{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cceb0c53-86e0-416b-b626-c8ba5e2f3695",
   "metadata": {},
   "source": [
    "### <center>San Jose State University<br>Department of Applied Data Science<br><br>**DATA 200<br>Computational Programming for Data Analytics**<br><br>Spring 2024<br>Instructor: Ron Mak<br><br>**Assignment #6<br>Matrix Multiplication with `numpy`**<br><br>Assigned: March 7, 2024<br>Due: March 14 at 5:30 PM<br><br>100 points maximum<br>Individual work only!</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65e169fd-3b42-444c-8002-0921ed6dfc01",
   "metadata": {},
   "source": [
    "## Store preferences"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "862fcbc4-5c38-4c87-b08f-8b6bd09405f0",
   "metadata": {},
   "source": [
    "#### Three stores A, B, and C compete for a given set of customers in a neighborhood.\n",
    "\n",
    "#### The diagram below shows the probabilities that a customer would stay in a store, or switch to another store after shopping for one year. The probabilities are shown as percentages. For example 75% means 0.75 probability.\n",
    "\n",
    "![Screenshot 2023-03-07 at 10.22.19 PM.png](attachment:db077723-2e8f-45e6-aca5-f5ba030ea43e.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68359bba-a104-4dc3-8c51-1be32e79e1f7",
   "metadata": {},
   "source": [
    "#### We can represent the probabilities as a **switch probabilities matrix**:\n",
    "|       | A    | B    | C    |\n",
    "| ---   | ---  | ---  | ---  |\n",
    "| **A** | 0.70 | 0.15 | 0.15 |\n",
    "| **B** | 0.20 | 0.80 | 0.15 |\n",
    "| **C** | 0.10 | 0.05 | 0.70 |\n",
    "#### Each column contains the probability of staying or switching. For example, the **B** column says the probability of switching from Store B to Store A is 15%, the probability of staying in Store B is 80%, and the probability of sitching to Store C is 5%."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34a059f2-963c-491a-9cd2-ad010e9d4c8f",
   "metadata": {},
   "source": [
    "#### We can represent the initial state of the proportion of customers in each store as a vector:\n",
    "|       | Initial state |\n",
    "| ---   | :-:  |\n",
    "| **A** | 0.15 |\n",
    "| **B** | 0.20 |\n",
    "| **C** | 0.65 |\n",
    "#### At the start, 15% of the customers shop at Store A, 20% shop at Store B, and 65% shop at Store C."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcb14e2d-7992-4a02-b34a-d89323eb421f",
   "metadata": {},
   "source": [
    "#### **PROBLEM 1.** [20 points] Create a `numpy` matrix (a 2-d array) `P` that contains the numeric values of the switch probabilities matrix. Print the matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d672e56-8f6e-4499-86aa-9799038a7e6b",
   "metadata": {},
   "source": [
    "#### **PROBLEM 2.**  [20 points] Create a `numpy` column vector `X` that contains the initial proportions of customers in the stores. Print the vector."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9654f68b-b04f-44c5-aa56-3340eda4fda8",
   "metadata": {},
   "source": [
    "#### Consider the following calculations;\n",
    "- #### What is the proportion of customers in the stores after Year 1? The new value of vector `X` is matrix `P` times the initial value of vector `X`.\n",
    "- #### The proportion of customers in the stores after Year 2? The new value of vector `X` is matrix `P` times the value of vector `X` after Year 1.\n",
    "- #### The proportion of customers in the stores after Year 3? The new value of vector `X` is matrix `P` times the value of vector `X` after Year 2.\n",
    "- #### Etc."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd668123-613d-41cd-847e-be5cf073e004",
   "metadata": {},
   "source": [
    "#### **PROBLEM 3.** [50 points] Repeatedly multiply matrix `P` times vector `X` and stop after 25 years. Print the value of `X` after each year. Print the values of `X` to 4 places after the decimal point."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8deba553-44b6-463f-852c-06e2d29a7a92",
   "metadata": {},
   "source": [
    "#### **PROBLEM 4.** [10 points] What appears to happen after Year 19?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16e76661-8a0f-4b30-a26e-7632938360ac",
   "metadata": {},
   "source": [
    "#### This is called a **Markov Chain**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f183ea3-a05c-42f5-a48e-cb972492391c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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