def test_gauss_vs_cq():
"""
Проверяем, как работают quad_gauss() и composite_quad() при одинакомом количестве обращений к функции
"""
x0, x1 = 0, np.pi/2
p = Harmonic(0, 1)
y0 = p[x0, x1]
n_nodes = 2
Y_gauss = []
Y_cquad = []
n_intervals = np.arange(1, 256, 5)
for n in n_intervals:
n_evals = n * n_nodes
Y_gauss.append(quad_gauss(p, x0, x1, n_evals))
Y_cquad.append(composite_quad(p, x0, x1, n, n_nodes))
accuracy_gauss = get_accuracy(Y_gauss, y0 * np.ones_like(Y_gauss))
accuracy_gauss[accuracy_gauss > 17] = 17
accuracy_cquad = get_accuracy(Y_cquad, y0 * np.ones_like(Y_cquad))
accuracy_cquad[accuracy_cquad > 17] = 17
plt.plot(np.log10(n_intervals), accuracy_gauss, '.:', label=f'gauss')
plt.plot(np.log10(n_intervals), accuracy_cquad, '.:', label=f'2-node CQ')
plt.legend()
plt.ylabel('accuracy')
plt.xlabel('log10(n_evals)')
plt.suptitle(f'test gauss vs CQ')
plt.show()
def test_harmonic(fname, func: callable):
"""
Сравниваем аппроксимацию алгебраическими многочленами и гармониками
"""
n = 50
dim = 21
m = 99
xs0 = np.linspace(-1, 1, n)
xs1 = np.linspace(-1, 1, m)
ys0 = func(xs0)
ys1 = func(xs1)
colors = 'br'
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(xs1, ys1, 'k-', label='exact')
ax1.plot(xs0, ys0, 'k.')
for color, approx_type in zip(colors, [Algebraic, Harmonic]):
approx = approx_type(xs0, ys0, dim)
ys1_num = approx(xs1)
ax1.plot(xs1, ys1_num, f'{color}-', label=approx.name)
ax2.plot(xs1, get_accuracy(ys1, ys1_num), f'{color}-', label=approx.name)
ax1.legend(), ax1.set_title(f'y(x)')
ax2.legend(), ax2.set_title('accuracy')
fig.suptitle(f'{fname}')
plt.show()
def on_forward(state):
loss = state['loss'].item()
accuracy = get_accuracy(state['output'].cpu(),
state['sample'][1].cpu())
state['iterator'].write('batch %d loss %.3f accuracy %.3f ' %
(state['t'], loss, accuracy),
end='\n')
def summarize_train(writer, global_step, last_time, model, opt, inputs,
targets, optimizer, loss, pred, ans):
if opt.summary_grad:
for name, param in model.named_parameters():
if not param.requires_grad:
continue
norm = torch.norm(param.grad.data.view(-1))
writer.add_scalar('gradient_norm/' + name, norm, global_step)
writer.add_scalar('input_stats/batch_size', targets.size(0), global_step)
if inputs is not None:
writer.add_scalar('input_stats/input_length', inputs.size(1),
global_step)
i_nonpad = (inputs != opt.src_pad_idx).view(-1).type(torch.float32)
writer.add_scalar('input_stats/inputs_nonpadding_frac',
i_nonpad.mean(), global_step)
writer.add_scalar('input_stats/target_length', targets.size(1),
global_step)
t_nonpad = (targets != opt.trg_pad_idx).view(-1).type(torch.float32)
writer.add_scalar('input_stats/target_nonpadding_frac', t_nonpad.mean(),
global_step)
writer.add_scalar('optimizer/learning_rate', optimizer.learning_rate(),
global_step)
writer.add_scalar('loss', loss.item(), global_step)
acc = utils.get_accuracy(pred, ans, opt.trg_pad_idx)
writer.add_scalar('training/accuracy', acc, global_step)
steps_per_sec = 100.0 / (time.time() - last_time)
