A new patch for that function.
- Corrected a logic error, added a compatibility f=str2funct(f) at the
beggining of the file.
- Changed function behavior to work with vectorized functions (improve
speed on loops).
- Added some documentation.
--
Joaquín Ignacio Aramendía <samsa...@gmail.com>
El lun, 31-10-2011 a las 16:59 +0000, Carnë Draug escribió:
> On 31 October 2011 15:20, Joaquín Ignacio Aramendía <samsa...@gmail.com>
> wrote:
> > 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)
>
> Hi,
>
> I have applied these changes, as it appears that it was not working
> before. Thank you very much.
>
> I have then made a few more changes of my own. If you plan to submit
> more patches to it, please checkout the latest development version.
>
> Carnë
--- deriv.m 2011-11-01 09:51:11.909621187 -0300
+++ deriv_updated.m 2011-11-01 16:00:25.283627939 -0300
@@ -13,28 +13,39 @@
## 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})
+## @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.
+## @var{f} must be a function handle or the name of a function that takes a vector @var{X}
+## and returns a vector of the same size and orientation as @var{X}. @var{X0}
+## must be a vector or a scalar.
+##
+## @var{h} defines the step taken for the derivative calculation. It defaults to 1e-7.
+##
+## @var{0} 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)
+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
if (nargin < 2)
error ("Not enough arguments.");
- elseif (!isa (f, 'function_handle') || !ischar (f)) # let's also support a string with str2func
+ elseif (!isa (f, 'function_handle'))
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 (!isvector (X0) || !isnumeric (X0))
+ 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))
@@ -57,26 +68,26 @@
case (2)
switch N
case (1)
- dx = (feval(f,x0+h)-feval(f,x0-h))/(2*h);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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
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