scipy.interpolate.UnivariateSpline¶
- class scipy.interpolate.UnivariateSpline(x, y, w=None, bbox=[None, None], k=3, s=None)[source]¶
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 : (N,) array_like
1-D array of independent input data. Must be increasing.
y : (N,) array_like
1-D array of dependent input data, of the same length as x.
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 <= 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
- 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 >>> import matplotlib.pyplot as plt >>> 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) >>> 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.
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.