cumav

mdtools.statistics.cumav(a, axis=None, out=None)[source]

Calculate the cumulative average.

Parameters:

a (array_like) – Array of values for which to calculate the cumulative average. The dtype is converted to numpy.float64.
axis (None or int, optional) – Axis along which the cumulative average is computed. The default is to compute the cumulative average of the flattened array.
out (array_like) – Alternative output array in which to place the result. It must have the same shape and buffer length as a.flatten() (if axis is None) or a (if axis is not None), but the type will be cast if necessary. See numpy.cumsum() for more details. Note that the result will be cast to the dtype of out, even if this dtype cannot hold the resulting values (e.g. if the dtype of out is int but the result contains floating point values, the fractional part of these floats is cut). So it’s safest, to parse an output array of dtype numpy.float64, also with respect to the accuracy of the average calculation (compare notes of numpy.mean()).

Returns:

rav (numpy.ndarray) – The cumulative average along the specified axis. The result has the same size as a, and also the same shape as a if axis is not None or if a is a 1-d array.

See also

numpy.cumsum(): Return the cumulative sum of the elements along a given axis
mdtools.statistics.movav(): Calculate a (weighted) moving average.

Notes

The cumulative average at the \(n\)-th position is given by

\[\mu_n = \frac{1}{n} \sum_{i=0}^{n} a_i\]

Examples

>>> a = np.arange(6)
>>> mdt.stats.cumav(a)
array([0. , 0.5, 1. , 1.5, 2. , 2.5])

>>> a = np.arange(6).reshape(2,3)
>>> mdt.stats.cumav(a)
array([0. , 0.5, 1. , 1.5, 2. , 2.5])
>>> mdt.stats.cumav(a, axis=0)
array([[0. , 1. , 2. ],
       [1.5, 2.5, 3.5]])
>>> mdt.stats.cumav(a, axis=1)
array([[0. , 0.5, 1. ],
       [3. , 3.5, 4. ]])

>>> a = np.arange(12).reshape(2,2,3)
>>> mdt.stats.cumav(a)
array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. , 5.5])
>>> mdt.stats.cumav(a, axis=0)
array([[[0., 1., 2.],
        [3., 4., 5.]],

       [[3., 4., 5.],
        [6., 7., 8.]]])
>>> mdt.stats.cumav(a, axis=1)
array([[[0. , 1. , 2. ],
        [1.5, 2.5, 3.5]],

       [[6. , 7. , 8. ],
        [7.5, 8.5, 9.5]]])
>>> mdt.stats.cumav(a, axis=2)
array([[[ 0. ,  0.5,  1. ],
        [ 3. ,  3.5,  4. ]],

       [[ 6. ,  6.5,  7. ],
        [ 9. ,  9.5, 10. ]]])