From c5d82d65af43d151439b5a496d965fc280e940e3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Pawe=C5=82=20Sk=C3=B3rzewski?= <pawel.skorzewski@amu.edu.pl>
Date: Tue, 18 Oct 2022 13:52:38 +0200
Subject: [PATCH] =?UTF-8?q?Wyk=C5=82ad=203?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 wyk/03_Regresja_liniowa_2.ipynb | 8562 +------------------------------
 1 file changed, 135 insertions(+), 8427 deletions(-)

diff --git a/wyk/03_Regresja_liniowa_2.ipynb b/wyk/03_Regresja_liniowa_2.ipynb
index 3e786c8..322d53d 100644
--- a/wyk/03_Regresja_liniowa_2.ipynb
+++ b/wyk/03_Regresja_liniowa_2.ipynb
@@ -47,46 +47,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "subslide"
-    }
-   },
+   "execution_count": 5,
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "y : price    x1: isNew    x2: rooms    x3: floor    x4: location x5: sqrMetres\n",
-      "476118.0     False        3            1            Centrum      78          \n",
-      "459531.0     False        3            2            Sołacz       62          \n",
-      "411557.0     False        3            0            Sołacz       15          \n",
-      "496416.0     False        4            0            Sołacz       14          \n",
-      "406032.0     False        3            0            Sołacz       15          \n",
-      "450026.0     False        3            1            Naramowice   80          \n",
-      "571229.15    False        2            4            Wilda        39          \n",
-      "325000.0     False        3            1            Grunwald     54          \n",
-      "268229.0     False        2            1            Grunwald     90          \n"
+      "       y:price  x1:isNew  x2:rooms  x3:floor   x4:location  x5:sqrMetres\n",
+      "1     476118.0     False         3         1       Centrum            78\n",
+      "2     459531.0     False         3         2        Sołacz            62\n",
+      "3     411557.0     False         3         0        Sołacz            15\n",
+      "4     496416.0     False         4         0        Sołacz            14\n",
+      "5     406032.0     False         3         0        Sołacz            15\n",
+      "...        ...       ...       ...       ...           ...           ...\n",
+      "1335  349000.0     False         4         0  Szczepankowo            29\n",
+      "1336  399000.0     False         5         0  Szczepankowo            68\n",
+      "1337  234000.0      True         2         7         Wilda            50\n",
+      "1338  210000.0      True         2         1         Wilda            65\n",
+      "1339  279000.0      True         2         2        Łazarz            36\n",
+      "\n",
+      "[1339 rows x 6 columns]\n"
      ]
     }
    ],
    "source": [
-    "import csv\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
     "\n",
-    "reader = csv.reader(open(\"data02_train.tsv\", encoding=\"utf-8\"), delimiter=\"\\t\")\n",
-    "for i, row in enumerate(list(reader)[:10]):\n",
-    "    if i == 0:\n",
-    "        print(\n",
-    "            \" \".join(\n",
-    "                [\n",
-    "                    \"{}: {:8}\".format(\"x\" + str(j) if j > 0 else \"y \", entry)\n",
-    "                    for j, entry in enumerate(row)\n",
-    "                ]\n",
-    "            )\n",
-    "        )\n",
