Numerical integration with array limits
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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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Shashank Prasanna
2013-4-29
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])
6 个评论
Christopher Kodama
2013-4-29
Mike Hosea
2013-5-2
Note that both quad and quadv are deprecated. Use integral instead. If you want to integrate a vector-valued problem, use
integral(...,'ArrayValued',true)
Wenjuan
2013-12-5
What if both limits are vectors as well? I don't think integral, quad or quadv can deal with this, but how to use arrayfun in this? Thanks.
Leo Simon
2014-2-11
I too would like to specify vector valued integration limits. If anybody from mathworks is listening could you please respond? This should be really easy to implement I imagine, and hopefully will be in the next release?
Mike Hosea
2014-3-10
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.
Ashish Bhatt
2017-4-10
it works with both array limits as well:
phi = matlabFunction(int(x^2,x,a,b));
arrayfun(phi,vec1,vec2)
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