Sliding windows and series

`sliding_window_view`

The function creates a view with all the windows of a given size, one per line. By aggregating each window, you get the moving average:

import numpy as np
from numpy.lib.stride_tricks import sliding_window_view

serie = np.array([1, 2, 3, 4, 5, 6], dtype=float)
janelas = sliding_window_view(serie, 3)
print(janelas)
print(janelas.mean(axis=1))
print(np.shares_memory(serie, janelas), janelas.flags["WRITEABLE"])

[[1. 2. 3.]
 [2. 3. 4.]
 [3. 4. 5.]
 [4. 5. 6.]]
[2. 3. 4. 5.]
True False

The windows were not copied: the last result shows that they share memory with the series. And it is read-only, because several windows point to the same numbers, and writing in one messes up the others. This view is possible because of the strides (chapter 29).

Two other forms of moving average

The cumulative sum allows calculating any moving average in one pass, regardless of the window size. Convolution is the "classic" form of signal processing:

def media_movel(x, k):
    acumulada = np.cumsum(np.insert(x, 0, 0.0))
    return (acumulada[k:] - acumulada[:-k]) / k


print(np.allclose(media_movel(serie, 3), janelas.mean(axis=1)))
print(np.convolve(serie, np.ones(3) / 3, mode="valid"))

True
[2. 3. 4. 5.]

Accumulators: running max and max drop

The accumulators store the result so far. The np.maximum.accumulate gives the highest value seen up to each point. With it, the maximum drawdown (drawdown) of a price series: the largest loss since a previous peak, a common risk measure in finance:

precos = np.array([100, 110, 105, 120, 90, 95], dtype=float)
pico = np.maximum.accumulate(precos)
queda = (precos - pico) / pico
print(pico, queda.min().round(3))

[100. 110. 110. 120. 120. 120.] -0.25

The maximum drawdown was 25%: from a peak of 120 to 90.

Windows in two dimensions

The same function accepts a window with one dimension per axis, and it is the basis of image filters. Here, each block of 3 by 3 from a 5 by 5 image becomes a window:

img = np.arange(25, dtype=float).reshape(5, 5)
blocos = sliding_window_view(img, (3, 3))
print(blocos.shape, blocos.mean(axis=(-1, -2))[0, 0])

(3, 3, 3, 3) 6.0

There are 3 × 3 = 9 possible windows, each with 3 × 3 values. The project in chapter 42 uses this to blur and detect edges in an image.