Logo Search packages:      
Sourcecode: octave3.2 version File versions

dSparse.cc

/*

Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009 David Bateman
Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004 Andy Adler

This file is part of Octave.

Octave is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

Octave is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <cfloat>

#include <iostream>
#include <vector>
#include <functional>

#include "quit.h"
#include "lo-ieee.h"
#include "lo-mappers.h"
#include "f77-fcn.h"
#include "dRowVector.h"
#include "oct-locbuf.h"

#include "dDiagMatrix.h"
#include "CSparse.h"
#include "boolSparse.h"
#include "dSparse.h"
#include "functor.h"
#include "oct-spparms.h"
#include "SparsedbleLU.h"
#include "MatrixType.h"
#include "oct-sparse.h"
#include "sparse-util.h"
#include "SparsedbleCHOL.h"
#include "SparseQR.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 seperate the problem into under-determined,
// well-determined and over-determined parts and solves them seperately
#ifndef USE_QRSOLVE
#include "sparse-dmsolve.cc"
#endif

// Fortran functions we call.
extern "C"
{
  F77_RET_T
  F77_FUNC (dgbtrf, DGBTRF) (const octave_idx_type&, const octave_idx_type&,
                       const octave_idx_type&, const octave_idx_type&,
                       double*, const octave_idx_type&,
                       octave_idx_type*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (dgbtrs, DGBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&,
                       const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, 
                       const double*, const octave_idx_type&,
                       const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dgbcon, DGBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
                       const octave_idx_type&, const octave_idx_type&, double*, 
                       const octave_idx_type&, const octave_idx_type*, const double&, 
                       double&, double*, octave_idx_type*, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dpbtrf, DPBTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
                       const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dpbtrs, DPBTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
                       const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, 
                       double*, const octave_idx_type&, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (dpbcon, DPBCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, 
                       const octave_idx_type&, double*, const octave_idx_type&, 
                       const double&, double&, double*, octave_idx_type*, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);
  F77_RET_T
  F77_FUNC (dptsv, DPTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*,
                     double*, const octave_idx_type&, octave_idx_type&);

  F77_RET_T
  F77_FUNC (dgtsv, DGTSV) (const octave_idx_type&, const octave_idx_type&, double*, double*,
                     double*, double*, const octave_idx_type&, octave_idx_type&);

  F77_RET_T
  F77_FUNC (dgttrf, DGTTRF) (const octave_idx_type&, double*, double*, double*, double*,
                       octave_idx_type*, octave_idx_type&);

  F77_RET_T
  F77_FUNC (dgttrs, DGTTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&,
                       const octave_idx_type&, const double*, const double*,
                       const double*, const double*, const octave_idx_type*,
                       double *, const octave_idx_type&, octave_idx_type&
                       F77_CHAR_ARG_LEN_DECL);

  F77_RET_T
  F77_FUNC (zptsv, ZPTSV) (const octave_idx_type&, const octave_idx_type&, double*, Complex*,
                     Complex*, const octave_idx_type&, octave_idx_type&);

  F77_RET_T
  F77_FUNC (zgtsv, ZGTSV) (const octave_idx_type&, const octave_idx_type&, Complex*, Complex*,
                     Complex*, Complex*, const octave_idx_type&, octave_idx_type&);

}

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, 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;
}

SparseMatrix::SparseMatrix (const PermMatrix& a)
  : MSparse<double> (a.rows (), a.cols (), a.rows ())
{
  octave_idx_type n = a.rows ();
  for (octave_idx_type i = 0; i <= n; i++) 
    cidx (i) = i;
  const Array<octave_idx_type> pv = a.pvec ();

  if (a.is_row_perm ())
    {
      for (octave_idx_type i = 0; i < n; i++)
        ridx (pv (i)) = i;
    }
  else
    {
      for (octave_idx_type i = 0; i < n; i++)
        ridx (i) = pv (i);
    }

  for (octave_idx_type i = 0; i < n; i++)
    data (i) = 1.0;
}

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::is_symmetric (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
{
  Array2<octave_idx_type> dummy_idx;
  return max (dummy_idx, dim);
}

SparseMatrix
SparseMatrix::max (Array2<octave_idx_type>& idx_arg, int dim) const
{
  SparseMatrix result;
  dim_vector dv = dims ();

  if (dv.numel () == 0 || dim > dv.length () || dim < 0)
    return result;
 
  octave_idx_type nr = dv(0);
  octave_idx_type nc = dv(1);

  if (dim == 0)
    {
      idx_arg.resize (1, nc);
      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
      {
        double tmp_max = octave_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 (xisnan (tmp))
            continue;
            else if (xisnan (tmp_max) || tmp > tmp_max)
            {
              idx_j = ridx (i);
              tmp_max = tmp;
            }

          }

        idx_arg.elem (j) = xisnan (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 (nr, 1, 0);

      for (octave_idx_type i = cidx(0); i < cidx(1); i++)
      idx_arg.elem(ridx(i)) = -1;

      for (octave_idx_type j = 0; j < nc; j++)
      for (octave_idx_type i = 0; i < nr; i++)
        {
          if (idx_arg.elem(i) != -1)
            continue;
          bool found = false;
          for (octave_idx_type k = cidx(j); k < cidx(j+1); k++)
            if (ridx(k) == i)
            {
              found = true;
              break;
            }
          
          if (!found)
            idx_arg.elem(i) = j;

        }

      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 (xisnan (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_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
{
  Array2<octave_idx_type> dummy_idx;
  return min (dummy_idx, dim);
}

