Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/optim-1.2.0/deriv.m b/octave_packages/optim-1.2.0/deriv.m
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+## Copyright (C) 2000 Ben Sapp <bsapp@nua.lampf.lanl.gov>
+## Copyright (C) 2011 Joaquín Ignacio Aramendía <samsagax@gmail.com>
+## Copyright (C) 2011 Carnë Draug <carandraug+dev@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/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{dx} =} deriv (@var{f}, @var{x0})
+## @deftypefnx {Function File} {@var{dx} =} deriv (@var{f}, @var{x0}, @var{h})
+## @deftypefnx {Function File} {@var{dx} =} deriv (@var{f}, @var{x0}, @var{h}, @var{O})
+## @deftypefnx {Function File} {@var{dx} =} deriv (@var{f}, @var{x0}, @var{h}, @var{O}, @var{N})
+## Calculate derivate of function @var{f}.
+##
+## @var{f} must be a function handle or the name of a function that takes @var{x0}
+## and returns a variable of equal length and orientation. @var{x0} must be a
+## numeric vector or scalar.
+##
+## @var{h} defines the step taken for the derivative calculation. Defaults to 1e-7.
+##
+## @var{O} defines the order of the calculation. Supported values are 2 (h^2 order)
+## or 4 (h^4 order). Defaults to 2.
+##
+## @var{N} defines the derivative order. Defaults to the 1st derivative of the
+## function. Can be up to the 4th derivative.
+##
+## Reference: Numerical Methods for Mathematics, Science, and Engineering by
+## John H. Mathews.
+## @end deftypefn
+
+function dx = deriv (f, x0, h = 0.0000001, O = 2, N = 1)
+
+  if (ischar(f))
+    f = str2func(f); # let's also support a string with str2func
+  endif
+
+  if (nargin < 2)
+    error ("Not enough arguments.");
+  elseif (!isa (f, 'function_handle'))
+    error ("The first argument 'f' must be a function handle.");
+  elseif (!isvector (x0) || !isnumeric (x0))
+    ## a scalar is 1x1 therefore counts as a vector too
+    error ("The second argument 'x0' must be a numeric vector.");
+  elseif (!isscalar (h) || !isnumeric (h))
+    error ("The third argument 'h' must be a scalar.");
+  elseif (!isscalar (O) || !isnumeric (O))
+    error ("The fourth argument 'O' must be a scalar.");
+  elseif (O != 2 && O != 4)
+    error ("Only order 2 or 4 is supported.");
+  elseif (!isscalar (N) || !isnumeric (N))
+    error ("The fifth argument 'N' must be a scalar.");
+  elseif ((N > 4) || (N < 1))
+    error("Only 1st,2nd,3rd or 4th order derivatives are acceptable.");
+  elseif (nargin > 5)
+    warning("Ignoring arguements beyond the 5th.");
+  endif
+
+  switch O
+    case (2)
+      switch N
+        case (1)
+          dx = (feval(f,x0+h)-feval(f,x0-h))/(2*h);
+        case (2)
+          dx = (feval(f,x0+h)-2*feval(f,x0)+feval(f,x0-h))/(h^2);
+        case (3)
+          dx = (feval(f,x0+2*h)-2*feval(f,x0+h)+2*feval(f,x0-h)-feval(f,x0-2*h))/(2*h^3);
+        case (4)
+          dx = (feval(f,x0+2*h)-4*feval(f,x0+h)+6*feval(f,x0)-4*feval(f,x0-h)+feval(f,x0-2*h))/(h^4);
+        otherwise
+          error("Only 1st,2nd,3rd or 4th order derivatives are acceptable.");
+      endswitch
+    case (4)
+      switch N
+        case (1)
+          dx = (-feval(f,x0+2*h)+8*feval(f,x0+h)-8*feval(f,x0-h)+feval(f,x0-2*h))/(12*h);
+        case (2)
+          dx = (-feval(f,x0+2*h)+16*feval(f,x0+h)-30*feval(f,x0)+16*feval(f,x0-h)-feval(f,x0-2*h))/(12*h^2);
+        case (3)
+          dx = (-feval(f,x0+3*h)+8*feval(f,x0+2*h)-13*feval(f,x0+h)+13*feval(f,x0-h)-8*feval(f,x0-2*h)+feval(f,x0-3*h))/(8*h^3);
+        case (4)
+          dx = (-feval(f,x0+3*h)+12*feval(f,x0+2*h)-39*feval(f,x0+h)+56*feval(f,x0)-39*feval(f,x0-h)+12*feval(f,x0-2*h)-feval(f,x0-3*h))/(6*h^4);
+        otherwise
+          error("Only 1st,2nd,3rd or 4th order derivatives are acceptable.");
+      endswitch
+    otherwise
+      error ("Only order 2 or 4 is supported.");
+  endswitch
+endfunction