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markov_chains_I
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‎lectures/_static/lecture_specific/graphviz/.ipynb_checkpoints/graphviz_generation-checkpoint.ipynb

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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 3,
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"id": "16e9379d-bf94-4c79-9a34-4dbc2cc41b0e",
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"metadata": {},
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"outputs": [
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"'../lake_model/lake_model_worker.png'"
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]
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},
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"execution_count": 12,
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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"G.edge('2', '2', label='(1-λ)(1-d)')\n",
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"G.edge('3', '3', label='(1-α)(1-d)')\n",
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"\n",
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"# Show graphviz\n",
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"# Save Plot\n",
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"G.render(filename='../lake_model/lake_model_worker')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "194ca10b-dd02-4210-adbc-c2bb8b699d45",
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"metadata": {},
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"source": [
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"## Markov Chains I\n",
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"\n",
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"### Example 1\n",
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"\n",
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"Hamilton on US unemployment data"
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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": 4,
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"id": "75e86ad6-d11c-4c36-920d-cbab0e3d97d2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'../markov_chains_I/hamilton.pdf'"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(comment='Graph')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"ng\")\n",
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"dot.node(\"mr\")\n",
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"dot.node(\"sr\")\n",
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"\n",
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"dot.edge(\"ng\", \"ng\", label=\"0.971\")\n",
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"dot.edge(\"ng\", \"mr\", label=\"0.029\")\n",
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"dot.edge(\"mr\", \"ng\", label=\"0.145\")\n",
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"\n",
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"dot.edge(\"mr\", \"mr\", label=\"0.778\")\n",
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"dot.edge(\"mr\", \"sr\", label=\"0.077\")\n",
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"dot.edge(\"sr\", \"mr\", label=\"0.508\")\n",
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"\n",
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"dot.edge(\"sr\", \"sr\", label=\"0.492\")\n",
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"dot\n",
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"\n",
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"dot.render(filename='../markov_chains_I/hamilton')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1b7b4b45-f6a4-495d-9115-638aafe9acd8",
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"metadata": {},
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"source": [
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"### Exercise 1\n",
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"\n",
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"Solution 2:"
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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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"id": "46c4612f-3f8b-4c83-b02a-81fe67545e8f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'../markov_chains_I/Temple.pdf'"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(comment='Graph')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"Growth\")\n",
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"dot.node(\"Stagnation\")\n",
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"dot.node(\"Collapse\")\n",
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"\n",
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"dot.edge(\"Growth\", \"Growth\", label=\"0.68\")\n",
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"dot.edge(\"Growth\", \"Stagnation\", label=\"0.12\")\n",
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"dot.edge(\"Growth\", \"Collapse\", label=\"0.20\")\n",
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"\n",
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"dot.edge(\"Stagnation\", \"Stagnation\", label=\"0.24\")\n",
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"dot.edge(\"Stagnation\", \"Growth\", label=\"0.50\")\n",
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"dot.edge(\"Stagnation\", \"Collapse\", label=\"0.26\")\n",
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"\n",
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"dot.edge(\"Collapse\", \"Collapse\", label=\"0.46\")\n",
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"dot.edge(\"Collapse\", \"Stagnation\", label=\"0.18\")\n",
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"dot.edge(\"Collapse\", \"Growth\", label=\"0.36\")\n",
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"\n",
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"dot\n",
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"\n",
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"dot.render(filename='../markov_chains_I/Temple')"
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]
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}
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],
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"metadata": {

