Module « scipy.interpolate »

Classe « UnivariateSpline »

Informations générales

Héritage

builtins.object
    UnivariateSpline

Définition

class UnivariateSpline(builtins.object):

Description _{[extrait de UnivariateSpline.__doc__]}

    1-D smoothing spline fit to a given set of data points.

    Fits a spline y = spl(x) of degree `k` to the provided `x`, `y` data.  `s`
    specifies the number of knots by specifying a smoothing condition.

    Parameters
    ----------
    x : (N,) array_like
        1-D array of independent input data. Must be increasing;
        must be strictly increasing if `s` is 0.
    y : (N,) array_like
        1-D array of dependent input data, of the same length as `x`.
    w : (N,) array_like, optional
        Weights for spline fitting.  Must be positive.  If `w` is None,
        weights are all equal. Default is None.
    bbox : (2,) array_like, optional
        2-sequence specifying the boundary of the approximation interval. If
        `bbox` is None, ``bbox=[x[0], x[-1]]``. Default is None.
    k : int, optional
        Degree of the smoothing spline.  Must be 1 <= `k` <= 5.
        ``k = 3`` is a cubic spline. Default is 3.
    s : float or None, optional
        Positive smoothing factor used to choose the number of knots.  Number
        of knots will be increased until the smoothing condition is satisfied::

            sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) <= s

        If `s` is None, ``s = len(w)`` which should be a good value if
        ``1/w[i]`` is an estimate of the standard deviation of ``y[i]``.
        If 0, spline will interpolate through all data points. Default is None.
    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.

        Default 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.

    See Also
    --------
    BivariateSpline :
        a base class for bivariate splines.
    SmoothBivariateSpline :
        a smoothing bivariate spline through the given points
    LSQBivariateSpline :
        a bivariate spline using weighted least-squares fitting
    RectSphereBivariateSpline :
        a bivariate spline over a rectangular mesh on a sphere
    SmoothSphereBivariateSpline :
        a smoothing bivariate spline in spherical coordinates
    LSQSphereBivariateSpline :
        a bivariate spline in spherical coordinates using weighted
        least-squares fitting
    RectBivariateSpline :
        a bivariate spline over a rectangular mesh
    InterpolatedUnivariateSpline :
        a interpolating univariate spline for a given set of data points.
    bisplrep :
        a function to find a bivariate B-spline representation of a surface
    bisplev :
        a function to evaluate a bivariate B-spline and its derivatives
    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`.

    **NaN handling**: If the input arrays contain ``nan`` values, the result
    is not useful, since the underlying spline fitting routines cannot deal
    with ``nan``. A workaround is to use zero weights for not-a-number
    data points:

    >>> from scipy.interpolate import UnivariateSpline
    >>> x, y = np.array([1, 2, 3, 4]), np.array([1, np.nan, 3, 4])
    >>> w = np.isnan(y)
    >>> y[w] = 0.
    >>> spl = UnivariateSpline(x, y, w=~w)

    Notice the need to replace a ``nan`` by a numerical value (precise value
    does not matter as long as the corresponding weight is zero.)

    Examples
    --------
    >>> import matplotlib.pyplot as plt
    >>> from scipy.interpolate import UnivariateSpline
    >>> rng = np.random.default_rng()
    >>> x = np.linspace(-3, 3, 50)
    >>> y = np.exp(-x**2) + 0.1 * rng.standard_normal(50)
    >>> plt.plot(x, y, 'ro', ms=5)

    Use the default value for the smoothing parameter:

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

    Manually change the amount of smoothing:

    >>> spl.set_smoothing_factor(0.5)
    >>> plt.plot(xs, spl(xs), 'b', lw=3)
    >>> plt.show()

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, x, y, w=None, bbox=[None, None], k=3, s=None, 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 object

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