%pylab inline
import torch
from torch.nn.parameter import Parameter

x = torch.rand([1000,2])
x_in_circle = ((x**2).sum(1) < 1)

def accuracy(pred_label):
    return (pred_label==x_in_circle).float().mean()

def show(pred_label):
    scatter(*x.numpy().T, c=pred_label.numpy())
    axis('equal')

def loss(prediction):
    return -(x_in_circle.float()     * prediction.log() +
             (1-x_in_circle.float()) * (1-prediction).log() ).mean()

show(x_in_circle)

class Linear(torch.nn.Module):
    def __init__(self, input_dim):
        super().__init__()
        self.w = Parameter(torch.ones(input_dim))
        self.b = Parameter(-torch.ones(1))
    
    def forward(self, x):
        return (x * self.w[None,:]).sum(dim=1) + self.b

class LinearClassifier(torch.nn.Module):
    def __init__(self, input_dim):
        super().__init__()
        self.linear = Linear(input_dim)
    
    def forward(self, x):
        logit = self.linear(x)
        return 1/(1+(-logit).exp())


classifier = LinearClassifier(2)

show(classifier(x).detach() > 0.5)

list(classifier.parameters())