bundles / scipy 1.17.1 / scipy / interpolate / _fitpack2 / LSQUnivariateSpline

class

`scipy.interpolate._fitpack2:LSQUnivariateSpline`

source: /scipy/interpolate/_fitpack2.py :783

Signature

   class     LSQUnivariateSpline (    x    ,    y    ,    t    ,    w    =  None   ,    bbox    =  [None, None]   ,    k    =  3   ,    ext    =  0   ,    check_finite    =  False     )

Members

__init__

Summary

1-D spline with explicit internal knots.

Extended Summary

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

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.

Array API Standard Support

LSQUnivariateSpline is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

See dev-arrayapi for more information.

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()

✗

Constructing lsq spline using the knots from another spline:

x = np.arange(10)
s = UnivariateSpline(x, x, s=0)

✓

s.get_knots()

✗

knt = s.get_knots()
s1 = LSQUnivariateSpline(x, x, knt[1:-1])    # Chop 1st and last knot

✓

s1.get_knots()

✗

Aliases

scipy.interpolate.LSQUnivariateSpline