这是一个比您上面提供的版本快得多的版本,并且在没有权重的情况下也使用简化的公式来获得更快的结果。
def gini(x, w=None):
# The rest of the code requires numpy arrays.
x = np.asarray(x)
if w is not None:
w = np.asarray(w)
sorted_indices = np.argsort(x)
sorted_x = x[sorted_indices]
sorted_w = w[sorted_indices]
# Force float dtype to avoid overflows
cumw = np.cumsum(sorted_w, dtype=float)
cumxw = np.cumsum(sorted_x * sorted_w, dtype=float)
return (np.sum(cumxw[1:] * cumw[:-1] - cumxw[:-1] * cumw[1:]) /
(cumxw[-1] * cumw[-1]))
else:
sorted_x = np.sort(x)
n = len(x)
cumx = np.cumsum(sorted_x, dtype=float)
# The above formula, with all weights equal to 1 simplifies to:
return (n + 1 - 2 * np.sum(cumx) / cumx[-1]) / n
这是一些测试代码以检查我们是否(大致)获得相同的结果:
>>> x = np.random.rand(1000000)
>>> w = np.random.rand(1000000)
>>> gini_max_ghenis(x, w)
0.33376310938610521
>>> gini(x, w)
0.33376310938610382
但是速度却大不相同:
%timeit gini(x, w)
203 ms ± 3.68 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit gini_max_ghenis(x, w)
55.6 s ± 3.35 s per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit gini_max_ghenis_no_pandas_ops(x, w)
1.62 s ± 75 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
如果您想获得最后的性能下降,可以使用numba或cython,但这只会获得百分之几的收益,因为大部分时间都花在了排序上。
%timeit ind = np.argsort(x); sx = x[ind]; sw = w[ind]
180 ms ± 4.82 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
:gini_max_ghenis是Max Ghenis的答案中使用的代码