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Module « scipy.stats »

Fonction circmean - module scipy.stats

Signature de la fonction circmean

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

Description

help(scipy.stats.circmean)

    


Compute the circular mean of a sample of angle observations.

Given :math:`n` angle observations :math:`x_1, \cdots, x_n` measured in
radians, their *circular mean* is defined by ([1]_, Eq. 2.2.4)

.. math::

   \mathrm{Arg} \left( \frac{1}{n} \sum_{k=1}^n e^{i x_k} \right)

where :math:`i` is the imaginary unit and :math:`\mathop{\mathrm{Arg}} z`
gives the principal value of the argument of complex number :math:`z`,
restricted to the range :math:`[0,2\pi]` by default.  :math:`z` in the
above expression is known as the `mean resultant vector`.

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
-------
circmean : float
    Circular mean, restricted to the range ``[low, high]``.
    
    If the mean resultant vector is zero, an input-dependent,
    implementation-defined number between ``[low, high]`` is returned.
    If the input array is empty, ``np.nan`` is returned.

See Also
--------

:func:`circstd`
    Circular standard deviation.
:func:`circvar`
    Circular variance.


Notes
-----

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] Mardia, K. V. and Jupp, P. E. *Directional Statistics*.
       John Wiley & Sons, 1999.

Examples
--------
For readability, all angles are printed out in degrees.

>>> import numpy as np
>>> from scipy.stats import circmean
>>> import matplotlib.pyplot as plt
>>> angles = np.deg2rad(np.array([20, 30, 330]))
>>> circmean = circmean(angles)
>>> np.rad2deg(circmean)
7.294976657784009

>>> mean = angles.mean()
>>> np.rad2deg(mean)
126.66666666666666

Plot and compare the circular mean against the arithmetic mean.

>>> plt.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
...          np.sin(np.linspace(0, 2*np.pi, 500)),
...          c='k')
>>> plt.scatter(np.cos(angles), np.sin(angles), c='k')
>>> plt.scatter(np.cos(circmean), np.sin(circmean), c='b',
...             label='circmean')
>>> plt.scatter(np.cos(mean), np.sin(mean), c='r', label='mean')
>>> plt.legend()
>>> plt.axis('equal')
>>> plt.show()

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