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How to find double integral in MATLAB

Asked by may on 16 Sep 2013

Given mean1, mean2, sigma1,sigma2, and u, I want to find the following integral:

for example: mean1=0, mean2=0, sigma1=0.2, sigma2=1, and u=0.4

F = @(x,y)normpdf(x, mean1, sigma1).*normpdf(y, mean2, sigma2).*dirac(x*y-u);
answer= integral2(F,-Inf,Inf,-Inf,Inf);

but I get the following error

|Error using integralCalc/finalInputChecks (line 511) Input function must return 'double' or 'single' values. Found 'function_handle'.|

I would appreciate if you could help me to fix my code. Thank you.

11 Comments

may on 17 Sep 2013

Thanks for your help. I think another way is to approximate the distribution of X*Y by producing some random numbers from the distribution of X and Y then multiply them all together and find its histogram.

Walter Roberson on 17 Sep 2013

If you define a true function you can use conditional logic for it.

function r = F(x)
  r = zeros(size(x));
  r(x==0) = whatever it should be;
  nzx = x(x ~=0);
  r(x~=0) = normpdf(nxz, mean1, sigma1).*normpdf(u./nzx, mean2, sigma2).*(1./abs(nzx);
end
may on 17 Sep 2013

Nice answer! Thank a lot!

may

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2 Answers

Answer by Sean de Wolski on 16 Sep 2013

Running your example I get an error saying the matrix dimensions must agree. Changing the x*y to x.*y inside of dirac allows it to run and returns an answer of zero

F = @(x,y)normpdf(x, mean1, sigma1).*normpdf(y, mean2, sigma2).*dirac(x.*y-u);
answer= integral2(F,-Inf,Inf,-Inf,Inf);

1 Comment

may on 16 Sep 2013

thank you, but now I get zero for all the inputs i am trying.

Sean de Wolski
Answer by Walter Roberson on 16 Sep 2013

Which dirac are you using? It appears you might be using dirac from the Symbolic toolbox, You should experiment with

class(dirac(5))   %for example

You might need something like double(dirac(x*y-u)) in your code instead of a plan dirac() call.

1 Comment

Walter Roberson on 16 Sep 2013

You should be using symbolic integration instead of numeric integration. symbolic integration is int() in the Symbolic Toolbox

Walter Roberson

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