NaN (Not a Number) problem in integration

Hi all. I am trying to calculate this integration, it gives NaN ,instead of pi/2. How can I solve the problem?

mz=zeros(4,1); h=zeros(4); I=eye(4);

f=@(x)(arrayfun(@(x)(exp(-mz'*(1./(h+((sin(x).^2).*I)))*mz)),x));

out = quad(f,0,pi/2)

Thanks

Answer 1

[José-Luis]

No, it should not give you pi/2. The way you have set up your matrices, the expression

h+((sin(x).^2).*I)))*mz

will always be equal to zero. Division by 0 = Inf.

[Serhat]

You misunderstood, ((h+((sin(x).^2).*I)).^-1)*mz is my function. So it equals 1/(I matrix) * mz and mz=0, then the function is 0=>exp(0)=1 isn't it?

[José-Luis]

I'm afraid it's not. Have you tried to visualize your function? Copy/pasting your code and running:

f(0) = NaN;
f(whatever) = NaN;

and that is because

exp(-mz'*(1./(h+((sin(x).^2).*I)))*mz)

will evaluate to NaN, with mz and I defined as you did. Maybe you have misplaced a parentheses?

[Serhat]

Now it works, you are right. I put parentheses at wrong places. Thank you very much.

f = @(theta)(arrayfun(@(x)(det(sigmaZ./sin(x).^2+eye(4,4)).^-1)*exp(-1*mZ'*1/(sigmaZ+sin(x).^2.*eye(4))*mZ),theta));

[José-Luis]

My pleasure.