{ "cells": [ { "cell_type": "markdown", "id": "56ff7eda", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "id": "84b7ac3c", "metadata": {}, "source": [ "# 2.5 Python Basics: An Introductory Example\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "id": "adf85dfd", "metadata": {}, "source": [ "## Contents\n", "\n", "- [An Introductory Example](#an-introductory-example) \n", " - [Overview](#Overview) \n", " - [The Task: Plotting a White Noise Process](#The-Task:-Plotting-a-White-Noise-Process) \n", " - [Version 1](#Version-1) \n", " - [Alternative Implementations](#Alternative-Implementations) \n", " - [Another Application](#Another-Application) \n", " - [Exercises](#Exercises) " ] }, { "cell_type": "markdown", "id": "123a514b", "metadata": {}, "source": [ "## Overview\n", "\n", "We’re now ready to start learning the Python language itself.\n", "\n", "In this lecture, we will write and then pick apart small Python programs.\n", "\n", "The objective is to introduce you to basic Python syntax and data structures.\n", "\n", "Deeper concepts will be covered in later lectures.\n", "\n", "You should have read the [lecture](https://python-programming.quantecon.org/getting_started.html) on getting started with Python before beginning this one." ] }, { "cell_type": "markdown", "id": "dd04aadf", "metadata": {}, "source": [ "## The Task: Plotting a White Noise Process\n", "\n", "Suppose we want to simulate and plot the white noise\n", "process $ \\epsilon_0, \\epsilon_1, \\ldots, \\epsilon_T $, where each draw $ \\epsilon_t $ is independent standard normal.\n", "\n", "In other words, we want to generate figures that look something like this:\n", "\n", "![https://python-programming.quantecon.org/_static/lecture_specific/python_by_example/test_program_1_updated.png](https://python-programming.quantecon.org/_static/lecture_specific/python_by_example/test_program_1_updated.png)\n", "\n", " \n", "(Here $ t $ is on the horizontal axis and $ \\epsilon_t $ is on the\n", "vertical axis.)\n", "\n", "We’ll do this in several different ways, each time learning something more\n", "about Python.\n", "\n", "We run the following command first, which helps ensure that plots appear in the\n", "notebook if you run it on your own machine." ] }, { "cell_type": "code", "execution_count": 1, "id": "0cc7e562", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "1671a1d3", "metadata": {}, "source": [ "## Version 1\n", "\n", "\n", "\n", "Here are a few lines of code that perform the task we set" ] }, { "cell_type": "code", "execution_count": 2, "id": "f9ef3835", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['figure.figsize'] = (5,3)\n", "\n", "ϵ_values = np.random.randn(100)\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "948de567", "metadata": {}, "source": [ "Let’s break this program down and see how it works.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "id": "f801fb81", "metadata": {}, "source": [ "### Imports\n", "\n", "The first two lines of the program import functionality from external code\n", "libraries.\n", "\n", "The first line imports [NumPy](https://python-programming.quantecon.org/numpy.html), a favorite Python package for tasks like\n", "\n", "- working with arrays (vectors and matrices) \n", "- common mathematical functions like `cos` and `sqrt` \n", "- generating random numbers \n", "- linear algebra, etc. \n", "\n", "\n", "After `import numpy as np` we have access to these attributes via the syntax `np.attribute`.\n", "\n", "Here’s two more examples" ] }, { "cell_type": "code", "execution_count": 3, "id": "a783ea17", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(4)" ] }, { "cell_type": "code", "execution_count": 4, "id": "6adab364", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3862943611198906" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.log(4)" ] }, { "cell_type": "markdown", "id": "ed236510", "metadata": {}, "source": [ "We could also use the following syntax:" ] }, { "cell_type": "code", "execution_count": 5, "id": "80d2daad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy\n", "\n", "numpy.sqrt(4)" ] }, { "cell_type": "markdown", "id": "71c05b11", "metadata": {}, "source": [ "But the former method (using the short name `np`) is convenient and more standard." ] }, { "cell_type": "markdown", "id": "b581441f", "metadata": {}, "source": [ "#### Why So Many Imports?