def test_composite_quad_degree(v):
"""
Проверяем сходимость СКФ при наличии неравных весов
Q: скорость сходимости оказывается дробной, почему?
"""
from .variants import params
a, b, alpha, beta, f = params(v)
x0, x1 = a, b
# a, b = -10, 10
L = 2
n_intervals = [L**q for q in range(2, 11)]
n_nodes = 3
exact = sp_quad(lambda x: f(x) / (x - a)**alpha / (b - x)**beta, x0, x1)[0]
Y = [
composite_quad(f,
x0,
x1,
n_intervals=n,
n_nodes=n_nodes,
a=a,
b=b,
alpha=alpha,
beta=beta) for n in n_intervals
]
accuracy = get_accuracy(Y, exact * np.ones_like(Y))
x = np.log10(n_intervals)
aitken_degree = aitken(*Y[5:8], L)
a1, a0 = np.polyfit(x, accuracy, 1)
assert a1 > 1, 'composite quad did not converge!'
fig, (ax1, ax2) = plt.subplots(1, 2)
# график весовой функции
xs = np.linspace(x0, x1, n_intervals[-1] + 1)
ys = 1 / ((xs - a)**alpha * (b - xs)**beta)
ax1.plot(xs, ys, label='weights')
ax = list(ax1.axis())
ax[2] = 0.
ax1.axis(ax)
ax1.set_xlabel('x')
ax1.set_ylabel('p(x)')
ax1.legend()
# график точности
ax2.plot(x, accuracy, 'kh')
ax2.plot(x, a1 * x + a0, 'b:', label=f'{a1:.2f}*x+{a0:.2f}')
ax2.set_xlabel('log10(n_intervals)')
ax2.set_ylabel('accuracy')
ax2.legend()
fig.suptitle(f'variant #{v} (alpha={alpha:4.2f}, beta={beta:4.2f})\n'
f'aitken estimation: {aitken_degree:.2f}')
fig.tight_layout()
plt.show()
def test_composite_quad_degree(v):
"""
Q: convergence maybe somewhat between 3 and 4, why?
"""
from variants import params
plt.figure()
a, b, alpha, beta, f = params(v)
x0, x1 = a, b
# a, b = -10, 10
exact = sp_quad(lambda x: f(x) / (x - a)**alpha / (b - x)**beta, x0, x1)[0]
# plot weights
xs = np.linspace(x0, x1, 101)[1:-1]
ys = 1 / ((xs - a)**alpha * (b - xs)**beta)
#my addition
# for x in xs:
# if (x-a)**alpha * (b-x)**beta:
# print("HERE")
# print(ys)
#
plt.subplot(1, 2, 1)
plt.plot(xs, ys, label='weights')
ax = list(plt.axis())
ax[2] = 0.
plt.axis(ax)
plt.xlabel('x')
plt.ylabel('p(x)')
plt.legend()
L = 2
n_intervals = [L**q for q in range(2, 10)]
n_nodes = 3
Y = [
composite_quad(f,
x0,
x1,
n_intervals=n,
n_nodes=n_nodes,
a=a,
b=b,
alpha=alpha,
beta=beta) for n in n_intervals
]
accuracy = get_log_error(Y, exact * np.ones_like(Y))
x = np.log10(n_intervals)
aitken_degree = aitken(*Y[5:8], L)
# plot acc
plt.subplot(1, 2, 2)
plt.plot(x, accuracy, 'kh')
plt.xlabel('log10(node count)')
plt.ylabel('accuracy')
plt.suptitle(f'variant #{v} (alpha={alpha:4.2f}, beta={beta:4.2f})\n'
f'aitken estimation: {aitken_degree:.2f}')
plt.show()
def test_composite_quad_degree(v):
"""
Q: convergence maybe somewhat between 3 and 4, why?
"""
from .variants import params
fig, (ax1, ax2) = plt.subplots(1, 2)
a, b, alpha, beta, f = params(v)
x0, x1 = a, b
# a, b = -10, 10
exact = sp_quad(lambda x: f(x) / (x - a)**alpha / (b - x)**beta, x0, x1)[0]
# plot weights
xs = np.linspace(x0, x1, 101)
ys = 1 / ((xs - a)**alpha * (b - xs)**beta)
ax1.plot(xs, ys, label='weights')
ax = list(ax1.axis())
ax[2] = 0.
ax1.axis(ax)
ax1.set_xlabel('x')
ax1.set_ylabel('p(x)')
ax1.legend()
L = 2
n_intervals = [L**q for q in range(2, 10)]
n_nodes = 4
Y = [
composite_quad(f,
x0,
x1,
n_intervals=n,
n_nodes=n_nodes,
a=a,
b=b,
alpha=alpha,
beta=beta) for n in n_intervals
]
accuracy = get_log_error(Y, exact * np.ones_like(Y))
x = np.log10(n_intervals)
k, b = np.polyfit(x, accuracy, 1)
assert k > 1, 'composite quad did not converge!'
aitken_degree = aitken(*Y[5:8], L)
# plot acc
ax2.plot(x, accuracy, 'kh')
ax2.plot(x, k * x + b, 'b:', label=f'{k:.2f}*x+{b:.2f}')
ax2.set_xlabel('log10(n_intervals)')
ax2.set_ylabel('accuracy')
ax2.legend()
fig.suptitle(f'variant #{v} (alpha={alpha:4.2f}, beta={beta:4.2f})\n'
f'aitken estimation: {aitken_degree:.2f}')
plt.show()