How to create random orthonormal matrix in python numpy

python numpy linear-algebra orthogonal
Dacion picture Dacion · Jul 18, 2016 · Viewed 19k times · Source

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.

Answer

Warren Weckesser picture Warren Weckesser · Jul 18, 2016

Version 0.18 of scipy has scipy.stats.ortho_group and scipy.stats.special_ortho_group. The pull request where it was added is https://github.com/scipy/scipy/pull/5622

For example,

In [24]: from scipy.stats import ortho_group  # Requires version 0.18 of scipy

In [25]: m = ortho_group.rvs(dim=3)

In [26]: m
Out[26]: 
array([[-0.23939017,  0.58743526, -0.77305379],
       [ 0.81921268, -0.30515101, -0.48556508],
       [-0.52113619, -0.74953498, -0.40818426]])

In [27]: np.set_printoptions(suppress=True)

In [28]: m.dot(m.T)
Out[28]: 
array([[ 1.,  0., -0.],
       [ 0.,  1.,  0.],
       [-0.,  0.,  1.]])

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