--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/liboctave/dMatrix.cc	Mon Jun 06 00:41:10 1994 +0000
@@ -0,0 +1,2432 @@
+// Matrix manipulations.                              -*- C++ -*-
+/*
+
+Copyright (C) 1992, 1993, 1994 John W. Eaton
+
+This file is part of Octave.
+
+Octave is free software; you can redistribute it and/or modify it
+under the terms of the GNU General Public License as published by the
+Free Software Foundation; either version 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 Octave; see the file COPYING.  If not, write to the Free
+Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
+
+*/
+
+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#if defined (__GNUG__)
+#pragma implementation
+#endif
+
+#include <sys/types.h>
+#include <iostream.h>
+#include <stdio.h>
+
+#include <Complex.h>
+
+#include "mx-base.h"
+#include "dbleDET.h"
+#include "mx-inlines.cc"
+#include "lo-error.h"
+#include "f77-uscore.h"
+
+// Fortran functions we call.
+
+extern "C"
+{
+  int F77_FCN (dgemm) (const char*, const char*, const int*,
+		       const int*, const int*, const double*,
+		       const double*, const int*, const double*,
+		       const int*, const double*, double*, const int*,
+		       long, long);
+
+  int F77_FCN (dgemv) (const char*, const int*, const int*,
+		       const double*, const double*, const int*,
+		       const double*, const int*, const double*,
+		       double*, const int*, long);
+
+  int F77_FCN (dgeco) (double*, const int*, const int*, int*, double*,
+		       double*);
+
+  int F77_FCN (dgesl) (const double*, const int*, const int*,
+		       const int*, double*, const int*); 
+
+  int F77_FCN (dgedi) (double*, const int*, const int*, const int*,
+		       double*, double*, const int*);
+
+  int F77_FCN (dgelss) (const int*, const int*, const int*, double*,
+			const int*, double*, const int*, double*,
+			const double*, int*, double*, const int*,
+			int*);
+
+// Note that the original complex fft routines were not written for
+// double complex arguments.  They have been modified by adding an
+// implicit double precision (a-h,o-z) statement at the beginning of
+// each subroutine.
+
+  int F77_FCN (cffti) (const int*, Complex*);
+
+  int F77_FCN (cfftf) (const int*, Complex*, Complex*);
+
+  int F77_FCN (cfftb) (const int*, Complex*, Complex*);
+}
+
+#define KLUDGE_MATRICES
+#define TYPE double
+#define KL_MAT_TYPE Matrix
+#include "mx-kludge.cc"
+#undef KLUDGE_MATRICES
+#undef TYPE
+#undef KL_MAT_TYPE
+
+/*
+ * Matrix class.
+ */
+
+Matrix::Matrix (const DiagMatrix& a)
+  : Array2<double> (a.rows (), a.cols (), 0.0)
+{
+  for (int i = 0; i < a.length (); i++)
+    elem (i, i) = a.elem (i, i);
+}
+
+#if 0
+Matrix&
+Matrix::resize (int r, int c)
+{
+  if (r < 0 || c < 0)
+    {
+      (*current_liboctave_error_handler)
+	("can't resize to negative dimensions");
+      return *this;
+    }
+
+  int new_len = r * c;
+  double* new_data = (double *) NULL;
+  if (new_len > 0)
+    {
+      new_data = new double [new_len];
+
+      int min_r = nr < r ? nr : r;
+      int min_c = nc < c ? nc : c;
+
+      for (int j = 0; j < min_c; j++)
+	for (int i = 0; i < min_r; i++)
+	  new_data[r*j+i] = elem (i, j);
+    }
+
+  delete [] data;
+  nr = r;
+  nc = c;
+  len = new_len;
+  data = new_data;
+
+  return *this;
+}
+
+Matrix&
+Matrix::resize (int r, int c, double val)
+{
+  if (r < 0 || c < 0)
+    {
+      (*current_liboctave_error_handler)
+	("can't resize to negative dimensions");
+      return *this;
+    }
+
+  int new_len = r * c;
+  double *new_data = (double *) NULL;
+  if (new_len > 0)
+    {
+      new_data = new double [new_len];
+
+// There may be faster or cleaner ways to do this.
+
+      if (r > nr || c > nc)
+	copy (new_data, new_len, val);
+
+      int min_r = nr < r ? nr : r;
+      int min_c = nc < c ? nc : c;
+
+      for (int j = 0; j < min_c; j++)
+	for (int i = 0; i < min_r; i++)
+	  new_data[r*j+i] = elem (i, j);
+    }
+
+  delete [] data;
+  nr = r;
+  nc = c;
+  len = new_len;
+  data = new_data;
+
+  return *this;
+}
+#endif
+
+int
+Matrix::operator == (const Matrix& a) const
+{
+  if (rows () != a.rows () || cols () != a.cols ())
+    return 0;
+
+  return equal (data (), a.data (), length ());
+}
+
+int
+Matrix::operator != (const Matrix& a) const
+{
+  return !(*this == a);
+}
+
+Matrix&
+Matrix::insert (const Matrix& a, int r, int c)
+{
+  int a_rows = a.rows ();
+  int a_cols = a.cols ();
+  if (r < 0 || r + a_rows - 1 > rows ()
+      || c < 0 || c + a_cols - 1 > cols ())
+    {
+      (*current_liboctave_error_handler) ("range error for insert");
+      return *this;
+    }
+
+  for (int j = 0; j < a_cols; j++)
+    for (int i = 0; i < a_rows; i++)
+      elem (r+i, c+j) = a.elem (i, j);
+
+  return *this;
+}
+
+Matrix&
+Matrix::insert (const RowVector& a, int r, int c)
+{
+  int a_len = a.length ();
+  if (r < 0 || r >= rows () || c < 0 || c + a_len - 1 > cols ())
+    {
+      (*current_liboctave_error_handler) ("range error for insert");
+      return *this;
+    }
+
+  for (int i = 0; i < a_len; i++)
+    elem (r, c+i) = a.elem (i);
+
+  return *this;
+}
+
+Matrix&
+Matrix::insert (const ColumnVector& a, int r, int c)
+{
+  int a_len = a.length ();
+  if (r < 0 || r + a_len - 1 > rows () || c < 0 || c >= cols ())
+    {
+      (*current_liboctave_error_handler) ("range error for insert");
+      return *this;
+    }
+
+  for (int i = 0; i < a_len; i++)
+    elem (r+i, c) = a.elem (i);
+
+  return *this;
+}
+
+Matrix&
+Matrix::insert (const DiagMatrix& a, int r, int c)
+{
+  if (r < 0 || r + a.rows () - 1 > rows ()
+      || c < 0 || c + a.cols () - 1 > cols ())
+    {
+      (*current_liboctave_error_handler) ("range error for insert");
+      return *this;
+    }
+
+  for (int i = 0; i < a.length (); i++)
+    elem (r+i, c+i) = a.elem (i, i);
+
+  return *this;
+}
+
+Matrix&
+Matrix::fill (double val)
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr > 0 && nc > 0)
+    for (int j = 0; j < nc; j++)
+      for (int i = 0; i < nr; i++)
+	elem (i, j) = val;
+
+  return *this;
+}
+
+Matrix&
+Matrix::fill (double val, int r1, int c1, int r2, int c2)
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0
+      || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc)
+    {
+      (*current_liboctave_error_handler) ("range error for fill");
