Learning-Sympy/Matrix-Determinant-Numpy.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Part B Problem \n",
    "\n",
    "Let $B_n$ denote that $n \\times n$ matrix with $(i, j)$'th enntry equal to:\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "b_{ij} = \\begin{cases}\n",
    "\\frac{1}{2j- i^2}, &\\text{ if } i > j \\\\\n",
    "\\frac{i}{i- j}+  \\frac{1}{n^2- j - i}, &\\text{ if } j>i \\\\\n",
    "0 &\\text{ if } i = j\n",
    "\\end{cases}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "Look at the numerical values of the determinant of $B_n$ for $3≤n≤30$ and display these values graphically. You should observe that the values seem to follow a pattern.\n",
    "\n",
    "  Look at the sequence and show  that  the  $n-\\log{}$  or  $\\log$-$\\log$  transformation  gives  a  fit  that  is  approximately  linear  and  hence obtain  and  test  a  formula  that  predicts  the  value  of  the  sequence.   Define  a  function  that  predicts the value of the determinant of $Bn$.\n",
    "  \n",
    "What is the largest percentage error that your formula has for $30≤n≤50$?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preamble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expressions in `Sympy` are generally immutable, matrices are the exception to this. A consequence of this is that attributes of matrix objects **occur in place**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to generate an empty matrix the `np.empty() function can be used (unlike the `zeros` function it does not set the values to zero and may be marginally faster):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[5.e-324, 0.e+000],\n       [5.e-324, 5.e-324]])"
     },
     "metadata": {},
     "execution_count": 65
    }
   ],
   "source": [
    "n = 2\n",
    "mymat = np.empty([n, n])\n",
    "mymat\n",
    "# mymat.row(2)[1] = 7 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then the values of the matrix may be modified by looping through the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "(0,0)\n(0,1)\n(1,0)\n(1,1)\n"
    }
   ],
   "source": [
    "for i in range(mymat.shape[0]):\n",
    "    for j in range(mymat.shape[1]):\n",
    "        print(\"(\" + str(i) + \",\" + str(j) + \")\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and so to assign the values based on the condition in the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.        , -0.5       , -0.14285714],\n       [-0.83333333,  0.        , -0.2       ],\n       [-0.3       , -0.75      ,  0.        ]])"
     },
     "metadata": {},
     "execution_count": 67
    }
   ],
   "source": [
    "def BuildMat(n):\n",
    "    mymat = np.empty([n, n])\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            # Increment i and j by one because they count from zero\n",
    "            i += 1; j += 1\n",
    "            if (i > j):\n",
    "                v = 1/(2*j - i**2)\n",
    "            elif (j > i):\n",
    "                v = 1/(i-j) + 1/(n**2 - j - i)\n",
    "            else:\n",
    "                v = 0\n",
    "            # Decrement i and j so the index lines up\n",
    "            i -= 1; j -= 1\n",
    "            mymat[j, i] = v\n",
    "    return mymat\n",
    "\n",
    "BuildMat(3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the Determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.11928571428571424"
     },
     "metadata": {},
     "execution_count": 68
    }
   ],
   "source": [
    "def detMat(n):\n",
    "    ## Sympy\n",
    "    # return Determinant(BuildMat(n)).doit()\n",
    "    ## Numpy\n",
    "    return np.linalg.det(BuildMat(n))\n",
