Nested integral within integral2
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I'm attempting to take the double integral (using integral2) of a function that is defined by an integral.
Here is what I am currently attempting:
t=linspace(0,1,50);
fun_1= @(v) exp(.071*v)
fun = @(x,y) 0.14*0.00607*integral(@(u)fun_1(u),0,x).*exp(-(x-y).^2).*0.14*0.00607*integral(@(u)fun_1(u),0,x);
for i=2:length(t)
for j=i:length(t)
A(i,j)=integral2(fun,t(i-1),t(i),t(j-1),t(j));
end
end
I'm receiving the error
Error using integral (line 86) A and B must be floating point scalars.
Can anyone provide any information on how to fix this problem.
采纳的回答
Mike Hosea
2013-8-24
The problem here is that integral2 requires that the integrand accept arrays as inputs and return arrays as outputs, but integral only accepts scalars for the left- and right-hand end points. You just need to vectorize the call to integral. Also, I assume you meant to use y in the second call to integral.
n = 12; % Increase to 50 when you're ready, but be prepared for a wait!
t = linspace(0,1,n);
fun_1 = @(v) exp(.071*v);
int_fun_1_scalar_inputs_only = @(x)integral(fun_1,0,x);
int_fun_1_vectorized = @(x)arrayfun(int_fun_1_scalar_inputs_only,x);
fun = @(x,y) 0.14*0.00607*int_fun_1_vectorized(x).*exp(-(x-y).^2) ...
.*0.14*0.00607.*int_fun_1_vectorized(y);
A = zeros(n); % Preallocate A
for i=2:n
for j=i:n
A(i,j)=integral2(fun,t(i-1),t(i),t(j-1),t(j));
end
end
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