L, B, cm);

              retval = SparseComplexMatrix
                       (static_cast<octave_idx_type> (X->nrow),
                        static_cast<octave_idx_type> (X->ncol),
                        static_cast<octave_idx_type> (X->nzmax));
              for (octave_idx_type j = 0;
                   j <= static_cast<octave_idx_type> (X->ncol); j++)
                retval.xcidx (j) = static_cast<octave_idx_type *>(X->p)[j];
              for (octave_idx_type j = 0;
                   j < static_cast<octave_idx_type> (X->nzmax); j++)
                {
                  retval.xridx (j) = static_cast<octave_idx_type *>(X->i)[j];
                  retval.xdata (j) = static_cast<Complex *>(X->x)[j];
                }

              CHOLMOD_NAME(free_sparse) (&X, cm);
              CHOLMOD_NAME(free_factor) (&L, cm);
              CHOLMOD_NAME(finish) (cm);
              static char blank_name[] = " ";
              CHOLMOD_NAME(print_common) (blank_name, cm);
            }
#else
          (*current_liboctave_warning_with_id_handler)
            ("Octave:missing-dependency",
             "support for CHOLMOD was unavailable or disabled "
             "when liboctave was built");

          mattype.mark_as_unsymmetric ();
          typ = MatrixType::Full;
#endif
        }

      if (typ == MatrixType::Full)
        {
#if defined (HAVE_UMFPACK)
          Matrix Control, Info;
          void *Numeric = factorize (err, rcond, Control, Info,
                                     sing_handler, calc_cond);

          if (err == 0)
            {
              // one iterative refinement instead of the default two in UMFPACK
              Control (UMFPACK_IRSTEP) = 1;
              octave_idx_type b_nr = b.rows ();
              octave_idx_type b_nc = b.cols ();
              int status = 0;
              double *control = Control.fortran_vec ();
              double *info = Info.fortran_vec ();
              const octave_idx_type *Ap = cidx ();
              const octave_idx_type *Ai = ridx ();
              const double *Ax = data ();

              OCTAVE_LOCAL_BUFFER (double, Bx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Bz, b_nr);

              // Take a first guess that the number of nonzero terms
              // will be as many as in b
              octave_idx_type x_nz = b.nnz ();
              octave_idx_type ii = 0;
              retval = SparseComplexMatrix (b_nr, b_nc, x_nz);

              OCTAVE_LOCAL_BUFFER (double, Xx, b_nr);
              OCTAVE_LOCAL_BUFFER (double, Xz, b_nr);

              retval.xcidx (0) = 0;
              for (octave_idx_type j = 0; j < b_nc; j++)
                {
                  for (octave_idx_type i = 0; i < b_nr; i++)
                    {
                      Complex c = b(i, j);
                      Bx[i] = c.real ();
                      Bz[i] = c.imag ();
                    }

                  status = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                  octave::to_suitesparse_intptr (Ap),
                                                  octave::to_suitesparse_intptr (Ai),
                                                  Ax, Xx, Bx, Numeric,
                                                  control, info);
                  int status2 = UMFPACK_DNAME (solve) (UMFPACK_A,
                                                       octave::to_suitesparse_intptr (Ap),
                                                       octave::to_suitesparse_intptr (Ai),
                                                       Ax, Xz, Bz,
                                                       Numeric, control, info);

                  if (status < 0 || status2 < 0)
                    {
                      UMFPACK_DNAME (report_status) (control, status);

                      // FIXME: Should this be a warning?
                      (*current_liboctave_error_handler)
                        ("SparseMatrix::solve solve failed");

                      err = -1;
                      break;
                    }

                  for (octave_idx_type i = 0; i < b_nr; i++)
                    {
                      Complex tmp = Complex (Xx[i], Xz[i]);
                      if (tmp != 0.0)
                        {
                          if (ii == x_nz)
                            {
                              // Resize the sparse matrix
                              octave_idx_type sz;
                              sz = (static_cast<double> (b_nc) - j) / b_nc
                                   * x_nz;
                              sz = x_nz + (sz > 100 ? sz : 100);
                              retval.change_capacity (sz);
                              x_nz = sz;
                            }
                          retval.xdata (ii) = tmp;
                          retval.xridx (ii++) = i;
                        }
                    }
                  retval.xcidx (j+1) = ii;
                }

              retval.maybe_compress ();

