def test_book_ex3_1():
moments = np.array([1, 5, 26, 140, 778, 4450, 26140, 157400])
w1 = 1/(2*np.sqrt(6) + 2**(3./2)*np.sqrt(3) + 12)
w2 = 1/(12 - 2*np.sqrt(6) - 2**(3./2)*np.sqrt(3))
abscissas = np.array([2.6656, 4.2580, 5.7420, 7.3344])
weights = np.array([w1, w2, w2, w1])
[xi, w] = wheeler_inversion(moments)
assert_almost_equal(np.max(np.abs(xi-abscissas)), 0, decimal=4)
assert_almost_equal(np.max(np.abs(w-weights)), 0)
def test_book_ex3_1():
moments = np.array([1, 5, 26, 140, 778, 4450, 26140, 157400])
w1 = 1 / (2 * np.sqrt(6) + 2**(3. / 2) * np.sqrt(3) + 12)
w2 = 1 / (12 - 2 * np.sqrt(6) - 2**(3. / 2) * np.sqrt(3))
abscissas = np.array([2.6656, 4.2580, 5.7420, 7.3344])
weights = np.array([w1, w2, w2, w1])
[xi, w] = wheeler_inversion(moments)
assert_almost_equal(np.max(np.abs(xi - abscissas)), 0, decimal=4)
assert_almost_equal(np.max(np.abs(w - weights)), 0)
def test_book_ex3_2():
moments = np.array([1, 0, 1, 0, 3, 0, 15, 0])
xi1 = np.sqrt(np.sqrt(6) + 3) # Taken from Maxima
xi2 = np.sqrt(3 - np.sqrt(6))
w1 = 1/(2*np.sqrt(6) + 2**(3./2)*np.sqrt(3) + 12)
w2 = 1/(12 - 2*np.sqrt(6) - 2**(3./2)*np.sqrt(3))
abscissas = np.array([-xi1, -xi2, xi2, xi1])
weights = np.array([w1, w2, w2, w1])
[xi, w] = wheeler_inversion(moments)
assert_almost_equal(np.max(np.abs(xi-abscissas)), 0)
assert_almost_equal(np.max(np.abs(w-weights)), 0)
def test_book_ex3_2():
moments = np.array([1, 0, 1, 0, 3, 0, 15, 0])
xi1 = np.sqrt(np.sqrt(6) + 3) # Taken from Maxima
xi2 = np.sqrt(3 - np.sqrt(6))
w1 = 1 / (2 * np.sqrt(6) + 2**(3. / 2) * np.sqrt(3) + 12)
w2 = 1 / (12 - 2 * np.sqrt(6) - 2**(3. / 2) * np.sqrt(3))
abscissas = np.array([-xi1, -xi2, xi2, xi1])
weights = np.array([w1, w2, w2, w1])
[xi, w] = wheeler_inversion(moments)
assert_almost_equal(np.max(np.abs(xi - abscissas)), 0)
assert_almost_equal(np.max(np.abs(w - weights)), 0)