    "detMat(3)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the Determinant of Various Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[1.0,\n 0.0,\n 0.0,\n -0.119,\n -0.035,\n -0.018,\n -0.013,\n -0.01,\n -0.008,\n -0.006,\n -0.005,\n -0.004,\n -0.004,\n -0.003,\n -0.003,\n -0.002,\n -0.002,\n -0.002,\n -0.002,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001,\n -0.001]"
     },
     "metadata": {},
     "execution_count": 69
    }
   ],
   "source": [
    "# We double all numbers using map() \n",
    "result = map(detMat, range(30)) \n",
    "# print(list(result))\n",
    "[round(num, 3) for num in list(result)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instead use absolute value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[1.0,\n 0.0,\n 0.0,\n 0.119,\n 0.035,\n 0.018,\n 0.013,\n 0.01,\n 0.008,\n 0.006,\n 0.005,\n 0.004,\n 0.004,\n 0.003,\n 0.003,\n 0.002,\n 0.002,\n 0.002,\n 0.002,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001,\n 0.001]"
     },
     "metadata": {},
     "execution_count": 70
    }
   ],
   "source": [
    "def detMat(n):\n",
    "    return abs(np.linalg.det(BuildMat(n)))\n",
    "\n",
    "# We double all numbers using map() \n",
    "result = map(detMat, range(30)) \n",
    "\n",
    "# print(list(result))\n",
    "[round(num, 3) for num in list(result)]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a Data Frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Matrix.Size  Determinant.Value\n0             0           1.000000\n1             1           0.000000\n2             2           0.000000\n3             3           0.119286\n4             4           0.035258\n5             5           0.018062\n6             6           0.013023\n7             7           0.009959\n8             8           0.007822\n9             9           0.006288\n10           10           0.005158\n11           11           0.004304\n12           12           0.003645\n13           13           0.003125\n14           14           0.002708\n15           15           0.002369\n16           16           0.002090\n17           17           0.001857\n18           18           0.001661\n19           19           0.001494\n20           20           0.001351\n21           21           0.001228\n22           22           0.001121\n23           23           0.001027\n24           24           0.000945\n25           25           0.000872\n26           26           0.000807\n27           27           0.000749\n28           28           0.000697\n29           29           0.000650\n"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data = {'Matrix.Size': range(30),\n",
    "        'Determinant.Value': list(map(detMat, range(30)))\n",
    "}\n",
    "\n",
    "\n",
    "\n",
    "df = pd.DataFrame(data, columns = ['Matrix.Size', 'Determinant.Value'])\n",
    "\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the Data frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that it is necessary to use `copy`, *Julia* and *Python* **unlike** *Mathematica* and ***R*** only create links between data, they do not create new objects, this can cause headaches when rounding data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<ggplot: (8770001690691)>"
     },
     "metadata": {},
     "execution_count": 72
    }
   ],
   "source": [
    "from plotnine import *\n",
    "import copy\n",
    "\n",
    "df_plot = copy.copy(df[3:])\n",
    "df_plot['Determinant.Value'] = df_plot['Determinant.Value'].astype(float).round(3)\n",
    "df_plot\n",
    "\n",
    "(\n",
    "    ggplot(df_plot, aes(x = 'Matrix.Size', y = 'Determinant.Value')) +\n",
    "        geom_point() +\n",
    "        theme_bw() +\n",
