# Function to create intermediate path strings
def transition_states(paths):
    unique_channels = set(x for element in paths for x in element)
    transition_states = {x + '>' + y: 0 for x in unique_channels for y in unique_channels}

    for possible_state in unique_channels:
        if possible_state not in ['Activation', 'Null']:
            for user_path in paths:
                if possible_state in user_path:
                    indices = [i for i, s in enumerate(user_path) if possible_state in s]
                    for col in indices:
                        transition_states[user_path[col] + '>' + user_path[col + 1]] += 1

    return transition_states

# Function to calculate transition probabilities
def transition_prob(trans_dict, paths):
    unique_channels = set(x for element in paths for x in element)
    trans_prob = dict()
    for state in unique_channels:
        if state not in ['Activation', 'Null']:
            counter = 0
            index = [i for i, s in enumerate(trans_dict) if state + '>' in s]
            for col in index:
                if trans_dict[list(trans_dict)[col]] > 0:
                    counter += trans_dict[list(trans_dict)[col]]
            for col in index:
                if trans_dict[list(trans_dict)[col]] > 0:
                    state_prob = float((trans_dict[list(trans_dict)[col]])) / float(counter)
                    trans_prob[list(trans_dict)[col]] = state_prob

    return trans_prob

# Function to create transition matrix
def transition_matrix(list_of_paths, transition_probabilities):
    trans_matrix = pd.DataFrame()
    unique_channels = set(x for element in list_of_paths for x in element)

    for channel in unique_channels:
        trans_matrix[channel] = 0.00
        trans_matrix.loc[channel] = 0.00
        trans_matrix.loc[channel][channel] = 1.0 if channel in ['Activation', 'Null'] else 0.0

    for key, value in transition_probabilities.items():
        origin, destination = key.split('>')
        trans_matrix.at[origin, destination] = value

    return trans_matrix

trans_states = transition_states(journeys['path'])
trans_prob = transition_prob(trans_states, journeys['path'])
trans_matrix = transition_matrix(journeys['path'], trans_prob)