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|---|---|---|
| @@ -0,0 +1,197 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "id": "20424303", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "\n", | ||
| "def viterbi_algorithm(S, Pi, E, P, Y):\n", | ||
| " K = len(S) # Length of state space will give K\n", | ||
| " T = len(Y) # Length of observation sequence will give T\n", | ||
| " \n", | ||
| " # Initialize matrices for Viterbi probabilities and paths\n", | ||
| " viterbi_prob = np.zeros((K, T))\n", | ||
| " viterbi_path = np.zeros((K, T))\n", | ||
| " \n", | ||
| " # Part I: Initialization\n", | ||
| " for i in range(K):\n", | ||
| " viterbi_prob[i][0] = Pi[i] * E[i][Y[0]]\n", | ||
| " viterbi_path[i][0] = 0\n", | ||
| " \n", | ||
| " # Part II: Compute Viterbi probabilities and path\n", | ||
| " for j in range(1, T):\n", | ||
| " for i in range(K):\n", | ||
| " viterbi_prob[i, j] = max(E[i][Y[j]] * P[k][i] * viterbi_prob[k, j-1] for k in range(K))\n", | ||
| " viterbi_path[i, j] = np.argmax([E[i][Y[j]] * P[k][i] * viterbi_prob[k, j-1] for k in range(K)])\n", | ||
| " \n", | ||
| " # Part III: Re-track the most likely path\n", | ||
| " x = []\n", | ||
| " x_t = np.argmax(viterbi_prob[:, T-1])\n", | ||
| " x.append(x_t)\n", | ||
| " for j in range(T-1, 0, -1):\n", | ||
| " x_prev = int(viterbi_path[int(x_t), j])\n", | ||
| " x.append(x_prev)\n", | ||
| " x_t = x_prev\n", | ||
| " \n", | ||
| " # Reverse path to get the correct order\n", | ||
| " x=x[::-1]\n", | ||
| " print(viterbi_prob)\n", | ||
| " print(viterbi_path)\n", | ||
| " \n", | ||
| " return x, np.max(viterbi_prob[:, T-1])\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "id": "4526f268", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "def forward_algorithm(S, Pi, E, P, Y, Pii=0):\n", | ||
| " K = len(S)\n", | ||
| " T = len(Y)\n", | ||
| " \n", | ||
| " forward_prob = np.zeros((K, T))\n", | ||
| " \n", | ||
| " # Part I: Initialization\n", | ||
| " for i in range(K):\n", | ||
| " forward_prob[i][0] = Pi[i] * E[i][Y[0]]\n", | ||
| " \n", | ||
| " # Part II: Recursion\n", | ||
| " for j in range(1, T):\n", | ||
| " for i in range(K):\n", | ||
| " forward_prob[i, j] = sum(forward_prob[k, j-1] * P[k][i] * E[i][Y[j]] for k in range(K))\n", | ||
| " \n", | ||
| " # Part III: Termination\n", | ||
| " total_prob = np.sum(forward_prob[:, T-1])\n", | ||
| " return total_prob\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "id": "6a25233e", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "[[2.800000e-01 1.120000e-02 9.600000e-04 2.400000e-04 4.800000e-04\n", | ||
| " 1.536000e-04 4.915200e-05 1.966080e-06 1.179648e-06 4.718592e-08]\n", | ||
| " [5.000000e-02 4.800000e-02 1.200000e-02 3.000000e-03 3.000000e-04\n", | ||
| " 4.320000e-05 9.216000e-06 7.372800e-06 7.372800e-07 2.654208e-07]\n", | ||
| " [1.600000e-01 2.240000e-02 2.880000e-03 7.200000e-04 3.600000e-04\n", | ||
| " 7.680000e-05 2.457600e-05 3.932160e-06 8.847360e-07 9.437184e-08]]\n", | ||
| "[[0. 0. 1. 1. 1. 0. 0. 0. 1. 0.]\n", | ||
| " [0. 2. 1. 1. 1. 2. 2. 2. 1. 2.]\n", | ||
| " [0. 0. 1. 1. 1. 0. 0. 0. 1. 0.]]\n", | ||
