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Lab03 #41

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Lab03 #41

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a734654
Add Lab03 Jupyter Notebook with excercises and solutions
Jayden-Gao Feb 17, 2024
ce78766
Add Lab03-2
Jayden-Gao Feb 18, 2024
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113 changes: 113 additions & 0 deletions Lab03/Lab/Lab03-2.2.ipynb
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@@ -0,0 +1,113 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "3503da6f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For convergence criterion 0.01:\n",
"Average number of draws: 228.51\n",
"Standard deviation of draws: 874.1452567508447\n",
"\n",
"For convergence criterion 0.001:\n",
"Average number of draws: 1204.11\n",
"Standard deviation of draws: 8195.205337140736\n",
"\n",
"For convergence criterion 0.0001:\n",
"Average number of draws: 6670.93\n",
"Standard deviation of draws: 29216.754593641985\n",
"\n",
"For convergence criterion 1e-05:\n",
"Average number of draws: 41313.39\n",
"Standard deviation of draws: 218969.87842234815\n",
"\n"
]
}
],
"source": [
"import random\n",
"import math\n",
"import numpy as np\n",
"\n",
"# Define the convergence criteria\n",
"convergence_criteria = [0.01, 0.001, 0.0001, 0.00001]\n",
"\n",
"# Function to estimate Pi given a convergence criterion\n",
"def estimate_pi(convergence_criterion):\n",
" pi = math.pi\n",
" n_draws = []\n",
"\n",
" for _ in range(10): # 10 runs\n",
" n = 0 # number of points falling in the unit circle\n",
" d = 0 # number of points falling in the unit square\n",
" \n",
" while True:\n",
" x = random.random()\n",
" y = random.random()\n",
" if x**2 + y**2 <= 1.0:\n",
" n += 1\n",
" d += 1\n",
" ratio = 4 * n / d\n",
" \n",
" # Check convergence criterion\n",
" if abs(ratio - pi) / pi <= convergence_criterion:\n",
" n_draws.append(d)\n",
" break\n",
"\n",
" return n_draws\n",
"\n",
"# Calculate statistics for each convergence criterion\n",
"for criterion in convergence_criteria:\n",
" all_draws = []\n",
"\n",
" # Perform 10 runs for the current criterion\n",
" for _ in range(10):\n",
" draws = estimate_pi(criterion)\n",
" all_draws.extend(draws)\n",
"\n",
" # Calculate and print statistics\n",
" average_draws = np.mean(all_draws)\n",
" std_draws = np.std(all_draws)\n",
" \n",
" print(f\"For convergence criterion {criterion}:\")\n",
" print(f\"Average number of draws: {average_draws}\")\n",
" print(f\"Standard deviation of draws: {std_draws}\")\n",
" print()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "de54eb99",
"metadata": {},
"outputs": [],
"source": []
}
],
"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
}
107 changes: 61 additions & 46 deletions Lab03/Lab/simulate_pi.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -2,20 +2,14 @@
"cells": [
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"# Simulating $\\pi$"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"The area of a circle $C$ is given as $|C| = \\pi r^2$ with $r$ as the radius.\n",
"\n",
Expand All @@ -34,10 +28,7 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"We can use this relationship to simulate the ratio of the areas to generate an estimate of $\\pi$.\n",
"\n",
Expand All @@ -50,9 +41,6 @@
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand All @@ -68,9 +56,6 @@
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand All @@ -84,9 +69,6 @@
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -121,9 +103,6 @@
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -158,9 +137,6 @@
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -5824,9 +5800,6 @@
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -5863,9 +5836,6 @@
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -5897,9 +5867,6 @@
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -5937,9 +5904,6 @@
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -5980,9 +5944,6 @@
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -6018,8 +5979,6 @@
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true,
"jupyter": {
"outputs_hidden": false
}
Expand Down Expand Up @@ -6221,6 +6180,62 @@
"xf"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enter the convergence criterion (e.g., 0.0001): 0.00001 \n",
"Enter the sentinel value for the number of draws: 100\n",
"Draw limit was exceeded.\n",
"Pi estimate: 3.28\n",
"Percentage difference: 4.405642668283338\n"
]
}
],
"source": [
"import random\n",
"import math\n",
"\n",
"# Prompt user for convergence criterion\n",
"convergence_criterion = float(input(\"Enter the convergence criterion (e.g., 0.0001): \"))\n",
"\n",
"# Prompt user for sentinel value\n",
"sentinel_value = int(input(\"Enter the sentinel value for the number of draws: \"))\n",
"\n",
"# True value of Pi\n",
"true_pi = math.pi\n",
"\n",
"n = 0 # number of points falling in the unit circle\n",
"d = 0 # number of points falling in the unit square\n",
"simulating = True # use as a sentinel\n",
"\n",
"while simulating:\n",
" x = random.random()\n",
" y = random.random()\n",
" if x**2 + y**2 <= 1.0:\n",
" n += 1\n",
" d += 1\n",
" ratio = 4 * n * 1.0 / d\n",
"\n",
" # Check convergence criterion\n",
" if abs(ratio - true_pi) / true_pi <= convergence_criterion:\n",
" print(\"Convergence criterion met.\")\n",
" print(\"Pi estimate:\", ratio)\n",
" break\n",
"\n",
" # Check sentinel value\n",
" if d >= sentinel_value:\n",
" print(\"Draw limit was exceeded.\")\n",
" print(\"Pi estimate:\", ratio)\n",
" print(\"Percentage difference:\", abs(ratio - true_pi) / true_pi * 100)\n",
" break\n"
]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -6231,7 +6246,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -6245,7 +6260,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.8"
"version": "3.11.5"
}
},
"nbformat": 4,
Expand Down
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