+      return *this;
+    }
+
+  if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; }
+  if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; }
+
+  for (int j = c1; j <= c2; j++)
+    for (int i = r1; i <= r2; i++)
+      elem (i, j) = val;
+
+  return *this;
+}
+
+Matrix
+Matrix::append (const Matrix& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != a.rows ())
+    {
+      (*current_liboctave_error_handler) ("row dimension mismatch for append");
+      return Matrix ();
+    }
+
+  int nc_insert = nc;
+  Matrix retval (nr, nc + a.cols ());
+  retval.insert (*this, 0, 0);
+  retval.insert (a, 0, nc_insert);
+  return retval;
+}
+
+Matrix
+Matrix::append (const RowVector& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != 1)
+    {
+      (*current_liboctave_error_handler) ("row dimension mismatch for append");
+      return Matrix ();
+    }
+
+  int nc_insert = nc;
+  Matrix retval (nr, nc + a.length ());
+  retval.insert (*this, 0, 0);
+  retval.insert (a, 0, nc_insert);
+  return retval;
+}
+
+Matrix
+Matrix::append (const ColumnVector& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != a.length ())
+    {
+      (*current_liboctave_error_handler) ("row dimension mismatch for append");
+      return Matrix ();
+    }
+
+  int nc_insert = nc;
+  Matrix retval (nr, nc + 1);
+  retval.insert (*this, 0, 0);
+  retval.insert (a, 0, nc_insert);
+  return retval;
+}
+
+Matrix
+Matrix::append (const DiagMatrix& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != a.rows ())
+    {
+      (*current_liboctave_error_handler) ("row dimension mismatch for append");
+      return *this;
+    }
+
+  int nc_insert = nc;
+  Matrix retval (nr, nc + a.cols ());
+  retval.insert (*this, 0, 0);
+  retval.insert (a, 0, nc_insert);
+  return retval;
+}
+
+Matrix
+Matrix::stack (const Matrix& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("column dimension mismatch for stack");
+      return Matrix ();
+    }
+
+  int nr_insert = nr;
+  Matrix retval (nr + a.rows (), nc);
+  retval.insert (*this, 0, 0);
+  retval.insert (a, nr_insert, 0);
+  return retval;
+}
+
+Matrix
+Matrix::stack (const RowVector& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nc != a.length ())
+    {
+      (*current_liboctave_error_handler)
+	("column dimension mismatch for stack");
+      return Matrix ();
+    }
+
+  int nr_insert = nr;
+  Matrix retval (nr + 1, nc);
+  retval.insert (*this, 0, 0);
+  retval.insert (a, nr_insert, 0);
+  return retval;
+}
+
+Matrix
+Matrix::stack (const ColumnVector& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nc != 1)
+    {
+      (*current_liboctave_error_handler)
+	("column dimension mismatch for stack");
+      return Matrix ();
+    }
+
+  int nr_insert = nr;
+  Matrix retval (nr + a.length (), nc);
+  retval.insert (*this, 0, 0);
+  retval.insert (a, nr_insert, 0);
+  return retval;
+}
+
+Matrix
+Matrix::stack (const DiagMatrix& a) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("column dimension mismatch for stack");
+      return Matrix ();
+    }
+
+  int nr_insert = nr;
+  Matrix retval (nr + a.rows (), nc);
+  retval.insert (*this, 0, 0);
+  retval.insert (a, nr_insert, 0);
+  return retval;
+}
+
+Matrix
+Matrix::transpose (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  Matrix result (nc, nr);
+  if (length () > 0)
+    {
+      for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  result.elem (j, i) = elem (i, j);
+    }
+  return result;
+}
+
+Matrix
+Matrix::extract (int r1, int c1, int r2, int c2) const
+{
+  if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; }
+  if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; }
+
+  int new_r = r2 - r1 + 1;
+  int new_c = c2 - c1 + 1;
+
+  Matrix result (new_r, new_c);
+
+  for (int j = 0; j < new_c; j++)
+    for (int i = 0; i < new_r; i++)
+      result.elem (i, j) = elem (r1+i, c1+j);
+
+  return result;
+}
+
+// extract row or column i.
+
+RowVector
+Matrix::row (int i) const
+{
+  int nc = cols ();
+  if (i < 0 || i >= rows ())
+    {
+      (*current_liboctave_error_handler) ("invalid row selection");
+      return RowVector ();
+    }
+
+  RowVector retval (nc);
+  for (int j = 0; j < nc; j++)
+    retval.elem (j) = elem (i, j);
+
+  return retval;
+}
+
+RowVector
+Matrix::row (char *s) const
+{
+  if (s == (char *) NULL)
+    {
+      (*current_liboctave_error_handler) ("invalid row selection");
+      return RowVector ();
+    }
+
+  char c = *s;
+  if (c == 'f' || c == 'F')
+    return row (0);
+  else if (c == 'l' || c == 'L')
+    return row (rows () - 1);
+  else
+    {
+      (*current_liboctave_error_handler) ("invalid row selection");
+      return RowVector ();
+    }
+}
+
+ColumnVector
+Matrix::column (int i) const
+{
+  int nr = rows ();
+  if (i < 0 || i >= cols ())
+    {
+      (*current_liboctave_error_handler) ("invalid column selection");
+      return ColumnVector ();
+    }
+
+  ColumnVector retval (nr);
+  for (int j = 0; j < nr; j++)
+    retval.elem (j) = elem (j, i);
+
+  return retval;
+}
+
+ColumnVector
+Matrix::column (char *s) const
+{
+  if (s == (char *) NULL)
+    {
+      (*current_liboctave_error_handler) ("invalid column selection");
+      return ColumnVector ();
+    }
+
+  char c = *s;
+  if (c == 'f' || c == 'F')
+    return column (0);
+  else if (c == 'l' || c == 'L')
+    return column (cols () - 1);
+  else
+    {
+      (*current_liboctave_error_handler) ("invalid column selection");
+      return ColumnVector ();
+    }
+}
+
+Matrix
+Matrix::inverse (void) const
+{
+  int info;
+  double rcond;
+  return inverse (info, rcond);
+}
+
+Matrix
+Matrix::inverse (int& info) const
+{
+  double rcond;
+  return inverse (info, rcond);
+}
+
+Matrix
+Matrix::inverse (int& info, double& rcond) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  int len = length ();
+  if (nr != nc || nr == 0 || nc == 0)
+    {
+      (*current_liboctave_error_handler) ("inverse requires square matrix");
+      return Matrix ();
+    }
+
+  info = 0;
+
+  int *ipvt = new int [nr];
+  double *z = new double [nr];
+  double *tmp_data = dup (data (), len);
+
+  F77_FCN (dgeco) (tmp_data, &nr, &nc, ipvt, &rcond, z);
+
+  if (rcond + 1.0 == 1.0)
+    {
+      info = -1;
+      copy (tmp_data, data (), len);  // Restore matrix contents.
