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snapshot 3.3.54
author John W. Eaton <jwe@octave.org>
date Fri, 19 Nov 2010 16:05:58 -0500
parents 231946a9ad55
children fd0a3ac60b0e
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/*

Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 2000, 2002, 2003,
              2004, 2005, 2006, 2007, 2008 John W. Eaton
Copyright (C) 2009, 2010 VZLU Prague

This file is part of Octave.

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

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

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

*/

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

#include <cassert>
#include <climits>

#include "Array-util.h"
#include "CColVector.h"
#include "CDiagMatrix.h"
#include "fCDiagMatrix.h"
#include "CMatrix.h"
#include "EIG.h"
#include "fEIG.h"
#include "dDiagMatrix.h"
#include "fDiagMatrix.h"
#include "dMatrix.h"
#include "PermMatrix.h"
#include "mx-cm-cdm.h"
#include "oct-cmplx.h"
#include "Range.h"
#include "quit.h"

#include "error.h"
#include "oct-obj.h"
#include "utils.h"
#include "xpow.h"

#ifdef _OPENMP
#include <omp.h>
#endif

static inline int
xisint (double x)
{
  return (D_NINT (x) == x
          && ((x >= 0 && x < INT_MAX)
              || (x <= 0 && x > INT_MIN)));
}

// Safer pow functions.
//
//       op2 \ op1:   s   m   cs   cm
//            +--   +---+---+----+----+
//   scalar   |     | 1 | 5 |  7 | 11 |
//                  +---+---+----+----+
//   matrix         | 2 | * |  8 |  * |
//                  +---+---+----+----+
//   complex_scalar | 3 | 6 |  9 | 12 |
//                  +---+---+----+----+
//   complex_matrix | 4 | * | 10 |  * |
//                  +---+---+----+----+

// -*- 1 -*-
octave_value
xpow (double a, double b)
{
  double retval;

  if (a < 0.0 && ! xisint (b))
    {
      Complex atmp (a);

      return std::pow (atmp, b);
    }
  else
    retval = std::pow (a, b);

  return retval;
}

// -*- 2 -*-
octave_value
xpow (double a, const Matrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      EIG b_eig (b);

      if (! error_state)
        {
          ComplexColumnVector lambda (b_eig.eigenvalues ());
          ComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              Complex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          ComplexDiagMatrix D (lambda);

          ComplexMatrix C = Q * D * Q.inverse ();
          if (a > 0)
            retval = real (C);
          else
            retval = C;
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 3 -*-
octave_value
xpow (double a, const Complex& b)
{
  Complex result = std::pow (a, b);
  return result;
}

// -*- 4 -*-
octave_value
xpow (double a, const ComplexMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      EIG b_eig (b);

      if (! error_state)
        {
          ComplexColumnVector lambda (b_eig.eigenvalues ());
          ComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              Complex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          ComplexDiagMatrix D (lambda);

          retval = ComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 5 -*-
octave_value
xpow (const Matrix& a, double b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          int btmp = static_cast<int> (b);
          if (btmp == 0)
            {
              retval = DiagMatrix (nr, nr, 1.0);
            }
          else
            {
              // Too much copying?
              // FIXME -- we shouldn't do this if the exponent is
              // large...

              Matrix atmp;
              if (btmp < 0)
                {
                  btmp = -btmp;

                  octave_idx_type info;
                  double rcond = 0.0;
                  MatrixType mattype (a);

                  atmp = a.inverse (mattype, info, rcond, 1);

                  if (info == -1)
                    warning ("inverse: matrix singular to machine\
 precision, rcond = %g", rcond);
                }
              else
                atmp = a;

              Matrix result (atmp);

              btmp--;

              while (btmp > 0)
                {
                  if (btmp & 1)
                    result = result * atmp;

                  btmp >>= 1;

                  if (btmp > 0)
                    atmp = atmp * atmp;
                }

              retval = result;
            }
        }
      else
        {
          EIG a_eig (a);

          if (! error_state)
            {
              ComplexColumnVector lambda (a_eig.eigenvalues ());
              ComplexMatrix Q (a_eig.eigenvectors ());

              for (octave_idx_type i = 0; i < nr; i++)
                lambda(i) = std::pow (lambda(i), b);

              ComplexDiagMatrix D (lambda);

              retval = ComplexMatrix (Q * D * Q.inverse ());
            }
          else
            error ("xpow: matrix diagonalization failed");
        }
    }

  return retval;
}

// -*- 5d -*-
octave_value
xpow (const DiagMatrix& a, double b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          DiagMatrix r (nr, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            r.dgelem (i) = std::pow (a.dgelem (i), b);
          retval = r;
        }
      else
        {
          ComplexDiagMatrix r (nr, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            r.dgelem (i) = std::pow (static_cast<Complex> (a.dgelem (i)), b);
          retval = r;
        }
    }

  return retval;
}

// -*- 5p -*-
octave_value
xpow (const PermMatrix& a, double b)
{
  octave_value retval;
  int btmp = static_cast<int> (b);
  if (btmp == b)
    return a.power (btmp);
  else
    return xpow (Matrix (a), b);
}