writer.add_scalar('global_step/sec', steps_per_sec, global_step)
def test_quad_vs_cq():
"""
Проверяем, как работают ИКФ и СКФ при одинакомом количестве обращений к функции
"""
x0, x1 = 0, np.pi/2
p = Harmonic(0, 1)
y0 = p[x0, x1]
n_nodes = 2
ys_nt_ct = []
ys_gauss = []
ys_cquad = []
n_intervals = 2 ** np.arange(8)
for n in n_intervals:
n_evals = n * n_nodes
ys_nt_ct.append(quad(p, x0, x1, np.linspace(0, 1, n_evals) * (x1-x0) + x0))
ys_gauss.append(quad_gauss(p, x0, x1, n_evals))
ys_cquad.append(composite_quad(p, x0, x1, n, n_nodes))
for ys, label in zip((ys_nt_ct, ys_gauss, ys_cquad),
(f'newton-cotes', f'gauss', f'{n_nodes}-node CQ')):
acc = get_accuracy(ys, y0 * np.ones_like(ys))
acc[acc > 17] = 17
plt.plot(np.log10(n_intervals), acc, '.:', label=label)
plt.legend()
plt.ylabel('accuracy')
plt.xlabel('log10(n_evals)')
plt.suptitle(f'test quad vs composite quad')
plt.show()
def test_adaptive(ode, y0):
"""
Проверяем алгоритмы выбора шага
"""
t0, t1 = 0, 4 * np.pi
atol = 1e-6
rtol = 1e-3
tss = []
yss = []
methods = (
(ExplicitEulerMethod(), AdaptType.RUNGE),
(RungeKuttaMethod(coeffs.rk4_coeffs), AdaptType.RUNGE),
(EmbeddedRungeKuttaMethod(coeffs.dopri_coeffs), AdaptType.EMBEDDED),
)
for method, adapt_type in methods:
ode.clear_call_counter()
ts, ys = adaptive_step_integration(method=method,
ode=ode,
y_start=y0,
t_span=(t0, t1),
adapt_type=adapt_type,
atol=atol,
rtol=rtol)
print(f'{method.name} took {ode.get_call_counter()} function calls')
tss.append(np.array(ts))
yss.append(ys)
ts = np.array(sorted([t for ts in tss for t in ts]))
exact = ode[ts].T
y0 = np.array([y[0] for y in exact])
# plots
fig1, ax1 = plt.subplots(num='y(t)')
fig1.suptitle('test_adaptive: y(t)')
ax1.set_xlabel('t'), ax1.set_ylabel('y')
ax1.plot(ts, y0, 'ko-', label='exact')
fig2, ax2 = plt.subplots(num='dt(t)')
fig2.suptitle('test_adaptive: step sizes')
ax2.set_xlabel('t'), ax2.set_ylabel('dt')
fig3, ax3 = plt.subplots(num='dy(t)')
fig3.suptitle('test_adaptive: accuracies')
ax3.set_xlabel('t'), ax3.set_ylabel('accuracy')
for (m, _), ts, ys in zip(methods, tss, yss):
ax1.plot(ts, [y[0] for y in ys], '.', label=m.name)
ax2.plot(ts[:-1], ts[1:] - ts[:-1], '.-', label=m.name)
ax3.plot(ts, get_accuracy(ode[ts].T, ys), '.-', label=m.name)
ax1.legend()
ax2.legend()
ax3.legend()
plt.show()
def test_quad_gauss_degree():
"""
Проверяем АСТ для ИКФ Гаусса
"""
x0, x1 = 0, 1
max_degree = 8
for deg in range(max_degree):
p = Monome(deg)
y0 = p[x0, x1]
node_counts = range(1, 6)
Y = [quad_gauss(p, x0, x1, node_count) for node_count in node_counts]
accuracy = get_accuracy(Y, y0 * np.ones_like(Y))
# Проверяем точность
for node_count, acc in zip(node_counts, accuracy):
if 2 * node_count >= deg + 1:
assert acc > 6
plt.plot(node_counts, accuracy, '.:', label=f'x^{deg}')
plt.legend()
plt.ylabel('accuracy')
plt.xlabel('node count')
plt.suptitle(f'test quad gauss')
plt.show()
def test_quad_degree():
"""
Проверяем АСТ для ИКФ
Q: почему в некоторых случаях x^n интегрируется почти без ошибок при n узлах ИКФ?