| "Most likely weather sequence: ['sunny', 'cloudy', 'cloudy', 'cloudy', 'rainy', 'rainy', 'sunny', 'cloudy', 'sunny', 'cloudy']\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "# Given data\n", | ||
| "S = ['rainy', 'cloudy', 'sunny']\n", | ||
| "Pi = [0.35, 0.25, 0.4]\n", | ||
| "P = [\n", | ||
| " [0.4, 0.2, 0.4],\n", | ||
| " [0.2, 0.5, 0.3],\n", | ||
| " [0.3, 0.6, 0.1]\n", | ||
| "]\n", | ||
| "E = [\n", | ||
| " [0.8, 0.1, 0.1],\n", | ||
| " [0.2, 0.5, 0.3],\n", | ||
| " [0.4, 0.2, 0.4]\n", | ||
| "]\n", | ||
| "#activities = ['read', 'read', 'shop', 'play', 'shop']\n", | ||
| "activities = ['read', 'shop', 'play', 'play', 'read', 'play', 'shop', 'shop', 'shop']\n", | ||
| "#observation_indices = [0, 0, 2, 1, 2] # Convert activities to observation indices(read->0,play->1,shop->2)\n", | ||
| " \n", | ||
| "# (a) Find the most likely weather sequence\n", | ||
| "most_likely_weather_sequence, _ = viterbi_algorithm(S, Pi, E, P, observation_indices)\n", | ||
| "print(\"Most likely weather sequence:\", [S[state] for state in most_likely_weather_sequence])" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 8, | ||
| "id": "50b47d13", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "[[2.00000000e-02 2.36250000e-01 7.44187500e-02 2.34419062e-02\n", | ||
| " 8.20466719e-04 2.81302875e-04 1.32915608e-04 2.29678171e-04\n", | ||
| " 8.03873600e-06 2.17045872e-05]\n", | ||
| " [1.80000000e-01 2.30400000e-02 4.25250000e-02 1.33953750e-02\n", | ||
| " 6.32931469e-03 1.21522842e-03 2.33323857e-04 2.98654536e-05\n", | ||
| " 6.20131063e-05 7.93767760e-06]\n", | ||
| " [3.50000000e-01 2.16000000e-02 1.41750000e-02 5.10300000e-03\n", | ||
| " 3.75070500e-03 1.77220811e-03 3.40263958e-04 2.79988628e-05\n", | ||
| " 3.21549440e-05 7.44157275e-06]]\n", | ||
| "[[0. 2. 0. 0. 0. 2. 2. 2. 0. 2.]\n", | ||
| " [0. 1. 0. 0. 0. 1. 1. 1. 0. 1.]\n", | ||
| " [0. 1. 0. 1. 1. 1. 1. 1. 0. 1.]]\n", | ||
| "Most likely sequence of aircraft control laws: ['direct', 'normal', 'normal', 'normal', 'alternate', 'alternate', 'direct', 'normal', 'direct', 'normal']\n", | ||
| "0.0011761669647830317\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "# Given data\n", | ||
| "S = ['normal', 'alternate', 'direct']\n", | ||
| "Pi = [0.2, 0.3, 0.5]\n", | ||
| "P = [\n", | ||
| " [0.35, 0.45, 0.2],\n", | ||
| " [0.28, 0.32, 0.4],\n", | ||
| " [0.75, 0.1, 0.15]\n", | ||
| "]\n", | ||
| "E = [\n", | ||
| " [0.1, 0.9],\n", | ||
| " [0.6, 0.4],\n", | ||
| " [0.7, 0.3]\n", | ||
| "]\n", | ||
| "pitch_data = ['up', 'down', 'down', 'down', 'up', 'up', 'up', 'down', 'up', 'down']\n", | ||
| "#pitch_data = ['up', 'down']\n", | ||
| "\n", | ||
| "# Convert pitch data to observation indices\n", | ||
| "observation_indices = [0 if pitch == 'up' else 1 for pitch in pitch_data]\n", | ||
| "\n", | ||
| "# Implement Viterbi algorithm\n", | ||
| "most_likely_control_sequence, _ = viterbi_algorithm(S, Pi, E, P, observation_indices)\n", | ||
| "print(\"Most likely sequence of aircraft control laws:\", [S[state] for state in most_likely_control_sequence])\n", | ||
| "print(forward_algorithm(S,Pi,E,P,observation_indices,Pii=0))" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.11.5" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |