--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/xpow.cc	Sun Aug 08 01:13:40 1993 +0000
@@ -0,0 +1,674 @@
+// xpow.cc                                               -*- C++ -*-
+/*
+
+Copyright (C) 1992, 1993 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 __GNUG__
+#pragma implementation
+#endif
+
+#include <assert.h>
+#include "error.h"
+#include "xpow.h"
+
+// This function also appears in tree-const.cc.  Maybe it should be a
+// member function of the Matrix class.
+
+static int
+any_element_is_negative (const Matrix& a)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      if (a.elem (i, j) < 0.0)
+	return 1;
+  return 0;
+}
+
+/*
+ * Safer pow functions.
+ *
+ *       op2 \ op1:   s   m   cs   cm
+ *            +--   +---+---+----+----+
+ *   scalar   |     | 1 | 5 |  7 | 11 |
+ *                  +---+---+----+----+
+ *   matrix         | 2 | E |  8 |  E |
+ *                  +---+---+----+----+
+ *   complex_scalar | 3 | 6 |  9 | 12 |
+ *                  +---+---+----+----+
+ *   complex_matrix | 4 | E | 10 |  E |
+ *                  +---+---+----+----+
+ *
+ *   E -> error, trapped in arith-ops.cc.
+ */
+
+tree_constant
+xpow (double a, double b)
+{
+  if (a < 0.0 && (int) b != b)
+    {
+      Complex atmp (a);
+      return tree_constant (pow (atmp, b));
+    }
+  else
+    return tree_constant (pow (a, b));
+}
+
+tree_constant
+xpow (double a, Matrix& b)
+{
+  tree_constant retval;
+
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    error ("for x^A, A must be square");
+  else
+    {
+      EIG b_eig (b);
+      ComplexColumnVector lambda (b_eig.eigenvalues ());
+      ComplexMatrix Q (b_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	{
+	  Complex elt = lambda.elem (i);
+	  if (imag (elt) == 0.0)
+	    lambda.elem (i) = pow (a, real (elt));
+	  else
+	    lambda.elem (i) = pow (a, elt);
+	}
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (double a, Complex& b)
+{
+  Complex result;
+  Complex atmp (a);
+  result = pow (atmp, b);
+  return tree_constant (result);
+}
+
+tree_constant
+xpow (double a, ComplexMatrix& b)
+{
+  tree_constant retval;
+
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    error ("for x^A, A must be square");
+  else
+    {
+      EIG b_eig (b);
+      ComplexColumnVector lambda (b_eig.eigenvalues ());
+      ComplexMatrix Q (b_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	{
+	  Complex elt = lambda.elem (i);
+	  if (imag (elt) == 0.0)
+	    lambda.elem (i) = pow (a, real (elt));
+	  else
+	    lambda.elem (i) = pow (a, elt);
+	}
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (Matrix& a, double b)
+{
+  tree_constant retval;
+
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    {
+      error ("for A^b, A must be square");
+      return retval;
+    }
+
+  if ((int) b == b)
+    {
+      int btmp = (int) b;
+      if (btmp == 0)
+	{
+	  DiagMatrix result (nr, nr, 1.0);
+	  retval = tree_constant (result);
+	}
+      else
+	{
+// Too much copying?
+// XXX FIXME XXX -- we shouldn\'t do this if the exponent is large...