\n", "\n", "Python programs typically require several import statements.\n", "\n", "The reason is that the core language is deliberately kept small, so that it’s easy to learn and maintain.\n", "\n", "When you want to do something interesting with Python, you almost always need\n", "to import additional functionality." ] }, { "cell_type": "markdown", "id": "a4540370", "metadata": {}, "source": [ "#### Packages\n", "\n", "\n", "\n", "As stated above, NumPy is a Python *package*.\n", "\n", "Packages are used by developers to organize code they wish to share.\n", "\n", "In fact, a package is just a directory containing\n", "\n", "1. files with Python code — called **modules** in Python speak \n", "1. possibly some compiled code that can be accessed by Python (e.g., functions compiled from C or FORTRAN code) \n", "1. a file called `__init__.py` that specifies what will be executed when we type `import package_name` \n", "\n", "\n", "You can check the location of your `__init__.py` for NumPy in python by running the code:" ] }, { "cell_type": "markdown", "id": "7c7e5c25", "metadata": { "hide-output": false }, "source": [ "```ipython\n", "import numpy as np\n", "\n", "print(np.__file__)\n", "```\n" ] }, { "cell_type": "markdown", "id": "368a8338", "metadata": {}, "source": [ "#### Subpackages\n", "\n", "\n", "\n", "Consider the line `ϵ_values = np.random.randn(100)`.\n", "\n", "Here `np` refers to the package NumPy, while `random` is a **subpackage** of NumPy.\n", "\n", "Subpackages are just packages that are subdirectories of another package.\n", "\n", "For instance, you can find folder `random` under the directory of NumPy." ] }, { "cell_type": "markdown", "id": "48753714", "metadata": {}, "source": [ "### Importing Names Directly\n", "\n", "Recall this code that we saw above" ] }, { "cell_type": "code", "execution_count": 6, "id": "d501633b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "\n", "np.sqrt(4)" ] }, { "cell_type": "markdown", "id": "a6648e84", "metadata": {}, "source": [ "Here’s another way to access NumPy’s square root function" ] }, { "cell_type": "code", "execution_count": 7, "id": "fafee420", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from numpy import sqrt\n", "\n", "sqrt(4)" ] }, { "cell_type": "markdown", "id": "63fb5694", "metadata": {}, "source": [ "This is also fine.\n", "\n", "The advantage is less typing if we use `sqrt` often in our code.\n", "\n", "The disadvantage is that, in a long program, these two lines might be\n", "separated by many other lines.\n", "\n", "Then it’s harder for readers to know where `sqrt` came from, should they wish to." ] }, { "cell_type": "markdown", "id": "a668dae2", "metadata": {}, "source": [ "### Random Draws\n", "\n", "Returning to our program that plots white noise, the remaining three lines\n", "after the import statements are" ] }, { "cell_type": "code", "execution_count": 8, "id": "dcc4d204", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ϵ_values = np.random.randn(100)\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c2a56d62", "metadata": {}, "source": [ "The first line generates 100 (quasi) independent standard normals and stores\n", "them in `ϵ_values`.\n", "\n", "The next two lines genererate the plot.