SparseMatrix
SparseMatrix::min (Array2<octave_idx_type>& idx_arg, int dim) const
{
  SparseMatrix result;
  dim_vector dv = dims ();

  if (dv.numel () == 0 || dim > dv.length () || dim < 0)
    return result;
 
  octave_idx_type nr = dv(0);
  octave_idx_type nc = dv(1);

  if (dim == 0)
    {
      idx_arg.resize (1, nc);
      octave_idx_type nel = 0;
      for (octave_idx_type j = 0; j < nc; j++)
      {
        double tmp_min = octave_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 (xisnan (tmp))
            continue;
            else if (xisnan (tmp_min) || tmp < tmp_min)
            {
              idx_j = ridx (i);
              tmp_min = tmp;
            }

          }

        idx_arg.elem (j) = xisnan (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 (nr, 1, 0);

      for (octave_idx_type i = cidx(0); i < cidx(1); i++)
      idx_arg.elem(ridx(i)) = -1;

      for (octave_idx_type j = 0; j < nc; j++)
      for (octave_idx_type i = 0; i < nr; i++)
        {
          if (idx_arg.elem(i) != -1)
            continue;
          bool found = false;
          for (octave_idx_type k = cidx(j); k < cidx(j+1); k++)
            if (ridx(k) == i)
            {
              found = true;
              break;
            }
          
          if (!found)
            idx_arg.elem(i) = j;

        }

      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 (xisnan (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_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;
}

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);

  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 possiblity 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);
    }

  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);
    }

  return r;
}

SparseMatrix 
atan2 (const double& x, const SparseMatrix& y)
{
  octave_idx_type nr = y.rows ();
  octave_idx_type nc = y.cols ();

  if (x == 0.)
    return SparseMatrix (nr, nc);
  else
    {
      // Its going to be basically full, so this is probably the
      // best way to handle it.
      Matrix tmp (nr, nc, atan2 (x, 0.));

      for (octave_idx_type j = 0; j < nc; j++)
      for (octave_idx_type i = y.cidx (j); i < y.cidx (j+1); i++)
        tmp.elem (y.ridx(i), j) = atan2 (x, y.data(i));

      return SparseMatrix (tmp);
    }
}

SparseMatrix 
atan2 (const SparseMatrix& x, const double& y)
{
  octave_idx_type nr = x.rows ();
  octave_idx_type nc = x.cols ();
  octave_idx_type nz = x.nnz ();

  SparseMatrix retval (nr, nc, nz);

  octave_idx_type ii = 0;
  retval.xcidx(0) = 0;
  for (octave_idx_type i = 0; i < nc; i++)
    {
      for (octave_idx_type j = x.cidx(i); j < x.cidx(i+1); j++)
      {
        double tmp = atan2 (x.data(j), y);
        if (tmp != 0.)
          {
            retval.xdata (ii) = tmp;
            retval.xridx (ii++) = x.ridx (j);
          }
      }
      retval.xcidx (i+1) = ii;
    }

  if (ii != nz)
    {
      SparseMatrix retval2 (nr, nc, ii);
      for (octave_idx_type i = 0; i < nc+1; i++)
      retval2.xcidx (i) = retval.cidx (i);
      for (octave_idx_type i = 0; i < ii; i++)
      {
        retval2.xdata (i) = retval.data (i);
        retval2.xridx (i) = retval.ridx (i);
      }
      return retval2;
    }
  else
    return retval;
}

SparseMatrix 
atan2 (const SparseMatrix& x, const SparseMatrix& y)
{
  SparseMatrix r;

  if ((x.rows() == y.rows()) && (x.cols() == y.cols())) 
    {
      octave_idx_type x_nr = x.rows ();
      octave_idx_type x_nc = x.cols ();

      octave_idx_type y_nr = y.rows ();
      octave_idx_type y_nc = y.cols ();

      if (x_nr != y_nr || x_nc != y_nc)
      gripe_nonconformant ("atan2", x_nr, x_nc, y_nr, y_nc);
      else
      {
        r = SparseMatrix (x_nr, x_nc, (x.nnz () + y.nnz ()));
       
        octave_idx_type jx = 0;
        r.cidx (0) = 0;
        for (octave_idx_type i = 0 ; i < x_nc ; i++)
          {
            octave_idx_type  ja = x.cidx(i);
            octave_idx_type  ja_max = x.cidx(i+1);
            bool ja_lt_max= ja < ja_max;
           
            octave_idx_type  jb = y.cidx(i);
            octave_idx_type  jb_max = y.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 && (x.ridx(ja) < y.ridx(jb))))
                {
                  r.ridx(jx) = x.ridx(ja);
                  r.data(jx) = atan2 (x.data(ja), 0.);
                  jx++;
                  ja++;
                  ja_lt_max= ja < ja_max;
                }
              else if (( !ja_lt_max ) ||
                     (jb_lt_max && (y.ridx(jb) < x.ridx(ja)) ) )
                {
                  jb++;
                  jb_lt_max= jb < jb_max;
                }
              else
                {
                  double tmp = atan2 (x.data(ja), y.data(jb));
                  if (tmp != 0.)
                  {
                          r.data(jx) = tmp;
                          r.ridx(jx) = x.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
    (*current_liboctave_error_handler) ("matrix size mismatch");

  return r;
}

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 &mattyp, 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");
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattyp.type ();
      mattyp.info ();

      if (typ == MatrixType::Diagonal ||
        typ == MatrixType::Permuted_Diagonal)
      {
        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., dmin = octave_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];
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;
}