+	  Matrix atmp;
+	  if (btmp < 0)
+	    {
+	      btmp = -btmp;
+	      atmp = a.inverse ();
+	    }
+	  else
+	    atmp = a;
+
+	  Matrix result (atmp);
+	  for (int i = 1; i < btmp; i++)
+	    result = result * atmp;
+
+	  retval = tree_constant (result);
+	}
+    }
+  else
+    {
+      EIG a_eig (a);
+      ComplexColumnVector lambda (a_eig.eigenvalues ());
+      ComplexMatrix Q (a_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	lambda.elem (i) = pow (lambda.elem (i), b);
+
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (Matrix& a, Complex& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    {
+      error ("for A^b, A must be square");
+      return tree_constant ();
+    }
+
+  EIG a_eig (a);
+  ComplexColumnVector lambda (a_eig.eigenvalues ());
+  ComplexMatrix Q (a_eig.eigenvectors ());
+
+  for (int i = 0; i < nr; i++)
+    lambda.elem (i) = pow (lambda.elem (i), b);
+
+  ComplexDiagMatrix D (lambda);
+
+  ComplexMatrix result = Q * D * Q.inverse ();
+
+  return tree_constant (result);
+}
+
+tree_constant
+xpow (Complex& a, double b)
+{
+  Complex result;
+  result = pow (a, b);
+  return tree_constant (result);
+}
+
+tree_constant
+xpow (Complex& a, Matrix& b)
+{
+  tree_constant retval;
+
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    {
+      error ("for x^A, A must be square");
+    }
+  else
+    {
+      EIG b_eig (b);
+      ComplexColumnVector lambda (b_eig.eigenvalues ());
+      ComplexMatrix Q (b_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	{
+	  Complex elt = lambda.elem (i);
+	  if (imag (elt) == 0.0)
+	    lambda.elem (i) = pow (a, real (elt));
+	  else
+	    lambda.elem (i) = pow (a, elt);
+	}
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (Complex& a, Complex& b)
+{
+  Complex result;
+  result = pow (a, b);
+  return tree_constant (result);
+}
+
+tree_constant
+xpow (Complex& a, ComplexMatrix& b)
+{
+  tree_constant retval;
+
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    error ("for x^A, A must be square");
+  else
+    {
+      EIG b_eig (b);
+      ComplexColumnVector lambda (b_eig.eigenvalues ());
+      ComplexMatrix Q (b_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	{
+	  Complex elt = lambda.elem (i);
+	  if (imag (elt) == 0.0)
+	    lambda.elem (i) = pow (a, real (elt));
+	  else
+	    lambda.elem (i) = pow (a, elt);
+	}
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (ComplexMatrix& a, double b)
+{
+  tree_constant retval;
+
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    {
+      error ("for A^b, A must be square");
+      return retval;
+    }
+
+  if ((int) b == b)
+    {
+      int btmp = (int) b;
+      if (btmp == 0)
+	{
+	  DiagMatrix result (nr, nr, 1.0);
+	  retval = tree_constant (result);
+	}
+      else
+	{
+// Too much copying?
+// XXX FIXME XXX -- we shouldn\'t do this if the exponent is large...
+	  ComplexMatrix atmp;
+	  if (btmp < 0)
+	    {
+	      btmp = -btmp;
+	      atmp = a.inverse ();
+	    }
+	  else
+	    atmp = a;
+
+	  ComplexMatrix result (atmp);
+	  for (int i = 1; i < btmp; i++)
+	    result = result * atmp;
+
+	  retval = tree_constant (result);
+	}
+    }
+  else
+    {
+      EIG a_eig (a);
+      ComplexColumnVector lambda (a_eig.eigenvalues ());
+      ComplexMatrix Q (a_eig.eigenvectors ());
+
+      for (int i = 0; i < nr; i++)
+	lambda.elem (i) = pow (lambda.elem (i), b);
+
+      ComplexDiagMatrix D (lambda);
+
+      ComplexMatrix result = Q * D * Q.inverse ();
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+xpow (ComplexMatrix& a, Complex& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  if (nr == 0 || nc == 0 || nr != nc)
+    {
+      error ("for A^b, A must be square");
+      return tree_constant ();
+    }
+
+  EIG a_eig (a);
+  ComplexColumnVector lambda (a_eig.eigenvalues ());
+  ComplexMatrix Q (a_eig.eigenvectors ());
+
+  for (int i = 0; i < nr; i++)
+    lambda.elem (i) = pow (lambda.elem (i), b);
+
+  ComplexDiagMatrix D (lambda);
+
+  ComplexMatrix result = Q * D * Q.inverse ();
+
+  return tree_constant (result);
+}
+
+/*
+ * 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.
