Asked by Christopher Kodama
on 29 Apr 2013

I'm trying to work with integrals that are functions of one of their limits:

For example,

phi = @(x) quad(@(L) besseli(1, (1+L)/(1-L)), 0, x);

What I'm trying to do is evaluate phi over an array of values, like:

phi([1,2,3,4]); %ERROR quad(@(L) besseli(1, (1+L)/(1-L)), 0, [1,2,3,4]); %ERROR

but these return errors. I could do this in a for loop, like:

nums=[1,2,3,4]; for(k=1:4) phi_eval = phi(nums(k)); end

but I was wondering if there was a better way to do things. Is there a no-for-loops way of doing this?

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Answer by Shashank Prasanna
on 29 Apr 2013

Accepted answer

Christopher, I can't run the loop as well. But phi([1,2,3,4]) will certainly not work because the vector is being passed to quad directly as limits which is wrong syntax for quad.

You can try the following:

arrayfun(phi,[1,2,3,4])

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Mike Hosea
on 10 Mar 2014

Please go to my profile. Where it says "email", click on "contact Mike Hosea" and tell me about your use cases for array-valued limits. If we're talking **generic** array limits, where there is no *a priori* relationship between the different elements of the limits, then no gain in efficiency can be had over writing a loop. E.g.

Q = zeros(size(a)); for k = 1:numel(Q) Q(k) = integral(f,a(k),b(k)); end

For scalar-valued integrations, that can also be accomplished efficiently with an application of arrayfun, e.g.

Qarray = @(a,b)arrayfun(@(ak,bk)integral(f,ak,bk),a,b); Q = Qarray(a,b);

However, if we are talking about table-building, where the limits represent a grid, then efficiency improvements are possible. The latter use case might be accomplished by some other means, however, such as providing scalar limits and a list of output points for the integrals over partial regions.

Opportunities for recent engineering grads.

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