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

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

Superclass – knots are specified by setting a smoothing condition
spline passing through all points
An older, non object-oriented wrapping of FITPACK

splev, sproot, splint, spalde

A similar class for two-dimensional spline interpolation


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


>>> from numpy import linspace,exp
>>> from numpy.random import randn
>>> from scipy.interpolate import LSQUnivariateSpline
>>> 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)

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


__call__(x[, nu]) Evaluate spline (or its nu-th derivative) at positions x.
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
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

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