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Module « scipy.stats »

Fonction circvar - module scipy.stats

Signature de la fonction circvar

def circvar(samples, high=6.283185307179586, low=0, axis=None, nan_policy='propagate', *, keepdims=False) 

Description

help(scipy.stats.circvar)

    


Compute the circular variance of a sample of angle observations.

Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
radians, their *circular variance* is defined by ([2]_, Eq. 2.3.3)

.. math::

   1 - \left| \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right|

where :math:`i` is the imaginary unit and :math:`|z|` gives the length
of the complex number :math:`z`.  :math:`|z|` in the above expression
is known as the `mean resultant length`.

Parameters
----------
samples : array_like
    Input array of angle observations.  The value of a full angle is
    equal to ``(high - low)``.
high : float, optional
    Upper boundary of the principal value of an angle.  Default is ``2*pi``.
low : float, optional
    Lower boundary of the principal value of an angle.  Default is ``0``.
axis : int or None, default: None
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
circvar : float
    Circular variance.  The returned value is in the range ``[0, 1]``,
    where ``0`` indicates no variance and ``1`` indicates large variance.
    
    If the input array is empty, ``np.nan`` is returned.

See Also
--------

:func:`circmean`
    Circular mean.
:func:`circstd`
    Circular standard deviation.


Notes
-----
In the limit of small angles, the circular variance is close to
half the 'linear' variance if measured in radians.

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] Fisher, N.I. *Statistical analysis of circular data*. Cambridge
       University Press, 1993.
.. [2] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
       John Wiley & Sons, 1999.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import circvar
>>> import matplotlib.pyplot as plt
>>> samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
...                       0.133, -0.473, -0.001, -0.348, 0.131])
>>> samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
...                       0.104, -0.136, -0.867,  0.012,  0.105])
>>> circvar_1 = circvar(samples_1)
>>> circvar_2 = circvar(samples_2)

Plot the samples.

>>> fig, (left, right) = plt.subplots(ncols=2)
>>> for image in (left, right):
...     image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
...                np.sin(np.linspace(0, 2*np.pi, 500)),
...                c='k')
...     image.axis('equal')
...     image.axis('off')
>>> left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
>>> left.set_title(f"circular variance: {np.round(circvar_1, 2)!r}")
>>> right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
>>> right.set_title(f"circular variance: {np.round(circvar_2, 2)!r}")
>>> plt.show()

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