{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Growth Curves\n",
    "- https://en.wikipedia.org/wiki/Growth_curve\n",
    "- https://docs.sympy.org/latest/modules/core.html#sympy.core.symbol.var\n",
    "- https://docs.sympy.org/latest/modules/plotting.html\n",
    "- https://matplotlib.org/3.2.1/gallery/color/named_colors.html\n",
    "- https://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html\n",
    "- https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html#numpy.arange\n",
    "- https://docs.sympy.org/latest/modules/utilities/lambdify.html#sympy.utilities.lambdify.lambdify"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Polynomials\" data-toc-modified-id=\"Polynomials-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Polynomials</a></span><ul class=\"toc-item\"><li><span><a href=\"#Constant\" data-toc-modified-id=\"Constant-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Constant</a></span></li><li><span><a href=\"#Linear\" data-toc-modified-id=\"Linear-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Linear</a></span></li><li><span><a href=\"#Quadratic\" data-toc-modified-id=\"Quadratic-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Quadratic</a></span></li><li><span><a href=\"#Cubic\" data-toc-modified-id=\"Cubic-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Cubic</a></span></li><li><span><a href=\"#Quartic\" data-toc-modified-id=\"Quartic-1.5\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Quartic</a></span></li><li><span><a href=\"#Quintic\" data-toc-modified-id=\"Quintic-1.6\"><span class=\"toc-item-num\">1.6&nbsp;&nbsp;</span>Quintic</a></span></li><li><span><a href=\"#Sextic\" data-toc-modified-id=\"Sextic-1.7\"><span class=\"toc-item-num\">1.7&nbsp;&nbsp;</span>Sextic</a></span></li><li><span><a href=\"#Septic\" data-toc-modified-id=\"Septic-1.8\"><span class=\"toc-item-num\">1.8&nbsp;&nbsp;</span>Septic</a></span></li><li><span><a href=\"#Octic\" data-toc-modified-id=\"Octic-1.9\"><span class=\"toc-item-num\">1.9&nbsp;&nbsp;</span>Octic</a></span></li><li><span><a href=\"#Nonic\" data-toc-modified-id=\"Nonic-1.10\"><span class=\"toc-item-num\">1.10&nbsp;&nbsp;</span>Nonic</a></span></li><li><span><a href=\"#Decic\" data-toc-modified-id=\"Decic-1.11\"><span class=\"toc-item-num\">1.11&nbsp;&nbsp;</span>Decic</a></span></li><li><span><a href=\"#Univariate-Polynomials-Summary\" data-toc-modified-id=\"Univariate-Polynomials-Summary-1.12\"><span class=\"toc-item-num\">1.12&nbsp;&nbsp;</span>Univariate Polynomials Summary</a></span></li></ul></li><li><span><a href=\"#Exponential-Functions\" data-toc-modified-id=\"Exponential-Functions-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Exponential Functions</a></span></li><li><span><a href=\"#Trigonometric-Functions\" data-toc-modified-id=\"Trigonometric-Functions-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Trigonometric Functions</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#Degrees-and-Radians\" data-toc-modified-id=\"Degrees-and-Radians-3.0.1\"><span class=\"toc-item-num\">3.0.1&nbsp;&nbsp;</span>Degrees and Radians</a></span></li></ul></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pytest\n",
    "import sympy\n",
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "curves = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sympy.plotting.plot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "    table { display: inline-block; }\n",
       "    td, tr, th { font-size: 1em; }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<style>\n",
    "    table { display: inline-block; }\n",
    "    td, tr, th { font-size: 1em; }\n",
    "</style>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomials\n",
    "- https://en.wikipedia.org/wiki/Polynomial\n",
    "- https://en.wikipedia.org/wiki/Degree_of_a_polynomial\n",
    "\n",
    "| polynomial name          | degree   | example equation | graph shape |\n",
    "|--------------------------|----------|------------------|-------------|\n",
    "| Constant                 | 0        | $y = 1$          | line        |\n",
    "| [Linear](#Linear)        | 1        | $y = m*x + b$    | line        |\n",
    "| [Quadratic](#Quadratic)  | 2        | $y = x^2$        | parabola    |\n",
    "| [Cubic](#Cubic)          | 3        | $y = x^3$        | hyperbola   |\n",
    "| [Quartic](#Quartic)      | 4        | $y = x^4$        |             |\n",
    "| [Quintic](#Quintic)      | 5        | $y = x^5$        |             |\n",
    "| [Sextic](#Sextic)        | 6        | $y = x^6$        |             |\n",
    "| [Septic](#Septic)        | 7        | $y = x^7$        |             |\n",
    "| [Octic](#Octic)          | 8        | $y = x^8$        |             |\n",
    "| Nonic                    | 9        | $y = x^9$        |             |\n",
    "| Decic                    | 10       | $y = x^{10}$     |             |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 1$"
      ],
      "text/plain": [
       "Eq(y, 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f18ceec0510>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.abc import y\n",
