octave-nkf: liboctave/dSparse.cc comparison

comparison liboctave/dSparse.cc @ 5164:57077d0ddc8e

[project @ 2005-02-25 19:55:24 by jwe]

author	jwe
date	Fri, 25 Feb 2005 19:55:28 +0000
parents
children	dbeafbc0ff64

comparison

equal deleted inserted replaced

-:9f3299378193
+:57077d0ddc8e
+/*
+Copyright (C) 2004 David Bateman
+Copyright (C) 1998-2004 Andy Adler
+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 2, 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 this program; see the file COPYING.  If not, write to the Free
+Software Foundation, 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
+*/
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+#include <cfloat>
+#include <iostream>
+#include <vector>
+#include "quit.h"
+#include "lo-ieee.h"
+#include "lo-mappers.h"
+#include "f77-fcn.h"
+#include "dRowVector.h"
+#include "CSparse.h"
+#include "boolSparse.h"
+#include "dSparse.h"
+#include "oct-spparms.h"
+#include "SparsedbleLU.h"
+#include "SparseType.h"
+// External UMFPACK functions in C
+extern "C" {
+#include "umfpack.h"
+}
+// Fortran functions we call.
+extern "C"
+{
+F77_RET_T
+F77_FUNC (dgbtrf, DGBTRF) (const int&, const int&, const int&,
+			     const int&, double*, const int&, int*, int&);
+F77_RET_T
+F77_FUNC (dgbtrs, DGBTRS) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, const int&, const int&,
+			     const double*, const int&,
+			     const int*, double*, const int&, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (dgbcon, DGBCON) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, const int&, double*,
+			     const int&, const int*, const double&,
+			     double&, double*, int*, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (dpbtrf, DPBTRF) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, double*, const int&, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (dpbtrs, DPBTRS) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, const int&, double*, const int&,
+			     double*, const int&, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (dpbcon, DPBCON) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, double*, const int&,
+			     const double&, double&, double*, int*, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (dptsv, DPTSV) (const int&, const int&, double*, double*,
+			   double*, const int&, int&);
+F77_RET_T
+F77_FUNC (dgtsv, DGTSV) (const int&, const int&, double*, double*,
+			   double*, double*, const int&, int&);
+F77_RET_T
+F77_FUNC (dgttrf, DGTTRF) (const int&, double*, double*, double*, double*,
+			     int*, int&);
+F77_RET_T
+F77_FUNC (dgttrs, DGTTRS) (F77_CONST_CHAR_ARG_DECL, const int&,
+			     const int&, const double*, const double*,
+			     const double*, const double*, const int*,
+			     double *, const int&, int&
+			     F77_CHAR_ARG_LEN_DECL);
+F77_RET_T
+F77_FUNC (zptsv, ZPTSV) (const int&, const int&, Complex*, Complex*,
+			   Complex*, const int&, int&);
+F77_RET_T
+F77_FUNC (zgtsv, ZGTSV) (const int&, const int&, Complex*, Complex*,
+			   Complex*, Complex*, const int&, int&);
+}
+SparseMatrix::SparseMatrix (const SparseBoolMatrix &a)
+: MSparse<double> (a.rows (), a.cols (), a.nnz ())
+{
+int nc = cols ();
+int nz = nnz ();
+for (int i = 0; i < nc + 1; i++)
+cidx (i) = a.cidx (i);
+for (int i = 0; i < nz; i++)
+{
+data (i) = a.data (i);
+ridx (i) = a.ridx (i);
+}
+}
+bool
+SparseMatrix::operator == (const SparseMatrix& a) const
+{
+int nr = rows ();
+int nc = cols ();
+int nz = nnz ();
+int nr_a = a.rows ();
+int nc_a = a.cols ();
+int nz_a = a.nnz ();
+if (nr != nr_a || nc != nc_a || nz != nz_a)
+return false;
+for (int i = 0; i < nc + 1; i++)
+if (cidx(i) != a.cidx(i))
+	return false;
+for (int 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
+{
+if (is_square () && rows () > 0)
+{
+for (int i = 0; i < rows (); i++)
+	for (int j = i+1; j < cols (); j++)
+	  if (elem (i, j) != elem (j, i))
+	    return false;
+return true;
+}
+return false;
+}
+SparseMatrix&
+SparseMatrix::insert (const SparseMatrix& a, int r, int c)
+{
+MSparse<double>::insert (a, r, c);
+return *this;
+}
+SparseMatrix
+SparseMatrix::max (int dim) const
+{
+Array2<int> dummy_idx;
+return max (dummy_idx, dim);
+}
+SparseMatrix
+SparseMatrix::max (Array2<int>& idx_arg, int dim) const
+{
+SparseMatrix result;
+dim_vector dv = dims ();
+if (dv.numel () == 0 || dim > dv.length () || dim < 0)
+return result;
+int nr = dv(0);
+int nc = dv(1);
+if (dim == 0)
+{
+idx_arg.resize (1, nc);
+int nel = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  double tmp_max = octave_NaN;
+	  int idx_j = 0;
+	  for (int 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 (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      double tmp = data (i);
+	      if (octave_is_NaN_or_NA (tmp))
+		continue;
+	      else if (octave_is_NaN_or_NA (tmp_max) || tmp > tmp_max)
+		{
+		  idx_j = ridx (i);
+		  tmp_max = tmp;
+		}
+	    }
+	  idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_j;
+	  if (tmp_max != 0.)
+	    nel++;
+	}
+result = SparseMatrix (1, nc, nel);
+int ii = 0;
+result.xcidx (0) = 0;
+for (int 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 (int i = cidx(0); i < cidx(1); i++)
+	idx_arg.elem(ridx(i)) = -1;
+for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  {
+	    if (idx_arg.elem(i) != -1)
+	      continue;
+	    bool found = false;
+	    for (int k = cidx(j); k < cidx(j+1); k++)
+	      if (ridx(k) == i)
+		{
+		  found = true;
+		  break;
+		}
+	    if (!found)
+	      idx_arg.elem(i) = j;
+	  }
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      int ir = ridx (i);
+	      int ix = idx_arg.elem (ir);
+	      double tmp = data (i);
+	      if (octave_is_NaN_or_NA (tmp))
+		continue;
+	      else if (ix == -1 || tmp > elem (ir, ix))
+		idx_arg.elem (ir) = j;
+	    }
+	}
+int nel = 0;
+for (int j = 0; j < nr; j++)
+	if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.)
+	  nel++;
+result = SparseMatrix (nr, 1, nel);
+int ii = 0;
+result.xcidx (0) = 0;
+result.xcidx (1) = nel;
+for (int 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<int> dummy_idx;
+return min (dummy_idx, dim);
+}
+SparseMatrix
+SparseMatrix::min (Array2<int>& idx_arg, int dim) const
+{
+SparseMatrix result;
+dim_vector dv = dims ();
+if (dv.numel () == 0 || dim > dv.length () || dim < 0)
+return result;
+int nr = dv(0);
+int nc = dv(1);
+if (dim == 0)
+{
+idx_arg.resize (1, nc);
+int nel = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  double tmp_min = octave_NaN;
+	  int idx_j = 0;
+	  for (int 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 (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      double tmp = data (i);
+	      if (octave_is_NaN_or_NA (tmp))
+		continue;
+	      else if (octave_is_NaN_or_NA (tmp_min) || tmp < tmp_min)
+		{
+		  idx_j = ridx (i);
+		  tmp_min = tmp;
+		}
+	    }
+	  idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_j;
+	  if (tmp_min != 0.)
+	    nel++;
+	}
+result = SparseMatrix (1, nc, nel);
+int ii = 0;
+result.xcidx (0) = 0;
+for (int 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 (int i = cidx(0); i < cidx(1); i++)
+	idx_arg.elem(ridx(i)) = -1;
+for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  {
+	    if (idx_arg.elem(i) != -1)
+	      continue;
+	    bool found = false;
+	    for (int k = cidx(j); k < cidx(j+1); k++)
+	      if (ridx(k) == i)
+		{
+		  found = true;
+		  break;
+		}
+	    if (!found)
+	      idx_arg.elem(i) = j;
+	  }
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      int ir = ridx (i);
+	      int ix = idx_arg.elem (ir);
+	      double tmp = data (i);
+	      if (octave_is_NaN_or_NA (tmp))
+		continue;
+	      else if (ix == -1 || tmp < elem (ir, ix))
+		idx_arg.elem (ir) = j;
+	    }
+	}
+int nel = 0;
+for (int j = 0; j < nr; j++)
+	if (idx_arg.elem(j) == -1 || elem (j, idx_arg.elem (j)) != 0.)
