๐Ÿ“ฆ furkan / pi-carlo

๐Ÿ“„ pi_carlo.ipynb ยท 655 lines
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655{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating pi with a random number generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recently, a friend asked me if I knew about Monte Carlo and told me that the number PI can be estimated with random numbers.\n",
    "\n",
    "I then decided to see if I could do that without looking up the solution.\n",
    "\n",
    "Here it goes..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: matplotlib<4 in ./venv/lib/python3.11/site-packages (3.8.2)\n",
      "Requirement already satisfied: numpy<2 in ./venv/lib/python3.11/site-packages (1.26.2)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (1.2.0)\n",
      "Requirement already satisfied: cycler>=0.10 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (4.44.3)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (1.4.5)\n",
      "Requirement already satisfied: packaging>=20.0 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (23.2)\n",
      "Requirement already satisfied: pillow>=8 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (10.1.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (3.1.1)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in ./venv/lib/python3.11/site-packages (from matplotlib<4) (2.8.2)\n",
      "Requirement already satisfied: six>=1.5 in ./venv/lib/python3.11/site-packages (from python-dateutil>=2.7->matplotlib<4) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install \"matplotlib<4\" \"numpy<2\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Set the global grid property\n",
    "plt.rcParams['axes.grid'] = True\n",
    "\n",
    "# Initialize random number generator\n",
    "rng = np.random.default_rng(seed=42)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random points (x, y pairs) uniformly distributed in the unit square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_pairs = 1_000\n",
    "\n",
    "# Generate both axes\n",
    "xy = rng.uniform(0, 1, number_of_pairs * 2)\n",
    "\n",
    "# Split into x and y\n",
    "x, y = np.array_split(xy, 2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def show_scatter(x, y):\n",
    "    plt.figure(figsize=(6, 6))\n",
    "    plt.scatter(x, y)\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "\n",
    "show_scatter(x, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remove points outside of the unit circle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = x**2 + y**2 <= 1\n",
    "x = x[mask]\n",
    "y = y[mask]\n",
    "\n",
    "show_scatter(x, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Map all points on the circle border"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distances_from_origin = np.sqrt(x**2 + y**2)\n",
    "\n",
    "x = np.divide(x, distances_from_origin)\n",
    "y = np.divide(y, distances_from_origin)\n",
    "\n",
    "show_scatter(x, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observe the distribution of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def show_histogram(x, bins: int = 30):\n",
    "    plt.figure(figsize=(6, 6))\n",
    "    plt.hist(x, bins=bins, edgecolor='black')\n",
    "    plt.show()\n",
    "\n",
    "show_histogram(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we get from x=0 to x=1, the circle border gets more perpendicular to the x axis, and the x values of the random numbers are more condensed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get all the distances between x values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_counterpart(x_or_y):\n",
    "    \"\"\"\n",
    "    Given an x value between 0 and 1,\n",
    "      find the y value that maps\n",
    "      that x value on the unit circle.\n",
    "    Works x->y and y->x.\n",
    "    \"\"\"\n",
    "    return np.sqrt(np.ones(x_or_y.shape) - x_or_y**2)\n",
    "\n",
    "def get_euclidian_distances(x1, x2):\n",
    "    \"\"\"\n",
    "    Given two x matrices,\n",
    "      find the euclidian distance between their\n",
    "      corresponding points on the unit circle.\n",
    "    It is an element-wise operation.\n",
    "    \"\"\"\n",
    "    y1 = get_counterpart(x1)\n",
    "    y2 = get_counterpart(x2)\n",
    "    return np.sqrt((x1 - x2)**2 + (y1 -y2)**2)\n",
    "\n",
    "x.sort()\n",
    "\n",
    "# Obtain each distance between neighboring points on the unit circle\n",
    "distances = get_euclidian_distances(x[:-1], x[1:])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estime pi by summing the distances (obtaining the length of the quarter circle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1375185348374206\n"
     ]
    }
   ],
   "source": [
    "quarter_circle_circumference = np.sum(distances)\n",
    "\n",
    "# pi is half a complete circle\n",
    "pi = quarter_circle_circumference * 2\n",
    "\n",