    "constant1 = sympy.Eq(y, 1)\n",
    "display(constant1)\n",
    "sympy.plotting.plot(constant1.rhs,\n",
    "    title='Constant (0) function\\n',\n",
    "    xlim=(-10, 10),\n",
    "    ylim=(0, 2),\n",
    "    legend=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear\n",
    "- https://en.wikipedia.org/wiki/Linear_equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.power.Pow"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'x**2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2}$"
      ],
      "text/plain": [
       "x**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = sympy.var('x')\n",
    "expression = x**2\n",
    "display(type(expression), str(expression), expression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.relational.Equality"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Eq(y, x**2)'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = x^{2}$"
      ],
      "text/plain": [
       "Eq(y, x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = sympy.var('x y')\n",
    "equality = sympy.Eq(y, x**2)\n",
    "display(type(equality), str(equality), equality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('y', 'x**2')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(y, x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y$"
      ],
      "text/plain": [
       "y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2}$"
      ],
      "text/plain": [
       "x**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# .lhs = left-hand side, .rhs = right-hand side\n",
    "display((str(equality.lhs), str(equality.rhs)))\n",
    "display((equality.lhs, equality.rhs))\n",
    "display(equality.lhs, equality.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = sympy.var('x y')\n",
    "linear1 = curves['linear1'] = sympy.Eq(y, x)\n",
    "linear2 = curves['linear2'] = sympy.Eq(y, 2*x)\n",
    "linear4 = curves['linear3'] = sympy.Eq(y, 2*x + 5)\n",
    "linear3 = curves['linear4'] = sympy.Eq(y, -1*x)\n",
    "linear_curves = {k:v for k,v in curves.items() if k.startswith('linear')}\n",
    "plot1 = sympy.plotting.plot(\n",
    "    *[v.rhs for v in linear_curves.values()],\n",
    "    title='Linear growth',\n",
    "    range=(x, -10, 10),\n",
    "    xlim=(-10, 10),\n",
    "    ylim=(-10, 10),\n",
    "    legend=True,\n",
    "    show=False)\n",
    "plot1[0].line_color = 'tab:red'\n",
    "plot1[1].line_color = 'tab:blue'\n",
    "plot1[2].line_color = 'tab:orange'\n",
    "plot1[3].line_color = 'tab:green'\n",
    "plot1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear1\tEq(y, x)\tEq(y, 10)\n",
      "linear2\tEq(y, 2*x)\tEq(y, 20)\n",
      "linear3\tEq(y, 2*x + 5)\tEq(y, 25)\n",
      "linear4\tEq(y, -x)\tEq(y, -10)\n"
     ]
    }
   ],
   "source": [
    "xval = dict(x=10)\n",
    "results = ((k, v, v.subs(xval)) for k, v in linear_curves.items())\n",
    "for key, eq, eq_subs in results:\n",
    "    print(f'{key}\\t{eq}\\t{eq_subs}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'x': 10}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 10}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'linear1'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = x$"
      ],
      "text/plain": [
       "Eq(y, x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 10$"
      ],
      "text/plain": [
       "Eq(y, 10)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'linear2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 2 x$"
      ],
      "text/plain": [
       "Eq(y, 2*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 20$"
      ],
      "text/plain": [
       "Eq(y, 20)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'linear3'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 2 x + 5$"
      ],
      "text/plain": [
       "Eq(y, 2*x + 5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 25$"
      ],
      "text/plain": [
       "Eq(y, 25)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'linear4'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = - x$"
      ],
      "text/plain": [
       "Eq(y, -x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = -10$"
      ],
      "text/plain": [
       "Eq(y, -10)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "xval = dict(x=10)\n",
    "print(xval)\n",
    "display(xval)\n",
    "print(\"\")\n",
    "\n",
    "for key, eq in linear_curves.items():\n",
    "    yval = eq.subs(xval)\n",
    "    display(key, eq, yval)\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10,  -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,   0,   1,   2,\n",
       "         3,   4,   5,   6,   7,   8,   9,  10])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "xval_ary = np.arange(-10, 10+1)\n",
    "xval_ary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Sympy.Eq.subs` sort of sometimes works with tuples?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = \\left( -10, \\  -9, \\  -8, \\  -7, \\  -6, \\  -5, \\  -4, \\  -3, \\  -2, \\  -1, \\  0, \\  1, \\  2, \\  3, \\  4, \\  5, \\  6, \\  7, \\  8, \\  9, \\  10\\right)$"
