From 5d7bdd5a05214dbce8537fe936cecc46ef09a96c Mon Sep 17 00:00:00 2001
From: gsingh58 <gurmail-singh@wisc.edu>
Date: Tue, 16 Apr 2024 06:10:19 -0500
Subject: [PATCH] Quiz 9 released

---
 lecture_material/21-linalg-2/21-linalg2.ipynb | 352 ++++++++++--------
 1 file changed, 200 insertions(+), 152 deletions(-)

diff --git a/lecture_material/21-linalg-2/21-linalg2.ipynb b/lecture_material/21-linalg-2/21-linalg2.ipynb
index d7848a3..2b412c5 100644
--- a/lecture_material/21-linalg-2/21-linalg2.ipynb
+++ b/lecture_material/21-linalg-2/21-linalg2.ipynb
@@ -1641,20 +1641,48 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 44,
    "id": "f719b210",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[10,  0,  1],\n",
+       "       [ 2,  8,  1],\n",
+       "       [ 4,  4,  1],\n",
+       "       [ 5,  5,  1]])"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "X"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 45,
    "id": "73e680f3",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[7.  ],\n",
+       "       [5.  ],\n",
+       "       [5.  ],\n",
+       "       [5.75]])"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "y"
    ]
@@ -1669,7 +1697,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 46,
    "id": "bf3ec400",
    "metadata": {},
    "outputs": [
@@ -1681,7 +1709,7 @@
        "       [2.  ]])"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1701,7 +1729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 47,
    "id": "b4c45f0e",
    "metadata": {},
    "outputs": [
@@ -1711,7 +1739,7 @@
        "(3, 3)"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 47,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1769,7 +1797,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 48,
    "id": "3506a459",
    "metadata": {},
    "outputs": [
@@ -1783,7 +1811,7 @@
        "       [8.5]])"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1802,7 +1830,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 49,
    "id": "96826616-3a4a-42da-8259-35ac984dc10e",
    "metadata": {},
    "outputs": [
@@ -1813,7 +1841,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[47], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinalg\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      2\u001b[0m c\n",
+      "Cell \u001b[0;32mIn[49], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinalg\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      2\u001b[0m c\n",
       "File \u001b[0;32m<__array_function__ internals>:200\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
       "File \u001b[0;32m~/.local/lib/python3.8/site-packages/numpy/linalg/linalg.py:373\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m    371\u001b[0m a, _ \u001b[38;5;241m=\u001b[39m _makearray(a)\n\u001b[1;32m    372\u001b[0m _assert_stacked_2d(a)\n\u001b[0;32m--> 373\u001b[0m \u001b[43m_assert_stacked_square\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    374\u001b[0m b, wrap \u001b[38;5;241m=\u001b[39m _makearray(b)\n\u001b[1;32m    375\u001b[0m t, result_t \u001b[38;5;241m=\u001b[39m _commonType(a, b)\n",
       "File \u001b[0;32m~/.local/lib/python3.8/site-packages/numpy/linalg/linalg.py:190\u001b[0m, in \u001b[0;36m_assert_stacked_square\u001b[0;34m(*arrays)\u001b[0m\n\u001b[1;32m    188\u001b[0m m, n \u001b[38;5;241m=\u001b[39m a\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m:]\n\u001b[1;32m    189\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m m \u001b[38;5;241m!=\u001b[39m n:\n\u001b[0;32m--> 190\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m LinAlgError(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mLast 2 dimensions of the array must be square\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
@@ -1836,7 +1864,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 50,
    "id": "85bd8103-328d-44c2-927a-6f078c24eb91",
    "metadata": {},
    "outputs": [
@@ -1848,7 +1876,7 @@
        "       [1.55555556]])"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 50,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1868,7 +1896,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 51,
    "id": "3c34b2fc-82e5-43b5-947f-d66bb4265118",
    "metadata": {},
    "outputs": [
@@ -1878,7 +1906,7 @@
        "(3, 5)"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1889,7 +1917,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 52,
    "id": "c7f1f1f6-2c54-4bf1-8570-b0857125a108",
    "metadata": {},
    "outputs": [
@@ -1899,7 +1927,7 @@
        "(5, 3)"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1910,7 +1938,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 53,
    "id": "8aa343c7-d041-4014-89b0-78a84f69846f",
    "metadata": {},
    "outputs": [
@@ -1920,7 +1948,7 @@
        "(3, 3)"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1946,7 +1974,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 54,
    "id": "243c2127",
    "metadata": {},
    "outputs": [
@@ -1960,7 +1988,7 @@
        "       [ 0.08333333,  0.08333333, -0.11111111,  0.47222222,  0.47222222]])"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1972,7 +2000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 55,
    "id": "1e0681e9",
    "metadata": {},
    "outputs": [
@@ -1986,7 +2014,7 @@
        "       [10,  4,  1]])"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1997,7 +2025,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 56,
    "id": "3e881e59",
    "metadata": {},
    "outputs": [
@@ -2011,7 +2039,7 @@
        "       [8.5]])"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 56,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2030,7 +2058,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 57,
    "id": "33aeabe1",
    "metadata": {},
    "outputs": [
@@ -2044,7 +2072,7 @@
        "       [8.23611111]])"
       ]
      },
-     "execution_count": 55,
