How to do this double integration using integral2? Thanks!

Hi, I'm trying to write some code to calculate accumulated the probability of using integral2. Here is my code:

clear;
ae=-4;be=4;
az=-8;bz=8;
fune=@(e)1/(be-ae)*(e>=ae).*(e<=be); % density of e
funz=@(z)1/(bz-az)*(z>=az).*(z<=bz); % density of z
funezt=@(ez,t)fune(ez(:)-t).*funz(t); 
funez=@(ez)integral(@(t)funezt(ez,t),az,bz,'ArrayValued',true); % density of ez=e+z computed via convolution
funez12=@(ez1,ez2)funez(ez1).*funez(ez2); % joint density of (ez1,ez2)
aaa=integral2(funez12,0,4,0,4); %double integration on [0,4]^2

However, this code didn't work and has the following error message:

Error using integral2Calc>integral2t/tensor (line 241)
Integrand output size does not match the input size.

Have no clue about how to fix it, and need some insights. Thanks!

Answer 1

[Ameer Hamza]

To use a function as input to integral2, the input and output dimension must be the same. However, in your case, if we input a 2x2 matrices to funez12, the output is 4x1. Changing the line like this will correct the error

funez12 = @(ez1,ez2)reshape(funez(ez1).*funez(ez2), size(ez1)); % joint density of (ez1,ez2)

However, the correct solution depends on how you interpret the entries in the matrix.

[Tmat]

Thanks a lot, Ameer, it worked!

[Ameer Hamza]

Glad to be of help.