scipy.interpolate.UnivariateSpline

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

One-dimensional smoothing spline fit to a given set of data points.

Fits a spline y=s(x) of degree k to the provided x, y data. s specifies the number of knots by specifying a smoothing condition.

Parameters :

x : array_like

1-D array of independent input data. Must be increasing.

y : array_like

1-D array of dependent input data, of the same length as x.

w : array_like, optional

Weights for spline fitting. Must be positive. If None (default), weights are all equal.

bbox : 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 <= 5.

s : float or None, optional

Positive smoothing factor used to choose the number of knots. Number of knots will be increased until the smoothing condition is satisfied:

sum((w[i]*(y[i]-s(x[i])))**2,axis=0) <= s

If None (default), s=len(w) which should be a good value if 1/w[i] is an estimate of the standard deviation of y[i]. If 0, spline will interpolate through all data points.

See also

InterpolatedUnivariateSpline

Subclass with smoothing forced to 0

LSQUnivariateSpline

Subclass in which knots are user-selected instead of being set by smoothing condition

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 UnivariateSpline
>>> x = linspace(-3, 3, 100)
>>> y = exp(-x**2) + randn(100)/10
>>> s = UnivariateSpline(x, y, s=1)
>>> xs = linspace(-3, 3, 1000)
>>> ys = s(xs)

xs,ys is now a smoothed, super-sampled version of the noisy gaussian x,y.

Methods

derivatives
get_coeffs
get_knots
get_residual
integral
roots
set_smoothing_factor