How can you use symbolic functions as inputs and outputs of regular matlab functions

I want to use a symbolic expression as an input to a regular old matlab function and I want the matlab function to return a different symbolic function. For example, I want to be able to go:

syms x;
f(x)=sin(x);
new_function=function_I_will_write(f);

And then new_function(x) will output the symbolic variable x or something.

[Matt Grant]

I'm finding that passing symbolic functions only works if you use the same name for the symbolic variable both inside and outside the function.

For example, the function I'm writing is supposed to output a symbolic function g(T), given some input function f(T). If I go:

syms T;
f1(T)=T;
f2(T)=my_routine(f1);

Where my_routine is:

    function g = my_routine(f)
       syms T;
       g(T)=1+f(T)
    end

then everything works fine. Ie, the output is:

f2(T) = 

T + 1

But if I try to make the output a function of something other than T, such doing:

    syms x;
    f1(x)=x;
    f2(x)=my_routine(f1);

then f2(x) comes out as a function of T instead of x, ie, I get:

    f2(x) =

    T + 1

Answer 1

[Walter Roberson]

In cases where function_I_will_write never compares the input to anything (e.g., tests for negative), and does not specifically test for numeric data types, it is common for passing symbolic expressions to "just work". There are cases where there are conflicts between numeric routines and symbolic routines. For example, if you have

syms x;
f(x)=sin(x);
X = sym('X', [1 10]);
result = my_routine( f(X) )

then you would have problems if my_routine is, for example,

function M = my_routine( v )
  M = max( diff(v) );

because diff() of symbolic values is differentiation whereas the routine is expecting to do numeric differences equivalent to v(2:end) - v(1:end-1) for vectors.

[Matt Grant]

I'm finding that passing symbolic functions only works if you use the same name for the symbolic variable both inside and outside the function.

For example, the function I'm writing is supposed to output a symbolic function g(T), given some input function f(T). If I go:

syms T;
f1(T)=T;
f2(T)=my_routine(f1);

Where my_routine is:

    function g = my_routine(f)
       syms T;
       g(T)=1+f(T)
    end

then everything works fine. Ie, the output is:

f2(T) = 

T + 1

But if I try to make the output a function of something other than T, such doing:

    syms x;
    f1(x)=x;
    f2(x)=my_routine(f1);

then f2(x) comes out as a function of T instead of x, ie, I get:

    f2(x) =

    T + 1

Answer 2

[Ethan Duckworth]

If I understand what you want to do, I think it can be done by querying the input to get the variable, then using whatever syms variable inside the function you want via subs, and then changing back for the output.

Here's an example:

function out = add_x(f)
syms y;
fvar = symvar(f);
f=subs(f,fvar,y);
out= y + f;
out = subs(out,y,fvar);
end

when I run this I get the following

syms t
f(t)=t^2
g = add_x(f) % ha ha, it's not x that's added

g(t)=t^2+t