{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [1,2,3,4,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = [2*x for x in data]\n",
    "data2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you may have guessed, x acts as a variable that takes on each value in the list data. The first part of the command computes 2*x for each x and assigns the resulting value to the same location in data2 that x was drawn from in data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian(N,s):\n",
    "    return math.sqrt(2/(math.pi*N))*math.exp(-2*s**2/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "gaussian(10,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ins=np.linspace(-10,10,100)\n",
    "data10=[gaussian(10,s) for s in ins]\n",
    "data20=[gaussian(20,s) for s in ins]\n",
    "data100=[gaussian(100,s) for s in ins]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(ins,data10)\n",
    "plt.ylabel('P(N,s)')\n",
    "plt.xlabel('s (imbalance)')\n",
    "plt.title('Gaussian with N=10')\n",
    "plt.savefig('Gauss10.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(ins,data20)\n",
    "plt.ylabel('P(N,s)')\n",
    "plt.xlabel('s (imbalance)')\n",
    "plt.title('Gaussian with N=20')\n",
    "plt.axis([-10,10,0,0.25])\n",
    "plt.savefig('Gauss20.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(ins,data100)\n",
    "plt.ylabel('P(N,s)')\n",
    "plt.xlabel('s (imbalance)')\n",
    "plt.title('Gaussian with N=100')\n",
    "plt.axis([-10,10,0,0.25])\n",
    "plt.savefig('Gauss100.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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