-    "    else:\n",
-    "        print(\" \".join([\"{:12}\".format(entry) for entry in row]))\n"
+    "data = pd.read_csv(\"data02_train.tsv\", sep=\"\\t\")\n",
+    "data.rename(columns={col: f\"x{i}:{col}\" if i > 0 else f\"y:{col}\" for i, col in enumerate(data.columns)}, inplace=True)\n",
+    "data.index = np.arange(1, len(data) + 1)\n",
+    "print(data)"
    ]
   },
   {
@@ -221,7 +213,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 6,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -231,33 +223,37 @@
    "source": [
     "# Wersje macierzowe funkcji rysowania wykresów punktowych oraz krzywej regresyjnej\n",
     "\n",
-    "\n",
-    "def hMx(theta, X):\n",
-    "    return X * theta\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
     "\n",
     "\n",
-    "def regdotsMx(X, y):\n",
+    "def h(theta, x):\n",
+    "    return x * theta\n",
+    "\n",
+    "\n",
+    "def regdots(x, y, xlabel=\"populacja\", ylabel=\"zysk\"):\n",
     "    fig = plt.figure(figsize=(16 * 0.6, 9 * 0.6))\n",
     "    ax = fig.add_subplot(111)\n",
     "    fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
-    "    ax.scatter([X[:, 1]], [y], c=\"r\", s=50, label=\"Dane\")\n",
+    "    ax.scatter([x[:, 1]], [y], c=\"r\", s=50, label=\"Dane\")\n",
     "\n",
-    "    ax.set_xlabel(\"Populacja\")\n",
-    "    ax.set_ylabel(\"Zysk\")\n",
+    "    ax.set_xlabel(xlabel)\n",
+    "    ax.set_ylabel(ylabel)\n",
     "    ax.margins(0.05, 0.05)\n",
     "    plt.ylim(y.min() - 1, y.max() + 1)\n",
-    "    plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n",
+    "    plt.xlim(np.min(x[:, 1]) - 1, np.max(x[:, 1]) + 1)\n",
     "    return fig\n",
     "\n",
     "\n",
-    "def reglineMx(fig, fun, theta, X):\n",
+    "def regline(fig, fun, theta, x):\n",
     "    ax = fig.axes[0]\n",
-    "    x0, x1 = np.min(X[:, 1]), np.max(X[:, 1])\n",
-    "    L = [x0, x1]\n",
-    "    LX = np.matrix([1, x0, 1, x1]).reshape(2, 2)\n",
+    "    x_min = np.min(x[:, 1])\n",
+    "    x_max = np.max(x[:, 1])\n",
+    "    x_range = [x_min, x_max]\n",
+    "    x_matrix = np.matrix([1, x_min, 1, x_max]).reshape(2, 2)\n",
     "    ax.plot(\n",
-    "        L,\n",
-    "        fun(theta, LX),\n",
+    "        x_range,\n",
+    "        fun(theta, x_matrix),\n",
     "        linewidth=\"2\",\n",
     "        label=(\n",
     "            r\"$y={theta0:.2}{op}{theta1:.2}x$\".format(\n",
@@ -273,7 +269,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 9,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -284,45 +280,41 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 1.  3.  1. 78.]\n",
-      " [ 1.  3.  2. 62.]\n",
-      " [ 1.  3.  0. 15.]\n",
-      " [ 1.  4.  0. 14.]\n",
-      " [ 1.  3.  0. 15.]]\n",
-      "(1339, 4)\n",
-      "\n",
-      "[[476118.]\n",
-      " [459531.]\n",
-      " [411557.]\n",
-      " [496416.]\n",
-      " [406032.]]\n",
-      "(1339, 1)\n"
+      "x[:5]=matrix([[ 1.,  3.,  1., 78.],\n",
+      "        [ 1.,  3.,  2., 62.],\n",
+      "        [ 1.,  3.,  0., 15.],\n",
+      "        [ 1.,  4.,  0., 14.],\n",
+      "        [ 1.,  3.,  0., 15.]])\n",
+      "x.shape=(1339, 4)\n",
+      "y[:5]=matrix([[476118.],\n",
+      "        [459531.],\n",
+      "        [411557.],\n",
+      "        [496416.],\n",
+      "        [406032.]])\n",
