scipy.interpolate.

LSQUnivariateSpline#

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

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 1.

bbox(2,) array_like, optional

2-sequence specifying the boundary of the approximation interval. If None (default), bbox = [x[0], x[-1]].

kint, optional

Degree of the smoothing spline. Must be 1 <= k <= 5. Default is k = 3, a cubic spline.

extint 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_finitebool, 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.

Methods

`__call__`(x[, nu, ext])	Evaluate spline (or its nu-th derivative) at positions x.
`antiderivative`([n])	Construct a new spline representing the antiderivative of this spline.
`derivative`([n])	Construct a new spline representing the derivative of this spline.
`derivatives`(x)	Return all derivatives of the spline at the point x.
`get_coeffs`()	Return spline coefficients.
`get_knots`()	Return positions of interior knots of the spline.
`get_residual`()	Return weighted sum of squared residuals of the spline approximation.
`integral`(a, b)	Return definite integral of the spline between two given points.
`roots`()	Return the zeros of the spline.
`set_smoothing_factor`(s)	Continue spline computation with the given smoothing factor s and with the knots found at the last call.

validate_input

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()

../../_images/scipy-interpolate-LSQUnivariateSpline-1_00_00.png

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.])