Let's say I have an N row by M column NumPy array. Each row contains the values of each of N functions, over M intervals. I have a vector X, which contains the x-values at which the functions were evaluated. I also have another NumPy array which is a 1D vector of length N. I want to interpolate each of the N functions to find their respective values at each of the N points in the vector. For instance, if I have
X = np.array([0.2,0.4,0.6,0.8])
matrix = np.array([[1,2,3,4],
[2,4,6,8],
[1,3,5,7]]) # N = 3, M = 4
vector = np.array([0.3, 0.6, 0.5])
def f(X, matrix, vector):
# Some code
return interpolated_values
interpolated_values should contain [1.5, 6, 4] because those are the values that each row of matrix has when linearly interpolated at the corresponding value of X.
I know I could do this using loops. But, if N is very large this would be slow. What should be in the function f to do this interpolation in parallel?
I guess the real issue comes in if X is is not the same vector for each of the N functions. I.e., X is no longer 1 x M, but it is instead N x M. Is there a way to parallelize the interpolation in this case (where the x-values of each function to be interpolated are not the same)?
Based on your requirement, the interp function would be beneficial to use.
import numpy as np
def f(X, matrix, vector):
interpolated_values = np.apply_along_axis(np.interp, 0, X, matrix, vector)
return interpolated_values
Explanation of the above code:
np.apply_along_axis(np.interp, 0, X, matrix, vector). This applies the np.interp function on each row of the matrix.np.interp. Interpolates the values of vector at the x-coordinates specified by X. Which will help you get the interpolated values for each function in parallel, and that should be much faster than using a loop if N is large.