Plane and testing
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src/plane.py
206
src/plane.py
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@ -1,97 +1,145 @@
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"""
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Wrapper of a numpy array of bits.
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Wrapper of a bitarray.
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For the sake of efficiency, rather than work with an (m x m x ... x m) N-dimensional grid, we instead work with
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a 1D array of size (N-1)^m and reshape the grid if ever necessary. All bits of any given row is represented by
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a number whose binary representation expands to the given number. A 1 at index i in turn corresponds to an on
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state at the ith index of the given row. This holds for 0 as well.
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For the sake of compactness, the use of numpy arrays have been completely abandoned as a representation
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of the data. This also allows for a bit more consistency throughout the library, where I've often used
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the flat iterator provided by numpy, and other times used the actual array.
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For example, given a 100 x 100 CAM, we represent this underneath as a 1-D array of 100 integers, each of which's
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binary expansion will be 100 bits long (and padded with 0's if necessary).
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The use of just a bitarray also means it is significantly more compact, indexing of a plane should be
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more efficient, and the entire association between an N-1 dimensional grid with the current shape of
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the plane is no longer a concern.
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@date: June 05, 2015
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"""
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import random
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import operator
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import numpy as np
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from functools import reduce
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from bitarray import bitarray
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from collections import deque
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class Plane:
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"""
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Represents a bit plane, with underlying usage of numpy arrays.
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Represents a cell plane, with underlying usage of bitarrays.
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The following allows conversion between our given representation of a grid, and the user's expected
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representation of a grid. This allows accessing of bits in the same manner as one would access a
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numpy grid, without the same bloat as a straightforward N-dimensional grid of booleans for instance.
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The following maintains the shape of a contiguous block of memory, allowing the user to interact
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with it as if it was a multidimensional array.
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"""
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def __init__(self, shape, grid = None):
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def __init__(self, shape, bits = None):
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"""
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Construction of a plane. There are three cases:
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If shape is the empty tuple, we have an undefined plane. Nothing is in it.
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If shape is length 1, we have a 1D plane. This is represented by a single number.
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Otherwise, we have an N-D plane. Everything operates as expected.
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"""
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self.grid = grid
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self.shape = shape
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self.N = 0 if not len(shape) else shape[-1]
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First, the user may pass in there own custom bitarray to allow manipulating the
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data in the same manner as it is done internally. When this happens, the product
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of the shape parameter's components must be equivalent to the length of the
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bitarray.
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if self.grid is None:
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if len(shape) == 1:
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self.grid = self.N * bitarray('0')
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else:
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self.grid = np.empty(shape[:-1], dtype=np.object)
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for i in range(self.grid.size):
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self.grid.flat[i] = self.N * bitarray('0')
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Otherwise, we determine a grid based off solely the shape parameter. If shape
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is the empty tuple, we have an undefined plane. Consequently nothing is in it.
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Lastly, the most common usage will be to define an N-D plane, where N is equivalent
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to the number of components in the shape. For example, @shape = (100,100,100) means
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we have a 3-D grid with 1000000 cells in total (not necessarily in the CAM, just
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the plane in question).
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"""
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# Keep track of dimensionality
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self.shape = shape
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self.N = len(shape)
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# Preprocess all index offsets instead of performing them each time accessing occurs
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prod = 1
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self.offsets = deque()
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for d in reversed(shape):
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self.offsets.appendleft(prod)
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prod *= d
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# Allow the user to override grid construction
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if bits is not None:
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if len(bits) != reduce(operator.mul, shape, 1):
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raise ValueError("Shape with incorrect dimensionality")
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self.bits = bits
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# Generate bitarray automatically
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else:
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self.bits = reduce(operator.mul, shape, 1) * bitarray('0')
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# Check if a plane has been updated recently
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# This should be changed to True if it is ever "ticked."
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self.dirty = False
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def __getitem__(self, index):
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"""
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Indices supported are the same as those of the numpy array, except for when accessing an individual bit.
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Indexing of a plane mirrors that of a numpy array.
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When reaching the "last" dimension of the given array, we access the bit of the number at the second
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to last dimension, since we are working in (N-1)-dimensional space. Unless this last dimension is reached,
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we always return a plane object (otherwise an actual 0 or 1).