\n", "\n", "We can and will look at various ways to configure and improve this plot below." ] }, { "cell_type": "markdown", "id": "c9889d3d", "metadata": {}, "source": [ "### Note: What is a Random Seeds" ] }, { "cell_type": "code", "execution_count": 9, "id": "11e485ed", "metadata": {}, "outputs": [], "source": [ "np.random.seed(100)" ] }, { "cell_type": "code", "execution_count": 10, "id": "4d8223a1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ϵ_values = np.random.randn(100)\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "4010760d", "metadata": {}, "outputs": [], "source": [ "np.random.seed(100)" ] }, { "cell_type": "code", "execution_count": 12, "id": "3f12df22", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ϵ_values = np.random.randn(100)\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4ed227fb", "metadata": {}, "source": [ "## Alternative Implementations\n", "\n", "Let’s try writing some alternative versions of [our first program](#ourfirstprog), which plotted IID draws from the standard normal distribution.\n", "\n", "The programs below are less efficient than the original one, and hence\n", "somewhat artificial.\n", "\n", "But they do help us illustrate some important Python syntax and semantics in a familiar setting." ] }, { "cell_type": "markdown", "id": "a864e098", "metadata": {}, "source": [ "### A Version with a For Loop\n", "\n", "Here’s a version that illustrates `for` loops and Python lists.\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 13, "id": "1676245d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts_length = 100\n", "ϵ_values = [] # empty list\n", "\n", "for i in range(ts_length):\n", " e = np.random.randn()\n", " ϵ_values.append(e)\n", "\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "093877de", "metadata": {}, "source": [ "In brief,\n", "\n", "- The first line sets the desired length of the time series. \n", "- The next line creates an empty *list* called `ϵ_values` that will store the $ \\epsilon_t $ values as we generate them. \n", "- The statement `# empty list` is a *comment*, and is ignored by Python’s interpreter. \n", "- The next three lines are the `for` loop, which repeatedly draws a new random number $ \\epsilon_t $ and appends it to the end of the list `ϵ_values`. \n", "- The last two lines generate the plot and display it to the user. \n", "\n", "\n", "Let’s study some parts of this program in more detail.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "id": "85eba02a", "metadata": {}, "source": [ "### Lists\n", "\n", "\n", "\n", "Consider the statement `ϵ_values = []`, which creates an empty list.\n", "\n", "Lists are a *native Python data structure* used to group a collection of objects.\n", "\n", "Items in lists are ordered, and duplicates are allowed in lists.\n", "\n", "For example, try" ] }, { "cell_type": "code", "execution_count": 14, "id": "ee1f60d5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "list" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = [10, 'foo', False]\n", "type(x)" ] }, { "cell_type": "markdown", "id": "abb82775", "metadata": {}, "source": [ "The first element of `x` is an [integer](https://en.wikipedia.org/wiki/Integer_%28computer_science%29), the next is a [string](https://en.wikipedia.org/wiki/String_%28computer_science%29), and the third is a [Boolean value](https://en.wikipedia.org/wiki/Boolean_data_type).\n", "\n", "When adding a value to a list, we can use the syntax `list_name.append(some_value)`" ] }, { "cell_type": "code", "execution_count": 15, "id": "dc1b46c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10, 'foo', False]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 16, "id": "2ce1d842", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10, 'foo', False, 2.5]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.append(2.5)\n", "x" ] }, { "cell_type": "markdown", "id": "2621e155", "metadata": {}, "source": [ "Here `append()` is what’s called a *method*, which is a function “attached to” an object—in this case, the list `x`.