def discriminant_function(x, mean, cov, d, P):
    if d == 1:
        output = -0.5*(x - mean) * (1/cov)
        output = output * (x - mean)
        output += -0.5*d*log(2*pi) - 0.5*log(cov) 

    else: 
        output = np.matmul(-0.5*(x - mean), np.linalg.inv(cov))
        output = np.matmul(output, (x - mean).T)
        output += -0.5*d*log(2*pi) - 0.5*log(np.linalg.det(cov)) 

    # Adding Prior Probability
    output += log(P)

    return output

n = len(data)
P = [1/n for i in range(n)]
d = len(data[0][0])

data = [
    # W1
    np.array([
        [-5.01, -8.12, -3.68],
        [-5.43, -3.48, -3.54],
        [1.08, -5.52, 1.66],
        [0.86, -3.78, -4.11],
        [-2.67, 0.63, 7.39],
        [4.94, 3.29, 2.08],
        [-2.51, 2.09, -2.59],
        [-2.25, -2.13, -6.94],
        [5.56, 2.86, -2.26],
        [1.03, -3.33, 4.33]
    ]),

    # W2
    np.array([
        [-0.91, -0.18, -0.05],
        [1.30, -2.06, -3.53],
        [-7.75, -4.54, -0.95],
        [-5.47, 0.50, 3.92],
        [6.14, 5.72, -4.85],
        [3.60, 1.26, 4.36],
        [5.37, -4.63, -3.65],
        [7.18, 1.46, -6.66],
        [-7.39, 1.17, 6.30],
        [-7.50, -6.32, -0.31]
    ]),

    # W3
    np.array([
        [5.35, 2.26, 8.13],
        [5.12, 3.22, -2.66],
        [-1.34, -5.31, -9.87],
        [4.48, 3.42, 5.19],
        [7.11, 2.39, 9.21],
        [7.17, 4.33, -0.98],
        [5.75, 3.97, 6.65],
        [0.77, 0.27, 2.41],
        [0.90, -0.43, -8.71],
        [3.52, -0.36, 6.43]
    ]) 
]

for j in range(n):
    print("\nData classes should be classified as:", j+1)
    total_count, count = 0, 0

    # Taking x as dataset belonging to class j + 1
    for x in data[j]:
        g_values = [0 for g in range(n)]        

        # Itering through each class' discriminant function
        for i in range(n):
            g_values[i] = discriminant_function(x, means[i], cov[i], d, P[i])

        # Now to output the maximum result 
        result = g_values.index(max(g_values)) + 1
        print(x, "\twas classified as", result)
        total_count, count = total_count + 1, (count + 1 if j == result - 1 else count)
        
    print("Success Rate:", (count/total_count)*100,"%")
    print("Fail Rate:", 100 - ((count/total_count))*100,"%")

n = len(data) - 1
P = [0.5, 0.5, 0]
d = 1

for j in range(n + 1):
    print("\nData classes should be classified as:", j+1)
    total_count, count = 0, 0

    # Taking x as dataset belonging to class j + 1
    for x in data[j]:
        g_values = [0 for g in range(n)]        # Array for all discrminant function outputs.

        # Itering through each class' discriminant function
        for i in range(n):
            g_values[i] = discriminant_function(x[0], means[i][0], cov[i][0][0], d, P[i])

        # Now to output the maximum result 
        result = g_values.index(max(g_values)) + 1
        print(x, "\twas classified as", result)
        total_count, count = total_count + 1, (count + 1 if j == result - 1 else count)
        
    print("Success Rate:", (count/total_count)*100,"%")
    print("Fail Rate:", 100 - ((count/total_count))*100,"%")

n = len(data) - 1
P = [0.5, 0.5, 0]
d = 2

n = len(data) - 1
P = [0.5, 0.5, 0]
d = 3

n = len(data) - 1
P = [0.5, 0.5, 0]
g_values = [0 for i in range(n)]

x = list(map(float, input("Enter the input vector: ").strip().split()))

d = 1
print("Case A: Using only feature vector x1")
for i in range(n):
    g_values[i] = discriminant_function(x[0], means[i][0], cov[i][0][0], d, P[i])

result = g_values.index(max(g_values)) + 1
print(x, "\twas classified as", result)

d = 2
print("\nCase B: Using only feature vectors x1 and x2")
for i in range(n):
    g_values[i] = discriminant_function(x[0:2], means[i][0:2], cov[i][0:2, 0:2], d, P[i])

result = g_values.index(max(g_values)) + 1
print(x, "\twas classified as", result)

d = 3
print("\nCase C: Using all feature vectors")
for i in range(n):
    g_values[i] = discriminant_function(x, means[i], cov[i], d, P[i])

result = g_values.index(max(g_values)) + 1
print(x, "\twas classified as", result)