Using numba for cosine similarity between a vector and rows in a matix

问题

Found this gist using numba for fast computation of cosine similarity.

import numba

@numba.jit(target='cpu', nopython=True)
def fast_cosine(u, v):
    m = u.shape[0]
    udotv = 0
    u_norm = 0
    v_norm = 0
    for i in range(m):
        if (np.isnan(u[i])) or (np.isnan(v[i])):
            continue

        udotv += u[i] * v[i]
        u_norm += u[i] * u[i]
        v_norm += v[i] * v[i]

    u_norm = np.sqrt(u_norm)
    v_norm = np.sqrt(v_norm)

    if (u_norm == 0) or (v_norm == 0):
        ratio = 1.0
    else:
        ratio = udotv / (u_norm * v_norm)
    return ratio

Results look promising (500ns vs. only 200us without jit decorator in my machine).

I would like to use numba to parallelize this computation between a vector u and a candidate matrix M -- i.e. cosine across each row.

Example:

def fast_cosine_matrix(u, M):
    """
    Return array of cosine similarity between u and rows in M
    >>> import numpy as np
    >>> u = np.random.rand(100)
    >>> M = np.random.rand(10, 100)
    >>> fast_cosine_matrix(u, M)
    """

One way is to just rewrite with second input a matrix. But I get a NotImplementedError if I try to iterate over the rows of a matrix. Going to try just using slices.

I thought about using vectorize but I can't get it to work.

回答1:

Alternative: make a Generalized UFunc with numba

@numba.guvectorize(["void(float64[:], float64[:], float64[:])"], "(n),(n)->()", target='parallel')
def fast_cosine_gufunc(u, v, result):
    m = u.shape[0]
    udotv = 0
    u_norm = 0
    v_norm = 0
    for i in range(m):
        if (np.isnan(u[i])) or (np.isnan(v[i])):
            continue

        udotv += u[i] * v[i]
        u_norm += u[i] * u[i]
        v_norm += v[i] * v[i]

    u_norm = np.sqrt(u_norm)
    v_norm = np.sqrt(v_norm)

    if (u_norm == 0) or (v_norm == 0):
        ratio = 1.0
    else:
        ratio = udotv / (u_norm * v_norm)
    result[:] = ratio


u = np.random.rand(100)
M = np.random.rand(100000, 100)

fast_cosine_gufunc(u, M[0,:])
fast_cosine_gufunc(u, M)

回答2:

Solution rewriting it a bit:

import numpy as np
import numba

@numba.jit(target='cpu', nopython=True, parallel=True)
def fast_cosine_matrix(u, M):
    scores = np.zeros(M.shape[0])
    for i in numba.prange(M.shape[0]):
        v = M[i]
        m = u.shape[0]
        udotv = 0
        u_norm = 0
        v_norm = 0
        for j in range(m):
            if (np.isnan(u[j])) or (np.isnan(v[j])):
                continue

            udotv += u[j] * v[j]
            u_norm += u[j] * u[j]
            v_norm += v[j] * v[j]

        u_norm = np.sqrt(u_norm)
        v_norm = np.sqrt(v_norm)

        if (u_norm == 0) or (v_norm == 0):
            ratio = 1.0
        else:
            ratio = udotv / (u_norm * v_norm)
        scores[i] = ratio
    return scores


u = np.random.rand(100)
M = np.random.rand(100000, 100)

fast_cosine_matrix(u, M)

来源：https://stackoverflow.com/questions/47315659/using-numba-for-cosine-similarity-between-a-vector-and-rows-in-a-matix