# 依赖: numpy
import numpy as np

def entropy_weight(X, benefit=None):
    X = np.asarray(X, dtype=float)
    if X.ndim != 2 or X.shape[0] < 2 or X.shape[1] < 1 or not np.isfinite(X).all():
        raise ValueError('需要至少两个方案和一个指标，且数据必须有限')
    benefit = np.ones(X.shape[1], dtype=bool) if benefit is None else np.asarray(benefit, bool)
    if benefit.shape != (X.shape[1],):
        raise ValueError('指标方向数量与列数不一致')
    span = np.ptp(X, axis=0)
    active = span > 1e-12
    if not active.any():
        raise ValueError('所有指标均为常量，无法从差异中确定熵权')
    Xn = (X - X.min(axis=0)) / np.where(active, span, 1)
    Xn[:, ~benefit] = 1 - Xn[:, ~benefit]
    P = (Xn + 1e-12) / (Xn + 1e-12).sum(axis=0, keepdims=True)
    divergence = np.maximum(0, 1 + (P*np.log(P)).sum(axis=0) / np.log(len(X)))
    divergence[~active] = 0  # 无区分度的常量指标不获得权重
    if divergence.sum() <= 1e-12:
        raise ValueError('差异不足以稳定确定熵权')
    return divergence / divergence.sum()

print('权重 =', entropy_weight([[1, 10], [2, 20], [3, 12]], benefit=[True, False]).round(4))