import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np

# Define the model with Dropout layers
class MC_Dropout_Model(nn.Module):
    def __init__(self, input_size, hidden_size, output_size, dropout_rate=0.5):
        super(MC_Dropout_Model, self).__init__()
        self.fc1 = nn.Linear(input_size, hidden_size)
        self.dropout = nn.Dropout(dropout_rate)
        self.fc2 = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        x = F.relu(self.fc1(x))
        x = self.dropout(x)  # Apply dropout during inference
        x = self.fc2(x)
        return x

# Function to perform MC Dropout inference
def mc_dropout_predict(model, x, n_samples=100):
    model.train()  # Keep dropout layers active during inference
    predictions = []

    with torch.no_grad():
        for _ in range(n_samples):
            predictions.append(model(x))

    # Stack predictions for each pass along a new dimension and calculate mean and variance
    predictions = torch.stack(predictions)
    mean_prediction = predictions.mean(dim=0)
    uncertainty = predictions.var(dim=0)

    return mean_prediction, uncertainty

# Example Usage
if __name__ == "__main__":
    # Initialize model, dummy data, and parameters
    input_size = 10
    hidden_size = 20
    output_size = 1
    dropout_rate = 0.5
    n_samples = 100

    model = MC_Dropout_Model(input_size, hidden_size, output_size, dropout_rate)

    # Dummy input tensor
    x = torch.randn((1, input_size))

    # Get predictions and uncertainty
    mean_prediction, uncertainty = mc_dropout_predict(model, x, n_samples=n_samples)

    print("Mean Prediction:", mean_prediction)
    print("Uncertainty (Variance):", uncertainty)