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Gaussian_Elimination.py
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Gaussian_Elimination.py
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#
# Filename: Gaussian_Elimination.py
#
# To invert a matrix to identity matrix.
#
# By Chong Zan Kai zkchong@gmail.com
# Last modified on 21-Jun-2015.
#
from bitstring import BitArray
#-----------------------------------------------------------------------
#
#-----------------------------------------------------------------------
class Gaussian_Elimination:
#
# To form a triangular matrix.
#
def form_triangle_matrix(self, input_list, aux_list = None):
dim_col = len(input_list[0])
dim_row = len(input_list)
for col_num in range(dim_col):
# print ('col_num = %d' % col_num)
# Search pivoting row.
pivoting_row_num= -1
for row_num in range(col_num, dim_row):
if input_list[row_num][col_num] == 1:
pivoting_row_num = row_num
break
# Throw error if cannot find.
assert (pivoting_row_num >= 0)
# print ('pivoting_row_num = %s' % pivoting_row_num)
# Move the pivoting row to the correct position
input_list.insert(col_num, input_list.pop(pivoting_row_num))
if aux_list:
aux_list.insert(col_num, aux_list.pop(pivoting_row_num))
# the current pivoting row is at location
# pivoting_row = input_list[col_num]
# print ('pivoting_row = %s' % pivoting_row.bin)
# Clean all the rows below, in which their $col_num is nonzero.
for row_num in range(col_num + 1, dim_row):
if input_list[row_num][col_num] == 1:
input_list[row_num] = input_list[row_num].__xor__(input_list[col_num])
if aux_list:
aux_list[row_num] = aux_list[row_num].__xor__(aux_list[col_num])
return
#
# Backward substitution.
#
def backward_substitution(self, input_list, aux_list = None):
dim_col = len(input_list[0])
# Starting from the rightmost column.
for col_num in reversed(range(1, dim_col)):
# pivoting_row = input_list[col_num]
# The row numbers should start from (col_num-1) to 0.
for row_num in reversed(range(col_num)):
# Clean all the rows above, in which thir $col_num is nonzero.
if input_list[row_num][col_num] == 1:
input_list[row_num] = input_list[row_num].__xor__(input_list[col_num])
if aux_list:
aux_list[row_num] = aux_list[row_num].__xor__(aux_list[col_num])
#-----------------------------------------------------------------------
# For testing.
#-----------------------------------------------------------------------
if __name__ == '__main__':
import sys
import random
#-------------------------------------------------------------------
# Necessary function
#-------------------------------------------------------------------
#
# To generate Random code's coded symbols.
#
def generate_coded_symbol(generator_row, message_symbol_list):
selected_list = [message_symbol_list[i] for i, g in enumerate(generator_row) if g == 1]
coded_symbol = BitArray( [0] * len(message_symbol_list[0]) )
for s in selected_list:
coded_symbol = coded_symbol.__xor__(s)
return coded_symbol
#
# To print the list in a nice format
#
def print_list(input_list):
for i, g in enumerate(input_list):
print ('[%02d]: %s' % (i, g.bin) )
#-------------------------------------------------------------------
randnum = random.randint(0,100000)
random.seed(randnum)
print ('randnum = %d' % randnum)
# Data
total_message_symbol = 10 # This message has $total_message_symbol symbols.
message_symbol_size = 10 # The message symbol has $message_symbol_size bits.
# Total generator row to generate.
total_generator_row = total_message_symbol + 10 # I will generate k+10 rows.
generator_list = []
data_list = []
coded_symbol_list = []
#
# Generate message symbols.
#
for i in range(total_message_symbol):
data_bitarr = BitArray([random.choice([0, 1]) for i in range(message_symbol_size)])
data_list.append(data_bitarr)
#
# Generate generator_list and coded_symbol_bv_list.
#
for i in range(total_generator_row):
generator_bitarr = BitArray([random.choice([0, 1]) for i in range(total_message_symbol) ])
generator_list.append( generator_bitarr )
coded_symbol_list.append( generate_coded_symbol(generator_bitarr, data_list) )
#
# Report
#
ge = Gaussian_Elimination()
print ('#------------------------------------------------------------')
print ('Sage 0: Original data')
print ('#------------------------------------------------------------')
print ('data_list :')
print_list (data_list)
print
print ('generator_list :')
print_list (generator_list)
print
print ('coded_symbol_list :')
print_list (coded_symbol_list)
print
print ('#------------------------------------------------------------')
print ('Step 1: form_triangle_matrix')
print ('#------------------------------------------------------------')
ge.form_triangle_matrix(generator_list, coded_symbol_list)
print ('generator_list :')
print_list (generator_list)
print
print ('coded_symbol_list :')
print_list (coded_symbol_list)
print
print ('#------------------------------------------------------------')
print ('Step 2: backward_substitution')
print ('#------------------------------------------------------------')
ge.backward_substitution(generator_list, coded_symbol_list)
print ('generator_list :')
print_list (generator_list)
print
print ('coded_symbol_list :')
print_list (coded_symbol_list)
print
print ('#------------------------------------------------------------')
print ('Step 3: Verification')
print ('#------------------------------------------------------------')
# print ('The first %d rows of coded_symbol_list')
print ('coded_symbol_list[0:total_message_symbol]:')
print_list (coded_symbol_list[0:total_message_symbol])
print
print ('data_list:')
print_list (data_list)
print
if coded_symbol_list[0:total_message_symbol] == data_list:
print ('Decoding correctly')
else:
print ('Decoding wrongly')