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pythonperformancenumpylinear-algebramatrix-multiplication
capybaralet
capybaralet

Reputation: 1867

How can I efficiently expand a factored tensor in numpy?

I have a 3D tensor factored as three 2D matrices, like equation 22 in this paper: http://www.iro.umontreal.ca/~memisevr/pubs/pami_relational.pdf

My question is, if I want to calculate the tensor explicitly, is there a better way than this in numpy?

W = np.zeros((100,100,100))
for i in range(100):
    for j in range(100):
        for k in range(100):
            W[i,j,k] = np.sum([wxf[i,f]*wyf[j,f]*wzf[k,f] for f in range(100)])

Upvotes: 1

Views: 82

Answers (2)

DSM
DSM

Reputation: 353059

I tend to use einsum for this stuff, just because it's usually the easiest to write:

def fast(wxf, wyf, wzf):
    return np.einsum('if,jf,kf->ijk', wxf, wyf, wzf)

def slow(wxf, wyf, wzf):
    N = len(wxf)
    W = np.zeros((N, N, N))
    for i in range(N):
        for j in range(N):
            for k in range(N):
                W[i,j,k] = np.sum([wxf[i,f]*wyf[j,f]*wzf[k,f] for f in range(N)]) 
    return W

def gen_ws(N):
    wxf = np.random.random((N,N))
    wyf = np.random.random((N,N))
    wzf = np.random.random((N,N))
    return wxf, wyf, wzf

gives

>>> ws = gen_ws(25)
>>> via_slow = slow(*ws)
>>> via_fast = fast(*ws)
>>> np.allclose(via_slow, via_fast)
True

and

>>> ws = gen_ws(100)
>>> %timeit fast(*ws)
10 loops, best of 3: 91.6 ms per loop

Upvotes: 2

Saullo G. P. Castro
Saullo G. P. Castro

Reputation: 58895

Your example makes it very straightforward to propose a solution using np.einsum():

W = np.einsum('ij,jf,kf->ijk', wxf, wyf, wzf)

Upvotes: 1

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