// -*- 6 -*-
octave_value
xpow (const Matrix& a, const Complex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      EIG a_eig (a);

      if (! error_state)
        {
          ComplexColumnVector lambda (a_eig.eigenvalues ());
          ComplexMatrix Q (a_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            lambda(i) = std::pow (lambda(i), b);

          ComplexDiagMatrix D (lambda);

          retval = ComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 7 -*-
octave_value
xpow (const Complex& a, double b)
{
  Complex result;

  if (xisint (b))
    result = std::pow (a, static_cast<int> (b));
  else
    result = std::pow (a, b);

  return result;
}

// -*- 8 -*-
octave_value
xpow (const Complex& a, const Matrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      EIG b_eig (b);

      if (! error_state)
        {
          ComplexColumnVector lambda (b_eig.eigenvalues ());
          ComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              Complex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          ComplexDiagMatrix D (lambda);

          retval = ComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 9 -*-
octave_value
xpow (const Complex& a, const Complex& b)
{
  Complex result;
  result = std::pow (a, b);
  return result;
}

// -*- 10 -*-
octave_value
xpow (const Complex& a, const ComplexMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      EIG b_eig (b);

      if (! error_state)
        {
          ComplexColumnVector lambda (b_eig.eigenvalues ());
          ComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              Complex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          ComplexDiagMatrix D (lambda);

          retval = ComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 11 -*-
octave_value
xpow (const ComplexMatrix& a, double b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          int btmp = static_cast<int> (b);
          if (btmp == 0)
            {
              retval = DiagMatrix (nr, nr, 1.0);
            }
          else
            {
              // Too much copying?
              // FIXME -- we shouldn't do this if the exponent is
              // large...

              ComplexMatrix atmp;
              if (btmp < 0)
                {
                  btmp = -btmp;

                  octave_idx_type info;
                  double rcond = 0.0;
                  MatrixType mattype (a);

                  atmp = a.inverse (mattype, info, rcond, 1);

                  if (info == -1)
                    warning ("inverse: matrix singular to machine\
 precision, rcond = %g", rcond);
                }
              else
                atmp = a;

              ComplexMatrix result (atmp);

              btmp--;

              while (btmp > 0)
                {
                  if (btmp & 1)
                    result = result * atmp;

                  btmp >>= 1;

                  if (btmp > 0)
                    atmp = atmp * atmp;
                }

              retval = result;
            }
        }
      else
        {
          EIG a_eig (a);

          if (! error_state)
            {
              ComplexColumnVector lambda (a_eig.eigenvalues ());
              ComplexMatrix Q (a_eig.eigenvectors ());

              for (octave_idx_type i = 0; i < nr; i++)
                lambda(i) = std::pow (lambda(i), b);

              ComplexDiagMatrix D (lambda);

              retval = ComplexMatrix (Q * D * Q.inverse ());
            }
          else
            error ("xpow: matrix diagonalization failed");
        }
    }

  return retval;
}

// -*- 12 -*-
octave_value
xpow (const ComplexMatrix& a, const Complex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      EIG a_eig (a);

      if (! error_state)
        {
          ComplexColumnVector lambda (a_eig.eigenvalues ());
          ComplexMatrix Q (a_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            lambda(i) = std::pow (lambda(i), b);

          ComplexDiagMatrix D (lambda);

          retval = ComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 12d -*-
octave_value
xpow (const ComplexDiagMatrix& a, const Complex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      ComplexDiagMatrix r (nr, nc);
      for (octave_idx_type i = 0; i < nc; i++)
        r(i, i) = std::pow (a(i, i), b);
      retval = r;
    }

  return retval;
}

// mixed
octave_value
xpow (const ComplexDiagMatrix& a, double b)
{
  return xpow (a, static_cast<Complex> (b));
}

octave_value
xpow (const DiagMatrix& a, const Complex& b)
{
  return xpow (ComplexDiagMatrix (a), b);
}


// Safer pow functions that work elementwise for matrices.
//
//       op2 \ op1:   s   m   cs   cm
//            +--   +---+---+----+----+
//   scalar   |     | * | 3 |  * |  9 |
//                  +---+---+----+----+
//   matrix         | 1 | 4 |  7 | 10 |
//                  +---+---+----+----+
//   complex_scalar | * | 5 |  * | 11 |
//                  +---+---+----+----+
//   complex_matrix | 2 | 6 |  8 | 12 |
//                  +---+---+----+----+
//
//   * -> not needed.

// FIXME -- these functions need to be fixed so that things
// like
//
//   a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b
//
// and
//
//   a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end
//
// produce identical results.  Also, it would be nice if -1^0.5
// produced a pure imaginary result instead of a complex number with a
// small real part.  But perhaps that's really a problem with the math
// library...