SparseMatrix 
SparseMatrix::tinverse (MatrixType &mattyp, 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");
  else
    {
      // Print spparms("spumoni") info if requested
      int typ = mattyp.type ();
      mattyp.info ();

      if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper || 
        typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower)
      {
        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 accross 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");
                    goto inverse_singular;
                  }

                  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");
                    goto inverse_singular;
                  }

                  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");
                  goto inverse_singular;
                }

              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 = mattyp.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 accross 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");
                    goto inverse_singular;
                  }

                  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");
                  goto inverse_singular;
                }

              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;     
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  return retval;

 inverse_singular:
  return SparseMatrix();
}

SparseMatrix
SparseMatrix::inverse (MatrixType &mattype, octave_idx_type& info, 
                   double& rcond, int, int calc_cond) const
{
  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.is_hermitian())
      {
        MatrixType tmp_typ (MatrixType::Upper);
        SparseCHOL 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 ();
            typ = MatrixType::Full;
          }
      }

      if (!mattype.is_hermitian())
      {
        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);
        SparseLU fact (*this, Qinit, Matrix(), false, false);
        rcond = fact.rcond();
        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, int) const
{
  DET retval;

#ifdef 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 (!xisnan (tmp))
      Control (UMFPACK_PRL) = tmp;

      tmp = octave_sparse_params::get_key ("piv_tol");
      if (!xisnan (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 (!xisnan (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, Ap, Ai, Ax, 1, control);

      void *Symbolic;
      Matrix Info (1, UMFPACK_INFO);
      double *info = Info.fortran_vec ();
      int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, 
                               Ax, 0, &Symbolic, control, info);

      if (status < 0)
      {
        (*current_liboctave_error_handler) 
          ("SparseMatrix::determinant symbolic factorization failed");

        UMFPACK_DNAME (report_status) (control, status);
        UMFPACK_DNAME (report_info) (control, info);

        UMFPACK_DNAME (free_symbolic) (&Symbolic) ;
      }
      else
      {
        UMFPACK_DNAME (report_symbolic) (Symbolic, control);

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

        rcond = Info (UMFPACK_RCOND);

        if (status < 0)
          {
            (*current_liboctave_error_handler) 
            ("SparseMatrix::determinant numeric factorization failed");

            UMFPACK_DNAME (report_status) (control, status);
            UMFPACK_DNAME (report_info) (control, info);

            UMFPACK_DNAME (free_numeric) (&Numeric);
          }
        else
          {
            UMFPACK_DNAME (report_numeric) (Numeric, control);

            double c10, e10;

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

            if (status < 0)
            {
              (*current_liboctave_error_handler) 
                ("SparseMatrix::determinant error calculating determinant");
              
              UMFPACK_DNAME (report_status) (control, status);
              UMFPACK_DNAME (report_info) (control, info);
            }
            else
            retval = DET (c10, e10, 10);

            UMFPACK_DNAME (free_numeric) (&Numeric);
          }
      }
    }
#else
  (*current_liboctave_error_handler) ("UMFPACK not installed");
#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");
  else 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)
      {
        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., dmin = octave_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.;
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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., dmin = octave_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.;
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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., dmin = octave_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.;
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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., dmin = octave_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.;
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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 non-zeros 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 non-zeros 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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }
  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");
  else 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)
      {
        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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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 non-zeros 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 non-zeros 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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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 non-zeros 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 non-zeros 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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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)
      {
        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 non-zeros 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 non-zeros 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
            (*current_liboctave_error_handler)
              ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
               rcond);
          }

        volatile double rcond_plus_one = rcond + 1.0;

        if (rcond_plus_one == 1.0 || xisnan (rcond))
          {
            err = -2;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision, rcond = %g",
               rcond);
          }
      }
      else
      (*current_liboctave_error_handler) ("incorrect matrix type");
    }

  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");
  else 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);
              }
          }
            
        octave_idx_type b_nc = b.cols();
        retval = b;
        double *result = retval.fortran_vec ();

        F77_XFCN (dptsv, DPTSV, (nr, b_nc, D, DL, result, 
                           b.rows(), 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);
              }
          }

        octave_idx_type b_nc = b.cols();
        retval = b;
        double *result = retval.fortran_vec ();

        F77_XFCN (dgtsv, DGTSV, (nr, b_nc, DL, D, DU, result, 
                           b.rows(), err));

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

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        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");
  else 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<octave_idx_type> ipvt (nr);
        octave_idx_type *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_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err));

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

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        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_XFCN (dgttrs, DGTTRS, 
                      (F77_CONST_CHAR_ARG2 (&job, 1),
                       nr, 1, DL, D, DU, DU2, pipvt, 
                       work, b.rows (), err
                       F77_CHAR_ARG_LEN (1)));

              // Count non-zeros 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");
  else 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);
              }
          }

        octave_idx_type b_nr = b.rows ();
        octave_idx_type b_nc = b.cols();
        rcond = 1.;

        retval = b;
        Complex *result = retval.fortran_vec ();
              
        F77_XFCN (zptsv, ZPTSV, (nr, b_nc, D, DL, result, 
                           b_nr, 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);
              }
          }

        octave_idx_type b_nr = b.rows();
        octave_idx_type b_nc = b.cols();
        rcond = 1.;

        retval = b;
        Complex *result = retval.fortran_vec ();
            
        F77_XFCN (zgtsv, ZGTSV, (nr, b_nc, DL, D, DU, result, 
                           b_nr, err));

        if (err != 0)
          {
            rcond = 0.;
            err = -2;
                  