    "print(pi)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid search various numbers of points on the circle to observe convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number_of_points_inside_unit_square=          10000, error=0.0000264447\n",
      "number_of_points_inside_unit_square=         100000, error=0.0000401923\n",
      "number_of_points_inside_unit_square=        1000000, error=0.0000037544\n",
      "number_of_points_inside_unit_square=       10000000, error=0.0000001447\n",
      "number_of_points_inside_unit_square=      100000000, error=0.0000000194\n",
      "\n",
      "Circumference method took: 14.25504916600039 seconds.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "from time import perf_counter\n",
    "\n",
    "def estimate_pi(points_inside_unit_square: int) -> float:\n",
    "    \"\"\"\n",
    "    Given an amount of number of random points, estimate pi.\n",
    "    \"\"\"\n",
    "\n",
    "    # Generate points\n",
    "    xy = rng.uniform(0, 1, points_inside_unit_square * 2)\n",
    "    x, y = np.array_split(xy, 2)\n",
    "\n",
    "    # Remove points outside of circle\n",
    "    mask = x**2 + y**2 <= 1\n",
    "    x = x[mask]\n",
    "    y = y[mask]\n",
    "\n",
    "    # Carry x values to the circle border\n",
    "    distances_from_origin = np.sqrt(x**2 + y**2)\n",
    "    x = np.divide(x, distances_from_origin)\n",
    "\n",
    "    # Sum over the distances between points on circle\n",
    "    x.sort()\n",
    "    distances = get_euclidian_distances(x[:-1], x[1:])\n",
    "    return np.sum(distances) * 2\n",
    "\n",
    "\n",
    "def get_error(pi_estimation: float) -> float:\n",
    "    \"\"\"\n",
    "    Get the relative error of the pi estimation.\n",
    "    \"\"\"\n",
    "    return abs(pi_estimation - math.pi) / math.pi\n",
    "\n",
    "\n",
    "numbers_of_points_inside_unit_square = [\n",
    "    10_000, 100_000, 1_000_000,\n",
    "    10_000_000, 100_000_000\n",
    "]\n",
    "errors = []\n",
    "\n",
    "start_time = perf_counter()\n",
    "for number_of_points_inside_unit_square in numbers_of_points_inside_unit_square:\n",
    "    pi = estimate_pi(number_of_points_inside_unit_square)\n",
    "    error = get_error(pi)\n",
    "    errors.append(error)\n",
    "    print(f\"{number_of_points_inside_unit_square=:>15}, {error=:.10f}\")\n",
    "end_time = perf_counter()\n",
    "\n",
    "print(f\"\\nCircumference method took: {end_time - start_time} seconds.\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(numbers_of_points_inside_unit_square, errors)\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel('random points on circle')\n",
    "plt.ylabel('error in PI estimation')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## UPDATE\n",
    "\n",
    "I showed this to my friend and found out that I did not have to make this as complicated as it is.\n",
    "\n",
    "Here is a version that uses the numbers of points before and after cleaning the points inside the square, outside the circle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number_of_points_inside_unit_square=          10000, error_area=0.0077644228\n",
      "number_of_points_inside_unit_square=         100000, error_area=0.0013137752\n",
      "number_of_points_inside_unit_square=        1000000, error_area=0.0000978314\n",
      "number_of_points_inside_unit_square=       10000000, error_area=0.0000083568\n",
      "number_of_points_inside_unit_square=      100000000, error_area=0.0000315297\n",
      "\\Area method took: 1.3466923750020214 seconds.\n"
     ]
    }
   ],
   "source": [
    "def estimate_pi_area(number_of_points_inside_unit_square) -> float:\n",
    "    xy = rng.uniform(0, 1, number_of_points_inside_unit_square * 2)\n",
    "    x, y = np.array_split(xy, 2)\n",
    "\n",
    "    mask = x**2 + y**2 <= 1\n",
    "    number_of_points_inside_unit_circle = np.sum(mask)\n",
    "\n",
    "    # pi * r^2 (r=1) = pi (our quarter circle is pi / 4)\n",
    "    entire_circle_area = number_of_points_inside_unit_circle * 4\n",
    "\n",
    "    return entire_circle_area / number_of_points_inside_unit_square\n",
    "\n",
    "errors_area = []\n",
    "\n",
    "start_time = perf_counter()\n",
    "for number_of_points_inside_unit_square in numbers_of_points_inside_unit_square:\n",
    "    pi = estimate_pi_area(number_of_points_inside_unit_square)\n",
    "    error_area = get_error(pi)\n",
    "    errors_area.append(error_area)\n",
    "    print(f\"{number_of_points_inside_unit_square=:>15}, {error_area=:.10f}\")\n",
    "end_time = perf_counter()\n",
    "\n",
    "print(f\"\\Area method took: {end_time - start_time} seconds.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if we can get closer sparing some of the gained speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number_of_points_inside_unit_square=      100000000, error_area=0.0000055947\n",
      "\\Area method with 400_000_000 took: 32.012539082999865 seconds.\n"
     ]
    }
   ],
   "source": [
    "start_time = perf_counter()\n",
    "largest_amount_in_list = numbers_of_points_inside_unit_square[-1]\n",
