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Re: Newton Raphson for nxn system using symbolic toolbox
Posted:
Nov 15, 2011 5:15 AM
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Christopher Creutzig <Christopher.Creutzig@mathworks.com> wrote in message <4EC235EE.9040108@mathworks.com>...
> On 11.11.11 16:17, Uwe Brauer wrote:
>
> > I can perfectly write matlab code for solving Newton Raphson for any nxn system, since Matlab uses dynamic memory,
> > and I have to use as a entry variable the system I want to solve and its jacobian.
> >
> > However when i only want to have the system and use Matlabs symbolic tool to calculate the jacobian I do not know how to do that since I don't know the size of the jacobian in advance.
>
> I still don't understand the problem. Something like the following
> sketch should work, no?
>
> ...
> J = jacobian(expression, vars);
> ...
> % within some loop:
> ...
> Fval = double(subs(expression, vars, values));
> Jac = double(subs(J, vars, values));
> ...
>
>
>
> Christopher
right, after thinking about it I came up with a similar solution,
BTW why do you use double?
function xvec=newtoniteratesymb(f,e,x0,TOL,nmax)
n=x0;
fev=subs(f,e,n);
jac=jacobian(f,e);
jacev=subs(jac,e,n);
xvec=x0;
k=1;
diff=100;
while diff>TOL & k<nmax
fev=subs(f,e,xvec(:,k));
jacev=subs(jac,e,xvec(:,k));
xvec(:,k+1)=xvec(:,k)- jacev\fev;
diff=max(max(xvec(:,k+1)-xvec(:,k)));
k=k+1;
end
thanks
Uwe
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