+      "y.shape=(1339, 1)\n"
      ]
     }
    ],
    "source": [
-    "# Wczytwanie danych z pliku za pomocą numpy – regresja liniowa wielu zmiennych – notacja macierzowa\n",
+    "# Wczytwanie danych z pliku – regresja liniowa wielu zmiennych – notacja macierzowa\n",
     "\n",
-    "import pandas\n",
+    "import pandas as pd\n",
     "\n",
-    "data = pandas.read_csv(\n",
+    "data = pd.read_csv(\n",
     "    \"data02_train.tsv\", delimiter=\"\\t\", usecols=[\"price\", \"rooms\", \"floor\", \"sqrMetres\"]\n",
     ")\n",
     "m, n_plus_1 = data.values.shape\n",
     "n = n_plus_1 - 1\n",
-    "Xn = data.values[:, 1:].reshape(m, n)\n",
+    "xn = data.values[:, 1:].reshape(m, n)\n",
     "\n",
     "# Dodaj kolumnę jedynek do macierzy\n",
-    "XMx = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
-    "yMx = np.matrix(data.values[:, 0]).reshape(m, 1)\n",
+    "x = np.matrix(np.concatenate((np.ones((m, 1)), xn), axis=1)).reshape(m, n_plus_1)\n",
+    "y = np.matrix(data.values[:, 0]).reshape(m, 1)\n",
     "\n",
-    "print(XMx[:5])\n",
-    "print(XMx.shape)\n",
-    "\n",
-    "print()\n",
-    "\n",
-    "print(yMx[:5])\n",
-    "print(yMx.shape)\n"
+    "print(f\"{x[:5]=}\")\n",
+    "print(f\"{x.shape=}\")\n",
+    "print(f\"{y[:5]=}\")\n",
+    "print(f\"{y.shape=}\")\n"
    ]
   },
   {
@@ -349,7 +341,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 10,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -373,16 +365,16 @@
     "from IPython.display import display, Math, Latex\n",
     "\n",
     "\n",
-    "def JMx(theta, X, y):\n",
+    "def J(theta, X, y):\n",
     "    \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n",
     "    m = len(y)\n",
-    "    J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n",
-    "    return J.item()\n",
+    "    cost = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n",
+    "    return cost.item()\n",
     "\n",
     "\n",
-    "thetaMx = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
+    "theta = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
     "\n",
-    "cost = JMx(thetaMx, XMx, yMx)\n",
+    "cost = J(theta, x, y)\n",
     "display(Math(r\"\\Large J(\\theta) = %.4f\" % cost))\n"
    ]
   },
@@ -410,7 +402,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 13,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "notes"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# Wyświetlanie macierzy w LaTeX-u\n",
+    "\n",
+    "\n",
+    "def latex_matrix(matrix):\n",
+    "    ltx = r\"\\left[\\begin{array}\"\n",
+    "    m, n = matrix.shape\n",
+    "    ltx += \"{\" + (\"r\" * n) + \"}\"\n",
+    "    for i in range(m):\n",
+    "        ltx += r\" & \".join([(\"%.4f\" % j.item()) for j in matrix[i]]) + r\" \\\\ \"\n",
+    "    ltx += r\"\\end{array}\\right]\"\n",
+    "    return ltx\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -434,20 +449,20 @@
     "from IPython.display import display, Math, Latex\n",
     "\n",
     "\n",
-    "def dJMx(theta, X, y):\n",
+    "def dJ(theta, X, y):\n",
     "    \"\"\"Wersja macierzowa gradientu funckji kosztu\"\"\"\n",
     "    return 1.0 / len(y) * (X.T * (X * theta - y))\n",
     "\n",
     "\n",
-    "thetaMx = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
+    "theta = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