+    }
+  else
+    {
+      int job = 1;
+      double dummy;
+
+      F77_FCN (dgedi) (tmp_data, &nr, &nc, ipvt, &dummy, z, &job);
+    }
+
+  delete [] ipvt;
+  delete [] z;
+
+  return Matrix (tmp_data, nr, nc);
+}
+
+ComplexMatrix
+Matrix::fourier (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  int npts, nsamples;
+  if (nr == 1 || nc == 1)
+    {
+      npts = nr > nc ? nr : nc;
+      nsamples = 1;
+    }
+  else
+    {
+      npts = nr;
+      nsamples = nc;
+    }
+
+  int nn = 4*npts+15;
+  Complex *wsave = new Complex [nn];
+  Complex *tmp_data = make_complex (data (), length ());
+
+  F77_FCN (cffti) (&npts, wsave);
+
+  for (int j = 0; j < nsamples; j++)
+    F77_FCN (cfftf) (&npts, &tmp_data[npts*j], wsave);
+
+  delete [] wsave;
+
+  return ComplexMatrix (tmp_data, nr, nc);
+}
+
+ComplexMatrix
+Matrix::ifourier (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  int npts, nsamples;
+  if (nr == 1 || nc == 1)
+    {
+      npts = nr > nc ? nr : nc;
+      nsamples = 1;
+    }
+  else
+    {
+      npts = nr;
+      nsamples = nc;
+    }
+
+  int nn = 4*npts+15;
+  Complex *wsave = new Complex [nn];
+  Complex *tmp_data = make_complex (data (), length ());
+
+  F77_FCN (cffti) (&npts, wsave);
+
+  for (int j = 0; j < nsamples; j++)
+    F77_FCN (cfftb) (&npts, &tmp_data[npts*j], wsave);
+
+  for (j = 0; j < npts*nsamples; j++)
+    tmp_data[j] = tmp_data[j] / (double) npts;
+
+  delete [] wsave;
+
+  return ComplexMatrix (tmp_data, nr, nc);
+}
+
+DET
+Matrix::determinant (void) const
+{
+  int info;
+  double rcond;
+  return determinant (info, rcond);
+}
+
+DET
+Matrix::determinant (int& info) const
+{
+  double rcond;
+  return determinant (info, rcond);
+}
+
+DET
+Matrix::determinant (int& info, double& rcond) const
+{
+  DET retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 0 || nc == 0)
+    {
+      double d[2];
+      d[0] = 1.0;
+      d[1] = 0.0;
+      retval = DET (d);
+    }
+  else
+    {
+      info = 0;
+      int *ipvt = new int [nr];
+
+      double *z = new double [nr];
+      double *tmp_data = dup (data (), length ());
+
+      F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z);
+
+      if (rcond + 1.0 == 1.0)
+	{
+	  info = -1;
+	  retval = DET ();
+	}
+      else
+	{
+	  int job = 10;
+	  double d[2];
+	  F77_FCN (dgedi) (tmp_data, &nr, &nr, ipvt, d, z, &job);
+	  retval = DET (d);
+	}
+
+      delete [] tmp_data;
+      delete [] ipvt;
+      delete [] z;
+    }
+
+  return retval;
+}
+
+Matrix
+Matrix::solve (const Matrix& b) const
+{
+  int info;
+  double rcond;
+  return solve (b, info, rcond);
+}
+
+Matrix
+Matrix::solve (const Matrix& b, int& info) const
+{
+  double rcond;
+  return solve (b, info, rcond);
+}
+
+Matrix
+Matrix::solve (const Matrix& b, int& info, double& rcond) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+  if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
+    {
+      (*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+      return Matrix ();
+    }
+
+  info = 0;
+  int *ipvt = new int [nr];
+
+  double *z = new double [nr];
+  double *tmp_data = dup (data (), length ());
+
+  F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z);
+
+  if (rcond + 1.0 == 1.0)
+    {
+      info = -2;
+    }
+  else
+    {
+      int job = 0;
+
+      double *result = dup (b.data (), b.length ());
+
+      int b_nc = b.cols ();
+      for (int j = 0; j < b_nc; j++)
+	F77_FCN (dgesl) (tmp_data, &nr, &nr, ipvt, &result[nr*j], &job);
+
+      retval = Matrix (result, b.rows (), b_nc);
+    }
+
+  delete [] tmp_data;
+  delete [] ipvt;
+  delete [] z;
+
+  return retval;
+}
+
+ComplexMatrix
+Matrix::solve (const ComplexMatrix& b) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b);
+}
+
+ComplexMatrix
+Matrix::solve (const ComplexMatrix& b, int& info) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b, info);
+}
+
+ComplexMatrix
+Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b, info, rcond);
+}
+
+ColumnVector
+Matrix::solve (const ColumnVector& b) const
+{
+  int info; double rcond;
+  return solve (b, info, rcond);
+}
+
+ColumnVector
+Matrix::solve (const ColumnVector& b, int& info) const
+{
+  double rcond;
+  return solve (b, info, rcond);
+}
+
+ColumnVector
+Matrix::solve (const ColumnVector& b, int& info, double& rcond) const
+{
+  ColumnVector retval;
+
+  int nr = rows ();
+  int nc = cols ();
+  if (nr == 0 || nc == 0 || nr != nc || nr != b.length ())
+    {
+      (*current_liboctave_error_handler)
+	("matrix dimension mismatch solution of linear equations");
+      return ColumnVector ();
+    }
+
+  info = 0;
+  int *ipvt = new int [nr];
+
+  double *z = new double [nr];
+  double *tmp_data = dup (data (), length ());
+
+  F77_FCN (dgeco) (tmp_data, &nr, &nr, ipvt, &rcond, z);
+
+  if (rcond + 1.0 == 1.0)
+    {
+      info = -2;
+    }
+  else
+    {
+      int job = 0;
+
+      int b_len = b.length ();
+
+      double *result = dup (b.data (), b_len);
+