\n", "\n", "We’ll learn all about methods [later on](https://python-programming.quantecon.org/oop_intro.html), but just to give you some idea,\n", "\n", "- Python objects such as lists, strings, etc. all have methods that are used to manipulate the data contained in the object. \n", "- String objects have [string methods](https://docs.python.org/3/library/stdtypes.html#string-methods), list objects have [list methods](https://docs.python.org/3/tutorial/datastructures.html#more-on-lists), etc. \n", "\n", "\n", "Another useful list method is `pop()`" ] }, { "cell_type": "code", "execution_count": 17, "id": "20b510ae", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10, 'foo', False, 2.5]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 18, "id": "e0f4985c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.5" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.pop()" ] }, { "cell_type": "code", "execution_count": 19, "id": "7840fbbc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10, 'foo', False]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "markdown", "id": "5bc40e53", "metadata": {}, "source": [ "Lists in Python are zero-based (as in C, Java or Go), so the first element is referenced by `x[0]`" ] }, { "cell_type": "code", "execution_count": 20, "id": "537085ff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x[0] # first element of x" ] }, { "cell_type": "code", "execution_count": 21, "id": "7137175e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'foo'" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x[1] # second element of x" ] }, { "cell_type": "markdown", "id": "8e4c3bb9", "metadata": {}, "source": [ "### The For Loop\n", "\n", "\n", "\n", "Now let’s consider the `for` loop from [the program above](#firstloopprog), which was" ] }, { "cell_type": "code", "execution_count": 22, "id": "4c9df0ed", "metadata": {}, "outputs": [], "source": [ "for i in range(ts_length):\n", " e = np.random.randn()\n", " ϵ_values.append(e)" ] }, { "cell_type": "markdown", "id": "e9a328dd", "metadata": {}, "source": [ "Python executes the two indented lines `ts_length` times before moving on.\n", "\n", "These two lines are called a `code block`, since they comprise the “block” of code that we are looping over.\n", "\n", "Unlike most other languages, Python knows the extent of the code block *only from indentation*.\n", "\n", "In our program, indentation decreases after line `ϵ_values.append(e)`, telling Python that this line marks the lower limit of the code block.\n", "\n", "More on indentation below—for now, let’s look at another example of a `for` loop" ] }, { "cell_type": "code", "execution_count": 23, "id": "3989d19d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The plural of dog is dogs\n", "The plural of cat is cats\n", "The plural of bird is birds\n" ] } ], "source": [ "animals = ['dog', 'cat', 'bird']\n", "for animal in animals:\n", " print(\"The plural of \" + animal + \" is \" + animal + \"s\")" ] }, { "cell_type": "markdown", "id": "6f6c25df", "metadata": {}, "source": [ "This example helps to clarify how the `for` loop works: When we execute a\n", "loop of the form" ] }, { "cell_type": "markdown", "id": "dbbce3d9", "metadata": { "hide-output": false }, "source": [ "```python3\n", "for variable_name in sequence:\n", " \n", "```\n" ] }, { "cell_type": "markdown", "id": "24e8c514", "metadata": {}, "source": [ "The Python interpreter performs the following:\n", "\n", "- For each element of the `sequence`, it “binds” the name `variable_name` to that element and then executes the code block. \n", "\n", "\n", "The `sequence` object can in fact be a very general object, as we’ll see\n", "soon enough." ] }, { "cell_type": "markdown", "id": "cd045b26", "metadata": {}, "source": [ "### A Comment on Indentation\n", "\n", "\n", "\n", "In discussing the `for` loop, we explained that the code blocks being looped over are delimited by indentation.\n", "\n", "In fact, in Python, **all** code blocks (i.e., those occurring inside loops, if clauses, function definitions, etc.) are delimited by indentation.\n", "\n", "Thus, unlike most other languages, whitespace in Python code affects the output of the program.