def test_bitmatrix_echelon(verbose = 0):
for ntest, (m, imin, imax) in enumerate(create_echelon_matrices()):
m1h = np.array(m, dtype = np.uint64, copy = True)
j0h, nh = imax + 1, imax - imin
lenh = bitmatrix64_echelon_h(m1h, len(m1h), j0h, nh)
m1h = list(m1h)
lenh_ref, m1h_ref = ref_echelon(m, j0h, nh)
ok_h = m1h == m1h_ref and lenh == lenh_ref
m1l = np.array(m, dtype = np.uint64, copy = True)
j0l, nl = imin, imax - imin
lenl = bitmatrix64_echelon_l(m1l, len(m1l), j0l, nl)
m1l = list(m1l)
lenl_ref, m1l_ref = ref_echelon(m, j0l, nl, False)
ok_l = m1l == m1l_ref and lenl == lenl_ref
ok = ok_h and ok_l
if verbose or not ok:
print("Test ", ntest)
print("m =", [hex(x) for x in m], j0h, nh)
print("echelon h", [hex(x) for x in m1h], lenh)
print("expected", [hex(x) for x in m1h_ref], lenh_ref)
if not ok_h:
err = "Error in function bitmatrix64_echelon_h"
raise ValueError(err)
print("m =", [hex(x) for x in m], j0l, nl)
print("echelon l", [hex(x) for x in m1l], lenl)
print("expected", [hex(x) for x in m1l_ref], lenl_ref)
if not ok_l:
err = "Error in function bitmatrix64_echelon_l"
raise ValueError(err)
def leech_echelon(a):
a = np.copy(a)
bitmatrix64_xch_bits(a, 12, 0x800)
bitmatrix64_rot_bits(a, 1, 12, 0)
k = bitmatrix64_echelon_h(a, len(a), 24, 24)
bitmatrix64_rot_bits(a, 11, 12, 0)
bitmatrix64_xch_bits(a, 12, 0x800)
return a[:k]
def test_leech2_matrix_basis():
for a in leech2_matrix_basis_testcases():
a1 = np.array(a, dtype=np.uint64)
k1 = bitmatrix64_echelon_h(a1, len(a1), 24, 24)
a1 = leech_echelon(a1)
a2 = np.zeros(24, dtype=np.uint64)
k2 = leech2_matrix_basis(a, len(a), a2, 24)
assert k1 == k2 # == k2a
assert (a1[:k1] == a2[:k1]).all()
def test_leech2_matrix_orthogonal():
for a in leech2_matrix_orthogonal_testcases():
a1 = np.copy(a)
o1 = np.zeros(24, dtype=np.uint64)
ko1 = leech2_matrix_orthogonal(a, o1, len(a))
o1 = o1[ko1:]
ka1 = bitmatrix64_echelon_h(a1, len(a1), 24, 24)
assert ka1 == ko1
for v in a1:
for w in o1:
assert gen_leech2_scalprod(v, w) == 0
def test_leech2_matrix_radical():
for a in leech2_matrix_orthogonal_testcases():
a1 = np.copy(a)
k1 = bitmatrix64_echelon_h(a1, len(a1), 24, 24)
a1 = a1[:k1]
o1 = np.zeros(24, dtype=np.uint64)
ko1 = leech2_matrix_orthogonal(a1, o1, len(a))
o1 = o1[ko1:]
ko1 = 24 - ko1
ko1 = bitmatrix64_echelon_h(o1, len(o1), 24, 24)
kcap = bitmatrix64_cap_h(a1, o1, 24, 24)
#print(k1, ko1, kcap)
kcap1 = kcap[0]
radical = a1[kcap1:k1]
radical = leech_echelon(radical)
a_copy = np.array(a, dtype=np.uint32)
a2 = np.zeros(24, dtype=np.uint64)
k2 = leech2_matrix_radical(a_copy, len(a_copy), a2, 24)
a2 = a2[:k2]
assert len(radical) == k2
assert (a2 == radical).all()