{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting in Python\n",
    "\"[`Matplotlib`](https://matplotlib.org/) is a comprehensive library for creating static, animated, and interactive visualizations in Python.\" There are several [tutorials](https://matplotlib.org/tutorials/index.html), where you can learn the usage. \"`matplotlib.pyplot` is a collection of functions that make matplotlib work like MATLAB. Each `pyplot` function makes some change to a figure: e.g., creates a figure, creates a plotting area in a figure, plots some lines in a plotting area, decorates the plot with labels, etc.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "list1 = range(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(list1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "list2 = [random.random() for _ in range(5)]\n",
    "print(list2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(list1, list2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(list1, list2, 'gs') # try: 'r^' 'gs' 'k--' 'b:' 'ro-'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(list1, list2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.bar(list1, list2, .7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = [i*0.01 for i in range(251)]\n",
    "t2 = [(i*0.01)**2 for i in range(251)]\n",
    "t3 = [(i*0.01)**3 for i in range(251)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(t, t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(t, t2, 'r', t, t3, 'g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12, 3))\n",
    "\n",
    "plt.subplot(131)\n",
    "plt.bar(list1,list2)\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.scatter(list1,list2)\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.plot(list1,list2)\n",
    "\n",
    "plt.suptitle('Functions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(8, 12))\n",
    "\n",
    "plt.subplot(311)\n",
    "plt.bar(list1,list2)\n",
    "plt.title(\"Bar\")\n",
    "\n",
    "plt.subplot(312)\n",
    "plt.scatter(list1,list2)\n",
    "plt.title(\"Scattered\")\n",
    "\n",
    "plt.subplot(313)\n",
    "plt.plot(list1,list2)\n",
    "plt.title(\"Plot\")\n",
    "\n",
    "plt.suptitle('Functions')\n",
    "\n",
    "plt.tight_layout()         \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Exercise:*** Copy the next code into a file named `4test.py` and run it from a terminal with the command `python3 4test.py 4` \n",
    "\n",
    "\n",
    "```Python\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import sys\n",
    "\n",
    "def my_plot():\n",
    "    \"\"\"\n",
    "    Plotting n random values.\n",
    "    n is read in from the terminal.\n",
    "    \"\"\"\n",
    "    \n",
    "    n = int(sys.argv[1])\n",
    "    \n",
    "    list1 = range(n)\n",
    "    list2 = [random.random() for _ in range(n)]\n",
    "    list3 = [i**2 for i in list2]\n",
    "    \n",
    "    plt.subplot(311)\n",
    "    plt.bar(list1,list1)\n",
    "    plt.subplot(312)\n",
    "    plt.bar(list1,list2)\n",
    "    plt.subplot(313)\n",
    "    plt.bar(list1,list3)\n",
    "    plt.show()\n",
    "\n",
    "def main():\n",
    "    my_plot()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For calculating factorial, binomial coefficient, exponential function you may use the `math` module: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the `math` module\n",
    "\n",
    "To compute the factorial or the exponential function you can use the `math` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "math.factorial(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a `comb` function to calculate the binomial coefficient (from Python 3.8 there also exists a function `math.comb()` for this):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def comb(n, m):\n",
    "    return math.factorial(n)//math.factorial(m)//math.factorial(n-m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "comb(25, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "math.exp(1), math.exp(2) # the e^x function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Exercise:*** Throw a die 10 times. What is the probability that you get 6 exactly 2 times. Calculate with the formula for the binomial distribution (the parameters will be $n=10$, $p=1/6$), and approximate it with Poisson-distribution, with the parameter $\\lambda$, where $\\lambda=n\\cdot p$ is the expected value of the binomial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "p = 1/6\n",
    "m = 2\n",
    "l = n*p  # lambda\n",
    "\n",
    "binomial_dist = comb(n, m) * p**m * (1-p)**(n-m)\n",
    "poison_dist = l**m * math.exp(-l) / math.factorial(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "binomial_dist, poison_dist"
   ]
  },
  {
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}