import numbers
import numpy as np
from numpy.lib.stride_tricks import as_strided
__all__ = ['view_as_blocks', 'view_as_windows']
def view_as_blocks(arr_in, block_shape):
"""Block view of the input n-dimensional array (using re-striding).
Blocks are non-overlapping views of the input array.
Parameters
----------
arr_in : ndarray
N-d input array.
block_shape : tuple
The shape of the block. Each dimension must divide evenly into the
corresponding dimensions of `arr_in`.
Returns
-------
arr_out : ndarray
Block view of the input array.
Examples
--------
>>> import numpy as np
>>> from skimage.util.shape import view_as_blocks
>>> A = np.arange(4*4).reshape(4,4)
>>> A
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
>>> B = view_as_blocks(A, block_shape=(2, 2))
>>> B[0, 0]
array([[0, 1],
[4, 5]])
>>> B[0, 1]
array([[2, 3],
[6, 7]])
>>> B[1, 0, 1, 1]
13
>>> A = np.arange(4*4*6).reshape(4,4,6)
>>> A # doctest: +NORMALIZE_WHITESPACE
array([[[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]],
[[24, 25, 26, 27, 28, 29],
[30, 31, 32, 33, 34, 35],
[36, 37, 38, 39, 40, 41],
[42, 43, 44, 45, 46, 47]],
[[48, 49, 50, 51, 52, 53],
[54, 55, 56, 57, 58, 59],
[60, 61, 62, 63, 64, 65],
[66, 67, 68, 69, 70, 71]],
[[72, 73, 74, 75, 76, 77],
[78, 79, 80, 81, 82, 83],
[84, 85, 86, 87, 88, 89],
[90, 91, 92, 93, 94, 95]]])
>>> B = view_as_blocks(A, block_shape=(1, 2, 2))
>>> B.shape
(4, 2, 3, 1, 2, 2)
>>> B[2:, 0, 2] # doctest: +NORMALIZE_WHITESPACE
array([[[[52, 53],
[58, 59]]],
[[[76, 77],
[82, 83]]]])
"""
if not isinstance(block_shape, tuple):
raise TypeError('block needs to be a tuple')
block_shape = np.array(block_shape)
if (block_shape <= 0).any():
raise ValueError("'block_shape' elements must be strictly positive")
if block_shape.size != arr_in.ndim:
raise ValueError("'block_shape' must have the same length "
"as 'arr_in.shape'")
arr_shape = np.array(arr_in.shape)
if (arr_shape % block_shape).sum() != 0:
raise ValueError("'block_shape' is not compatible with 'arr_in'")
# -- restride the array to build the block view
new_shape = tuple(arr_shape // block_shape) + tuple(block_shape)
new_strides = tuple(arr_in.strides * block_shape) + arr_in.strides
arr_out = as_strided(arr_in, shape=new_shape, strides=new_strides)
return arr_out
def view_as_windows(arr_in, window_shape, step=1):
"""Rolling window view of the input n-dimensional array.
Windows are overlapping views of the input array, with adjacent windows
shifted by a single row or column (or an index of a higher dimension).
Parameters
----------
arr_in : ndarray
N-d input array.
window_shape : integer or tuple of length arr_in.ndim
Defines the shape of the elementary n-dimensional orthotope
(better know as hyperrectangle [1]_) of the rolling window view.
If an integer is given, the shape will be a hypercube of
sidelength given by its value.
step : integer or tuple of length arr_in.ndim
Indicates step size at which extraction shall be performed.
If integer is given, then the step is uniform in all dimensions.
Returns
-------
arr_out : ndarray
(rolling) window view of the input array.
Notes
-----
One should be very careful with rolling views when it comes to
memory usage. Indeed, although a 'view' has the same memory
footprint as its base array, the actual array that emerges when this
'view' is used in a computation is generally a (much) larger array
than the original, especially for 2-dimensional arrays and above.
For example, let us consider a 3 dimensional array of size (100,
100, 100) of ``float64``. This array takes about 8*100**3 Bytes for
storage which is just 8 MB. If one decides to build a rolling view
on this array with a window of (3, 3, 3) the hypothetical size of
the rolling view (if one was to reshape the view for example) would
be 8*(100-3+1)**3*3**3 which is about 203 MB! The scaling becomes
even worse as the dimension of the input array becomes larger.
References
----------
.. [1] https://en.wikipedia.org/wiki/Hyperrectangle
Examples
--------
>>> import numpy as np
>>> from skimage.util.shape import view_as_windows
>>> A = np.arange(4*4).reshape(4,4)
>>> A
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
>>> window_shape = (2, 2)
>>> B = view_as_windows(A, window_shape)
>>> B[0, 0]
array([[0, 1],
[4, 5]])
>>> B[0, 1]
array([[1, 2],
[5, 6]])
>>> A = np.arange(10)
>>> A
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> window_shape = (3,)
>>> B = view_as_windows(A, window_shape)
>>> B.shape
(8, 3)
>>> B
array([[0, 1, 2],
[1, 2, 3],
[2, 3, 4],
[3, 4, 5],
[4, 5, 6],
[5, 6, 7],
[6, 7, 8],
[7, 8, 9]])
>>> A = np.arange(5*4).reshape(5, 4)
>>> A
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
>>> window_shape = (4, 3)
>>> B = view_as_windows(A, window_shape)
>>> B.shape
(2, 2, 4, 3)
>>> B # doctest: +NORMALIZE_WHITESPACE
array([[[[ 0, 1, 2],
[ 4, 5, 6],
[ 8, 9, 10],
[12, 13, 14]],
[[ 1, 2, 3],
[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15]]],
[[[ 4, 5, 6],
[ 8, 9, 10],
[12, 13, 14],
[16, 17, 18]],
[[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15],
[17, 18, 19]]]])
"""
# -- basic checks on arguments
if not isinstance(arr_in, np.ndarray):
raise TypeError("`arr_in` must be a numpy ndarray")
ndim = arr_in.ndim
if isinstance(window_shape, numbers.Number):
window_shape = (window_shape,) * ndim
if not (len(window_shape) == ndim):
raise ValueError("`window_shape` is incompatible with `arr_in.shape`")
if isinstance(step, numbers.Number):
if step < 1:
raise ValueError("`step` must be >= 1")
step = (step,) * ndim
if len(step) != ndim:
raise ValueError("`step` is incompatible with `arr_in.shape`")
arr_shape = np.array(arr_in.shape)
window_shape = np.array(window_shape, dtype=arr_shape.dtype)
if ((arr_shape - window_shape) < 0).any():
raise ValueError("`window_shape` is too large")
if ((window_shape - 1) < 0).any():
raise ValueError("`window_shape` is too small")
# -- build rolling window view
slices = tuple(slice(None, None, st) for st in step)
window_strides = np.array(arr_in.strides)
indexing_strides = arr_in[slices].strides
win_indices_shape = (((np.array(arr_in.shape) - np.array(window_shape))
// np.array(step)) + 1)
new_shape = tuple(list(win_indices_shape) + list(window_shape))
strides = tuple(list(indexing_strides) + list(window_strides))
arr_out = as_strided(arr_in, shape=new_shape, strides=strides)
return arr_out