movav

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

Calculate the moving average.

Also known as rolling average or running average.

Parameters:

a (array_like) – Array of values for which to calculate the moving average. The dtype is converted to numpy.float64.
wlen (int) – Length of the averaging window (corresponds to \(k\) in the formula below). Must be at least one and not greater than the size of a (if axis is None) or the length of a along the given axis (if axis is not None).
axis (None or int, optional) – Axis along which to compute the moving average. The default is to compute the moving average of the flattened array.
out (array_like) – Alternative output array in which to place the result. The first wlen - 1 elements along the given axis must be discarded after receiving the result. out 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:

mav (numpy.ndarray) – The moving average along the specified axis. The result has the same shape as a except along the given axis where the length is smaller by wlen - 1.

See also

mdtools.statistics.cumav(): Calculate the cumulative average.

Notes

The moving average at the \(m\)-th position with a window size of \(k\) is given by

\[\mu_m^k = \frac{1}{k} \sum_{i=m}^{m+k-1} a_i\]

This function implements the moving average according to the following formula using numpy.cumsum():

\[\mu_m^k = \frac{1}{k} \left( \sum_{i=0}^{m+k-1} a_i - \sum_{i=0}^{m-1} a_i \right)\]

Examples

>>> a = np.arange(6)
>>> mdt.stats.movav(a, wlen=3)
array([1., 2., 3., 4.])
>>> mdt.stats.movav(a, wlen=4)
array([1.5, 2.5, 3.5])

>>> a = np.arange(12).reshape(3,4)
>>> mdt.stats.movav(a, wlen=5)
array([2., 3., 4., 5., 6., 7., 8., 9.])
>>> mdt.stats.movav(a, wlen=2, axis=0)
array([[2., 3., 4., 5.],
       [6., 7., 8., 9.]])
>>> mdt.stats.movav(a, wlen=2, axis=1)
array([[ 0.5,  1.5,  2.5],
       [ 4.5,  5.5,  6.5],
       [ 8.5,  9.5, 10.5]])

>>> a = np.arange(36).reshape(3,3,4)
>>> mdt.stats.movav(a, wlen=29)
array([14., 15., 16., 17., 18., 19., 20., 21.])
>>> mdt.stats.movav(a, wlen=2, axis=0)
array([[[ 6.,  7.,  8.,  9.],
        [10., 11., 12., 13.],
        [14., 15., 16., 17.]],

       [[18., 19., 20., 21.],
        [22., 23., 24., 25.],
        [26., 27., 28., 29.]]])
>>> mdt.stats.movav(a, wlen=2, axis=1)
array([[[ 2.,  3.,  4.,  5.],
        [ 6.,  7.,  8.,  9.]],

       [[14., 15., 16., 17.],
        [18., 19., 20., 21.]],

       [[26., 27., 28., 29.],
        [30., 31., 32., 33.]]])
>>> mdt.stats.movav(a, wlen=3, axis=2)
array([[[ 1.,  2.],
        [ 5.,  6.],
        [ 9., 10.]],

       [[13., 14.],
        [17., 18.],
        [21., 22.]],

       [[25., 26.],
        [29., 30.],
        [33., 34.]]])