(Below is kinda note-to-self. This is the re-write of an old blog entry, based on Generating correlated random numbers by Thijs van den Berg)
Say I want to generate 3 series of random numbers correlated according to the following correlation matrix:
from scipy.linalg import cholesky # Correlation matrix corr_mat= np.array([[1.0, 0.6, 0.3], [0.6, 1.0, 0.5], [0.3, 0.5, 1.0]]) # Compute the (upper) Cholesky decomposition matrix upper_chol = cholesky(corr_mat) # Generate 3 series of normally distributed (Gaussian) numbers rnd = np.random.normal(0.0, 1.0, size=(10**7, 3)) # Finally, compute the inner product of upper_chol and rnd ans = rnd @ upper_chol
Now, one can check results are consistent:
# One can check results are consistent from scipy.stats import pearsonr corr_0_1 , _ = pearsonr(ans[:,0], ans[:,1]) #corr_0_1 #0.60013025775533102 corr_0_2 , _ = pearsonr(ans[:,0], ans[:,2]) #corr_0_2 #0.30049740204791148 corr_1_2 , _ = pearsonr(ans[:,1], ans[:,2]) #corr_1_2 #0.50026641543258898
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