notebook_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Math 266 Python Exercise 1. Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25e6dab7-01d3-4ddb-90c6-da7d27e291f9",
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   "source": [
    "You are currently viewing a Jupyter notebook. Recall that a notebook contains text and code cells. This is a text cell. To execute or \"run\" a cell you can hover your mouse over the cell and press the run arrow on the left side of the cell or press shift enter."
   ]
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  {
   "cell_type": "markdown",
   "id": "feb90558-e120-4fe3-9b98-d1f3ebf164f9",
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   "source": [
    "When you exit Google Colab this notebook will not persist on your G drive.  So you need to save a copy in your Google Drive known as your \"G drive\". To do this click the file tab above and select \"save a copy in drive\".  Once you have done this you can exit and then return, reload and edit the notebook further if you like."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9449588-0265-4bf1-ac5e-110c0acb0f06",
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   "source": [
    "In this exercise we will show how to create and manipulate matrices using Python.  We will introduce the notion of a \"data matrix\".  Which is simple a matrix that holds data.  Specifically we will look at a \"ratings matrix\".  This matrix stores the ratings that users gave specific movies.  Each row in this matrix will correspond to a user and each column a movie.  Since the columns are just identified by numbers we use a python dictionary that will map column numbers into movie names.  This all we become more clear as you work the exercises."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07cf0a70-b09b-4b13-8ac5-951d448d03f7",
   "metadata": {},
   "source": [
    "For this exercise please read each cell below and follow instructions. The output for some command cells could already be displayed but you need to rerun each cell."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a53b53b9-6123-46f9-87c2-5177debec3b3",
   "metadata": {},
   "source": [
    "Execute the following cell to load necessary modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e791c658-5e3c-41da-92f2-371c880d9c33",
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   "outputs": [],
   "source": [
    "! pip install wget\n",
    "import numpy as np\n",
    "import wget\n",
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f692d92b-8855-407b-9849-7977b50504b0",
   "metadata": {},
   "source": [
    "## Create a matrix using numpy\n",
    "\n",
    "To create the matrix:  \n",
    "\n",
    "$ \\begin{bmatrix}1 & 2 \\\\3 & 4 \\end{bmatrix} $\n",
    "\n",
    " execute the cell below. After execution try experimenting by changing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9c6f243-dad4-4888-96ac-c55f9f09fbab",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = np.array([[1,20],[3,4]])\n",
    "print(mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad205c75-0d59-45bb-b690-b06b604a5396",
   "metadata": {},
   "source": [
    "We can perform various operations or \"methods\" on the matrix by appending a period  and then the  command to the matrix name.  For example to find the average of all the values in the matrix  called \"mat\" you should enter\"\n",
    "```Python\n",
    "mat.mean()\n",
    "```\n",
    "To see this in action execute the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ad164680-c581-4f56-a5c8-63512d2993ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6a628c5a-7032-470f-918c-a842c9942bc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat.mean(axis=0)  # this command will find the mean of each column.  Change axis to 1 to see the row mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8277e809-8060-4b25-b811-f1b0a743d17f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "mat.shape # this tells us the size or \"shape\" of the matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7a522a97-c16c-4752-92f0-835aec7a9b85",
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   "outputs": [],
   "source": [
    "3*mat # this command returns a scalar multiple of the matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05ed57b0-b0d2-4132-a807-7bf44d60ea42",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(mat) # note that the original matrix is not changed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8469e20-b860-4726-a769-f786134bc98d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = 3 * mat # this command will change the original matix\n",
    "print(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6599ff3c-63f0-413c-97cc-b8803dac99fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat = np.arange(1,26).reshape(5,5)  # here we create a new 5X5 matrix\n",
