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 : sequence

input dimension of data points – must be increasing

y : sequence

input dimension of data points

w : sequence or None, optional

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

bbox : sequence or None, 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

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