     "\n",
     "display(\n",
     "    Math(\n",
     "        r\"\\large \\theta = \"\n",
-    "        + LatexMatrix(thetaMx)\n",
+    "        + latex_matrix(theta)\n",
     "        + r\"\\quad\"\n",
     "        + r\"\\large \\nabla J(\\theta) = \"\n",
-    "        + LatexMatrix(dJMx(thetaMx, XMx, yMx))\n",
+    "        + latex_matrix(dJ(theta, x, y))\n",
     "    )\n",
     ")\n"
    ]
@@ -476,7 +491,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 16,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -500,7 +515,7 @@
     "# Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\n",
     "\n",
     "\n",
-    "def GDMx(fJ, fdJ, theta, X, y, alpha, eps):\n",
+    "def gradient_descent(fJ, fdJ, theta, X, y, alpha, eps):\n",
     "    current_cost = fJ(theta, X, y)\n",
     "    history = [[current_cost, theta]]\n",
     "    while True:\n",
@@ -515,16 +530,15 @@
     "    return theta, history\n",
     "\n",
     "\n",
-    "thetaStartMx = np.zeros((n + 1, 1))\n",
+    "theta_start = np.zeros((n + 1, 1))\n",
     "\n",
     "# Zmieniamy wartości alpha (rozmiar kroku) oraz eps (kryterium stopu)\n",
-    "thetaBestMx, history = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.0001, eps=0.1)\n",
+    "theta_best, history = gradient_descent(J, dJ, theta_start, x, y, alpha=0.0001, eps=0.1)\n",
     "\n",
-    "######################################################################\n",
     "display(\n",
     "    Math(\n",
     "        r\"\\large\\textrm{Wynik:}\\quad \\theta = \"\n",
-    "        + LatexMatrix(thetaBestMx)\n",
+    "        + latex_matrix(theta_best)\n",
     "        + (r\" \\quad J(\\theta) = %.4f\" % history[-1][0])\n",
     "        + r\" \\quad \\textrm{po %d iteracjach}\" % len(history)\n",
     "    )\n",
@@ -583,1095 +597,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 18,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
     }
    },
    "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "x and y must be the same size",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn [18], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m theta_start \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros((\u001b[39m2\u001b[39m, \u001b[39m1\u001b[39m))\n\u001b[0;32m----> 3\u001b[0m fig \u001b[39m=\u001b[39m regdots(x[\u001b[39m1\u001b[39m], y)\n",
+      "Cell \u001b[0;32mIn [6], line 15\u001b[0m, in \u001b[0;36mregdots\u001b[0;34m(x, y, xlabel, ylabel)\u001b[0m\n\u001b[1;32m     13\u001b[0m ax \u001b[39m=\u001b[39m fig\u001b[39m.\u001b[39madd_subplot(\u001b[39m111\u001b[39m)\n\u001b[1;32m     14\u001b[0m fig\u001b[39m.\u001b[39msubplots_adjust(left\u001b[39m=\u001b[39m\u001b[39m0.1\u001b[39m, right\u001b[39m=\u001b[39m\u001b[39m0.9\u001b[39m, bottom\u001b[39m=\u001b[39m\u001b[39m0.1\u001b[39m, top\u001b[39m=\u001b[39m\u001b[39m0.9\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m ax\u001b[39m.\u001b[39;49mscatter([x[:, \u001b[39m1\u001b[39;49m]], [y], c\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mr\u001b[39;49m\u001b[39m\"\u001b[39;49m, s\u001b[39m=\u001b[39;49m\u001b[39m50\u001b[39;49m, label\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mDane\u001b[39;49m\u001b[39m\"\u001b[39;49m)\n\u001b[1;32m     17\u001b[0m ax\u001b[39m.\u001b[39mset_xlabel(xlabel)\n\u001b[1;32m     18\u001b[0m ax\u001b[39m.\u001b[39mset_ylabel(ylabel)\n",