    "new_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63fc4b97-601a-4763-afde-46669c45e91d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(new_mat) # below we see the same matrix with rows and columns labeled in bold.\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9275966-2fd2-421a-8815-f9018e529495",
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   "source": [
    "## Matrix indexing\n",
    "In the above display we see python index values start at zero. To access the (i,j) entry the matrix call mat you enter:\n",
    "```python\n",
    "mat[i,j]\n",
    "\n",
    "```\n",
    "Again be aware that Python uses zero based indexing.  For example to access the entry in the first row and column of new_mat.  We issue the command below.  Experiment and change i,j values and rerun the cell and compare your results with the matrix above.\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e442ea42-b663-4165-8a71-a3b2a7e47d5a",
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   "outputs": [],
   "source": [
    "new_mat[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "edf03e20-76dd-4585-a992-806e34bb990e",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat[1] # this returns the entire second row ~ experiment!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "184018ad-1d51-4f83-9034-a60ad19a2506",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat[:,1] # this returns an entire column. However notice a column vector is not returned, just an array.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c06224a-f947-49e3-bae7-7c650406e753",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat[:,1].reshape(5,1) # here we convert the array to a column\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb460714-6663-4045-9514-2a872b8a6f5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat.sum(axis=0) # returns the sum of all the columns (axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f60e6bf-09fb-4eec-ae0f-a3113c850427",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_mat.sum(axis=1) # returns the sum of all the rows (axis = 1), confirm the sum of elements in the first row is 15"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc52c8eb-defc-4c1f-9cfc-2c4ee2c448e4",
   "metadata": {},
   "source": [
    "<h1 style=\"color red; > Matrix Applications </h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32d60438-e470-452f-8bf2-d715da3b81a7",
   "metadata": {},
   "source": [
    "## Matrix Applications\n",
    "    \n",
    "    In our first application we will investigate the use of a matrix to store movie ratings data. In the image below we see a  partial display of a ratings matrix. Note that User-0 gave movie-0 a rating of 5.  A zero indicates that the user did not rate the movie. For example User-1 did not rate Movies 1-8."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2485113d-4468-475e-8371-41f955a2c6ba",
   "metadata": {},
   "source": [
    "![ratings](https://github.com/rmartin977/Math-266/blob/main/ratings_matrix.png?raw=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb7aec1e-67d2-47b5-9323-de66a1322a3f",
   "metadata": {},
   "source": [
    "Execute the following cell to load the ratings matrix that we will be working with in this exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a15d38e4-51fd-41f3-87f6-ac86565ff121",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_1 = wget.download(\"https://github.com/rmartin977/Math-266/blob/main/ratings_matrix.npy?raw=true\")\n",
    "ratings = np.load(file_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a57fd6c-cfed-4a4e-8fbf-b702c8eb0ce4",
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings.shape  # notice there are 1682 movies and 943 users"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2e18deb-3111-49e1-aad8-e0a049bcedb8",
   "metadata": {},
   "source": [
    "Execute the cell below to view part of the ratings matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "593f9a72-6b15-48ca-8bf4-a804afef0840",
   "metadata": {},
   "outputs": [],
   "source": [
    "rdf = pd.DataFrame(ratings) # below we get a view the first 5 rows and 15 columns of our ratings matrix.\n",
    "#                             It is not necessary to understand the code that generates  this output.\n",
    "rdf.iloc[:5,:15] # User ID-12 gave Movie ID-4 1 star."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22633b9a-48e5-4494-b0fa-bcf28f265bef",
   "metadata": {},
   "source": [
    "To convert movie ID's to titles we need to download a python dictionary.\n",
    "https://www.w3schools.com/python/python_dictionaries.asp\n",
    "\n",
    "Execute the following cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e7928dcc-4ee9-4c01-8a1f-dd4b488a5613",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_2 = wget.download(\"https://github.com/rmartin977/Math-266/blob/main/dictionary.npy?raw=true\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c4736c18-b47b-48ab-8935-5936e850f2fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "titles = np.load(file_2,allow_pickle=True).item()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e795b1a3-cd6a-4e3e-8de7-4ac3c92d5ba4",
