def test_weighted_quad_degree():
"""
Проверяем АСТ для ИКФ с весами
Посчитаем n-ый момент весовой функции двумя способами:
- через moments()
- численно через quad()
"""
x0, x1 = 1, 3
alpha = 0.14
beta = 0.88
max_degree = 7
for deg in range(1, max_degree):
p = Monome(deg)
xs = np.linspace(x0, x1, 6)[1:-1] # 4 points => accuracy degree is 3
res = quad(p, x0, x1, xs, a=x0, alpha=alpha)
ans = moments(deg, x0, x1, a=x0, alpha=alpha)[-1]
d = abs(res - ans)
print(f'{deg:2}-a: {res:8.3f} vs {ans:8.3f}, delta = {d:e}')
if deg < len(xs):
assert d < 1e-6
res = quad(p, x0, x1, xs, b=x1, beta=beta)
ans = moments(deg, x0, x1, b=x1, beta=beta)[-1]
d = abs(res - ans)
print(f'{deg:2}-b: {res:8.3f} vs {ans:8.3f}, delta = {d:e}')
if deg < len(xs):
assert d < 1e-6
def test_weighted_quad_degree():
"""
check weighted quadrature degree
we compare n-th moment of weight function calculated in two ways:
- by moments()
- numerically by quad()
"""
x0, x1 = 1, 3
alpha = 0.14
beta = 0.88
max_degree = 7
for deg in range(1, max_degree):
p = Monome(deg)
xs = np.linspace(x0, x1, 6)[1:-1] # 4 points => accuracy degree is 3
res = quad(p, x0, x1, xs, a=x0, alpha=alpha)
ans = moments(deg, x0, x1, a=x0, alpha=alpha)[-1]
d = abs(res - ans)
print(f'{deg:2}-a: {res:8.3f} vs {ans:8.3f}, delta = {d:e}')
if deg < len(xs):
assert d < 1e-6
res = quad(p, x0, x1, xs, b=x1, beta=beta)
ans = moments(deg, x0, x1, b=x1, beta=beta)[-1]
d = abs(res - ans)
print(f'{deg:2}-b: {res:8.3f} vs {ans:8.3f}, delta = {d:e}')
if deg < len(xs):
assert d < 1e-6