Karl
0
Why when performing numerical integration in Matlab with integral does this case need 'ArrayValued' to be set to true:
f = @(x) 5;
integral(f,0,2,'ArrayValued',true)
... while in this case the option isn't needed?:
f = @(x) x;
integral(f,0,2)
From the documentation for integral describing the integrand argument:
For scalar-valued problems, the function
y = fun(x)must accept a vector argument,x, and return a vector result,y. This generally means thatfunmust use array operators instead of matrix operators. For example, use.*(times) rather than*(mtimes). If you set the'ArrayValued'option totrue, then fun must accept a scalar and return an array of fixed size.
So, a constant function like f = @(x) 5 does not return a result the same size as x if x is a vector. The integral function requires this because under the hood it is vectorized for scalar functions for performance – it actually evaluates the integrand at multiple points simultaneously with a single function call.
You can make your constant function compliant and not require 'ArrayValued' to be true with something like this:
f = @(x) 5+0*x;
integral(f,0,2)