# Window utilities¶

`allel.``moving_statistic`(values, statistic, size, start=0, stop=None, step=None)

Calculate a statistic in a moving window over values.

Parameters: values : array_like The data to summarise. statistic : function The statistic to compute within each window. size : int The window size (number of values). start : int, optional The index at which to start. stop : int, optional The index at which to stop. step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. out : ndarray, shape (n_windows,)

Examples

```>>> import allel
>>> values = [2, 5, 8, 16]
>>> allel.stats.moving_statistic(values, np.sum, size=2)
array([ 7, 24])
>>> allel.stats.moving_statistic(values, np.sum, size=2, step=1)
array([ 7, 13, 24])
```
`allel.``windowed_statistic`(pos, values, statistic, size=None, start=None, stop=None, step=None, windows=None, fill=nan)

Calculate a statistic from items in windows over a single chromosome/contig.

Parameters: pos : array_like, int, shape (n_items,) The item positions in ascending order, using 1-based coordinates.. values : array_like, int, shape (n_items,) The values to summarise. May also be a tuple of values arrays, in which case each array will be sliced and passed through to the statistic function as separate arguments. statistic : function The statistic to compute. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. fill : object, optional The value to use where a window is empty, i.e., contains no items. out : ndarray, shape (n_windows,) The value of the statistic for each window. windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates. counts : ndarray, int, shape (n_windows,) The number of items in each window.

Notes

The window stop positions are included within a window.

The final window will be truncated to the specified stop position, and so may be smaller than the other windows.

Examples

Count non-zero (i.e., True) items in non-overlapping windows:

```>>> import allel
>>> pos = [1, 7, 12, 15, 28]
>>> values = [True, False, True, False, False]
>>> nnz, windows, counts = allel.stats.windowed_statistic(
...     pos, values, statistic=np.count_nonzero, size=10
... )
>>> nnz
array([1, 1, 0])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 28]])
>>> counts
array([2, 2, 1])
```

Compute a sum over items in half-overlapping windows:

```>>> values = [3, 4, 2, 6, 9]
>>> x, windows, counts = allel.stats.windowed_statistic(
...     pos, values, statistic=np.sum, size=10, step=5, fill=0
... )
>>> x
array([ 7, 12,  8,  0,  9])
>>> windows
array([[ 1, 10],
[ 6, 15],
[11, 20],
[16, 25],
[21, 28]])
>>> counts
array([2, 3, 2, 0, 1])
```
`allel.``windowed_count`(pos, size=None, start=None, stop=None, step=None, windows=None)

Count the number of items in windows over a single chromosome/contig.

Parameters: pos : array_like, int, shape (n_items,) The item positions in ascending order, using 1-based coordinates.. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. counts : ndarray, int, shape (n_windows,) The number of items in each window. windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates.

Notes

The window stop positions are included within a window.

The final window will be truncated to the specified stop position, and so may be smaller than the other windows.

Examples

Non-overlapping windows:

```>>> import allel
>>> pos = [1, 7, 12, 15, 28]
>>> counts, windows = allel.stats.windowed_count(pos, size=10)
>>> counts
array([2, 2, 1])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 28]])
```

Half-overlapping windows:

```>>> counts, windows = allel.stats.windowed_count(pos, size=10, step=5)
>>> counts
array([2, 3, 2, 0, 1])
>>> windows
array([[ 1, 10],
[ 6, 15],
[11, 20],
[16, 25],
[21, 28]])
```
`allel.``per_base`(x, windows, is_accessible=None, fill=nan)

Calculate the per-base value of a windowed statistic.

Parameters: x : array_like, shape (n_windows,) The statistic to average per-base. windows : array_like, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions using 1-based coordinates. is_accessible : array_like, bool, shape (len(contig),), optional Boolean array indicating accessibility status for all positions in the chromosome/contig. fill : object, optional Use this value where there are no accessible bases in a window. y : ndarray, float, shape (n_windows,) The input array divided by the number of (accessible) bases in each window. n_bases : ndarray, int, shape (n_windows,) The number of (accessible) bases in each window
`allel.``equally_accessible_windows`(is_accessible, size)

Create windows each containing the same number of accessible bases.

Parameters: is_accessible : array_like, bool, shape (n_bases,) Array defining accessible status of all bases on a contig/chromosome. size : int Window size (number of accessible bases). windows : ndarray, int, shape (n_windows, 2) Window start/stop positions (1-based).