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bundles / scipy latest / scipy / linalg / _decomp_svd / subspace_angles

function

scipy.linalg._decomp_svd:subspace_angles

source: /scipy/linalg/_decomp_svd.py :440

Signature

def   subspace_angles ( A ,  B )

Summary

Compute the subspace angles between two matrices.

Extended Summary

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details. Note that calls with zero-size batches are unsupported and will raise a ValueError.

Parameters

A : (M, N) array_like

The first input array.

B : (M, K) array_like

The second input array.

Returns

angles : ndarray, shape (min(N, K),)

The subspace angles between the column spaces of A and B in descending order.

Notes

This computes the subspace angles according to the formula provided in [1]. For equivalence with MATLAB and Octave behavior, use angles[0].

Examples

An Hadamard matrix, which has orthogonal columns, so we expect that the suspace angle to be :math:`\frac{\pi}{2}`: 
import numpy as np
from scipy.linalg import hadamard, subspace_angles
rng = np.random.default_rng()
H = hadamard(4)
print(H)
✓
np.rad2deg(subspace_angles(H[:, :2], H[:, 2:]))
✗
And the subspace angle of a matrix to itself should be zero: 
subspace_angles(H[:, :2], H[:, :2]) <= 2 * np.finfo(float).eps
✗
The angles between non-orthogonal subspaces are in between these extremes: 
x = rng.standard_normal((4, 3))
✓
np.rad2deg(subspace_angles(x[:, :2], x[:, [2]]))
✗

See also

orth
svd

Aliases

  • scipy.linalg.subspace_angles

Referenced by

This package