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# -*- coding: utf-8 -*-
import sys
import pytest
from fpylll import GSO, IntegerMatrix, LLL
from fpylll.config import float_types, int_types
from copy import copy
import tools
if sys.maxsize >= 2**62:
dimensions = ((0, 0), (2, 2), (3, 3), (10, 10), (30, 30), (50, 50), (60, 60))
else:
dimensions = ((0, 0), (2, 2), (3, 3), (10, 10), (30, 30))
def make_integer_matrix(m, n, int_type="mpz"):
A = IntegerMatrix(m, n, int_type=int_type)
A.randomize("qary", k=m//2, bits=max(1, m))
return A
def test_gso_init():
for int_type in int_types:
for m, n in dimensions:
A = make_integer_matrix(m, n, int_type=int_type)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
del M
U = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A), U=U, float_type=float_type)
del M
UinvT = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A), U=U, UinvT=UinvT, float_type=float_type)
del M
def test_gso_d():
for int_type in int_types:
for m, n in dimensions:
A = make_integer_matrix(m, n, int_type=int_type)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
assert M.d == m
def test_gso_int_gram_enabled():
for int_type in int_types:
for m, n in dimensions:
A = make_integer_matrix(m, n, int_type=int_type)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
assert M.int_gram_enabled is False
assert M.transform_enabled is False
M = GSO.Mat(copy(A), float_type=float_type, flags=GSO.INT_GRAM)
assert M.int_gram_enabled is True
assert M.transform_enabled is False
if m and n:
U = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A), U=U, float_type=float_type)
assert M.transform_enabled is True
assert M.inverse_transform_enabled is False
UinvT = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A), U=U, UinvT=UinvT, float_type=float_type)
assert M.transform_enabled is True
assert M.inverse_transform_enabled is True
def test_gso_update_gso():
EPSILON = 0.0001
for int_type in int_types:
for m, n in dimensions:
A = make_integer_matrix(m, n, int_type=int_type)
LLL.reduction(A)
r00 = []
re00 = []
g00 = []
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
M.update_gso()
if (m, n) == (0, 0):
continue
r00.append(M.get_r(0, 0))
re00.append(M.get_r_exp(0, 0)[0])
g00.append(M.get_gram(0, 0))
for i in range(1, len(r00)):
assert r00[0] == pytest.approx(r00[i], rel=EPSILON)
assert re00[0] == pytest.approx(re00[i], rel=EPSILON)
assert g00[0] == pytest.approx(g00[i], rel=EPSILON)
def test_gso_babai():
for int_type in int_types:
for m, n in ((0, 0), (2, 2), (3, 3), (10, 10), (30, 30)):
if m <= 2 or n <= 2:
continue
A = make_integer_matrix(m, n, int_type=int_type)
v = list(A[0])
LLL.reduction(A)
for float_type in float_types:
M = GSO.Mat(copy(A), update=True, float_type=float_type)
try:
w = M.babai(v)
v_ = IntegerMatrix.from_iterable(1, m, w) * A
v_ = list(v_[0])
assert v == v_
except NotImplementedError:
pass
def test_gso_conversion():
for int_type in int_types:
for m, n in ((0, 0), (2, 2), (3, 3), (10, 10), (30, 30)):
if m <= 2 or n <= 2:
continue
A = make_integer_matrix(m, n, int_type=int_type)
v = list(A[0])
LLL.reduction(A)
for float_type in float_types:
M = GSO.Mat(copy(A), update=True, float_type=float_type)
try:
w = M.from_canonical(v)
v_ = [int(round(v__)) for v__ in M.to_canonical(w)]
assert v == v_
except NotImplementedError:
pass
def test_gso_coherence_gram_matrix():
"""
Test if the GSO is coherent if it is given a matrix A or its associated
Gram matrix A*A^T
"""
EPSILON = 0.0001
for int_type in int_types:
for m, n in dimensions:
# long is not tested for high dimensions because of integer overflow
if m > 20 and int_type == "long":
continue
A = make_integer_matrix(m, n, int_type=int_type).transpose()
G = tools.compute_gram(A)
for float_type in float_types:
M_A = GSO.Mat(copy(A), float_type=float_type, gram=False, flags=GSO.INT_GRAM)
M_A.update_gso()
M_G = GSO.Mat(copy(G), float_type=float_type, gram=True, flags=GSO.INT_GRAM)
M_G.update_gso()
# Check that the gram matrix coincide
for i in range(m):
for j in range(i):
assert M_A.get_int_gram(i, j) == G[i, j]
# Check if computations coincide
for i in range(m):
assert M_A.get_r(i, i) == pytest.approx(M_G.get_r(i, i), rel=EPSILON)
for j in range(i):
assert M_A.get_r(i, j) == pytest.approx(M_G.get_r(i, j), rel=EPSILON)
assert M_A.get_mu(i, j) == pytest.approx(M_G.get_mu(i, j), rel=EPSILON)
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