      ],
      "text/plain": [
       "Eq(y, (-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xval = dict(x=tuple(range(-10, 10+1)))\n",
    "#xval = {'x': list(range(-10, 10+1))}\n",
    "linear1.subs(xval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Sort of?\n",
    "import pytest\n",
    "with pytest.raises(AttributeError):\n",
    "    linear2.subs(xval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Sympy.Eq.subs` doesn't work with arrays either:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 2 x$"
      ],
      "text/plain": [
       "Eq(y, 2*x)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xval = dict(x=xval_ary)\n",
    "linear2.subs(xval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead, with SymPy expressions, we can `lambdify`\n",
    "in order to *vectorize* calculations with multiple values in an array instead of calling `Eq.subs` a bunch of times (which is slow):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function _lambdifygenerated(x)>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear2_func = sympy.lambdify(x, linear2.rhs, 'numpy')\n",
    "linear2_func"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(numpy.ndarray,\n",
       " array([-20, -18, -16, -14, -12, -10,  -8,  -6,  -4,  -2,   0,   2,   4,\n",
       "          6,   8,  10,  12,  14,  16,  18,  20]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary = linear2_func(xval_ary)\n",
    "type(ary), ary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create a `pandas.DataFrame` with a column for each function and an index:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>linear1</th>\n",
       "      <th>linear2</th>\n",
       "      <th>linear3</th>\n",
       "      <th>linear4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-10</th>\n",
       "      <td>-10</td>\n",
       "      <td>-20</td>\n",
       "      <td>-15</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9</th>\n",
       "      <td>-9</td>\n",
       "      <td>-18</td>\n",
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       "      <td>9</td>\n",
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       "    <tr>\n",
       "      <th>-8</th>\n",
       "      <td>-8</td>\n",
       "      <td>-16</td>\n",
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       "      <td>8</td>\n",
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       "      <th>-7</th>\n",
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       "      <th>-6</th>\n",
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       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>-5</th>\n",
       "      <td>-5</td>\n",
       "      <td>-10</td>\n",
       "      <td>-5</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>-4</th>\n",
       "      <td>-4</td>\n",
       "      <td>-8</td>\n",
       "      <td>-3</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>-3</th>\n",
       "      <td>-3</td>\n",
       "      <td>-6</td>\n",
       "      <td>-1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-2</th>\n",
       "      <td>-2</td>\n",
       "      <td>-4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1</th>\n",
       "      <td>-1</td>\n",
       "      <td>-2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>-2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>13</td>\n",
       "      <td>-4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>15</td>\n",
       "      <td>-5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>12</td>\n",
       "      <td>17</td>\n",
       "      <td>-6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>14</td>\n",
       "      <td>19</td>\n",
       "      <td>-7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "      <td>21</td>\n",
       "      <td>-8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>18</td>\n",
       "      <td>23</td>\n",
       "      <td>-9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
       "      <td>-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     linear1  linear2  linear3  linear4\n",
       "-10      -10      -20      -15       10\n",
       "-9        -9      -18      -13        9\n",
       "-8        -8      -16      -11        8\n",
       "-7        -7      -14       -9        7\n",
       "-6        -6      -12       -7        6\n",
       "-5        -5      -10       -5        5\n",
       "-4        -4       -8       -3        4\n",
       "-3        -3       -6       -1        3\n",
       "-2        -2       -4        1        2\n",
       "-1        -1       -2        3        1\n",
       " 0         0        0        5        0\n",
       " 1         1        2        7       -1\n",
       " 2         2        4        9       -2\n",
       " 3         3        6       11       -3\n",
       " 4         4        8       13       -4\n",
       " 5         5       10       15       -5\n",
       " 6         6       12       17       -6\n",
       " 7         7       14       19       -7\n",
