How to assign values to variables in a handle function?

Question

This is simplified but take as an example the following MATLAB function handle:

F = @(x)[x(1)-x(2);x(2)-x(3)]

The system has of course has many solutions. Is it possible to obtain a solution for a function like this one after substituting at least one variable? For example, substituting x(3)=1 the function would become:

G = @(x)[x(1)-x(2);x(2)-1]

And a solution for the other variables can be obtained. I use fsolve and it works quite well for the system of equations I have. Of course what I need to do can be done using the Symbolic Toolbox, but calling it in a big for loop makes it too slow to use for my code.

I'm trying to come up with some code that can return G given F and a set of indices in x to replace with given values.

Answer 1

What you're basically asking to do is have G call F with values in x reassigned based on a logical replacement index index and a set of replacement values values, which is doable but messy since anonymous functions can only have a single executable statement.

The solution is similar to what is done in this answer, but instead of using the functional form for subscripted reference we'll need to use the functional form for subscripted assignment: subsasgn. Here's what it would look like:

F = @(x)[x(1)-x(2); x(2)-x(3)];
values = [3 2 1];
index = logical([0 0 1]);
G = @(x) F(subsasgn(x, struct('type', '()', 'subs', {{index}}), values(index)));

And here's a test:

>> F([3 2 3])

ans =

     1
    -1

>> F([3 2 1])  % Replace the last element by 1

ans =

     1
     1

>> G([3 2 3])  % G handles replacing the last element by 1

ans =

     1
     1