+	  nel++;
+result = SparseMatrix (nr, 1, nel);
+int ii = 0;
+result.xcidx (0) = 0;
+result.xcidx (1) = nel;
+for (int 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::concat (const SparseMatrix& rb, const Array<int>& 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<int>& 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)
+{
+int nr = a.rows ();
+int nc = a.cols ();
+int nz = a.nnz ();
+SparseMatrix r (nr, nc, nz);
+for (int i = 0; i < nc +1; i++)
+r.cidx(i) = a.cidx(i);
+for (int i = 0; i < nz; i++)
+{
+r.data(i) = real (a.data(i));
+r.ridx(i) = a.ridx(i);
+}
+return r;
+}
+SparseMatrix
+imag (const SparseComplexMatrix& a)
+{
+int nr = a.rows ();
+int nc = a.cols ();
+int nz = a.nnz ();
+SparseMatrix r (nr, nc, nz);
+for (int i = 0; i < nc +1; i++)
+r.cidx(i) = a.cidx(i);
+for (int i = 0; i < nz; i++)
+{
+r.data(i) = imag (a.data(i));
+r.ridx(i) = a.ridx(i);
+}
+return r;
+}
+SparseMatrix
+atan2 (const double& x, const SparseMatrix& y)
+{
+int nr = y.rows ();
+int 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 (int j = 0; j < nc; j++)
+	for (int 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)
+{
+int nr = x.rows ();
+int nc = x.cols ();
+int nz = x.nnz ();
+SparseMatrix retval (nr, nc, nz);
+int ii = 0;
+retval.xcidx(0) = 0;
+for (int i = 0; i < nc; i++)
+{
+for (int 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 (int i = 0; i < nc+1; i++)
+	retval2.xcidx (i) = retval.cidx (i);
+for (int 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()))
+{
+int x_nr = x.rows ();
+int x_nc = x.cols ();
+int y_nr = y.rows ();
+int 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 ()));
+	  int jx = 0;
+	  r.cidx (0) = 0;
+	  for (int i = 0 ; i < x_nc ; i++)
+	    {
+	      int  ja = x.cidx(i);
+	      int  ja_max = x.cidx(i+1);
+	      bool ja_lt_max= ja < ja_max;
+	      int  jb = y.cidx(i);
+	      int  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
+{
+int info;
+double rcond;
+return inverse (info, rcond, 0, 0);
+}
+SparseMatrix
+SparseMatrix::inverse (int& info) const
+{
+double rcond;
+return inverse (info, rcond, 0, 0);
+}
+SparseMatrix
+SparseMatrix::inverse (int& info, double& rcond, int force, int calc_cond) const
+{
+info = -1;
+(*current_liboctave_error_handler)
+("SparseMatrix::inverse not implemented yet");
+return SparseMatrix ();
+}
+DET
+SparseMatrix::determinant (void) const
+{
+int info;
+double rcond;
+return determinant (info, rcond, 0);
+}
+DET
+SparseMatrix::determinant (int& info) const
+{
+double rcond;
+return determinant (info, rcond, 0);
+}
+DET
+SparseMatrix::determinant (int& err, double& rcond, int) const
+{
+DET retval;
+int nr = rows ();
+int nc = cols ();
+if (nr == 0 || nc == 0 || nr != nc)
+{
+double d[2];
+d[0] = 1.0;
+d[1] = 0.0;
+retval = DET (d);
+}
+else
+{
+err = 0;
+// Setup the control parameters
+Matrix Control (UMFPACK_CONTROL, 1);
+double *control = Control.fortran_vec ();
+umfpack_di_defaults (control);
+double tmp = Voctave_sparse_controls.get_key ("spumoni");
+if (!xisnan (tmp))
+	Control (UMFPACK_PRL) = tmp;
+tmp = Voctave_sparse_controls.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 = Voctave_sparse_controls.get_key ("autoamd");
+if (!xisnan (tmp))
+	Control (UMFPACK_FIXQ) = tmp;
+// Turn-off UMFPACK scaling for LU
+Control (UMFPACK_SCALE) = UMFPACK_SCALE_NONE;
+umfpack_di_report_control (control);
+const int *Ap = cidx ();
+const int *Ai = ridx ();
+const double *Ax = data ();
+umfpack_di_report_matrix (nr, nc, Ap, Ai, Ax, 1, control);
+void *Symbolic;
+Matrix Info (1, UMFPACK_INFO);
+double *info = Info.fortran_vec ();
+int status = umfpack_di_qsymbolic (nr, nc, Ap, Ai, Ax, NULL,
+					 &Symbolic, control, info);
+if (status < 0)
+	{
+	  (*current_liboctave_error_handler)
+	    ("SparseMatrix::determinant symbolic factorization failed");
+	  umfpack_di_report_status (control, status);
+	  umfpack_di_report_info (control, info);
+	  umfpack_di_free_symbolic (&Symbolic) ;
+	}
+else
+	{
+	  umfpack_di_report_symbolic (Symbolic, control);
+	  void *Numeric;
+	  status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+				       control, info) ;
+	  umfpack_di_free_symbolic (&Symbolic) ;
+	  rcond = Info (UMFPACK_RCOND);
+	  if (status < 0)
+	    {
+	      (*current_liboctave_error_handler)
+		("SparseMatrix::determinant numeric factorization failed");
+	      umfpack_di_report_status (control, status);
+	      umfpack_di_report_info (control, info);
+	      umfpack_di_free_numeric (&Numeric);
+	    }
+	  else
+	    {
+	      umfpack_di_report_numeric (Numeric, control);
+	      double d[2];
+	      status = umfpack_di_get_determinant (&d[0], &d[1], Numeric,
+						   info);
+	      if (status < 0)
+		{
+		  (*current_liboctave_error_handler)
+		    ("SparseMatrix::determinant error calculating determinant");
+		  umfpack_di_report_status (control, status);
+		  umfpack_di_report_info (control, info);
+		  umfpack_di_free_numeric (&Numeric);
+		}
+	      else
+		retval = DET (d);
+	    }
+	}
+}
+return retval;
+}
+Matrix
+SparseMatrix::dsolve (SparseType &mattype, const Matrix& b, int& err,
+		      double& rcond, solve_singularity_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Diagonal ||
+	  typ == SparseType::Permuted_Diagonal)
+	{
+	  retval.resize (b.rows (), b.cols());
+	  if (typ == SparseType::Diagonal)
+	    for (int j = 0; j < b.cols(); j++)
+	      for (int i = 0; i < nr; i++)
+		retval(i,j) = b(i,j) / data (i);
+	  else
+	    for (int j = 0; j < b.cols(); j++)
+	      for (int i = 0; i < nr; i++)
+		retval(i,j) = b(ridx(i),j) / data (i);
+	  double dmax = 0., dmin = octave_Inf;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double tmp = fabs(data(i));
+	      if (tmp > dmax)
+		dmax = tmp;
+	      if (tmp < dmin)
+		dmin = tmp;
+	    }
+	  rcond = dmin / dmax;
+	}
+else
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseMatrix
+SparseMatrix::dsolve (SparseType &mattype, const SparseMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Diagonal ||
+	  typ == SparseType::Permuted_Diagonal)
+	{
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  if (typ == SparseType::Diagonal)
+	    for (int j = 0; j < b.cols(); j++)
+	      {
+		for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		  {
+		    retval.xridx (ii) = b.ridx(i);
+		    retval.xdata (ii++) = b.data(i) / data (b.ridx (i));
+		  }
+		retval.xcidx(j+1) = ii;
+	      }
+	  else
+	    for (int j = 0; j < b.cols(); j++)
+	      {
+		for (int i = 0; i < nr; i++)
+		  {
+		    bool found = false;
+		    int 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) = i;
+			retval.xdata (ii++) = b.data(k) / data (i);
+		      }
+		  }
+		retval.xcidx(j+1) = ii;
+	      }
+	  double dmax = 0., dmin = octave_Inf;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double tmp = fabs(data(i));
+	      if (tmp > dmax)
+		dmax = tmp;
+	      if (tmp < dmin)
+		dmin = tmp;
+	    }
+	  rcond = dmin / dmax;
+	}
+else
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+ComplexMatrix
+SparseMatrix::dsolve (SparseType &mattype, const ComplexMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Diagonal ||
+	  typ == SparseType::Permuted_Diagonal)
+	{
+	  retval.resize (b.rows (), b.cols());
+	  if (typ == SparseType::Diagonal)
+	    for (int j = 0; j < b.cols(); j++)
+	      for (int i = 0; i < nr; i++)
+		retval(i,j) = b(i,j) / data (i);
+	  else
+	    for (int j = 0; j < b.cols(); j++)
+	      for (int i = 0; i < nr; i++)
+		retval(i,j) = b(ridx(i),j) / data (i);
+	  double dmax = 0., dmin = octave_Inf;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double tmp = fabs(data(i));
+	      if (tmp > dmax)
+		dmax = tmp;
+	      if (tmp < dmin)
+		dmin = tmp;
+	    }
+	  rcond = dmin / dmax;
+	}
+else
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseComplexMatrix
+SparseMatrix::dsolve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Diagonal ||
+	  typ == SparseType::Permuted_Diagonal)
+	{
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseComplexMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  if (typ == SparseType::Diagonal)
+	    for (int j = 0; j < b.cols(); j++)
+	      {
+		for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		  {
+		    retval.xridx (ii) = b.ridx(i);
+		    retval.xdata (ii++) = b.data(i) / data (b.ridx (i));
+		  }
+		retval.xcidx(j+1) = ii;
+	      }
+	  else
+	    for (int j = 0; j < b.cols(); j++)
+	      {
+		for (int i = 0; i < nr; i++)
+		  {
+		    bool found = false;
+		    int 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) = i;
+			retval.xdata (ii++) = b.data(k) / data (i);
+		      }
+		  }
+		retval.xcidx(j+1) = ii;
+	      }
+	  double dmax = 0., dmin = octave_Inf;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double tmp = fabs(data(i));
+	      if (tmp > dmax)
+		dmax = tmp;
+	      if (tmp < dmin)
+		dmin = tmp;
+	    }
+	  rcond = dmin / dmax;
+	}
+else
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+Matrix
+SparseMatrix::utsolve (SparseType &mattype, const Matrix& b, int& err,
+		       double& rcond,
+		       solve_singularity_handler sing_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Upper ||
+	  typ == SparseType::Upper)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  int b_cols = b.cols ();
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  if (typ == SparseType::Permuted_Upper)
+	    {
+	      retval.resize (b.rows (), b.cols ());
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+		(*current_liboctave_warning_handler)
+		  ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_cols; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = b(i,j);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx+1)-1) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  for (int i = 0; i < nr; i++)
+		    retval (i, j) = work[p_perm[i]];
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[q_perm[j]] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] = work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work[i]);
+		      work[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      retval = b;
+	      double *x_vec = retval.fortran_vec ();
+	      for (int j = 0; j < b_cols; j++)
+		{
+		  int offset = j * nr;
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      if (x_vec[k+offset] != 0.)
+			{
+			  if (ridx(cidx(k+1)-1) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = x_vec[k+offset] /
+			    data(cidx(k+1)-1);
+			  x_vec[k+offset] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      x_vec[iidx+offset] =
+				x_vec[iidx+offset] - tmp * data(i);
+			    }
+			}
+		    }
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k+1)-1);
+			  work[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int 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);
+	      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);
+	      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 (SparseType &mattype, const SparseMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Upper ||
+	  typ == SparseType::Upper)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  int x_nz = b_nz;
+	  if (typ == SparseType::Permuted_Upper)
+	    {
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+	      (*current_liboctave_warning_handler)
+		("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx+1)-1) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int i = 0; i < nr; i++)
+		    if (work[p_perm[i]] != 0.)
+		      {
+			retval.xridx(ii) = i;
+			retval.xdata(ii++) = work[p_perm[i]];
+		      }
+		  retval.xcidx(j+1) = ii;
+		}
+	      retval.maybe_compress ();
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[q_perm[j]] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] = work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work[i]);
+		      work[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      if (work[k] != 0.)
