orthogonal_procrustes(A, B, check_finite=True)

Given matrices A and B of equal shape, find an orthogonal matrix R that most closely maps A to B using the algorithm given in .

Notes

Note that unlike higher level Procrustes analyses of spatial data, this function only uses orthogonal transformations like rotations and reflections, and it does not use scaling or translation.

Parameters

A : (M, N) array_like

Matrix to be mapped.

B : (M, N) array_like

Target matrix.

check_finite : bool, optional

Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Raises

ValueError

If the input array shapes don't match or if check_finite is True and the arrays contain Inf or NaN.

Returns

R : (N, N) ndarray

The matrix solution of the orthogonal Procrustes problem. Minimizes the Frobenius norm of (A @ R) - B , subject to R.T @ R = I .

scale : float

Sum of the singular values of A.T @ B .

Compute the matrix solution of the orthogonal Procrustes problem.

Examples

>>> from scipy.linalg import orthogonal_procrustes
... A = np.array([[ 2,  0,  1], [-2,  0,  0]])

Flip the order of columns and check for the anti-diagonal mapping

>>> R, sca = orthogonal_procrustes(A, np.fliplr(A))
... R
array([[-5.34384992e-17,  0.00000000e+00,  1.00000000e+00],
       [ 0.00000000e+00,  1.00000000e+00,  0.00000000e+00],
       [ 1.00000000e+00,  0.00000000e+00, -7.85941422e-17]])

>>> sca
9.0

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._procrustes.orthogonal_procrustes

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GitHub : /scipy/linalg/_procrustes.py#12
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