How to make a function handle from variable consisting of a function

I have a problem like this for example.

   x = sym('x',[7,1]);
   phi = [ (10001*x2)/800000 - (10001*x1)/400000 + (10001*x3)/600000 - (10001*x4)/1600000 + (10001*x5)/3000000 +  (10001*x6*x7)/200000];
   % ** This phi was copied from output just so you see how it looks

Is there a way I can make a function handle kind of like this?

   phi1 = @(x)phi

(I know this doesn't work but hopefully you get what I am trying to do) Basically I can't explicitly write out the function because it is generated from another algorithm. I don't know the syntax, or if you can even do this.

Also, can someone explain the difference between the operator @ and matlabFunction? Thanks!

Answer 1

[Star Strider]

You can’t get there directly because of the way the Symbolic Math Toolbox creates function calls with matlabFunction:

phi0 = matlabFunction(phi);
phi1 = @(x) phi0(x(1),x(2),x(3),x(4),x(5),x(6),x(7))

A subs call didn’t work, so typing it manually was the only option.

[Kristoffer Lindvall]

Thank you! It works... it might not be pretty but it works. Now the only problem is I have to craete the matlabFunction Like several hundred times so the code is still quite slow. My solver runs A LOT faster, but I kind go plus minus zero because of matlabFunction.

[Star Strider]

My pleasure!

The Symbolic Math Toolbox is not intended for iterative problems, so it can be very slow.

It looks as though you’re multiplying an unknown (‘x’) and a numeric vector. What specifically are you doing that requires the Symbolic Math Toolbox? (I’m thinking there might be an easier and more efficient way to do what you want.)

[Kristoffer Lindvall]

I am analytically iterating forth a set of equations that I solve with a semi implicit root solver. The entire program, which is too long to show here, is using a spectral method to solve a time dependent problem by taking as big of a time interval "leap" as possible for it to converge. I am trying to make my code run as fast in Matlab as it does in Maple. Matlab should include a way to make function handles on the fly like we just did without using the matlabFunction command.

I realize it is hard for me to explain why I need to do it analytically. That is how the algorithms for the method are written. I am struggling to find a way to do it numerically.

[Star Strider]

My approach would be to use the Optimization Toolbox function fsolve to find the roots, assuming I understood the problem well enough to formulate the function to give to it, and if it is possible to do it without the Symbolic Math Toolbox.

The Symbolic Math Toolbox solve function would avoid the necessity of creating an anonymous function, but I doubt it would be faster.