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How to use integral with an implicit function defined through a sum

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Alex Dytso
Alex Dytso 2020-7-16
回答： Steven Lord 2020-7-16
Suppose we have a function define as follows:
fz=@(z) exp(-(z).^2/2);
g=@(y) sum ( v(1:n/2).*fz((y- v(n/2+1:n))));
here v is a vector of length n that is known and is used to define the fucntion g.
Now I want to integrated g from [-5,5] using command
integral(@(y) g(y), -5,5).
I, however, get an error that matrix dimensions must agree.
I get where the issue is. It occurs because I defined a function through a vector and pass another vector as input.
Is there a way of fixing this?

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Steven Lord
Steven Lord 2020-7-16
By default, integral will call your function with an array and expects your function to return an array of the same size as the output. If you specify the name-value pair arguments 'ArrayValued', true in your integral call it will instead call your function with a scalar and expect an array as output.
v = 2:5;
y1 = integral(@(x) x.^v, 0, 1, 'ArrayValued', true)
y2 = integral(@(x) x.^v, 0, 1) % Throws an error

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