+			{
+			  if (ridx(cidx(k+1)-1) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[k] / data(cidx(k+1)-1);
+			  work[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int 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 ();
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k+1)-1);
+			  work[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int 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);
+	      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);
+	      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 (SparseType &mattype, const ComplexMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Upper ||
+	  typ == SparseType::Upper)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  int b_nc = b.cols ();
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  if (typ == SparseType::Permuted_Upper)
+	    {
+	      retval.resize (b.rows (), b.cols ());
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+	      (*current_liboctave_warning_handler)
+		("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = b(i,j);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx+1)-1) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  for (int i = 0; i < nr; i++)
+		    retval (i, j) = work[p_perm[i]];
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[q_perm[j]] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work2[iidx] != 0.)
+			{
+			  double tmp = work2[iidx] / data(cidx(iidx+1)-1);
+			  work2[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work2[idx2] = work2[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      retval = b;
+	      Complex *x_vec = retval.fortran_vec ();
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  int offset = j * nr;
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      if (x_vec[k+offset] != 0.)
+			{
+			  if (ridx(cidx(k+1)-1) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = x_vec[k+offset] /
+			    data(cidx(k+1)-1);
+			  x_vec[k+offset] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      x_vec[iidx+offset] =
+				x_vec[iidx+offset] - tmp * data(i);
+			    }
+			}
+		    }
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k+1)-1);
+			  work[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int 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);
+	      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);
+	      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 (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Upper ||
+	  typ == SparseType::Upper)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseComplexMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  int x_nz = b_nz;
+	  if (typ == SparseType::Permuted_Upper)
+	    {
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+	      (*current_liboctave_warning_handler)
+		("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx+1)-1) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int i = 0; i < nr; i++)
+		    if (work[p_perm[i]] != 0.)
+		      {
+			retval.xridx(ii) = i;
+			retval.xdata(ii++) = work[p_perm[i]];
+		      }
+		  retval.xcidx(j+1) = ii;
+		}
+	      retval.maybe_compress ();
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[q_perm[j]] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      int iidx = q_perm[k];
+		      if (work2[iidx] != 0.)
+			{
+			  double tmp = work2[iidx] / data(cidx(iidx+1)-1);
+			  work2[iidx] = tmp;
+			  for (int i = cidx(iidx); i < cidx(iidx+1)-1; i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work2[idx2] = work2[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = nr-1; k >= 0; k--)
+		    {
+		      if (work[k] != 0.)
+			{
+			  if (ridx(cidx(k+1)-1) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[k] / data(cidx(k+1)-1);
+			  work[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int 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 ();
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[j] = 1.;
+		  for (int k = j; k >= 0; k--)
+		    {
+		      if (work2[k] != 0.)
+			{
+			  double tmp = work2[k] / data(cidx(k+1)-1);
+			  work2[k] = tmp;
+			  for (int i = cidx(k); i < cidx(k+1)-1; i++)
+			    {
+			      int iidx = ridx(i);
+			      work2[iidx] = work2[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  rcond = 1. / ainvnorm / anorm;
+	triangular_error:
+	  if (err != 0)
+	    {
+	      if (sing_handler)
+		sing_handler (rcond);
+	      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);
+	      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 (SparseType &mattype, const Matrix& b, int& err,
+		       double& rcond,
+		       solve_singularity_handler sing_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Lower ||
+	  typ == SparseType::Lower)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  int b_cols = b.cols ();
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  if (typ == SparseType::Permuted_Lower)
+	    {
+	      retval.resize (b.rows (), b.cols ());
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+		(*current_liboctave_warning_handler)
+		  ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_cols; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = b(i,j);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx)) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  for (int i = 0; i < nr; i++)
+		    retval (i, j) = work[p_perm[i]];
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[q_perm[j]] = 1.;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] = work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work[i]);
+		      work[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      retval = b;
+	      double *x_vec = retval.fortran_vec ();
+	      for (int j = 0; j < b_cols; j++)
+		{
+		  int offset = j * nr;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      if (x_vec[k+offset] != 0.)
+			{
+			  if (ridx(cidx(k)) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = x_vec[k+offset] /
+			    data(cidx(k));
+			  x_vec[k+offset] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      x_vec[iidx+offset] =
+				x_vec[iidx+offset] - tmp * data(i);
+			    }
+			}
+		    }
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k < nr; k++)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k));
+			  work[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = j; i < nr; 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);
+	      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);
+	      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 (SparseType &mattype, const SparseMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Lower ||
+	  typ == SparseType::Lower)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  int x_nz = b_nz;
+	  if (typ == SparseType::Permuted_Lower)
+	    {
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+		(*current_liboctave_warning_handler)
+		  ("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx)) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int i = 0; i < nr; i++)
+		    if (work[p_perm[i]] != 0.)
+		      {
+			retval.xridx(ii) = i;
+			retval.xdata(ii++) = work[p_perm[i]];
+		      }
+		  retval.xcidx(j+1) = ii;
+		}
+	      retval.maybe_compress ();
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[q_perm[j]] = 1.;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  double tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] = work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work[i]);
+		      work[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      if (work[k] != 0.)
+			{
+			  if (ridx(cidx(k)) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  double tmp = work[k] / data(cidx(k));
+			  work[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int 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 ();
+	      // Calculation of 1-norm of inv(*this)
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k < nr; k++)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k));
+			  work[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = j; i < nr; 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);
+	      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);
+	      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 (SparseType &mattype, const ComplexMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Lower ||
+	  typ == SparseType::Lower)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  int b_nc = b.cols ();
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  if (typ == SparseType::Permuted_Lower)
+	    {
+	      retval.resize (b.rows (), b.cols ());
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+	      (*current_liboctave_warning_handler)
+		("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = b(i,j);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx)) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  for (int i = 0; i < nr; i++)
+		    retval (i, j) = work[p_perm[i]];
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[q_perm[j]] = 1.;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work2[iidx] != 0.)
+			{
+			  double tmp = work2[iidx] / data(cidx(iidx+1)-1);
+			  work2[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work2[idx2] = work2[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      retval = b;
+	      Complex *x_vec = retval.fortran_vec ();
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  int offset = j * nr;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      if (x_vec[k+offset] != 0.)
+			{
+			  if (ridx(cidx(k)) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = x_vec[k+offset] /
+			    data(cidx(k));
+			  x_vec[k+offset] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      x_vec[iidx+offset] =
+				x_vec[iidx+offset] - tmp * data(i);
+			    }
+			}
+		    }
+		}
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work, nr);
+	      for (int i = 0; i < nr; i++)
+		work[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work[j] = 1.;
+		  for (int k = j; k < nr; k++)
+		    {
+		      if (work[k] != 0.)
+			{
+			  double tmp = work[k] / data(cidx(k));
+			  work[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = j; i < nr; 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);
+	      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);
+	      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 (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Permuted_Lower ||
+	  typ == SparseType::Lower)
+	{
+	  double anorm = 0.;
+	  double ainvnorm = 0.;
+	  rcond = 0.;
+	  // Calculate the 1-norm of matrix for rcond calculation
+	  for (int j = 0; j < nr; j++)
+	    {
+	      double atmp = 0.;
+	      for (int i = cidx(j); i < cidx(j+1); i++)
+		atmp += fabs(data(i));
+	      if (atmp > anorm)
+		anorm = atmp;
+	    }
+	  int b_nr = b.rows ();
+	  int b_nc = b.cols ();
+	  int b_nz = b.nnz ();
+	  retval = SparseComplexMatrix (b_nr, b_nc, b_nz);
+	  retval.xcidx(0) = 0;
+	  int ii = 0;
+	  int x_nz = b_nz;
+	  if (typ == SparseType::Permuted_Lower)
+	    {
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      int *p_perm = mattype.triangular_row_perm ();
+	      int *q_perm = mattype.triangular_col_perm ();
+	      (*current_liboctave_warning_handler)
+		("SparseMatrix::solve XXX FIXME XXX permuted triangular code not tested");
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work[iidx] != 0.)
+			{
+			  if (ridx(cidx(iidx)) != iidx)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[iidx] / data(cidx(iidx+1)-1);
+			  work[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work[idx2] =
+				work[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int i = 0; i < nr; i++)
+		    if (work[p_perm[i]] != 0.)
+		      {
+			retval.xridx(ii) = i;
+			retval.xdata(ii++) = work[p_perm[i]];
+		      }
+		  retval.xcidx(j+1) = ii;
+		}
+	      retval.maybe_compress ();
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[q_perm[j]] = 1.;
+		  for (int k = 0; k < nr; k++)
+		    {
+		      int iidx = q_perm[k];
+		      if (work2[iidx] != 0.)
+			{
+			  double tmp = work2[iidx] / data(cidx(iidx+1)-1);
+			  work2[iidx] = tmp;
+			  for (int i = cidx(iidx)+1; i < cidx(iidx+1); i++)
+			    {
+			      int idx2 = q_perm[ridx(i)];
+			      work2[idx2] = work2[idx2] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = 0; i < j+1; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  else
+	    {
+	      OCTAVE_LOCAL_BUFFER (Complex, work, nr);
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < nr; i++)
+		    work[i] = 0.;
+		  for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+		    work[b.ridx(i)] = b.data(i);
+		  for (int k = 0; k < nr; k++)
+		    {
+		      if (work[k] != 0.)
+			{
+			  if (ridx(cidx(k)) != k)
+			    {
+			      err = -2;
+			      goto triangular_error;
+			    }
+			  Complex tmp = work[k] / data(cidx(k));
+			  work[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work[iidx] = work[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  // Count non-zeros in work vector and adjust space in
+		  // retval if needed
+		  int new_nnz = 0;
+		  for (int i = 0; i < nr; i++)
+		    if (work[i] != 0.)
+		      new_nnz++;
+		  if (ii + new_nnz > x_nz)
+		    {
+		      // Resize the sparse matrix
+		      int sz = new_nnz * (b_nc - j) + x_nz;
+		      retval.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  for (int 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 ();
+	      // Calculation of 1-norm of inv(*this)
+	      OCTAVE_LOCAL_BUFFER (double, work2, nr);
+	      for (int i = 0; i < nr; i++)
+		work2[i] = 0.;
+	      for (int j = 0; j < nr; j++)
+		{
+		  work2[j] = 1.;
+		  for (int k = j; k < nr; k++)
+		    {
+		      if (work2[k] != 0.)
