How to split a function according to their variables?

Hi. I want to split function according to their variables.

For example

f(x1,x2,y1,y2) = 10*x1 + 20*x2 + 10*y1 + 10*y2 ;

And I want to split like below.

f(x1) = 10*x1 ;
f(x2) = 20*x2 ; 
f(y1) = 10*y1 ; 
f(y2) = 20*y2 ; 

Please help me...!

[KSSV]

Already you have done it....what else you want?

[연승 김]

I think I gave a wrong example.... sorry about it.

If there is a more complecated function, how can I do this automatically??

It means I don't have to code the function f(x1), f(x2), f(y1), f(y2) each one by one.

f(x1,x2,y1,y2) = 10*x1 + 20*x2 + 10*y1 + 10*y2 + log(x1) + 1/x1 + 1/y1 ;
f(x1) = 10*x1 + log(x1) + 1/x1  ;
f(x2) = 20*x2 ; 
f(y1) = 10*y1 + 1/y1  ; 
f(y2) = 20*y2 ; 

Answer 1

[DGM]

There's probably a better way, but I never really use symbolic stuff. I'll just throw this out there. I renamed the functions just for clarity purposes in the scope of this example.

syms x1 x2 y1 y2
fparent(x1,x2,y1,y2) = 10*x1 + 20*x2 + 10*y1 + 10*y2 + log(x1) + 1/x1 + 1/y1;

C = cell2sym(children(fparent))

C = 

f_x1(x1) = sum(C(has(C,x1)))

f_x1(x1) = 

f_x2(x2) = sum(C(has(C,x2)))

f_x2(x2) = 

f_y1(y1) = sum(C(has(C,y1)))

f_y1(y1) = 

f_y2(y2) = sum(C(has(C,y2)))

f_y2(y2) = 

If you're using something older than R2020b, you'll have to remove the cell2sym() call.

Mind you, this all assumes that the expression is a simple sum (hence the use of sum() to reconstruct the subexpressions). What's supposed to happen if the function expression is something like this?

fparent(x1,x2,y1,y2) = exp(x1*sin(log(x2)))/(y1*x1 + atan(y2));

[Walter Roberson]

DGM's use of has() is better than what I came up with.

[연승 김]

Thank you for your kind!!

C = cell2sym(children(fparent))

This code works well^^

Answer 2

[Walter Roberson]

syms x1 x2 y1 y2
f(x1,x2,y1,y2) = 10*x1 + 20*x2 + 10*y1 + 10*y2 + log(x1) + 1/x1 + 1/y1 ;
fx1 = mapSymType(f, "plus", @(X) SelectPlus(X, x1))

fx1(x1, x2, y1, y2) = 

fx2 = mapSymType(f, "plus", @(X) SelectPlus(X, x2))

fx2(x1, x2, y1, y2) = 

fy1 = mapSymType(f, "plus", @(X) SelectPlus(X, y1))

fy1(x1, x2, y1, y2) = 

fy2 = mapSymType(f, "plus", @(X) SelectPlus(X, y2))

fy2(x1, x2, y1, y2) = 

function selected = SelectPlus(Expression, var)
   ch = children(Expression);
   selected_ch = ch(cellfun(@(X) ismember(var, symvar(X)), ch));
   selected = sum([selected_ch{:}]);
   if isempty(selected); selected = sym(0); end
end

[연승 김]

Thank you for your kind.

You are genius for me!!!