/usr/share/octave/packages/3.2/optim-1.0.17/deriv.m is in octave-optim 1.0.17-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | ## 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, 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 -*-
## @deftypefn {Function File} {dx =} deriv (@var{f}, @var{x0})
## @deftypefnx {Function File} {dx =} deriv (@var{f}, @var{x0}, @var{h})
## @deftypefnx {Function File} {dx =} deriv (@var{f}, @var{x0}, @var{h}, @var{O})
## @deftypefnx {Function File} {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 while @var{x0}
## must be a scalar.The optional arguments @var{h}, @var{O} and @var{N} default
## to 1e-7, 2, and 1 respectively.
##
## 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 (nargin < 2)
error ("Not enough arguments.");
elseif (!isa (f, 'function_handle') || !ischar (f)) # let's also support a string with str2func
error ("The first argument 'f' must be a function handle.");
elseif (!isscalar (x0) || !isnumeric (x0))
error ("The second argument 'x0' must be a scalar.");
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
if (ischar (f))
f = str2func (f);
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
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