+ */
+
+tree_constant
+elem_xpow (double a, Matrix& b)
+{
+  tree_constant retval;
+
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+// For now, assume the worst.
+  if (a < 0.0)
+    {
+      Complex atmp (a);
+      ComplexMatrix result (nr, nc);
+      for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  result.elem (i, j) = pow (atmp, b.elem (i, j));
+
+      retval = tree_constant (result);
+    }
+  else
+    {
+      Matrix result (nr, nc);
+      for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  result.elem (i, j) = pow (a, b.elem (i, j)); 
+
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+elem_xpow (double a, ComplexMatrix& b)
+{
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a, b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (Matrix& a, double b)
+{
+  tree_constant retval;
+
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  if ((int) b != b && any_element_is_negative (a))
+    {
+      ComplexMatrix result (nr, nc);
+      for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  {
+	    Complex atmp (a.elem (i, j));
+	    result.elem (i, j) = pow (atmp, b);
+	  }
+
+      retval = tree_constant (result);
+    }
+  else
+    {
+      Matrix result (nr, nc);
+      for (int j = 0; j < nc; j++)
+	for (int i = 0; i < nr; i++)
+	  result.elem (i, j) = pow (a.elem (i, j), b);
+
+      retval = tree_constant (result);
+    }
+
+  return retval;
+}
+
+tree_constant
+elem_xpow (Matrix& a, Matrix& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  assert (nr == b.rows () && nc == b.columns ());
+
+  int convert_to_complex = 0;
+  int i;
+  for (int j = 0; j < nc; j++)
+    for (i = 0; i < nr; i++)
+      {
+	double atmp = a.elem (i, j);
+	double btmp = b.elem (i, j);
+	if (atmp < 0.0 && (int) btmp != btmp)
+	  {
+	    convert_to_complex = 1;
+	    goto done;
+	  }
+      }
+
+ done:
+
+  if (convert_to_complex)
+    {
+      ComplexMatrix complex_result (nr, nc);
+
+      for (j = 0; j < nc; j++)
+	for (i = 0; i < nr; i++)
+	  {
+	    Complex atmp (a.elem (i, j));
+	    Complex btmp (b.elem (i, j));
+	    complex_result.elem (i, j) = pow (atmp, btmp);
+	  }
+      return tree_constant (complex_result);
+    }
+  else
+    {
+      Matrix result (nr, nc);
+
+      for (j = 0; j < nc; j++)
+	for (i = 0; i < nr; i++)
+	  result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j));
+
+      return tree_constant (result);
+    }
+}
+
+tree_constant
+elem_xpow (Matrix& a, Complex& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b);
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (Matrix& a, ComplexMatrix& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  assert (nr == b.rows () && nc == b.columns ());
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (Complex& a, Matrix& b)
+{
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a, b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (Complex& a, ComplexMatrix& b)
+{
+  int nr = b.rows ();
+  int nc = b.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a, b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (ComplexMatrix& a, double b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b);
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (ComplexMatrix& a, Matrix& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  assert (nr == b.rows () && nc == b.columns ());
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (ComplexMatrix& a, Complex& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  ComplexMatrix result (nr, nc);
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b);
+
+  return tree_constant (result);
+}
+
+tree_constant
+elem_xpow (ComplexMatrix& a, ComplexMatrix& b)
+{
+  int nr = a.rows ();
+  int nc = a.columns ();
+
+  ComplexMatrix result (nr, nc);
+
+  for (int j = 0; j < nc; j++)
+    for (int i = 0; i < nr; i++)
+      result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j));
+
+  return tree_constant (result);
+}
+
+/*
+;;; Local Variables: ***
+;;; mode: C++ ***
+;;; page-delimiter: "^/\\*" ***
+;;; End: ***
+*/