              UMFPACK_DNAME (report_info) (control, info);

              UMFPACK_DNAME (free_numeric) (&Numeric);
            }
          else
            mattype.mark_as_rectangular ();
#else
          octave_unused_parameter (rcond);
          octave_unused_parameter (sing_handler);
          octave_unused_parameter (calc_cond);

          (*current_liboctave_error_handler)
            ("support for UMFPACK was unavailable or disabled "
             "when liboctave was built");
#endif
        }
      else if (typ != MatrixType::Hermitian)
        (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

Matrix
SparseMatrix::solve (MatrixType& mattype, const Matrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (MatrixType& mattype, const Matrix& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (MatrixType& mattype, const Matrix& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& err,
                     double& rcond, solve_singularity_handler sing_handler,
                     bool singular_fallback) const
{
  Matrix retval;
  int typ = mattype.type (false);

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  // Only calculate the condition number for CHOLMOD/UMFPACK
  if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal)
    retval = dsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    retval = utsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    retval = ltsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian)
    retval = bsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Tridiagonal
           || typ == MatrixType::Tridiagonal_Hermitian)
    retval = trisolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
    retval = fsolve (mattype, b, err, rcond, sing_handler, true);
  else if (typ != MatrixType::Rectangular)
    (*current_liboctave_error_handler) ("unknown matrix type");

  // Rectangular or one of the above solvers flags a singular matrix
  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#if defined (USE_QRSOLVE)
      retval = qrsolve (*this, b, err);
#else
      retval = dmsolve<Matrix, SparseMatrix, Matrix> (*this, b, err);
#endif
    }

  return retval;
}

SparseMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseMatrix& b,
                     octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler,
                     bool singular_fallback) const
{
  SparseMatrix retval;
  int typ = mattype.type (false);

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal)
    retval = dsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    retval = utsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    retval = ltsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian)
    retval = bsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Tridiagonal
           || typ == MatrixType::Tridiagonal_Hermitian)
    retval = trisolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
    retval = fsolve (mattype, b, err, rcond, sing_handler, true);
  else if (typ != MatrixType::Rectangular)
    (*current_liboctave_error_handler) ("unknown matrix type");

  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#if defined (USE_QRSOLVE)
      retval = qrsolve (*this, b, err);
#else
      retval = dmsolve<SparseMatrix, SparseMatrix, SparseMatrix>
               (*this, b, err);
#endif
    }

  return retval;
}

ComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const ComplexMatrix& b,
                     octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler,
                     bool singular_fallback) const
{
  ComplexMatrix retval;
  int typ = mattype.type (false);

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal)
    retval = dsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    retval = utsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    retval = ltsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian)
    retval = bsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Tridiagonal
           || typ == MatrixType::Tridiagonal_Hermitian)
    retval = trisolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
    retval = fsolve (mattype, b, err, rcond, sing_handler, true);
  else if (typ != MatrixType::Rectangular)
    (*current_liboctave_error_handler) ("unknown matrix type");

  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#if defined (USE_QRSOLVE)
      retval = qrsolve (*this, b, err);
#else
      retval = dmsolve<ComplexMatrix, SparseMatrix, ComplexMatrix>
               (*this, b, err);
#endif
    }

  return retval;
}

SparseComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (MatrixType& mattype, const SparseComplexMatrix& b,
                     octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler,
                     bool singular_fallback) const
{
  SparseComplexMatrix retval;
  int typ = mattype.type (false);

  if (typ == MatrixType::Unknown)
    typ = mattype.type (*this);

  if (typ == MatrixType::Diagonal || typ == MatrixType::Permuted_Diagonal)
    retval = dsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper)
    retval = utsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
    retval = ltsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Banded || typ == MatrixType::Banded_Hermitian)
    retval = bsolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Tridiagonal
           || typ == MatrixType::Tridiagonal_Hermitian)
    retval = trisolve (mattype, b, err, rcond, sing_handler, false);
  else if (typ == MatrixType::Full || typ == MatrixType::Hermitian)
    retval = fsolve (mattype, b, err, rcond, sing_handler, true);
  else if (typ != MatrixType::Rectangular)
    (*current_liboctave_error_handler) ("unknown matrix type");