       " 8         8       16       21       -8\n",
       " 9         9       18       23       -9\n",
       " 10       10       20       25      -10"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = linear_df = pd.DataFrame(index=xval_ary)\n",
    "for k, v in linear_curves.items():\n",
    "    df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "linear_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access DataFrame rows by integer location with `DataFrame.iloc`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(linear1   -10\n",
       " linear2   -20\n",
       " linear3   -15\n",
       " linear4    10\n",
       " Name: -10, dtype: int64,\n",
       " linear1    10\n",
       " linear2    20\n",
       " linear3    25\n",
       " linear4   -10\n",
       " Name: 10, dtype: int64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_df.iloc[0], linear_df.iloc[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access DataFrame rows by index value and column name with `DataFrame.loc`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(linear1    0\n",
       " linear2    0\n",
       " linear3    5\n",
       " linear4    0\n",
       " Name: 0, dtype: int64,\n",
       " 5)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_df.loc[0], linear_df.loc[0, 'linear3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>linear1</th>\n",
       "      <th>linear2</th>\n",
       "      <th>linear3</th>\n",
       "      <th>linear4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6.204837</td>\n",
       "      <td>12.409674</td>\n",
       "      <td>12.409674</td>\n",
       "      <td>6.204837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-10.000000</td>\n",
       "      <td>-20.000000</td>\n",
       "      <td>-15.000000</td>\n",
       "      <td>-10.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-5.000000</td>\n",
       "      <td>-10.000000</td>\n",
       "      <td>-5.000000</td>\n",
       "      <td>-5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>10.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         linear1    linear2    linear3    linear4\n",
       "count  21.000000  21.000000  21.000000  21.000000\n",
       "mean    0.000000   0.000000   5.000000   0.000000\n",
       "std     6.204837  12.409674  12.409674   6.204837\n",
       "min   -10.000000 -20.000000 -15.000000 -10.000000\n",
       "25%    -5.000000 -10.000000  -5.000000  -5.000000\n",
       "50%     0.000000   0.000000   5.000000   0.000000\n",
       "75%     5.000000  10.000000  15.000000   5.000000\n",
       "max    10.000000  20.000000  25.000000  10.000000"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# linear_df.plot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f18cc2075d0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_df.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-20"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.min().min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f18cc11a6d0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_minmax(df):\n",
    "    # ymin = min(df[col].min() for col in df)\n",
    "    # ymax = max(df[col].max() for col in df.columns)\n",
    "    _min = df.min().min()\n",
    "    _max = df.max().max()\n",
    "    return _min, _max\n",
    "\n",
    "\n",
    "def format_plot(df, *, eqdict, **kwargs):\n",
    "    legendloc = kwargs.pop('legendloc', 'upper center')\n",
    "    minmax = list(get_minmax(df))\n",
    "    default_xlim = kwargs.get('default_xlim', [-10, 1000])\n",
    "    if minmax[0] == np.inf:\n",
    "        minmax[0] = kwargs.get('xlim', default_xlim)[0]\n",
    "    if minmax[1] == np.inf:\n",
    "        minmax[1] = kwargs.get('xlim', default_xlim)[-1]\n",
    "    ytick_step = (minmax[1] - minmax[0]) // 20\n",
    "    table = kwargs.pop('table', True)\n",
    "    yticks = np.arange(*np.round(minmax), ytick_step)\n",
    "    dfplot = df.plot(\n",
    "        table=table,\n",
    "        grid=kwargs.pop('grid', True),\n",
    "        xlim=kwargs.pop('xlim', None),\n",
    "        ylim=kwargs.pop('ylim', None),\n",
    "        xticks=kwargs.pop('xticks', df.index),\n",
    "        yticks=kwargs.pop('yticks', yticks),\n",
    "        **kwargs)\n",
    "    if eqdict:\n",
    "        current_handles, current_labels = dfplot.get_legend_handles_labels()\n",
    "        labels = [sympy.latex(eqdict[x], mode='inline') for x in current_labels]\n",
    "        dfplot.legend(current_handles, labels, loc=legendloc)\n",
    "    if table:\n",
    "        dfplot.xaxis.set_minor_locator(plt.NullLocator())\n",
    "        dfplot.xaxis.set_major_formatter(plt.NullFormatter())\n",
    "        dfplot.tick_params(axis=\"x\", direction=\"in\")\n",
    "    return dfplot\n",
    "format_plot(linear_df, eqdict=linear_curves, title=\"Linear (1) functions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quadratic\n",
    "- https://en.wikipedia.org/wiki/Quadratic_function\n",
    "- Polynomial of degree 2: $y = x^2$\n",
