{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graphing Equations\n",
    "\n",
    "Lets revisit high school and think about those tiny screens a lot of us had to use.\n",
    "\n",
    "We may recreate those kinds of plots, of mathematical functions, quite straightforwardly.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define a domain from -5 to 5, of 100 points, and plot some XY curves that show some functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "domain = np.linspace(-5.0,5.0,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.power(domain, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline  \n",
    "# \"magic\" command telling Jupyter NB to embed plots\n",
    "\n",
    "# always label and title your plot, at minimum\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"Parabolic Curve\")\n",
    "p = plt.plot(domain, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x3 = np.power(domain, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"X to the 3rd Power\")\n",
    "p = plt.plot(domain, x3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def poly(x):\n",
    "    return (x - 3) * (x + 5) * (x - 1) * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Poly = np.vectorize(poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = Poly(domain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"4th Degree Polynomial\")\n",
    "plt.grid()\n",
    "p = plt.plot(domain, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y0 = np.sin(domain)\n",
    "y1 = np.cos(domain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"Sine & Cosine\")\n",
    "plt.grid()\n",
    "plt.plot(domain, y0, color = \"orange\", label=\"Sine\")\n",
    "plt.plot(domain, y1, color = \"green\", label=\"Cosine\")\n",
    "p = plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've plotted some data, lets organize the data into a data table, or \"data frame\" to be more precise.  Pandas is all about the DataFrame object.\n",
    "\n",
    "Our domain is a 1-D ndarray lets remember.  As such, we may turn it into a Series, which is the one dimensional equivalent in pandas.  DataFrames are 2-dimensional and above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "col0 = pd.Series(domain)\n",
    "col1 = pd.Series(np.power(domain,2))\n",
    "col2 = pd.Series(x3)\n",
    "col3 = Poly(domain)\n",
    "\n",
    "datadict = {\"Input\":col0, \"Parabola\":col1, \"3rd Power\":col2, \"Polynomial\":col3}\n",
    "df = pd.DataFrame(datadict, columns = [\"Input\", \"Parabola\", \"3rd Power\", \"Polynomial\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without the ```columns``` argument, there's no guarantee that ```datadict``` will gives us the left-to-right column order we desire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we're starting to introduce how data may be selected by numeric indexes, yes, but also by labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.loc[:,\"3rd Power\"].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.loc[:10,[\"Input\", \"3rd Power\"]]  # rows 0-10 inclusive, two columns"
   ]
  }
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