\cidZddlmZddlmZddlmZmZmZm Z dgZ eddg ed d dd Z dS)z+ Solve the orthogonal Procrustes problem. )_apply_over_batch)svd)array_namespacexp_capabilities_asarrayis_numpyorthogonal_procrustesF)z dask.arrayz+full_matrices=True is not supported by dask)jax_jit skip_backends)A)BrTcPt||}t|||d}t|||d}|jdkrtd|j|j|jkr td|jd|jdt |r4t |j||zj\}}}n>|j |j||zj\}}}||z}| |}||fS)aW Compute the matrix solution of the orthogonal (or unitary) Procrustes problem. Given matrices `A` and `B` of the same shape, find an orthogonal (or unitary in the case of complex input) 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.conj().T @ R = I``. scale : float Sum of the singular values of ``A.conj().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. 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 As an example of the unitary Procrustes problem, generate a random complex matrix ``A``, a random unitary matrix ``Q``, and their product ``B``. >>> shape = (4, 4) >>> rng = np.random.default_rng(589234981235) >>> A = rng.random(shape) + rng.random(shape)*1j >>> Q = rng.random(shape) + rng.random(shape)*1j >>> Q, _ = np.linalg.qr(Q) >>> B = A @ Q `orthogonal_procrustes` recovers the unitary matrix ``Q`` from ``A`` and ``B``. >>> R, _ = orthogonal_procrustes(A, B) >>> np.allclose(R, Q) True T)xp check_finitesubokrz$expected ndim to be 2, but observed zthe shapes of A and B differ (z vs )) rrndim ValueErrorshaper rTconjlinalgsum) r rrruwvtRscales h/var/www/html/mdtn/previsions/meteo_cartes/venv/lib/python3.11/site-packages/scipy/linalg/_procrustes.pyr r s l A  Br DAAAAr DAAAAv{{HHHIIIw!'Q!'QQqwQQQRRR ||7bggajj(+,,1bb9==!# "2!5661b BA FF1IIE e8ON)T) __doc__scipy._lib._utilr _decomp_svdrscipy._lib._array_apirrrr __all__r r"r!r)s /.....VVVVVVVVVVVV # # PQ8X&&ddd'&  dddr"