            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");
          }
      }
      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");
  else 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<octave_idx_type> ipvt (nr);
        octave_idx_type *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_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err));

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

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");
          } 
        else 
          { 
            rcond = 1.;
            char job = 'N';
            octave_idx_type b_nr = 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 non-zero 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 (octave_idx_type i = 0; i < b_nr; i++)
                {
                  Complex c = b (i,j);
                  Bx[i] = std::real (c);
                  Bz[i] = std::imag (c);
                }

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

              if (err != 0)
                {
                  (*current_liboctave_error_handler)
                  ("SparseMatrix::solve solve failed");

                  err = -1;
                  break;
                }

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

              if (err != 0)
                {
                  (*current_liboctave_error_handler)
                  ("SparseMatrix::solve solve failed");

                  err = -1;
                  break;
                }

              // Count non-zeros 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");
  else 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)
      {
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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();

        char job = 'L';
        F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                             nr, n_lower, tmp_data, ldm, err
                             F77_CHAR_ARG_LEN (1)));
          
        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 (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

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

              octave_idx_type b_nc = b.cols ();

              F77_XFCN (dpbtrs, DPBTRS, 
                      (F77_CONST_CHAR_ARG2 (&job, 1),
                       nr, n_lower, b_nc, tmp_data,
                       ldm, result, b.rows(), err
                       F77_CHAR_ARG_LEN (1)));

              if (err != 0)
                {
                  (*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
        octave_idx_type n_upper = mattype.nupper ();
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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 (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)
          {
            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;
            }
          }

        Array<octave_idx_type> ipvt (nr);
        octave_idx_type *pipvt = ipvt.fortran_vec ();

        F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, 
                             ldm, pipvt, 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
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        else 
          {
            if (calc_cond)
            {
              char job = '1';
              Array<double> z (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

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

              octave_idx_type b_nc = b.cols ();

              char job = 'N';
              F77_XFCN (dgbtrs, DGBTRS, 
                      (F77_CONST_CHAR_ARG2 (&job, 1),
                       nr, n_lower, n_upper, b_nc, tmp_data,
                       ldm, pipvt, result, b.rows(), err
                       F77_CHAR_ARG_LEN (1)));
            }
          }
      }
      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");
  else 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)
      {
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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();

        char job = 'L';
        F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                             nr, n_lower, tmp_data, ldm, err
                             F77_CHAR_ARG_LEN (1)));
          
        if (err != 0) 
          {
            mattype.mark_as_unsymmetric ();
            typ = MatrixType::Banded;
            rcond = 0.0;
            err = 0;
          } 
        else 
          {
            if (calc_cond)
            {
              Array<double> z (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

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

              // Take a first guess that the number of non-zero 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 (octave_idx_type i = 0; i < b_nr; i++)
                  Bx[i] = b.elem (i, j);

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

                  if (err != 0)
                  {
                    (*current_liboctave_error_handler) 
                      ("SparseMatrix::solve solve failed");
                    err = -1;
                    break;
                  }

                  for (octave_idx_type 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 = x_nz * 
                            (b_nc - j) / b_nc;
                          sz = (sz > 10 ? sz : 10) + x_nz;
                          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
        octave_idx_type n_upper = mattype.nupper ();
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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 (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)
          {
            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;
            }
          }

        Array<octave_idx_type> ipvt (nr);
        octave_idx_type *pipvt = ipvt.fortran_vec ();

        F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, 
                             ldm, pipvt, err));
          
        if (err != 0) 
          {
            err = -2;
            rcond = 0.0;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        else 
          {
            if (calc_cond)
            {
              char job = '1';
              Array<double> z (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     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_XFCN (dgbtrs, DGBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, n_upper, 1, tmp_data,
                         ldm, pipvt, work, b.rows (), err
                         F77_CHAR_ARG_LEN (1)));

                  // Count non-zeros 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");
  else 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)
      {
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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();

        char job = 'L';
        F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                             nr, n_lower, tmp_data, ldm, err
                             F77_CHAR_ARG_LEN (1)));
          
        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 (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

            if (err == 0)
            {
              octave_idx_type b_nr = 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 (octave_idx_type i = 0; i < b_nr; i++)
                  {
                    Complex c = b (i,j);
                    Bx[i] = std::real (c);
                    Bz[i] = std::imag (c);
                  }

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

                  if (err != 0)
                  {
                    (*current_liboctave_error_handler) 
                      ("SparseMatrix::solve solve failed");
                    err = -1;
                    break;
                  }

                  F77_XFCN (dpbtrs, DPBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, 1, tmp_data,
                         ldm, Bz, b.rows(), err
                         F77_CHAR_ARG_LEN (1)));

                  if (err != 0)
                  {
                    (*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
        octave_idx_type n_upper = mattype.nupper ();
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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 (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)
          {
            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;
            }
          }

        Array<octave_idx_type> ipvt (nr);
        octave_idx_type *pipvt = ipvt.fortran_vec ();

        F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, 
                             ldm, pipvt, err));
          
        if (err != 0) 
          {
            err = -2;
            rcond = 0.0;

            if (sing_handler)
            {
            sing_handler (rcond);
            mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        else 
          {
            if (calc_cond)
            {
              char job = '1';
              Array<double> z (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

            if (err == 0)
            {
              char job = 'N';
              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] = std::real (c);
                    Bz[i] = std::imag  (c);
                  }

                  F77_XFCN (dgbtrs, DGBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, n_upper, 1, tmp_data,
                         ldm, pipvt, Bx, b.rows (), err
                         F77_CHAR_ARG_LEN (1)));

