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Fonction orthogonal_procrustes - module scipy.linalg

Signature de la fonction orthogonal_procrustes

def orthogonal_procrustes(A, B, check_finite=True) 

Description

orthogonal_procrustes.__doc__

    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