Why is NumPy's `repmat` faster than `kron` to repeat blocks of arrays?

Question

Why is the repmat function from numpy.matlib so much faster than numpy.kron (i.e., Kronecker Product) to repeat blocks of matrices?

A MWE would be:

test_N = 1000
test_vec = np.random.rand(test_N, 2)
rep_vec = np.matlib.repmat(test_vec, 100, 1)
kron_vec = kron(ones((100,1)), test_vec)

%%timeit
rep_vec = np.matlib.repmat(test_vec, 10, 1)
53.5 µs ± 2.42 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

%%timeit
kron_vec = kron(test_vec, ones((10,1)))
1.65 ms ± 228 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Answer 1

Some of my own timings:

In [361]: timeit kron_vec = np.kron(np.ones((10,1)), test_vec)
131 µs ± 871 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Your

kron_vec = kron(test_vec, ones((10,1)))
1.65 ms

looks more like a ones((100,1)) time test.

Mine is longer than others, but not as drastically so.

A similar multiplication approach (like the outer of kron, but no need for the concatenate step):

In [362]: timeit (test_vec*np.ones((10,1,1))).reshape(-1,2)
61.2 µs ± 38.9 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

repmat:

In [363]: timeit rep_vec = matlib.repmat(test_vec,10,1)
94.2 µs ± 32.6 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Using tile instead:

In [364]: timeit np.tile(test_vec,(10,1))
20.4 µs ± 17.8 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

and repeat directly:

In [365]: timeit x = test_vec[None,:,:].repeat(10,0).reshape(-1,2)
12.2 µs ± 371 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)