"""多項式迴歸程式碼實現"""

import torch
from torch.autograd import Variable
import torch.nn as nn
import torch.optim as optim
import matplotlib.pyplot as plt
import numpy as np


def make_features(x):
    """Builds features i.e. a matrix with columns [x, x^2, x^3]."""
    x = x.unsqueeze(1)

    return torch.cat([x ** i for
 
 i in range(1, 4)], 1)


def f(x):
    """Approximated function."""
    return x.mm(W_target) + b_target[0]


def get_batch(batch_size=32):
    """Builds a batch i.e. (x, f(x)) pair."""
    random = torch.randn(batch_size)
    random = np.sort(random)
    random = torch.Tensor(random)
    x = make_features(random)
    y = f(x)
    if
 
 torch.cuda.is_available():
        return Variable(x).cuda(), Variable(y).cuda()
    else:
        return Variable(x), Variable(y)


# Define model
class poly_model(nn.Module):
    def __init__(self):
        super(poly_model, self).__init__()
        self.poly = nn.Linear(3, 1)

    def forward(self, x)
 
:
        out = self.poly(x)
        return out


if __name__ == '__main__':
    W_target = torch.FloatTensor([0.5, 3, 2.4]).unsqueeze(1)
    b_target = torch.FloatTensor([0.9])

    if torch.cuda.is_available():
        model = poly_model().cuda()
    else:
        model = poly_model()

    criterion = nn.MSELoss()

    optimizer = optim.SGD(model.parameters(), lr=1e-3)

    epoch = 0
    while True:
        # Get data
        batch_x, batch_y = get_batch()

        # Forward pass
        output = model(batch_x)
        loss = criterion(output, batch_y)
        print_loss = loss.item()
        # Reset gradients
        optimizer.zero_grad()
        # Backward pass
        loss.backward()
        # update parameters
        optimizer.step()
        epoch += 1
        if print_loss < 1e-3:
            break

    print("Loss: {:.6f}  after {} batches".format(loss.item(), epoch))

    print(
        "==> Learned function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(model.poly.bias[0], model.poly.weight[0][0],
                                                                                       model.poly.weight[0][1],
                                                                                       model.poly.weight[0][2]))
    print("==> Actual function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(b_target[0], W_target[0][0],
                                                                                        W_target[1][0], W_target[2][0]))

    predict = model(batch_x)

    batch_x = batch_x.cpu()
    batch_y = batch_y.cpu()
    x = batch_x.numpy()[:, 0]
    plt.plot(x, batch_y.numpy(), 'ro')

    predict = predict.cpu()
    predict = predict.data.numpy()

    plt.plot(x, predict, 'b')
    plt.show()