"""
x0, x1 = 0, 1
max_degree = 7
max_nodes = 7
for deg in range(max_degree):
p = Monome(deg)
y0 = p[x0, x1]
node_counts = range(1, max_nodes+1)
Y = [quad(p, x0, x1, np.linspace(x0, x1, node_count)) for node_count in node_counts]
# Y = [quad(p, x0, x1, x0 + (x1-x0) * np.random.random(node_count)) for node_count in max_node_count]
accuracy = get_accuracy(Y, y0 * np.ones_like(Y))
# Проверяем точность
for node_count, acc in zip(node_counts, accuracy):
if node_count >= deg + 1:
assert acc > 6
plt.plot(node_counts, accuracy, '.:', label=f'x^{deg}')
plt.legend()
plt.ylabel('accuracy')
plt.xlabel('node_count')
plt.suptitle(f'test quad')
plt.show()
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(n_nodes):
"""
Проверяем 2-, 3-, 5-узловые СКФ
Q: объясните скорость сходимости для каждого случая
"""
fig, ax = plt.subplots(1, 2)
x0, x1 = 0, 1
L = 2
n_intervals = [L ** q for q in range(0, 8)]
for i, degree in enumerate((5, 6)):
p = Monome(degree)
Y = [composite_quad(p, x0, x1, n_intervals=n, n_nodes=n_nodes) for n in n_intervals]
accuracy = get_accuracy(Y, p[x0, x1] * np.ones_like(Y))
x = np.log10(n_intervals)
# оценка сходимости
ind = np.isfinite(x) & np.isfinite(accuracy)
k, b = np.polyfit(x[ind], accuracy[ind], 1)
aitken_degree = aitken(*Y[0:6:2], L ** 2)
ax[i].plot(x, k*x+b, 'b:', label=f'{k:.2f}*x+{b:.2f}')
ax[i].plot(x, aitken_degree*x+b, 'm:', label=f'aitken ({aitken_degree:.2f})')
ax[i].plot(x, accuracy, 'kh', label=f'accuracy for x^{degree}')
ax[i].set_title(f'{n_nodes}-node CQ for x^{degree}')
ax[i].set_xlabel('log10(n_intervals)')
ax[i].set_ylabel('accuracy')
ax[i].legend()
if n_nodes < degree:
assert np.abs(aitken_degree - k) < 0.5, \
f'Aitken estimation {aitken_degree:.2f} is too far from actual {k:.2f}'
plt.show()
def test_convergence(self):
"""
Проверка сходимости
"""
func = np.abs
a, b = -5, 5
interp_params = [
# color, interp_name, nodes_type, label
['b', LaGrange, NodeType.EQ],
['r', LaGrange, NodeType.CHEB],
['c', Spline3, NodeType.EQ],
]
node_params = [
# n_nodes, style
[5, '-'],
[17, '--'],
[65, ':'],
# [257, '-.'],
]
# точки, в которых будем сравнивать с точным значением
m = 1025
xs_dense = np.linspace(a, b, m)
ys_dense = func(xs_dense)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 6))
ax1.plot(xs_dense, ys_dense, 'k-', label='exact')
for (color, interp_name, nodes_type) in interp_params:
for (n_nodes, style) in node_params:
xs = self._get_nodes(nodes_type, a, b, n_nodes)
ys = func(xs)
interp = interp_name(xs, ys)
ys_dense_num = interp(xs_dense)
label = f'{interp.name}-{str(nodes_type.name)}-{n_nodes}'
ax1.plot(xs_dense,
ys_dense_num,
f'{color}{style}',
label=label)
ax1.plot(xs, ys, f'{color}.')