  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#if defined (USE_QRSOLVE)
      retval = qrsolve (*this, b, err);
#else
      retval = dmsolve<SparseComplexMatrix, SparseMatrix, SparseComplexMatrix>
               (*this, b, err);
#endif
    }

  return retval;
}

ColumnVector
SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b) const
{
  octave_idx_type info; double rcond;
  return solve (mattype, b, info, rcond);
}

ColumnVector
SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond);
}

ColumnVector
SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

ColumnVector
SparseMatrix::solve (MatrixType& mattype, const ColumnVector& b,
                     octave_idx_type& info, double& rcond,
                     solve_singularity_handler sing_handler) const
{
  Matrix tmp (b);
  return solve (mattype, tmp, info, rcond,
                sing_handler).column (static_cast<octave_idx_type> (0));
}

ComplexColumnVector
SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b,
                     octave_idx_type& info,
                     double& rcond) const
{
  return solve (mattype, b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b,
                     octave_idx_type& info, double& rcond,
                     solve_singularity_handler sing_handler) const
{
  ComplexMatrix tmp (b);
  return solve (mattype, tmp, info, rcond,
                sing_handler).column (static_cast<octave_idx_type> (0));
}

Matrix
SparseMatrix::solve (const Matrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (const Matrix& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (const Matrix& b, octave_idx_type& info,
                     double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

Matrix
SparseMatrix::solve (const Matrix& b, octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, err, rcond, sing_handler);
}

SparseMatrix
SparseMatrix::solve (const SparseMatrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (const SparseMatrix& b,
                     octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (const SparseMatrix& b,
                     octave_idx_type& info, double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

SparseMatrix
SparseMatrix::solve (const SparseMatrix& b, octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, err, rcond, sing_handler);
}

ComplexMatrix
SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, nullptr);
}

ComplexMatrix
SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& info,
                     double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

ComplexMatrix
SparseMatrix::solve (const ComplexMatrix& b, octave_idx_type& err,
                     double& rcond,
                     solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, err, rcond, sing_handler);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b, octave_idx_type& info,
                     double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b,
                     octave_idx_type& err, double& rcond,
                     solve_singularity_handler sing_handler) const
{
  MatrixType mattype (*this);
  return solve (mattype, b, err, rcond, sing_handler);
}

ColumnVector
SparseMatrix::solve (const ColumnVector& b) const
{
  octave_idx_type info; double rcond;
  return solve (b, info, rcond);
}

ColumnVector
SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond);
}

ColumnVector
SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info,
                     double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

ColumnVector
SparseMatrix::solve (const ColumnVector& b, octave_idx_type& info,
                     double& rcond,
                     solve_singularity_handler sing_handler) const
{
  Matrix tmp (b);
  return solve (tmp, info, rcond,
                sing_handler).column (static_cast<octave_idx_type> (0));
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b) const
{
  octave_idx_type info;
  double rcond;
  return solve (b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info,
                     double& rcond) const
{
  return solve (b, info, rcond, nullptr);
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info,
                     double& rcond,
                     solve_singularity_handler sing_handler) const
{
  ComplexMatrix tmp (b);
  return solve (tmp, info, rcond,
                sing_handler).column (static_cast<octave_idx_type> (0));
}

// other operations.

