Problem: Integrating symbolic expression with dblquad

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Jakob Sievers 2012-1-7

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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?

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Answer 1

Walter Roberson 2012-1-7

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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.

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Answer 2

Jakob Sievers 2012-1-7

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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.

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Walter Roberson 2012-1-7

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 2012-1-8