+      F77_FCN (dgesl) (tmp_data, &nr, &nr, ipvt, result, &job);
+
+      retval = ColumnVector (result, b_len);
+    }
+
+  delete [] tmp_data;
+  delete [] ipvt;
+  delete [] z;
+
+  return retval;
+}
+
+ComplexColumnVector
+Matrix::solve (const ComplexColumnVector& b) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b);
+}
+
+ComplexColumnVector
+Matrix::solve (const ComplexColumnVector& b, int& info) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b, info);
+}
+
+ComplexColumnVector
+Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.solve (b, info, rcond);
+}
+
+Matrix
+Matrix::lssolve (const Matrix& b) const
+{
+  int info;
+  int rank;
+  return lssolve (b, info, rank);
+}
+
+Matrix
+Matrix::lssolve (const Matrix& b, int& info) const
+{
+  int rank;
+  return lssolve (b, info, rank);
+}
+
+Matrix
+Matrix::lssolve (const Matrix& b, int& info, int& rank) const
+{
+  int nrhs = b.cols ();
+
+  int m = rows ();
+  int n = cols ();
+
+  if (m == 0 || n == 0 || m != b.rows ())
+    {
+      (*current_liboctave_error_handler)
+	("matrix dimension mismatch in solution of least squares problem");
+      return Matrix ();
+    }
+
+  double *tmp_data = dup (data (), length ());
+
+  int nrr = m > n ? m : n;
+  Matrix result (nrr, nrhs);
+
+  int i, j;
+  for (j = 0; j < nrhs; j++)
+    for (i = 0; i < m; i++)
+      result.elem (i, j) = b.elem (i, j);
+
+  double *presult = result.fortran_vec ();
+
+  int len_s = m < n ? m : n;
+  double *s = new double [len_s];
+  double rcond = -1.0;
+  int lwork;
+  if (m < n)
+    lwork = 3*m + (2*m > nrhs ? (2*m > n ? 2*m : n) : (nrhs > n ? nrhs : n));
+  else
+    lwork = 3*n + (2*n > nrhs ? (2*n > m ? 2*n : m) : (nrhs > m ? nrhs : m));
+
+  double *work = new double [lwork];
+
+  F77_FCN (dgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s,
+		    &rcond, &rank, work, &lwork, &info);
+
+  Matrix retval (n, nrhs);
+  for (j = 0; j < nrhs; j++)
+    for (i = 0; i < n; i++)
+      retval.elem (i, j) = result.elem (i, j);
+
+  delete [] tmp_data;
+  delete [] s;
+  delete [] work;
+
+  return retval;
+}
+
+ComplexMatrix
+Matrix::lssolve (const ComplexMatrix& b) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b);
+}
+
+ComplexMatrix
+Matrix::lssolve (const ComplexMatrix& b, int& info) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b);
+}
+
+ComplexMatrix
+Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b);
+}
+
+ColumnVector
+Matrix::lssolve (const ColumnVector& b) const
+{
+  int info;
+  int rank; return lssolve (b, info, rank);
+}
+
+ColumnVector
+Matrix::lssolve (const ColumnVector& b, int& info) const
+{
+  int rank;
+  return lssolve (b, info, rank);
+}
+
+ColumnVector
+Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const
+{
+  int nrhs = 1;
+
+  int m = rows ();
+  int n = cols ();
+
+  if (m == 0 || n == 0 || m != b.length ())
+    {
+      (*current_liboctave_error_handler)
+	("matrix dimension mismatch in solution of least squares problem");
+      return ColumnVector ();
+    }
+
+  double *tmp_data = dup (data (), length ());
+
+  int nrr = m > n ? m : n;
+  ColumnVector result (nrr);
+
+  int i;
+  for (i = 0; i < m; i++)
+    result.elem (i) = b.elem (i);
+
+  double *presult = result.fortran_vec ();
+
+  int len_s = m < n ? m : n;
+  double *s = new double [len_s];
+  double rcond = -1.0;
+  int lwork;
+  if (m < n)
+    lwork = 3*m + (2*m > nrhs ? (2*m > n ? 2*m : n) : (nrhs > n ? nrhs : n));
+  else
+    lwork = 3*n + (2*n > nrhs ? (2*n > m ? 2*n : m) : (nrhs > m ? nrhs : m));
+
+  double *work = new double [lwork];
+
+  F77_FCN (dgelss) (&m, &n, &nrhs, tmp_data, &m, presult, &nrr, s,
+		    &rcond, &rank, work, &lwork, &info);
+
+  ColumnVector retval (n);
+  for (i = 0; i < n; i++)
+    retval.elem (i) = result.elem (i);
+
+  delete [] tmp_data;
+  delete [] s;
+  delete [] work;
+
+  return retval;
+}
+
+ComplexColumnVector
+Matrix::lssolve (const ComplexColumnVector& b) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b);
+}
+
+ComplexColumnVector
+Matrix::lssolve (const ComplexColumnVector& b, int& info) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b, info);
+}
+
+ComplexColumnVector
+Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const
+{
+  ComplexMatrix tmp (*this);
+  return tmp.lssolve (b, info, rank);
+}
+
+Matrix&
+Matrix::operator += (const Matrix& a)
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix += operation attempted");
+      return *this;
+    }
+
+  if (nr == 0 || nc == 0)
+    return *this;
+
+  double *d = fortran_vec (); // Ensures only one reference to my privates!
+
+  add2 (d, a.data (), length ());
+
+  return *this;
+}
+
+Matrix&
+Matrix::operator -= (const Matrix& a)
+{
+  int nr = rows ();
+  int nc = cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix -= operation attempted");
+      return *this;
+    }
+
+  if (nr == 0 || nc == 0)
+    return *this;
+
+  double *d = fortran_vec (); // Ensures only one reference to my privates!
