Classe « LSQUnivariateSpline »

Informations générales

Héritage

builtins.object
    UnivariateSpline
        LSQUnivariateSpline

Définition

class LSQUnivariateSpline(UnivariateSpline):

help(LSQUnivariateSpline)

1-D spline with explicit internal knots.

.. legacy:: class

    Specifically, we recommend using `make_lsq_spline` instead.


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 1.
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
--------
>>> import numpy as np
>>> 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__

Liste des méthodes

Toutes les méthodes Méthodes d'instance Méthodes statiques

Signature de la méthode	Description

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