calculating the integration, arrayfun problem???

Hi all. I have a question. My code is

f = @(theta)(arrayfun(@(x,y)(det(sigmaZ/sin(x).^2 + eye(4)))^-1,theta));
out = quad(f,0,pi/2);

I want to add the expression "exp((sin(x)^2.*eye(4))^-1)" to my code.

But when I type f like this

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

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

It gives an error again. How can I fix it?

Error using arrayfun Non-scalar in Uniform output, at index 1, output 1. Set 'UniformOutput' to false.

Error in @(theta)(arrayfun(@(x,y)((det(sigmaZ/sin(x).^2+I))^-1)*exp(((sin(x).^2).*eye(4))^-1),theta))

Error in quad (line 72) y = f(x, varargin{:});

Error in Union_bound_rayleigh (line 104) out = quad(f,0,pi/2);

[Azzi Abdelmalek]

why @(x,y)

y is not used

[Azzi Abdelmalek]

can you writte the function you want to compute? ( without arrayfun)

Answer 1

[Honglei Chen]

First of all, like @Azzi mentioned in the comment, your y is unused.

It's not clear what you want to do, but

exp(((sin(x).^2).*eye(4))^-1

returns a matrix, but the expression in front of it returns a scalar for each input. Therefore, the entire expression gives a matrix. Even if you set 'UniformOutput' to false, I don't think quad can deal with it directly. So I would suggest you to check your equation again and make sure that's what you want.

[Serhat]

sigmaZ=rand(4,4);

mZ=1;

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

I know the expression inside exp is a matrix. That is why I am in trouble to calculate the integral. Isn't it possible to evaluate this in matlab?

Answer 2

[Mike Hosea]

I'm not sure what type of mathematical problem you are trying to express and solve. If you have a function f(x) which returns a 4-by-4 matrix when given a scalar x, then each element of y = f(x) can be considered a function of x. Say f(x) = [f1(x),f2(x);f3(x),f4(x)]. Then

Q = integral(f,a,b,'ArrayValued',true)

will return a 4-by-4 matrix Q where Q(1,1) = integral(f1,a,b), Q(2,1) = integral(f2,a,b), etc.

If, however, your function y = f(x) is supposed to return a scalar y given a scalar x, then the integrators expect f to be defined in such a way that if x is a vector or matrix, the function is evaluated at each element. So, if you give an input of x = [1,2,3,4], it expects y = [f(1),f(2),f(3),f(4)] to be returned. ARRAYFUN is a handy way of making that work for a function f that is not written to work "elementwise" like that, but actually here again

Q = integral(f,a,b,'ArrayValued',true)

solves the problem because if you tell INTEGRAL that f is an array-valued function, it won't dare to call it with more than a scalar.

If you don't have r2012a, you won't have INTEGRAL. In that case, if you are trying to compute a matrix output, try using QUADV instead of QUAD. You won't need ARRAYFUN with QUADV.