    "- The graph of a univariate quadratic function is a **parabola**; is *parabolic*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>quadratic1</th>\n",
       "      <th>quadratic2</th>\n",
       "      <th>quadratic3</th>\n",
       "      <th>quadratic4</th>\n",
       "      <th>quadratic5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-10</th>\n",
       "      <td>100</td>\n",
       "      <td>110</td>\n",
       "      <td>225</td>\n",
       "      <td>25</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9</th>\n",
       "      <td>81</td>\n",
       "      <td>91</td>\n",
       "      <td>196</td>\n",
       "      <td>16</td>\n",
       "      <td>162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-8</th>\n",
       "      <td>64</td>\n",
       "      <td>74</td>\n",
       "      <td>169</td>\n",
       "      <td>9</td>\n",
       "      <td>128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-7</th>\n",
       "      <td>49</td>\n",
       "      <td>59</td>\n",
       "      <td>144</td>\n",
       "      <td>4</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-6</th>\n",
       "      <td>36</td>\n",
       "      <td>46</td>\n",
       "      <td>121</td>\n",
       "      <td>1</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     quadratic1  quadratic2  quadratic3  quadratic4  quadratic5\n",
       "-10         100         110         225          25         200\n",
       "-9           81          91         196          16         162\n",
       "-8           64          74         169           9         128\n",
       "-7           49          59         144           4          98\n",
       "-6           36          46         121           1          72"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quadratic1 = curves['quadratic1'] = sympy.Eq(y, x**2)\n",
    "quadratic2 = curves['quadratic2'] = sympy.Eq(y, x**2+10)\n",
    "quadratic3 = curves['quadratic3'] = sympy.Eq(y, (x-5)**2)\n",
    "quadratic3 = curves['quadratic4'] = sympy.Eq(y, (x+5)**2)\n",
    "quadratic4 = curves['quadratic5'] = sympy.Eq(y, 2*x**2)\n",
    "quadratic_curves = {k:v for k,v in curves.items() if k.startswith('quadratic')}\n",
    "df = quadratic_df = pd.DataFrame(index=xval_ary)\n",
    "for k, v in quadratic_curves.items():\n",
    "    df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "quadratic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f18cbf4ead0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "format_plot(quadratic_df, eqdict=quadratic_curves, figsize=(8, 6), title=\"Quadratic (2) functions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cubic\n",
    "- https://en.wikipedia.org/wiki/Qubic_function\n",
    "- Polynomial of degree 3: $y = x^3$\n",
    "- The graph of a univariate cubic function is a **hyperbola**; is *hyperbola*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cubic1</th>\n",
       "      <th>cubic2</th>\n",
       "      <th>cubic3</th>\n",
       "      <th>cubic4</th>\n",
       "      <th>cubic5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-10</th>\n",
       "      <td>-1000</td>\n",
       "      <td>-990</td>\n",
       "      <td>-3375</td>\n",
       "      <td>-125</td>\n",
       "      <td>-2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9</th>\n",
       "      <td>-729</td>\n",
       "      <td>-719</td>\n",
       "      <td>-2744</td>\n",
       "      <td>-64</td>\n",
       "      <td>-1458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-8</th>\n",
       "      <td>-512</td>\n",
       "      <td>-502</td>\n",
       "      <td>-2197</td>\n",
       "      <td>-27</td>\n",
       "      <td>-1024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-7</th>\n",
       "      <td>-343</td>\n",
       "      <td>-333</td>\n",
       "      <td>-1728</td>\n",
       "      <td>-8</td>\n",
       "      <td>-686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-6</th>\n",
       "      <td>-216</td>\n",
       "      <td>-206</td>\n",
       "      <td>-1331</td>\n",
       "      <td>-1</td>\n",
       "      <td>-432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     cubic1  cubic2  cubic3  cubic4  cubic5\n",
       "-10   -1000    -990   -3375    -125   -2000\n",
       "-9     -729    -719   -2744     -64   -1458\n",
       "-8     -512    -502   -2197     -27   -1024\n",
       "-7     -343    -333   -1728      -8    -686\n",
       "-6     -216    -206   -1331      -1    -432"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cubic1 = curves['cubic1'] = sympy.Eq(y, x**3)\n",
    "cubic2 = curves['cubic2'] = sympy.Eq(y, x**3+10)\n",
    "cubic3 = curves['cubic3'] = sympy.Eq(y, (x-5)**3)\n",
    "cubic3 = curves['cubic4'] = sympy.Eq(y, (x+5)**3)\n",
    "cubic4 = curves['cubic5'] = sympy.Eq(y, 2*x**3)\n",
    "cubic_curves = {k:v for k,v in curves.items() if k.startswith('cubic')}\n",
    "df = cubic_df = pd.DataFrame(index=xval_ary)\n",
    "for k, v in cubic_curves.items():\n",