ax2.plot(xs_dense,
get_accuracy(ys_dense, ys_dense_num),
f'{color}{style}',
label=label)
ax1.set_title(f'y(x)')
ax1.axis([a, b, -1, 6])
ax1.legend()
ax2.set_title('accuracy')
ax2.legend()
plt.show()
def evaluate(loader, model):
print("Evaluate")
# Set model to eval
model.eval()
accuracy = AverageMeter()
positive_accuracy = AverageMeter()
negative_accuracy = AverageMeter()
y_true = None
y_scores = None
with torch.no_grad():
for batch_idx, (x, y) in enumerate(loader):
x = x.to(device=device).to(torch.float32)
y = y.to(device=device).to(torch.float32)
scores = model(x)
scores = torch.squeeze(scores, 2)
y = torch.unsqueeze(y, 1)
loss = criterion(scores, y)
scores = torch.squeeze(scores, 1)
y = torch.squeeze(y, 1)
if y_true is None:
y_true = y
y_scores = scores
else:
y_true = torch.cat((y_true, y))
y_scores = torch.cat((y_scores, scores))
acc = get_accuracy(y, scores)
# neg_acc, pos_acc = get_accuracy_per_class(y.cpu(), scores.cpu())
accuracy.update(acc)
# positive_accuracy.update(pos_acc)
# negative_accuracy.update(neg_acc)
auc = roc_auc_score(y_true.cpu(), y_scores.cpu())
wandb.log({
"valid_acc": accuracy.avg,
# "positive_acc": positive_accuracy.avg,
# "negative_acc": negative_accuracy.avg,
"valid_loss": loss.item(),
"AUC": auc
})
accuracy.reset()
# Set model back to train
model.train()
def test_optimization(eps_y, check_accuracy, student, n_dim, projection):
N = student
A = np.array([[4, 1, 1], [1, 6 + .2 * N, -1], [1, -1, 8 + .2 * N]],
dtype='float')[:n_dim, :n_dim]
b = np.array([1, -2, 3], dtype='float').T[:n_dim]
x0 = np.zeros_like(b)
x1 = np.linalg.solve(A, -b)
y1 = (1 / 2 * x1.T @ A @ x1 + b.T @ x1).item()
eps_x = np.sqrt(eps_y)
methods = ['mngs', 'mps', 'newton']
styles = ['go:', 'bo:', 'mo:']
fig = plt.figure()
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122, projection=projection)
for i, method in enumerate(methods):
optimization.func.calls = 0
xs, ys = getattr(optimization, method)(A=A,
b=b,
x0=x0,
eps=eps_y,
max_iter=30)
assert np.equal(x0, xs[0]).all(), 'xs should start with initial point'
if check_accuracy:
assert np.linalg.norm(
x1 - xs[-1]
) < eps_x, 'last xs should be close enough to the optimum'
assert np.linalg.norm(
y1 - ys[-1]
) < eps_y, 'last ys should be close enough to the optimum'
assert optimization.func.calls == len(ys), f'function was called {optimization.func.calls} times, ' \
f'but there is {len(ys)} point in the output'
ax1.plot(get_accuracy(ys, y1 * np.ones_like(ys)),
styles[i],
label=method)
ax2.plot(*list(np.array(xs).T), styles[i], label=method)
ax2.plot(*[[x] for x in x1], 'kp', label='exact')
ax = ax1.axis()
ax1.plot(ax[:2], -np.log10([eps_y, eps_y]), 'k-')
ax1.set_xlabel('N iter')
ax1.set_ylabel('accuracy')
ax1.legend()
ax2.legend()
fig.suptitle(f'Results for {n_dim}D')
plt.show()
def _test_case(self, fname, func: callable, a, b, n_nodes, interp_params):
"""
Общий метод проверки
"""
k_dense = 10
m = k_dense * n_nodes
# точки, в которых будем сравнивать с точным значением
xs_dense = np.array(
sorted([
*np.linspace(a, b, m),
*self._get_nodes(NodeType.EQ, a, b, n_nodes),
*self._get_nodes(NodeType.CHEB, a, b, n_nodes)
]))
ys_dense = func(xs_dense)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 6))
ax1.plot(xs_dense, ys_dense, 'k-', label='exact')
for (color, interp_name, nodes_type) in interp_params:
xs = self._get_nodes(nodes_type, a, b, n_nodes)
ys = func(xs)
interp = interp_name(xs, ys)
# проверяем, что попали в узлы интерполяции
ys_num = interp(xs)
assert (np.abs(ys - ys_num) < 1e-6).all()
# смотрим, как у нас дела в остальных точках интервала
ys_dense_num = interp(xs_dense)
label = f'{interp.name}-{str(nodes_type.name)}'
ax1.plot(xs_dense, ys_dense_num, f'{color}:', label=label)
ax1.plot(xs, ys, f'{color}.')
