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