Problem: Integrating symbolic expression with dblquad

Hi there

I have a long list of symbolic functions which I would like to integrate with dblquad (this is an example of one such function):

sym x y
FUN(ii)=1/(x^(4/7)*exp(1/(8*x))*exp(y^2/(3*x^(2/5))));
IntFUN(ii)=dblquad(@(x,y) FUN(ii),0.1,400,0,200)

But the integration itself fails (error: Matrix dimensions must agree). If instead I do it with "." before all */^ it works fine:

IntFUN(ii)=dblquad(@(x,y) 1./(x.^(4./7).*exp(1./(8.*x)).*exp(y.^2./(3.*x.^(2./5)))),0.1,400,0,200)

   ans =

103.9509

Problem is, symbolic math apparently doesn't store the use of "." so I can't just convert all expressions to char, find the operators, add a "." and convert back to sym.

How do I solve this problem?

Answer 1

[Walter Roberson]

Use matlabFunction to convert the symbolic expression to a function handle.

You should not be using a symbolic expression for dblquad() -- dblquad() must be passed a function handle, and a symbolic expression is not a function handle.

Answer 2

[Jakob Sievers]

Thank you very much. That's exactly the piece of the puzzle I was missing.

You wouldn't happen to know if there's any fast way to do dblquad calls to a series of these functions (as defined through matlabFunctions)? The thing is, I have a few thousands of these equations, all of same structure but with varying constants. Since the equation appears unsolvable in an analytical form I have until now just set it up as a loop which runs dblquad for each equation, but more-often than not there are more clever, and timesaving, methods out there. I'm just not aware of any clever ways around this one.

[Walter Roberson]

If the structure is the same but the constants are different, you could use symbolic variables for the constants, matlabFunction() up the result, and pass the constants in using (e.g.)

@(x,y) mf_FUN{i}(x, y, c1, c2, c3)

where c1, c2, c3 had been retrieved (or calculated if appropriate)

[Jakob Sievers]

Thanks for your help. I will try this approach.