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scipy.signal.unique_roots(p, tol=0.001, rtype='min')[source]

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


p : array_like

The list of roots.

tol : float, optional

The tolerance for two roots to be considered equal. Default is 1e-3.

rtype : {‘max’, ‘min, ‘avg’}, optional

How to determine the returned root if multiple roots are within tol of each other.

  • ‘max’: pick the maximum of those roots.
  • ‘min’: pick the minimum of those roots.
  • ‘avg’: take the average of those roots.

pout : ndarray

The list of unique roots, sorted from low to high.

mult : ndarray

The multiplicity of each root.


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.


>>> 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])