ax2.plot(xs_dense,
get_accuracy(ys_dense, ys_dense_num),
f'{color}-',
label=label)
ax1.set_title(f'{fname}')
ax1.legend()
ax2.set_title('accuracy')
ax2.legend()
plt.show()
def test_polynomial(fname, func: callable):
"""
Сравниваем аппроксимацию алгебраическими многочленами и многочленами Лежандра
"""
n = 15
dim = 5
m = 101
xs0 = np.linspace(-1, 1, n)
xs1 = np.linspace(-1, 1, m)
ys0 = func(xs0)
ys1 = func(xs1)
colors = 'bg'
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.set_title(f'{fname}')
ax2.set_title('accuracy')
ax1.plot(xs1, ys1, 'k-', label='exact')
ax1.plot(xs0, ys0, 'k.')
coeffs = []
for color, approx_type in zip(colors, [Algebraic, Legendre]):
approx = approx_type(xs0, ys0, dim)
ys1_num = approx(xs1)
coeffs.append(approx.coeffs)
ax1.plot(xs1, ys1_num, f'{color}-', label=approx.name)
ax2.plot(xs1,
get_accuracy(ys1, ys1_num),
f'{color}-',
label=approx.name)
assert (len(approx.coeffs) == dim
), f'{approx_type} polynome length should be {dim}'
assert (all(abs(ys1 - ys1_num) < 1)
), f'{approx_type} polynome approximation is too bad'
alg_poly = coeffs[0]
leg_poly = P.legendre.leg2poly(coeffs[1])
assert (all(
abs(alg_poly -
leg_poly) < 1e-3)), 'algebraic and legendre are not consistent'
ax1.legend()
ax2.legend()
plt.show()
def test_multi_step():
"""
Проверяем методы Адамса
Q: сравните правые графики для обоих случаев и объясните разницу
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = np.pi
dt = 0.1
f = Harmonic(y0, 1, 1)
ts = np.arange(t0, t1 + dt, dt)
exact = f[ts].T
for one_step_method in [
RungeKuttaMethod(collection.rk4_coeffs),
ExplicitEulerMethod(),
]:
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
for p, c in adams_coeffs.items():
f.clear_call_counter()
t_adams, y_adams = adams(f,
y0,
ts,
c,
one_step_method=one_step_method)
n_calls = f.get_call_counter()
print(
f'{p}-order multi-step with one-step {one_step_method.name}: {n_calls} function calls'
)
err = get_accuracy(exact, y_adams)
label = f"Adams's order {p}"
ax1.plot(t_adams, [y[0] for y in y_adams], '.--', label=label)
ax2.plot(t_adams, err, '.--', label=label)
ax1.legend(), ax1.set_title('y(t)')
ax2.legend(), ax2.set_title('accuracy')
fig.suptitle(
f'test_multi_step\none step method: {one_step_method.name}')
fig.tight_layout()
plt.show()
def test_one_step():
"""
Проверяем методы Эйлера и Рунге-Кутты
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = np.pi
ode = Harmonic(y0, 1, 1)
for dt in [0.1, 0.01]:
ts = np.arange(t0, t1 + dt, dt)
exact = ode[ts].T
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
colors = 'rgbcmyk'
for i, method in enumerate([
ExplicitEulerMethod(),
ImplicitEulerMethod(),
RungeKuttaMethod(collection.rk4_coeffs),
RungeKuttaMethod(collection.dopri_coeffs),
]):
ode.clear_call_counter()
_, y = fix_step_integration(method, ode, y0, ts)
n_calls = ode.get_call_counter()
print(
f'One-step {method.name}: {len(y)-1} steps, {n_calls} function calls'
)
ax1.plot(ts, [_y[0] for _y in y],
f'{colors[i]}.--',
label=method.name)
ax2.plot(ts,
get_accuracy(exact, y),
f'{colors[i]}.--',
label=method.name)
ax1.legend(), ax1.set_title('y(t)')
ax2.legend(), ax2.set_title('accuracy')
fig.suptitle(f'test_one_step, dt={dt}')
fig.tight_layout()
plt.show()
def outer_loop(self, batch, is_train):
train_inputs, train_targets, test_inputs, test_targets = self.unpack_batch(batch)
loss_log = 0
acc_log = 0
grad_list = []
loss_list = []
