How do I convert multivariate function handle to symbolic function? Anyone has any ideas?

My function handle is as follows,

g=@(p)p(1)+p(2)

I can compute using function handle using something like

g([1,2])

Now I want to convert it to a symbolic function, but seems MATLAB has trouble assuming p(1) and p(2) as symbol. So

syms p(1) 
sym(g)

doesn't work. I guess I might need to change p(1),p(2) to p1,p2, but this is hard, too. Anyone can help?

Answer 1

[Walter Roberson]

P = sym('p', [1 2]);
G = g(P);

now G will be a symbolic expression in p1, p2. You can then convert it to a symbolic function by using

Gsym = feval(symengine, 'fp::unapply', G, P(1), P(2));

[Shawn Miller]

Thanks, could you please explain the second line a bit? Also, how do I call Gsym? It seems Gsym(1,2) doesn't work and can't compute Gsym at (1,2)

[Walter Roberson]

G = g(P) is just calling the function handle g passing in the vector [p1 p2] so the result for that g would be the symbolic expression p1+p2 .

I have no information about the ability to use sym() to convert an anonymous function to a symbolic function. I would not have guessed that it could be done, but I do not know.

Accordingly, the third line is the code to convert the expression G into a symbolic function by using the facilities of the symbolic engine, http://www.mathworks.com/help/symbolic/mupad_ref/fp-unapply.html . The result will be a symbolic function. Using it might require, for example,

feval(symengine, Gsym, 1, 2)

A symbolic function is a MuPAD procedure that returns one or more outputs and which might have 0 or more inputs and 0 or more statements.

You can also have anonymous functions in MATLAB which happen to involve terms that are symbolic. I suspect that this must be pretty close to how

syms f(x)

is implemented, except with the default variables decided by the name of the dummy arguments of the anonymous function. I do not, however, have the Symbolic Toolbox to check this detail.

[Shawn Miller]

Seems G=symfun(G,symvar(G)) also works.

[Walter Roberson]

Ah, that sounds good.