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# scipy.stats.circvar

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

  Compute the circular variance for samples assumed to be in a range.

  Parameters:
    samples array_like

      Input array.

    high float or int, optional

      High boundary for the sample range. Default is `2*pi`.

    low float or int, optional

      Low boundary for the sample range. 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.

  See also

  `circmean`

    Circular mean.

  `circstd`

    Circular standard deviation.

  Notes

  This uses the following definition of circular variance: `1-R`, where `R` is the mean resultant vector. The returned value is in the range [0, 1], 0 standing for no variance, and 1 for a large variance. In the limit of small angles, this value is similar to half the ‘linear’ variance.

  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.

  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()