// -*- 1 -*-
octave_value
elem_xpow (double a, const Matrix& b)
{
  octave_value retval;

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

  double d1, d2;

  if (a < 0.0 && ! b.all_integers (d1, d2))
    {
      Complex atmp (a);
      ComplexMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (atmp, b (i, j));
          }

      retval = result;
    }
  else
    {
      Matrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a, b (i, j));
          }

      retval = result;
    }

  return retval;
}

// -*- 2 -*-
octave_value
elem_xpow (double a, const ComplexMatrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  ComplexMatrix result (nr, nc);
  Complex atmp (a);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (atmp, b (i, j));
      }

  return result;
}

static inline bool 
same_sign (double a, double b)
{
  return (a >= 0 && b >= 0) || (a <= 0 && b <= 0);
}

octave_value
elem_xpow (double a, const Range& r)
{
  octave_value retval;

  // Only optimize powers with ranges that are integer and monotonic in
  // magnitude.
  if (r.nelem () > 1 && r.all_elements_are_ints ()
      && same_sign (r.base (), r.limit ()))
    {
      octave_idx_type n = r.nelem ();
      Matrix result (1, n);
      if (same_sign (r.base (), r.inc ()))
        {
          double base = std::pow (a, r.base ());
          double inc = std::pow (a, r.inc ());
          result(0) = base;
          for (octave_idx_type i = 1; i < n; i++)
            result(i) = (base *= inc);
        }
      else
        {
          // Don't use Range::limit () here.
          double limit = std::pow (a, r.base () + (n-1) * r.inc ());
          double inc = std::pow (a, -r.inc ());
          result(n-1) = limit;
          for (octave_idx_type i = n-2; i >= 0; i--)
            result(i) = (limit *= inc);
        }

      retval = result;
    }  
  else
    retval = elem_xpow (a, r.matrix_value ());

  return retval;
}

// -*- 3 -*-
octave_value
elem_xpow (const Matrix& a, double b)
{
  octave_value retval;

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

  if (! xisint (b) && a.any_element_is_negative ())
    {
      ComplexMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit (); 
      
            Complex atmp (a (i, j));

            result (i, j) = std::pow (atmp, b);
          }

      retval = result;
    }
  else
    {
      Matrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b);
          }

      retval = result;
    }

  return retval;
}

// -*- 4 -*-
octave_value
elem_xpow (const Matrix& a, const Matrix& b)
{
  octave_value retval;

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

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  int convert_to_complex = 0;
  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        double atmp = a (i, j);
        double btmp = b (i, j);
        if (atmp < 0.0 && static_cast<int> (btmp) != btmp)
          {
            convert_to_complex = 1;
            goto done;
          }
      }

done:

  if (convert_to_complex)
    {
      ComplexMatrix complex_result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            Complex atmp (a (i, j));
            Complex btmp (b (i, j));
            complex_result (i, j) = std::pow (atmp, btmp);
          }

      retval = complex_result;
    }
  else
    {
      Matrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b (i, j));
          }

      retval = result;
    }

  return retval;
}

// -*- 5 -*-
octave_value
elem_xpow (const Matrix& a, const Complex& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (Complex (a (i, j)), b);
      }

  return result;
}

// -*- 6 -*-
octave_value
elem_xpow (const Matrix& a, const ComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (Complex (a (i, j)), b (i, j));
      }

  return result;
}

// -*- 7 -*-
octave_value
elem_xpow (const Complex& a, const Matrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        double btmp = b (i, j);
        if (xisint (btmp))
          result (i, j) = std::pow (a, static_cast<int> (btmp));
        else
          result (i, j) = std::pow (a, btmp);
      }

  return result;
}

// -*- 8 -*-
octave_value
elem_xpow (const Complex& a, const ComplexMatrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a, b (i, j));
      }

  return result;
}

octave_value
elem_xpow (const Complex& a, const Range& r)
{
  octave_value retval;

  // Only optimize powers with ranges that are integer and monotonic in
  // magnitude.
  if (r.nelem () > 1 && r.all_elements_are_ints ()
      && same_sign (r.base (), r.limit ()))
    {
      octave_idx_type n = r.nelem ();
      ComplexMatrix result (1, n);

      if (same_sign (r.base (), r.inc ()))
        {
          Complex base = std::pow (a, r.base ());
          Complex inc = std::pow (a, r.inc ());
          result(0) = base;
          for (octave_idx_type i = 1; i < n; i++)
            result(i) = (base *= inc);
        }
      else
        {
          // Don't use Range::limit () here.
          Complex limit = std::pow (a, r.base () + (n-1) * r.inc ());
          Complex inc = std::pow (a, -r.inc ());
          result(n-1) = limit;
          for (octave_idx_type i = n-2; i >= 0; i--)
            result(i) = (limit *= inc);
        }

      retval = result;
    }  
  else
    retval = elem_xpow (a, r.matrix_value ());


  return retval;
}

// -*- 9 -*-
octave_value
elem_xpow (const ComplexMatrix& a, double b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  ComplexMatrix result (nr, nc);

  if (xisint (b))
    {
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), static_cast<int> (b));
          }
    }
  else
    {
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b);
          }
    }

  return result;
}

// -*- 10 -*-
octave_value
elem_xpow (const ComplexMatrix& a, const Matrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        double btmp = b (i, j);
        if (xisint (btmp))
          result (i, j) = std::pow (a (i, j), static_cast<int> (btmp));
        else
          result (i, j) = std::pow (a (i, j), btmp);
      }

  return result;
}

// -*- 11 -*-
octave_value
elem_xpow (const ComplexMatrix& a, const Complex& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a (i, j), b);
      }

  return result;
}

// -*- 12 -*-
octave_value
elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  ComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a (i, j), b (i, j));
      }

  return result;
}

// Safer pow functions that work elementwise for N-d arrays.
//
//       op2 \ op1:   s   nd  cs   cnd
//            +--   +---+---+----+----+
//   scalar   |     | * | 3 |  * |  9 |
//                  +---+---+----+----+
//   N_d            | 1 | 4 |  7 | 10 |
//                  +---+---+----+----+
//   complex_scalar | * | 5 |  * | 11 |
//                  +---+---+----+----+
//   complex_N_d    | 2 | 6 |  8 | 12 |
//                  +---+---+----+----+
//
//   * -> not needed.