bool
SparseMatrix::any_element_is_negative (bool neg_zero) const
{
  octave_idx_type nel = nnz ();

  if (neg_zero)
    {
      for (octave_idx_type i = 0; i < nel; i++)
        if (lo_ieee_signbit (data (i)))
          return true;
    }
  else
    {
      for (octave_idx_type i = 0; i < nel; i++)
        if (data (i) < 0)
          return true;
    }

  return false;
}

bool
SparseMatrix::any_element_is_nan (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);
      if (octave::math::isnan (val))
        return true;
    }

  return false;
}

bool
SparseMatrix::any_element_is_inf_or_nan (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);
      if (octave::math::isinf (val) || octave::math::isnan (val))
        return true;
    }

  return false;
}

bool
SparseMatrix::any_element_not_one_or_zero (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);
      if (val != 0.0 && val != 1.0)
        return true;
    }

  return false;
}

bool
SparseMatrix::all_elements_are_zero (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    if (data (i) != 0)
      return false;

  return true;
}

bool
SparseMatrix::all_elements_are_int_or_inf_or_nan (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);
      if (octave::math::isnan (val) || octave::math::x_nint (val) == val)
        continue;
      else
        return false;
    }

  return true;
}

// Return nonzero if any element of M is not an integer.  Also extract
// the largest and smallest values and return them in MAX_VAL and MIN_VAL.

bool
SparseMatrix::all_integers (double& max_val, double& min_val) const
{
  octave_idx_type nel = nnz ();

  if (nel == 0)
    return false;

  max_val = data (0);
  min_val = data (0);

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);

      if (val > max_val)
        max_val = val;

      if (val < min_val)
        min_val = val;

      if (octave::math::x_nint (val) != val)
        return false;
    }

  return true;
}

bool
SparseMatrix::too_large_for_float (void) const
{
  return test_any (octave::too_large_for_float);
}

SparseBoolMatrix
SparseMatrix::operator ! (void) const
{
  if (any_element_is_nan ())
    octave::err_nan_to_logical_conversion ();

  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();
  octave_idx_type nz1 = nnz ();
  octave_idx_type nz2 = nr*nc - nz1;

  SparseBoolMatrix r (nr, nc, nz2);

  octave_idx_type ii = 0;
  octave_idx_type jj = 0;
  r.cidx (0) = 0;
  for (octave_idx_type i = 0; i < nc; i++)
    {
      for (octave_idx_type j = 0; j < nr; j++)
        {
          if (jj < cidx (i+1) && ridx (jj) == j)
            jj++;
          else
            {
              r.data (ii) = true;
              r.ridx (ii++) = j;
            }
        }
      r.cidx (i+1) = ii;
    }

  return r;
}

// FIXME: Do these really belong here?  Maybe they should be in a base class?

SparseBoolMatrix
SparseMatrix::all (int dim) const
{
  SPARSE_ALL_OP (dim);
}

SparseBoolMatrix
SparseMatrix::any (int dim) const
{
  SPARSE_ANY_OP (dim);
}

SparseMatrix
SparseMatrix::cumprod (int dim) const
{
  SPARSE_CUMPROD (SparseMatrix, double, cumprod);
}

SparseMatrix
SparseMatrix::cumsum (int dim) const
{
  SPARSE_CUMSUM (SparseMatrix, double, cumsum);
}

SparseMatrix
SparseMatrix::prod (int dim) const
{
  if ((rows () == 1 && dim == -1) || dim == 1)
    return transpose ().prod (0).transpose ();
  else
    {
      SPARSE_REDUCTION_OP (SparseMatrix, double, *=,
                           (cidx (j+1) - cidx (j) < nr ? 0.0 : 1.0), 1.0);
    }
}

SparseMatrix
SparseMatrix::sum (int dim) const
{
  SPARSE_REDUCTION_OP (SparseMatrix, double, +=, 0.0, 0.0);
}

SparseMatrix
SparseMatrix::sumsq (int dim) const
{
#define ROW_EXPR                                \
  double d = data (i);                          \
  tmp[ridx (i)] += d * d

#define COL_EXPR                                \
  double d = data (i);                          \
  tmp[j] += d * d

  SPARSE_BASE_REDUCTION_OP (SparseMatrix, double, ROW_EXPR, COL_EXPR,
                            0.0, 0.0);

