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import math
import numpy as np
import torch
from torch import nn
from d2l import torch as d2l

# +
MAX_DEGREE = 20 
N_TRAIN = 100
N_TEST = 100 
 
true_w = np.zeros(MAX_DEGREE)  # Allocate lots of empty space
true_w[0:4] = np.array([5, 1.2, -3.4, 5.6])

features = np.random.normal(size=(N_TRAIN + N_TEST, 1))
np.random.shuffle(features)
poly_features = np.power(features, np.arange(MAX_DEGREE).reshape(1, -1))
for i in range(MAX_DEGREE):
    poly_features[:, i] /= math.gamma(i + 1)
labels = np.dot(poly_features, true_w)
labels += np.random.normal(scale=0.1, size=labels.shape)

# +
true_w, features, poly_features, labels = [torch.tensor(x, dtype=
    d2l.float32) for x in [true_w, features, poly_features, labels]]

features[:2], poly_features[:2, :], labels[:2]


# -

def evaluate_loss(net, data_iter, loss):
    metric = d2l.Accumulator(2)
    for X, y in data_iter:
        out = net(X)
        y = y.reshape(out.shape)
        l = loss(out, y)
        metric.add(l.sum(), l.numel())
    return metric[0] / metric[1]


def train(train_features, test_features, train_labels, test_labels,
          num_epochs=400):
    loss = nn.MSELoss()
    input_shape = train_features.shape[-1]
    net = nn.Sequential(nn.Linear(input_shape, 1, bias=False))
    batch_size = min(10, train_labels.shape[0])
    train_iter = d2l.load_array((train_features, train_labels.reshape(-1, 1)),
                                batch_size)
    test_iter = d2l.load_array((test_features, test_labels.reshape(-1, 1)),
                               batch_size, is_train=False)
    trainer = torch.optim.SGD(net.parameters(), lr=0.01)
    animator = d2l.Animator(xlabel='epoch', ylabel='loss', yscale='log',
                            xlim=[1, num_epochs], ylim=[1e-3, 1e2],
                            legend=['train', 'test'])
    for epoch in range(num_epochs):
        d2l.train_epoch_ch3(net, train_iter, loss, trainer)
        if epoch == 0 or (epoch + 1) % 20 == 0:
            animator.add(epoch + 1, (evaluate_loss(
                net, train_iter, loss), evaluate_loss(net, test_iter, loss)))
    print('weight:', net[0].weight.data.numpy())


train(poly_features[:N_TRAIN, :4], poly_features[N_TRAIN:, :4],
      labels[:N_TRAIN], labels[N_TRAIN:])

train(poly_features[:N_TRAIN, :2], poly_features[N_TRAIN:, :2],
      labels[:N_TRAIN], labels[N_TRAIN:])

train(poly_features[:N_TRAIN, :], poly_features[N_TRAIN:, :],
      labels[:N_TRAIN], labels[N_TRAIN:], num_epochs=1500)



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