   "metadata": {},
   "source": [
    "## The dictionary called \"titles\" will map movie ids to movie names.  Execute the following cell to see the first 10 entries in the dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e23a9b4-f4bb-4fba-b884-12f433fef5fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "dict(list(titles.items())[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b8d6787-ce02-459c-8451-30ffd57e23f8",
   "metadata": {
    "tags": []
   },
   "source": [
    "## To determine the title for a given Movie ID just enter titles[ID].  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "425175df-481c-4f18-a717-d4a8f3f62f53",
   "metadata": {},
   "outputs": [],
   "source": [
    "titles[0]# Note the ID-0 corresponds to \"Toy Story\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45ad8ee4-3196-4ca3-aec7-a29e5f7650ee",
   "metadata": {},
   "source": [
    "How to find a rating.  To see what rating a given user gave a given movie just enter:  ratings(movie_id,user_id)\n",
    "\n",
    "Execute the following cell to see what rating user #22 gave to movie id 0.  We should see 5 stars was given."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c67aae40-9bb6-4e50-ba90-22c79d7b4037",
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings[0,22] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "662d269a-3c4c-4fd1-ad4d-99fbc2675ccc",
   "metadata": {},
   "source": [
    "Suppose we want to know what movie got the largest overall score.  That is, we total the ratings for each movie and determine which one got the largest result.  To do this we simply sum all the rows and find the largest outcome. Note that we store all of the totals in array called \"scores\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "805dba98-2983-4407-a4f4-ffa8b7fbadc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = ratings.sum(axis=1) # scores is an array of scores for each row\n",
    "scores.shape # the size of array is the number of movies  1682"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a70acdf-bf45-4cdb-a693-b4d78a3c9823",
   "metadata": {},
   "outputs": [],
   "source": [
    "scores[:10] # this displays the first 10 scores, notice movie ID-1 got a score of 420."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f06fb67e-8e59-4e60-b2a4-d4cc51619f09",
   "metadata": {},
   "outputs": [],
   "source": [
    "scores.max() # this tells us the largest value in the scores array is 2541. \n",
    "#            But what movie does this correspond to? We use the numpy argmax function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbada7f8-b8a6-4f66-9998-bbe25b53139e",
   "metadata": {},
   "source": [
    "The max function returns the maximum value in an array.  The argmax function will return the index or position in the array where the maximum occurs. execute the cell below and note that the maximum in scores occurs at index value 49."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcb37705-d6a8-432c-9d9a-3a9944363466",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.argmax(scores) # movie ID-49 go the largest score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d36fb69f-84cd-4b80-a610-6f00abaadb5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "scores[49] # Yep ID-49 got 2541 stars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d5d4744-0daa-42de-b803-4876bc99785c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#and the winner is:\n",
    "titles[49]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e01acdec-0b53-4a7e-b87c-ced9cb05cdf6",
   "metadata": {},
   "source": [
    "This is just the beginning of our exploring the ratings matrix.  Much more later but enough for now."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "687be57d-f3ed-4d53-aa2e-5b3b17fa984e",
   "metadata": {},
   "source": [
    "## Your turn...\n",
    "Answer the following 6 questions.  Go to gradescope  Project #2 ~ python exericse 1. and enter your answers.\n",
    "\n",
    "1. What rating did user 12 give to the movie 'Toy Story\"?\n",
    "2. What is the title of the movie with ID-22?\n",
    "3. What is total score for movie ID-22?\n",
    "4. What user awarded the most points or stars?\n",
    "5. What movie comes in second place in terms of largest overall score.  Hint: look at np.argsort.  To get help on a command type np.argsort? in command cell and execute.\n",
    "6. What is the average rating for \"Star Wars (1977)\" movie id 49?  You can not include the zeros when computing the average.  Hint: look at the np.count_nonzero command.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4bd8db4e-b7fc-4363-8ba8-bc98b1595947",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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