                  F77_XFCN (dgbtrs, DGBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, n_upper, 1, tmp_data,
                         ldm, pipvt, Bz, b.rows (), err
                         F77_CHAR_ARG_LEN (1)));

                  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");
  else 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)
      {
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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();

        char job = 'L';
        F77_XFCN (dpbtrf, DPBTRF, (F77_CONST_CHAR_ARG2 (&job, 1),
                             nr, n_lower, tmp_data, ldm, err
                             F77_CHAR_ARG_LEN (1)));
          
        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 (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     rcond);
                }
            }
            else
            rcond = 1.;

            if (err == 0)
            {
              octave_idx_type b_nr = 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 non-zero 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 (octave_idx_type i = 0; i < b_nr; i++)
                  {
                    Complex c = b (i,j);
                    Bx[i] = std::real (c);
                    Bz[i] = std::imag (c);
                  }

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

                  if (err != 0)
                  {
                    (*current_liboctave_error_handler) 
                      ("SparseMatrix::solve solve failed");
                    err = -1;
                    break;
                  }

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

                  if (err != 0)
                  {
                    (*current_liboctave_error_handler)
                      ("SparseMatrix::solve solve failed");

                    err = -1;
                    break;
                  }

                  // Count non-zeros 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
        octave_idx_type n_upper = mattype.nupper ();
        octave_idx_type n_lower = mattype.nlower ();
        octave_idx_type 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 (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)
          {
            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;
            }
          }

        Array<octave_idx_type> ipvt (nr);
        octave_idx_type *pipvt = ipvt.fortran_vec ();

        F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data, 
                             ldm, pipvt, err));
          
        if (err != 0) 
          {
            err = -2;
            rcond = 0.0;

            if (sing_handler)
            {
              sing_handler (rcond);
              mattype.mark_as_rectangular ();
            }
            else
            (*current_liboctave_error_handler)
              ("matrix singular to machine precision");

          } 
        else 
          {
            if (calc_cond)
            {
              char job = '1';
              Array<double> z (3 * nr);
              double *pz = z.fortran_vec ();
              Array<octave_idx_type> iz (nr);
              octave_idx_type *piz = iz.fortran_vec ();

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

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

              volatile double rcond_plus_one = rcond + 1.0;

              if (rcond_plus_one == 1.0 || xisnan (rcond))
                {
                  err = -2;

                  if (sing_handler)
                  {
                    sing_handler (rcond);
                    mattype.mark_as_rectangular ();
                  }
                  else
                  (*current_liboctave_error_handler)
                    ("matrix singular to machine precision, rcond = %g",
                     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 = 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)] = std::real (c);
                    Bz[b.ridx(i)] = std::imag (c);
                  }

                  F77_XFCN (dgbtrs, DGBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, n_upper, 1, tmp_data,
                         ldm, pipvt, Bx, b.rows (), err
                         F77_CHAR_ARG_LEN (1)));

                  F77_XFCN (dgbtrs, DGBTRS, 
                        (F77_CONST_CHAR_ARG2 (&job, 1),
                         nr, n_lower, n_upper, 1, tmp_data,
                         ldm, pipvt, Bz, b.rows (), err
                         F77_CHAR_ARG_LEN (1)));

                  // Count non-zeros 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 = 0;
  err = 0;

#ifdef 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 (!xisnan (tmp))
    Control (UMFPACK_PRL) = tmp;
  tmp = octave_sparse_params::get_key ("piv_tol");
  if (!xisnan (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 (!xisnan (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, Ap, Ai, Ax, 1, control);

  void *Symbolic;
  Info = Matrix (1, UMFPACK_INFO);
  double *info = Info.fortran_vec ();
  int status = UMFPACK_DNAME (qsymbolic) (nr, nc, Ap, Ai, Ax, 0,
                             &Symbolic, control, info);

  if (status < 0)
    {
      (*current_liboctave_error_handler) 
      ("SparseMatrix::solve symbolic factorization failed");
      err = -1;

      UMFPACK_DNAME (report_status) (control, status);
      UMFPACK_DNAME (report_info) (control, info);

      UMFPACK_DNAME (free_symbolic) (&Symbolic) ;
    }
  else
    {
      UMFPACK_DNAME (report_symbolic) (Symbolic, control);

      status = UMFPACK_DNAME (numeric) (Ap, 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 || xisnan (rcond))
      {
        UMFPACK_DNAME (report_numeric) (Numeric, control);

        err = -2;

        if (sing_handler)
          sing_handler (rcond);
        else
          (*current_liboctave_error_handler)
            ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
             rcond);

      }
      else if (status < 0)
        {
          (*current_liboctave_error_handler) 
            ("SparseMatrix::solve numeric factorization failed");

          UMFPACK_DNAME (report_status) (control, status);
          UMFPACK_DNAME (report_info) (control, info);
            
          err = -1;
        }
      else
        {
          UMFPACK_DNAME (report_numeric) (Numeric, control);
        }
    }

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

#else
  (*current_liboctave_error_handler) ("UMFPACK not installed");
#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");
  else 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)
      {
#ifdef 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;
            cm->print_function = 0;
          }
        else
          {
            cm->print = static_cast<int> (spu) + 2;
            cm->print_function =&SparseCholPrint;
          }

        cm->error_handler = &SparseCholError;
        cm->complex_divide = CHOLMOD_NAME(divcomplex);
        cm->hypotenuse = CHOLMOD_NAME(hypot);

        cm->final_ll = true;

