"""shape.py - Padding & Block or rolling window views into arrays. `view_as_windows` and `view_as_blocks` were brought into this project from `scikit-image` in order to avoid adding same package as a dependency. It was originally released under the BSD 3-clause license, retained in `skfuzzy`. """ from __future__ import print_function 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 The n-dimensional 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 skfuzzy 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]]]]) """ # -- basic checks on arguments 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 arr_in = np.ascontiguousarray(arr_in) 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): """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 The n-dimensional input array. window_shape: tuple Defines the shape of the elementary n-dimensional orthotope (better know as hyperrectangle [1]_) of the rolling window view. 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] http://en.wikipedia.org/wiki/Hyperrectangle Examples -------- >>> import numpy as np >>> from skfuzzy 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") if not isinstance(window_shape, tuple): raise TypeError("'window_shape' must be a tuple") if not (len(window_shape) == arr_in.ndim): raise ValueError("'window_shape' 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 arr_in = np.ascontiguousarray(arr_in) new_shape = tuple(arr_shape - window_shape + 1) + tuple(window_shape) new_strides = arr_in.strides + arr_in.strides arr_out = as_strided(arr_in, shape=new_shape, strides=new_strides) return arr_out