'''
Question 1 Skeleton Code

Here you should implement and evaluate the Conditional Gaussian classifier.
'''

import data
import numpy as np
# Import pyplot - plt.imshow is useful!
import matplotlib.pyplot as plt

def compute_mean_mles(train_data, train_labels):
    '''
    Compute the mean estimate for each digit class

    Should return a numpy array of size (10,64)
    The ith row will correspond to the mean estimate for digit class i
    '''
    means = np.zeros((10, 64))
    # Compute means
    return means

def compute_sigma_mles(train_data, train_labels):
    '''
    Compute the covariance estimate for each digit class

    Should return a three dimensional numpy array of shape (10, 64, 64)
    consisting of a covariance matrix for each digit class 
    '''
    covariances = np.zeros((10, 64, 64))
    # Compute covariances
    return covariances

def generative_likelihood(digits, means, covariances):
    '''
    Compute the generative log-likelihood:
        log p(x|y,mu,Sigma)

    Should return an n x 10 numpy array 
    '''
    return None

def conditional_likelihood(digits, means, covariances):
    '''
    Compute the conditional likelihood:

        log p(y|x, mu, Sigma)

    This should be a numpy array of shape (n, 10)
    Where n is the number of datapoints and 10 corresponds to each digit class
    '''
    return None

def avg_conditional_likelihood(digits, labels, means, covariances):
    '''
    Compute the average conditional likelihood over the true class labels

        AVG( log p(y_i|x_i, mu, Sigma) )

    i.e. the average log likelihood that the model assigns to the correct class label
    '''
    cond_likelihood = conditional_likelihood(digits, means, covariances)

    # Compute as described above and return
    return None

def classify_data(digits, means, covariances):
    '''
    Classify new points by taking the most likely posterior class
    '''
    cond_likelihood = conditional_likelihood(digits, means, covariances)
    # Compute and return the most likely class
    pass

def main():
    train_data, train_labels, test_data, test_labels = data.load_all_data('data')

    # Fit the model
    means = compute_mean_mles(train_data, train_labels)
    covariances = compute_sigma_mles(train_data, train_labels)

    # Evaluation

if __name__ == '__main__':
    main()