# scipy.signal.unique_roots

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

  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])