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

        A->p = cidx();
        A->i = ridx();
        A->nzmax = nnz();
        A->packed = true;
        A->sorted = true;
        A->nz = 0;
#ifdef IDX_TYPE_LONG
        A->itype = CHOLMOD_LONG;
#else
        A->itype = CHOLMOD_INT;
#endif
        A->dtype = CHOLMOD_DOUBLE;
        A->stype = 1;
        A->xtype = CHOLMOD_REAL;

        if (nr < 1)
          A->x = &dummy;
        else
          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;
        if (nc < 1 || b.cols() < 1)
          B->x = &dummy;
        else
          // We won't alter it, honest :-)
          B->x = const_cast<double *>(b.fortran_vec());

        cholmod_factor *L;
        BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        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;

        END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

        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 || xisnan (rcond))
            {
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                (*current_liboctave_error_handler)
                  ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
                   rcond);
            
              return retval;
            }

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

            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];
            }

            BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            CHOLMOD_NAME(free_dense) (&X, cm);
            CHOLMOD_NAME(free_factor) (&L, cm);
            CHOLMOD_NAME(finish) (cm);
            static char tmp[] = " ";
            CHOLMOD_NAME(print_common) (tmp, cm);
            END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          }
#else
        (*current_liboctave_warning_handler)
          ("CHOLMOD not installed");

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

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

        if (err == 0)
          {
            const double *Bx = b.fortran_vec ();
            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, Ap, 
                                   Ai, Ax, &result[iidx], &Bx[iidx],
                                   Numeric, control, info);
              if (status < 0)
                {
                  (*current_liboctave_error_handler) 
                  ("SparseMatrix::solve solve failed");

                  UMFPACK_DNAME (report_status) (control, status);
                  
                  err = -1;
              
                  break;
                }
            }

            UMFPACK_DNAME (report_info) (control, info);
            
            UMFPACK_DNAME (free_numeric) (&Numeric);
          }
        else
          mattype.mark_as_rectangular ();

#else
        (*current_liboctave_error_handler) ("UMFPACK not installed");
#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");
  else 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)
      {
#ifdef 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;
            cm->print_function = 0;
          }
        else
          {
            cm->print = static_cast<int> (spu) + 2;
            cm->print_function =&SparseCholPrint;
          }

        cm->error_handler = &SparseCholError;
        cm->complex_divide = CHOLMOD_NAME(divcomplex);
        cm->hypotenuse = CHOLMOD_NAME(hypot);

        cm->final_ll = true;

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

        A->p = cidx();
        A->i = ridx();
        A->nzmax = nnz();
        A->packed = true;
        A->sorted = true;
        A->nz = 0;
#ifdef IDX_TYPE_LONG
        A->itype = CHOLMOD_LONG;
#else
        A->itype = CHOLMOD_INT;
#endif
        A->dtype = CHOLMOD_DOUBLE;
        A->stype = 1;
        A->xtype = CHOLMOD_REAL;

        if (nr < 1)
          A->x = &dummy;
        else
          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 = 0;
#ifdef IDX_TYPE_LONG
        B->itype = CHOLMOD_LONG;
#else
        B->itype = CHOLMOD_INT;
#endif
        B->dtype = CHOLMOD_DOUBLE;
        B->stype = 0;
        B->xtype = CHOLMOD_REAL;

        if (b.rows() < 1 || b.cols() < 1)
          B->x = &dummy;
        else
          B->x = b.data();

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

        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 || xisnan (rcond))
            {
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                (*current_liboctave_error_handler)
                  ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
                   rcond);
            
              return retval;
            }

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

            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];
            }

            BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            CHOLMOD_NAME(free_sparse) (&X, cm);
            CHOLMOD_NAME(free_factor) (&L, cm);
            CHOLMOD_NAME(finish) (cm);
            static char tmp[] = " ";
            CHOLMOD_NAME(print_common) (tmp, cm);
            END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          }
#else
        (*current_liboctave_warning_handler)
          ("CHOLMOD not installed");

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

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

        if (err == 0)
          {
            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 non-zero 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, Ap, 
                                   Ai, Ax, Xx, Bx, Numeric, control, 
                                   info);
              if (status < 0)
                {
                  (*current_liboctave_error_handler) 
                  ("SparseMatrix::solve solve failed");

                  UMFPACK_DNAME (report_status) (control, status);
              
                  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 = x_nz * (b_nc - j) / b_nc;
                        sz = (sz > 10 ? sz : 10) + x_nz;
                        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
        (*current_liboctave_error_handler) ("UMFPACK not installed");
#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");
  else 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)
      {
#ifdef 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;
            cm->print_function = 0;
          }
        else
          {
            cm->print = static_cast<int> (spu) + 2;
            cm->print_function =&SparseCholPrint;
          }

        cm->error_handler = &SparseCholError;
        cm->complex_divide = CHOLMOD_NAME(divcomplex);
        cm->hypotenuse = CHOLMOD_NAME(hypot);

        cm->final_ll = true;

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

        A->p = cidx();
        A->i = ridx();
        A->nzmax = nnz();
        A->packed = true;
        A->sorted = true;
        A->nz = 0;
#ifdef IDX_TYPE_LONG
        A->itype = CHOLMOD_LONG;
#else
        A->itype = CHOLMOD_INT;
#endif
        A->dtype = CHOLMOD_DOUBLE;
        A->stype = 1;
        A->xtype = CHOLMOD_REAL;

        if (nr < 1)
          A->x = &dummy;
        else
          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;
        if (nc < 1 || b.cols() < 1)
          B->x = &dummy;
        else
          // We won't alter it, honest :-)
          B->x = const_cast<Complex *>(b.fortran_vec());

        cholmod_factor *L;
        BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        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;
        END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

