`scipy.interpolate._interpolate:PPoly.from_spline`

source: /scipy/interpolate/_interpolate.py :1196

Summary

Construct a piecewise polynomial from a spline

Parameters

tck: A spline, as returned by splrep or a BSpline object.
extrapolate : bool or 'periodic', optional: If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. If 'periodic', periodic extrapolation is used. Default is True.

Examples

Construct an interpolating spline and convert it to a `PPoly` instance

import numpy as np
from scipy.interpolate import splrep, PPoly
x = np.linspace(0, 1, 11)
y = np.sin(2*np.pi*x)
tck = splrep(x, y, s=0)
p = PPoly.from_spline(tck)
isinstance(p, PPoly)

✓

Note that this function only supports 1D splines out of the box. If the ``tck`` object represents a parametric spline (e.g. constructed by `splprep` or a `BSpline` with ``c.ndim > 1``), you will need to loop over the dimensions manually.

from scipy.interpolate import splprep, splev
t = np.linspace(0, 1, 11)
x = np.sin(2*np.pi*t)
y = np.cos(2*np.pi*t)
(t, c, k), u = splprep([x, y], s=0)

✓

Note that ``c`` is a list of two arrays of length 11.

unew = np.arange(0, 1.01, 0.01)
out = splev(unew, (t, c, k))

✓

To convert this spline to the power basis, we convert each component of the list of b-spline coefficients, ``c``, into the corresponding cubic polynomial.

polys = [PPoly.from_spline((t, cj, k)) for cj in c]
polys[0].c.shape

✓

Note that the coefficients of the polynomials `polys` are in the power basis and their dimensions reflect just that: here 4 is the order (degree+1), and 14 is the number of intervals---which is nothing but the length of the knot array of the original `tck` minus one. Optionally, we can stack the components into a single `PPoly` along the third dimension:

cc = np.dstack([p.c for p in polys])    # has shape = (4, 14, 2)
poly = PPoly(cc, polys[0].x)
np.allclose(poly(unew).T,     # note the transpose to match `splev`
            out, atol=1e-15)

✓

Aliases

scipy.interpolate.PPoly.from_spline