Skip to main content
`Ctrl`+`K`
scipy.stats.mstats.

# hmean

scipy.stats.mstats.hmean(a, axis=0, dtype=None, *, weights=None, nan_policy='propagate', keepdims=False)

  Calculate the weighted harmonic mean along the specified axis.

  The weighted harmonic mean of the array \(a_i\) associated to weights \(w_i\) is:

  \[\frac{ \sum_{i=1}^n w_i }{ \sum_{i=1}^n \frac{w_i}{a_i} } \, ,\]

  and, with equal weights, it gives:

  \[\frac{ n }{ \sum_{i=1}^n \frac{1}{a_i} } \, .\]
  Parameters:
    a array_like

      Input array, masked array or object that can be converted to an array.

    axis int or None, default: 0

      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.

    dtype dtype, optional

      Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.

    weights array_like, optional

      The weights array can either be 1-D (in which case its length must be the size of a along the given axis) or of the same shape as a. Default is None, which gives each value a weight of 1.0.

      Added in version 1.9.

    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:
    hmean ndarray

      See dtype parameter above.

  See also

  `numpy.mean`

    Arithmetic average

  `numpy.average`

    Weighted average

  `gmean`

    Geometric mean

  Notes

  The sample harmonic mean is the reciprocal of the mean of the reciprocals of the observations.

  The harmonic mean is computed over a single dimension of the input array, axis=0 by default, or all values in the array if axis=None. float64 intermediate and return values are used for integer inputs.

  The harmonic mean is only defined if all observations are non-negative; otherwise, the result is NaN.

  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

  `hmean` 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 | ⚠️ no JIT | ⚠️ no JIT
  Dask | ⚠️ computes graph | n/a

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

  References

  [1]

  “Weighted Harmonic Mean”, Wikipedia, https://en.wikipedia.org/wiki/Harmonic_mean#Weighted_harmonic_mean

  [2]

  Ferger, F., “The nature and use of the harmonic mean”, Journal of the American Statistical Association, vol. 26, pp. 36-40, 1931

  Examples

      >>> from scipy.stats import hmean
      >>> hmean([1, 4])
      1.6000000000000001
      >>> hmean([1, 2, 3, 4, 5, 6, 7])
      2.6997245179063363
      >>> hmean([1, 4, 7], weights=[3, 1, 3])
      1.9029126213592233