\n", "\n", "Once you get used to it, this is a good thing: It\n", "\n", "- forces clean, consistent indentation, improving readability \n", "- removes clutter, such as the brackets or end statements used in other languages \n", "\n", "\n", "On the other hand, it takes a bit of care to get right, so please remember:\n", "\n", "- The line before the start of a code block always ends in a colon \n", " - `for i in range(10):` \n", " - `if x > y:` \n", " - `while x < 100:` \n", " - etc., etc. \n", "- All lines in a code block **must have the same amount of indentation**. \n", "- The Python standard is 4 spaces, and that’s what you should use. " ] }, { "cell_type": "markdown", "id": "e210f170", "metadata": {}, "source": [ "### While Loops\n", "\n", "\n", "\n", "The `for` loop is the most common technique for iteration in Python.\n", "\n", "But, for the purpose of illustration, let’s modify [the program above](#firstloopprog) to use a `while` loop instead.\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 24, "id": "2c9effd1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts_length = 100\n", "ϵ_values = []\n", "i = 0\n", "while i < ts_length:\n", " e = np.random.randn()\n", " ϵ_values.append(e)\n", " i = i + 1\n", "plt.plot(ϵ_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "bae1c9a2", "metadata": {}, "source": [ "A while loop will keep executing the code block delimited by indentation until the condition (`i < ts_length`) is satisfied.\n", "\n", "In this case, the program will keep adding values to the list `ϵ_values` until `i` equals `ts_length`:" ] }, { "cell_type": "code", "execution_count": 25, "id": "7f9acae6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "i == ts_length #the ending condition for the while loop" ] }, { "cell_type": "markdown", "id": "f6a4977e", "metadata": {}, "source": [ "Note that\n", "\n", "- the code block for the `while` loop is again delimited only by indentation. \n", "- the statement `i = i + 1` can be replaced by `i += 1`. " ] }, { "cell_type": "markdown", "id": "9fe1230f", "metadata": {}, "source": [ "## Another Application\n", "\n", "Let’s do one more application before we turn to exercises.\n", "\n", "In this application, we plot the balance of a bank account over time.\n", "\n", "There are no withdraws over the time period, the last date of which is denoted\n", "by $ T $.\n", "\n", "The initial balance is $ b_0 $ and the interest rate is $ r $.\n", "\n", "The balance updates from period $ t $ to $ t+1 $ according to $ b_{t+1} = (1 + r) b_t $.\n", "\n", "In the code below, we generate and plot the sequence $ b_0, b_1, \\ldots, b_T $.\n", "\n", "Instead of using a Python list to store this sequence, we will use a NumPy\n", "array." ] }, { "cell_type": "code", "execution_count": 26, "id": "f3463484", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r = 0.025 # interest rate\n", "T = 50 # end date\n", "b = np.empty(T+1) # an empty NumPy array, to store all b_t\n", "b[0] = 10 # initial balance\n", "\n", "for t in range(T):\n", " b[t+1] = (1 + r) * b[t]\n", "\n", "plt.plot(b, label='bank balance')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9278f1b9", "metadata": {}, "source": [ "The statement `b = np.empty(T+1)` allocates storage in memory for `T+1`\n", "(floating point) numbers.\n", "\n", "These numbers are filled in by the `for` loop.\n", "\n", "Allocating memory at the start is more efficient than using a Python list and\n", "`append`, since the latter must repeatedly ask for storage space from the\n", "operating system.\n", "\n", "Notice that we added a legend to the plot — a feature you will be asked to\n", "use in the exercises." ] }, { "cell_type": "markdown", "id": "0e323dec", "metadata": {}, "source": [ "## Exercises\n", "\n", "Now we turn to exercises. It is important that you complete them before\n", "continuing, since they present new concepts we will need." ] }, { "cell_type": "markdown", "id": "bf406a06", "metadata": {}, "source": [ "## Exercise 3.1\n", "\n", "Your first task is to simulate and plot the correlated time series\n", "\n", "$$\n", "x_{t+1} = \\alpha \\, x_t + \\epsilon_{t+1}\n", "\\quad \\text{where} \\quad\n", "x_0 = 0\n", "\\quad \\text{and} \\quad t = 0,\\ldots,T\n", "$$\n", "\n", "The sequence of shocks $ \\{\\epsilon_t\\} $ is assumed to be IID and standard normal.