+			{
+			  double tmp = work2[k] / data(cidx(k));
+			  work2[k] = tmp;
+			  for (int i = cidx(k)+1; i < cidx(k+1); i++)
+			    {
+			      int iidx = ridx(i);
+			      work2[iidx] = work2[iidx] - tmp * data(i);
+			    }
+			}
+		    }
+		  double atmp = 0;
+		  for (int i = j; i < nr; i++)
+		    {
+		      atmp += fabs(work2[i]);
+		      work2[i] = 0.;
+		    }
+		  if (atmp > ainvnorm)
+		    ainvnorm = atmp;
+		}
+	    }
+	  rcond = 1. / ainvnorm / anorm;
+	triangular_error:
+	  if (err != 0)
+	    {
+	      if (sing_handler)
+		sing_handler (rcond);
+	      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);
+	      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 (SparseType &mattype, const Matrix& b, int& err,
+		       double& rcond,
+		       solve_singularity_handler sing_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Tridiagonal_Hermitian)
+	{
+	  OCTAVE_LOCAL_BUFFER (double, D, nr);
+	  OCTAVE_LOCAL_BUFFER (double, DL, nr - 1);
+	  if (mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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);
+		  }
+	    }
+	  int 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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dptsv");
+	  else if (err != 0)
+	    {
+	      err = 0;
+	      mattype.mark_as_unsymmetric ();
+	      typ = SparseType::Tridiagonal;
+	    }
+	  else
+	    rcond = 1.;
+	}
+if (typ == SparseType::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 ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		  DU[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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] = data(i);
+		  }
+	    }
+	  int 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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgtsv");
+	  else if (err != 0)
+	    {
+	      rcond = 0.;
+	      err = -2;
+	      if (sing_handler)
+		sing_handler (rcond);
+	      else
+		(*current_liboctave_error_handler)
+		  ("matrix singular to machine precision");
+	    }
+	  else
+	    rcond = 1.;
+	}
+else if (typ != SparseType::Tridiagonal_Hermitian)
+	       (*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseMatrix
+SparseMatrix::trisolve (SparseType &mattype, const SparseMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+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 == SparseType::Tridiagonal ||
+	  typ == SparseType::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<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  if (mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		  DU[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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] = data(i);
+		  }
+	    }
+	  F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgttrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  char job = 'N';
+		  volatile int x_nz = b.nnz ();
+		  int b_nc = b.cols ();
+		  retval = SparseMatrix (nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  volatile int ii = 0;
+		  OCTAVE_LOCAL_BUFFER (double, work, nr);
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < nr; i++)
+			work[i] = 0.;
+		      for (int 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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgttrs");
+			  break;
+			}
+		      // Count non-zeros in work vector and adjust
+		      // space in retval if needed
+		      int new_nnz = 0;
+		      for (int i = 0; i < nr; i++)
+			if (work[i] != 0.)
+			  new_nnz++;
+		      if (ii + new_nnz > x_nz)
+			{
+			  // Resize the sparse matrix
+			  int sz = new_nnz * (b_nc - j) + x_nz;
+			  retval.change_capacity (sz);
+			  x_nz = sz;
+			}
+		      for (int 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 != SparseType::Tridiagonal_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+ComplexMatrix
+SparseMatrix::trisolve (SparseType &mattype, const ComplexMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+// Note can't treat symmetric case as there is no dpttrf function
+if (typ == SparseType::Tridiagonal_Hermitian)
+	{
+	  OCTAVE_LOCAL_BUFFER (Complex, D, nr);
+	  OCTAVE_LOCAL_BUFFER (Complex, DL, nr - 1);
+	  if (mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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);
+		  }
+	    }
+	  int b_nr = b.rows ();
+	  int 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 (f77_exception_encountered)
+	    {
+	      (*current_liboctave_error_handler)
+		("unrecoverable error in zptsv");
+	      err = -1;
+	    }
+	  else if (err != 0)
+	    {
+	      err = 0;
+	      mattype.mark_as_unsymmetric ();
+	      typ = SparseType::Tridiagonal;
+	    }
+	}
+if (typ == SparseType::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 ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		  DU[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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] = data(i);
+		  }
+	    }
+	  int b_nr = b.rows();
+	  int 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 (f77_exception_encountered)
+	    {
+	      (*current_liboctave_error_handler)
+		("unrecoverable error in zgtsv");
+	      err = -1;
+	    }
+	  else if (err != 0)
+	    {
+	      rcond = 0.;
+	      err = -2;
+	      if (sing_handler)
+		sing_handler (rcond);
+	      else
+		(*current_liboctave_error_handler)
+		  ("matrix singular to machine precision");
+	    }
+	}
+else if (typ != SparseType::Tridiagonal_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseComplexMatrix
+SparseMatrix::trisolve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+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 == SparseType::Tridiagonal ||
+	  typ == SparseType::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<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  if (mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int 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 (int i = 0; i < nr - 1; i++)
+		{
+		  D[i+1] = 0.;
+		  DL[i] = 0.;
+		  DU[i] = 0.;
+		}
+	      for (int j = 0; j < nc; j++)
+		for (int 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] = data(i);
+		  }
+	    }
+	  F77_XFCN (dgttrf, DGTTRF, (nr, DL, D, DU, DU2, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgttrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  rcond = 1.;
+		  char job = 'N';
+		  int b_nr = b.rows ();
+		  int 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 int x_nz = b.nnz ();
+		  volatile int ii = 0;
+		  retval = SparseComplexMatrix (b_nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < b_nr; i++)
+			{
+			  Complex c = b (i,j);
+			  Bx[i] = ::real (c);
+			  Bz[i] = ::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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgttrs");
+			  break;
+			}
+		      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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgttrs");
+			  break;
+			}
+		      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
+		      int new_nnz = 0;
+		      for (int i = 0; i < nr; i++)
+			if (Bx[i] != 0. || Bz[i] != 0.)
+			  new_nnz++;
+		      if (ii + new_nnz > x_nz)
+			{
+			  // Resize the sparse matrix
+			  int sz = new_nnz * (b_nc - j) + x_nz;
+			  retval.change_capacity (sz);
+			  x_nz = sz;
+			}
+		      for (int 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 != SparseType::Tridiagonal_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+Matrix
+SparseMatrix::bsolve (SparseType &mattype, const Matrix& b, int& err,
+		       double& rcond,
+		       solve_singularity_handler sing_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Banded_Hermitian)
+	{
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      {
+		int ri = ridx (i);
+		if (ri >= j)
+		  m_band(ri - j, j) = data(i);
+	      }
+	  // Calculate the norm of the matrix, for later use.
+	  // double 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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dpbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  // Matrix is not positive definite!! Fall through to
+		  // unsymmetric banded solver.
+		  mattype.mark_as_unsymmetric ();
+		  typ = SparseType::Banded;
+		  err = 0;
+		}
+	      else
+		{
+		  // Unfortunately, the time to calculate the condition
+		  // number is dominant for narrow banded matrices and
+		  // so we rely on the "err" flag from xPBTRF to flag
+		  // singularity. The commented code below is left here
+		  // for reference
+		  //Array<double> z (3 * nr);
+		  //double *pz = z.fortran_vec ();
+		  //Array<int> iz (nr);
+		  //int *piz = iz.fortran_vec ();
+		  //
+		  //F77_XFCN (dpbcon, DGBCON,
+		  //	(F77_CONST_CHAR_ARG2 (&job, 1),
+		  //	 nr, n_lower, tmp_data, ldm,
+		  //	 anorm, rcond, pz, piz, err
+		  //	 F77_CHAR_ARG_LEN (1)));
+		  //
+		  //
+		  //if (f77_exception_encountered)
+		  //	(*current_liboctave_error_handler)
+		  //	  ("unrecoverable error in dpbcon");
+		  //
+		  //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);
+		  //    else
+		  //      (*current_liboctave_error_handler)
+		  //        ("matrix singular to machine precision, rcond = %g",
+		  //         rcond);
+		  //  }
+		  //else
+		  //    REST OF CODE, EXCEPT rcond=1
+		  rcond = 1.;
+		  retval = b;
+		  double *result = retval.fortran_vec ();
+		  int 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 (f77_exception_encountered)
+		    (*current_liboctave_error_handler)
+		      ("unrecoverable error in dpbtrs");
+		  if (err != 0)
+		    {
+		      (*current_liboctave_error_handler)
+			("SparseMatrix::solve solve failed");
+		      err = -1;
+		    }
+		}
+	    }
+	}
+if (typ == SparseType::Banded)
+	{
+	  // Create the storage for the banded form of the sparse matrix
+	  int n_upper = mattype.nupper ();
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_upper + 2 * n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      m_band(ridx(i) - j + n_lower + n_upper, j) = data(i);
+	  Array<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data,
+				     ldm, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgbtrf");
+	  else
+	    {
+	      // Throw-away extra info LAPACK gives so as to not
+	      // change output.
