I want to integrate a function using quadpy. I noticed that quadpy passes numpy arrays as arguments to the function. For example, if I define f = lambda x: x**2, then quadpy will integrate passing a vector like x = [0, 0.3, 0.7, 1].
The function I want to integrate is long (300 lines of code) and when I coded it I was thinking in passing two real numbers as arguments, not vectors. Now that I want to integrate or plot, it seems very important that my function can handle vectors. Which methods or tricks do you know to vectorize a function? numpy.vectorize does not seem to work in every case.
In my case, one of the problems is:
def f(t):
U = np.array([[1, 0, 0 ],
[0, np.cos(t), np.sin(t)],
[0, -np.sin(t), np.cos(t)]])
V = np.array([[np.cos(t), 0, np.sin(t)],
[0, 1, 0 ],
[-np.sin(t), 0, np.cos(t)]])
return U @ V
When I run the code, quadpy replaces, say, np.cos(t) by an array, so the system throws an error telling me that I should specify 'dtype=object', and then the program collapses when it tries to operate U @ V over vectors.
How can I deal with these kind of problems? Other problem is that I multiply, say, constant(t)*vector(l),
so the constant becomes a vector, vector(l) becomes an array of arrays, and the system starts to complain again. Should I always define my functions bearing vectorization in mind?
Check https://github.com/sigma-py/quadpy/wiki/Dimensionality-of-input-and-output-arrays on what the dimensions of the input array mean, and how to construct an output array.