def find_error(error_syndrome):
comparison = (error_syndrome[0], error_syndrome[1], error_syndrome[2])
try:
column_map = {
(zero, zero, one):
list2vec([one, zero, zero, zero, zero, zero, zero]),
(zero, one, zero):
list2vec([zero, one, zero, zero, zero, zero, zero]),
(zero, one, one):
list2vec([zero, zero, one, zero, zero, zero, zero]),
(one, zero, zero):
list2vec([zero, zero, zero, one, zero, zero, zero]),
(one, zero, one):
list2vec([zero, zero, zero, zero, one, zero, zero]),
(one, one, zero):
list2vec([zero, zero, zero, zero, zero, one, zero]),
(one, one, one):
list2vec([zero, zero, zero, zero, zero, zero, one])
}
return column_map[comparison]
except KeyError:
return list2vec([zero, zero, zero, zero, zero, zero, zero])
import cancer_data
import vec
from vector import vecutil
from matrix import matutil
import math
test_ident = matutil.rowdict2mat({
0: vecutil.list2vec([1, 0, 0]),
1: vecutil.list2vec([0, 1, 0]),
2: vecutil.list2vec([0, 0, 1]),
})
test_1 = vecutil.list2vec([-1, -1, -1])
test_2 = vecutil.list2vec([1, 1, 1])
def read_training_data():
return cancer_data.read_training_data('inner_product/train.data')
def signum(u):
"""
input: a Vec u
output: the Vec v with the same domain as u such that
+1 if u[d] >= 0
v[d]= {
-1 if u[d] < 0
"""
return vec.Vec(u.D, {d: 1 if u[d] >= 0 else -1 for d in u.D})
assert (signum(vec.Vec({'A', 'B'}, {
def find_error_matrix(S):
return coldict2mat(
{c: find_error(list2vec([S[r, c] for r in S.D[0]]))
for c in S.D[1]})
from matrix.matutil import listlist2mat, coldict2mat
from matrix.bitutil import mat2bits, bits2mat, str2bits, bits2str, noise
from vector.vecutil import list2vec
from GF2 import zero, one
G = listlist2mat([
[one, zero, one, one],
[one, one, zero, one],
[zero, zero, zero, one],
[one, one, one, zero],
[zero, zero, one, zero],
[zero, one, zero, zero],
[one, zero, zero, zero],
])
message1 = list2vec([one, zero, zero, one])
encoded = G * message1
print("the encoding of the message [one, 0, 0, one] is ", encoded)
def extract_original(encoded):
decoded = [encoded[6], encoded[5], encoded[4], encoded[2]]
return decoded
print("\ndecoded %s" % extract_original(encoded))
# we know that the kernel is trivial because G's row space spans GF(1)^4, and therefore that
# G represents a one-to-one function, and therefore that it is invertible
def get_column(m, colno):
return G * list2vec([m[r, colno] for r in m.D[0]])
def adjust(v, multipliers):
return vecutil.list2vec([v[d] * multipliers[d] for d in v.D])
('y2', 'x1'): -x1,
('y2', 'x2'): -x2,
('y2', 'x3'): -1
})
return [u, v]
w = Vec(D, {
('y1', 'x1'): 1
})
l0, l1 = make_equations(358, 36, 0, 0)
l4, l5 = make_equations(329, 597, 0, 1)
l2, l3 = make_equations(592, 157, 0, 1)
l6, l7 = make_equations(580, 483, 0, 1)
L = matutil.rowdict2mat({
0: l0,
1: l1,
2: l2,
3: l3,
4: l4,
5: l5,
6: l6,
7: l7,
8: w,
})
b = vecutil.list2vec([0, 0, 0, 0, 0, 0, 0, 0, 1])
print(solver.solve(L, b))
def test_method_orthogonal(method):
b = vecutil.list2vec([1, 1, 1])
v1 = vecutil.list2vec([0, 2, 2])
v2 = vecutil.list2vec([0, 1, -1])
vlist = [v1, v2]
return method(b, vlist)