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  char job = '1';
+		  // Unfortunately, the time to calculate the condition
+		  // number is dominant for narrow banded matrices and
+		  // so we rely on the "err" flag from xPBTRF to flag
+		  // singularity. The commented code below is left here
+		  // for reference
+		  //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 (f77_exception_encountered)
+		  //  (*current_liboctave_error_handler)
+		  //    ("unrecoverable error in dgbcon");
+		  //
+		  // 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);
+		  //    else
+		  //      (*current_liboctave_error_handler)
+		  //        ("matrix singular to machine precision, rcond = %g",
+		  //         rcond);
+		  //  }
+		  //else
+		  //  REST OF CODE, EXCEPT rcond=1
+		  rcond = 1.;
+		  retval = b;
+		  double *result = retval.fortran_vec ();
+		  int b_nc = b.cols ();
+		  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)));
+		  if (f77_exception_encountered)
+		    (*current_liboctave_error_handler)
+		      ("unrecoverable error in dgbtrs");
+		}
+	    }
+	}
+else if (typ != SparseType::Banded_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseMatrix
+SparseMatrix::bsolve (SparseType &mattype, const SparseMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Banded_Hermitian)
+	{
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      {
+		int ri = ridx (i);
+		if (ri >= j)
+		  m_band(ri - j, j) = data(i);
+	      }
+	  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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dpbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  mattype.mark_as_unsymmetric ();
+		  typ = SparseType::Banded;
+		  err = 0;
+		}
+	      else
+		{
+		  rcond = 1.;
+		  int b_nr = b.rows ();
+		  int 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 int x_nz = b.nnz ();
+		  volatile int ii = 0;
+		  retval = SparseMatrix (b_nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int 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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dpbtrs");
+			  err = -1;
+			  break;
+			}
+		      if (err != 0)
+			{
+			  (*current_liboctave_error_handler)
+			    ("SparseMatrix::solve solve failed");
+			  err = -1;
+			  break;
+			}
+		      for (int i = 0; i < b_nr; i++)
+			{
+			  double tmp = Bx[i];
+			  if (tmp != 0.0)
+			    {
+			      if (ii == x_nz)
+				{
+				  // Resize the sparse matrix
+				  int 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 == SparseType::Banded)
+	{
+	  // Create the storage for the banded form of the sparse matrix
+	  int n_upper = mattype.nupper ();
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_upper + 2 * n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      m_band(ridx(i) - j + n_lower + n_upper, j) = data(i);
+	  Array<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data,
+				     ldm, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  char job = 'N';
+		  volatile int x_nz = b.nnz ();
+		  int b_nc = b.cols ();
+		  retval = SparseMatrix (nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  volatile int ii = 0;
+		  OCTAVE_LOCAL_BUFFER (double, work, nr);
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < nr; i++)
+			work[i] = 0.;
+		      for (int 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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgbtrs");
+			  break;
+			}
+		      // Count non-zeros in work vector and adjust
+		      // space in retval if needed
+		      int new_nnz = 0;
+		      for (int i = 0; i < nr; i++)
+			if (work[i] != 0.)
+			  new_nnz++;
+		      if (ii + new_nnz > x_nz)
+			{
+			  // Resize the sparse matrix
+			  int sz = new_nnz * (b_nc - j) + x_nz;
+			  retval.change_capacity (sz);
+			  x_nz = sz;
+			}
+		      for (int 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 != SparseType::Banded_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+ComplexMatrix
+SparseMatrix::bsolve (SparseType &mattype, const ComplexMatrix& b, int& err,
+		     double& rcond, solve_singularity_handler sing_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Banded_Hermitian)
+	{
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      {
+		int ri = ridx (i);
+		if (ri >= j)
+		  m_band(ri - j, j) = data(i);
+	      }
+	  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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dpbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  // Matrix is not positive definite!! Fall through to
+		  // unsymmetric banded solver.
+		  mattype.mark_as_unsymmetric ();
+		  typ = SparseType::Banded;
+		  err = 0;
+		}
+	      else
+		{
+		  rcond = 1.;
+		  int b_nr = b.rows ();
+		  int 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 int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < b_nr; i++)
+			{
+			  Complex c = b (i,j);
+			  Bx[i] = ::real (c);
+			  Bz[i] = ::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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dpbtrs");
+			  err = -1;
+			  break;
+			}
+		      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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dpbtrs");
+			  err = -1;
+			  break;
+			}
+		      if (err != 0)
+			{
+			  (*current_liboctave_error_handler)
+			    ("SparseMatrix::solve solve failed");
+			  err = -1;
+			  break;
+			}
+		      for (int i = 0; i < b_nr; i++)
+			retval (i, j) = Complex (Bx[i], Bz[i]);
+		    }
+		}
+	    }
+	}
+if (typ == SparseType::Banded)
+	{
+	  // Create the storage for the banded form of the sparse matrix
+	  int n_upper = mattype.nupper ();
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_upper + 2 * n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      m_band(ridx(i) - j + n_lower + n_upper, j) = data(i);
+	  Array<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data,
+				     ldm, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  char job = 'N';
+		  int b_nc = b.cols ();
+		  retval.resize (nr,b_nc);
+		  OCTAVE_LOCAL_BUFFER (double, Bz, nr);
+		  OCTAVE_LOCAL_BUFFER (double, Bx, nr);
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < nr; i++)
+			{
+			  Complex c = b (i, j);
+			  Bx[i] = ::real (c);
+			  Bz[i] = ::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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgbtrs");
+			  break;
+			}
+		      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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgbtrs");
+			  break;
+			}
+		      for (int i = 0; i < nr; i++)
+			retval (i, j) = Complex (Bx[i], Bz[i]);
+		    }
+		}
+	    }
+	}
+else if (typ != SparseType::Banded_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseComplexMatrix
+SparseMatrix::bsolve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+volatile int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Banded_Hermitian)
+	{
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      {
+		int ri = ridx (i);
+		if (ri >= j)
+		  m_band(ri - j, j) = data(i);
+	      }
+	  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 (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dpbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  // Matrix is not positive definite!! Fall through to
+		  // unsymmetric banded solver.
+		  mattype.mark_as_unsymmetric ();
+		  typ = SparseType::Banded;
+		  err = 0;
+		}
+	      else
+		{
+		  rcond = 1.;
+		  int b_nr = b.rows ();
+		  int 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 int x_nz = b.nnz ();
+		  volatile int ii = 0;
+		  retval = SparseComplexMatrix (b_nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < b_nr; i++)
+			{
+			  Complex c = b (i,j);
+			  Bx[i] = ::real (c);
+			  Bz[i] = ::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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dpbtrs");
+			  err = -1;
+			  break;
+			}
+		      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 (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dpbtrs");
+			  err = -1;
+			  break;
+			}
+		      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
+		      int new_nnz = 0;
+		      for (int i = 0; i < nr; i++)
+			if (Bx[i] != 0. || Bz[i] != 0.)
+			  new_nnz++;
+		      if (ii + new_nnz > x_nz)
+			{
+			  // Resize the sparse matrix
+			  int sz = new_nnz * (b_nc - j) + x_nz;
+			  retval.change_capacity (sz);
+			  x_nz = sz;
+			}
+		      for (int 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 == SparseType::Banded)
+	{
+	  // Create the storage for the banded form of the sparse matrix
+	  int n_upper = mattype.nupper ();
+	  int n_lower = mattype.nlower ();
+	  int ldm = n_upper + 2 * n_lower + 1;
+	  Matrix m_band (ldm, nc);
+	  double *tmp_data = m_band.fortran_vec ();
+	  if (! mattype.is_dense ())
+	    {
+	      int ii = 0;
+	      for (int j = 0; j < ldm; j++)
+		for (int i = 0; i < nc; i++)
+		  tmp_data[ii++] = 0.;
+	    }
+	  for (int j = 0; j < nc; j++)
+	    for (int i = cidx(j); i < cidx(j+1); i++)
+	      m_band(ridx(i) - j + n_lower + n_upper, j) = data(i);
+	  Array<int> ipvt (nr);
+	  int *pipvt = ipvt.fortran_vec ();
+	  F77_XFCN (dgbtrf, DGBTRF, (nr, nr, n_lower, n_upper, tmp_data,
+				     ldm, pipvt, err));
+	  if (f77_exception_encountered)
+	    (*current_liboctave_error_handler)
+	      ("unrecoverable error in dgbtrf");
+	  else
+	    {
+	      rcond = 0.0;
+	      if (err != 0)
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("matrix singular to machine precision");
+		}
+	      else
+		{
+		  char job = 'N';
+		  volatile int x_nz = b.nnz ();
+		  int b_nc = b.cols ();
+		  retval = SparseComplexMatrix (nr, b_nc, x_nz);
+		  retval.xcidx(0) = 0;
+		  volatile int ii = 0;
+		  OCTAVE_LOCAL_BUFFER (double, Bx, nr);
+		  OCTAVE_LOCAL_BUFFER (double, Bz, nr);
+		  for (volatile int j = 0; j < b_nc; j++)
+		    {
+		      for (int i = 0; i < nr; i++)
+			{
+			  Bx[i] = 0.;
+			  Bz[i] = 0.;
+			}
+		      for (int i = b.cidx(j); i < b.cidx(j+1); i++)
+			{
+			  Complex c = b.data(i);
+			  Bx[b.ridx(i)] = ::real (c);
+			  Bz[b.ridx(i)] = ::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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgbtrs");
+			  break;
+			}
+		      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)));
+		      if (f77_exception_encountered)
+			{
+			  (*current_liboctave_error_handler)
+			    ("unrecoverable error in dgbtrs");
+			  break;
+			}
+		      // Count non-zeros in work vector and adjust
+		      // space in retval if needed
+		      int new_nnz = 0;
+		      for (int i = 0; i < nr; i++)
+			if (Bx[i] != 0. || Bz[i] != 0.)
