I want a vaule of function instead of formula

I have a little complex function that need to be integrated twice. But the result is a formula that I programed. How can I fix it?

This is my code that has simplified:

syms a b x y
fun1= @(a,b,x,y)
    exp(-( (a-x0).^2+(b-y0).^2 ).^2).*...
    exp(-1i.*(k.* ( (a-x0).^2+(b-y0).^2 )./2) ) .*...
    exp(-1i.*2.*pi.*(a.*(x-x0)+b.*(y-y0)));
f0=int(fun1,a,-limit,limit);
f0=int(f0,b,-limit,limit);

I don't need to get a more precise value. Maybe could use "double" or something.

And I tried "subs" that I found in another question place, but it has an error.

Answer 1

[Sugandhi]

Hi Jacky Wang,

I understand that you want value of a complex function that need to be integrated twice.

To obtain a numerical solution for the double integral, the following might be a possible workaround:

Use the `vpa` function to evaluate the symbolic expression at a given precision. And then use the `double` function to convert the result to a double-precision floating-point number.

Here's an example of how the code can be modified to obtain a numerical solution:

syms a b x y 
fun1 = exp(-( (a-x0).^2+(b-y0).^2 ).^2).*... 
    exp(-1i.*(k.* ( (a-x0).^2+(b-y0).^2 )./2) ) .*... 
    exp(-1i.*2.*pi.*(a.*(x-x0)+b.*(y-y0))); 

% Define limits and precision 
limit = 10; 
precision = 10; 

% Evaluate double integral using symbolic math 
f0_sym = int(fun1,a,-limit,limit); 
f0_sym = int(f0_sym,b,-limit,limit); 

% Evaluate symbolic expression at given precision 
f0_precise = vpa(f0_sym, precision); 

% Convert result to double-precision floating-point number 
f0_numeric = double(f0_precise); 

In this example, the `vpa` function is used to evaluate the symbolic expression at a precision of 10 decimal digits. Adjust the `precision` argument as needed to obtain the desired level of accuracy. The `double` function is then used to convert the resulting vpa object to a double-precision floating-point number.

For more understanding, kindly go through following links:

• For vpa function- https://www.mathworks.com/help/symbolic/vpa.html?searchHighlight=vpa&s_tid=srchtitle_vpa_1
• For double function- https://www.mathworks.com/help/symbolic/double.html?searchHighlight=double&s_tid=srchtitle_double_2