subspace_angles(A, B)
This computes the subspace angles according to the formula provided in . For equivalence with MATLAB and Octave behavior, use angles[0]
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The subspace angles between the column spaces of A and B in descending order.
Compute the subspace angles between two matrices.
An Hadamard matrix, which has orthogonal columns, so we expect that the suspace angle to be $\frac{\pi}{2}$ :
>>> from numpy.random import default_rng
... from scipy.linalg import hadamard, subspace_angles
... rng = default_rng()
... H = hadamard(4)
... print(H) [[ 1 1 1 1] [ 1 -1 1 -1] [ 1 1 -1 -1] [ 1 -1 -1 1]]
>>> np.rad2deg(subspace_angles(H[:, :2], H[:, 2:])) array([ 90., 90.])
And the subspace angle of a matrix to itself should be zero:
>>> subspace_angles(H[:, :2], H[:, :2]) <= 2 * np.finfo(float).eps array([ True, True], dtype=bool)
The angles between non-orthogonal subspaces are in between these extremes:
>>> x = rng.standard_normal((4, 3))See :
... np.rad2deg(subspace_angles(x[:, :2], x[:, [2]])) array([ 55.832]) # random
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp_svd.subspace_angles
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