Old engine for Continuous Time Bayesian Networks. Superseded by reCTBN. 🐍
https://github.com/madlabunimib/PyCTBN
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
89 lines
2.7 KiB
89 lines
2.7 KiB
"""
|
|
Solve the orthogonal Procrustes problem.
|
|
|
|
"""
|
|
import numpy as np
|
|
from .decomp_svd import svd
|
|
|
|
|
|
__all__ = ['orthogonal_procrustes']
|
|
|
|
|
|
def orthogonal_procrustes(A, B, check_finite=True):
|
|
"""
|
|
Compute the matrix solution of the orthogonal Procrustes problem.
|
|
|
|
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 [1]_.
|
|
|
|
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.
|
|
|
|
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``.
|
|
|
|
Raises
|
|
------
|
|
ValueError
|
|
If the input array shapes don't match or if check_finite is True and
|
|
the arrays contain Inf or NaN.
|
|
|
|
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.
|
|
|
|
.. versionadded:: 0.15.0
|
|
|
|
References
|
|
----------
|
|
.. [1] Peter H. Schonemann, "A generalized solution of the orthogonal
|
|
Procrustes problem", Psychometrica -- Vol. 31, No. 1, March, 1996.
|
|
|
|
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
|
|
|
|
"""
|
|
if check_finite:
|
|
A = np.asarray_chkfinite(A)
|
|
B = np.asarray_chkfinite(B)
|
|
else:
|
|
A = np.asanyarray(A)
|
|
B = np.asanyarray(B)
|
|
if A.ndim != 2:
|
|
raise ValueError('expected ndim to be 2, but observed %s' % A.ndim)
|
|
if A.shape != B.shape:
|
|
raise ValueError('the shapes of A and B differ (%s vs %s)' % (
|
|
A.shape, B.shape))
|
|
# Be clever with transposes, with the intention to save memory.
|
|
u, w, vt = svd(B.T.dot(A).T)
|
|
R = u.dot(vt)
|
|
scale = w.sum()
|
|
return R, scale
|
|
|