generate_knots#
- scipy.interpolate.generate_knots(x, y, *, w=None, xb=None, xe=None, k=3, s=0, nest=None)[source]#
- Replicate FITPACK’s constructing the knot vector. - Parameters:
- x, yarray_like
- The data points defining the curve - y = f(x).
- warray_like, optional
- Weights. 
- xbfloat, optional
- The boundary of the approximation interval. If None (default), is set to - x[0].
- xefloat, optional
- The boundary of the approximation interval. If None (default), is set to - x[-1].
- kint, optional
- The spline degree. Default is cubic, - k = 3.
- sfloat, optional
- The smoothing factor. Default is - s = 0.
- nestint, optional
- Stop when at least this many knots are placed. 
 
- Yields:
- tndarray
- Knot vectors with an increasing number of knots. The generator is finite: it stops when the smoothing critetion is satisfied, or when then number of knots exceeds the maximum value: the user-provided nest or x.size + k + 1 — which is the knot vector for the interpolating spline. 
 
 - Notes - The routine generates successive knots vectors of increasing length, starting from - 2*(k+1)to- len(x) + k + 1, trying to make knots more dense in the regions where the deviation of the LSQ spline from data is large.- When the maximum number of knots, - len(x) + k + 1is reached (this happens when- sis small and- nestis large), the generator stops, and the last output is the knots for the interpolation with the not-a-knot boundary condition.- Knots are located at data sites, unless - kis even and the number of knots is- len(x) + k + 1. In that case, the last output of the generator has internal knots at Greville sites,- (x[1:] + x[:-1]) / 2.- Added in version 1.15.0. - Examples - Generate some noisy data and fit a sequence of LSQ splines: - >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.interpolate import make_lsq_spline, generate_knots >>> rng = np.random.default_rng() >>> x = np.linspace(-3, 3, 50) >>> y = np.exp(-x**2) + 0.1 * rng.standard_normal(size=50) - >>> knots = list(generate_knots(x, y, s=1e-10)) >>> for t in knots[::3]: ... spl = make_lsq_spline(x, y, t) ... xs = xs = np.linspace(-3, 3, 201) ... plt.plot(xs, spl(xs), '-', label=f'n = {len(t)}', lw=3, alpha=0.7) >>> plt.plot(x, y, 'o', label='data') >>> plt.plot(xs, np.exp(-xs**2), '--') >>> plt.legend() - Note that increasing the number of knots make the result follow the data more and more closely. - Also note that a step of the generator may add multiple knots: - >>> [len(t) for t in knots] [8, 9, 10, 12, 16, 24, 40, 48, 52, 54] 