Module « scipy.interpolate »

Classe « LSQUnivariateSpline »

Informations générales

Héritage

builtins.object
    UnivariateSpline
        LSQUnivariateSpline

Définition

class LSQUnivariateSpline(UnivariateSpline):

Description _{[extrait de LSQUnivariateSpline.__doc__]}

    1-D spline with explicit internal knots.

    Fits a spline y = spl(x) of degree `k` to the provided `x`, `y` data.  `t`
    specifies the internal knots of the spline

    Parameters
    ----------
    x : (N,) array_like
        Input dimension of data points -- must be increasing
    y : (N,) array_like
        Input dimension of data points
    t : (M,) array_like
        interior knots of the spline.  Must be in ascending order and::

            bbox[0] < t[0] < ... < t[-1] < bbox[-1]

    w : (N,) array_like, optional
        weights for spline fitting. Must be positive. If None (default),
        weights are all equal.
    bbox : (2,) array_like, optional
        2-sequence specifying the boundary of the approximation interval. If
        None (default), ``bbox = [x[0], x[-1]]``.
    k : int, optional
        Degree of the smoothing spline.  Must be 1 <= `k` <= 5.
        Default is `k` = 3, a cubic spline.
    ext : int or str, optional
        Controls the extrapolation mode for elements
        not in the interval defined by the knot sequence.

        * if ext=0 or 'extrapolate', return the extrapolated value.
        * if ext=1 or 'zeros', return 0
        * if ext=2 or 'raise', raise a ValueError
        * if ext=3 of 'const', return the boundary value.

        The default value is 0.

    check_finite : bool, optional
        Whether to check that the input arrays contain only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination or non-sensical results) if the inputs
        do contain infinities or NaNs.
        Default is False.

    Raises
    ------
    ValueError
        If the interior knots do not satisfy the Schoenberg-Whitney conditions

    See Also
    --------
    UnivariateSpline :
        a smooth univariate spline to fit a given set of data points.
    InterpolatedUnivariateSpline :
        a interpolating univariate spline for a given set of data points.
    splrep :
        a function to find the B-spline representation of a 1-D curve
    splev :
        a function to evaluate a B-spline or its derivatives
    sproot :
        a function to find the roots of a cubic B-spline
    splint :
        a function to evaluate the definite integral of a B-spline between two
        given points
    spalde :
        a function to evaluate all derivatives of a B-spline

    Notes
    -----
    The number of data points must be larger than the spline degree `k`.

    Knots `t` must satisfy the Schoenberg-Whitney conditions,
    i.e., there must be a subset of data points ``x[j]`` such that
    ``t[j] < x[j] < t[j+k+1]``, for ``j=0, 1,...,n-k-2``.

    Examples
    --------
    >>> from scipy.interpolate import LSQUnivariateSpline, UnivariateSpline
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()
    >>> x = np.linspace(-3, 3, 50)
    >>> y = np.exp(-x**2) + 0.1 * rng.standard_normal(50)

    Fit a smoothing spline with a pre-defined internal knots:

    >>> t = [-1, 0, 1]
    >>> spl = LSQUnivariateSpline(x, y, t)

    >>> xs = np.linspace(-3, 3, 1000)
    >>> plt.plot(x, y, 'ro', ms=5)
    >>> plt.plot(xs, spl(xs), 'g-', lw=3)
    >>> plt.show()

    Check the knot vector:

    >>> spl.get_knots()
    array([-3., -1., 0., 1., 3.])

    Constructing lsq spline using the knots from another spline:

    >>> x = np.arange(10)
    >>> s = UnivariateSpline(x, x, s=0)
    >>> s.get_knots()
    array([ 0.,  2.,  3.,  4.,  5.,  6.,  7.,  9.])
    >>> knt = s.get_knots()
    >>> s1 = LSQUnivariateSpline(x, x, knt[1:-1])    # Chop 1st and last knot
    >>> s1.get_knots()
    array([ 0.,  2.,  3.,  4.,  5.,  6.,  7.,  9.])

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, x, y, t, w=None, bbox=[None, None], k=3, ext=0, check_finite=False)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe UnivariateSpline

__call__, __init_subclass__, __subclasshook__, antiderivative, derivative, derivatives, get_coeffs, get_knots, get_residual, integral, roots, set_smoothing_factor, validate_input

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__