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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
function %g=numdiff(%__func,%x,%dx)
// given a function %__func from R^n to R^p
//computes the matrix g such as
// [ d f ]
// [ i ]
//g = [ ---- ]
// ij [ d x ]
// [ j ]
// using finite difference methods
if type(%__func)==15 then
params=%__func;params(1)=null();
%__func=%__func(1)
else
params=list()
end
if type(%__func)==10 then //hard coded function given by its name
error(msprintf(gettext('%s: Hard coded function not allowed, create a Scilab function using call.'),'numdiff'));
end
%x=%x(:);
%n=size(%x,'*')
if argn(2)<3 then
%dx=sqrt(%eps)*(1+1d-3*abs(%x))
end
if size(params)==0 then
%y0=%__func(%x)
%g(size(%y0,1),%n)=0
for %j=1:%n
%v=0*%x;%v(%j)=%dx(%j);
%g(:,%j)=(-%y0+%__func(%x+%v))/%dx(%j);
end
else
%y0=%__func(%x,params(:))
%g(size(%y0,1),%n)=0
for %j=1:%n
%v=0*%x;%v(%j)=%dx(%j);
%g(:,%j)=(-%y0+%__func(%x+%v,params(:)))/%dx(%j);
end
end
endfunction
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