Difference between np.dot, np.tensordot, and np.matmul

code:python

import numpy as np

def same_matrix(A, B):

return (A.shape == B.shape) and all(A.flatten() == B.flatten())

# 3-dim

T1 = np.arange(27).reshape(3, 3, 3)

T2 = np.arange(27).reshape(3, 3, 3) + 1

assert same_matrix(

np.einsum('ijk,jkl->il', T1, T2),

np.tensordot(T1, T2))

assert same_matrix(

np.einsum('ijk,lkm->ijlm', T1, T2),

np.dot(T1, T2))

assert same_matrix(

np.einsum('ijk,ikm->ijm', T1, T2),

np.matmul(T1, T2))

In addition, I did it in 4 dimensions and 2 dimensions.

code:python

# 4-dim

T1 = np.arange(81).reshape(3, 3, 3, 3)

T2 = np.arange(81).reshape(3, 3, 3, 3) + 1

assert same_matrix(

np.einsum('ijkl,klmn->ijmn', T1, T2),

np.tensordot(T1, T2))

assert same_matrix(

np.einsum('ijkl,mnlo->ijkmno', T1, T2),

np.dot(T1, T2))

assert same_matrix(

np.einsum('ijkl,ijlm->ijkm', T1, T2),

np.matmul(T1, T2))

# 2-dim

T1 = np.arange(9).reshape(3, 3)

T2 = np.arange(9).reshape(3, 3) + 1

assert same_matrix(

np.einsum('ij,ij->', T1, T2),

np.tensordot(T1, T2))

assert same_matrix(

np.einsum('ij,jk->ik', T1, T2),

np.dot(T1, T2))

assert same_matrix(

np.einsum('ij,jk->ik', T1, T2),

np.matmul(T1, T2))

Commentary

code:python

assert same_matrix(

np.einsum('ijk,jkl->il', T1, T2),

np.tensordot(T1, T2))

tensordor crushes the two behind T1 and the two in front of T2. Therefore, jk in ijk and jk in jkl are collapsed and il remains. You can specify the number of collapses by an option.

code:python

assert same_matrix(

np.einsum('ijk,lkm->ijlm', T1, T2),

np.dot(T1, T2))

DOT crushes the last one in T1 and the second from the end in T2. So the k in ijk and the k in lkm are crushed, leaving ijlm.

code:python

assert same_matrix(

np.einsum('ijk,ikm->ijm', T1, T2),

np.matmul(T1, T2))

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