def test_recursivity(self):
for n in range(2, 10):
for k in range(1, n):
with self.subTest(name='({}, {})'.format(n, k)):
self.assertEqual(
mathbox.binomial(n, k),
mathbox.binomial(n - 1, k - 1) +
mathbox.binomial(n - 1, k))
def setUp(self):
super().setUp()
self.M = [4, 3, 2]
self.h_vec = {
1: np.arange(1,
binomial(self.M[0], 1) + 1),
2: np.arange(1,
binomial(self.M[1] + 1, 2) + 1),
3: np.arange(1,
binomial(self.M[2] + 2, 3) + 1)
}
self.h_tri = {
1: np.array([1, 2, 3, 4]),
2: np.array([[1, 2, 3], [0, 4, 5], [0, 0, 6]]),
3: np.array([[[1, 2], [0, 3]], [[0, 0], [0, 4]]])
}
self.h_sym = {
1: np.array([1, 2, 3, 4]),
2: np.array([[1., 1, 3 / 2], [1, 4, 5 / 2], [3 / 2, 5 / 2, 6]]),
3: np.array([[[1., 2 / 3], [2 / 3, 1]], [[2 / 3, 1], [1, 4]]])
}
def setUp(self):
self.M = 4
self.h_vec = {
2: np.arange(1,
binomial(self.M + 1, 2) + 1),
3: np.arange(1,
binomial(self.M + 2, 3) + 1)
}
self.h_tri = {
2:
np.array([[1, 2, 3, 4], [0, 5, 6, 7], [0, 0, 8, 9], [0, 0, 0,
10]]),
3:
np.array([[[1, 2, 3, 4], [0, 5, 6, 7], [0, 0, 8, 9], [0, 0, 0,
10]],
[[0, 0, 0, 0], [0, 11, 12, 13], [0, 0, 14, 15],
[0, 0, 0, 16]],
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 17, 18],
[0, 0, 0, 19]],
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0,
20]]])
}
self.h_sym = {
2:
np.array([[1, 1, 1.5, 2], [1, 5, 3, 3.5], [1.5, 3, 8, 4.5],
[2, 3.5, 4.5, 10]]),
3:
np.array([[[1., 2 / 3, 1, 4 / 3], [2 / 3, 5 / 3, 1, 7 / 6],
[1, 1, 8 / 3, 1.5], [4 / 3, 7 / 6, 1.5, 10 / 3]],
[[2 / 3, 5 / 3, 1, 7 / 6], [5 / 3, 11, 4, 13 / 3],
[1, 4, 14 / 3, 2.5], [7 / 6, 13 / 3, 2.5, 16 / 3]],
[[1, 1, 8 / 3, 1.5], [1, 4, 14 / 3, 2.5],
[8 / 3, 14 / 3, 17, 6], [1.5, 2.5, 6, 19 / 3]],
[[4 / 3, 7 / 6, 1.5, 10 / 3],
[7 / 6, 13 / 3, 2.5, 16 / 3], [1.5, 2.5, 6, 19 / 3],
[10 / 3, 16 / 3, 19 / 3, 20]]])
}
def test_symmetry(self):
for n in range(1, 10):
for k in range(1, n):
with self.subTest(name='({}, {})'.format(n, k)):
self.assertEqual(mathbox.binomial(n, k),
mathbox.binomial(n, n - k))
def test_n_choose_n(self):
for n in range(1, 10):
with self.subTest(i=n):
self.assertEqual(mathbox.binomial(n, n), 1)
def test_form_as_list(self):
M = self.Mmax
N = self.Nmax
val = binomial(M + N, N) - 1 + binomial(M, 2)
nb_coeff = series_nb_coeff(N, M, form=self.form_list)
self.assertEqual(nb_coeff, val)
def test_nb_coeff_triangular_form(self):
for N, M in self.iter_obj:
with self.subTest(i=(N, M)):
nb_coeff = series_nb_coeff(N, M, form='tri')
self.assertEqual(nb_coeff, binomial(M + N, N) - 1)
def test_nb_coeff_symmetric_form(self):
for N, M in self.iter_obj:
with self.subTest(i=(N, M)):
nb_coeff = kernel_nb_coeff(N, M, form='sym')
self.assertEqual(nb_coeff, binomial(M + N - 1, N))
