Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/linalg/_procrustes.py

@@ -0,0 +1,89 @@
+"""
+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