+      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/__init__.py:1423\u001b[0m, in \u001b[0;36m_preprocess_data.<locals>.inner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1420\u001b[0m \u001b[39m@functools\u001b[39m\u001b[39m.\u001b[39mwraps(func)\n\u001b[1;32m   1421\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39minner\u001b[39m(ax, \u001b[39m*\u001b[39margs, data\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs):\n\u001b[1;32m   1422\u001b[0m     \u001b[39mif\u001b[39;00m data \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m-> 1423\u001b[0m         \u001b[39mreturn\u001b[39;00m func(ax, \u001b[39m*\u001b[39;49m\u001b[39mmap\u001b[39;49m(sanitize_sequence, args), \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m   1425\u001b[0m     bound \u001b[39m=\u001b[39m new_sig\u001b[39m.\u001b[39mbind(ax, \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs)\n\u001b[1;32m   1426\u001b[0m     auto_label \u001b[39m=\u001b[39m (bound\u001b[39m.\u001b[39marguments\u001b[39m.\u001b[39mget(label_namer)\n\u001b[1;32m   1427\u001b[0m                   \u001b[39mor\u001b[39;00m bound\u001b[39m.\u001b[39mkwargs\u001b[39m.\u001b[39mget(label_namer))\n",
+      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/axes/_axes.py:4512\u001b[0m, in \u001b[0;36mAxes.scatter\u001b[0;34m(self, x, y, s, c, marker, cmap, norm, vmin, vmax, alpha, linewidths, edgecolors, plotnonfinite, **kwargs)\u001b[0m\n\u001b[1;32m   4510\u001b[0m y \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mma\u001b[39m.\u001b[39mravel(y)\n\u001b[1;32m   4511\u001b[0m \u001b[39mif\u001b[39;00m x\u001b[39m.\u001b[39msize \u001b[39m!=\u001b[39m y\u001b[39m.\u001b[39msize:\n\u001b[0;32m-> 4512\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39m\"\u001b[39m\u001b[39mx and y must be the same size\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m   4514\u001b[0m \u001b[39mif\u001b[39;00m s \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m   4515\u001b[0m     s \u001b[39m=\u001b[39m (\u001b[39m20\u001b[39m \u001b[39mif\u001b[39;00m mpl\u001b[39m.\u001b[39mrcParams[\u001b[39m'\u001b[39m\u001b[39m_internal.classic_mode\u001b[39m\u001b[39m'\u001b[39m] \u001b[39melse\u001b[39;00m\n\u001b[1;32m   4516\u001b[0m          mpl\u001b[39m.\u001b[39mrcParams[\u001b[39m'\u001b[39m\u001b[39mlines.markersize\u001b[39m\u001b[39m'\u001b[39m] \u001b[39m*\u001b[39m\u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m)\n",
+      "\u001b[0;31mValueError\u001b[0m: x and y must be the same size"
+     ]
+    },
     {
      "data": {
-      "image/svg+xml": [
-       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
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"iVBORw0KGgoAAAANSUhEUgAAAz4AAAHhCAYAAACvPGsLAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/av/WaAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAgDElEQVR4nO3df2zdZb3A8U/b0VOItAznuh/34C54ARXYcGO14EK4qTSRTPfHDXWYbVlARCcBGq9s/FhFdN1VIEukuDDxYnKDmy6ChC1FrCxGqVnc1gTiNoJzbiG22/SunUVb1n7vH4bjrevGTmk7+vh6JeePPTzPOc8hD/O8/Z4fJVmWZQEAAJCw0jO9AQAAgLEmfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkFR0+P//5z2PhwoUxY8aMKCkpiWeeeeZt12zbti0+8pGPRC6Xiw984APx5JNPjmCrAAAAI1N0+PT29sbs2bOjpaXltOb/7ne/ixtuuCGuu+666OjoiDvvvDNuueWWeP7554veLAAAwEiUZFmWjXhxSUk8/fTTsWjRopPOufvuu2PLli3xyiuvFMY+/elPx9GjR6O1tXWkDw0AAHDaJo31A7S3t0ddXd2Qsfr6+rjzzjtPuqavry/6+voKfx4cHIw//elP8d73vjdKSkrGaqsAAMC7QJZlcezYsZgxY0aUlo7O1xKMefh0dnZGdXX1kLHq6uro6emJv/zlL3H22WefsKa5uTkeeOCBsd4aAADwLnbw4MH4l3/5l1G5rzEPn5FYtWpVNDY2Fv7c3d0dF1xwQRw8eDAqKyvP4M4AAICx1tPTE/l8Ps4999xRu88xD59p06ZFV1fXkLGurq6orKwc9mpPREQul4tcLnfCeGVlpfABAIB/EqP5MZcx/x2f2traaGtrGzL2wgsvRG1t7Vg/NAAAQESMIHz+/Oc/R0dHR3R0dETE376uuqOjIw4cOBARf3ub2tKlSwvzb7vttti3b198+ctfjj179sRjjz0WP/jBD+Kuu+4anWcAAADwNooOn1//+tdx5ZVXxpVXXhkREY2NjXHllVfG6tWrIyLiD3/4QyGCIiL+9V//NbZs2RIvvPBCzJ49Ox5++OH4zne+E/X19aP0FAAAAE7tHf2Oz3jp6emJqqqq6O7u9hkfAABI3Fi8/h/zz/gAAACcacIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSN6LwaWlpiVmzZkVFRUXU1NTE9u3bTzl/3bp1cckll8TZZ58d+Xw+7rrrrvjrX/86og0DAAAUq+jw2bRpUzQ2NkZTU1Ps3LkzZs+eHfX19XHo0KFh5z/11FOxcuXKaGpqit27d8cTTzwRmzZtinvuuecdbx4AAOB0FB0+jzzySHz2s5+N5cuXx4c+9KFYv359nHPOOfHd73532PkvvfRSXHPNNXHTTTfFrFmz4vrrr4/Fixe/7VUiAACA0VJU+PT398eOHTuirq7u73dQWhp1dXXR3t4+7Jqrr746duzYUQidffv2xdatW+MTn/jEO9g2AADA6ZtUzOQjR47EwMBAVFdXDxmvrq6OPXv2DLvmpptuiiNHjsTHPvaxyLIsjh8/Hrfddtsp3+rW19cXfX19hT/39PQUs00AAIAhxvxb3bZt2xZr1qyJxx57LHbu3Bk/+tGPYsuWLfHggw+edE1zc3NUVVUVbvl8fqy3CQAAJKwky7LsdCf39/fHOeecE5s3b45FixYVxpctWxZHjx6NH//4xyesWbBgQXz0ox+Nb37zm4Wx//mf/4lbb701/vznP0dp6YntNdwVn3w+H93d3VFZWXm62wUAACagnp6eqKqqGtXX/0Vd8SkvL4+5c+dGW1tbYWxwcDDa2tqitrZ22DVvvPHGCXFTVlYWEREna65cLheVlZVDbgAAACNV1Gd8IiIaGxtj2bJlMW/evJg/f36sW7cuent7Y/ny5RERsXTp0pg5c2Y0NzdHRMTChQvjkUceiSuvvDJqamritddei/vvvz8WLlxYCCAAAICxVHT4NDQ0xOHDh2P16tXR2dkZc+bMidbW1sIXHhw4cGDIFZ777rsvSkpK4r777ovXX3893ve+98XChQvj61//+ug9CwAAgFMo6jM+Z8pYvMcPAAB4dzrjn/EBAACYiIQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJG1H4tLS0xKxZs6KioiJqampi+/btp5x/9OjRWLFiRUyfPj1yuVxcfPHFsXXr1hFtGAAAoFiTil2wadOmaGxsjPXr10dNTU2sW7cu6uvrY+/evTF16tQT5vf398fHP/7xmDp1amzevDlmzpwZv//97+O8884bjf0DAAC8rZIsy7JiFtTU1MRVV10Vjz76aEREDA4ORj6fj9tvvz1Wrlx5wvz169fHN7/5zdizZ0+cddZZI9pkT09PVFVVRXd3d1RWVo7oPgAAgIlhLF7/F/VWt/7+/tixY0fU1dX9/Q5KS6Ouri7a29uHXfPss89GbW1trFixIqqrq+Oyyy6LNWvWxMDAwEkfp6+vL3p6eobcAAAARqqo8Dly5EgMDAxEdXX1kPHq6uro7Owcds2+ffti8+bNMTAwEFu3bo37778/Hn744fja17520sdpbm6Oqqqqwi2fzxezTQAAgCHG/FvdBgcHY+rUqfH444/H3Llzo6GhIe69995Yv379SdesWrUquru7C7eDBw+O9TYBAICEFfXlBlOmTImysrLo6uoaMt7V1RXTpk0bds306dPjrLPOirKyssLYBz/4wejs7Iz+/v4oLy8/YU0ul4tcLlfM1gAAAE6qqCs+5eXlMXfu3GhrayuMDQ4ORltbW9TW1g675pprronXXnstBgcHC2OvvvpqTJ8+fdjoAQAAGG1Fv9WtsbExNmzYEN/73vdi9+7d8fnPfz56e3tj+fLlERGxdOnSWLVqVWH+5z//+fjTn/4Ud9xxR7z66quxZcuWWLNmTaxYsWL0ngUAAMApFP07Pg0NDXH48OFYvXp1dHZ2xpw5c6K1tbXwhQcHDhyI0tK/91Q+n4/nn38+7rrrrrjiiiti5syZcccdd8Tdd989es8CAADgFIr+HZ8zwe/4AADAP48z/js+AAAAE5HwAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5AkfAAAgecIHAABInvABAACSJ3wAAIDkCR8AACB5wgcAAEie8AEAAJInfAAAgOQJHwAAIHnCBwAASJ7wAQAAkid8AACA5I0ofFpaWmLWrFlRUVERNTU1sX379tNat3HjxigpKYlFixaN5GEBAABGpOjw2bRpUzQ2NkZTU1Ps3LkzZs+eHfX19XHo0KFTrtu/f3986UtfigULFox4swAAACNRdPg88sgj8dnPfjaWL18eH/rQh2L9+vVxzjnnxHe/+92TrhkYGIjPfOYz8cADD8SFF174jjYMAABQrKLCp7+/P3bs2BF1dXV/v4PS0qirq4v29vaTrvvqV78aU6dOjZtvvvm0Hqevry96enqG3AAAAEaqqPA5cuRIDAwMRHV19ZDx6urq6OzsHHbNL37xi3jiiSdiw4YNp/04zc3NUVVVVbjl8/litgkAADDEmH6r27Fjx2LJkiWxYcOGmDJlymmvW7VqVXR3dxduBw8eHMNdAgAAqZtUzOQpU6ZEWVlZdHV1DRnv6uqKadOmnTD/t7/9bezfvz8WLlxYGBscHPzbA0+aFHv37o2LLrrohHW5XC5yuVwxWwMAADipoq74lJeXx9y5c6Otra0wNjg4GG1tbVFbW3vC/EsvvTRefvnl6OjoKNw++clPxnXXXRcdHR3ewgYAAIyLoq74REQ0NjbGsmXLYt68eTF//vxYt25d9Pb2xvLlyyMiYunSpTFz5sxobm6OioqKuOyyy4asP++88yIiThgHAAAYK0WHT0NDQxw+fDhWr14dnZ2dMWfOnGhtbS184cGBAweitHRMPzoEAABQlJIsy7IzvYm309PTE1VVVdHd3R2VlZVnejsAAMAYGovX/y7NAAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkb0Th09LSErNmzYqKioqoqamJ7du3n3Tuhg0bYsGCBTF58uSYPHly1NXVnXI+AADAaCs6fDZt2hSNjY3R1NQUO3fujNmzZ0d9fX0cOnRo2Pnbtm2LxYsXx4svvhjt7e2Rz+fj+uuvj9dff/0dbx4AAOB0lGRZlhWzoKamJq666qp49NFHIyJicHAw8vl83H777bFy5cq3XT8wMBCTJ0+ORx99NJYuXXpaj9nT0xNVVVXR3d0dlZWVxWwXAACYYMbi9X9RV3z6+/tjx44dUVdX9/c7KC2Nurq6aG9vP637eOONN+LNN9+M888//6Rz+vr6oqenZ8gNAABgpIoKnyNHjsTAwEBUV1cPGa+uro7Ozs7Tuo+77747ZsyYMSSe/lFzc3NUVVUVbvl8vphtAgAADDGu3+q2du3a2LhxYzz99NNRUVFx0nmrVq2K7u7uwu3gwYPjuEsAACA1k4qZPGXKlCgrK4uurq4h411dXTFt2rRTrn3ooYdi7dq18dOf/jSuuOKKU87N5XKRy+WK2RoAAMBJFXXFp7y8PObOnRttbW2FscHBwWhra4va2tqTrvvGN74RDz74YLS2tsa8efNGvlsAAIARKOqKT0REY2NjLFu2LObNmxfz58+PdevWRW9vbyxfvjwiIpYuXRozZ86M5ubmiIj4r//6r1i9enU89dRTMWvWrMJngd7znvfEe97znlF8KgAAAMMrOnwaGhri8OHDsXr16ujs7Iw5c+ZEa2tr4QsPDhw4EKWlf7+Q9O1vfzv6+/vjP/7jP4bcT1NTU3zlK195Z7sHAAA4DUX/js+Z4Hd8AADgn8cZ/x0fAACAiUj4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyRM+AABA8kYUPi0tLTFr1qyoqKiImpqa2L59+ynn//CHP4xLL700Kioq4vLLL4+tW7eOaLMAAAAjUXT4bNq0KRobG6OpqSl27twZs2fPjvr6+jh06NCw81966aVYvHhx3HzzzbFr165YtGhRLFq0KF555ZV3vHkAAIDTUZJlWVbMgpqamrjqqqvi0UcfjYiIwcHByOfzcfvtt8fKlStPmN/Q0BC9vb3x3HPPFcY++tGPxpw5c2L9+vWn9Zg9PT1RVVUV3d3dUVlZWcx2AQCACWYsXv9PKmZyf39/7NixI1atWlUYKy0tjbq6umhvbx92TXt7ezQ2Ng4Zq6+vj2eeeeakj9PX1xd9fX2FP3d3d0fE3/4FAAAAaXvrdX+R12hOqajwOXLkSAwMDER1dfWQ8erq6tizZ8+wazo7O4ed39nZedLHaW5ujgceeOCE8Xw+X8x2AQCACeyPf/xjVFVVjcp9FRU+42XVqlVDrhIdPXo03v/+98eBAwdG7YnD/9fT0xP5fD4OHjzo7ZSMGeeM8eCcMdacMcZDd3d3XHDBBXH++eeP2n0WFT5TpkyJsrKy6OrqGjLe1dUV06ZNG3bNtGnTipofEZHL5SKXy50wXlVV5T8wxlRlZaUzxphzzhgPzhljzRljPJSWjt6v7xR1T+Xl5TF37txoa2srjA0ODkZbW1vU1tYOu6a2tnbI/IiIF1544aTzAQAARlvRb3VrbGyMZcuWxbx582L+/Pmxbt266O3tjeXLl0dExNKlS2PmzJnR3NwcERF33HFHXHvttfHwww/HDTfcEBs3boxf//rX8fjjj4/uMwEAADiJosOnoaEhDh8+HKtXr47Ozs6YM2dOtLa2Fr7A4MCBA0MuSV199dXx1FNPxX333Rf33HNP/Nu//Vs888wzcdlll532Y+ZyuWhqahr27W8wGpwxxoNzxnhwzhhrzhjjYSzOWdG/4wMAADDRjN6nhQAAAN6lhA8AAJA84QMAACRP+AAAAMl714RPS0tLzJo1KyoqKqKmpia2b99+yvk//OEP49JLL42Kioq4/PLLY+vWreO0UyaqYs7Yhg0bYsGCBTF58uSYPHly1NXVve2ZhIji/y57y8aNG6OkpCQWLVo0thtkwiv2jB09ejRWrFgR06dPj1wuFxdffLH/zeRtFXvO1q1bF5dcckmcffbZkc/n46677oq//vWv47RbJpqf//znsXDhwpgxY0aUlJTEM88887Zrtm3bFh/5yEcil8vFBz7wgXjyySeLftx3Rfhs2rQpGhsbo6mpKXbu3BmzZ8+O+vr6OHTo0LDzX3rppVi8eHHcfPPNsWvXrli0aFEsWrQoXnnllXHeORNFsWds27ZtsXjx4njxxRejvb098vl8XH/99fH666+P886ZSIo9Z2/Zv39/fOlLX4oFCxaM006ZqIo9Y/39/fHxj3889u/fH5s3b469e/fGhg0bYubMmeO8cyaSYs/ZU089FStXroympqbYvXt3PPHEE7Fp06a45557xnnnTBS9vb0xe/bsaGlpOa35v/vd7+KGG26I6667Ljo6OuLOO++MW265JZ5//vniHjh7F5g/f362YsWKwp8HBgayGTNmZM3NzcPOv/HGG7MbbrhhyFhNTU32uc99bkz3ycRV7Bn7R8ePH8/OPffc7Hvf+95YbZEEjOScHT9+PLv66quz73znO9myZcuyT33qU+OwUyaqYs/Yt7/97ezCCy/M+vv7x2uLJKDYc7ZixYrs3//934eMNTY2Ztdcc82Y7pM0RET29NNPn3LOl7/85ezDH/7wkLGGhoasvr6+qMc641d8+vv7Y8eOHVFXV1cYKy0tjbq6umhvbx92TXt7+5D5ERH19fUnnc8/t5GcsX/0xhtvxJtvvhnnn3/+WG2TCW6k5+yrX/1qTJ06NW6++ebx2CYT2EjO2LPPPhu1tbWxYsWKqK6ujssuuyzWrFkTAwMD47VtJpiRnLOrr746duzYUXg73L59+2Lr1q3xiU98Ylz2TPpG67X/pNHc1EgcOXIkBgYGorq6esh4dXV17NmzZ9g1nZ2dw87v7Owcs30ycY3kjP2ju+++O2bMmHHCf3TwlpGcs1/84hfxxBNPREdHxzjskIluJGds37598bOf/Sw+85nPxNatW+O1116LL3zhC/Hmm29GU1PTeGybCWYk5+ymm26KI0eOxMc+9rHIsiyOHz8et912m7e6MWpO9tq/p6cn/vKXv8TZZ599Wvdzxq/4wLvd2rVrY+PGjfH0009HRUXFmd