    "    df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "cubic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f18cbeac790>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "format_plot(cubic_df, eqdict=cubic_curves, table=False, figsize=(8, 6), title=\"Cubic (3) functions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quartic\n",
    "- https://en.wikipedia.org/wiki/Quartic_function\n",
    "- Polynomial of degree 4: $y = x^4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>quartic1</th>\n",
       "      <th>quartic2</th>\n",
       "      <th>quartic3</th>\n",
       "      <th>quartic4</th>\n",
       "      <th>quartic5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-15</th>\n",
       "      <td>50625</td>\n",
       "      <td>50635</td>\n",
       "      <td>160000</td>\n",
       "      <td>10000</td>\n",
       "      <td>101250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-14</th>\n",
       "      <td>38416</td>\n",
       "      <td>38426</td>\n",
       "      <td>130321</td>\n",
       "      <td>6561</td>\n",
       "      <td>76832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-13</th>\n",
       "      <td>28561</td>\n",
       "      <td>28571</td>\n",
       "      <td>104976</td>\n",
       "      <td>4096</td>\n",
       "      <td>57122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-12</th>\n",
       "      <td>20736</td>\n",
       "      <td>20746</td>\n",
       "      <td>83521</td>\n",
       "      <td>2401</td>\n",
       "      <td>41472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-11</th>\n",
       "      <td>14641</td>\n",
       "      <td>14651</td>\n",
       "      <td>65536</td>\n",
       "      <td>1296</td>\n",
       "      <td>29282</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     quartic1  quartic2  quartic3  quartic4  quartic5\n",
       "-15     50625     50635    160000     10000    101250\n",
       "-14     38416     38426    130321      6561     76832\n",
       "-13     28561     28571    104976      4096     57122\n",
       "-12     20736     20746     83521      2401     41472\n",
       "-11     14641     14651     65536      1296     29282"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_polynomial_df(deg, name, xmin=-10, xmax=10, xstep=1, scalar=2):\n",
    "    curves = {}\n",
    "    curves[f'{name}1'] = sympy.Eq(y, x**deg)\n",
    "    curves[f'{name}2'] = sympy.Eq(y, x**deg+10)\n",
    "    curves[f'{name}3'] = sympy.Eq(y, (x-5)**deg)\n",
    "    curves[f'{name}4'] = sympy.Eq(y, (x+5)**deg)\n",
    "    curves[f'{name}5'] = sympy.Eq(y, scalar*x**deg)\n",
    "    xval_ary = np.arange(xmin, xmax, xstep)\n",
    "    df = pd.DataFrame(index=xval_ary)\n",
    "    for k, v in curves.items():\n",
    "        df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "    return df, curves\n",
    "\n",
    "quartic_df, quartic_curves = get_polynomial_df(4, 'quartic', -15, 15)\n",
    "curves.update(quartic_curves)\n",
    "quartic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(quartic_df, eqdict=quartic_curves, table=False, figsize=(8, 6), title=\"Quartic (4) functions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quintic\n",
    "- https://en.wikipedia.org/wiki/Quintic_function\n",
    "- Polynomial of degree 5: $y = x^5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "quintic_df, quintic_curves = get_polynomial_df(5, 'quintic', xmin=-30, xmax=30, xstep=2, scalar=10)\n",
    "curves.update(quintic_curves)\n",
    "quintic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(quintic_df, eqdict=quintic_curves,\n",
    "            title='Quintic (5) functions',\n",
    "            table=False,\n",
    "            legendloc='lower center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "qplot1 = sympy.plotting.plot(\n",
    "    *[x.rhs for x in quintic_curves.values()],\n",
    "    range=(x, -20, 20),\n",
    "    xlim=(-10, 10),\n",
    "    #ylim=get_minmax(quintic_df),\n",
    "    ylim=(-50, 50),\n",
    "    title='Quintic (5) functions\\n',\n",
    "    legend=True,\n",
    "    show=False,\n",
    ")\n",
    "qplot1[0].line_color = 'tab:red'\n",
    "qplot1[1].line_color = 'tab:blue'\n",
    "qplot1[2].line_color = 'tab:orange'\n",
    "qplot1[3].line_color = 'tab:green'\n",
    "qplot1[4].line_color = 'tab:purple'\n",
    "qplot1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sextic\n",
    "- https://en.wikipedia.org/wiki/Sextic_function\n",
    "- Polynomial of degree 6: $y = x^6$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sextic_df, sextic_curves = get_polynomial_df(6, 'sextic', xmin=-30, xmax=30, xstep=2, scalar=5)\n",
    "curves.update(sextic_curves)\n",
    "sextic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(sextic_df, eqdict=sextic_curves,\n",
    "            title='Sextic (6) functions',\n",
    "            table=False,\n",
    "            legendloc='upper center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sxplot1 = sympy.plotting.plot(\n",
    "    *[x.rhs for x in sextic_curves.values()],\n",
    "    range=(x, -20, 20),\n",
    "    xlim=(-10, 10),\n",
    "    #ylim=get_minmax(quintic_df),\n",
    "    ylim=(-10, 30),\n",
    "    title='Sextic (6) functions\\n',\n",