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Unless accessing the "last" dimension of the given array, we return another plane with
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the sliced bitarray as the underlying bits parameter. This allows for chaining access operators.
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That being said, it is preferable to use a tuple for accessing as opposed to a sequence of
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bracket indexing, as this does not create as many planes in the process.
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Note this function is much slower than accessing the grid directly. To forsake some convenience for the
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considerable speed boost is understandable; access by plane only for this convenience.
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If the "last" dimension is reached, we simply return the bit at the given index.
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"""
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# Given coordinates of a grid. This may or may not access the last dimension.
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# If it does not, can simply return the new plane given the subset accessed.
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# If it does, we access up to the bitarray, then access the desired bit(s)
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# If it does, we return the actual bit.
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if type(index) is tuple:
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if len(index) == len(self.shape):
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b_array = self.grid[index[:-1]]
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return b_array[index[-1]]
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offset = sum([x*y for (x,y) in zip(index, self.offsets)])
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if len(index) == self.N:
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return self.bits[offset]
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else:
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subgrid = self.grid[index]
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return Plane(subgrid.shape + (self.N,), subgrid)
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remain = self.shape[len(index):]
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shift = self.offsets[len(index)-1]
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return Plane(remain, bits[offset:offset+shift])
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# If we've reached the last dimension, the grid of the plane is just a bitarray
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# (we remove an additional dimension and instead store the bitarray for space's sake).
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# If a list of elements are passed, we must access them individually (bitarray does
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# not have built in support for this).
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elif len(self.shape) == 1:
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if type(index) is list:
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return list(map(lambda x: self.grid[x], index))
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# A list accessor allows one to access multiple elements at the offsets specified
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# by the list elements. For example, for a plane P, P[[1, 4, 6]] returns a list
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# containing the 1, 4, and 6th element.
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elif type(index) is list:
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elements = []
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for idx in index:
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elements.append(self[idx])
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return elements
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# Otherwise we were passed a simply number and we access the element like normal
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# (making sure to consider the shape of the plane of course)
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elif self.N == 1:
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return self.bits[index]
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else:
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delta = self.offsets[0]
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offset = index * delta
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return Plane(self.shape[1:], self.bits[offset:offset+delta])
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def __setitem__(self, index, value):
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"""
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Assigns a bit or slice of bits to a given index.
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Very similar to __getitem__ with a couple of caveats. Value should always
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be a single bit (either 0 or 1), but the index can still be a tuple, list,
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etc. The given value is assigned to all components of a given index.
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For example, with a plane P with shape (100, 100), P[0] = 1 sets the first
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100 elements (the 100 bits in the first row) to 1.
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"""
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if type(index) is tuple:
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offset = sum([x*y for (x,y) in zip(index, self.offsets)])
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if len(index) == self.N:
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self.bits[offset] = value
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else:
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return self.grid[index]
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shift = self.offsets[len(index)-1]
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self.bits[offset:offset+shift] = value
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# Any other means of indexing simply indexes the grid as expected, and wraps
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# the result in a plane object for consistent accessing. An attribute error
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# can occur once we reach the last dimension, and try to determine the shape
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# of a bitarray
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tmp = self.grid[index]
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try:
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return Plane(tmp.shape + (self.N,), tmp)
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except AttributeError:
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return Plane((self.N,), tmp)
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elif type(index) is list:
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elements = []
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for idx in index:
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self[idx] = value
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elif self.N == 1:
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self.bits[index] = value
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else:
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delta = self.offsets[0]
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offset = index * delta
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self.bits[offset:offset+delta] = value
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def randomize(self):
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"""
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@ -103,42 +151,18 @@ class Plane:
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the same value. I'm not really too interested in figuring this out, so I use the alternate
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method below.