4OiTh27FgsWbIkNmzYEFOmTDnT2yFRg4ODMXXq1Hj88cdj7ty50dDQEPfee2+sX7/+TG+NhGzbti3WrFkTjz32WOzcuTN+9KMfxZYtW+LBBx8801uDIc74FZ8pU6ZEWVlZdHV1DRnv6uqKadOmDbtm2rRpRc3nn9tIzthbHnrooVi7dm389Kc/jSuuuGIst8kEV+w5++1vfxv79++PhQsXFsYGBwcjImLSpEmxd+/euOiii8Z200woI/m7bPr06XHWWWdFWVlZYeyDH/xgdHZ2Rn9/f5SXl4/pnpl4RnLO7r///liyZEnccsstERFx+eWXR29vb9x6661x7733Rmmp/5+dd+Zkr/0rKytP+2pPxLvgik95eXnMnTs32traCmODg4PR1tYWtbW1w66pra0dMj8i4oUXXjjpfP65jeSMRUR84xvfiAcffDBaW1tj3rx547FVJrBiz9mll14aL7/8cnR0dBRun/zkJwvfWJPP58dz+0wAI/m77JprronXXnutENUREa+++mpMnz5d9DCskZyzN95444S4eSu2//bZdXhnRu21f3HfuzA2Nm7cmOVyuezJJ5/MfvOb32S33nprdt5552WdnZ1ZlmXZkiVLspUrVxbm//KXv8wmTZqUPfTQQ9nu3buzpqam7KyzzspefvnlM/UUeJcr9oytXbs2Ky8vzzZv3pz94Q9/KNyOHTt2pp4CE0Cx5+wf+VY33k6xZ+zAgQPZueeem33xi1/M9u7dmz333HPZ1KlTs6997Wtn6ikwARR7zpqamrJzzz03+/73v5/t27cv+8lPfpJddNFF2Y033nimngLvcseOHct27dqV7dq1K4uI7JFHHsl27dqV/f73v8+yLMtWrlyZLVmypDB/37592TnnnJP953/+Z7Z79+6spaUlKysry1pbW4t63HdF+GRZln3rW9/KLrjggqy8vDybP39+9qtf/arwz6699tps2bJlQ+b/4Ac/yC6++OKsvLw8+/CHP5xt2bJlnHfMRFPMGXv/+9+fRcQJt6ampvHfOBNKsX+X/X/Ch9NR7Bl76aWXspqamiyXy2UXXnhh9vWvfz07fvz4OO+aiaaYc/bmm29mX/nKV7KLLrooq6ioyPL5fPaFL3wh+9///d/x3zgTwosvvjjs66y3ztWyZcuya6+99oQ1c+bMycrLy7MLL7ww++///u+iH7cky1yDBAAA0nbGP+MDAAAw1oQPAACQPOEDAAAkT/gAAADJEz4AAEDyhA8AAJA84QMAACRP+AAAAMkTPgAAQPKEDwAAkDzhAwAAJE/4AAAAyfs/oHyzuxnlbAQAAAAASUVORK5CYII=",
       "text/plain": [
        "<Figure size 960x540 with 1 Axes>"
       ]
@@ -1681,28 +630,18 @@
     }
    ],
    "source": [
-    "# Wczytwanie danych z pliku za pomocą numpy – wersja macierzowa\n",
-    "data = np.loadtxt(\"data01_train.csv\", delimiter=\",\")\n",
-    "m, n_plus_1 = data.shape\n",
-    "n = n_plus_1 - 1\n",
-    "Xn = data[:, 0:n].reshape(m, n)\n",
+    "theta_start = np.zeros((2, 1))\n",
     "\n",
-    "# Dodaj kolumnę jedynek do macierzy\n",
-    "XMx = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
-    "yMx = np.matrix(data[:, 1]).reshape(m, 1)\n",
-    "\n",
-    "thetaStartMx = np.zeros((2, 1))\n",
-    "\n",
-    "fig = regdotsMx(XMx, yMx)\n",
-    "theta_e1, history1 = GDMx(\n",
-    "    JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.01\n",
-    ")  # niebieska linia\n",
-    "reglineMx(fig, hMx, theta_e1, XMx)\n",
-    "theta_e2, history2 = GDMx(\n",
-    "    JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.000001\n",
-    ")  # pomarańczowa linia\n",
-    "reglineMx(fig, hMx, theta_e2, XMx)\n",
-    "legend(fig)\n"
+    "fig = regdots(x[1], y)\n",
+    "# theta_e1, history1 = GDMx(\n",
+    "#     JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.01\n",
+    "# )  # niebieska linia\n",
+    "# reglineMx(fig, hMx, theta_e1, XMx)\n",
+    "# theta_e2, history2 = GDMx(\n",
+    "#     JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.000001\n",
+    "# )  # pomarańczowa linia\n",
+    "# reglineMx(fig, hMx, theta_e2, XMx)\n",
+    "# legend(fig)\n"
    ]
   },
   {
@@ -1731,9 +670,9 @@
     "display(\n",
     "    Math(\n",
     "        r\"\\theta_{10^{-2}} = \"\n",
-    "        + LatexMatrix(theta_e1)\n",
+    "        + latex_matrix(theta_e1)\n",
     "        + r\"\\quad\\theta_{10^{-6}} = \"\n",
-    "        + LatexMatrix(theta_e2)\n",
+    "        + latex_matrix(theta_e2)\n",
     "    )\n",
     ")\n"
    ]
@@ -2148,3602 +1087,7 @@
    "outputs": [
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