From octave-sources-request at bevo dot che dot wisc dot edu Mon Sep 24 11:34:37 2001
Subject: fminbnd.m
From: Andreas Helms <helms at astro dot physik dot uni-potsdam dot de>
To: octave-sources at bevo dot che dot wisc dot edu
Date: Mon, 24 Sep 2001 18:34:27 +0200

I modified the fminbnd function from the Octave repository at sourceforge
so it can be used with functions with more than one parameter.

Andreas


## Copyright (C) 2000 Ben Sapp.  All rights reserved.
## Modification by Andreas Helms
## 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.

## -*- texinfo -*-
##  at deftypefn {Function File} {[@var{x}] =}  
## fminbnd( at var{f},@var{lb},@var{ub},@var{[options]},@var{P1},@var{P2}, ...)
## 
## Find the minimum of a scalar function with the Golden Search method.
## 
##  at strong{Inputs}
##  at table @var 
##  at item f 
## A string contining the name of the function to minimiz
##  at item lb
## Value to use as an initial lower bound on  at var{x} dot 
##  at item ub 
## Value to use as an initial upper bound on  at var{x} dot 
##  at item options
## Vector with control parameters (For compatibily with MATLAB, not used 
## here) 
##  at item P1,P2, ...
## Optional parameter for function  at var{f} 
##
##  at end table
##  at end deftypefn

function min = fminbnd(_func,lb,ub, options, ...)

  delta = 1e-17;
  gr = (sqrt(5)-1)/2;
  width = (ub-lb);
  out = lb:(width/3):ub;
  out(2) = out(4)-gr*width;
  out(3) = out(1)+gr*width;
  upper = feval(_func,out(3), all_va_args);
  lower = feval(_func,out(2), all_va_args);
  while((out(3)-out(2)) > delta) #this will not work for symmetric funcs
    if(upper > lower)
      out(4) = out(3);
      out(3) = out(2);
      width = out(4)-out(1);
      out(2) = out(4)-gr*width;
      upper = lower;
      lower = feval(_func,out(2), all_va_args);
    else
      out(1) = out(2);
      out(2) = out(3);
      width = out(4)-out(1);
      out(3) = out(1)+width*gr;
      lower = upper;
      upper = feval(_func,out(3), all_va_args);
    endif
  endwhile
  min = out(2);
endfunction