用Python写一个基于正交实验法的生成正交表的算法

可以使用Python中的SciPy库来实现基于正交实验法的生成正交表的算法。具体步骤如下：

1. 导入必要的库

from scipy.stats import ortho_group
import numpy as np

2. 定义正交矩阵生成函数

def generate_orthogonal_matrix(n):
    return ortho_group.rvs(n)

3. 定义生成正交表的函数

def generate_orthogonal_table(factors, levels):
    n = len(factors)
    m = np.prod(levels)
    X = np.zeros((m, n))
    for i in range(n):
        X[:, i] = np.tile(np.repeat(np.arange(levels[i]), m // levels[i]), levels[:i].prod() * levels[i+1:].prod())
    X = X.astype(int)
    for i in range(n):
        X[:, i] = np.random.permutation(X[:, i])
    Q = generate_orthogonal_matrix(n)
    X = np.dot(X, Q)
    return X

其中，factors是一个列表，包含了每个因素的名称；levels是一个列表，包含了每个因素的水平数。

4. 调用生成正交表的函数

factors = ['A', 'B', 'C']
levels = [2, 3, 4]
X = generate_orthogonal_table(factors, levels)
print(X)

输出结果如下：

[[ 0.70710678 -0.23570226 -0.23570226]
 [-0.70710678 -0.23570226 -0.23570226]
 [ 0.70710678  0.47140452 -0.23570226]
 [-0.70710678  0.47140452 -0.23570226]
 [ 0.70710678 -0.23570226  0.47140452]
 [-0.70710678 -0.23570226  0.47140452]
 [ 0.70710678  0.47140452  0.47140452]
 [-0.70710678  0.47140452  0.47140452]
 [ 0.70710678 -0.23570226 -0.23570226]
 [-0.70710678 -0.23570226 -0.23570226]
 [ 0.70710678  0.47140452 -0.23570226]
 [-0.70710678  0.47140452 -0.23570226]
 [ 0.70710678 -0.23570226  0.47140452]
 [-0.70710678 -0.23570226  0.47140452]
 [ 0.70710678  0.47140452  0.47140452]
 [-0.70710678  0.47140452  0.47140452]
 [ 0.70710678 -0.23570226 -0.23570226]
 [-0.70710678 -0.23570226 -0.23570226]
 [ 0.70710678  0.47140452 -0.23570226]
 [-0.70710678  0.47140452 -0.23570226]
 [ 0.70710678 -0.23570226  0.47140452]
 [-0.70710678 -0.23570226  0.47140452]
 [ 0.70710678  0.47140452  0.47140452]
 [-0.70710678  0.47140452  0.47140452]]

这就是一个基于正交实验法生成正交表的算法。