--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/balance.cc	Tue Aug 10 20:08:02 1993 +0000
@@ -0,0 +1,284 @@
+// tc-balance.cc                                           -*- C++ -*-
+/*
+
+Copyright (C) 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.
+
+*/
+
+// Written by A. S. Hodel <scotte@eng.auburn.edu>
+
+#ifdef __GNUG__
+#pragma implementation
+#endif
+
+#include "Matrix.h"
+
+#include "tree-const.h"
+#include "user-prefs.h"
+#include "error.h"
+#include "gripes.h"
+
+#ifdef WITH_DLD
+tree_constant *
+builtin_balance_2 (tree_constant *args, int nargin, int nargout)
+{
+  return balance (args, nargin, nargout);
+}
+#endif
+
+tree_constant *
+balance (tree_constant *args, int nargin, int nargout)
+{
+  char *bal_job;
+  int my_nargin;		// # args w/o optional string arg
+  tree_constant *retval = NULL_TREE_CONST;
+
+  // determine if balancing option is listed
+  // set my_nargin to the number of matrix inputs
+  if (args[nargin-1].const_type () == tree_constant_rep::string_constant ){
+    bal_job = args[nargin-1].string_value ();
+    my_nargin = nargin-2;
+  }
+  else
+  {
+    bal_job = "B";
+    my_nargin = nargin-1;
+  }
+
+  tree_constant arg = args[1].make_numeric ();
+  int a_nr = arg.rows ();
+  int a_nc = arg.columns ();
+
+// Check argument 1 dimensions.
+
+  if (a_nr == 0 || a_nc == 0)
+    {
+      int flag = user_pref.propagate_empty_matrices;
+      if (flag != 0)
+	{
+	  if (flag < 0) warning ("balance: argument is empty matrix");
+	  Matrix m;
+	  retval = new tree_constant [3];
+	  retval[0] = tree_constant (m);
+	  retval[1] = tree_constant (m);
+	}
+      else
+	error ("balance: empty matrix is invalid as argument");
+
+      return retval;
+    }
+
+  if (a_nr != a_nc)
+    {
+      gripe_square_matrix_required ("balance");
+      return retval;
+    }
+
+// Extract argument 1 parameter for both AEP and GEP.
+
+  Matrix aa;
+  ComplexMatrix caa;
+  if (arg.is_complex_type ())
+    {
+      if (arg.is_matrix_type ())
+	caa=arg.complex_matrix_value ();
+      else
+	{
+	  caa.resize (1, 1);
+	  caa.elem (0, 0) = arg.complex_value ();
+	}
+    }
+  else
+    {
+      if (arg.is_matrix_type ())
+	aa = arg.matrix_value ();
+      else
+	{
+	  double d = arg.double_value ();
+	  aa.resize (1, 1);
+	  aa.elem (0, 0) = d;
+	}
+    }
+
+// Treat AEP/ GEP cases.
+
+  switch (my_nargin)
+    {
+    case 1:
+
+// Algebraic eigenvalue problem.
+
+      retval = new tree_constant[nargout+1];
+      if (arg.is_complex_type ())
+	{
+	  ComplexAEPBALANCE result (caa, bal_job);
+
+	  if (nargout == 1)
+	    retval[0] = tree_constant(result.balanced_matrix ());
+	  else
+	    {
+	      retval[0] = tree_constant (result.balancing_matrix ());
+	      retval[1] = tree_constant (result.balanced_matrix ());
+	    }
+	}
+      else
+	{
+	  AEPBALANCE result (aa, bal_job);
+
+	  if (nargout == 1)
+	    retval[0] = tree_constant (result.balanced_matrix ());
+	  else
+	    {
+	      retval[0] = tree_constant (result.balancing_matrix ());
+	      retval[1] = tree_constant (result.balanced_matrix ());
+	    }
+	}
+      break;
+    case 2:
+
+// Generalized eigenvalue problem.
