I have a symmetric positive-definite matrix (e.g. Covariance matrix), and I want to calculate its inverse. In math, I know that it is more efficient to use Cholesky decomposition to invert the matrix, especially if your matrix is big. But I was not sure how does "numpy.lianlg.inv()" works. Say I have the following code:
import numpy as np
X = np.arange(10000).reshape(100,100)
X = X + X.T - np.diag(X.diagonal()) # symmetry
X = np.dot(X,X.T) # positive-definite
# simple inversion:
inverse1 = np.linalg.inv(X)
# Cholesky decomposition inversion:
c = np.linalg.inv(np.linalg.cholesky(X))
inverse2 = np.dot(c.T,c)
Which one is more efficient (inverse1 or inverse2)? If the second one is more efficient, why is numpy.linalg.inv() not using this instead?