#undef ROW_EXPR
#undef COL_EXPR
}

SparseMatrix
SparseMatrix::abs (void) const
{
  octave_idx_type nz = nnz ();

  SparseMatrix retval (*this);

  for (octave_idx_type i = 0; i < nz; i++)
    retval.data (i) = fabs (retval.data (i));

  return retval;
}

SparseMatrix
SparseMatrix::diag (octave_idx_type k) const
{
  return MSparse<double>::diag (k);
}

Matrix
SparseMatrix::matrix_value (void) const
{
  return Sparse<double>::array_value ();
}

std::ostream&
operator << (std::ostream& os, const SparseMatrix& a)
{
  octave_idx_type nc = a.cols ();

  // add one to the printed indices to go from
  //  zero-based to one-based arrays
  for (octave_idx_type j = 0; j < nc; j++)
    {
      octave_quit ();
      for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++)
        {
          os << a.ridx (i) + 1 << ' '  << j + 1 << ' ';
          octave::write_value<double> (os, a.data (i));
          os << "\n";
        }
    }

  return os;
}

std::istream&
operator >> (std::istream& is, SparseMatrix& a)
{
  typedef SparseMatrix::element_type elt_type;

  return read_sparse_matrix<elt_type> (is, a, octave::read_value<double>);
}

SparseMatrix
SparseMatrix::squeeze (void) const
{
  return MSparse<double>::squeeze ();
}

SparseMatrix
SparseMatrix::reshape (const dim_vector& new_dims) const
{
  return MSparse<double>::reshape (new_dims);
}

SparseMatrix
SparseMatrix::permute (const Array<octave_idx_type>& vec, bool inv) const
{
  return MSparse<double>::permute (vec, inv);
}

SparseMatrix
SparseMatrix::ipermute (const Array<octave_idx_type>& vec) const
{
  return MSparse<double>::ipermute (vec);
}

// matrix by matrix -> matrix operations

SparseMatrix
operator * (const SparseMatrix& m, const SparseMatrix& a)
{
  SPARSE_SPARSE_MUL (SparseMatrix, double, double);
}

Matrix
operator * (const Matrix& m, const SparseMatrix& a)
{
  FULL_SPARSE_MUL (Matrix, double);
}

Matrix
mul_trans (const Matrix& m, const SparseMatrix& a)
{
  FULL_SPARSE_MUL_TRANS (Matrix, double, );
}

Matrix
operator * (const SparseMatrix& m, const Matrix& a)
{
  SPARSE_FULL_MUL (Matrix, double);
}

Matrix
trans_mul (const SparseMatrix& m, const Matrix& a)
{
  SPARSE_FULL_TRANS_MUL (Matrix, double, );
}

// diag * sparse and sparse * diag

SparseMatrix
operator * (const DiagMatrix& d, const SparseMatrix& a)
{
  return do_mul_dm_sm<SparseMatrix> (d, a);
}

SparseMatrix
operator * (const SparseMatrix& a, const DiagMatrix& d)
{
  return do_mul_sm_dm<SparseMatrix> (a, d);
}

SparseMatrix
operator + (const DiagMatrix& d, const SparseMatrix& a)
{
  return do_add_dm_sm<SparseMatrix> (d, a);
}

SparseMatrix
operator - (const DiagMatrix& d, const SparseMatrix& a)
{
  return do_sub_dm_sm<SparseMatrix> (d, a);
}

SparseMatrix
operator + (const SparseMatrix& a, const DiagMatrix& d)
{
  return do_add_sm_dm<SparseMatrix> (a, d);
}

SparseMatrix
operator - (const SparseMatrix& a, const DiagMatrix& d)
{
  return do_sub_sm_dm<SparseMatrix> (a, d);
}

// perm * sparse and sparse * perm

SparseMatrix
operator * (const PermMatrix& p, const SparseMatrix& a)
{
  return octinternal_do_mul_pm_sm (p, a);
}

SparseMatrix
operator * (const SparseMatrix& a, const PermMatrix& p)
{
  return octinternal_do_mul_sm_pm (a, p);
}

// FIXME: it would be nice to share code among the min/max functions below.