// FIXME -- these functions need to be fixed so that things
// like
//
//   a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b
//
// and
//
//   a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end
//
// produce identical results.  Also, it would be nice if -1^0.5
// produced a pure imaginary result instead of a complex number with a
// small real part.  But perhaps that's really a problem with the math
// library...

// -*- 1 -*-
octave_value
elem_xpow (double a, const NDArray& b)
{
  octave_value retval;

  if (a < 0.0 && ! b.all_integers ())
    {
      Complex atmp (a);
      ComplexNDArray result (b.dims ());
      for (octave_idx_type i = 0; i < b.length (); i++)
        {
          octave_quit ();
          result(i) = std::pow (atmp, b(i));
        }

      retval = result;
    }
  else
    {
      NDArray result (b.dims ());
      for (octave_idx_type i = 0; i < b.length (); i++)
        {
          octave_quit ();
          result (i) = std::pow (a, b(i));
        }

      retval = result;
    }

  return retval;
}

// -*- 2 -*-
octave_value
elem_xpow (double a, const ComplexNDArray& b)
{
  ComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a, b(i));
    }

  return result;
}

// -*- 3 -*-
octave_value
elem_xpow (const NDArray& a, double b)
{
  octave_value retval;

  if (! xisint (b))
    {
      if (a.any_element_is_negative ())
        {
          ComplexNDArray result (a.dims ());

          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();

              Complex atmp (a (i));

              result(i) = std::pow (atmp, b);
            }

          retval = result;
        }
      else
        {
          NDArray result (a.dims ());
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), b);
            }

          retval = result;
        }
    }
  else
    {
      NoAlias<NDArray> result (a.dims ());

      int ib = static_cast<int> (b);
      if (ib == 2)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = a(i) * a(i);
        }
      else if (ib == 3)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = a(i) * a(i) * a(i);
        }
      else if (ib == -1)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = 1.0 / a(i);
        }
      else
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), ib);
            }
        }

      retval = result;
    }

  return retval;
}

// -*- 4 -*-
octave_value
elem_xpow (const NDArray& a, const NDArray& b)
{
  octave_value retval;

  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  int len = a.length ();

  bool convert_to_complex = false;

  for (octave_idx_type i = 0; i < len; i++)
    {
      octave_quit ();
      double atmp = a(i);
      double btmp = b(i);
      if (atmp < 0.0 && static_cast<int> (btmp) != btmp)
        {
          convert_to_complex = true;
          goto done;
        }
    }

done:

  if (convert_to_complex)
    {
      ComplexNDArray complex_result (a_dims);

      for (octave_idx_type i = 0; i < len; i++)
        {
          octave_quit ();
          Complex atmp (a(i));
          complex_result(i) = std::pow (atmp, b(i));
        }

      retval = complex_result;
    }
  else
    {
      NDArray result (a_dims);

      for (octave_idx_type i = 0; i < len; i++)
        {
          octave_quit ();
          result(i) = std::pow (a(i), b(i));
        }

      retval = result;
    }

  return retval;
}

// -*- 5 -*-
octave_value
elem_xpow (const NDArray& a, const Complex& b)
{
  ComplexNDArray result (a.dims ());

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b);
    }

  return result;
}

// -*- 6 -*-
octave_value
elem_xpow (const NDArray& a, const ComplexNDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  ComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b(i));
    }

  return result;
}

// -*- 7 -*-
octave_value
elem_xpow (const Complex& a, const NDArray& b)
{
  ComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      double btmp = b(i);
      if (xisint (btmp))
        result(i) = std::pow (a, static_cast<int> (btmp));
      else
        result(i) = std::pow (a, btmp);
    }

  return result;
}

// -*- 8 -*-
octave_value
elem_xpow (const Complex& a, const ComplexNDArray& b)
{
  ComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a, b(i));
    }

  return result;
}

// -*- 9 -*-
octave_value
elem_xpow (const ComplexNDArray& a, double b)
{
  ComplexNDArray result (a.dims ());

  if (xisint (b))
    {
      if (b == -1)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result.xelem (i) = 1.0 / a(i);
        }
      else
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), static_cast<int> (b));
            }
        }
    }
  else
    {
      for (octave_idx_type i = 0; i < a.length (); i++)
        {
          octave_quit ();
          result(i) = std::pow (a(i), b);
        }
    }

  return result;
}

// -*- 10 -*-
octave_value
elem_xpow (const ComplexNDArray& a, const NDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  ComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      double btmp = b(i);
      if (xisint (btmp))
        result(i) = std::pow (a(i), static_cast<int> (btmp));
      else
        result(i) = std::pow (a(i), btmp);
    }

  return result;
}

// -*- 11 -*-
octave_value
elem_xpow (const ComplexNDArray& a, const Complex& b)
{
  ComplexNDArray result (a.dims ());

