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NotesParametersRaises

Notes

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

InterpolatedUnivariateSpline

a interpolating univariate spline for a given set of data points.

UnivariateSpline

a smooth univariate spline to fit a given set of data points.

spalde

a function to evaluate all derivatives of a B-spline

splev

a function to evaluate a B-spline or its derivatives

splint

a function to evaluate the definite integral of a B-spline between two given points

splrep

a function to find the B-spline representation of a 1-D curve

sproot

a function to find the roots of a cubic B-spline

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)

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()

spl.get_knots()

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()

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them