+			  new_nnz++;
+		      if (ii + new_nnz > x_nz)
+			{
+			  // Resize the sparse matrix
+			  int sz = new_nnz * (b_nc - j) + x_nz;
+			  retval.change_capacity (sz);
+			  x_nz = sz;
+			}
+		      for (int 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 != SparseType::Banded_Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+void *
+SparseMatrix::factorize (int& err, double &rcond, Matrix &Control, Matrix &Info,
+			 solve_singularity_handler sing_handler) const
+{
+// The return values
+void *Numeric;
+err = 0;
+// Setup the control parameters
+Control = Matrix (UMFPACK_CONTROL, 1);
+double *control = Control.fortran_vec ();
+umfpack_di_defaults (control);
+double tmp = Voctave_sparse_controls.get_key ("spumoni");
+if (!xisnan (tmp))
+Control (UMFPACK_PRL) = tmp;
+tmp = Voctave_sparse_controls.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 = Voctave_sparse_controls.get_key ("autoamd");
+if (!xisnan (tmp))
+Control (UMFPACK_FIXQ) = tmp;
+umfpack_di_report_control (control);
+const int *Ap = cidx ();
+const int *Ai = ridx ();
+const double *Ax = data ();
+int nr = rows ();
+int nc = cols ();
+umfpack_di_report_matrix (nr, nc, Ap, Ai, Ax, 1, control);
+void *Symbolic;
+Info = Matrix (1, UMFPACK_INFO);
+double *info = Info.fortran_vec ();
+int status = umfpack_di_qsymbolic (nr, nc, Ap, Ai, Ax, NULL,
+				     &Symbolic, control, info);
+if (status < 0)
+{
+(*current_liboctave_error_handler)
+	("SparseMatrix::solve symbolic factorization failed");
+err = -1;
+umfpack_di_report_status (control, status);
+umfpack_di_report_info (control, info);
+umfpack_di_free_symbolic (&Symbolic) ;
+}
+else
+{
+umfpack_di_report_symbolic (Symbolic, control);
+status = umfpack_di_numeric (Ap, Ai, Ax, Symbolic, &Numeric,
+				   control, info) ;
+umfpack_di_free_symbolic (&Symbolic) ;
+#ifdef HAVE_LSSOLVE
+rcond = Info (UMFPACK_RCOND);
+volatile double rcond_plus_one = rcond + 1.0;
+if (status == UMFPACK_WARNING_singular_matrix ||
+	  rcond_plus_one == 1.0 || xisnan (rcond))
+	{
+	  umfpack_di_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
+#endif
+	if (status < 0)
+	  {
+	    (*current_liboctave_error_handler)
+	      ("SparseMatrix::solve numeric factorization failed");
+	    umfpack_di_report_status (control, status);
+	    umfpack_di_report_info (control, info);
+	    err = -1;
+	  }
+	else
+	  {
+	    umfpack_di_report_numeric (Numeric, control);
+	  }
+}
+if (err != 0)
+umfpack_di_free_numeric (&Numeric);
+return Numeric;
+}
+Matrix
+SparseMatrix::fsolve (SparseType &mattype, const Matrix& b, int& err,
+		     double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+Matrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Hermitian)
+	{
+	  // XXX FIXME XXX Write the cholesky solver and only fall
+	  // through if cholesky factorization fails
+	  (*current_liboctave_warning_handler)
+	    ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done");
+	  mattype.mark_as_unsymmetric ();
+	  typ = SparseType::Full;
+	}
+if (typ == SparseType::Full)
+	{
+	  Matrix Control, Info;
+	  void *Numeric =
+	    factorize (err, rcond, Control, Info, sing_handler);
+	  if (err == 0)
+	    {
+	      const double *Bx = b.fortran_vec ();
+	      retval.resize (b.rows (), b.cols());
+	      double *result = retval.fortran_vec ();
+	      int b_nr = b.rows ();
+	      int b_nc = b.cols ();
+	      int status = 0;
+	      double *control = Control.fortran_vec ();
+	      double *info = Info.fortran_vec ();
+	      const int *Ap = cidx ();
+	      const int *Ai = ridx ();
+	      const double *Ax = data ();
+	      for (int j = 0, iidx = 0; j < b_nc; j++, iidx += b_nr)
+		{
+		  status = umfpack_di_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_di_report_status (control, status);
+		      err = -1;
+		      break;
+		    }
+		}
+#ifndef HAVE_LSSOLVE
+	      rcond = Info (UMFPACK_RCOND);
+	      volatile double rcond_plus_one = rcond + 1.0;
+	      if (status == UMFPACK_WARNING_singular_matrix ||
+		  rcond_plus_one == 1.0 || xisnan (rcond))
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
+		       rcond);
+		}
+#endif
+	      umfpack_di_report_info (control, info);
+	      umfpack_di_free_numeric (&Numeric);
+	    }
+	}
+else if (typ != SparseType::Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseMatrix
+SparseMatrix::fsolve (SparseType &mattype, const SparseMatrix& b, int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Hermitian)
+	{
+	  // XXX FIXME XXX Write the cholesky solver and only fall
+	  // through if cholesky factorization fails
+	  (*current_liboctave_warning_handler)
+	    ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done");
+	  mattype.mark_as_unsymmetric ();
+	  typ = SparseType::Full;
+	}
+if (typ == SparseType::Full)
+	{
+	  Matrix Control, Info;
+	  void *Numeric = factorize (err, rcond, Control, Info,
+				     sing_handler);
+	  if (err == 0)
+	    {
+	      int b_nr = b.rows ();
+	      int b_nc = b.cols ();
+	      int status = 0;
+	      double *control = Control.fortran_vec ();
+	      double *info = Info.fortran_vec ();
+	      const int *Ap = cidx ();
+	      const int *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
+	      int x_nz = b.nnz ();
+	      int ii = 0;
+	      retval = SparseMatrix (b_nr, b_nc, x_nz);
+	      retval.xcidx(0) = 0;
+	      for (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < b_nr; i++)
+		    Bx[i] = b.elem (i, j);
+		  status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, Xx,
+					     Bx, Numeric, control,
+					     info);
+		  if (status < 0)
+		    {
+		      (*current_liboctave_error_handler)
+			("SparseMatrix::solve solve failed");
+		      umfpack_di_report_status (control, status);
+		      err = -1;
+		      break;
+		    }
+		  for (int i = 0; i < b_nr; i++)
+		    {
+		      double tmp = Xx[i];
+		      if (tmp != 0.0)
+			{
+			  if (ii == x_nz)
+			    {
+			      // Resize the sparse matrix
+			      int 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 ();
+#ifndef HAVE_LSSOLVE
+	      rcond = Info (UMFPACK_RCOND);
+	      volatile double rcond_plus_one = rcond + 1.0;
+	      if (status == UMFPACK_WARNING_singular_matrix ||
+		  rcond_plus_one == 1.0 || xisnan (rcond))
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
+		       rcond);
+		}
+#endif
+	      umfpack_di_report_info (control, info);
+	      umfpack_di_free_numeric (&Numeric);
+	    }
+	}
+else if (typ != SparseType::Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+ComplexMatrix
+SparseMatrix::fsolve (SparseType &mattype, const ComplexMatrix& b, int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+ComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Hermitian)
+	{
+	  // XXX FIXME XXX Write the cholesky solver and only fall
+	  // through if cholesky factorization fails
+	  (*current_liboctave_warning_handler)
+	    ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done");
+	  mattype.mark_as_unsymmetric ();
+	  typ = SparseType::Full;
+	}
+if (typ == SparseType::Full)
+	{
+	  Matrix Control, Info;
+	  void *Numeric = factorize (err, rcond, Control, Info,
+				     sing_handler);
+	  if (err == 0)
+	    {
+	      int b_nr = b.rows ();
+	      int b_nc = b.cols ();
+	      int status = 0;
+	      double *control = Control.fortran_vec ();
+	      double *info = Info.fortran_vec ();
+	      const int *Ap = cidx ();
+	      const int *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 (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < b_nr; i++)
+		    {
+		      Complex c = b (i,j);
+		      Bx[i] = ::real (c);
+		      Bz[i] = ::imag (c);
+		    }
+		  status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax,
+					     Xx, Bx, Numeric, control,
+					     info);
+		  int status2 = umfpack_di_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_di_report_status (control, status);
+		      err = -1;
+		      break;
+		    }
+		  for (int i = 0; i < b_nr; i++)
+		    retval (i, j) = Complex (Xx[i], Xz[i]);
+		}
+#ifndef HAVE_LSSOLVE
+	      rcond = Info (UMFPACK_RCOND);
+	      volatile double rcond_plus_one = rcond + 1.0;
+	      if (status == UMFPACK_WARNING_singular_matrix ||
+		  rcond_plus_one == 1.0 || xisnan (rcond))
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
+		       rcond);
+		}
+#endif
+	      umfpack_di_report_info (control, info);
+	      umfpack_di_free_numeric (&Numeric);
+	    }
+	}
+else if (typ != SparseType::Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+SparseComplexMatrix
+SparseMatrix::fsolve (SparseType &mattype, const SparseComplexMatrix& b,
+		      int& err, double& rcond,
+		      solve_singularity_handler sing_handler) const
+{
+SparseComplexMatrix retval;
+int nr = rows ();
+int nc = cols ();
+err = 0;
+if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+(*current_liboctave_error_handler)
+("matrix dimension mismatch solution of linear equations");
+else
+{
+// Print spparms("spumoni") info if requested
+int typ = mattype.type ();
+mattype.info ();
+if (typ == SparseType::Hermitian)
+	{
+	  // XXX FIXME XXX Write the cholesky solver and only fall
+	  // through if cholesky factorization fails
+	  (*current_liboctave_warning_handler)
+	    ("SparseMatrix::solve XXX FIXME XXX Cholesky code not done");
+	  mattype.mark_as_unsymmetric ();
+	  typ = SparseType::Full;
+	}
+if (typ == SparseType::Full)
+	{
+	  Matrix Control, Info;
+	  void *Numeric = factorize (err, rcond, Control, Info,
+				     sing_handler);
+	  if (err == 0)
+	    {
+	      int b_nr = b.rows ();
+	      int b_nc = b.cols ();
+	      int status = 0;
+	      double *control = Control.fortran_vec ();
+	      double *info = Info.fortran_vec ();
+	      const int *Ap = cidx ();
+	      const int *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
+	      int x_nz = b.nnz ();
+	      int 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 (int j = 0; j < b_nc; j++)
+		{
+		  for (int i = 0; i < b_nr; i++)
+		    {
+		      Complex c = b (i,j);
+		      Bx[i] = ::real (c);
+		      Bz[i] = ::imag (c);
+		    }
+		  status = umfpack_di_solve (UMFPACK_A, Ap, Ai, Ax, Xx,
+					     Bx, Numeric, control,
+					     info);
+		  int status2 = umfpack_di_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_di_report_status (control, status);
+		      err = -1;
+		      break;
+		    }
+		  for (int 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
+			      int 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 ();
+#ifndef HAVE_LSSOLVE
+	      rcond = Info (UMFPACK_RCOND);
+	      volatile double rcond_plus_one = rcond + 1.0;
+	      if (status == UMFPACK_WARNING_singular_matrix ||
+		  rcond_plus_one == 1.0 || xisnan (rcond))
+		{
+		  err = -2;
+		  if (sing_handler)
+		    sing_handler (rcond);
+		  else
+		    (*current_liboctave_error_handler)
+		      ("SparseMatrix::solve matrix singular to machine precision, rcond = %g",
+		       rcond);
+		}
+#endif
+	      umfpack_di_report_info (control, info);
+	      umfpack_di_free_numeric (&Numeric);
+	    }
+	}
+else if (typ != SparseType::Hermitian)
+	(*current_liboctave_error_handler) ("incorrect matrix type");
+}
+return retval;
+}
+Matrix
+SparseMatrix::solve (SparseType &mattype, const Matrix& b) const
+{
+int info;
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& info,