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b);
    }

  return result;
}

// -*- 12 -*-
octave_value
elem_xpow (const ComplexNDArray& a, const ComplexNDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  ComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b(i));
    }

  return result;
}

static inline int
xisint (float x)
{
  return (D_NINT (x) == x
          && ((x >= 0 && x < INT_MAX)
              || (x <= 0 && x > INT_MIN)));
}

// Safer pow functions.
//
//       op2 \ op1:   s   m   cs   cm
//            +--   +---+---+----+----+
//   scalar   |     | 1 | 5 |  7 | 11 |
//                  +---+---+----+----+
//   matrix         | 2 | * |  8 |  * |
//                  +---+---+----+----+
//   complex_scalar | 3 | 6 |  9 | 12 |
//                  +---+---+----+----+
//   complex_matrix | 4 | * | 10 |  * |
//                  +---+---+----+----+

// -*- 1 -*-
octave_value
xpow (float a, float b)
{
  float retval;

  if (a < 0.0 && ! xisint (b))
    {
      FloatComplex atmp (a);

      return std::pow (atmp, b);
    }
  else
    retval = std::pow (a, b);

  return retval;
}

// -*- 2 -*-
octave_value
xpow (float a, const FloatMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      FloatEIG b_eig (b);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (b_eig.eigenvalues ());
          FloatComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              FloatComplex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          FloatComplexDiagMatrix D (lambda);

          FloatComplexMatrix C = Q * D * Q.inverse ();

          if (a > 0)
            retval = real (C);
          else
            retval = C;
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 3 -*-
octave_value
xpow (float a, const FloatComplex& b)
{
  FloatComplex result = std::pow (a, b);
  return result;
}

// -*- 4 -*-
octave_value
xpow (float a, const FloatComplexMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      FloatEIG b_eig (b);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (b_eig.eigenvalues ());
          FloatComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              FloatComplex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          FloatComplexDiagMatrix D (lambda);

          retval = FloatComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 5 -*-
octave_value
xpow (const FloatMatrix& a, float b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          int btmp = static_cast<int> (b);
          if (btmp == 0)
            {
              retval = FloatDiagMatrix (nr, nr, 1.0);
            }
          else
            {
              // Too much copying?
              // FIXME -- we shouldn't do this if the exponent is
              // large...

              FloatMatrix atmp;
              if (btmp < 0)
                {
                  btmp = -btmp;

                  octave_idx_type info;
                  float rcond = 0.0;
                  MatrixType mattype (a);

                  atmp = a.inverse (mattype, info, rcond, 1);

                  if (info == -1)
                    warning ("inverse: matrix singular to machine\
 precision, rcond = %g", rcond);
                }
              else
                atmp = a;

              FloatMatrix result (atmp);

              btmp--;

              while (btmp > 0)
                {
                  if (btmp & 1)
                    result = result * atmp;

                  btmp >>= 1;

                  if (btmp > 0)
                    atmp = atmp * atmp;
                }

              retval = result;
            }
        }
      else
        {
          FloatEIG a_eig (a);

          if (! error_state)
            {
              FloatComplexColumnVector lambda (a_eig.eigenvalues ());
              FloatComplexMatrix Q (a_eig.eigenvectors ());

              for (octave_idx_type i = 0; i < nr; i++)
                lambda(i) = std::pow (lambda(i), b);

              FloatComplexDiagMatrix D (lambda);

              retval = FloatComplexMatrix (Q * D * Q.inverse ());
            }
          else
            error ("xpow: matrix diagonalization failed");
        }
    }

  return retval;
}

// -*- 5d -*-
octave_value
xpow (const FloatDiagMatrix& a, float b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          FloatDiagMatrix r (nr, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            r.dgelem (i) = std::pow (a.dgelem (i), b);
          retval = r;
        }
      else
        {
          FloatComplexDiagMatrix r (nr, nc);
          for (octave_idx_type i = 0; i < nc; i++)
            r.dgelem (i) = std::pow (static_cast<FloatComplex> (a.dgelem (i)), b);
          retval = r;
        }
    }

  return retval;
}

// -*- 6 -*-
octave_value
xpow (const FloatMatrix& a, const FloatComplex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      FloatEIG a_eig (a);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (a_eig.eigenvalues ());
          FloatComplexMatrix Q (a_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            lambda(i) = std::pow (lambda(i), b);

          FloatComplexDiagMatrix D (lambda);

          retval = FloatComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 7 -*-
octave_value
xpow (const FloatComplex& a, float b)
{
  FloatComplex result;

  if (xisint (b))
    result = std::pow (a, static_cast<int> (b));
  else
    result = std::pow (a, b);

  return result;
}

// -*- 8 -*-
octave_value
xpow (const FloatComplex& a, const FloatMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      FloatEIG b_eig (b);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (b_eig.eigenvalues ());
          FloatComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              FloatComplex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          FloatComplexDiagMatrix D (lambda);

          retval = FloatComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 9 -*-
octave_value
xpow (const FloatComplex& a, const FloatComplex& b)
{
  FloatComplex result;
  result = std::pow (a, b);
  return result;
}