for (train_input, train_target, test_input, test_target) in zip(train_inputs, train_targets, test_inputs, test_targets):
with higher.innerloop_ctx(self.network, self.inner_optimizer, track_higher_grads=False) as (fmodel, diffopt):
for step in range(self.args.n_inner):
self.inner_loop(fmodel, diffopt, train_input, train_target)
train_logit = fmodel(train_input)
in_loss = F.cross_entropy(train_logit, train_target)
test_logit = fmodel(test_input)
outer_loss = F.cross_entropy(test_logit, test_target)
loss_log += outer_loss.item()/self.batch_size
with torch.no_grad():
acc_log += get_accuracy(test_logit, test_target).item()/self.batch_size
if is_train:
params = list(fmodel.parameters(time=-1))
in_grad = torch.nn.utils.parameters_to_vector(torch.autograd.grad(in_loss, params, create_graph=True))
outer_grad = torch.nn.utils.parameters_to_vector(torch.autograd.grad(outer_loss, params))
implicit_grad = self.cg(in_grad, outer_grad, params)
grad_list.append(implicit_grad)
loss_list.append(outer_loss.item())
if is_train:
self.outer_optimizer.zero_grad()
weight = torch.ones(len(grad_list))
weight = weight / torch.sum(weight)
grad = mix_grad(grad_list, weight)
grad_log = apply_grad(self.network, grad)
self.outer_optimizer.step()
return loss_log, acc_log, grad_log
else:
return loss_log, acc_log
def test_multi_step():
"""
test Adams method
Q: compare the right plot for both cases and explain the difference
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = 1.
dt = 0.1
f = Harmonic(y0, 1, 1)
ts = np.arange(t0, t1 + dt, dt)
exact = f[ts].T
for one_step_method in [
RungeKuttaMethod(collection.rk4_coeffs),
ExplicitEulerMethod(),
]:
_, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
for p, c in adams_coeffs.items():
f.clear_call_counter()
t_adams, y_adams = adams(f,
y0,
ts,
c,
one_step_method=one_step_method)
n_calls = f.get_call_counter()
print(
f'{p}-order multi-step with one-step {one_step_method.name}: {n_calls} function calls'
)
err = get_accuracy(exact, y_adams)
label = f"Adams's order {p}"
ax1.plot(t_adams, [y[0] for y in y_adams], '.--', label=label)
ax2.plot(t_adams, err, '.--', label=label)
ax1.set_xlabel('t'), ax1.set_ylabel('y'), ax1.legend()
ax2.set_xlabel('t'), ax2.set_ylabel('accuracy'), ax2.legend()
plt.suptitle(
f'test_multi_step\none step method: {one_step_method.name}')
plt.show()
def test_one_step():
"""
test Euler and RK methods
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = np.pi / 2
dt = 0.1
f = Harmonic(y0, 1, 1)
ts = np.arange(t0, t1 + dt, dt)
exact = f[ts].T
_, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
colors = 'rgbcmyk'
for i, method in enumerate([
ExplicitEulerMethod(),
ImplicitEulerMethod(),
RungeKuttaMethod(collection.rk4_coeffs),
RungeKuttaMethod(collection.dopri_coeffs),
]):
f.clear_call_counter()
_, y = fix_step_integration(method, f, y0, ts)
n_calls = f.get_call_counter()
print(
f'One-step {method.name}: {len(y)-1} steps, {n_calls} function calls'
)
ax1.plot(ts, [_y[0] for _y in y], f'{colors[i]}.--', label=method.name)
ax2.plot(ts,
get_accuracy(exact, y),
f'{colors[i]}.--',
label=method.name)
ax1.set_xlabel('t'), ax1.set_ylabel('y'), ax1.legend()
ax2.set_xlabel('t'), ax2.set_ylabel('accuracy'), ax2.legend()
plt.suptitle('test_one_step')
plt.show()
def test_quad_degree():
"""
Проверяем АСТ для ИКФ
Q: почему в некоторых случаях x^n интегрируется почти без ошибок при n узлах ИКФ?