    "    legend=True,\n",
    "    show=False,\n",
    ")\n",
    "sxplot1[0].line_color = 'tab:red'\n",
    "sxplot1[1].line_color = 'tab:blue'\n",
    "sxplot1[2].line_color = 'tab:orange'\n",
    "sxplot1[3].line_color = 'tab:green'\n",
    "sxplot1[4].line_color = 'tab:purple'\n",
    "sxplot1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Septic\n",
    "- https://en.wikipedia.org/wiki/Septic_function\n",
    "- Polynomial of degree 7: $y = x^7$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "septic_df, septic_curves = get_polynomial_df(7, 'septic', xmin=-50, xmax=50, xstep=4, scalar=5)\n",
    "curves.update(septic_curves)\n",
    "septic_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(septic_df, eqdict=septic_curves,\n",
    "            title='Septic (7) functions',\n",
    "            table=False,\n",
    "            legendloc='lower center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "spplot1 = sympy.plotting.plot(\n",
    "    *[x.rhs for x in septic_curves.values()],\n",
    "    range=(x, -20, 20),\n",
    "    xlim=(-10, 10),\n",
    "    #ylim=get_minmax(quintic_df),\n",
    "    ylim=(-10, 30),\n",
    "    title='Septic (7) functions\\n',\n",
    "    legend=True,\n",
    "    show=False,\n",
    ")\n",
    "spplot1[0].line_color = 'tab:red'\n",
    "spplot1[1].line_color = 'tab:blue'\n",
    "spplot1[2].line_color = 'tab:orange'\n",
    "spplot1[3].line_color = 'tab:green'\n",
    "spplot1[4].line_color = 'tab:purple'\n",
    "spplot1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Octic\n",
    "- https://en.wikipedia.org/wiki/Octic_function\n",
    "- Polynomial of degree 8: $y = x^8$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonic\n",
    "- https://en.wikipedia.org/wiki/Nonic_function\n",
    "- Polynomial of degree 9: $y = x^9$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decic\n",
    "- https://en.wikipedia.org/wiki/Decic_function\n",
    "- Polynomial of degree 10: $y = x^{10}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Univariate Polynomials Summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ups_curves = {k:v for k,v in curves.items() if k.endswith('1')}\n",
    "ups_curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_ups_df(curves, xmin=-20, xmax=20, xstep=2):\n",
    "    xval_ary = np.arange(xmin, xmax, xstep)\n",
    "    df = pd.DataFrame(index=xval_ary)\n",
    "    for k, v in curves.items():\n",
    "        df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "    return df\n",
    "ups_df = get_ups_df(ups_curves)\n",
    "ups_df.columns = [sympy.latex(eq, mode='inline') for eq in ups_curves.values()]\n",
    "ups_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(\n",
    "    ups_df, eqdict=None,\n",
    "    table=False,\n",
    "    title='Univariate Polynomials',\n",
    "    legendloc='lower right',\n",
    "    figsize=(8, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(\n",
    "    get_ups_df(ups_curves, xmin=-5, xmax=5, xstep=0.1),\n",
    "    eqdict=ups_curves,\n",
    "    table=False,\n",
    "    title='Univariate Polynomials',\n",
    "    legendloc='lower right',\n",
    "    xticks=np.arange(-5, 5, 1),\n",
    "    ylim=(-20, 20),\n",
    "    figsize=(8, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exponential Functions\n",
    "- https://en.wikipedia.org/wiki/Exponential_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_exponential_df(xmin=-10, xmax=10, xstep=1):\n",
    "    name='exp'\n",
    "    curves = {}\n",
    "    curves[f'{name}0'] = sympy.Eq(y, 0**x)\n",
    "    curves[f'{name}1'] = sympy.Eq(y, 1**x)\n",
    "    curves[f'{name}2'] = sympy.Eq(y, 2**x)\n",
    "    curves[f'{name}3'] = sympy.Eq(y, 2**(x*2))\n",
    "    curves[f'{name}4'] = sympy.Eq(y, 2**(x*3))\n",
    "    xval_ary = np.arange(xmin, xmax, xstep).astype(np.float64)\n",
    "    df = pd.DataFrame(index=xval_ary)\n",
    "    for k, v in curves.items():\n",
    "        df[k] = sympy.lambdify(x, v.rhs, 'numpy')(xval_ary)\n",
    "    return df, curves\n",
    "\n",
    "exponential_df, exponential_curves = get_exponential_df(xmin=-15, xmax=15, xstep=0.5)\n",
    "curves.update(exponential_curves)\n",
    "exponential_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%debug\n",
    "kwargs = dict(\n",
    "    eqdict=exponential_curves,\n",
    "    table=False,\n",
    "    title='Exponential Curves',\n",
    "    legendloc='lower right',\n",
    "    xticks=np.arange(-15, 15, 1),\n",
    "    ylim=(0, 10),\n",
    "    figsize=(8, 5))\n",
    "\n",
    "format_plot(\n",
    "    exponential_df,\n",
    "    **kwargs\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%debug\n",
    "format_plot(\n",
    "    exponential_df,\n",
    "    **{**kwargs,\n",
    "       'ylim':(0, 1000)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "format_plot(\n",
    "    exponential_df,\n",
    "    **{**kwargs,\n",
    "       'ylim':(0, 10000),\n",
    "       'logy': True,\n",
    "       'title':'Exponential Curves (logy=True)',\n",
