/usr/share/octave/packages/optim-1.3.0/poly_2_ex.m is in octave-optim 1.3.0-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | ## Copyright (C) 2002 Etienne Grossmann. All rights reserved.
##
## 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 2, or (at your option) any
## later version.
##
## This 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.
## ex = poly_2_ex (l, f) - Extremum of a 1-var deg-2 polynomial
##
## l : 3 : Values of variable at which polynomial is known.
## f : 3 : f(i) = Value of the degree-2 polynomial at l(i).
##
## ex : 1 : Value for which f reaches its 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_ex (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
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