        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 || xisnan (rcond))
            {
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                (*current_liboctave_error_handler)
                  ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
                   rcond);
            
              return retval;
            }

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

            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];
            }

            BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            CHOLMOD_NAME(free_dense) (&X, cm);
            CHOLMOD_NAME(free_factor) (&L, cm);
            CHOLMOD_NAME(finish) (cm);
            static char tmp[] = " ";
            CHOLMOD_NAME(print_common) (tmp, cm);
            END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          }
#else
        (*current_liboctave_warning_handler)
          ("CHOLMOD not installed");

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

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

        if (err == 0)
          {
            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] = std::real (c);
                  Bz[i] = std::imag (c);
                }

              status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap, 
                                   Ai, Ax, Xx, Bx, Numeric, control, 
                                   info);
              int status2 = UMFPACK_DNAME (solve) (UMFPACK_A,
                                      Ap, Ai, Ax, Xz, Bz, Numeric, 
                                      control, info) ;

              if (status < 0 || status2 < 0)
                {
                  (*current_liboctave_error_handler) 
                  ("SparseMatrix::solve solve failed");

                  UMFPACK_DNAME (report_status) (control, status);
                  
                  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
        (*current_liboctave_error_handler) ("UMFPACK not installed");
#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");
  else 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)
      {
#ifdef 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;
            cm->print_function = 0;
          }
        else
          {
            cm->print = static_cast<int> (spu) + 2;
            cm->print_function =&SparseCholPrint;
          }

        cm->error_handler = &SparseCholError;
        cm->complex_divide = CHOLMOD_NAME(divcomplex);
        cm->hypotenuse = CHOLMOD_NAME(hypot);

        cm->final_ll = true;

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

        A->p = cidx();
        A->i = ridx();
        A->nzmax = nnz();
        A->packed = true;
        A->sorted = true;
        A->nz = 0;
#ifdef IDX_TYPE_LONG
        A->itype = CHOLMOD_LONG;
#else
        A->itype = CHOLMOD_INT;
#endif
        A->dtype = CHOLMOD_DOUBLE;
        A->stype = 1;
        A->xtype = CHOLMOD_REAL;

        if (nr < 1)
          A->x = &dummy;
        else
          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 = 0;
#ifdef IDX_TYPE_LONG
        B->itype = CHOLMOD_LONG;
#else
        B->itype = CHOLMOD_INT;
#endif
        B->dtype = CHOLMOD_DOUBLE;
        B->stype = 0;
        B->xtype = CHOLMOD_COMPLEX;

        if (b.rows() < 1 || b.cols() < 1)
          B->x = &dummy;
        else
          B->x = b.data();

        cholmod_factor *L;
        BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        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;
        END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

        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 || xisnan (rcond))
            {
              err = -2;

              if (sing_handler)
                {
                  sing_handler (rcond);
                  mattype.mark_as_rectangular ();
                }
              else
                (*current_liboctave_error_handler)
                  ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
                   rcond);
            
              return retval;
            }

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

            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];
            }

            BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            CHOLMOD_NAME(free_sparse) (&X, cm);
            CHOLMOD_NAME(free_factor) (&L, cm);
            CHOLMOD_NAME(finish) (cm);
            static char tmp[] = " ";
            CHOLMOD_NAME(print_common) (tmp, cm);
            END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          }
#else
        (*current_liboctave_warning_handler)
          ("CHOLMOD not installed");

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

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

        if (err == 0)
          {
            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 non-zero 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] = std::real (c);
                  Bz[i] = std::imag (c);
                }

              status = UMFPACK_DNAME (solve) (UMFPACK_A, Ap,
                                   Ai, Ax, Xx, Bx, Numeric, control, 
                                   info);
              int status2 = UMFPACK_DNAME (solve) (UMFPACK_A,
                                      Ap, Ai, Ax, Xz, Bz, Numeric, 
                                      control, info) ;

              if (status < 0 || status2 < 0)
                {
                  (*current_liboctave_error_handler) 
                  ("SparseMatrix::solve solve failed");

                  UMFPACK_DNAME (report_status) (control, status);
                  
                  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 = x_nz * (b_nc - j) / b_nc;
                        sz = (sz > 10 ? sz : 10) + x_nz;
                        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
        (*current_liboctave_error_handler) ("UMFPACK not installed");
#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, 0);
}

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

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

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");
      return Matrix ();
    }

  // Rectangular or one of the above solvers flags a singular matrix
  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#ifdef 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, 0);
}

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

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

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");
      return SparseMatrix ();
    }

  if (singular_fallback && mattype.type (false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#ifdef 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, 0);
}

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

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

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");
      return ComplexMatrix ();
    }

  if (singular_fallback && mattype.type(false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#ifdef 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, 0);
}

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

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

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");
      return SparseComplexMatrix ();
    }

  if (singular_fallback && mattype.type(false) == MatrixType::Rectangular)
    {
      rcond = 1.;
#ifdef 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, 0);
}

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, 0);
}

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

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

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, 0);
}

Matrix
SparseMatrix::solve (const Matrix& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, 0);
}

Matrix
SparseMatrix::solve (const Matrix& b, octave_idx_type& info, 
                 double& rcond) const
{
  return solve (b, info, rcond, 0);
}

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, 0);
}

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

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

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, 0);
}

ComplexMatrix
SparseMatrix::solve (const ComplexMatrix& b, 
                 octave_idx_type& info, double& rcond) const
{
  return solve (b, info, rcond, 0);
}

