Make an double integral function

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pankaj singh 2021-11-25

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回答： Bjorn Gustavsson 2021-11-25

I want to make the double integration function (as per the formula shown in figure below) and then evaluate the integral for the given range of x and y. Please help me make the function.

My code is something like this but gives error:

fun = @(x,y) 1/sqrt(2*pi).*exp(-x.^2/2).*exp(-1/2.*(y+(u_j-u_m)/sigma_sq)).^2);
q = integral2(fun,y,Inf,-Inf,inf);

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Answer 1

Bjorn Gustavsson 2021-11-25

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By putting the product inside the first pair of square brackets you've made the formula look a little bit confusing - since the only factors that depend on j and m_n are outside that parenthesized factor, but I'll give it a try...

The inner integral over x is just the error-function:

(erf(y/2^(1/2)) + 1)/2

This should give you a modified function, something like this:

fun = @(y) ((erf((2^(1/2)*y)/2) + 1))/2.*exp(-1/2*(y+(u_j-u_m)/s_n).^2);

Which for your desired values of u_j, u_m and s_n will integrate just fine from -inf to inf.

HTH