    "        labs(x = \"Matrix Size\", y = \"|Determinant Value|\") +\n",
    "        ggtitle('Magnitude of Determinant Given Matrix Size')\n",
    "\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case it appears that the determinant scales exponentially, we can attempt to model that linearly using `scikit`, this is significantly more complex than simply using ***R***. [^lrpy]\n",
    "\n",
    "[^lrpy]: https://towardsdatascience.com/linear-regression-in-6-lines-of-python-5e1d0cd05b8d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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4Gd09Z1m7tW34hX4+o0aF8f358+Huu8O6c+fgd7/LnSPYuBGefDJsHzMmBH/20NCiReFIQURGtCShvx2oN7PZQCewCri7T5stwJr0eP9y4IS7H02f1fM0sN/dHy1iv4fMkePdBa0fEUaNCqd+1tfDqlVhnTscPJhbCJ5/Hp56KmzPDCdlHxEsXhzmDkRkxOg39N39jJmtAbYSTtl8xt1bzey+9PYngJcIZ+60E07ZTM82sgL4K2CPme1Mr/uWu79U1L0ooWk11XTmCfhpNRUWdmbhYrC5c+ErXwnr3OHQodyhoc2bw4QxhOGka67JLQTXXhuuUhaRYSnRefpDbTidstl3TB+gekwV3/nyopExvFNs7nD4cO4RQVMTdHWF7aNGhTmF7NNHlywJp5WKSMkU7Tz9chhOoQ/D9Oyd4cQdOjtzTx9tboa33w7bzcKcQvZZQ0uXhl8yFZGiUOhL+R05klsEmpvDOgiF4FOfyh0aWro03NtARApWzIuzpEA6MkibNi0sX/xi77q3384tBL/6FfzoR73b6+tzC0FDQ/gxOhEpCn3TLzLNAQzAsWPnHxG89Vbv9jlzzr9d5aRJ5euvyDCk4Z0yWfHIP+U926eupppfP3RjnmdIXu++e34hOHSod/usWecXgsmTy9VbkbLT8E6ZVOR5/eUweTLccktYMt57L7cQZK4lyJg5M3doqLERrrxy6PsuMowp9IssmvP6y2HSJLj55rBk/PGP0NKSe+bQCy/0bp8+PbcINDbClClD33eRYUKhX2QP3jov75j+g7fOu+BzNPE7CFdcATfeGJaMEydCIcg+KvjZz8KppQBTp+YOCzU2hgln3a5SIqDQL7JMWCcN8RH1g24jxeWXww03hCXj5MlwD4LsOYIXX+wtBFddlXs00NgIdXUqBFJxNJFbZpr4LaMPPgh3JcueI9i3L/wgHUBt7fmFYMYMFQIZljSRO0IUOvGroaAimjABVqwIS8apU72FIDM8tG1buFcBhAnm7DmChoZwJpEKgYwQCv0yK2TiV0NBQ2DcOLj++rBkdHfD7t25hWDt2nD3MggTzNkXkzU2hmsLVAhkGFLol1khE78D+W1/HRkUQXU1LF8eloyPPoI9e3LnCB59NNzPGMJVxA0NuUcFc+eGH6QTKSOFfpkVMvE7kKEgHRmUyCWXQCoVlozTp2Hv3twjgu9/PxQIgIkTw+8LZc8R1NerEMiQUugPA3curUsUwoVeA6AjgyE2dmzvt/uMnh5obc2dLP6Hf4APPwzbJ0zoLQSZo4J588K9CkRKQKE/ghR6DUCpjwxUIBIYMybcT2DJEvjrvw7renpg//7coaEnnwxzBxDuPbBkSe7Q0Pz54e5lIoOkf0UjSKHXAJTyyGAgQ0cqEmljxoRbTS5eDPembzJ35gy8/nru0NDTT4fhIQjzCtdemzs0dPXV4bVECqDz9CtYob/4OfuhF8n3r8GANx/5Qs66Qq8vGMivj0ZfJM6ehba23CuLW1rC9QUQblS/eHHu6aPXXBOGmSQ6Ok9fSnpkUOjQUaHzC6U+khgRBaWqKtx6csECuOeesO7cOXjjjdyhoeeeg/Xrw/axY3sLQWZ4aOHCMPEsgkK/4iWdJIbC5gwKHToaTkViKIamSlaARo1i86kJrH1rCkfG3Mi0277Ag9+r586JH+ZOFv/jP4Z5AghDQIsW5c4RLFoUjhQkOgp9+VghRwaFTioPpyJR6qOOUhagvO03t8KXF3HnqlWwalVo6A4HD8KOHRx46Zec+OdXqX9uIzVPPRW2jx4djgCyjwgWL4bq6pIeMQ2b4jmA9pVCoS85kh4ZFDp0NJyKRKmPOkpZgBK3N4O5c9n8/qU8PP0yuv/yDnBn+ol3aHj3Tf5m4gnmdR6AzZvDhDFAVRUn5nyKs+Omc1PtHPZO+TP29cwubcEaTsWzjMOHQ1mAEoW+md0GPAZUAU+5+yN9tlt6+x3AKeDr7r4jyXNl5Cpk6Gg4FYlSH3WUsgANqmCZ0VEzhY6aKTTXVPPrZ24MRwSHD388NLTvf/+cz73xW/5y1zYAztoo3vjEDN588VPw9S+GI4IlS2D8+JIWw0Lbl7ovw60ADUa/oW9mVcA64PNAB7DdzLa4+76sZrcD9ellObAeWJ7wuRKJ4VIkSn3UUcoCVPSCZRbuODZzJnzpS9x95nrcnSkn/8Cid9pZ+HY7C9/5HY0HmuD+bb3PmT+fb46awp6r/ow9U+ay78o5/OmSccneswTrh7R4ppWrAA1Wkm/6y4B2dz8IYGYbgZVAdnCvBJ71cP7nq2ZWY2ZTgVkJniuSV6mKRKmPOkpZgIaqYL09cTJvT5zMtvrrgPSpuF+dn3MdwWde+Q1fav0FAOcw3pxUx54pc3lr1tXwy/HhSuPLLx90X5K0L3vxHGDbgawfrCShXwccznrcQfg231+buoTPBcDMVgOrAWbOnJmgWyK5Ci0SpTrqKGUBKmvBmjYtLH/xFwD8uqWT7z37CnM7DrDo7XYWvfM7lh9u5c59r8BLT4Qn19d/PFn836/4JP/+D6M4VlV9/msPsu/DqXiWugANVpLQz/f7sH2v4blQmyTPDSvdNwAbIFyclaBfIkOmkCJRaPtSvzaUsmB9jrVbp/DK8U/3tq0bk3tB2W9+Axs38hngt0DnpKnsrJ3L72fP59qVN7Hik/nDbaQWz1IXoMHq94pcM7se+La735p+/DCAu38nq82TwC/d/cfpx23ADYThnYs+Nx9dkStSYd59N7cQNDfDoUO922fNyv2JiYaGcMOaYWS4n72T9IrcJKE/GjgA3AR0AtuBu929NavNF4A1hLN3lgOPu/uyJM/NR6EvEoE//CH8rER2ITh4sHf7zJm51xE0NsKVV5avv8Nc0X6Gwd3PmNkaYCvhtMtn3L3VzO5Lb38CeIkQ+O2EUzbvvdhzB7hPIlJJPvEJuPnmsGT88Y+9hSBzZPDCC73bp08/vxBMmTL0fR/B9INrIjK8nTgRCkH28NCBA+EaA4CpU88fGpo2LbrbVeoH10SkMlx+OdxwQ1gyTp6EnTtzh4ZefLG3EFx1VW4haGyEurroCkE+Cn0RGXkuuww++9mwZHzwAezalfvDcy+/HH6ZFKC29vxCMGNGdIVAoS8ilWHCBFixIiwZp071FoLM8NC2beFeBRDOEMqeH2hoCGcSVXAhUOiLSOUaNw6uvz4sGd3dsHt37hzB2rXh7mUAkyb1FoLMn3PmVEwhUOiLSFyqq2H58rBkfPgh7NmTWwgefTTczxigpqb3pveZo4K5c2HUqLLswmAo9EVELr0UPv3psGR89BHs3Zs7NPT443D6dNg+cWL4faHsOYL6+mFfCBT6IiL5XHJJb5hnnD4Nra25RwTr1oUCAWFeIVMIMkcF8+aFW18OEzpPX0RkMHp6YP/+3NNHd+0KcwcA48eHexBkF4L588Pdy4qoaD/DUA4KfREZ0c6cgddfzx0aamkJZxNBmFfoWwgWLBhUIVDoi4gMJ2fPQltb7tBQS0u4vgB65xVeeWVAZwrpilwRkeGkqip8m1+wAO65J6w7dw7eeKO3CJw8WfJTQxX6IiLlMmpUmOidNw/uvnto3nJI3kVERIYFhb6ISEQU+iIiEVHoi4hERKEvIhIRhb6ISEQU+iIiEVHoi4hEZFj+DIOZdQG/L3c/8pgMvFvuTgyRWPY1lv2EePY1lv2E3H39pLvX9veEYRn6w5WZNSX5bYtKEMu+xrKfEM++xrKfMLB91fCOiEhEFPoiIhFR6BdmQ7k7MIRi2ddY9hPi2ddY9hMGsK8a0xcRiYi+6YuIREShLyISEYV+QmZ2yMz2mNlOM6uYezma2TNmdszM9matm2Rm28zsjfSfV5Szj8VygX39tpl1pj/XnWZ2Rzn7WAxmNsPMfmFm+82s1czuT6+vuM/1IvtaUZ+rmV1qZr81s13p/fwv6fUFf6Ya00/IzA4BKXevqIs+zOzPgQ+AZ919YXrd/wDec/dHzOwh4Ap3/0/l7GcxXGBfvw184O7fLWffisnMpgJT3X2HmV0GNAN3Al+nwj7Xi+zrV6igz9XMDBjv7h+Y2Rjgn4H7gS9T4Geqb/qRc/dfAe/1Wb0S+EH67z8g/Cca8S6wrxXH3Y+6+470308C+4E6KvBzvci+VhQP0ndQZ0x6cQbwmSr0k3Pg52bWbGary92ZErvK3Y9C+E8FXFnm/pTaGjPbnR7+GfFDHtnMbBawFHiNCv9c++wrVNjnamZVZrYTOAZsc/cBfaYK/eRWuHsDcDvwN+mhAhn51gNzgSXAUeB7Ze1NEZnZBOB54AF3f7/c/SmlPPtacZ+ru5919yXAdGCZmS0cyOso9BNy9yPpP48BLwDLytujknonPVaaGTM9Vub+lIy7v5P+z3QO+J9UyOeaHvd9Hvihu29Kr67IzzXfvlbq5wrg7seBXwK3MYDPVKGfgJmNT08SYWbjgVuAvRd/1oi2Bfha+u9fA/5PGftSUpn/MGlfogI+1/Sk39PAfnd/NGtTxX2uF9rXSvtczazWzGrSf68GbgZeZwCfqc7eScDM5hC+3QOMBn7k7v+tjF0qGjP7MXAD4Sda3wH+M7AZ+AkwE3gL+DfuPuInQC+wrzcQhgAcOAT828wY6UhlZp8B/h+wBziXXv0twlh3RX2uF9nXu6igz9XMFhMmaqsIX9Z/4u7/1cw+QYGfqUJfRCQiGt4REYmIQl9EJCIKfRGRiCj0RUQiotAXEYmIQl9EJCIKfRGRiPx/IZKbBGyeTc0AAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt  # To visualize\n",
    "import pandas as pd  # To read data\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "df_slice = df[3:]\n",
    "\n",
    "X = df_slice.iloc[:, 0].values.reshape(-1, 1)  # values converts it into a numpy array\n",
    "Y = df_slice.iloc[:, 1].values.reshape(-1, 1)  # -1 means that calculate the dimension of rows, but have 1 column\n",
    "linear_regressor = LinearRegression()  # create object for the class\n",
    "linear_regressor.fit(X, Y)  # perform linear regression\n",
    "Y_pred = linear_regressor.predict(X)  # make predictions\n",
    "\n",
    "\n",
    "\n",
    "plt.scatter(X, Y)\n",
    "plt.plot(X, Y_pred, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([5.37864677])"
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log Transform the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `log` function is actually provided by `sympy`, to do this quicker in `numpy` use `np.log()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# # pyperclip.copy(df.columns[0])\n",
    "# #df['Determinant.Value'] = \n",
    "# #[ np.log(val) for val in df['Determinant.Value']]\n",
    "\n",
    "df_log = df\n",
    "\n",
    "df_log['Determinant.Value'] = [ np.log(val) for val in df['Determinant.Value'] ]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to only have well defined values, consider only after size 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    Matrix.Size  Determinant.Value\n3             3          -2.126234\n4             4          -3.345075\n5             5          -4.013934\n6             6          -4.341001\n7             7          -4.609294\n8             8          -4.850835\n9             9          -5.069048\n10           10          -5.267129\n11           11          -5.448099\n12           12          -5.614501\n13           13          -5.768414\n14           14          -5.911529\n15           15          -6.045230\n16           16          -6.170659\n17           17          -6.288765\n18           18          -6.400347\n19           19          -6.506082\n20           20          -6.606547\n21           21          -6.702237\n22           22          -6.793585\n23           23          -6.880964\n24           24          -6.964704\n25           25          -7.045094\n26           26          -7.122390\n27           27          -7.196822\n28           28          -7.268592\n29           29          -7.337885",