#define EMPTY_RETURN_CHECK(T)                   \
  if (nr == 0 || nc == 0)                       \
    return T (nr, nc);

SparseMatrix
min (double d, const SparseMatrix& m)
{
  SparseMatrix result;

  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (SparseMatrix);

  // Count the number of nonzero elements
  if (d < 0.)
    {
      result = SparseMatrix (nr, nc, d);
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
          {
            double tmp = octave::math::min (d, m.data (i));
            if (tmp != 0.)
              {
                octave_idx_type idx = m.ridx (i) + j * nr;
                result.xdata (idx) = tmp;
                result.xridx (idx) = m.ridx (i);
              }
          }
    }
  else
    {
      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
          if (octave::math::min (d, m.data (i)) != 0.)
            nel++;

      result = SparseMatrix (nr, nc, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
            {
              double tmp = octave::math::min (d, m.data (i));

              if (tmp != 0.)
                {
                  result.xdata (ii) = tmp;
                  result.xridx (ii++) = m.ridx (i);
                }
            }
          result.xcidx (j+1) = ii;
        }
    }

  return result;
}

SparseMatrix
min (const SparseMatrix& m, double d)
{
  return min (d, m);
}

SparseMatrix
min (const SparseMatrix& a, const SparseMatrix& b)
{
  SparseMatrix r;

  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();

  if (a_nr == b_nr && a_nc == b_nc)
    {
      r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ()));

      octave_idx_type jx = 0;
      r.cidx (0) = 0;
      for (octave_idx_type i = 0 ; i < a_nc ; i++)
        {
          octave_idx_type ja = a.cidx (i);
          octave_idx_type ja_max = a.cidx (i+1);
          bool ja_lt_max = ja < ja_max;

          octave_idx_type jb = b.cidx (i);
          octave_idx_type jb_max = b.cidx (i+1);
          bool jb_lt_max = jb < jb_max;

          while (ja_lt_max || jb_lt_max)
            {
              octave_quit ();
              if ((! jb_lt_max) || (ja_lt_max && (a.ridx (ja) < b.ridx (jb))))
                {
                  double tmp = octave::math::min (a.data (ja), 0.);
                  if (tmp != 0.)
                    {
                      r.ridx (jx) = a.ridx (ja);
                      r.data (jx) = tmp;
                      jx++;
                    }
                  ja++;
                  ja_lt_max= ja < ja_max;
                }
              else if ((! ja_lt_max)
                       || (jb_lt_max && (b.ridx (jb) < a.ridx (ja))))
                {
                  double tmp = octave::math::min (0., b.data (jb));
                  if (tmp != 0.)
                    {
                      r.ridx (jx) = b.ridx (jb);
                      r.data (jx) = tmp;
                      jx++;
                    }
                  jb++;
                  jb_lt_max= jb < jb_max;
                }
              else
                {
                  double tmp = octave::math::min (a.data (ja), b.data (jb));
                  if (tmp != 0.)
                    {
                      r.data (jx) = tmp;
                      r.ridx (jx) = a.ridx (ja);
                      jx++;
                    }
                  ja++;
                  ja_lt_max= ja < ja_max;
                  jb++;
                  jb_lt_max= jb < jb_max;
                }
            }
          r.cidx (i+1) = jx;
        }

      r.maybe_compress ();
    }
  else
    {
      if (a_nr == 0 || a_nc == 0)
        r.resize (a_nr, a_nc);
      else if (b_nr == 0 || b_nc == 0)
        r.resize (b_nr, b_nc);
      else
        octave::err_nonconformant ("min", a_nr, a_nc, b_nr, b_nc);
    }

  return r;
}

SparseMatrix
max (double d, const SparseMatrix& m)
{
  SparseMatrix result;

  octave_idx_type nr = m.rows ();
  octave_idx_type nc = m.columns ();

  EMPTY_RETURN_CHECK (SparseMatrix);

