Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / optim-1.2.0 / __poly_2_extrema.m

diff --git a/octave_packages/optim-1.2.0/__poly_2_extrema.m b/octave_packages/optim-1.2.0/__poly_2_extrema.m
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+## Copyright (C) 2002 Etienne Grossmann <etienne@egdn.net>
+## Copyright (C) 2009 Levente Torok <TorokLev@gmail.com>
+##
+## This program 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.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+##  ex = poly_2_ex (l, f)       - Extremum of a 1-var deg-2 polynomial
+##
+## l  : 3 : variable values
+## f  : 3 : f(i) = value of polynomial at l(i)
+## 
+## ex : 1 : Value at which f reaches an extremum
+## 
+## Assuming that f(i) = a*l(i)^2 + b* l(i) + c = P(l(i)) for some a, b, c,
+## ex is the extremum of the polynome P.
+
+function ex = __poly_2_extrema (l, f)
+
+### This somewhat helps if solution is very close to one of the points.
+[f,i] = sort (f);
+l = l(i); 
+
+
+m = (l(2) - l(1))/(l(3) - l(1));
+d = (2*(f(1)*(m-1)+f(2)-f(3)*m));
+if abs (d) < eps,
+  printf ("poly_2_ex : divisor is small (solution at infinity)\n");
+  printf ("%8.3e %8.3e %8.3e, %8.3e %8.3e\n",\
+         f(1), diff (f), diff (sort (l)));
+
+  ex = (2*(l(1)>l(2))-1)*inf;
+  ## keyboard
+else
+  ex  =  ((l(3) - l(1))*((f(1)*(m^2-1) + f(2) - f(3)*m^2))) / d ;
+
+## Not an improvement
+#  n = ((l(2)+l(3))*(l(2)-l(3)) + 2*(l(3)-l(2))*l(1)) / (l(3)-l(1))^2 ;
+#  ex =  ((l(3) - l(1))*((f(1)*n + f(2) - f(3)*m^2))) / \
+#      (2*(f(1)*(m-1)+f(2)-f(3)*m));
+#  if ex != ex0,
+#    ex -  ex0
+#  end
+  ex = l(1) + ex;
+end