      "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>Matrix.Size</th>\n      <th>Determinant.Value</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>-2.126234</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>-3.345075</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>5</td>\n      <td>-4.013934</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>6</td>\n      <td>-4.341001</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>7</td>\n      <td>-4.609294</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>8</td>\n      <td>-4.850835</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>9</td>\n      <td>-5.069048</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>10</td>\n      <td>-5.267129</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>11</td>\n      <td>-5.448099</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>12</td>\n      <td>-5.614501</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>13</td>\n      <td>-5.768414</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>14</td>\n      <td>-5.911529</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>15</td>\n      <td>-6.045230</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>16</td>\n      <td>-6.170659</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>17</td>\n      <td>-6.288765</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>18</td>\n      <td>-6.400347</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>19</td>\n      <td>-6.506082</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>20</td>\n      <td>-6.606547</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>21</td>\n      <td>-6.702237</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>22</td>\n      <td>-6.793585</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>23</td>\n      <td>-6.880964</td>\n    </tr>\n    <tr>\n      <th>24</th>\n      <td>24</td>\n      <td>-6.964704</td>\n    </tr>\n    <tr>\n      <th>25</th>\n      <td>25</td>\n      <td>-7.045094</td>\n    </tr>\n    <tr>\n      <th>26</th>\n      <td>26</td>\n      <td>-7.122390</td>\n    </tr>\n    <tr>\n      <th>27</th>\n      <td>27</td>\n      <td>-7.196822</td>\n    </tr>\n    <tr>\n      <th>28</th>\n      <td>28</td>\n      <td>-7.268592</td>\n    </tr>\n    <tr>\n      <th>29</th>\n      <td>29</td>\n      <td>-7.337885</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 75
    }
   ],
   "source": [
    "df_plot = df_log[3:]\n",
    "df_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A limitation of the *Python* `plotnine` library (compared to *Ggplot2* in ***R***) is that it isn't possible to round values in the `aesthetics` layer, a further limitation with `pandas` also exists when compared to ***R*** that makes rounding data very clusy to do.\n",
    "\n",