// -*- 10 -*-
octave_value
xpow (const FloatComplex& a, const FloatComplexMatrix& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for x^A, A must be square");
  else
    {
      FloatEIG b_eig (b);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (b_eig.eigenvalues ());
          FloatComplexMatrix Q (b_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            {
              FloatComplex elt = lambda(i);
              if (std::imag (elt) == 0.0)
                lambda(i) = std::pow (a, std::real (elt));
              else
                lambda(i) = std::pow (a, elt);
            }
          FloatComplexDiagMatrix D (lambda);

          retval = FloatComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 11 -*-
octave_value
xpow (const FloatComplexMatrix& a, float b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      if (static_cast<int> (b) == b)
        {
          int btmp = static_cast<int> (b);
          if (btmp == 0)
            {
              retval = FloatDiagMatrix (nr, nr, 1.0);
            }
          else
            {
              // Too much copying?
              // FIXME -- we shouldn't do this if the exponent is
              // large...

              FloatComplexMatrix atmp;
              if (btmp < 0)
                {
                  btmp = -btmp;

                  octave_idx_type info;
                  float rcond = 0.0;
                  MatrixType mattype (a);

                  atmp = a.inverse (mattype, info, rcond, 1);

                  if (info == -1)
                    warning ("inverse: matrix singular to machine\
 precision, rcond = %g", rcond);
                }
              else
                atmp = a;

              FloatComplexMatrix result (atmp);

              btmp--;

              while (btmp > 0)
                {
                  if (btmp & 1)
                    result = result * atmp;

                  btmp >>= 1;

                  if (btmp > 0)
                    atmp = atmp * atmp;
                }

              retval = result;
            }
        }
      else
        {
          FloatEIG a_eig (a);

          if (! error_state)
            {
              FloatComplexColumnVector lambda (a_eig.eigenvalues ());
              FloatComplexMatrix Q (a_eig.eigenvectors ());

              for (octave_idx_type i = 0; i < nr; i++)
                lambda(i) = std::pow (lambda(i), b);

              FloatComplexDiagMatrix D (lambda);

              retval = FloatComplexMatrix (Q * D * Q.inverse ());
            }
          else
            error ("xpow: matrix diagonalization failed");
        }
    }

  return retval;
}

// -*- 12 -*-
octave_value
xpow (const FloatComplexMatrix& a, const FloatComplex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      FloatEIG a_eig (a);

      if (! error_state)
        {
          FloatComplexColumnVector lambda (a_eig.eigenvalues ());
          FloatComplexMatrix Q (a_eig.eigenvectors ());

          for (octave_idx_type i = 0; i < nr; i++)
            lambda(i) = std::pow (lambda(i), b);

          FloatComplexDiagMatrix D (lambda);

          retval = FloatComplexMatrix (Q * D * Q.inverse ());
        }
      else
        error ("xpow: matrix diagonalization failed");
    }

  return retval;
}

// -*- 12d -*-
octave_value
xpow (const FloatComplexDiagMatrix& a, const FloatComplex& b)
{
  octave_value retval;

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

  if (nr == 0 || nc == 0 || nr != nc)
    error ("for A^b, A must be square");
  else
    {
      FloatComplexDiagMatrix r (nr, nc);
      for (octave_idx_type i = 0; i < nc; i++)
        r(i, i) = std::pow (a(i, i), b);
      retval = r;
    }

  return retval;
}

// mixed
octave_value
xpow (const FloatComplexDiagMatrix& a, float b)
{
  return xpow (a, static_cast<FloatComplex> (b));
}

octave_value
xpow (const FloatDiagMatrix& a, const FloatComplex& b)
{
  return xpow (FloatComplexDiagMatrix (a), b);
}

// Safer pow functions that work elementwise for matrices.
//
//       op2 \ op1:   s   m   cs   cm
//            +--   +---+---+----+----+
//   scalar   |     | * | 3 |  * |  9 |
//                  +---+---+----+----+
//   matrix         | 1 | 4 |  7 | 10 |
//                  +---+---+----+----+
//   complex_scalar | * | 5 |  * | 11 |
//                  +---+---+----+----+
//   complex_matrix | 2 | 6 |  8 | 12 |
//                  +---+---+----+----+
//
//   * -> not needed.

// FIXME -- these functions need to be fixed so that things
// like
//
//   a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b
//
// and
//
//   a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end
//
// produce identical results.  Also, it would be nice if -1^0.5
// produced a pure imaginary result instead of a complex number with a
// small real part.  But perhaps that's really a problem with the math
// library...

