Python:具有N个均值和相同协方差矩阵的多元法线样本 [英] Python: Sample from multivariate normal with N means and same covariance matrix
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问题描述
假设我想从多个正态分布中使用相同的协方差矩阵(同一性)但均值不同的样本进行10次采样,这些均方根存储为以下矩阵的行:
Suppose I want to sample 10 times from multiple normal distributions with the same covariance matrix (identity) but different means, which are stored as rows of the following matrix:
means = np.array([[1, 5, 2],
[6, 2, 7],
[1, 8, 2]])
我该如何以最有效的方式做到这一点(即避免循环)
How can I do that in the most efficient way possible (i.e. avoiding loops)
我尝试过这样:
scipy.stats.multivariate_normal(means, np.eye(2)).rvs(10)
和
np.random.multivariate_normal(means, np.eye(2))
但是他们抛出一个错误,说均值应该是一维.
But they throw an error saying mean should be 1D.
import scipy
np.r_[[scipy.stats.multivariate_normal(means[i, :], np.eye(3)).rvs() for i in range(len(means))]]
推荐答案
您的协方差矩阵表明样本是独立的.您可以立即对其进行采样:
Your covariance matrix indicate that the sample are independent. You can just sample them at once:
num_samples = 10
flat_means = means.ravel()
# build block covariance matrix
cov = np.eye(3)
block_cov = np.kron(np.eye(3), cov)
out = np.random.multivariate_normal(flat_means, cov=block_cov, size=num_samples)
out = out.reshape((-1,) + means.shape)
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