def orthonormalization(L):
"""
input: a list L of linearly independent Vecs
output: a list L* of len(L) orthonormal Vecs such that,
for i = 1, ..., len(L), the first i Vecs of L*
and the first i vecs of L span the same space
"""
orthed_up = orthogonalize(L)
norms = [vec_norm(v) for v in orthed_up]
return [(1 / norms[i] * orthed_up[i]) for i in range(len(orthed_up))]
orth_test_list = [
vecutil.list2vec([4, 3, 1, 2]),
vecutil.list2vec([8, 9, -5, -5]),
vecutil.list2vec([10, 1, -1, 5])
]
orth_test = orthonormalization(orth_test_list)
orth_test_rounded = [(vecutil.list2vec([round(o[d], 2) for d in o.D]))
for o in orth_test]
assert (orth_test_rounded == [
Vec({0, 1, 2, 3}, {
0: 0.73,
1: 0.55,
2: 0.18,
3: 0.37
}),
Vec({0, 1, 2, 3}, {
def test_method_non_orthogonal(method):
first = vecutil.list2vec([1, 0])
second = vecutil.list2vec([math.sqrt(2) / 2, math.sqrt(2) / 2])
vlist = [first, second]
b = vecutil.list2vec([1, 1])
return method(b, vlist)
# c) SAME DIMENSION SAME RANK
from vec import Vec
from dimension import independence
from vector import vecutil
from matrix import matutil
# 6.7.6
def my_is_independent(L):
n = len(L)
rank = independence.rank(L)
return n == rank
a = [vecutil.list2vec([1, 2, 3]), vecutil.list2vec([2, 2, 2])]
assert (my_is_independent(a) == True)
assert (my_is_independent([
vecutil.list2vec(v) for v in [[2, 4, 0], [8, 16, 4], [0, 0, 7]]
]) == False)
# 6.7.7
def my_rank(L):
while not independence.is_independent(L):
L.pop()
return len(L)
my_rank_test = [
vecutil.list2vec(v) for v in [[1, 2, 3], [4, 5, 6], [1.1, 1.1, 1.1]]
def row_rearrange_algorithm(rowlist):
col_label_list = sorted(rowlist[0].D, key=hash)
new_rowlist = []
rows_left = set(range(len(rowlist)))
for c in col_label_list:
rows_with_nonzero = [r for r in rows_left if rowlist[r][c] != 0]
if rows_with_nonzero != []:
pivot = rows_with_nonzero[0]
new_rowlist.append(rowlist[pivot])
for r in rows_with_nonzero[1:]:
multiplier = rowlist[r][c] / rowlist[pivot][c]
rowlist[r] -= multiplier * rowlist[pivot]
rows_left.remove(pivot)
return new_rowlist
def print_rowlist(rowlist):
as_mat = matutil.rowdict2mat(rowlist)
print("%s" % as_mat)
test = [[0, 2, 3, 4, 5], [0, 0, 0, 3, 2], [1, 2, 3, 4, 5], [0, 0, 0, 6, 7],
[0, 0, 0, 9, 9]]
a = [vecutil.list2vec(v) for v in test]
print_rowlist(row_rearrange_algorithm(a))
def create_random_vector(n): return list2vec([randGF2() for i in range(n)])
from GF2 import one
from vector.vecutil import list2vec
from dimension import independence
from matrix import bitutil, matutil
import random
a0 = list2vec([one, one, 0, one, 0, one])
b0 = list2vec([one, one, 0, 0, 0, one])
def randGF2():
return random.randint(0, 1) * one
def create_random_vector(n):
return list2vec([randGF2() for i in range(n)])
def choose_secret_vector(s, t):
"""
input: GF(2) field elements s and t (i.e bits)
output: a random 6-vector u such that a0 * u = s and b0 * u = t
"""
u = create_random_vector(6)
while a0 * u != s and b0 * u != t:
u = create_random_vector(6)
return u
s = 0
t = one
u = choose_secret_vector(s, t)
print(u)
def generate_remaining_vectors():