// -*- 1 -*-
octave_value
elem_xpow (float a, const FloatMatrix& b)
{
  octave_value retval;

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

  float d1, d2;

  if (a < 0.0 && ! b.all_integers (d1, d2))
    {
      FloatComplex atmp (a);
      FloatComplexMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (atmp, b (i, j));
          }

      retval = result;
    }
  else
    {
      FloatMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a, b (i, j));
          }

      retval = result;
    }

  return retval;
}

// -*- 2 -*-
octave_value
elem_xpow (float a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  FloatComplexMatrix result (nr, nc);
  FloatComplex atmp (a);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (atmp, b (i, j));
      }

  return result;
}

// -*- 3 -*-
octave_value
elem_xpow (const FloatMatrix& a, float b)
{
  octave_value retval;

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

  if (! xisint (b) && a.any_element_is_negative ())
    {
      FloatComplexMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit (); 
      
            FloatComplex atmp (a (i, j));

            result (i, j) = std::pow (atmp, b);
          }

      retval = result;
    }
  else
    {
      FloatMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b);
          }

      retval = result;
    }

  return retval;
}

// -*- 4 -*-
octave_value
elem_xpow (const FloatMatrix& a, const FloatMatrix& b)
{
  octave_value retval;

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

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  int convert_to_complex = 0;
  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        float atmp = a (i, j);
        float btmp = b (i, j);
        if (atmp < 0.0 && static_cast<int> (btmp) != btmp)
          {
            convert_to_complex = 1;
            goto done;
          }
      }

done:

  if (convert_to_complex)
    {
      FloatComplexMatrix complex_result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            FloatComplex atmp (a (i, j));
            FloatComplex btmp (b (i, j));
            complex_result (i, j) = std::pow (atmp, btmp);
          }

      retval = complex_result;
    }
  else
    {
      FloatMatrix result (nr, nc);

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b (i, j));
          }

      retval = result;
    }

  return retval;
}

// -*- 5 -*-
octave_value
elem_xpow (const FloatMatrix& a, const FloatComplex& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (FloatComplex (a (i, j)), b);
      }

  return result;
}

// -*- 6 -*-
octave_value
elem_xpow (const FloatMatrix& a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (FloatComplex (a (i, j)), b (i, j));
      }

  return result;
}

// -*- 7 -*-
octave_value
elem_xpow (const FloatComplex& a, const FloatMatrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        float btmp = b (i, j);
        if (xisint (btmp))
          result (i, j) = std::pow (a, static_cast<int> (btmp));
        else
          result (i, j) = std::pow (a, btmp);
      }

  return result;
}

// -*- 8 -*-
octave_value
elem_xpow (const FloatComplex& a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = b.rows ();
  octave_idx_type nc = b.cols ();

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a, b (i, j));
      }

  return result;
}

// -*- 9 -*-
octave_value
elem_xpow (const FloatComplexMatrix& a, float b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  FloatComplexMatrix result (nr, nc);

  if (xisint (b))
    {
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), static_cast<int> (b));
          }
    }
  else
    {
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          {
            octave_quit ();
            result (i, j) = std::pow (a (i, j), b);
          }
    }

  return result;
}

// -*- 10 -*-
octave_value
elem_xpow (const FloatComplexMatrix& a, const FloatMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        float btmp = b (i, j);
        if (xisint (btmp))
          result (i, j) = std::pow (a (i, j), static_cast<int> (btmp));
        else
          result (i, j) = std::pow (a (i, j), btmp);
      }

  return result;
}

// -*- 11 -*-
octave_value
elem_xpow (const FloatComplexMatrix& a, const FloatComplex& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a (i, j), b);
      }

  return result;
}

// -*- 12 -*-
octave_value
elem_xpow (const FloatComplexMatrix& a, const FloatComplexMatrix& b)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

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

  if (nr != b_nr || nc != b_nc)
    {
      gripe_nonconformant ("operator .^", nr, nc, b_nr, b_nc);
      return octave_value ();
    }

  FloatComplexMatrix result (nr, nc);

  for (octave_idx_type j = 0; j < nc; j++)
    for (octave_idx_type i = 0; i < nr; i++)
      {
        octave_quit ();
        result (i, j) = std::pow (a (i, j), b (i, j));
      }

  return result;
}

// Safer pow functions that work elementwise for N-d arrays.
//
//       op2 \ op1:   s   nd  cs   cnd
//            +--   +---+---+----+----+
//   scalar   |     | * | 3 |  * |  9 |
//                  +---+---+----+----+
//   N_d            | 1 | 4 |  7 | 10 |
//                  +---+---+----+----+
//   complex_scalar | * | 5 |  * | 11 |
//                  +---+---+----+----+
//   complex_N_d    | 2 | 6 |  8 | 12 |
//                  +---+---+----+----+
//
//   * -> not needed.

// FIXME -- these functions need to be fixed so that things
// like
//
//   a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b
//
// and
//
//   a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end
//
// produce identical results.  Also, it would be nice if -1^0.5
// produced a pure imaginary result instead of a complex number with a
// small real part.  But perhaps that's really a problem with the math
// library...

