# Hidden Markov Model: Forward Algorithm implementation in Python

I am learning Hidden Markov Model and its implementation for Stock Price Prediction. I am trying to implement the Forward Algorithm according to this paper.

Here I found an implementation of the Forward Algorithm in Python.

import pandas as pd
import numpy as np

V = np.array([0, 1, 1, 2, 0, 1, 2, 0, 1, 0, 2])

# Transition Probabilities
a = np.array(((0.54, 0.46), (0.49, 0.51)))

# Emission Probabilities
b = np.array(((0.16, 0.26, 0.58), (0.25, 0.28, 0.47)))

# # Equal Probabilities for the initial distribution
pi = np.array((0.5, 0.5))

def forward(V, a, b, pi):
alpha = np.zeros((V.shape[0], a.shape[0]))
alpha[0, :] = initial_distribution * b[:, V[0]]

for t in range(1, V.shape[0]):
for j in range(a.shape[0]):
alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]]

return alpha

alpha = forward(V, a, b, pi)


But it seems to me that it does not include (c) and (d) steps from the algorithm. So I added them:

def forward(V, a, b, pi):
p = 1
alpha = np.zeros((V.shape[0], a.shape[0]))
alpha[0, :] = pi * b[:, V[0]]

for t in range(1, V.shape[0]):
probability_of_observation = 0 #my code
for j in range(a.shape[0]):
alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]]
probability_of_observation += alpha[t, j]  #my code
p = p * probability_of_observation #my code

return p #changed

p = forward(V, a, b, pi)  #changed


Does my code coincide with the given algorithm?