Hi there:
I've modified the deriv.m function (Seems to be a work in progress as it
won't work at all).
I changed some checks so the funcion passed can be a single-variable
function handle. Also fixed two bugs:
changed is_scalar to isscalar near line 27, and added N=1 as default is
missing.
Further notice: I should consider putting the N parameter as the first
optional parameter, so you can take the Nth derivative of a function
with the default order (O) and step (h)
--
Joaquín Ignacio Aramendía <samsa...@gmail.com>
## Copyright (C) 2000 Ben Sapp. 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.
## deriv(f,x0[,h,O,N])
## Reference -> Numerical Methods for Mathematics, Science, and
## Engineering by John H. Mathews.
function dx = deriv(f,x0,varargin)
if(nargin < 2)
error("not enough arguments\n");
endif
if(!isa(f, 'function_handle'))
error("The first argument must be a function handle\n");
endif
if(!isscalar(x0))
error("The second argument must be a scalar.\n");
endif
if(nargin >= 3)
va_arg_cnt = 1;
h = varargin{va_arg_cnt++};
if(!is_scalar(h))
error("h must be a scalar.");
endif
if(nargin >= 4)
O = varargin{va_arg_cnt++};
if((O != 2) && (O != 4))
error("Only order 2 or 4 is supported.\n");
endif
if(nargin >= 5)
N = varargin{va_arg_cnt++};
if((N > 4)||(N < 1))
error("Only 1st,2nd,3rd or 4th order derivatives are acceptable.\n");
endif
if(nargin >= 6)
warning("Ignoring arguements beyond the 5th.\n");
endif
endif
endif
else
h = 0.0000001;
O = 2;
N = 1;
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("I can only take the 1st,2nd,3rd or 4th derivative\n");
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("I can only take the 1st,2nd,3rd or 4th derivative\n");
endswitch
otherwise
error("Only order 4 or 2 supported\n");
endswitch
endfunction
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