+		     double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (SparseType &mattype, const Matrix& b, int& err,
+		     double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+int typ = mattype.type ();
+if (typ == SparseType::Unknown)
+typ = mattype.type (*this);
+if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal)
+return dsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper)
+return utsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower)
+return ltsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian)
+return bsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Tridiagonal ||
+	   typ == SparseType::Tridiagonal_Hermitian)
+return trisolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Full || typ == SparseType::Hermitian)
+return fsolve (mattype, b, err, rcond, sing_handler);
+else
+{
+(*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+return Matrix ();
+}
+}
+SparseMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b) const
+{
+int info;
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b,
+		     int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+int typ = mattype.type ();
+if (typ == SparseType::Unknown)
+typ = mattype.type (*this);
+if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal)
+return dsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper)
+return utsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower)
+return ltsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian)
+return bsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Tridiagonal ||
+	   typ == SparseType::Tridiagonal_Hermitian)
+return trisolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Full || typ == SparseType::Hermitian)
+return fsolve (mattype, b, err, rcond, sing_handler);
+else
+{
+(*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+return SparseMatrix ();
+}
+}
+ComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b) const
+{
+int info;
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b,
+			    int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const ComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+int typ = mattype.type ();
+if (typ == SparseType::Unknown)
+typ = mattype.type (*this);
+if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal)
+return dsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper)
+return utsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower)
+return ltsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian)
+return bsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Tridiagonal ||
+	   typ == SparseType::Tridiagonal_Hermitian)
+return trisolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Full || typ == SparseType::Hermitian)
+return fsolve (mattype, b, err, rcond, sing_handler);
+else
+{
+(*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+return ComplexMatrix ();
+}
+}
+SparseComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b) const
+{
+int info;
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (SparseType &mattype, const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+int typ = mattype.type ();
+if (typ == SparseType::Unknown)
+typ = mattype.type (*this);
+if (typ == SparseType::Diagonal || typ == SparseType::Permuted_Diagonal)
+return dsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Upper || typ == SparseType::Permuted_Upper)
+return utsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Lower || typ == SparseType::Permuted_Lower)
+return ltsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Banded || typ == SparseType::Banded_Hermitian)
+return bsolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Tridiagonal ||
+	   typ == SparseType::Tridiagonal_Hermitian)
+return trisolve (mattype, b, err, rcond, sing_handler);
+else if (typ == SparseType::Full || typ == SparseType::Hermitian)
+return fsolve (mattype, b, err, rcond, sing_handler);
+else
+{
+(*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+return SparseComplexMatrix ();
+}
+}
+ColumnVector
+SparseMatrix::solve (SparseType &mattype, const ColumnVector& b) const
+{
+int info; double rcond;
+return solve (mattype, b, info, rcond);
+}
+ColumnVector
+SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond);
+}
+ColumnVector
+SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info, double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+ColumnVector
+SparseMatrix::solve (SparseType &mattype, const ColumnVector& b, int& info, double& rcond,
+	       solve_singularity_handler sing_handler) const
+{
+Matrix tmp (b);
+return solve (mattype, tmp, info, rcond, sing_handler).column (0);
+}
+ComplexColumnVector
+SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b) const
+{
+int info;
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info) const
+{
+double rcond;
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info,
+		     double& rcond) const
+{
+return solve (mattype, b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (SparseType &mattype, const ComplexColumnVector& b, int& info, double& rcond,
+	       solve_singularity_handler sing_handler) const
+{
+ComplexMatrix tmp (b);
+return solve (mattype, tmp, info, rcond, sing_handler).column (0);
+}
+Matrix
+SparseMatrix::solve (const Matrix& b) const
+{
+int info;
+double rcond;
+return solve (b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (const Matrix& b, int& info) const
+{
+double rcond;
+return solve (b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (const Matrix& b, int& info,
+		     double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+Matrix
+SparseMatrix::solve (const Matrix& b, int& err,
+		     double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseType mattype (*this);
+return solve (mattype, b, err, rcond, sing_handler);
+}
+SparseMatrix
+SparseMatrix::solve (const SparseMatrix& b) const
+{
+int info;
+double rcond;
+return solve (b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (const SparseMatrix& b,
+		     int& info) const
+{
+double rcond;
+return solve (b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (const SparseMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+SparseMatrix
+SparseMatrix::solve (const SparseMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseType mattype (*this);
+return solve (mattype, b, err, rcond, sing_handler);
+}
+ComplexMatrix
+SparseMatrix::solve (const ComplexMatrix& b,
+			    int& info) const
+{
+double rcond;
+return solve (b, info, rcond, 0);
+}
+ComplexMatrix
+SparseMatrix::solve (const ComplexMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+ComplexMatrix
+SparseMatrix::solve (const ComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseType mattype (*this);
+return solve (mattype, b, err, rcond, sing_handler);
+}
+SparseComplexMatrix
+SparseMatrix::solve (const SparseComplexMatrix& b) const
+{
+int info;
+double rcond;
+return solve (b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (const SparseComplexMatrix& b,
+		     int& info) const
+{
+double rcond;
+return solve (b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (const SparseComplexMatrix& b,
+		     int& info, double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+SparseComplexMatrix
+SparseMatrix::solve (const SparseComplexMatrix& b,
+		     int& err, double& rcond,
+		     solve_singularity_handler sing_handler) const
+{
+SparseType mattype (*this);
+return solve (mattype, b, err, rcond, sing_handler);
+}
+ColumnVector
+SparseMatrix::solve (const ColumnVector& b) const
+{
+int info; double rcond;
+return solve (b, info, rcond);
+}
+ColumnVector
+SparseMatrix::solve (const ColumnVector& b, int& info) const
+{
+double rcond;
+return solve (b, info, rcond);
+}
+ColumnVector
+SparseMatrix::solve (const ColumnVector& b, int& info, double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+ColumnVector
+SparseMatrix::solve (const ColumnVector& b, int& info, double& rcond,
+	       solve_singularity_handler sing_handler) const
+{
+Matrix tmp (b);
+return solve (tmp, info, rcond, sing_handler).column (0);
+}
+ComplexColumnVector
+SparseMatrix::solve (const ComplexColumnVector& b) const
+{
+int info;
+double rcond;
+return solve (b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (const ComplexColumnVector& b, int& info) const
+{
+double rcond;
+return solve (b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (const ComplexColumnVector& b, int& info,
+		     double& rcond) const
+{
+return solve (b, info, rcond, 0);
+}
+ComplexColumnVector
+SparseMatrix::solve (const ComplexColumnVector& b, int& info, double& rcond,
+	       solve_singularity_handler sing_handler) const
+{
+ComplexMatrix tmp (b);
+return solve (tmp, info, rcond, sing_handler).column (0);
+}
+Matrix
+SparseMatrix::lssolve (const Matrix& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+Matrix
+SparseMatrix::lssolve (const Matrix& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+Matrix
+SparseMatrix::lssolve (const Matrix& b, int& info, int& rank) const
+{
+info = -1;
+(*current_liboctave_error_handler)
+("SparseMatrix::lssolve not implemented yet");
+return Matrix ();
+}
+SparseMatrix
+SparseMatrix::lssolve (const SparseMatrix& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+SparseMatrix
+SparseMatrix::lssolve (const SparseMatrix& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+SparseMatrix
+SparseMatrix::lssolve (const SparseMatrix& b, int& info, int& rank) const
+{
+info = -1;
+(*current_liboctave_error_handler)
+("SparseMatrix::lssolve not implemented yet");
+return SparseMatrix ();
+}
+ComplexMatrix
+SparseMatrix::lssolve (const ComplexMatrix& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+ComplexMatrix
+SparseMatrix::lssolve (const ComplexMatrix& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+ComplexMatrix
+SparseMatrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const
+{
+info = -1;
+(*current_liboctave_error_handler)
+("SparseMatrix::lssolve not implemented yet");
+return ComplexMatrix ();
+}
+SparseComplexMatrix
+SparseMatrix::lssolve (const SparseComplexMatrix& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+SparseComplexMatrix
+SparseMatrix::lssolve (const SparseComplexMatrix& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+SparseComplexMatrix
+SparseMatrix::lssolve (const SparseComplexMatrix& b, int& info,
+		       int& rank) const
+{
+info = -1;
+(*current_liboctave_error_handler)
+("SparseMatrix::lssolve not implemented yet");
+return SparseComplexMatrix ();
+}
+ColumnVector
+SparseMatrix::lssolve (const ColumnVector& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+ColumnVector
+SparseMatrix::lssolve (const ColumnVector& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+ColumnVector
+SparseMatrix::lssolve (const ColumnVector& b, int& info, int& rank) const
+{
+Matrix tmp (b);
+return lssolve (tmp, info, rank).column (0);
+}
+ComplexColumnVector
+SparseMatrix::lssolve (const ComplexColumnVector& b) const
+{
+int info;
+int rank;
+return lssolve (b, info, rank);
+}
+ComplexColumnVector
+SparseMatrix::lssolve (const ComplexColumnVector& b, int& info) const
+{
+int rank;
+return lssolve (b, info, rank);
+}
+ComplexColumnVector
+SparseMatrix::lssolve (const ComplexColumnVector& b, int& info,
+		       int& rank) const
+{
+ComplexMatrix tmp (b);
+return lssolve (tmp, info, rank).column (0);
+}
+// other operations.