// -*- 1 -*-
octave_value
elem_xpow (float a, const FloatNDArray& b)
{
  octave_value retval;

  if (a < 0.0 && ! b.all_integers ())
    {
      FloatComplex atmp (a);
      FloatComplexNDArray result (b.dims ());
      for (octave_idx_type i = 0; i < b.length (); i++)
        {
          octave_quit ();
          result(i) = std::pow (atmp, b(i));
        }

      retval = result;
    }
  else
    {
      FloatNDArray result (b.dims ());
      for (octave_idx_type i = 0; i < b.length (); i++)
        {
          octave_quit ();
          result (i) = std::pow (a, b(i));
        }

      retval = result;
    }

  return retval;
}

// -*- 2 -*-
octave_value
elem_xpow (float a, const FloatComplexNDArray& b)
{
  FloatComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a, b(i));
    }

  return result;
}

// -*- 3 -*-
octave_value
elem_xpow (const FloatNDArray& a, float b)
{
  octave_value retval;

  if (! xisint (b))
    {
      if (a.any_element_is_negative ())
        {
          FloatComplexNDArray result (a.dims ());

          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();

              FloatComplex atmp (a (i));

              result(i) = std::pow (atmp, b);
            }

          retval = result;
        }
      else
        {
          FloatNDArray result (a.dims ());
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), b);
            }

          retval = result;
        }
    }
  else
    {
      NoAlias<FloatNDArray> result (a.dims ());

      int ib = static_cast<int> (b);
      if (ib == 2)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = a(i) * a(i);
        }
      else if (ib == 3)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = a(i) * a(i) * a(i);
        }
      else if (ib == -1)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result(i) = 1.0f / a(i);
        }
      else
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), ib);
            }
        }

      retval = result;
    }

  return retval;
}

// -*- 4 -*-
octave_value
elem_xpow (const FloatNDArray& a, const FloatNDArray& b)
{
  octave_value retval;

  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  int len = a.length ();

  bool convert_to_complex = false;

  for (octave_idx_type i = 0; i < len; i++)
    {
      octave_quit ();
      float atmp = a(i);
      float btmp = b(i);
      if (atmp < 0.0 && static_cast<int> (btmp) != btmp)
        {
          convert_to_complex = true;
          goto done;
        }
    }

done:

  if (convert_to_complex)
    {
      FloatComplexNDArray complex_result (a_dims);

      for (octave_idx_type i = 0; i < len; i++)
        {
          octave_quit ();
          FloatComplex atmp (a(i));
          complex_result(i) = std::pow (atmp, b(i));
        }

      retval = complex_result;
    }
  else
    {
      FloatNDArray result (a_dims);

      for (octave_idx_type i = 0; i < len; i++)
        {
          octave_quit ();
          result(i) = std::pow (a(i), b(i));
        }

      retval = result;
    }

  return retval;
}

// -*- 5 -*-
octave_value
elem_xpow (const FloatNDArray& a, const FloatComplex& b)
{
  FloatComplexNDArray result (a.dims ());

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b);
    }

  return result;
}

// -*- 6 -*-
octave_value
elem_xpow (const FloatNDArray& a, const FloatComplexNDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  FloatComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b(i));
    }

  return result;
}

// -*- 7 -*-
octave_value
elem_xpow (const FloatComplex& a, const FloatNDArray& b)
{
  FloatComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      float btmp = b(i);
      if (xisint (btmp))
        result(i) = std::pow (a, static_cast<int> (btmp));
      else
        result(i) = std::pow (a, btmp);
    }

  return result;
}

// -*- 8 -*-
octave_value
elem_xpow (const FloatComplex& a, const FloatComplexNDArray& b)
{
  FloatComplexNDArray result (b.dims ());

  for (octave_idx_type i = 0; i < b.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a, b(i));
    }

  return result;
}

// -*- 9 -*-
octave_value
elem_xpow (const FloatComplexNDArray& a, float b)
{
  FloatComplexNDArray result (a.dims ());

  if (xisint (b))
    {
      if (b == -1)
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            result.xelem (i) = 1.0f / a(i);
        }
      else
        {
          for (octave_idx_type i = 0; i < a.length (); i++)
            {
              octave_quit ();
              result(i) = std::pow (a(i), static_cast<int> (b));
            }
        }
    }
  else
    {
      for (octave_idx_type i = 0; i < a.length (); i++)
        {
          octave_quit ();
          result(i) = std::pow (a(i), b);
        }
    }

  return result;
}

// -*- 10 -*-
octave_value
elem_xpow (const FloatComplexNDArray& a, const FloatNDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  FloatComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      float btmp = b(i);
      if (xisint (btmp))
        result(i) = std::pow (a(i), static_cast<int> (btmp));
      else
        result(i) = std::pow (a(i), btmp);
    }

  return result;
}

// -*- 11 -*-
octave_value
elem_xpow (const FloatComplexNDArray& a, const FloatComplex& b)
{
  FloatComplexNDArray result (a.dims ());

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b);
    }

  return result;
}

// -*- 12 -*-
octave_value
elem_xpow (const FloatComplexNDArray& a, const FloatComplexNDArray& b)
{
  dim_vector a_dims = a.dims ();
  dim_vector b_dims = b.dims ();

  if (a_dims != b_dims)
    {
      gripe_nonconformant ("operator .^", a_dims, b_dims);
      return octave_value ();
    }

  FloatComplexNDArray result (a_dims);

  for (octave_idx_type i = 0; i < a.length (); i++)
    {
      octave_quit ();
      result(i) = std::pow (a(i), b(i));
    }

  return result;
}