CODEWITHSUNDEEP
matlabnumerical-integration
user2288327
user2288327

Reputation: 1

Integrating a multi-variable function over a single variable without defining a new function

I have a function f = @(x,y,z) ... I want to perform a finite numerical integral over x with given numerical values for y and z.

At present, I do this as follows - 

f2 = @(x) f(x,5,10)
integral(f2,-1,1)

(5 and 10 are really just some y and z that have assumed certain values over the course of the program).

My question is as follows -

Since I have to do this integral over many many values of (y,z) (in a loop typically). Everytime, I have to redefine a function. This presumably makes my program very slow. Is there a more optimal way to go about doing this operation wherein I don't have to constantly redefine my function. I need the program to run faster.

Thanks!

Upvotes: 0

Views: 2676

Answers (2)

chgreer
chgreer

Reputation: 43

I was able to speed up some looping code (an MCMC) with many integrals using the composite Simpson's method detailed in "Writing Fast Matlab Code" available at the File Exchange:

http://www.mathworks.com/matlabcentral/fileexchange/5685

From the document, here is a one dimensional integration as an example:

h = (b − a)/(N−1);
x = (a:h:b).';
w = ones(1,N); w(2:2:N−1) = 4; w(3:2:N−2) = 2; w = w*h/3; 
I = w * f(x);

The document shows 2 and 3d examples as well.

As a downside, the code forgoes some of the adaptive step size in some of the built-in quadrature methods. However, this method is so blazingly fast, I was able to just brute-force integrate to such a high precision that this isn't an issue. (My integrals are all relatively tame, though.)

Hope this helps.

Upvotes: 0

user2271770
user2271770

Reputation:

Anonymous functions are slow. How about rewriting f and f2 as nested functions? For example:

function result = iterate_trough(A, B)

        result = 0;
        for a = 1:2:A, for b = 5:5:B
                result = result + quad(@f2,-1,1);
        end; end;

        function r  = f(x,y,z),  r  = x+y+z;     end
        function r2 = f2(x),     r2 = f(x,a,b);  end
end

Would this diminish the flexibility of your code?

Later edit: Or even better, eliminating the overhead of calling f:

function result = iterate_trough(A, B)

        result = 0;
        for a = 1:2:A, for b = 5:5:B
                result = result + quad(@f2,-1,1);
        end; end;

        function r2 = f2(x),  r2 = x+a+b;  end
end

Upvotes: 1

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