Vous êtes un professionnel et vous avez besoin d'une formation ? Machine Learning
avec Scikit-Learn Voir le programme détaillé

Module « scipy.linalg »

Fonction qr_delete - module scipy.linalg

Signature de la fonction qr_delete

def qr_delete(Q, R, k, p=1, which='row', overwrite_qr=False, check_finite=True) 

Description

help(scipy.linalg.qr_delete)

qr_delete(Q, R, k, int p=1, which=u'row', overwrite_qr=False, check_finite=True)


    QR downdate on row or column deletions



    If ``A = Q R`` is the QR factorization of ``A``, return the QR

    factorization of ``A`` where ``p`` rows or columns have been removed

    starting at row or column ``k``.



    Parameters

    ----------

    Q : (M, M) or (M, N) array_like

        Unitary/orthogonal matrix from QR decomposition.

    R : (M, N) or (N, N) array_like

        Upper triangular matrix from QR decomposition.

    k : int

        Index of the first row or column to delete.

    p : int, optional

        Number of rows or columns to delete, defaults to 1.

    which: {'row', 'col'}, optional

        Determines if rows or columns will be deleted, defaults to 'row'

    overwrite_qr : bool, optional

        If True, consume Q and R, overwriting their contents with their

        downdated versions, and returning appropriately sized views.

        Defaults to False.

    check_finite : bool, optional

        Whether to check that the input matrix contains 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.

        Default is True.



    Returns

    -------

    Q1 : ndarray

        Updated unitary/orthogonal factor

    R1 : ndarray

        Updated upper triangular factor



    See Also

    --------

    qr, qr_multiply, qr_insert, qr_update



    Notes

    -----

    This routine does not guarantee that the diagonal entries of ``R1`` are

    positive.



    .. versionadded:: 0.16.0



    References

    ----------

    .. [1] Golub, G. H. & Van Loan, C. F. Matrix Computations, 3rd Ed.

           (Johns Hopkins University Press, 1996).



    .. [2] Daniel, J. W., Gragg, W. B., Kaufman, L. & Stewart, G. W.

           Reorthogonalization and stable algorithms for updating the

           Gram-Schmidt QR factorization. Math. Comput. 30, 772-795 (1976).



    .. [3] Reichel, L. & Gragg, W. B. Algorithm 686: FORTRAN Subroutines for

           Updating the QR Decomposition. ACM Trans. Math. Softw. 16, 369-377

           (1990).



    Examples

    --------

    >>> import numpy as np

    >>> from scipy import linalg

    >>> a = np.array([[  3.,  -2.,  -2.],

    ...               [  6.,  -9.,  -3.],

    ...               [ -3.,  10.,   1.],

    ...               [  6.,  -7.,   4.],

    ...               [  7.,   8.,  -6.]])

    >>> q, r = linalg.qr(a)



    Given this QR decomposition, update q and r when 2 rows are removed.



    >>> q1, r1 = linalg.qr_delete(q, r, 2, 2, 'row', False)

    >>> q1

    array([[ 0.30942637,  0.15347579,  0.93845645],  # may vary (signs)

           [ 0.61885275,  0.71680171, -0.32127338],

           [ 0.72199487, -0.68017681, -0.12681844]])

    >>> r1

    array([[  9.69535971,  -0.4125685 ,  -6.80738023],  # may vary (signs)

           [  0.        , -12.19958144,   1.62370412],

           [  0.        ,   0.        ,  -0.15218213]])



    The update is equivalent, but faster than the following.



    >>> a1 = np.delete(a, slice(2,4), 0)

    >>> a1

    array([[ 3., -2., -2.],

           [ 6., -9., -3.],

           [ 7.,  8., -6.]])

    >>> q_direct, r_direct = linalg.qr(a1)



    Check that we have equivalent results:



    >>> np.dot(q1, r1)

    array([[ 3., -2., -2.],

           [ 6., -9., -3.],

           [ 7.,  8., -6.]])

    >>> np.allclose(np.dot(q1, r1), a1)

    True



    And the updated Q is still unitary:



    >>> np.allclose(np.dot(q1.T, q1), np.eye(3))

    True



    

Vous êtes un professionnel et vous avez besoin d'une formation ? Programmation Python
Les fondamentaux Voir le programme détaillé