考慮這個 python 代碼，我在其中嘗試計算向量到矩陣每一行的歐幾里距離。與我能找到的使用 Tullio.jl 的最佳 Julia 版本相比，它非常慢。python 版本需要30s而 Julia 版本只需要75ms。我確信我在 Python 方面沒有做得最好。有更快的解決方案嗎？歡迎使用 Numba 和 numpy 解決方案。import numpy as np# generatea = np.random.rand(4000000, 128)b = np.random.rand(128)print(a.shape)print(b.shape)def lin_norm_ever(a, b): return np.apply_along_axis(lambda x: np.linalg.norm(x - b), 1, a)import timet = time.time()res = lin_norm_ever(a, b)print(res.shape)elapsed = time.time() - tprint(elapsed)朱莉婭版本using Tulliofunction comp_tullio(a, c) dist = zeros(Float32, size(a, 2)) @tullio dist[i] = (c[j] - a[j,i])^2 distend@time comp_tullio(a, c)@benchmark comp_tullio(a, c) # 75ms on my computer
1 回答
慕沐林林
TA貢獻2016條經驗 獲得超9個贊
為了獲得最佳性能，我將在此示例中使用 Numba。我還添加了來自 Divakars 鏈接答案的 2 種方法以進行比較。
代碼
import numpy as np
import numba as nb
from scipy.spatial.distance import cdist
@nb.njit(fastmath=True,parallel=True,cache=True)
def dist_1(mat,vec):
res=np.empty(mat.shape[0],dtype=mat.dtype)
for i in nb.prange(mat.shape[0]):
acc=0
for j in range(mat.shape[1]):
acc+=(mat[i,j]-vec[j])**2
res[i]=np.sqrt(acc)
return res
#from https://stackoverflow.com/a/52364284/4045774
def dist_2(mat,vec):
return cdist(mat, np.atleast_2d(vec)).ravel()
#from https://stackoverflow.com/a/52364284/4045774
def dist_3(mat,vec):
M = mat.dot(vec)
d = np.einsum('ij,ij->i',mat,mat) + np.inner(vec,vec) -2*M
return np.sqrt(d)
時序
#Float64
a = np.random.rand(4000000, 128)
b = np.random.rand(128)
%timeit dist_1(a,b)
#122 ms ± 3.86 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit dist_2(a,b)
#484 ms ± 3.02 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit dist_3(a,b)
#432 ms ± 14.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
#Float32
a = np.random.rand(4000000, 128).astype(np.float32)
b = np.random.rand(128).astype(np.float32)
%timeit dist_1(a,b)
#68.6 ms ± 414 μs per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit dist_2(a,b)
#2.2 s ± 32.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
#looks like there is a costly type-casting to float64
%timeit dist_3(a,b)
#228 ms ± 8.13 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
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