+
+  subtract2 (d, a.data (), length ());
+
+  return *this;
+}
+
+Matrix&
+Matrix::operator += (const DiagMatrix& a)
+{
+  if (rows () != a.rows () || cols () != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix += operation attempted");
+      return *this;
+    }
+
+  for (int i = 0; i < a.length (); i++)
+    elem (i, i) += a.elem (i, i);
+
+  return *this;
+}
+
+Matrix&
+Matrix::operator -= (const DiagMatrix& a)
+{
+  if (rows () != a.rows () || cols () != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix += operation attempted");
+      return *this;
+    }
+
+  for (int i = 0; i < a.length (); i++)
+    elem (i, i) -= a.elem (i, i);
+
+  return *this;
+}
+
+// unary operations
+
+Matrix
+Matrix::operator ! (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+
+  Matrix b (nr, nc);
+
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      b.elem (i, j) = ! elem (i, j);
+
+  return b;
+}
+
+// matrix by scalar -> matrix operations.
+
+ComplexMatrix
+operator + (const Matrix& a, const Complex& s)
+{
+  return ComplexMatrix (add (a.data (), a.length (), s),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator - (const Matrix& a, const Complex& s)
+{
+  return ComplexMatrix (subtract (a.data (), a.length (), s),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator * (const Matrix& a, const Complex& s)
+{
+  return ComplexMatrix (multiply (a.data (), a.length (), s),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator / (const Matrix& a, const Complex& s)
+{
+  return ComplexMatrix (divide (a.data (), a.length (), s),
+			a.rows (), a.cols ());
+}
+
+// scalar by matrix -> matrix operations.
+
+ComplexMatrix
+operator + (const Complex& s, const Matrix& a)
+{
+  return ComplexMatrix (add (s, a.data (), a.length ()),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator - (const Complex& s, const Matrix& a)
+{
+  return ComplexMatrix (subtract (s, a.data (), a.length ()),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator * (const Complex& s, const Matrix& a)
+{
+  return ComplexMatrix (multiply (a.data (), a.length (), s),
+			a.rows (), a.cols ());
+}
+
+ComplexMatrix
+operator / (const Complex& s, const Matrix& a)
+{
+  return ComplexMatrix (divide (s, a.data (), a.length ()),
+			a.rows (), a.cols ());
+}
+
+// matrix by column vector -> column vector operations
+
+ColumnVector
+operator * (const Matrix& m, const ColumnVector& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nc != a.length ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix multiplication attempted");
+      return ColumnVector ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ColumnVector (0);
+
+  char trans = 'N';
+  int ld = nr;
+  double alpha = 1.0;
+  double beta  = 0.0;
+  int i_one = 1;
+
+  double *y = new double [nr];
+
+  F77_FCN (dgemv) (&trans, &nr, &nc, &alpha, m.data (), &ld, a.data (),
+		   &i_one, &beta, y, &i_one, 1L); 
+
+  return ColumnVector (y, nr);
+}
+
+ComplexColumnVector
+operator * (const Matrix& m, const ComplexColumnVector& a)
+{
+  ComplexMatrix tmp (m);
+  return tmp * a;
+}
+
+// matrix by diagonal matrix -> matrix operations
+
+Matrix
+operator + (const Matrix& m, const DiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix addition attempted");
+      return Matrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return Matrix (nr, nc);
+
+  Matrix result (m);
+  int a_len = a.length ();
+  for (int i = 0; i < a_len; i++)
+    result.elem (i, i) += a.elem (i, i);
+
+  return result;
+}
+
+Matrix
+operator - (const Matrix& m, const DiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix subtraction attempted");
+      return Matrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return Matrix (nr, nc);
+
+  Matrix result (m);
+  int a_len = a.length ();
+  for (int i = 0; i < a_len; i++)
+    result.elem (i, i) -= a.elem (i, i);
+
+  return result;
+}
+
+Matrix
+operator * (const Matrix& m, const DiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  int a_nr = a.rows ();
+  int a_nc = a.cols ();
+  if (nc != a_nr)
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix multiplication attempted");
+      return Matrix ();
+    }
+
+  if (nr == 0 || nc == 0 || a_nc == 0)
+    return Matrix (nr, a_nc, 0.0);
+
+  double *c = new double [nr*a_nc];
+  double *ctmp = (double *) NULL;
+
+  int a_len = a.length ();
+  for (int j = 0; j < a_len; j++)
+    {
+      int idx = j * nr;
+      ctmp = c + idx;
+      if (a.elem (j, j) == 1.0)
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = m.elem (i, j);
+	}
+      else if (a.elem (j, j) == 0.0)
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = 0.0;
+	}
+      else
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = a.elem (j, j) * m.elem (i, j);
+	}
+    }
+
+  if (a_nr < a_nc)
+    {
+      for (int i = nr * nc; i < nr * a_nc; i++)
+	ctmp[i] = 0.0;
+    }
+
+  return Matrix (c, nr, a_nc);
+}
+
+ComplexMatrix
+operator + (const Matrix& m, const ComplexDiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix addition attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ComplexMatrix (nr, nc);
+
+  ComplexMatrix result (m);
+  for (int i = 0; i < a.length (); i++)
+    result.elem (i, i) += a.elem (i, i);
+
+  return result;
+}
+
+ComplexMatrix
+operator - (const Matrix& m, const ComplexDiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix subtraction attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ComplexMatrix (nr, nc);
+
+  ComplexMatrix result (m);
+  for (int i = 0; i < a.length (); i++)
+    result.elem (i, i) -= a.elem (i, i);
+
+  return result;
+}
+
+ComplexMatrix
+operator * (const Matrix& m, const ComplexDiagMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  int a_nr = a.rows ();
+  int a_nc = a.cols ();
