using integral2 on a matrix with function handler components
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Let's say that I have the following function: A = @(x,y) [x,x+y;x-y,y]; and I want to calculate the following integral: Q = integral2(A,0,2,3,5) How can I do this? How can I access and use the function that is defined inside the component i and j of my matrix? I cannot use e_i*A*e_j' because it is still matrix.
P.S. Here I know my function, but in my code I have a product of two different function handler matrix, thus I do not know my function s.t. I know here.
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Star Strider
il 25 Apr 2014
Modificato: Star Strider
il 25 Apr 2014
It seems that integral2 doesn’t take matrix integrands, but integral will, with the 'ArrayValued',true option.
This looks slightly strange, but see if it does what you want it to:
A = @(x,y) [x, x+y; x-y, y];
Q = integral(@(y) integral(@(x)A(x,y) ,0,2, 'ArrayValued',true), 3,5, 'ArrayValued',true)
It does produce the correct results with the matrix in your example. (Hand-calculating them to check it is fairly straightforward, if slightly tedious.)
Q =
4.0000e+000 20.0000e+000
-12.0000e+000 16.0000e+000
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Star Strider
il 25 Apr 2014
Modificato: Star Strider
il 25 Apr 2014
My pleasure!
I also experimented with separating the matrix into its components and using integral2 with each of them. That actually took much longer than the nested integral call with the 'ArrayValued',true option.
In the situation you describe, it will probably be necessary for you to loop over the double integral (or nested single integrals), integrating over a short sub-interval each time and substituting the value calculated by the outer integral in the inner integral at the end of each loop. It’s not ideal, but it’s probably the only way to approach that problem. The nested single integrals with the 'ArrayValued',true option will let you integrate your matrix, though.
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Navid
il 25 Apr 2014
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Star Strider
il 25 Apr 2014
Nesting two calls to integral works, without having to break the matrix apart into its components.
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