201 lines
153 KiB
Plaintext
201 lines
153 KiB
Plaintext
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{
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"metadata": {
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.4-final"
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},
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"orig_nbformat": 2,
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3",
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"language": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2,
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"\n",
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"from constants import *\n",
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"from maths import gaussian\n",
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"from markov import MarkovModel"
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]
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},
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{
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"source": [
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"State Probability Functions (1)\n",
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"==================="
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"output_type": "display_data",
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"data": {
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"text/plain": "<Figure size 432x288 with 1 Axes>",
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},
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"metadata": {
|
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"needs_background": "light"
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}
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}
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],
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"source": [
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"x = np.linspace(-5, 10, 120)\n",
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"\n",
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"state_1_y = [gaussian(i, state1.mean, state1.std_dev) for i in x]\n",
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"state_2_y = [gaussian(i, state2.mean, state2.std_dev) for i in x]\n",
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"\n",
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"plt.plot(x, state_1_y, c='r', label=\"State 1\")\n",
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"plt.plot(x, state_2_y, c='b', label=\"State 2\")\n",
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"\n",
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"plt.legend()\n",
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"plt.title(\"State Probability Density Functions\")\n",
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"\n",
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"plt.ylabel(\"Probability Density\")\n",
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"plt.grid(linestyle=\"--\")\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"source": [
|
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"Output Probability Densities (2)\n",
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"=========="
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"3.8 -> State 1: 0.02185157424475792, State 2: 0.5471239427774459\n4.2 -> State 1: 0.009496655019831194, State 2: 0.5471239427774459\n3.4 -> State 1: 0.04499247209432338, State 2: 0.3947074079064296\n-0.4 -> State 1: 0.16833223796171576, State 2: 1.500652790137751e-09\n1.9 -> State 1: 0.2509478601290037, State 2: 0.006331212017054291\n3.0 -> State 1: 0.08289761566062391, State 2: 0.2054255182126689\n1.6 -> State 1: 0.2933877723035829, State 2: 0.001596702666402633\n1.9 -> State 1: 0.2509478601290037, State 2: 0.006331212017054291\n5.0 -> State 1: 0.0012852324969092556, State 2: 0.2054255182126689\n"
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]
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}
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],
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"source": [
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"for obs in observations:\n",
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" print(f'{obs} -> State 1: {gaussian(obs, state1.mean, state1.std_dev)}, State 2: {gaussian(obs, state2.mean, state2.std_dev)}')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
|
|||
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"output_type": "display_data",
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"data": {
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|||
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"text/plain": "<Figure size 432x288 with 1 Axes>",
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|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"x = np.linspace(-5, 10, 120)\n",
|
|||
|
|
"\n",
|
|||
|
|
"state_1_y = [gaussian(i, state1.mean, state1.std_dev) for i in x]\n",
|
|||
|
|
"state_2_y = [gaussian(i, state2.mean, state2.std_dev) for i in x]\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.plot(x, state_1_y, c='r', label=\"State 1\")\n",
|
|||
|
|
"plt.plot(x, state_2_y, c='b', label=\"State 2\")\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.legend()\n",
|
|||
|
|
"plt.title(\"State Probability Density Functions\")\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.ylabel(\"Probability Density\")\n",
|
|||
|
|
"plt.grid(linestyle=\"--\")\n",
|
|||
|
|
"\n",
|
|||
|
|
"state1_pd = [gaussian(i, state1.mean, state1.std_dev) for i in observations]\n",
|
|||
|
|
"state2_pd = [gaussian(i, state2.mean, state2.std_dev) for i in observations]\n",
|
|||
|
|
"\n",
|
|||
|
|
"#############################################\n",
|
|||
|
|
"# Observation Marks \n",
|
|||
|
|
"#############################################\n",
|
|||
|
|
"\n",
|
|||
|
|
"config = {\n",
|
|||
|
|
" \"s\": 65,\n",
|
|||
|
|
" \"marker\": 'x'\n",
|
|||
|
|
"}\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.scatter(observations, state1_pd, color=(0.5, 0, 0), **config)\n",
|
|||
|
|
"plt.scatter(observations, state2_pd, color=(0, 0, 0.5), **config)\n",
|
|||
|
|
"\n",
|
|||
|
|
"plt.show()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 6,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"name": "stdout",
|
|||
|
|
"text": [
|
|||
|
|
"[0.00961469 0.30638941]\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "execute_result",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
"array([[0.00961469, 1. , 1. , 1. , 1. ,\n",
|
|||
|
|
" 1. , 1. , 1. , 1. ],\n",
|
|||
|
|
" [0.30638941, 1. , 1. , 1. , 1. ,\n",
|
|||
|
|
" 1. , 1. , 1. , 1. ]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"execution_count": 6
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"model = MarkovModel(states=[state1, state2], observations=observations, state_transitions=state_transition)\n",
|
|||
|
|
"model.populate_forward()\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(model.forward[:, 0])\n",
|
|||
|
|
"\n",
|
|||
|
|
"model.forward\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": []
|
|||
|
|
}
|
|||
|
|
]
|
|||
|
|
}
|