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"""
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if len(self.shape) > 0:
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import random as r
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max_u = 2**self.N - 1
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gen = lambda: bin(r.randrange(0, max_u))[2:]
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if len(self.shape) == 1:
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self.grid = bitarray(gen().zfill(self.N))
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else:
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for i in range(self.grid.size):
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self.grid.flat[i] = bitarray(gen().zfill(self.N))
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if self.N > 0:
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max_unsigned = reduce(operator.mul, self.shape, 1)
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sequence = bin(random.randrange(0, max_unsigned))[2:]
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self.bits = bitarray(sequence.zfill(max_unsigned))
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def flatten(self, coordinate):
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def matrix(self):
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"""
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Converts a coordinate (which could be used to access a bit in a plane) and "flattens" it.
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Convert bitarray into a corresponding numpy matrix.
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By this we mean we convert the coordinate into an index and bit offset corresponding to
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the plane grid converted to 1D (think numpy.ndarray.flat).
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This should not be used for computation! This is merely a convenience method
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for displaying out to matplotlib via the AxesImages plotting methods.
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"""
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flat_index, gridprod = 0, 1
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for i in reversed(range(len(coordinate[:-1]))):
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flat_index += coordinate[i] * gridprod
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gridprod *= self.shape[i]
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return flat_index, coordinate[-1]
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def bits(self):
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"""
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Expands out bitarray into individual bits.
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This is useful for display in matplotlib for example, but does take a dimension more space.
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"""
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if len(self.shape) == 1:
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return np.array(self.grid)
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else:
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tmp = np.array([list(self.grid.flat[i]) for i in range(self.grid.size)])
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return np.reshape(tmp, self.shape)
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tmp = np.array(self.bits)
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return np.reshape(tmp, self.shape)
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@ -0,0 +1,96 @@
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import os, sys
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sys.path.insert(0, os.path.join('..', 'src'))
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import plane
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class TestProperties:
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"""
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"""
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def setUp(self):
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self.plane2d = plane.Plane((100, 100))
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self.plane3d = plane.Plane((100, 100, 100))
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def test_bitsLength(self):
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"""
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Bit expansion.
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"""
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assert len(self.plane2d.bits) == 100 * 100
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assert len(self.plane3d.bits) == 100 * 100 * 100
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def test_randomize(self):
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"""
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Randomization.
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"""
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bits2d = self.plane2d.bits
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bits3d = self.plane3d.bits
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self.plane2d.randomize()
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self.plane3d.randomize()
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assert bits2d != self.plane2d.bits
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assert bits3d != self.plane3d.bits
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assert len(self.plane2d.bits) == 100 * 100
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assert len(self.plane3d.bits) == 100 * 100 * 100
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class TestIndexing:
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"""
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"""
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def setUp(self):
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self.plane2d = plane.Plane((100, 100))
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self.plane3d = plane.Plane((100, 100, 100))
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def test_tupleAssignment(self):
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"""
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Tuple Assignment.
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"""
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self.plane2d[(1, 0)] = 1
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self.plane3d[(1, 0, 0)] = 1
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def test_listAssignment(self):
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"""
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List Assignment.
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"""
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self.plane2d[[0]] = 1
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self.plane3d[[0]] = 1
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self.plane2d[[[(4, 5)], 5, (2, 2)]] = 1
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self.plane3d[[[(4, 5)], 5, (2, 2)]] = 1
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def test_singleAssignment(self):
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"""
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Single Assignment.
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"""
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self.plane2d[0][0] = 1
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self.plane3d[0][0] = 1
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def test_tupleAccessing(self):
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"""
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Tuple Accessing.
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"""
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self.plane2d[(1, 0)] = 1
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assert self.plane2d[(1, 0)] == 1
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self.plane3d[(1, 0)] = 1
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for i in range(10):
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assert self.plane3d[(1, 0, i)] == 1
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def test_listAccessing(self):
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"""
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List Accessing.
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"""
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self.plane2d[[(0, 4), (1, 5)]] = 1
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assert self.plane2d[[(0, 4), (1, 5), (1, 6)]] == [1, 1, 0]
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self.plane3d[[(0, 4)]] = 1
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assert self.plane3d[[(0, 4, 1), (0, 4, 9), (1, 6, 0)]] == [1, 1, 0]
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def test_singleAccessing(self):
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"""
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Single Accessing.
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"""
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self.plane2d[0] = 1
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for i in range(10):
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assert self.plane2d[0][i] == 1
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