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Classe « PPoly »

Méthode scipy.interpolate.PPoly.from_spline

Signature de la méthode from_spline

def from_spline(tck, extrapolate=None) 

Description

help(PPoly.from_spline)

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)
True

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)
True

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