scipy.interpolate.LSQUnivariateSpline

class scipy.interpolate.LSQUnivariateSpline(x, y, t, w=None, bbox=[None, None], k=3)

One-dimensional spline with explicit internal knots.

Fits a spline y=s(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 equal.

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.

Raises:

ValueError

If the interior knots do not satisfy the Schoenberg-Whitney conditions

See also

UnivariateSpline

Superclass – knots are specified by setting a smoothing condition

InterpolatedUnivariateSpline

spline passing through all points

splrep

An older, non object-oriented wrapping of FITPACK

splev, sproot, splint, spalde

BivariateSpline

A similar class for two-dimensional spline interpolation

Notes

The number of data points must be larger than the spline degree k.

Examples

>>> from numpy import linspace,exp
>>> from numpy.random import randn
>>> from scipy.interpolate import LSQUnivariateSpline
>>> import matplotlib.pyplot as plt
>>> x = linspace(-3,3,100)
>>> y = exp(-x**2) + randn(100)/10
>>> t = [-1,0,1]
>>> s = LSQUnivariateSpline(x,y,t)
>>> xs = linspace(-3,3,1000)
>>> ys = s(xs)
>>> plt.plot(x, y, '.-')
>>> plt.plot(xs, ys)
>>> plt.show()

xs,ys is now a smoothed, super-sampled version of the noisy gaussian x,y with knots [-3,-1,0,1,3]

(Source code)

Methods

__call__(x[, nu])	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 (boundary and interior) knots of the spline.
get_residual()	Return weighted sum of squared residuals of the spline approximation: sum((w[i] * (y[i]-s(x[i])))**2, axis=0).
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.