    "In order to round data use the `numpy` library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    Matrix.Size  Determinant.Value\n3             3             -2.126\n4             4             -3.345\n5             5             -4.014\n6             6             -4.341\n7             7             -4.609\n8             8             -4.851\n9             9             -5.069\n10           10             -5.267\n11           11             -5.448\n12           12             -5.615\n13           13             -5.768\n14           14             -5.912\n15           15             -6.045\n16           16             -6.171\n17           17             -6.289\n18           18             -6.400\n19           19             -6.506\n20           20             -6.607\n21           21             -6.702\n22           22             -6.794\n23           23             -6.881\n24           24             -6.965\n25           25             -7.045\n26           26             -7.122\n27           27             -7.197\n28           28             -7.269\n29           29             -7.338",
      "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>Matrix.Size</th>\n      <th>Determinant.Value</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>-2.126</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>-3.345</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>5</td>\n      <td>-4.014</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>6</td>\n      <td>-4.341</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>7</td>\n      <td>-4.609</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>8</td>\n      <td>-4.851</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>9</td>\n      <td>-5.069</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>10</td>\n      <td>-5.267</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>11</td>\n      <td>-5.448</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>12</td>\n      <td>-5.615</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>13</td>\n      <td>-5.768</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>14</td>\n      <td>-5.912</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>15</td>\n      <td>-6.045</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>16</td>\n      <td>-6.171</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>17</td>\n      <td>-6.289</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>18</td>\n      <td>-6.400</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>19</td>\n      <td>-6.506</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>20</td>\n      <td>-6.607</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>21</td>\n      <td>-6.702</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>22</td>\n      <td>-6.794</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>23</td>\n      <td>-6.881</td>\n    </tr>\n    <tr>\n      <th>24</th>\n      <td>24</td>\n      <td>-6.965</td>\n    </tr>\n    <tr>\n      <th>25</th>\n      <td>25</td>\n      <td>-7.045</td>\n    </tr>\n    <tr>\n      <th>26</th>\n      <td>26</td>\n      <td>-7.122</td>\n    </tr>\n    <tr>\n      <th>27</th>\n      <td>27</td>\n      <td>-7.197</td>\n    </tr>\n    <tr>\n      <th>28</th>\n      <td>28</td>\n      <td>-7.269</td>\n    </tr>\n    <tr>\n      <th>29</th>\n      <td>29</td>\n      <td>-7.338</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 76
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "df_plot['Determinant.Value'] = df_plot['Determinant.Value'].astype(float).round(3)\n",
    "df_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<ggplot: (8770002281897)>"
     },
     "metadata": {},
     "execution_count": 77
    }
   ],
   "source": [
    "from plotnine import *\n",
    "\n",
    "\n",
    "(ggplot(df_plot[3:], aes(x = 'Matrix.Size', y = 'Determinant.Value')) +\n",
    "   geom_point(fill= \"Blue\") +\n",
    "   labs(x = \"Matrix Size\", y = \"Determinant Value\",\n",
    "        title = \"Plot of Determinant Values\") +\n",
    "   theme_bw() +\n",
    "   stat_smooth(method = 'lm')\n",
    ")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "df_slice = df_plot[3:]\n",
