ó ʽ÷Xc@`sWdZddlmZmZmZddlZddlmZdgZ e d„Z dS(s+ Solve the orthogonal Procrustes problem. i(tdivisiontprint_functiontabsolute_importNi(tsvdtorthogonal_procrustescC`sä|r'tj|ƒ}tj|ƒ}ntj|ƒ}tj|ƒ}|jdkrjtd|jƒ‚n|j|jkr›td|j|jfƒ‚nt|jj|ƒjƒ\}}}|j|ƒ}|j ƒ}||fS(s 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 [1]_. 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. Returns ------- R : (N, N) ndarray The matrix solution of the orthogonal Procrustes problem. Minimizes the Frobenius norm of dot(A, R) - B, subject to dot(R.T, R) == I. scale : float Sum of the singular values of ``dot(A.T, B)``. Raises ------ ValueError If the input arrays are incompatibly shaped. This may also be raised if matrix A or B contains an inf or nan and check_finite is True, or if the matrix product AB contains an inf or nan. Notes ----- .. versionadded:: 0.15.0 References ---------- .. [1] Peter H. Schonemann, "A generalized solution of the orthogonal Procrustes problem", Psychometrica -- Vol. 31, No. 1, March, 1996. is&expected ndim to be 2, but observed %ss'the shapes of A and B differ (%s vs %s)( tnptasarray_chkfinitet asanyarraytndimt ValueErrortshapeRtTtdottsum(tAtBt check_finitetutwtvttRtscale((s7/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_procrustes.pyRs0$ ( t__doc__t __future__RRRtnumpyRt decomp_svdRt__all__tTrueR(((s7/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_procrustes.pyts