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

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Abhijit Kale
Abhijit Kale 2020-12-1
评论： Abhijit Kale 2020-12-1
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?

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Walter Roberson
Walter Roberson 2020-12-1
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.
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Walter Roberson
Walter Roberson 2020-12-1
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.

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