+  if (nc != a_nr)
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix multiplication attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0 || a_nc == 0)
+    return ComplexMatrix (nr, a_nc, 0.0);
+
+  Complex *c = new Complex [nr*a_nc];
+  Complex *ctmp = (Complex *) NULL;
+
+  for (int j = 0; j < a.length (); j++)
+    {
+      int idx = j * nr;
+      ctmp = c + idx;
+      if (a.elem (j, j) == 1.0)
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = m.elem (i, j);
+	}
+      else if (a.elem (j, j) == 0.0)
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = 0.0;
+	}
+      else
+	{
+	  for (int i = 0; i < nr; i++)
+	    ctmp[i] = a.elem (j, j) * m.elem (i, j);
+	}
+    }
+
+  if (a_nr < a_nc)
+    {
+      for (int i = nr * nc; i < nr * a_nc; i++)
+	ctmp[i] = 0.0;
+    }
+
+  return ComplexMatrix (c, nr, a_nc);
+}
+
+// matrix by matrix -> matrix operations
+
+Matrix
+operator * (const Matrix& m, const Matrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  int a_nr = a.rows ();
+  int a_nc = a.cols ();
+  if (nc != a_nr)
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix multiplication attempted");
+      return Matrix ();
+    }
+
+  if (nr == 0 || nc == 0 || a_nc == 0)
+    return Matrix (nr, a_nc, 0.0);
+
+  char trans  = 'N';
+  char transa = 'N';
+
+  int ld  = nr;
+  int lda = a_nr;
+
+  double alpha = 1.0;
+  double beta  = 0.0;
+
+  double *c = new double [nr*a_nc];
+
+  F77_FCN (dgemm) (&trans, &transa, &nr, &a_nc, &nc, &alpha, m.data (),
+		   &ld, a.data (), &lda, &beta, c, &nr, 1L, 1L);
+
+  return Matrix (c, nr, a_nc);
+}
+
+ComplexMatrix
+operator * (const Matrix& m, const ComplexMatrix& a)
+{
+  ComplexMatrix tmp (m);
+  return tmp * a;
+}
+
+ComplexMatrix
+operator + (const Matrix& m, const ComplexMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix addition attempted");
+      return ComplexMatrix ();
+    }
+
+  return ComplexMatrix (add (m.data (), a.data (), m.length ()), nr, nc);
+}
+
+ComplexMatrix
+operator - (const Matrix& m, const ComplexMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix subtraction attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ComplexMatrix (nr, nc);
+
+  return ComplexMatrix (subtract (m.data (), a.data (), m.length ()), nr, nc);
+}
+
+ComplexMatrix
+product (const Matrix& m, const ComplexMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix product attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ComplexMatrix (nr, nc);
+
+  return ComplexMatrix (multiply (m.data (), a.data (), m.length ()), nr, nc);
+}
+
+ComplexMatrix
+quotient (const Matrix& m, const ComplexMatrix& a)
+{
+  int nr = m.rows ();
+  int nc = m.cols ();
+  if (nr != a.rows () || nc != a.cols ())
+    {
+      (*current_liboctave_error_handler)
+	("nonconformant matrix quotient attempted");
+      return ComplexMatrix ();
+    }
+
+  if (nr == 0 || nc == 0)
+    return ComplexMatrix (nr, nc);
+
+  return ComplexMatrix (divide (m.data (), a.data (), m.length ()), nr, nc);
+}
+
+// other operations.
+
+Matrix
+map (d_d_Mapper f, const Matrix& a)
+{
+  Matrix b (a);
+  b.map (f);
+  return b;
+}
+
+void
+Matrix::map (d_d_Mapper f)
+{
+  double *d = fortran_vec (); // Ensures only one reference to my privates!
+
+  for (int i = 0; i < length (); i++)
+    d[i] = f (d[i]);
+}
+
+// XXX FIXME XXX Do these really belong here?  They should maybe be
+// cleaned up a bit, no?  What about corresponding functions for the
+// Vectors?
+
+Matrix
+Matrix::all (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  Matrix retval;
+  if (nr > 0 && nc > 0)
+    {
+      if (nr == 1)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 1.0;
+	  for (int j = 0; j < nc; j++)
+	    {
+	      if (elem (0, j) == 0.0)
+		{
+		  retval.elem (0, 0) = 0.0;
+		  break;
+		}
+	    }
+	}
+      else if (nc == 1)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 1.0;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      if (elem (i, 0) == 0.0)
+		{
+		  retval.elem (0, 0) = 0.0;
+		  break;
+		}
+	    }
+	}
+      else
+	{
+	  retval.resize (1, nc);
+	  for (int j = 0; j < nc; j++)
+	    {
+	      retval.elem (0, j) = 1.0;
+	      for (int i = 0; i < nr; i++)
+		{
+		  if (elem (i, j) == 0.0)
+		    {
+		      retval.elem (0, j) = 0.0;
+		      break;
+		    }
+		}
+	    }
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::any (void) const
+{
+  int nr = rows ();
+  int nc = cols ();
+  Matrix retval;
+  if (nr > 0 && nc > 0)
+    {
+      if (nr == 1)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 0.0;
+	  for (int j = 0; j < nc; j++)
+	    {
+	      if (elem (0, j) != 0.0)
+		{
+		  retval.elem (0, 0) = 1.0;
+		  break;
+		}
+	    }
+	}
+      else if (nc == 1)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 0.0;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      if (elem (i, 0) != 0.0)
+		{
+		  retval.elem (0, 0) = 1.0;
+		  break;
+		}
+	    }
+	}
+      else
+	{
+	  retval.resize (1, nc);
+	  for (int j = 0; j < nc; j++)
+	    {
+	      retval.elem (0, j) = 0.0;
+	      for (int i = 0; i < nr; i++)
+		{
+		  if (elem (i, j) != 0.0)
+		    {
+		      retval.elem (0, j) = 1.0;
+		      break;
+		    }
+		}
+	    }
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::cumprod (void) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 1)
+    {
+      retval.resize (1, nc);
+      if (nc > 0)
+	{
+	  double prod = elem (0, 0);
+	  for (int j = 0; j < nc; j++)
+	    {
+	      retval.elem (0, j) = prod;
+	      if (j < nc - 1)
+		prod *= elem (0, j+1);
+	    }
+	}
+    }
+  else if (nc == 1)
+    {
+      retval.resize (nr, 1);
+      if (nr > 0)
+	{
+	  double prod = elem (0, 0);
+	  for (int i = 0; i < nr; i++)
+	    {
+	      retval.elem (i, 0) = prod;
+	      if (i < nr - 1)
