{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "incomplete-repeat",
   "metadata": {},
   "source": [
    "#### Usual imports and creation of the random number generator object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "alone-polls",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "rng = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cardiac-offense",
   "metadata": {},
   "source": [
    "#### Randomly generate 30 points, each with 2 dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "registered-halifax",
   "metadata": {},
   "outputs": [],
   "source": [
    "randomPoints = rng.random((30,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "spectacular-cornell",
   "metadata": {},
   "source": [
    "#### All the following code cells do the same: scatter the points in a plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "recognized-shakespeare",
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = randomPoints[:, 0]\n",
    "ys = randomPoints[:, 1]\n",
    "plt.scatter(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "respective-continent",
   "metadata": {},
   "outputs": [],
   "source": [
    "xs, ys = randomPoints.T\n",
    "plt.scatter(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "traditional-actress",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(*randomPoints.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "endless-castle",
   "metadata": {},
   "source": [
    "#### Specify 2 focus points to use for our naive clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "vital-commercial",
   "metadata": {},
   "outputs": [],
   "source": [
    "focusPoints = np.array(((0, 0.5),\n",
    "                        (1, 0.5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "requested-script",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(*randomPoints.T)\n",
    "plt.scatter(*focusPoints.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "scheduled-sally",
   "metadata": {},
   "source": [
    "#### Working implementation that assigns each random point to either the left or the right cluster, depending on which focus point is closer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "centered-earthquake",
   "metadata": {},
   "outputs": [],
   "source": [
    "leftPoints = []\n",
    "rightPoints = []\n",
    "for i in range(30):\n",
    "    if np.linalg.norm(randomPoints[i] - focusPoints[0]) < np.linalg.norm(randomPoints[i] - focusPoints[1]):\n",
    "        leftPoints.append(randomPoints[i])\n",
    "    else:\n",
    "        rightPoints.append(randomPoints[i])\n",
    "plt.scatter(*np.array(leftPoints).T)\n",
    "plt.scatter(*np.array(rightPoints).T)\n",
    "plt.scatter(*focusPoints.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baking-leader",
   "metadata": {},
   "source": [
    "#### More efficient and concise implementation that makes use of numpy functions and broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "atomic-spyware",
   "metadata": {},
   "outputs": [],
   "source": [
    "distanceVectors = randomPoints[np.newaxis, :, :] - focusPoints[:, np.newaxis, :]\n",
    "distances = np.linalg.norm(distanceVectors, axis = 2)\n",
    "clusterIndexes = np.argmin(distances, axis = 0)\n",
    "for i in range(focusPoints.shape[0]): plt.scatter(*randomPoints[clusterIndexes == i].T)\n",
    "plt.scatter(*focusPoints.T)"
   ]
  }
 ],
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