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scipy.stats.

# circmean

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

  Compute the circular mean of a sample of angle observations.

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

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

  where \(i\) is the imaginary unit and \(\mathop{\mathrm{Arg}} z\) gives the principal value of the argument of complex number \(z\), restricted to the range \([0,2\pi]\) by default. \(z\) 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

  `circstd`

    Circular standard deviation.

  `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`.

  Array API Standard Support

  `circmean` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  > See Support for the array API standard for more information.

  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()