def test_bugs_get_snf(self):
mat = IntMat3x3([-1, 1, 1, 1, -1, 1, 1, 1, -1])
ori_mat = copy.copy(mat)
snf_D, snf_S, snf_T = mat.get_snf()
SAT = numpy.matmul(snf_S, numpy.matmul(ori_mat.mat, snf_T))
wanted_mat = numpy.array([1, 0, 0, 0, 2, 0, 0, 0, 2]).reshape((3, 3))
numpy.testing.assert_almost_equal(SAT, wanted_mat)
numpy.testing.assert_almost_equal(snf_D, wanted_mat)
def test_dead_loop_bug(self):
mat = IntMat3x3([1, 0, 0, 1, 1, 0, 0, 0, 7])
# import pdb; pdb.set_trace()
ori_mat = copy.copy(mat)
snf_D, snf_S, snf_T = mat.get_snf()
SAT = numpy.matmul(snf_S, numpy.matmul(ori_mat.mat, snf_T))
wanted_mat = numpy.array([1, 0, 0, 0, 1, 0, 0, 0, 7]).reshape((3, 3))
numpy.testing.assert_almost_equal(SAT, wanted_mat)
numpy.testing.assert_almost_equal(snf_D, wanted_mat)
def test_positive_diag(self):
mat = IntMat3x3([2, 0, 0, 0, 6, 0, 0, 0, -12])
ori_mat = copy.copy(mat)
mat._positive_diag()
wanted_mat = numpy.array([2, 0, 0, 0, 6, 0, 0, 0, 12]).reshape((3, 3))
wanted_op = numpy.array([1, 0, 0, 0, 1, 0, 0, 0, -1]).reshape((3, 3))
numpy.testing.assert_almost_equal(mat.mat, wanted_mat)
numpy.testing.assert_almost_equal(mat.opL, wanted_op)
# make sure operation is right, which can restore origin matrix
wanted = mat.mat
got = numpy.matmul(mat.opL, numpy.matmul(ori_mat.mat, mat.opR))
numpy.testing.assert_almost_equal(got, wanted)
def test_second_exact_division(self):
mat = IntMat3x3([1, 0, 0, 0, 1, 0, 0, 1, 7])
ori_mat = copy.copy(mat)
mat._second_exact_division()
wanted_mat = numpy.array([1, 0, 0, 0, 1, 0, 0, 0, 7]).reshape((3, 3))
wanted_op = numpy.array([1, 0, 0, 0, 1, 0, 0, -1, 1]).reshape((3, 3))
numpy.testing.assert_almost_equal(mat.mat, wanted_mat)
numpy.testing.assert_almost_equal(mat.opL, wanted_op)
# make sure operation is right, which can restore origin matrix
wanted = mat.mat
got = numpy.matmul(mat.opL, numpy.matmul(ori_mat.mat, mat.opR))
numpy.testing.assert_almost_equal(got, wanted)
def test_set_zero(self):
mat = IntMat3x3([3, 4, 5, 0, 1, 2, 6, 7, 8])
ori_mat = copy.copy(mat)
r, s, t = extended_gcd(mat.mat[0, 0], mat.mat[2, 0])
mat._set_zero(0, 2, mat.mat[0, 0], mat.mat[2, 0], r, s, t)
wanted_mat = numpy.array([3, 4, 5, 0, 1, 2, 0, -1, -2]).reshape((3, 3))
wanted_op = numpy.array([1, 0, 0, 0, 1, 0, -2, 0, 1]).reshape((3, 3))
numpy.testing.assert_almost_equal(mat.mat, wanted_mat)
numpy.testing.assert_almost_equal(mat.opL, wanted_op)
# make sure operation is right, which can restore origin matrix
wanted = mat.mat
got = numpy.matmul(mat.opL, numpy.matmul(ori_mat.mat, mat.opR))
numpy.testing.assert_almost_equal(got, wanted)
def test_det_1_bug(self):
"""
需要保证左乘和右乘矩阵的行列式为1
"""
mat = IntMat3x3([7, -5, -3, 3, 1, 6, -5, -5, 5])
ori_mat = copy.copy(mat)
# import pdb; pdb.set_trace()
snf_D, snf_S, snf_T = mat.get_snf()
SAT = numpy.matmul(snf_S, numpy.matmul(ori_mat.mat, snf_T))
wanted_mat = numpy.array([1, 0, 0, 0, 1, 0, 0, 0, 500]).reshape((3, 3))
numpy.testing.assert_almost_equal(SAT, wanted_mat)
numpy.testing.assert_almost_equal(snf_D, wanted_mat)
numpy.testing.assert_almost_equal(numpy.linalg.det(snf_S), 1)
numpy.testing.assert_almost_equal(numpy.linalg.det(snf_T), 1)
def test_snf_random(self):
for i in range(100):
mat = self._get_random_mat()
mat = IntMat3x3(mat)
ori_mat = copy.copy(mat)
snf_D, snf_S, snf_T = mat.get_snf()
SAT = numpy.matmul(snf_S, numpy.matmul(ori_mat.mat, snf_T))
# print("mat", ori_mat.mat)
# print("snf_D", snf_D)
# print("snf_S", snf_S)
# print("snf_T", snf_T)
# print("det S", numpy.linalg.det(snf_S))
# print("det T", numpy.linalg.det(snf_T))
numpy.testing.assert_almost_equal(SAT, snf_D)
numpy.testing.assert_almost_equal(numpy.linalg.det(snf_S), 1)
numpy.testing.assert_almost_equal(numpy.linalg.det(snf_T), 1)
def setUp(self):
self.mat = IntMat3x3([0, 1, 2, 3, 4, 5, 6, 7, 8])
self.realmat = IntMat3x3([2, 4, 4, -6, 6, 12, 10, -4, -16])
def test_snf_diag_incremental(self):
for i in range(10):
mat = numpy.random.randint(100, size=9).reshape((3, 3))
mat = IntMat3x3(mat)
list_diag = numpy.diagonal(mat.mat).tolist()
self.assertTrue(sorted(list_diag), list_diag)
def test_snf_diag_positive(self):
for i in range(10):
mat = numpy.random.randint(100, size=9).reshape((3, 3))
mat = IntMat3x3(mat)
self.assertTrue(numpy.all(mat.mat >= numpy.zeros_like(mat.mat)))
def test_snf_diag(self):
for i in range(100):
mat = numpy.random.randint(100, size=9).reshape((3, 3))
mat = IntMat3x3(mat)
snf_D, _, _ = mat.get_snf()
self.assertTrue(self.is_diag(snf_D))
