![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\" "\\"Open"){kind=icon}
![\"Download\"](\"https://img.shields.io/badge/Github-Download-blue.svg\" "\\"Download"){kind=icon}
"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# IMPORT DATA FILES USED BY THIS NOTEBOOK\n",
"import os, requests\n",
"\n",
"file_links = [(\"data/fifth_republic.txt\", \"https://ndcbe.github.io/cbe-xx258/data/fifth_republic.txt\"),\n",
" (\"data/hats.txt\", \"https://ndcbe.github.io/cbe-xx258/data/hats.txt\")]\n",
"\n",
"# This cell has been added by nbpages. Run this cell to download data files required for this notebook.\n",
"\n",
"for filepath, fileurl in file_links:\n",
" stem, filename = os.path.split(filepath)\n",
" if stem:\n",
" if not os.path.exists(stem):\n",
" os.mkdir(stem)\n",
" if not os.path.isfile(filepath):\n",
" with open(filepath, 'wb') as f:\n",
" response = requests.get(fileurl)\n",
" f.write(response.content)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "Z_7CzQztmUoo",
"nbpages": {
"level": 1,
"link": "[1.4 Functions, Scoping, and Other Fun Stuff](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4-Functions,-Scoping,-and-Other-Fun-Stuff)",
"section": "1.4 Functions, Scoping, and Other Fun Stuff"
}
},
"source": [
"# 1.4 Functions, Scoping, and Other Fun Stuff\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[1.4 Functions, Scoping, and Other Fun Stuff](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4-Functions,-Scoping,-and-Other-Fun-Stuff)",
"section": "1.4 Functions, Scoping, and Other Fun Stuff"
}
},
"source": [
"**Reference**: Chapter 3 of *Computational Nuclear Engineering and Radiological Science Using Python*, R. McClarren (2018) "
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[1.4.1 Learning Objectives](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.1-Learning-Objectives)",
"section": "1.4.1 Learning Objectives"
}
},
"source": [
"## 1.4.1 Learning Objectives\n",
"\n",
"After studying this notebook, completing the activities, and asking questions in class, you should be able to:"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "Vvv-zUXfmUop",
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"source": [
"## 1.4.2 Functions\n",
"\n",
"### Motivating Example"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "x5araXX7mUoq",
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"source": [
"Why use functions? We want to write, debug, and test code **once** and then **reuse** as much as possible.\n",
"\n",
"In a few class sessions, we'll formulate mass balances as linear systems and solve them using Python. But for now, let's just consider a problem you would expect to see in math class:\n",
"\n",
"We want to solve the linear system,\n",
"\n",
"$$\\mathrm{Eqn.~1}:\\quad 4.5 x + 3 y = 10.5\\\\\\mathrm{Eqn.~2}:\\quad 1.5 x + 3 y = 7.5.$$\n",
"\n",
"One way to do this is using Python as calculator. In the comments below, we walk through the steps."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 87
},
"colab_type": "code",
"executionInfo": {
"elapsed": 750,
"status": "ok",
"timestamp": 1548171075668,
"user": {
"displayName": "Alexander Dowling",
"photoUrl": "https://lh3.googleusercontent.com/-LChdQ2m5OQE/AAAAAAAAAAI/AAAAAAAAAA0/JeXJe4vQJ7M/s64/photo.jpg",
"userId": "00988067626794866502"
},
"user_tz": 300
},
"id": "9F-6X4lhmUos",
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
},
"outputId": "44077880-5b15-46b6-a4a3-9d43943c2c98"
},
"outputs": [],
"source": [
"\"\"\"python code to solve \n",
"4.5 x + 3 y = 10.5\n",
"1.5 x + 3 y = 7.5\n",
"by solving the second equation for y first,\n",
"and then solving for x\"\"\"\n",
"#step 1 solve for y, multiply equation 2 by -3, \n",
