如何在python numpy中创建随机正交矩阵 [英] How to create random orthonormal matrix in python numpy

问题描述

是否可以调用一种方法在python中创建随机正交矩阵?可能使用numpy吗?还是有一种使用多个numpy方法创建正交矩阵的方法?谢谢.

Is there a method that I can call to create a random orthonormal matrix in python? Possibly using numpy? Or is there a way to create a orthonormal matrix using multiple numpy methods? Thanks.

推荐答案

这是从rvs方法. rel ="noreferrer"> https://github.com/scipy/scipy/pull/5622/files ，变化很小-足以作为独立的numpy函数运行.

This is the rvs method pulled from the https://github.com/scipy/scipy/pull/5622/files, with minimal change - just enough to run as a stand alone numpy function.

import numpy as np    

def rvs(dim=3):
     random_state = np.random
     H = np.eye(dim)
     D = np.ones((dim,))
     for n in range(1, dim):
         x = random_state.normal(size=(dim-n+1,))
         D[n-1] = np.sign(x[0])
         x[0] -= D[n-1]*np.sqrt((x*x).sum())
         # Householder transformation
         Hx = (np.eye(dim-n+1) - 2.*np.outer(x, x)/(x*x).sum())
         mat = np.eye(dim)
         mat[n-1:, n-1:] = Hx
         H = np.dot(H, mat)
         # Fix the last sign such that the determinant is 1
     D[-1] = (-1)**(1-(dim % 2))*D.prod()
     # Equivalent to np.dot(np.diag(D), H) but faster, apparently
     H = (D*H.T).T
     return H

它符合沃伦的测试， https://stackoverflow.com/a/38426572/901925

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