+		prod *= elem (i+1, 0);
+	    }
+	}
+    }
+  else
+    {
+      retval.resize (nr, nc);
+      if (nr > 0 && nc > 0)
+	{
+	  for (int j = 0; j < nc; j++)
+	    {
+	      double prod = elem (0, j);
+	      for (int i = 0; i < nr; i++)
+		{
+		  retval.elem (i, j) = prod;
+		  if (i < nr - 1)
+		    prod *= elem (i+1, j);
+		}
+	    }
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::cumsum (void) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 1)
+    {
+      retval.resize (1, nc);
+      if (nc > 0)
+	{
+	  double sum = elem (0, 0);
+	  for (int j = 0; j < nc; j++)
+	    {
+	      retval.elem (0, j) = sum;
+	      if (j < nc - 1)
+		sum += elem (0, j+1);
+	    }
+	}
+    }
+  else if (nc == 1)
+    {
+      retval.resize (nr, 1);
+      if (nr > 0)
+	{
+	  double sum = elem (0, 0);
+	  for (int i = 0; i < nr; i++)
+	    {
+	      retval.elem (i, 0) = sum;
+	      if (i < nr - 1)
+		sum += elem (i+1, 0);
+	    }
+	}
+    }
+  else
+    {
+      retval.resize (nr, nc);
+      if (nr > 0 && nc > 0)
+	{
+	  for (int j = 0; j < nc; j++)
+	    {
+	      double sum = elem (0, j);
+	      for (int i = 0; i < nr; i++)
+		{
+		  retval.elem (i, j) = sum;
+		  if (i < nr - 1)
+		    sum += elem (i+1, j);
+		}
+	    }
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::prod (void) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 1.0;
+      for (int j = 0; j < nc; j++)
+	retval.elem (0, 0) *= elem (0, j);
+    }
+  else if (nc == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 1.0;
+      for (int i = 0; i < nr; i++)
+	retval.elem (0, 0) *= elem (i, 0);
+    }
+  else
+    {
+      if (nc == 0)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 1.0;
+	}
+      else
+	retval.resize (1, nc);
+
+      for (int j = 0; j < nc; j++)
+	{
+	  retval.elem (0, j) = 1.0;
+	  for (int i = 0; i < nr; i++)
+	    retval.elem (0, j) *= elem (i, j);
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::sum (void) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 0.0;
+      for (int j = 0; j < nc; j++)
+	retval.elem (0, 0) += elem (0, j);
+    }
+  else if (nc == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 0.0;
+      for (int i = 0; i < nr; i++)
+	retval.elem (0, 0) += elem (i, 0);
+    }
+  else
+    {
+      if (nc == 0)
+	{
+	  retval.resize (1, 1);
+	  retval.elem (0, 0) = 0.0;
+	}
+      else
+	retval.resize (1, nc);
+
+      for (int j = 0; j < nc; j++)
+	{
+	  retval.elem (0, j) = 0.0;
+	  for (int i = 0; i < nr; i++)
+	    retval.elem (0, j) += elem (i, j);
+	}
+    }
+  return retval;
+}
+
+Matrix
+Matrix::sumsq (void) const
+{
+  Matrix retval;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 0.0;
+      for (int j = 0; j < nc; j++)
+	{
+	  double d = elem (0, j);
+	  retval.elem (0, 0) += d * d;
+	}
+    }
+  else if (nc == 1)
+    {
+      retval.resize (1, 1);
+      retval.elem (0, 0) = 0.0;
+      for (int i = 0; i < nr; i++)
+	{
+	  double d = elem (i, 0);
+	  retval.elem (0, 0) += d * d;
+	}
+    }
+  else
+    {
+      retval.resize (1, nc);
+      for (int j = 0; j < nc; j++)
+	{
+	  retval.elem (0, j) = 0.0;
+	  for (int i = 0; i < nr; i++)
+	    {
+	      double d = elem (i, j);
+	      retval.elem (0, j) += d * d;
+	    }
+	}
+    }
+  return retval;
+}
+
+ColumnVector
+Matrix::diag (void) const
+{
+  return diag (0);
+}
+
+ColumnVector
+Matrix::diag (int k) const
+{
+  int nnr = rows ();
+  int nnc = cols ();
+  if (k > 0)
+    nnc -= k;
+  else if (k < 0)
+    nnr += k;
+
+  ColumnVector d;
+
+  if (nnr > 0 && nnc > 0)
+    {
+      int ndiag = (nnr < nnc) ? nnr : nnc;
+
+      d.resize (ndiag);
+
+      if (k > 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    d.elem (i) = elem (i, i+k);
+	}
+      else if ( k < 0)
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    d.elem (i) = elem (i-k, i);
+	}
+      else
+	{
+	  for (int i = 0; i < ndiag; i++)
+	    d.elem (i) = elem (i, i);
+	}
+    }
+  else
+    cerr << "diag: requested diagonal out of range\n";
+
+  return d;
+}
+
+ColumnVector
+Matrix::row_min (void) const
+{
+  ColumnVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nr);
+
+      for (int i = 0; i < nr; i++)
+	{
+	  double res = elem (i, 0);
+	  for (int j = 1; j < nc; j++)
+	    if (elem (i, j) < res)
+	      res = elem (i, j);
+	  result.elem (i) = res;
+	}
+    }
+
+  return result;
+}
+
+ColumnVector
+Matrix::row_min_loc (void) const
+{
+  ColumnVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nr);
+
+      for (int i = 0; i < nr; i++)
+        {
+          int res = 0;
+          for (int j = 0; j < nc; j++)
+            if (elem (i, j) < elem (i, res))
+              res = j;
+          result.elem (i) = (double) (res + 1);
+        }
+    }
+
+  return result;
+}
+
+ColumnVector
+Matrix::row_max (void) const
+{
+  ColumnVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nr);
+
+      for (int i = 0; i < nr; i++)
+	{
+	  double res = elem (i, 0);
+	  for (int j = 1; j < nc; j++)
+	    if (elem (i, j) > res)
+	      res = elem (i, j);
+	  result.elem (i) = res;
+	}
+    }
+
+  return result;
+}
+
+ColumnVector
+Matrix::row_max_loc (void) const
+{
+  ColumnVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nr);
+
+      for (int i = 0; i < nr; i++)
+        {
+          int res = 0;
+          for (int j = 0; j < nc; j++)
+            if (elem (i, j) > elem (i, res))
+              res = j;
+          result.elem (i) = (double) (res + 1);
+        }
+    }
+
+  return result;
+}
+
+RowVector
+Matrix::column_min (void) const
+{
+  RowVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nc);
+
+      for (int j = 0; j < nc; j++)
+	{
+	  double res = elem (0, j);
+	  for (int i = 1; i < nr; i++)
+	    if (elem (i, j) < res)
+	      res = elem (i, j);