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, 0);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b, 
                 octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, 0);
}

SparseComplexMatrix
SparseMatrix::solve (const SparseComplexMatrix& b,
                 octave_idx_type& info, double& rcond) const
{
  return solve (b, info, rcond, 0);
}

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, 0);
}

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, 0);
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const
{
  double rcond;
  return solve (b, info, rcond, 0);
}

ComplexColumnVector
SparseMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, 
                 double& rcond) const
{
  return solve (b, info, rcond, 0);
}

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 (xisnan (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 (xisinf (val) || xisnan (val))
      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 (xisnan (val) || D_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 (D_NINT (val) != val)
      return false;
    }

  return true;
}

bool
SparseMatrix::too_large_for_float (void) const
{
  octave_idx_type nel = nnz ();

  for (octave_idx_type i = 0; i < nel; i++)
    {
      double val = data (i);

      if (val > FLT_MAX || val < FLT_MIN)
      return true;
    }

  return false;
}

SparseBoolMatrix 
SparseMatrix::operator ! (void) const 
{ 
  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) < nc ? 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
{
  octave_idx_type nr = rows ();
  octave_idx_type nc = cols ();

  Matrix retval (nr, nc, 0.0);
  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = cidx(j); i < cidx(j+1); i++)
      retval.elem (ridx(i), j) = data (i);

  return retval;
}

SparseMatrix
SparseMatrix::map (dmapper fcn) const
{
  return MSparse<double>::map<double> (func_ptr (fcn));
}

SparseComplexMatrix
SparseMatrix::map (cmapper fcn) const
{
  return MSparse<double>::map<Complex> (func_ptr (fcn));
}

SparseBoolMatrix
SparseMatrix::map (bmapper fcn) const
{
  return MSparse<double>::map<bool> (func_ptr (fcn));
}

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_double (os, a.data(i));
      os << "\n";
      }
   }

  return os;
}

std::istream&
operator >> (std::istream& is, SparseMatrix& a)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();
  octave_idx_type nz = a.nzmax ();

  if (nr > 0 && nc > 0)
    {
      octave_idx_type itmp, jtmp, jold = 0;
      double tmp;
      octave_idx_type ii = 0;
       
      a.cidx (0) = 0;
      for (octave_idx_type i = 0; i < nz; i++)
      {
        is >> itmp;
        itmp--;
        is >> jtmp;
        jtmp--;
        tmp = octave_read_double (is);
        
        if (is)
          {
            if (jold != jtmp)
            {
              for (octave_idx_type j = jold; j < jtmp; j++)
                a.cidx(j+1) = ii;
              
              jold = jtmp;
            }
            a.data (ii) = tmp;
            a.ridx (ii++) = itmp;
          }
        else
          goto done;
      }

      for (octave_idx_type j = jold; j < nc; j++)
      a.cidx(j+1) = ii;
    }
  
 done:

  return is;
}

SparseMatrix
SparseMatrix::squeeze (void) const 
{ 
  return MSparse<double>::squeeze (); 
}

SparseMatrix
SparseMatrix::index (idx_vector& i, int resize_ok) const 
{ 
  return MSparse<double>::index (i, resize_ok); 
}

SparseMatrix
SparseMatrix::index (idx_vector& i, idx_vector& j, int resize_ok) const 
{ 
  return MSparse<double>::index (i, j, resize_ok); 
}
  
SparseMatrix
SparseMatrix::index (Array<idx_vector>& ra_idx, int resize_ok) const 
{ 
  return MSparse<double>::index (ra_idx, resize_ok); 
}

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, 0.);
}

Matrix
mul_trans (const Matrix& m, const SparseMatrix& a)
{
  FULL_SPARSE_MUL_TRANS (Matrix, double, 0., );
}

Matrix
operator * (const SparseMatrix& m, const Matrix& a)
{
  SPARSE_FULL_MUL (Matrix, double, 0.);
}

Matrix
trans_mul (const SparseMatrix& m, const Matrix& a)
{
  SPARSE_FULL_TRANS_MUL (Matrix, double, 0., );
}

// 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 non-zero 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 = xmin (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 (xmin (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 = xmin (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;

  if ((a.rows() == b.rows()) && (a.cols() == b.cols())) 
    {
      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)
      gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc);
      else
      {
        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 = xmin (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 = xmin (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 = xmin (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
    (*current_liboctave_error_handler) ("matrix size mismatch");

  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 non-zero 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 = xmax (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 (xmax (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 = xmax (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;

  if ((a.rows() == b.rows()) && (a.cols() == b.cols())) 
    {
      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)
      gripe_nonconformant ("min", a_nr, a_nc, b_nr, b_nc);
      else
      {
        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 = xmax (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 = xmax (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 = xmax (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
    (*current_liboctave_error_handler) ("matrix size mismatch");

  return r;
}

SPARSE_SMS_CMP_OPS (SparseMatrix, 0.0, , double, 0.0, )
SPARSE_SMS_BOOL_OPS (SparseMatrix, double, 0.0)

SPARSE_SSM_CMP_OPS (double, 0.0, , SparseMatrix, 0.0, )
SPARSE_SSM_BOOL_OPS (double, SparseMatrix, 0.0)

SPARSE_SMSM_CMP_OPS (SparseMatrix, 0.0, , SparseMatrix, 0.0, )
SPARSE_SMSM_BOOL_OPS (SparseMatrix, SparseMatrix, 0.0)

/*
;;; Local Variables: ***
;;; mode: C++ ***
;;; End: ***
*/

Generated by  Doxygen 1.6.0   Back to index