def test_divide():
X = np.array([[1, 5],
[14, 2],
[13, 5]])
Y = np.array([[2, 3],
[2, 4],
[2, 11]])
pm = np.array([[12, 2],
[13, 4],
[ 0, 8],
[14, 1],
[ 0, 2],
[ 0, 4],
[ 0, 8],
[15, 1],
[ 0, 2],
[ 0, 4],
[ 0, 8],
[ 0, 1],
[ 0, 2],
[ 0, 4],
[ 0, 8]])
right_div = np.array([[4, 8],
[4, 4],
[4, 8]])
assert_equal(right_div, gf.divide(X, Y, pm))
def decode(self, W, method='euclid'):
assert method == 'euclid' or method == 'pgz'
t = self.R.shape[0] // 2
n = W.shape[1]
is_nan = False
assert n == self.pm.shape[0]
res = np.zeros_like(W, dtype=object)
for i in range(W.shape[0]):
w = W[i]
s = gf.polyval(w, self.R, self.pm)
if (s == 0).all():
res[i] = w
continue
if method == 'euclid':
s = s[::-1]
z = np.zeros(2 * t + 2, dtype=np.int64)
z[0] = 1
s = np.concatenate((s, np.array([1])))
r, a, lam = gf.euclid(z, s, self.pm, max_deg=t)
else:
lam = np.nan
for errors in range(t, 0, -1):
A = [[s[k] for k in range(j, j + errors)]
for j in range(errors)]
A = np.array(A)
b = [s[k] for k in range(errors, errors * 2)]
b = np.array(b)
lam = gf.linsolve(A, b, self.pm)
if lam is not np.nan:
break
if lam is np.nan:
res[i] = np.nan
is_nan = True
continue
lam = np.concatenate((lam, np.array([1])))
values = gf.polyval(lam, self.pm[:, 1], self.pm)
num_roots = 0
#res[i] = w
for j in range(values.shape[0]):
if values[j] == 0:
root = self.pm[j, 1]
alpha = gf.divide(1, root, self.pm)
index = self.pm[alpha - 1, 0]
w[n - index - 1] = 1 - w[n - index - 1]
num_roots += 1
if num_roots != lam.shape[0] - 1:
res[i] = np.nan
is_nan = True
continue
res[i] = w
if not is_nan:
res = res.astype(np.int64)
return res
def _decode(self, w, method):
t = self.R.shape[0] // 2
syndromes = gf.polyval(w, self.R, self.pm)
if np.sum(syndromes != 0) == 0:
return w
if method == 'pgz':
lambda_ = np.nan
for nu in range(t, 0, -1):
a = np.array([[syndromes[j] for j in range(i, nu + i)]
for i in range(nu)],
dtype=np.int)
b = np.array([syndromes[i] for i in range(nu, 2 * nu)],
dtype=np.int)
lambda_ = gf.linsolve(a, b, self.pm)
if lambda_ is not np.nan:
break
if lambda_ is np.nan:
return np.full(self.n, np.nan, dtype=np.int)
lambda_ = np.concatenate([lambda_, [1]])
elif method == 'euclid':
z = np.zeros([2 * t + 2], dtype=np.int)
z[0] = 1
syndromic_polynom = np.concatenate([syndromes[::-1], [1]])
_, _, lambda_ = gf.euclid(z, syndromic_polynom, self.pm, max_deg=t)
else:
raise ValueError
n_roots = 0
locators_values = gf.polyval(lambda_, np.arange(1, self.n + 1),
self.pm)
for idx in range(1, self.n + 1):
if not locators_values[idx - 1]:
position = self.n - self.pm[gf.divide(1, idx, self.pm) - 1,
0] - 1
w[position] = 1 - w[position]
n_roots += 1
if n_roots != lambda_.shape[0] - 1:
return np.full(self.n, np.nan, dtype=np.int)
return w
def test_divide_all(self):
pm = gf.gen_pow_matrix(357)
for elem1 in pm[:, 1]:
for elem2 in pm[:, 1]:
a = gf.divide(np.array([[elem1]]), np.array([[elem2]]), pm)
self.assertEqual(elem1, gf.prod(a, np.array([[elem2]]), pm))
def test_divide_inverse(self):
pm = gf.gen_pow_matrix(88479)
for elem in pm[:, 1]:
inverse = gf.divide(np.array([[1]]), np.array([[elem]]), pm)
self.assertEqual(1, gf.prod(inverse, np.array([[elem]]), pm))
def test_divide_itself(self):
pm = gf.gen_pow_matrix(54193)
for elem in pm[:, 1]:
self.assertEqual(
1, gf.divide(np.array([[elem]]), np.array([[elem]]), pm))
def test_divide_zero_2(self):
pm = gf.gen_pow_matrix(10187)
for elem in pm[:, 1]:
self.assertEqual(
0, gf.divide(np.array([[0]]), np.array([[elem]]), pm))
def test_divide_zero(self):
pm = gf.gen_pow_matrix(104155)
self.assertRaises(
BaseException,
lambda: gf.divide(np.array([[pm[-1, 1]]]), np.array([[0]]), pm))
