Ug ,dZddlZddlmZdgZddZdS) z+ Solve the orthogonal Procrustes problem. N)svdorthogonal_procrustesTc|r)tj|}tj|}n(tj|}tj|}|jdkrt d|jz|j|jkr t d|jd|jdt |j|j\}}}||}| }||fS)a 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, 1966. :doi:`10.1007/BF02289451` Examples -------- >>> import numpy as np >>> 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 z&expected ndim to be 2, but observed %szthe shapes of A and B differ (z vs )) npasarray_chkfinite asanyarrayndim ValueErrorshaperTdotsum)AB check_finiteuwvtRscales W/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/linalg/_procrustes.pyrr s@   # #   # # M!   M!  v{{AAFJKKKw!'Q!'QQqwQQQRRR13771::<  HAq" b A EEGGE e8O)T)__doc__numpyr _decomp_svdr__all__rrrr!s] # #NNNNNNr