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Module « scipy.interpolate »

Fonction sproot - module scipy.interpolate

Signature de la fonction sproot

def sproot(tck, mest=10) 

Description

help(scipy.interpolate.sproot)

Find the roots of a cubic B-spline.

.. legacy:: function

    Specifically, we recommend constructing a `BSpline` object and using the
    following pattern: `PPoly.from_spline(spl).roots()`.

Given the knots (>=8) and coefficients of a cubic B-spline return the
roots of the spline.

Parameters
----------
tck : tuple or a BSpline object
    If a tuple, then it should be a sequence of length 3, containing the
    vector of knots, the B-spline coefficients, and the degree of the
    spline.
    The number of knots must be >= 8, and the degree must be 3.
    The knots must be a montonically increasing sequence.
mest : int, optional
    An estimate of the number of zeros (Default is 10).

Returns
-------
zeros : ndarray
    An array giving the roots of the spline.

See Also
--------
splprep, splrep, splint, spalde, splev
bisplrep, bisplev
BSpline

Notes
-----
Manipulating the tck-tuples directly is not recommended. In new code,
prefer using the `BSpline` objects.

References
----------
.. [1] C. de Boor, "On calculating with b-splines", J. Approximation
    Theory, 6, p.50-62, 1972.
.. [2] M. G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths
    Applics, 10, p.134-149, 1972.
.. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs
    on Numerical Analysis, Oxford University Press, 1993.

Examples
--------

For some data, this method may miss a root. This happens when one of
the spline knots (which FITPACK places automatically) happens to
coincide with the true root. A workaround is to convert to `PPoly`,
which uses a different root-finding algorithm.

For example,

>>> x = [1.96, 1.97, 1.98, 1.99, 2.00, 2.01, 2.02, 2.03, 2.04, 2.05]
>>> y = [-6.365470e-03, -4.790580e-03, -3.204320e-03, -1.607270e-03,
...      4.440892e-16,  1.616930e-03,  3.243000e-03,  4.877670e-03,
...      6.520430e-03,  8.170770e-03]
>>> from scipy.interpolate import splrep, sproot, PPoly
>>> tck = splrep(x, y, s=0)
>>> sproot(tck)
array([], dtype=float64)

Converting to a PPoly object does find the roots at ``x=2``:

>>> ppoly = PPoly.from_spline(tck)
>>> ppoly.roots(extrapolate=False)
array([2.])


Further examples are given :ref:`in the tutorial
<tutorial-interpolate_splXXX>`.

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