+SparseMatrix
+SparseMatrix::map (d_d_Mapper f) const
+{
+int nr = rows ();
+int nc = cols ();
+int nz = nnz ();
+bool f_zero = (f(0.0) == 0.0);
+// Count number of non-zero elements
+int nel = (f_zero ? 0 : nr*nc - nz);
+for (int i = 0; i < nz; i++)
+if (f (data(i)) != 0.0)
+nel++;
+SparseMatrix retval (nr, nc, nel);
+if (f_zero)
+{
+int ii = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double tmp = f (elem (i, j));
+	      if (tmp != 0.0)
+		{
+		  retval.data(ii) = tmp;
+		  retval.ridx(ii++) = i;
+		}
+	    }
+	  retval.cidx(j+1) = ii;
+	}
+}
+else
+{
+int ii = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      retval.data(ii) = f (elem(i));
+	      retval.ridx(ii++) = ridx(i);
+	    }
+	  retval.cidx(j+1) = ii;
+	}
+}
+return retval;
+}
+SparseBoolMatrix
+SparseMatrix::map (b_d_Mapper f) const
+{
+int nr = rows ();
+int nc = cols ();
+int nz = nnz ();
+bool f_zero = f(0.0);
+// Count number of non-zero elements
+int nel = (f_zero ? 0 : nr*nc - nz);
+for (int i = 0; i < nz; i++)
+if (f (data(i)) != 0.0)
+nel++;
+SparseBoolMatrix retval (nr, nc, nel);
+if (f_zero)
+{
+int ii = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = 0; i < nr; i++)
+	    {
+	      bool tmp = f (elem (i, j));
+	      if (tmp)
+		{
+		  retval.data(ii) = tmp;
+		  retval.ridx(ii++) = i;
+		}
+	    }
+	  retval.cidx(j+1) = ii;
+	}
+}
+else
+{
+int ii = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int i = cidx(j); i < cidx(j+1); i++)
+	    {
+	      retval.data(ii) = f (elem(i));
+	      retval.ridx(ii++) = ridx(i);
+	    }
+	  retval.cidx(j+1) = ii;
+	}
+}
+return retval;
+}
+SparseMatrix&
+SparseMatrix::apply (d_d_Mapper f)
+{
+*this = map (f);
+return *this;
+}
+bool
+SparseMatrix::any_element_is_negative (bool neg_zero) const
+{
+int nel = nnz ();
+if (neg_zero)
+{
+for (int i = 0; i < nel; i++)
+	if (lo_ieee_signbit (data (i)))
+	  return true;
+}
+else
+{
+for (int i = 0; i < nel; i++)
+	if (data (i) < 0)
+	  return true;
+}
+return false;
+}
+bool
+SparseMatrix::any_element_is_inf_or_nan (void) const
+{
+int nel = nnz ();
+for (int i = 0; i < nel; i++)
+{
+double val = data (i);
+if (xisinf (val) || xisnan (val))
+	return true;
+}
+return false;
+}
+bool
+SparseMatrix::all_elements_are_int_or_inf_or_nan (void) const
+{
+int nel = nnz ();
+for (int 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
+{
+int nel = nnz ();
+if (nel == 0)
+return false;
+max_val = data (0);
+min_val = data (0);
+for (int 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
+{
+int nel = nnz ();
+for (int 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
+{
+int nr = rows ();
+int nc = cols ();
+int nz1 = nnz ();
+int nz2 = nr*nc - nz1;
+SparseBoolMatrix r (nr, nc, nz2);
+int ii = 0;
+int jj = 0;
+r.cidx (0) = 0;
+for (int i = 0; i < nc; i++)
+{
+for (int 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;
+}
+// XXX FIXME XXX 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
+{
+SPARSE_REDUCTION_OP (SparseMatrix, double, *=, 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 = elem (i, j); \
+tmp[i] += d * d
+#define COL_EXPR \
+double d = elem (i, j); \
+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
+{
+int nz = nnz ();
+SparseMatrix retval (*this);
+for (int i = 0; i < nz; i++)
+retval.data(i) = fabs(retval.data(i));
+return retval;
+}
+SparseMatrix
+SparseMatrix::diag (int k) const
+{
+int nnr = rows ();
+int nnc = cols ();
+if (k > 0)
+nnc -= k;
+else if (k < 0)
+nnr += k;
+SparseMatrix d;
+if (nnr > 0 && nnc > 0)
+{
+int ndiag = (nnr < nnc) ? nnr : nnc;
+// Count the number of non-zero elements
+int nel = 0;
+if (k > 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    if (elem (i, i+k) != 0.)
+	      nel++;
+	}
+else if ( k < 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    if (elem (i-k, i) != 0.)
+	      nel++;
+	}
+else
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    if (elem (i, i) != 0.)
+	      nel++;
+	}
+d = SparseMatrix (ndiag, 1, nel);
+d.xcidx (0) = 0;
+d.xcidx (1) = nel;
+int ii = 0;
+if (k > 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    {
+	      double tmp = elem (i, i+k);
+	      if (tmp != 0.)
+		{
+		  d.xdata (ii) = tmp;
+		  d.xridx (ii++) = i;
+		}
+	    }
+	}
+else if ( k < 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    {
+	      double tmp = elem (i-k, i);
+	      if (tmp != 0.)
+		{
+		  d.xdata (ii) = tmp;
+		  d.xridx (ii++) = i;
+		}
+	    }
+	}
+else
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    {
+	      double tmp = elem (i, i);
+	      if (tmp != 0.)
+		{
+		  d.xdata (ii) = tmp;
+		  d.xridx (ii++) = i;
+		}
+	    }
+	}
+}
+else
+(*current_liboctave_error_handler)
+("diag: requested diagonal out of range");
+return d;
+}
+Matrix
+SparseMatrix::matrix_value (void) const
+{
+int nr = rows ();
+int nc = cols ();
+Matrix retval (nr, nc, 0.0);
+for (int j = 0; j < nc; j++)
+for (int i = cidx(j); i < cidx(j+1); i++)
+retval.elem (ridx(i), j) = data (i);
+return retval;
+}
+std::ostream&
+operator << (std::ostream& os, const SparseMatrix& a)
+{
+int nc = a.cols ();
+// add one to the printed indices to go from
+//  zero-based to one-based arrays
+for (int j = 0; j < nc; j++)  {
+OCTAVE_QUIT;
+for (int 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)
+{
+int nr = a.rows ();
+int nc = a.cols ();
+int nz = a.nnz ();
+if (nr < 1 || nc < 1)
+is.clear (std::ios::badbit);
+else
+{
+int itmp, jtmp, jold = 0;
+double tmp;
+int ii = 0;
+a.cidx (0) = 0;
+for (int i = 0; i < nz; i++)
+	{
+	  is >> itmp;
+	  itmp--;
+	  is >> jtmp;
+	  jtmp--;
+	  tmp = octave_read_double (is);
+	  if (is)
+	    {
+	      if (jold != jtmp)
+		{
+		  for (int j = jold; j < jtmp; j++)
+		    a.cidx(j+1) = ii;
+		  jold = jtmp;
+		}
+	      a.data (ii) = tmp;
+	      a.ridx (ii++) = itmp;
+	    }
+	  else
+	    goto done;
+	}
+for (int 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<int>& vec, bool inv) const
+{
+return MSparse<double>::permute (vec, inv);
+}
+SparseMatrix
+SparseMatrix::ipermute (const Array<int>& vec) const
+{
+return MSparse<double>::ipermute (vec);
+}
+// matrix by matrix -> matrix operations
+SparseMatrix
+operator * (const SparseMatrix& m, const SparseMatrix& a)
+{
+#ifdef HAVE_SPARSE_BLAS
+// XXX FIXME XXX Isn't there a sparse BLAS ??
+#else
+// Use Andy's sparse matrix multiply function
+SPARSE_SPARSE_MUL (SparseMatrix, double);
+#endif
+}
+// XXX FIXME XXX -- 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;
+int nr = m.rows ();
+int nc = m.columns ();
+EMPTY_RETURN_CHECK (SparseMatrix);
+// Count the number of non-zero elements
+if (d < 0.)
+{
+result = SparseMatrix (nr, nc, d);
+for (int j = 0; j < nc; j++)
+	for (int i = m.cidx(j); i < m.cidx(j+1); i++)
+	  {
+	    double tmp = xmin (d, m.data (i));
+	    if (tmp != 0.)
+	      {
+		int idx = m.ridx(i) + j * nr;
+		result.xdata(idx) = tmp;
+		result.xridx(idx) = m.ridx(i);
+	      }
+	  }
+}
+else
+{
+int nel = 0;
+for (int j = 0; j < nc; j++)
+	for (int i = m.cidx(j); i < m.cidx(j+1); i++)
+	  if (xmin (d, m.data (i)) != 0.)
+	    nel++;
+result = SparseMatrix (nr, nc, nel);
+int ii = 0;
+result.xcidx(0) = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int 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()))
+{
+int a_nr = a.rows ();
+int a_nc = a.cols ();
+int b_nr = b.rows ();
+int 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 ()));
+	  int jx = 0;
+	  r.cidx (0) = 0;
+	  for (int i = 0 ; i < a_nc ; i++)
+	    {
+	      int  ja = a.cidx(i);
+	      int  ja_max = a.cidx(i+1);
+	      bool ja_lt_max= ja < ja_max;
+	      int  jb = b.cidx(i);
+	      int  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;
+int nr = m.rows ();
+int nc = m.columns ();
+EMPTY_RETURN_CHECK (SparseMatrix);
+// Count the number of non-zero elements
+if (d > 0.)
+{
+result = SparseMatrix (nr, nc, d);
+for (int j = 0; j < nc; j++)
+	for (int i = m.cidx(j); i < m.cidx(j+1); i++)
+	  {
+	    double tmp = xmax (d, m.data (i));
+	    if (tmp != 0.)
+	      {
+		int idx = m.ridx(i) + j * nr;
+		result.xdata(idx) = tmp;
+		result.xridx(idx) = m.ridx(i);
+	      }
+	  }
+}
+else
+{
+int nel = 0;
+for (int j = 0; j < nc; j++)
+	for (int i = m.cidx(j); i < m.cidx(j+1); i++)
+	  if (xmax (d, m.data (i)) != 0.)
+	    nel++;
+result = SparseMatrix (nr, nc, nel);
+int ii = 0;
+result.xcidx(0) = 0;
+for (int j = 0; j < nc; j++)
+	{
+	  for (int 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()))
+{
+int a_nr = a.rows ();
+int a_nc = a.cols ();
+int b_nr = b.rows ();
+int 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 ()));
+	  int jx = 0;
+	  r.cidx (0) = 0;
+	  for (int i = 0 ; i < a_nc ; i++)
+	    {
+	      int  ja = a.cidx(i);
+	      int  ja_max = a.cidx(i+1);
+	      bool ja_lt_max= ja < ja_max;
+	      int  jb = b.cidx(i);
+	      int  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: ***
+*/

Mercurial > hg > octave-nkf

comparison liboctave/dSparse.cc @ 5164:57077d0ddc8e