    "\n",
    "X = df_slice.iloc[:, 0].values.reshape(-1, 1)  # values converts it into a numpy array\n",
    "Y = df_slice.iloc[:, 1].values.reshape(-1, 1)  # -1 means that calculate the dimension of rows, but have 1 column\n",
    "linear_regressor = LinearRegression()  # create object for the class\n",
    "linear_regressor.fit(X, Y)  # perform linear regression\n",
    "Y_pred = linear_regressor.predict(X)  # make predictions\n",
    "\n",
    "\n",
    "\n",
    "plt.scatter(X, Y)\n",
    "plt.plot(X, Y_pred, color='red')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "y = -0.12* x-4.02\n"
    }
   ],
   "source": [
    "m = linear_regressor.fit(X, Y).coef_[0][0]\n",
    "b = linear_regressor.fit(X, Y).intercept_[0]\n",
    "\n",
    "print(\"y = \" + str(m.round(2)) + \"* x\" + str(b.round(2)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the model is:\n",
    "\n",
    "$$\n",
    "\\text{abs}(\\text{Det}(M)) = -4n - 0.12\n",
    "$$\n",
    "\n",
    "where:\n",
    "- $n$ is the size of the square matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Largest Percentage Error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the largest percentage error for $n \\in [30, 50]$ it will be necessary to calculate the determinants for the larger range, compressing all the previous steps and calculating the model based on the larger amount of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "y = -0.05* x-5.92\n"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data = {'Matrix.Size': range(30, 50),\n",
    "        'Determinant.Value': list(map(detMat, range(30, 50)))\n",
    "}\n",
    "df = pd.DataFrame(data, columns = ['Matrix.Size', 'Determinant.Value'])\n",
    "df['Determinant.Value'] = [ np.log(val) for val in df['Determinant.Value']]\n",
    "df\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "\n",
    "X = df.iloc[:, 0].values.reshape(-1, 1)  # values converts it into a numpy array\n",
    "Y = df.iloc[:, 1].values.reshape(-1, 1)  # -1 means that calculate the dimension of rows, but have 1 column\n",
    "linear_regressor = LinearRegression()  # create object for the class\n",
    "linear_regressor.fit(X, Y)  # perform linear regression\n",
    "Y_pred = linear_regressor.predict(X)  # make predictions\n",
    "\n",
    "m = linear_regressor.fit(X, Y).coef_[0][0]\n",
    "b = linear_regressor.fit(X, Y).intercept_[0]\n",
    "\n",
    "print(\"y = \" + str(m.round(2)) + \"* x\" + str(b.round(2)))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-5.41415364e-03],\n       [-3.51384602e-03],\n       [-1.90798428e-03],\n       [-5.74487234e-04],\n       [ 5.06726599e-04],\n       [ 1.35396448e-03],\n       [ 1.98395424e-03],\n       [ 2.41201322e-03],\n       [ 2.65219545e-03],\n       [ 2.71742022e-03],\n       [ 2.61958495e-03],\n       [ 2.36966444e-03],\n       [ 1.97779855e-03],\n       [ 1.45336983e-03],\n       [ 8.05072416e-04],\n       [ 4.09734813e-05],\n       [-8.31432011e-04],\n       [-1.80517224e-03],\n       [-2.87375452e-03],\n       [-4.03112573e-03]])"
     },
     "metadata": {},
     "execution_count": 83
    }
   ],
   "source": [
    "Y_hat = linear_regressor.predict(X)\n",
    "res_per = (Y - Y_hat)/Y_hat\n",
    "res_per\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "The Maximum Percentage error is 0.27% which corresponds to a matrix of size 39\n"
    }
   ],
   "source": [
    "max_res = np.max(res_per)\n",
    "max_ind = np.where(res_per == max_res)[0][0] + 30\n",
    "\n",
    "print(\"The Maximum Percentage error is \" + str(max_res.round(4) * 100) + \"% which corresponds to a matrix of size \" + str(max_ind))\n",
    "\n"
   ]
  }
 ]
}