Suppose I have a very computationally expensive function f(x). I want to compute some values of it, and then just access them instead of evaluating the function every time with new x values.
See the following simple example to illustrate what I mean:
import numpy as np
x = np.linspace(-3, 3, 6001)
fx = x**2
x = np.round(x, 3)
#I want to evaluate the function for the following w:
w = np.random.rand(10000)
#Rounding is necessary, so that the w match the x.
w = np.round(w, 3)
fx_w = []
for i in range(w.size):
fx_w.append(fx[x==w[i]])
fx_w = np.asarray(fx_w)
So, I'd like to have f(w) computed from the values already generated for x. Of course, a for loop is out of the question, so my question is: how can I implement this somewhat efficiently?
You can use searchsorted to find the corresponding indices of your prepared function array. This will be an approximation. Rounding is not necessary.
import numpy as np
np.random.seed(42)
x = np.linspace(-3, 3, 6001)
fx = x ** 2
w = np.random.rand(10000)
result = fx[np.searchsorted(x, w)]
print('aprox. F(x):', result)
print('real F(x):', w ** 2)
Output
aprox. F(x): [0.140625 0.904401 0.535824 ... 0.896809 0.158404 0.047524 ]
real F(x): [0.1402803 0.90385769 0.53581513 ... 0.89625588 0.1579967 0.04714996]
Your function has to be much more computationally intensive to justify this approach
%timeit fx[np.searchsorted(x, w)] #1000 loops, best of 5: 992 µs per loop
%timeit w ** 2 #100000 loops, best of 5: 3.81 µs per loop