"## and add to first equation\n",
"LHS_coefficient = -3*3 + 3 #the coefficient for y\n",
"RHS = -3*7.5 + 10.5 #the right-hand side\n",
"\n",
"print('LHS_coefficient:',LHS_coefficient)\n",
"print('RHS:',RHS)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"source": [
"Mathematical, we started by multiplying equation 2,\n",
"\n",
"$$1.5 x + 3 y = 7.5$$\n",
"\n",
"by -3,\n",
"\n",
"$$(-3) \\times 1.5 x + (-3) \\times 3 y = (-3) \\times 7.5$$\n",
"\n",
"\n",
"and then added this scaled equation 2 to equation 1, giving:\n",
"\n",
"$$(4.5 - 3 \\times 1.5) x + (3 - 3 \\times 3) y = 10.5 - 3 \\times 7.5$$\n",
"\n",
"Notice that our choice of scaling equation 2 by -3 means that the coefficient for x becomes zero after addition addition. The coefficient for $y$ is `LHS_coefficient` is our code. `RHS` is the right hand side of the new equation.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The solution to:\n",
"4.5 x + 3 y = 10.5\n",
"1.5 x + 3 y = 7.5\n",
" is x = 1.0 y= 2.0\n"
]
}
],
"source": [
"#now divide right-hand side by left-hand side coefficient\n",
"y = RHS / LHS_coefficient\n",
"#plug y into first equation\n",
"x = (10.5 - 3*y)/4.5 \n",
"#print the solution, note \\n produces a linebreak\n",
"print(\"The solution to:\\n4.5 x + 3 y = 10.5\\n1.5 x + 3 y = 7.5\\n is x =\",\n",
" x,\"y=\",y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "192rbx9dmUow",
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"source": [
"How to extend this code to another linear system?\n",
"\n",
"**Let's define a function** that will solve the system for (almost) any coefficients and right-hand side. \n",
"\n",
"I'll define such a function to solve $$a_1 x + b_1 y = c_1\\\\ a_2 x + b_2 y = c_2.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbgrader": {
"grade": false,
"locked": false,
"solution": false
},
"nbpages": {
"level": 2,
"link": "[1.4.2 Functions](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.2-Functions)",
"section": "1.4.2 Functions"
}
},
"source": [
"
\n",
"def volume(radius):\n",
" \"\"\"compute volume of a sphere\n",
"\n",
" Args:\n",
" radius: float giving the radius of the sphere\n",
"\n",
" Returns:\n",
" volume of the sphere as a float\n",
" \"\"\"\n",
" return 4.0/3.0*math.pi*radius**3\n",
"\n",
"def surface_area(radius):\n",
" \"\"\"compute surface area of a sphere\n",
"\n",
" Args:\n",
" radius: float giving the radius of the sphere\n",
"\n",
" Returns:\n",
" surface area of the sphere as a float\n",
" \"\"\"\n",
" return 4.0*math.pi*radius**2\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "tlLecRQrmUp-",
"nbpages": {
"level": 2,
"link": "[1.4.5 Modules](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.5-Modules)",
"section": "1.4.5 Modules"
}
},
"source": [
"I can use the help function to tell me about the module:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 305
},
"colab_type": "code",
"executionInfo": {
"elapsed": 214,
"status": "error",
"timestamp": 1548342630031,
"user": {
"displayName": "Alexander Dowling",
"photoUrl": "https://lh3.googleusercontent.com/-LChdQ2m5OQE/AAAAAAAAAAI/AAAAAAAAAA0/JeXJe4vQJ7M/s64/photo.jpg",
"userId": "00988067626794866502"
},
"user_tz": 300
},
"id": "vLceeHInmUp-",
"nbpages": {
"level": 2,
"link": "[1.4.5 Modules](https://ndcbe.github.io/cbe-xx258/01.04-Functions-scoping.html#1.4.5-Modules)",
"section": "1.4.5 Modules"
},
"outputId": "4523bd79-84b2-4676-b141-ee0478b99e47"
},
"outputs": [
{
"ename": "ModuleNotFoundError",
"evalue": "No module named 'sphere'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m
"
]
}
],
"metadata": {
"colab": {
"name": "L3-Functions-Scoping-Etc.ipynb",
"provenance": [],
"version": "0.3.2"
},
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}