\n", "\n", "In your solution, restrict your import statements to" ] }, { "cell_type": "code", "execution_count": 27, "id": "4da50a38", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "53e448a3", "metadata": {}, "source": [ "Set $ T=200 $ and $ \\alpha = 0.9 $." ] }, { "cell_type": "markdown", "id": "8eeda2bc", "metadata": {}, "source": [ "## Solution to[ Exercise 3.1](https://python-programming.quantecon.org/#pbe_ex1)\n", "\n", "Here’s one solution." ] }, { "cell_type": "code", "execution_count": 28, "id": "4578e185", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α = 0.9\n", "T = 200\n", "x = np.empty(T+1)\n", "x[0] = 0\n", "\n", "for t in range(T):\n", " x[t+1] = α * x[t] + np.random.randn()\n", "\n", "plt.plot(x)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b1ee91d3", "metadata": {}, "source": [ "## Exercise 3.2\n", "\n", "Starting with your solution to exercise 1, plot three simulated time series,\n", "one for each of the cases $ \\alpha=0 $, $ \\alpha=0.8 $ and $ \\alpha=0.98 $.\n", "\n", "Use a `for` loop to step through the $ \\alpha $ values.\n", "\n", "If you can, add a legend, to help distinguish between the three time series.\n", "\n", "Hints:\n", "\n", "- If you call the `plot()` function multiple times before calling `show()`, all of the lines you produce will end up on the same figure. \n", "- For the legend, noted that the expression `'foo' + str(42)` evaluates to `'foo42'`. " ] }, { "cell_type": "markdown", "id": "682f5011", "metadata": {}, "source": [ "## Solution to[ Exercise 3.2](https://python-programming.quantecon.org/#pbe_ex2)" ] }, { "cell_type": "code", "execution_count": 29, "id": "c74097b2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α_values = [0.0, 0.8, 0.98]\n", "T = 200\n", "x = np.empty(T+1)\n", "\n", "for α in α_values:\n", " x[0] = 0\n", " for t in range(T):\n", " x[t+1] = α * x[t] + np.random.randn()\n", " plt.plot(x, label=f'$\\\\alpha = {α}$')\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6cd8434a", "metadata": {}, "source": [ "Note: `f'\\$\\\\alpha = {α}\\$'` in the solution is an application of [f-String](https://docs.python.org/3/tutorial/inputoutput.html#tut-f-strings), which allows you to use `{}` to contain an expression.\n", "\n", "The contained expression will be evaluated, and the result will be placed into the string." ] }, { "cell_type": "markdown", "id": "710b5d7c", "metadata": {}, "source": [ "## Exercise 3.3\n", "\n", "Similar to the previous exercises, plot the time series\n", "\n", "$$\n", "x_{t+1} = \\alpha \\, |x_t| + \\epsilon_{t+1}\n", "\\quad \\text{where} \\quad\n", "x_0 = 0\n", "\\quad \\text{and} \\quad t = 0,\\ldots,T\n", "$$\n", "\n", "Use $ T=200 $, $ \\alpha = 0.9 $ and $ \\{\\epsilon_t\\} $ as before.\n", "\n", "Search online for a function that can be used to compute the absolute value $ |x_t| $." ] }, { "cell_type": "markdown", "id": "1cd2da19", "metadata": {}, "source": [ "## Solution to[ Exercise 3.3](https://python-programming.quantecon.org/#pbe_ex3)\n", "\n", "Here’s one solution:" ] }, { "cell_type": "code", "execution_count": 30, "id": "8996551f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α = 0.9\n", "T = 200\n", "x = np.empty(T+1)\n", "x[0] = 0\n", "\n", "for t in range(T):\n", " x[t+1] = α * np.abs(x[t]) + np.random.randn()\n", "\n", "plt.plot(x)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "97ff965f", "metadata": {}, "source": [ "## Exercise 3.4\n", "\n", "One important aspect of essentially all programming languages is branching and\n", "conditions.\n", "\n", "In Python, conditions are usually implemented with if–else syntax.