    "      })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trigonometric Functions\n",
    "- https://docs.scipy.org/doc/numpy/reference/routines.math.html#trigonometric-functions\n",
    "- https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html\n",
    "- https://docs.sympy.org/latest/modules/functions/elementary.html#sympy-functions-elementary-trigonometric\n",
    "- https://docs.sympy.org/latest/modules/functions/elementary.html#sin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Degrees and Radians\n",
    "- $360\\ {degrees} = 2 \\pi\\ {radians}$\n",
    "- $2 \\pi\\ {radians} = 360\\ {degrees}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degrees = [0, 45, 90, 180, 270, 360, 360*2, 360*2+90]\n",
    "vals_rad = [np.deg2rad(n) for n in degrees]\n",
    "vals_rad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals_nested_lists = [[n, np.deg2rad(n), np.deg2rad(n)/np.pi] for n in degrees]\n",
    "vals_nested_lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.asarray(vals_nested_lists), np.asmatrix(vals_nested_lists)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's already not easy to remember which column is which with these nested lists, arrays, and matrices.\n",
    "Instead, we could create a `pandas.DataFrame`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df_rad_deg = pd.DataFrame.from_records(\n",
    "    vals_nested_lists,\n",
    "    columns=['degrees', 'radians', 'pi radians'],\n",
    "    index=[x[0] for x in vals_nested_lists])\n",
    "\n",
    "df2 = df_rad_deg2 = pd.DataFrame(index=degrees)\n",
    "df2['degrees'] = df2.index\n",
    "df2['radians'] = df2['degrees'].apply(np.deg2rad)\n",
    "df2['pi radians'] = df2['radians'] / np.pi\n",
    "\n",
    "assert df_rad_deg.equals(df_rad_deg2)\n",
    "# df2\n",
    "df_rad_deg2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FWIW (for what it's worth), we could calculate the same values with (comparatively slow) *list comprehensions*, or with fast *vectorized array operations* (that can be done in parallel):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pytest.raises(TypeError):\n",
    "    vals_rad / np.pi\n",
    "list_comprehension = [x / np.pi for x in vals_rad]\n",
    "list_comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vectorized_array_operation = np.asarray(vals_rad) / np.pi\n",
    "vectorized_array_operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.testing.assert_allclose(list_comprehension, vectorized_array_operation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degs = np.rad2deg(np.arange(0, 4.5+0.5, 0.5) * np.pi)\n",
    "degs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**SymPy**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degs_sympy = sympy.deg(np.arange(0, 4.5+0.5, 0.5) * np.pi)\n",
    "degs_sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degs_sympy.astype(np.float)\n",
    "#degs_sympy.astype(np.float32)\n",
    "#degs_sympy.astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degs_sympy = sympy.deg(np.arange(0, 4.5+0.5, 0.5) * sympy.pi)\n",
    "degs_sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "degs_sympy.astype(np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setcolors(plot, colors=None):\n",
    "    if colors is None:\n",
    "        colors = [f'tab:{c}' for c in 'red blue orange green purple'.split()]\n",
    "    for p, color in itertools.zip_longest(plot, colors):\n",
    "        if p:\n",
    "            p.line_color = color\n",
    "    return plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sincomponents_plots(powerscalar=1, ylim1=None, ylim2=None):\n",
    "    pows = powerscalar\n",
    "    cm = components = {}\n",
    "    cm['a'] = sympy.sin(x)**(1*pows)\n",
    "    cm['b'] = sympy.sin(x)**(1*pows)*2\n",
    "    cm['c'] = sympy.sin(x)**(2*pows)\n",
    "    cm['d'] = sympy.sin(x)**(3*pows)+1\n",
    "    cm['e'] = sympy.sin(x)**(1*pows)+2\n",
    "    display(cm)\n",
    "\n",
    "    sinplots = sympy.plotting.plot(\n",
    "        *components.values(),\n",
    "        ylim=ylim1 if ylim1 is not None else (0, 3),\n",
    "        legend=True,\n",
    "        show=False,\n",
    "        title='sin(x) independent components\\n'\n",
    "    )\n",
    "    setcolors(sinplots)\n",
    "    sinplots.show()\n",
    "\n",
    "    sinplot = sympy.plotting.plot(\n",
    "        sympy.sin(x),\n",
    "        sum(tuple(components.values())[:-2]),\n",
    "        sum(tuple(components.values())[:-1]),\n",
    "        sum(tuple(components.values())),\n",
    "        ylim=ylim2 if ylim2 is not None else (-3, 9),\n",
    "        legend=True,\n",
    "        show=False,\n",
    "        title='sum(sin(x) components) plots\\n')\n",
    "    setcolors(sinplot)\n",
    "    sinplot.show()\n",
    "    return components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cmp1 = sincomponents_plots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cmp1_inv = sincomponents_plots(-1, ylim1=(-6, 6), ylim2=(-6, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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