‎lectures/_static/lecture_specific/graphviz/graphviz_generation.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "ccd1c797-db85-4293-8436-0cd442d1d9ae",
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"metadata": {},
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"source": [
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"# Code for Graphviz Plots "
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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": 1,
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"id": "6f6a377d-1fc8-4f2a-8e92-b550a7c92828",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Requirement already satisfied: graphviz in /Users/humphreyyang/anaconda3/envs/quantecon/lib/python3.9/site-packages (0.20.1)\n"
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]
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}
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],
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"source": [
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"!pip install graphviz"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ad403a5a-868c-45ed-a360-a81aee9cfd38",
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"metadata": {},
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"source": [
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"```{admonition} graphviz\n",
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":class: warning\n",
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"If you are running this lecture locally it requires [graphviz](https://www.graphviz.org)\n",
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"to be installed on your computer. Installation instructions for graphviz can be found\n",
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"[here](https://www.graphviz.org/download/) \n",
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"```"
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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": 2,
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"id": "428161a2-e0d5-402e-bf16-1d1e460a30e7",
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"metadata": {},
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"outputs": [],
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"source": [
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"from graphviz import Digraph\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "75d07327-0fcc-41f1-8d36-b8b8d4eb1060",
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"metadata": {},
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"source": [
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"## Lake Model"
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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": 3,
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"id": "16e9379d-bf94-4c79-9a34-4dbc2cc41b0e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'../lake_model/lake_model_worker.png'"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Create Digraph object\n",
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"G = Digraph(format='png')\n",
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"G.attr(rankdir='LR')\n",
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"\n",
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"# Add nodes\n",
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"G.attr('node', shape='circle')\n",
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"G.node('1', 'New entrants', color='blue')\n",
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"G.node('2', 'Unemployed')\n",
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"G.node('3', 'Employed')\n",
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"\n",
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"# Add edges\n",
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"G.edge('1', '2', label='b')\n",
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"G.edge('2', '3', label='λ(1-d)')\n",
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"G.edge('3', '2', label='α(1-d)')\n",
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"G.edge('2', '2', label='(1-λ)(1-d)')\n",
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"G.edge('3', '3', label='(1-α)(1-d)')\n",
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"\n",
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"# Save Plot\n",
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"G.render(filename='../lake_model/lake_model_worker')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "194ca10b-dd02-4210-adbc-c2bb8b699d45",
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"metadata": {},
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"source": [
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"## Markov Chains I\n",
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"\n",
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"### Example 1\n",
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"\n",
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"Hamilton on US unemployment data"
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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": 6,
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"id": "75e86ad6-d11c-4c36-920d-cbab0e3d97d2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'../markov_chains_I/Hamilton.png'"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(format='png')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"ng\")\n",
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"dot.node(\"mr\")\n",
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"dot.node(\"sr\")\n",
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"\n",
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"dot.edge(\"ng\", \"ng\", label=\"0.971\")\n",
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"dot.edge(\"ng\", \"mr\", label=\"0.029\")\n",
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"dot.edge(\"mr\", \"ng\", label=\"0.145\")\n",
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"\n",
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"dot.edge(\"mr\", \"mr\", label=\"0.778\")\n",
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"dot.edge(\"mr\", \"sr\", label=\"0.077\")\n",
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"dot.edge(\"sr\", \"mr\", label=\"0.508\")\n",
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"\n",
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"dot.edge(\"sr\", \"sr\", label=\"0.492\")\n",
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"dot\n",
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"\n",
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"dot.render(filename='../markov_chains_I/Hamilton')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1b7b4b45-f6a4-495d-9115-638aafe9acd8",
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"metadata": {},
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"source": [
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"### Exercise 1\n",
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"\n",
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"Solution 2:"
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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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"id": "46c4612f-3f8b-4c83-b02a-81fe67545e8f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'../markov_chains_I/Temple.png'"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(format='png')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"Growth\")\n",
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"dot.node(\"Stagnation\")\n",
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"dot.node(\"Collapse\")\n",
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"\n",
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"dot.edge(\"Growth\", \"Growth\", label=\"0.68\")\n",
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"dot.edge(\"Growth\", \"Stagnation\", label=\"0.12\")\n",
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"dot.edge(\"Growth\", \"Collapse\", label=\"0.20\")\n",
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"\n",
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"dot.edge(\"Stagnation\", \"Stagnation\", label=\"0.24\")\n",
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"dot.edge(\"Stagnation\", \"Growth\", label=\"0.50\")\n",
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"dot.edge(\"Stagnation\", \"Collapse\", label=\"0.26\")\n",
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"\n",
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"dot.edge(\"Collapse\", \"Collapse\", label=\"0.46\")\n",
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"dot.edge(\"Collapse\", \"Stagnation\", label=\"0.18\")\n",
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"dot.edge(\"Collapse\", \"Growth\", label=\"0.36\")\n",
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"\n",
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"dot\n",
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"\n",
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"dot.render(filename='../markov_chains_I/Temple')"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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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": "3.9.16"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎lectures/_static/lecture_specific/markov_chains_I/Hamilton.png

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‎lectures/_static/lecture_specific/markov_chains_I/Temple.png

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