Module « scipy.linalg »

Fonction null_space - module scipy.linalg

Signature de la fonction null_space

def null_space(A, rcond=None) 

Description

null_space.__doc__

    Construct an orthonormal basis for the null space of A using SVD

    Parameters
    ----------
    A : (M, N) array_like
        Input array
    rcond : float, optional
        Relative condition number. Singular values ``s`` smaller than
        ``rcond * max(s)`` are considered zero.
        Default: floating point eps * max(M,N).

    Returns
    -------
    Z : (N, K) ndarray
        Orthonormal basis for the null space of A.
        K = dimension of effective null space, as determined by rcond

    See also
    --------
    svd : Singular value decomposition of a matrix
    orth : Matrix range

    Examples
    --------
    1-D null space:

    >>> from scipy.linalg import null_space
    >>> A = np.array([[1, 1], [1, 1]])
    >>> ns = null_space(A)
    >>> ns * np.sign(ns[0,0])  # Remove the sign ambiguity of the vector
    array([[ 0.70710678],
           [-0.70710678]])

    2-D null space:

    >>> from numpy.random import default_rng
    >>> rng = default_rng()
    >>> B = rng.random((3, 5))
    >>> Z = null_space(B)
    >>> Z.shape
    (5, 2)
    >>> np.allclose(B.dot(Z), 0)
    True

    The basis vectors are orthonormal (up to rounding error):

    >>> Z.T.dot(Z)
    array([[  1.00000000e+00,   6.92087741e-17],
           [  6.92087741e-17,   1.00000000e+00]])