A: Поскольку многочлен Лагранжа Ln является алгебраическим многочленом степени n − 1, то по построению, он имеет
алгебраический порядок точности не ниже n − 1. Однако если n нечетно, т.е. когда середина отрезка [a, b] входит
в состав сетки, то формула оказывается точна и для многочленов степени n.
"""
x0, x1 = 0, 1
max_degree = 7
max_nodes = 7
for deg in range(max_degree):
p = Monome(deg)
y0 = p[x0, x1]
node_counts = range(1, max_nodes + 1)
Y = [
quad(p, x0, x1, np.linspace(x0, x1, node_count))
for node_count in node_counts
]
# Y = [quad(p, x0, x1, x0 + (x1-x0) * np.random.random(node_count)) for node_count in node_counts]
accuracy = get_accuracy(Y, y0 * np.ones_like(Y))
# Проверяем точность
for node_count, acc in zip(node_counts, accuracy):
if node_count >= deg + 1:
assert acc > 6
plt.plot(node_counts, accuracy, '.:', label=f'x^{deg}')
plt.legend()
plt.ylabel('accuracy')
plt.xlabel('node_count')
plt.suptitle(f'test quad')
plt.show()
def test_iteratives(tol, check):
"""
Сравниваем итерационные методы
Q: который метод лучше? Почему?
Q: почему во втором случае мы не всегда можем достичь заданной точности?
"""
n = 5
A = np.array([
[n + 2, 1, 1],
[1, n + 4, 1],
[1, 1, n + 6],
],
dtype='float64')
b = np.array([n + 4, n + 6, n + 8], dtype='float64') * np.pi
methods = [richardson, jacobi, seidel]
colors = 'mgb'
names = ['Richardson', 'Jacobi', 'Gauss-Seidel']
for method, color, name in zip(methods, colors, names):
xs, ys = method(A, b, tol)
plt.plot(range(len(ys)),
get_accuracy(ys, np.zeros_like(ys), eps=tol / 10),
f'{color}.-',
label=name)
if check:
assert np.linalg.norm(A @ xs[-1] -
b) <= tol, f'{name} method failed'
axes = plt.axis()
plt.plot(axes[:2], -np.log10([tol, tol]), 'k:', label='tolerance')
plt.title(f'test iterative methods for tol {tol}')
plt.ylabel('accuracy')
plt.xlabel('N iter')
plt.legend()
plt.show()
def evaluate(loader, model):
print("Evaluate")
# Set model to eval
model.eval()
accuracy = AverageMeter()
positive_accuracy = AverageMeter()
negative_accuracy = AverageMeter()
with torch.no_grad():
for batch_idx, (x, y) in enumerate(loader):
x = x.to(device=device)
y = y.to(device=device).to(torch.float32)
y = torch.unsqueeze(y, 1)
scores = model(x)
loss = criterion(scores, y)
scores = torch.squeeze(scores, 1)
y = torch.squeeze(y, 1)
acc = get_accuracy(y, scores)
neg_acc, pos_acc = get_accuracy_per_class(y.cpu(), scores.cpu())
accuracy.update(acc)
positive_accuracy.update(pos_acc)
negative_accuracy.update(neg_acc)
wandb.log({
"valid_acc": accuracy.avg,
"positive_acc": positive_accuracy.avg,
"negative_acc": negative_accuracy.avg,
"valid_loss": loss.item()
})
# Set model back to train
model.train()
def test_fast_inv_sqrt():
"""
Проверяем быстрое вычисление обратного квадратного корня при помощи трюка с плавающей запятой
https://en.wikipedia.org/wiki/Fast_inverse_square_root
"""
def fast_inv_sqrt(x, n_iter=1):
c = 0x5f3759df
s = tc.float2bin(x)
i = c - tc.bin2dec(f'0{s[:-1]}', signed=False)
y = tc.bin2float(tc.dec2bin(i, signed=False))
for _ in range(n_iter):
y *= 1.5 - 0.5 * x * y * y
return y
X = np.linspace(0, 16, 100)[1:]
Y0 = np.power(X, -0.5)
Y = [[fast_inv_sqrt(x, n_iter=i) for x in X] for i in range(3)]
colors = 'rgb'
