`integral` function: "Output of the function must be same size as input" error

I am trying to use the integral function in MatLab, but I get the following error depending on the anonymous function I use.

f = @(x) x;
integral(f, 1, 2) % WORKS %

ans = 1.5

% Change function
f = @(x) 1;
integral(f, 1, 2) % ERROR %

Error using integralCalc/finalInputChecks (line 526)

Output of the function must be the same size as the input. If FUN is an array-valued integrand, set the 'ArrayValued'

option to true.

What is this error, and why is it sensitive to the function I use?

Answer 1

[Walter Roberson]

integral() will call the given function with a vector of values, and the function must return one value for each element in the vector.

f = @(x) 1;

however, that code returns the scalar constant 1, rather than one 1 for each element of the input x. You should instead code

f = @(x) ones(size(x));

Alternately you can code

integral(f, 1, 2, 'arrayvalued', true)

but that can be slower as it forces integral() to not use vectorized calls.

[Abhijit Kale]

I see. So it's like using vector ops to speed things up. I suppose I would also need to to use element-wise operator in my functions to accomodate that?

[Walter Roberson]

It isn't just "like" using vector ops to speed things up, it is using that.

https://www.mathworks.com/help/matlab/ref/integral.html#btbbkta-1-fun

For scalar-valued problems, the function y = fun(x) must accept a vector argument, x, and return a vector result, y. This generally means that fun must use array operators instead of matrix operators. For example, use .* (times) rather than * (mtimes). If you set the 'ArrayValued' option to true, then fun must accept a scalar and return an array of fixed size.

[Abhijit Kale]

Alrighty! Thanks