  // Count the number of nonzero elements
  if (d > 0.)
    {
      result = SparseMatrix (nr, nc, d);
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
          {
            double tmp = octave::math::max (d, m.data (i));

            if (tmp != 0.)
              {
                octave_idx_type idx = m.ridx (i) + j * nr;
                result.xdata (idx) = tmp;
                result.xridx (idx) = m.ridx (i);
              }
          }
    }
  else
    {
      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
          if (octave::math::max (d, m.data (i)) != 0.)
            nel++;

      result = SparseMatrix (nr, nc, nel);

      octave_idx_type ii = 0;
      result.xcidx (0) = 0;
      for (octave_idx_type j = 0; j < nc; j++)
        {
          for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++)
            {
              double tmp = octave::math::max (d, m.data (i));
              if (tmp != 0.)
                {
                  result.xdata (ii) = tmp;
                  result.xridx (ii++) = m.ridx (i);
                }
            }
          result.xcidx (j+1) = ii;
        }
    }

  return result;
}

SparseMatrix
max (const SparseMatrix& m, double d)
{
  return max (d, m);
}

SparseMatrix
max (const SparseMatrix& a, const SparseMatrix& b)
{
  SparseMatrix r;

  octave_idx_type a_nr = a.rows ();
  octave_idx_type a_nc = a.cols ();
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();

  if (a_nr == b_nr && a_nc == b_nc)
    {
      r = SparseMatrix (a_nr, a_nc, (a.nnz () + b.nnz ()));

      octave_idx_type jx = 0;
      r.cidx (0) = 0;
      for (octave_idx_type i = 0 ; i < a_nc ; i++)
        {
          octave_idx_type ja = a.cidx (i);
          octave_idx_type ja_max = a.cidx (i+1);
          bool ja_lt_max = ja < ja_max;

          octave_idx_type jb = b.cidx (i);
          octave_idx_type jb_max = b.cidx (i+1);
          bool jb_lt_max = jb < jb_max;

          while (ja_lt_max || jb_lt_max)
            {
              octave_quit ();
              if ((! jb_lt_max) || (ja_lt_max && (a.ridx (ja) < b.ridx (jb))))
                {
                  double tmp = octave::math::max (a.data (ja), 0.);
                  if (tmp != 0.)
                    {
                      r.ridx (jx) = a.ridx (ja);
                      r.data (jx) = tmp;
                      jx++;
                    }
                  ja++;
                  ja_lt_max= ja < ja_max;
                }
              else if ((! ja_lt_max)
                       || (jb_lt_max && (b.ridx (jb) < a.ridx (ja))))
                {
                  double tmp = octave::math::max (0., b.data (jb));
                  if (tmp != 0.)
                    {
                      r.ridx (jx) = b.ridx (jb);
                      r.data (jx) = tmp;
                      jx++;
                    }
                  jb++;
                  jb_lt_max= jb < jb_max;
                }
              else
                {
                  double tmp = octave::math::max (a.data (ja), b.data (jb));
                  if (tmp != 0.)
                    {
                      r.data (jx) = tmp;
                      r.ridx (jx) = a.ridx (ja);
                      jx++;
                    }
                  ja++;
                  ja_lt_max= ja < ja_max;
                  jb++;
                  jb_lt_max= jb < jb_max;
                }
            }
          r.cidx (i+1) = jx;
        }

      r.maybe_compress ();
    }
  else
    {
      if (a_nr == 0 || a_nc == 0)
        r.resize (a_nr, a_nc);
      else if (b_nr == 0 || b_nc == 0)
        r.resize (b_nr, b_nc);
      else
        octave::err_nonconformant ("max", a_nr, a_nc, b_nr, b_nc);
    }

  return r;
}

SPARSE_SMS_CMP_OPS (SparseMatrix, double)
SPARSE_SMS_BOOL_OPS (SparseMatrix, double)

SPARSE_SSM_CMP_OPS (double, SparseMatrix)
SPARSE_SSM_BOOL_OPS (double, SparseMatrix)

SPARSE_SMSM_CMP_OPS (SparseMatrix, SparseMatrix)
SPARSE_SMSM_BOOL_OPS (SparseMatrix, SparseMatrix)