Nesting multidimensional integrals when the integrand has if-else statements

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Adamya Goyal 2021-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/1442869-nesting-multidimensional-integrals-when-the-integrand-has-if-else-statements

编辑： Adamya Goyal 2021-8-29

Hi, I am trying to do a multidimensional nested integral of a function that has if-else conditions in it. I know how to do nesting of integrals but I don't understand why I am getting the following error. Please see the code below. My issue is that Matlab throws a "Could not complete in 10000 steps" error even if the integrand is simple and regular. Is there a way to avoid this? Thanks.

func1 = @(k,p,v)integrdef(k,p,v);
func2 = @(p)integral2(@(k,v)arrayfun(@(k,v)func1(k,p,v),k,v),0,5,0,3);
%Ignore this line %func3 = integral(func2,0,7,'ArrayValued',true) %Ignore this line
func2(2)
function integrout=integrdef(a,b,c)
if (a>2) && (b>1)
    integr = a.*b.*c;
else
    integr = 0;
end
integrout = integr;
end

The output is as follows:

>> UpSEplusVert_pureintra_calc1
Warning: Reached the maximum number of function
evaluations (10000). The result fails the
global error test. 
> In integral2Calc>integral2t (line 129)
  In integral2Calc (line 9)
  In integral2 (line 106)
  In UpSEplusVert_pureintra_calc1>@(p)integral2(@(k,v)arrayfun(@(k,v)func1(k,p,v),k,v),0,5,0,3)
  In UpSEplusVert_pureintra_calc1 (line 15) 
ans =
   9.4496e+01

It gives nearly the correct answer but I'd like high precision i.e. low global error. The exact answer is 94.5 but I get 94.496 instead. My actual goal is to do a 4-D integral using "integral3" and "integral" nesting, but for simplicity I have created a model example above which is only 3-D and solved it using a nesting of "integral2" and "integral" for illustration. Thanks.