def test_smith_normal_form():
one = np.matrix([[1, 1],[0, 1]])
assert np.all(smith_normal_form(one)[0] == np.eye(2))
two = np.matrix([[1, 0],[1, 1]])
assert np.all(smith_normal_form(two)[0] == np.eye(2))
three = np.matrix([[1, -17], [0, 1]])
assert np.all(smith_normal_form(three)[0] == np.eye(2))
four = np.matrix([[1, 3], [4, -9]])
four = smith_normal_form(four)[0]
assert four[0, 0] == 1
assert four[1, 0] == 0
assert four[0, 1] == 0
five = np.matrix([[100, 0], [41, 89]])
five = smith_normal_form(five)[0]
assert all_zero_facade(five)
assert divides(five[0, 0], five[1, 1])
six = np.matrix([[-5, -2], [-2, -4]])
assert np.all(smith_normal_form(six)[0] == np.matrix([[1, 0], [0, 16]]))
seven = np.matrix([[-2, 1, 0, 0, 0],
[1, -3, 1, 1, 0],
[0, 1, -2, 0, 0],
[0, 1, 0, -2, 1],
[0, 0, 0, 1, -2]])
smith_seven = np.matrix(np.eye(5))
smith_seven[4, 4] = 16
assert np.all(smith_seven == smith_normal_form(seven)[0])
eight = np.matrix([[88, 56, 97],
[31, 32, 12],
[78, 58, 43]])
smith_eight = np.matrix(np.eye(3))
smith_eight[2, 2] = 30098
assert np.all(smith_eight == smith_normal_form(eight)[0])
def test_random_smith_normal_form(m):
'''Checks that the smith normal form routine behaves appropriately'''
s, _ = smith_normal_form(m)
def close_enough(a, b, max_rel_diff):
# Don't have a good workaround for this.
a = math.fabs(a)
b = math.fabs(b)
if math.log(a + 1) > 15:
return True
diff = math.fabs(a - b)
largest = max(a, b)
return diff <= largest * max_rel_diff
assert close_enough(det(m), det(s), 0.1)
assert is_diagonal(s)
assert diagonal_chaining(s)
for i in xrange(s.shape[0] - 1):
if not divides(s[i, i], s[i + 1, i + 1]):
print s
print m
assert divides(s[i, i], s[i + 1, i + 1])