    "\n",
    "# 4 times the largest example in circumference method\n",
    "larger_amount_test_area = largest_amount_in_list * 4\n",
    "pi = estimate_pi_area(larger_amount_test_area)\n",
    "error_area = get_error(pi)\n",
    "errors_area.append(error_area)\n",
    "print(f\"{number_of_points_inside_unit_square=:>15}, {error_area=:.10f}\")\n",
    "end_time = perf_counter()\n",
    "\n",
    "print(f\"\\Area method with {larger_amount_test_area:_} took: {end_time - start_time} seconds.\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(numbers_of_points_inside_unit_square + [larger_amount_test_area],\n",
    "         errors_area, label=\"area method\")\n",
    "plt.plot(numbers_of_points_inside_unit_square, errors, label=\"circumference method\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel('random points on circle')\n",
    "plt.ylabel('error in PI estimation')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area method is much much simpler. After learning about it, I was a bit ashamed of having added all that [complexity](https://grugbrain.dev/#grug-on-complexity), but it turns out it was improving performance. Let's drop one final plot to better compare runtimes and call it a day."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number_of_points_inside_unit_square=          10000, error=0.0006619905\n",
      "number_of_points_inside_unit_square=          10000, error_area=0.0038220571\n",
      "number_of_points_inside_unit_square=         100000, error=0.0000117467\n",
      "number_of_points_inside_unit_square=         100000, error_area=0.0001423948\n",
      "number_of_points_inside_unit_square=        1000000, error=0.0000034482\n",
      "number_of_points_inside_unit_square=        1000000, error_area=0.0004785300\n",
      "number_of_points_inside_unit_square=       10000000, error=0.0000003295\n",
      "number_of_points_inside_unit_square=       10000000, error_area=0.0001714588\n",
      "number_of_points_inside_unit_square=      100000000, error=0.0000000743\n",
      "number_of_points_inside_unit_square=      100000000, error_area=0.0001217046\n",
      "number_of_points_inside_unit_square=      500000000, error_area=0.0000182473\n"
     ]
    }
   ],
   "source": [
    "def estimate_pi_circumference_with_time(\n",
    "        number_of_points_inside_unit_square\n",
    "    ) -> tuple:\n",
    "    \"\"\"\n",
    "    Estimate pi with circumference method.\n",
    "    Returns a tuple with error in pi estimation, and the runtime.\n",
    "    \"\"\"\n",
    "    start_time = perf_counter()\n",
    "    pi = estimate_pi(number_of_points_inside_unit_square)\n",
    "    error = get_error(pi)\n",
    "    print(f\"{number_of_points_inside_unit_square=:>15}, {error=:.10f}\")\n",
    "    end_time = perf_counter()\n",
    "    return (error, end_time - start_time)\n",
    "\n",
    "\n",
    "def estimate_pi_area_with_time(\n",
    "        number_of_points_inside_unit_square\n",
    "    ) -> tuple:\n",
    "    \"\"\"\n",
    "    Estimate pi with area method.\n",
    "    Returns a tuple with error in pi estimation, and the runtime.\n",
    "    \"\"\"\n",
    "    start_time = perf_counter()\n",
    "    pi = estimate_pi_area(number_of_points_inside_unit_square)\n",
    "    error_area = get_error(pi)\n",
    "    print(f\"{number_of_points_inside_unit_square=:>15}, {error_area=:.10f}\")\n",
    "    end_time = perf_counter()\n",
    "    return (error_area, end_time - start_time)\n",
    "\n",
    "numbers_of_points_inside_unit_square = [\n",
    "    10_000, 100_000, 1_000_000,\n",
    "    10_000_000, 100_000_000\n",
    "]\n",
    "errors_circumference = []\n",
    "runtimes_circumference = []\n",
    "errors_area = []\n",
    "runtimes_area = []\n",
    "\n",
    "for number_of_points_inside_unit_square in numbers_of_points_inside_unit_square:\n",
    "    error_circumference, runtime_circumference = (\n",
    "        estimate_pi_circumference_with_time(number_of_points_inside_unit_square)\n",
    "    )\n",
    "    errors_circumference.append(error_circumference)\n",
    "    runtimes_circumference.append(runtime_circumference)\n",
    "\n",
    "    error_area, runtime_area = (\n",
    "        estimate_pi_area_with_time(number_of_points_inside_unit_square)\n",
    "    )\n",
    "    errors_area.append(error_area)\n",
    "    runtimes_area.append(runtime_area)\n",
    "\n",
    "larger_amount_test_area = numbers_of_points_inside_unit_square[-1] * 5\n",
    "error_area, runtime_area = estimate_pi_area_with_time(larger_amount_test_area)\n",
    "errors_area.append(error_area)\n",
    "runtimes_area.append(runtime_area)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(runtimes_area, errors_area, label=\"area method\")\n",
    "plt.plot(runtimes_circumference, errors_circumference,\n",
    "         label=\"circumference method\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('error in PI estimation')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}