Sliding windows using as_strided, with the results zero padded in order to keep the last indices

sliding_window.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Sliding windows module.
"""

import numpy as np

from numpy.lib.stride_tricks import as_strided


__all__ = ['sliding_window']


def norm_shape(shape):
    """
    Normalize numpy array shapes so they're always expressed as a tuple,
    even for one-dimensional shapes.

    Parameters
        shape - an int, or a tuple of ints

    Returns
        a shape tuple
    """
    try:
        i = int(shape)
        return (i,)
    except TypeError:
        pass  # shape was not a number
    try:
        t = tuple(shape)
        return t
    except TypeError:
        pass  # shape was not iterable
    raise TypeError('shape must be an int, or a tuple of ints')


def sliding_window(a, ws, ss=None, flatten=True):
    """
    Return a sliding window over a in any number of dimensions

    Parameters:
        a  - an n-dimensional numpy array
        ws - an int (a is 1D) or tuple (a is 2D or greater) representing the size
             of each dimension of the window
        ss - an int (a is 1D) or tuple (a is 2D or greater) representing the
             amount to slide the window in each dimension. If not specified, it
             defaults to ws.
        flatten - if True, all slices are flattened, otherwise, there is an
                  extra dimension for each dimension of the input.

    Returns
        an array containing each n-dimensional window from a

    Code is modified from:
    http://www.johnvinyard.com/blog/?p=268
    """

    if None is ss:
        # ss was not provided. the windows will not overlap in any direction.
        ss = ws
    assert np.all(np.zeros(a.ndim) < np.asarray(ss)) and np.all(np.asarray(ss) <= np.asarray(ws)), \
      "Step size must be greater than zero and less than or equal to window size."
    ws = norm_shape(ws)
    ss = norm_shape(ss)

    # convert ws, ss, and a.shape to numpy arrays so that we can do math in every
    # dimension at once.
    ws = np.array(ws)
    ss = np.array(ss)
    shape = np.array(a.shape)


    # ensure that ws, ss, and a.shape all have the same number of dimensions
    ls = [len(shape), len(ws), len(ss)]
    if 1 != len(set(ls)):
        raise ValueError(\
        'a.shape, ws and ss must all have the same length. They were %s' % str(ls))

    # ensure that ws is smaller than a in every dimension
    if np.any(ws > shape):
        raise ValueError(\
        'ws cannot be larger than a in any dimension.\
 a.shape was %s and ws was %s' % (str(a.shape), str(ws)))

    # how many slices will there be in each dimension?
    newshape = norm_shape(np.ceil((shape - (ws - ss)) / ss.astype(np.float)))
    # the shape of the strided array will be the number of slices in each dimension
    # plus the shape of the window (tuple addition)
    newshape += norm_shape(ws)
    # pad with step size (ss) zeros on each dimension in order to not get garbage from the last indices
    na = np.zeros(np.array(shape) + ss)
    na[tuple(map(lambda s: slice(0, -s), ss))] = a
    # the strides tuple will be the array's strides multiplied by step size, plus
    # the array's strides (tuple addition)
    newstrides = norm_shape(np.array(na.strides) * ss) + na.strides

    strided = as_strided(na, shape = newshape, strides = newstrides)
    if not flatten:
        return strided

    # Collapse strided so that it has one more dimension than the window.  I.e.,
    # the new array is a flat list of slices.
    meat = len(ws) if ws.shape else 0
    firstdim = (np.product(newshape[:-meat]),) if ws.shape else ()
    dim = firstdim + (newshape[-meat:])
    # remove any dimensions with size 1
    dim = filter(lambda i : i != 1, dim)
    return strided.reshape(dim)

This code is modified from http://www.johnvinyard.com/blog/?p=268

I noticed there is a problem with the version that uses as_strided, in that it loses values from the array’s last indices, if the array’s shape doesn’t fit with the window and step size values.

The version presented here is fixed so that it zero pads the last slices in N dimensions.