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(X, Y0, 'k-', label='exact')
for i in range(3):
ax1.plot(X,
Y[i],
f'{colors[i]}.:',
label=f'{i}-iterations approximation')
ax1.legend()
for i in range(3):
ax2.plot(X,
get_accuracy(Y0, Y[i]),
f'{colors[i]}.:',
label=f'{i}-iterations accuracy')
ax2.legend()
plt.show()
conv_stride=1,
first_pool_size=None,
first_pool_stride=None,
block_sizes=[2, 2, 2, 2],
block_strides=[1, 2, 2, 2],
data_format='channels_first')
############################################
# Loss, Accuracy, Train, Summary and Saver #
############################################
weight_decay = 2e-4
logits = resnet(images, training=True)
cross_entropy = utils.get_cross_entropy(logits, labels)
accuracy = utils.get_accuracy(logits, labels)
tf.summary.scalar('cross_entropy', cross_entropy)
tf.summary.scalar('accuracy', accuracy)
reg_loss = utils.get_reg_loss(weight_decay)
tf.summary.scalar('reg_loss', reg_loss)
total_loss = cross_entropy + reg_loss
tf.summary.scalar('total_loss', total_loss)
global_step = tf.train.create_global_step()
learning_rate = utils.configure_learning_rate(global_step, TRAIN_SAMPLES,
FLAGS)
tf.summary.scalar('learning_rate', learning_rate)
optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,
label_batch = [item[1] for item in query_set]
label_example = label2tensor(label_batch)
label_dict = label_example[0]
logging.info('select labels:{}'.format(' '.join(list(label_dict.keys()))))
# train
model.train()
class_vector, prob = model(query_set=query_batch, support_set=train_batch)
loss = loss_f(prob, label_example[1])
logging.info('training loss: {}'.format(loss.data))
optimize.zero_grad()
loss.backward()
optimize.step()
accuracy = get_accuracy(prob, labels=label_example[1])
logging.info('eval accuracy: {}'.format(accuracy))
# eval
# model.eval()
#
# valid_batch = data_loader.build_example(valid_set, labeled=True)
# valid_label = [label_dict[item[1]] for item in valid_set]
#
# with torch.no_grad():
# class_vector_valid, prob_valid = model(query_set=valid_batch, class_vector=class_vector, mode='eval')
# valid_accuracy = get_accuracy(prob_valid, valid_label)
# logging.info('eval accuracy: {}'.format(valid_accuracy))
optimizer.zero_grad()
global_step += 1
validation_loss = 0
correct_count = 0
model.eval()
for batch in val_dataloader:
if torch.cuda.is_available():
batch = (item.cuda() for item in batch)
input_ids, input_mask, segment_ids, label_ids = batch
with torch.no_grad():
val_logits = model(input_ids, segment_ids, input_mask)
val_loss = loss_fct(val_logits.view(-1, 2), label_ids.view(-1))
correct_count = get_accuracy(val_logits.view(-1, 2),
label_ids.view(-1), correct_count)
validation_loss += val_loss.item()
training_loss = training_loss / len(train_dataloader)
validation_loss = validation_loss / len(val_data)
accuracy = correct_count / len(val_data)
logging.info(
'{}/{}, train loss: {}, validation loss: {}, val_accuracy: {}'.format(
i, epochs, training_loss, validation_loss, accuracy))
if validation_loss < last_val_loss:
model_to_save = model.module if hasattr(model, 'module') else model
output_model_file = os.path.join(args.output_dir,
'model_' + str(i) + '.bin')
torch.save(model_to_save.state_dict(), output_model_file)
output_config_file = os.path.join(args.output_dir,