classmethod PPoly.from_spline(tck, extrapolate=None)[source]#

Construct a piecewise polynomial from a spline


A spline, as returned by splrep or a BSpline object.

extrapolatebool 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.


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
(4, 14)

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)