scipy.interpolate.LSQUnivariateSpline¶
- 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
- 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
- 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]
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.