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Module « scipy.signal »

Fonction unique_roots - module scipy.signal

Signature de la fonction unique_roots

def unique_roots(p, tol=0.001, rtype='min') 

Description

help(scipy.signal.unique_roots)

Determine unique roots and their multiplicities from a list of roots.

Parameters
----------
p : array_like
    The list of roots.
tol : float, optional
    The tolerance for two roots to be considered equal in terms of
    the distance between them. Default is 1e-3. Refer to Notes about
    the details on roots grouping.
rtype : {'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}, optional
    How to determine the returned root if multiple roots are within
    `tol` of each other.

      - 'max', 'maximum': pick the maximum of those roots
      - 'min', 'minimum': pick the minimum of those roots
      - 'avg', 'mean': take the average of those roots

    When finding minimum or maximum among complex roots they are compared
    first by the real part and then by the imaginary part.

Returns
-------
unique : ndarray
    The list of unique roots.
multiplicity : ndarray
    The multiplicity of each root.

Notes
-----
If we have 3 roots ``a``, ``b`` and ``c``, such that ``a`` is close to
``b`` and ``b`` is close to ``c`` (distance is less than `tol`), then it
doesn't necessarily mean that ``a`` is close to ``c``. It means that roots
grouping is not unique. In this function we use "greedy" grouping going
through the roots in the order they are given in the input `p`.

This utility function is not specific to roots but can be used for any
sequence of values for which uniqueness and multiplicity has to be
determined. For a more general routine, see `numpy.unique`.

Examples
--------
>>> from scipy import signal
>>> vals = [0, 1.3, 1.31, 2.8, 1.25, 2.2, 10.3]
>>> uniq, mult = signal.unique_roots(vals, tol=2e-2, rtype='avg')

Check which roots have multiplicity larger than 1:

>>> uniq[mult > 1]
array([ 1.305])

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