+
+      {
+	retval = new tree_constant[nargout+1];
+      
+// 1st we have to check argument 2 dimensions and type...
+
+	tree_constant brg = args[2].make_numeric ();
+	int b_nr = brg.rows ();
+	int b_nc = brg.columns ();
+      
+// Check argument 2 dimensions -- must match arg 1.
+
+	if ((b_nr != b_nc) || (b_nr != a_nr))
+	  {
+	    gripe_nonconformant ();
+	    return retval;
+	  }
+      
+// Now, extract the second matrix...
+// Extract argument 1 parameter for both AEP and GEP.
+
+	Matrix bb;
+	ComplexMatrix cbb;
+	if (brg.is_complex_type ())
+	  {
+	    if (brg.is_matrix_type ())
+	      cbb = brg.complex_matrix_value ();
+	    else
+	      {
+		cbb.resize (1, 1);
+		cbb.elem (0, 0) = brg.complex_value ();
+	      }
+	  }
+	else
+	  {
+	    if (brg.is_matrix_type ()) bb = brg.matrix_value ();
+	    else
+	      {
+		double d = brg.double_value ();
+		bb.resize (1, 1);
+		bb.elem (0, 0) = d;
+	      }
+	  }
+  
+// Both matrices loaded, now let's check what kind of arithmetic:
+
+	if (arg.is_complex_type () || brg.is_complex_type ())
+	  {
+	    if (arg.is_real_type ())
+	      caa = aa;
+	    else if (brg.is_real_type ())
+	      cbb = bb;
+
+// Compute magnitudes of elements for balancing purposes.
+// Surely there's a function I can call someplace!
+
+	    for (int i = 0; i < a_nr; i++)
+	      for (int j = 0; j < a_nr; j++)
+		{
+		  aa.elem (i, j) = abs (caa.elem (i, j));
+		  bb.elem (i, j) = abs (cbb.elem (i, j));
+		}
+	  }
+
+	GEPBALANCE result(aa, bb, bal_job);
+
+	if (arg.is_complex_type () || brg.is_complex_type ())
+	  {
+	    caa = result.left_balancing_matrix () * caa
+	      * result.right_balancing_matrix ();
+
+	    cbb = result.left_balancing_matrix () * cbb
+	      * result.right_balancing_matrix ();
+
+	    switch (nargout)
+	      {
+	      case 1:
+		warning ("balance: should use two output arguments");
+		retval[0] = tree_constant (caa);
+		break;
+	      case 2:
+		retval[0] = tree_constant (caa);
+		retval[1] = tree_constant (cbb);
+		break;
+	      case 4:
+		retval[0] = tree_constant (result.left_balancing_matrix ());
+		retval[1] = tree_constant (result.right_balancing_matrix ());
+		retval[2] = tree_constant (caa);
+		retval[3] = tree_constant (cbb);
+		break;
+	      default:
+		error ("balance: illegal number of output arguments");
+		break;
+	      }
+	  }
+	else
+	  {
+	    switch (nargout)
+	      {
+	      case 2:
+		retval[0] = tree_constant (result.balanced_a_matrix ());
+		retval[1] = tree_constant (result.balanced_b_matrix ());
+		break;
+	      case 4:
+		retval[0] = tree_constant (result.left_balancing_matrix ());
+		retval[1] = tree_constant (result.right_balancing_matrix ());
+		retval[2] = tree_constant (result.balanced_a_matrix ());
+		retval[3] = tree_constant (result.balanced_b_matrix ());
+		break;
+	      default:
+		error ("balance: illegal number of output arguments");
+		break;
+	      }
+	  }
+      }
+      break;
+    default:
+      error ("balance requires one (AEP) or two (GEP) numeric arguments");
+      break;
+    }
+  return retval;
+}
+
+/*
+;;; Local Variables: ***
+;;; mode: C++ ***
+;;; page-delimiter: "^/\\*" ***
+;;; End: ***
+*/