\n", "\n", "Here’s an example, that prints -1 for each negative number in an array and 1\n", "for each nonnegative number" ] }, { "cell_type": "code", "execution_count": 31, "id": "6080e122", "metadata": {}, "outputs": [], "source": [ "numbers = [-9, 2.3, -11, 0]" ] }, { "cell_type": "code", "execution_count": 32, "id": "165fb094", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1\n", "1\n", "-1\n", "1\n" ] } ], "source": [ "for x in numbers:\n", " if x < 0:\n", " print(-1)\n", " else:\n", " print(1)" ] }, { "cell_type": "markdown", "id": "e5a8f5fd", "metadata": {}, "source": [ "Now, write a new solution to Exercise 3 that does not use an existing function\n", "to compute the absolute value.\n", "\n", "Replace this existing function with an if–else condition." ] }, { "cell_type": "markdown", "id": "4cadf82a", "metadata": {}, "source": [ "## Solution to[ Exercise 3.4](https://python-programming.quantecon.org/#pbe_ex4)\n", "\n", "Here’s one way:" ] }, { "cell_type": "code", "execution_count": 33, "id": "da4679e0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α = 0.9\n", "T = 200\n", "x = np.empty(T+1)\n", "x[0] = 0\n", "\n", "for t in range(T):\n", " if x[t] < 0:\n", " abs_x = - x[t]\n", " else:\n", " abs_x = x[t]\n", " x[t+1] = α * abs_x + np.random.randn()\n", "\n", "plt.plot(x)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cd087f1b", "metadata": {}, "source": [ "Here’s a shorter way to write the same thing:" ] }, { "cell_type": "code", "execution_count": 34, "id": "84d67d27", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "α = 0.9\n", "T = 200\n", "x = np.empty(T+1)\n", "x[0] = 0\n", "\n", "for t in range(T):\n", " abs_x = - x[t] if x[t] < 0 else x[t]\n", " x[t+1] = α * abs_x + np.random.randn()\n", "\n", "plt.plot(x)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1c7fc965", "metadata": {}, "source": [ "## Exercise 3.5\n", "\n", "Here’s a harder exercise, that takes some thought and planning.\n", "\n", "The task is to compute an approximation to $ \\pi $ using [Monte Carlo](https://en.wikipedia.org/wiki/Monte_Carlo_method).\n", "\n", "Use no imports besides" ] }, { "cell_type": "code", "execution_count": 35, "id": "3c65f875", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "id": "133925e8", "metadata": {}, "source": [ "Your hints are as follows:\n", "\n", "- If $ U $ is a bivariate uniform random variable on the unit square $ (0, 1)^2 $, then the probability that $ U $ lies in a subset $ B $ of $ (0,1)^2 $ is equal to the area of $ B $. \n", "- If $ U_1,\\ldots,U_n $ are IID copies of $ U $, then, as $ n $ gets large, the fraction that falls in $ B $, converges to the probability of landing in $ B $. \n", "- For a circle, $ area = \\pi * radius^2 $. " ] }, { "cell_type": "markdown", "id": "e25a7b53", "metadata": {}, "source": [ "## Solution to[ Exercise 3.5](https://python-programming.quantecon.org/#pbe_ex5)\n", "\n", "Consider the circle of diameter 1 embedded in the unit square.\n", "\n", "Let $ A $ be its area and let $ r=1/2 $ be its radius.\n", "\n", "If we know $ \\pi $ then we can compute $ A $ via\n", "$ A = \\pi r^2 $.\n", "\n", "But here the point is to compute $ \\pi $, which we can do by\n", "$ \\pi = A / r^2 $.\n", "\n", "Summary: If we can estimate the area of a circle with diameter 1, then dividing\n", "by $ r^2 = (1/2)^2 = 1/4 $ gives an estimate of $ \\pi $.\n", "\n", "We estimate the area by sampling bivariate uniforms and looking at the\n", "fraction that falls into the circle." ] }, { "cell_type": "code", "execution_count": 36, "id": "e59ff3dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.143048\n" ] } ], "source": [ "n = 1000000 # sample size for Monte Carlo simulation\n", "\n", "count = 0\n", "for i in range(n):\n", "\n", " # drawing random positions on the square\n", " u, v = np.random.uniform(), np.random.uniform()\n", "\n", " # check whether the point falls within the boundary\n", " # of the unit circle centred at (0.5,0.5)\n", " d = np.sqrt((u - 0.5)**2 + (v - 0.5)**2)\n", "\n", " # if it falls within the inscribed circle, \n", " # add it to the count\n", " if d < 0.5:\n", " count += 1\n", "\n", "area_estimate = count / n\n", "\n", "print(area_estimate * 4) # dividing by radius**2" ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 5 }