import torch
import torch.nn.functional as F
from torch.autograd import grad

# Define our data and initial parameters
y = torch.tensor([1.0])  # Ground truth label
x1 = torch.tensor([1.1])  # Input feature
w1 = torch.tensor([2.2], requires_grad=True)  # Trainable weight
b = torch.tensor([0.0], requires_grad=True)   # Trainable bias

# Forward pass: compute prediction
z = x1 * w1 + b        # Linear combination
a = torch.sigmoid(z)   # Sigmoid activation
print(f"Prediction: {a.item():.4f}")

# Compute loss
loss = F.binary_cross_entropy(a, y)
print(f"Loss: {loss.item():.4f}")

# Method 1: Manual gradient computation
grad_w1 = grad(loss, w1, retain_graph=True)[0]
grad_b = grad(loss, b, retain_graph=True)[0]
print(f"Weight gradient: {grad_w1.item():.4f}")
print(f"Bias gradient: {grad_b.item():.4f}")

        __
        __