I need to obtain the covariance between an array a of shape (M1, M2, N) and another array b of shape (N,).
What I currently do is use a for block:
import numpy as np
M1, M2, N = 23, 50, 117
a = np.random.uniform(-2., 2., (M1, M2, N))
b = np.random.uniform(-1., 1., N)
c = []
for i in range(M1):
for j in range(M2):
c.append(np.cov(a[i][j], b)[0, 1])
but it gets a bit slow for large (M1, M2). Is there a way to speed this up?
You can always calculate the cov by hand. Here are two suggestions using dot and einsum respectively.
import numpy as np
M1, M2, N = 23, 50, 117
a = np.random.uniform(-2., 2., (M1, M2, N))
b = np.random.uniform(-1., 1., N)
c = []
for i in range(M1):
for j in range(M2):
c.append(np.cov(a[i][j], b)[0, 1])
c1 = np.reshape(c, (M1, M2))
ac = a - a.mean(axis=-1, keepdims=True)
bc = (b - b.mean()) / (N-1)
c2 = np.dot(ac, bc)
c3 = np.einsum('ijk,k->ij', ac, bc)
print(np.allclose(c1, c2))
print(np.allclose(c1, c3))
Prints
True
True
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