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#!/usr/bin/env python
#
# Copyright 2015 Free Software Foundation, Inc.
#
# SPDX-License-Identifier: GPL-3.0-or-later
#
#
from __future__ import print_function
from __future__ import division
from __future__ import unicode_literals
import numpy as np
import time, sys
import copy
def bsc_channel(p):
'''
binary symmetric channel (BSC)
output alphabet Y = {0, 1} and
W(0|0) = W(1|1) and W(1|0) = W(0|1)
this function returns a prob's vector for a BSC
p denotes an erroneous transition
'''
if not (p >= 0.0 and p <= 1.0):
print("given p is out of range!")
return np.array([], dtype=float)
# 0 -> 0, 0 -> 1, 1 -> 0, 1 -> 1
W = np.array([[1 - p, p], [p, 1 - p]], dtype=float)
return W
def power_of_2_int(num):
return int(np.log2(num))
def is_power_of_two(num):
if type(num) != int:
return False # make sure we only compute integers.
return num != 0 and ((num & (num - 1)) == 0)
def bit_reverse(value, n):
# is this really missing in NumPy???
seq = np.int(value)
rev = np.int(0)
rmask = np.int(1)
lmask = np.int(2 ** (n - 1))
for i in range(n // 2):
shiftval = n - 1 - (i * 2)
rshift = np.left_shift(np.bitwise_and(seq, rmask), shiftval)
lshift = np.right_shift(np.bitwise_and(seq, lmask), shiftval)
rev = np.bitwise_or(rev, rshift)
rev = np.bitwise_or(rev, lshift)
rmask = np.left_shift(rmask, 1)
lmask = np.right_shift(lmask, 1)
if not n % 2 == 0:
rev = np.bitwise_or(rev, np.bitwise_and(seq, rmask))
return rev
def bit_reverse_vector(vec, n):
return np.array([bit_reverse(e, n) for e in vec], dtype=vec.dtype)
def get_Bn(n):
# this is a bit reversal matrix.
lw = power_of_2_int(n) # number of used bits
indexes = [bit_reverse(i, lw) for i in range(n)]
Bn = np.zeros((n, n), type(n))
for i, index in enumerate(indexes):
Bn[i][index] = 1
return Bn
def get_Fn(n):
# this matrix defines the actual channel combining.
if n == 1:
return np.array([1, ])
nump = power_of_2_int(n) - 1 # number of Kronecker products to calculate
F2 = np.array([[1, 0], [1, 1]], np.int)
Fn = F2
for i in range(nump):
Fn = np.kron(Fn, F2)
return Fn
def get_Gn(n):
# this matrix is called generator matrix
if not is_power_of_two(n):
print("invalid input")
return None
if n == 1:
return np.array([1, ])
Bn = get_Bn(n)
Fn = get_Fn(n)
Gn = np.dot(Bn, Fn)
return Gn
def unpack_byte(byte, nactive):
if np.amin(byte) < 0 or np.amax(byte) > 255:
return None
if not byte.dtype == np.uint8:
byte = byte.astype(np.uint8)
if nactive == 0:
return np.array([], dtype=np.uint8)
return np.unpackbits(byte)[-nactive:]
def pack_byte(bits):
if len(bits) == 0:
return 0
if np.amin(bits) < 0 or np.amax(bits) > 1: # only '1' and '0' in bits array allowed!
return None
bits = np.concatenate((np.zeros(8 - len(bits), dtype=np.uint8), bits))
res = np.packbits(bits)[0]
return res
def show_progress_bar(ndone, ntotal):
nchars = 50
fract = (1. * ndone / ntotal)
percentage = 100. * fract
ndone_chars = int(nchars * fract)
nundone_chars = nchars - ndone_chars
sys.stdout.write('\r[{0}{1}] {2:5.2f}% ({3} / {4})'.format('=' * ndone_chars, ' ' * nundone_chars, percentage, ndone, ntotal))
def mutual_information(w):
'''
calculate mutual information I(W)
I(W) = sum over y e Y ( sum over x e X ( ... ) )
.5 W(y|x) log frac { W(y|x) }{ .5 W(y|0) + .5 W(y|1) }
'''
ydim, xdim = np.shape(w)
i = 0.0
for y in range(ydim):
for x in range(xdim):
v = w[y][x] * np.log2(w[y][x] / (0.5 * w[y][0] + 0.5 * w[y][1]))
i += v
i /= 2.0
return i
def bhattacharyya_parameter(w):
'''
bhattacharyya parameter is a measure of similarity between two prob. distributions
THEORY: sum over all y e Y for sqrt( W(y|0) * W(y|1) )
Implementation:
Numpy vector of dimension (2, mu//2)
holds probabilities P(x|0), first vector for even, second for odd.
'''
dim = np.shape(w)
if len(dim) != 2:
raise ValueError
if dim[0] > dim[1]:
raise ValueError
z = np.sum(np.sqrt(w[0] * w[1]))
# need all
return z
def main():
print('helper functions')
for i in range(9):
print(i, 'is power of 2: ', is_power_of_two(i))
n = 6
m = 2 ** n
pos = np.arange(m)
rev_pos = bit_reverse_vector(pos, n)
print(pos)
print(rev_pos)
f = np.linspace(.01, .29, 10)
e = np.linspace(.03, .31, 10)
b = np.array([e, f])
zp = bhattacharyya_parameter(b)
print(zp)
a = np.sum(np.sqrt(e * f))
print(a)
if __name__ == '__main__':
main()
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