Mastering Numerical Computing with NumPy

Cholesky decomposition

If you have a square matrix, you can also apply Cholesky decomposition, where you decompose a matrix (M) into two triangular matrices (U and U^T). Cholesky decomposition helps you to simplify computational complexity. It can be summed up in the following formula:

M=U^TU

The following is an illustration of Cholesky decomposition:

Let's see how it's implemented using numpy:

from numpy import arrayfrom scipy.linalg import choleskyM = np.array([[1, 3, 4],[2, 13, 15],[5, 31, 33]])print(M)# Output[[ 1  3  4] [ 2 13 15] [ 5 31 33]]L = cholesky(M)print(L)# Output[[1.         3.         4.        ] [0.         2.         1.5       ][0.         0.         3.84057287]]L.T.dot(L)# Outputarray([[ ...