+	  result.elem (j) = res;
+	}
+    }
+
+  return result;
+}
+RowVector
+Matrix::column_min_loc (void) const
+{
+  RowVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nc);
+
+      for (int j = 0; j < nc; j++)
+        {
+          int res = 0;
+          for (int i = 0; i < nr; i++)
+            if (elem (i, j) < elem (res, j))
+              res = i;
+          result.elem (j) = (double) (res + 1);
+        }
+    }
+
+  return result;
+}
+
+
+RowVector
+Matrix::column_max (void) const
+{
+  RowVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nc);
+
+      for (int j = 0; j < nc; j++)
+	{
+	  double res = elem (0, j);
+	  for (int i = 1; i < nr; i++)
+	    if (elem (i, j) > res)
+	      res = elem (i, j);
+	  result.elem (j) = res;
+	}
+    }
+
+  return result;
+}
+
+RowVector
+Matrix::column_max_loc (void) const
+{
+  RowVector result;
+
+  int nr = rows ();
+  int nc = cols ();
+
+  if (nr > 0 && nc > 0)
+    {
+      result.resize (nc);
+
+      for (int j = 0; j < nc; j++)
+        {
+          int res = 0;
+          for (int i = 0; i < nr; i++)
+            if (elem (i, j) > elem (res, j))
+              res = i;
+          result.elem (j) = (double) (res + 1);
+        }
+    }
+
+  return result;
+}
+
+ostream&
+operator << (ostream& os, const Matrix& a)
+{
+//  int field_width = os.precision () + 7;
+  for (int i = 0; i < a.rows (); i++)
+    {
+      for (int j = 0; j < a.cols (); j++)
+	os << " " /* setw (field_width) */ << a.elem (i, j);
+      os << "\n";
+    }
+  return os;
+}
+
+istream&
+operator >> (istream& is, Matrix& a)
+{
+  int nr = a.rows ();
+  int nc = a.cols ();
+
+  if (nr < 1 || nc < 1)
+    is.clear (ios::badbit);
+  else
+    {
+      double tmp;
+      for (int i = 0; i < nr; i++)
+	for (int j = 0; j < nc; j++)
+	  {
+	    is >> tmp;
+	    if (is)
+	      a.elem (i, j) = tmp;
+	    else
+	      break;
+	  }
+    }
+
+  return is;
+}
+
+/*
+ * Read an array of data froma file in binary format.
+ */
+int
+Matrix::read (FILE *fptr, int size, Matrix::conversion conv)
+{
+// Allocate buffer pointers.
+
+  union
+    {
+      void *vd;
+      char *ch;
+      u_char *uc;
+//    s_char *sc; // Some systems may need this?
+      short *sh;
+      u_short *us;
+      int *in;
+      u_int *ui;
+      long *ln;
+      u_long *ul;
+      float *fl;
+      double *db;
+    }
+  buf;
+
+  buf.db = fortran_vec ();
+
+// Read data directly into matrix data array.
+
+  int count = fread (buf.ch, size, length (), fptr);
+
+// Convert data to double.
+
+  int k;
+
+  switch (conv)
+    {
+    case CNV_DOUBLE:
+      break;
+
+    case CNV_CHAR:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.ch[k];
+      break;
+
+    case CNV_UCHAR:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.uc[k];
+      break;
+
+// Some systems may need this??
+//    case CNV_SCHAR:
+//      for (k = count - 1; k > -1; k--)
+//	buf.db[k] = buf.sc[k];
+//      break;
+
+    case CNV_SHORT:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.sh[k];
+      break;
+
+    case CNV_USHORT:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.us[k];
+      break;
+
+    case CNV_INT:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.in[k];
+      break;
+
+    case CNV_UINT:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.ui[k];
+      break;
+
+    case CNV_LONG:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.ln[k];
+      break;
+
+    case CNV_ULONG:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.ul[k];
+      break;
+
+    case CNV_FLOAT:
+      for (k = count - 1; k > -1; k--)
+	buf.db[k] = buf.fl[k];
+      break;
+
+    default:
+      return 0;
+    }
+
+  return count;
+}
+
+/*
+ * Write the data array to a file in binary format.
+ */
+int
+Matrix::write (FILE *fptr, int size, Matrix::conversion conv)
+{
+// Allocate buffer pointers.
+
+  union
+    {
+      void *vd;
+      char *ch;
+      u_char *uc;
+//    s_char *sc; // Some systems may need this?
+      short *sh;
+      u_short *us;
+      int *in;
+      u_int *ui;
+      long *ln;
+      u_long *ul;
+      float *fl;
+      double *db;
+    }
+  buf;
+
+  int len = length ();
+
+  if (conv != CNV_DOUBLE)
+    buf.db = new double [len];
+
+  double *bufi = fortran_vec ();
+
+// Convert from double to correct size.
+
+  int k;
+
+  switch (conv)
+    {
+    case CNV_DOUBLE:
+      buf.db = bufi;
+      break;
+
+    case CNV_CHAR:
+      for (k = 0; k < len; k++)
+	buf.ch[k] = (char) bufi[k];
+      break;
+
+    case CNV_UCHAR:
+      for (k = 0; k < len; k++)
+	buf.uc[k] = (u_char) bufi[k];
+      break;
+
+// Some systems may need this?
+//    case CNV_SCHAR:
+//      for (k = 0; k < len; k++)
+//	buf.uc[k] = (s_char) bufi[k];
+//      break;
+
+    case CNV_SHORT:
+      for (k = 0; k < len; k++)
+	buf.sh[k] = (short) bufi[k];
+      break;
+
+    case CNV_USHORT:
+      for (k = 0; k < len; k++)
+	buf.us[k] = (u_short) bufi[k];
+      break;
+
+    case CNV_INT:
+      for (k = 0; k < len; k++)
+	buf.in[k] = (int) bufi[k];
+      break;
+
+    case CNV_UINT:
+      for (k = 0; k < len; k++)
+	buf.ui[k] = (u_int) bufi[k];
+      break;
+
+    case CNV_LONG:
+      for (k = 0; k < len; k++)
+	buf.ln[k] = (long) bufi[k];
+      break;
+
+    case CNV_ULONG:
+      for (k = 0; k < len; k++)
+	buf.ul[k] = (u_long) bufi[k];
+      break;
+
+    case CNV_FLOAT:
+      for (k = 0; k < len; k++)
+	buf.fl[k] = (float) bufi[k];
+      break;
+
+    default:
+      return 0;
+  }
+
+// Write data from converted matrix data array.
+
+  int count = fwrite (buf.ch, size, length (), fptr);
+
+  if (conv != CNV_DOUBLE)
+    delete [] buf.db;
+
+  return count;
+}
+
+/*
+;;; Local Variables: ***
+;;; mode: C++ ***
+;;; page-delimiter: "^/\\*" ***
+;;; End: ***
+*/