+     "execution_count": 57,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2065,7 +2093,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 58,
    "id": "921938e2",
    "metadata": {},
    "outputs": [
@@ -2097,53 +2125,53 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>5.805660</td>\n",
-       "      <td>10.829947</td>\n",
+       "      <td>3.446640</td>\n",
+       "      <td>8.385673</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
-       "      <td>4.505769</td>\n",
-       "      <td>7.700637</td>\n",
+       "      <td>2.756737</td>\n",
+       "      <td>6.352920</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
-       "      <td>8.016641</td>\n",
-       "      <td>15.834128</td>\n",
+       "      <td>2.661216</td>\n",
+       "      <td>4.678290</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
-       "      <td>4.363379</td>\n",
-       "      <td>7.800512</td>\n",
+       "      <td>6.697058</td>\n",
+       "      <td>12.212893</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
-       "      <td>3.531965</td>\n",
-       "      <td>5.616152</td>\n",
+       "      <td>3.297570</td>\n",
+       "      <td>5.771224</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
-       "      <td>3.591809</td>\n",
-       "      <td>6.293603</td>\n",
+       "      <td>6.056054</td>\n",
+       "      <td>11.692736</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
-       "      <td>2.836593</td>\n",
-       "      <td>5.717766</td>\n",
+       "      <td>-0.013447</td>\n",
+       "      <td>-0.743050</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
-       "      <td>2.103368</td>\n",
-       "      <td>3.913067</td>\n",
+       "      <td>6.231591</td>\n",
+       "      <td>12.346966</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
-       "      <td>4.850006</td>\n",
-       "      <td>10.235146</td>\n",
+       "      <td>4.932291</td>\n",
+       "      <td>8.789199</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9</th>\n",
-       "      <td>2.299206</td>\n",
-       "      <td>3.985440</td>\n",
+       "      <td>6.032112</td>\n",
+       "      <td>11.899764</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
@@ -2151,19 +2179,19 @@
       ],
       "text/plain": [
        "          x          y\n",
-       "0  5.805660  10.829947\n",
-       "1  4.505769   7.700637\n",
-       "2  8.016641  15.834128\n",
-       "3  4.363379   7.800512\n",
-       "4  3.531965   5.616152\n",
-       "5  3.591809   6.293603\n",
-       "6  2.836593   5.717766\n",
-       "7  2.103368   3.913067\n",
-       "8  4.850006  10.235146\n",
-       "9  2.299206   3.985440"
+       "0  3.446640   8.385673\n",
+       "1  2.756737   6.352920\n",
+       "2  2.661216   4.678290\n",
+       "3  6.697058  12.212893\n",
+       "4  3.297570   5.771224\n",
+       "5  6.056054  11.692736\n",
+       "6 -0.013447  -0.743050\n",
+       "7  6.231591  12.346966\n",
+       "8  4.932291   8.789199\n",
+       "9  6.032112  11.899764"
       ]
      },
-     "execution_count": 56,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2177,7 +2205,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 59,
    "id": "0d1fcbc0-244a-45f3-a459-7b49e617d8bf",
    "metadata": {},
    "outputs": [
@@ -2187,13 +2215,13 @@
        "<Axes: xlabel='x', ylabel='y'>"
       ]
      },
-     "execution_count": 57,
+     "execution_count": 59,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 500x500 with 1 Axes>"
       ]
@@ -2208,26 +2236,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 60,
    "id": "8304b0fb",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[5.80566022],\n",
-       "       [4.50576881],\n",
-       "       [8.0166413 ],\n",
-       "       [4.36337898],\n",
-       "       [3.53196483],\n",
-       "       [3.59180888],\n",
-       "       [2.83659263],\n",
-       "       [2.10336819],\n",
-       "       [4.85000576],\n",
-       "       [2.29920602]])"
+       "array([[ 3.4466405 ],\n",
+       "       [ 2.75673688],\n",
+       "       [ 2.66121603],\n",
+       "       [ 6.69705754],\n",
+       "       [ 3.29756984],\n",
+       "       [ 6.05605371],\n",
+       "       [-0.01344656],\n",
+       "       [ 6.23159147],\n",
+       "       [ 4.93229064],\n",
+       "       [ 6.03211196]])"
       ]
      },
-     "execution_count": 58,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2239,36 +2267,56 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 61,
    "id": "b9f4403e",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[0.16524954, 0.12825005, 0.22818184, 0.12419713, 0.10053216,\n",
-       "        0.10223553, 0.08073942, 0.05986927, 0.13804824, 0.0654435 ],\n",
-       "       [0.12825005, 0.09953477, 0.17709177, 0.09638931, 0.07802294,\n",
-       "        0.07934492, 0.0626618 , 0.0464645 , 0.10713915, 0.05079065],\n",
-       "       [0.22818184, 0.17709177, 0.31508079, 0.17149537, 0.13881802,\n",
-       "        0.14117009, 0.11148757, 0.0826694 , 0.19062143, 0.09036648],\n",
-       "       [0.12419713, 0.09638931, 0.17149537, 0.09334324, 0.07555728,\n",
-       "        0.07683749, 0.06068159, 0.04499614, 0.10375337, 0.04918559],\n",
-       "       [0.10053216, 0.07802294, 0.13881802, 0.07555728, 0.06116032,\n",
-       "        0.06219659, 0.0491191 , 0.03642241, 0.08398382, 0.03981358],\n",
-       "       [0.10223553, 0.07934492, 0.14117009, 0.07683749, 0.06219659,\n",
-       "        0.06325043, 0.04995135, 0.03703954, 0.08540681, 0.04048817],\n",
-       "       [0.08073942, 0.0626618 , 0.11148757, 0.06068159, 0.0491191 ,\n",
-       "        0.04995135, 0.03944854, 0.02925158, 0.06744911, 0.0319751 ],\n",
-       "       [0.05986927, 0.0464645 , 0.0826694 , 0.04499614, 0.03642241,\n",
-       "        0.03703954, 0.02925158, 0.0216904 , 0.05001434, 0.02370993],\n",
-       "       [0.13804824, 0.10713915, 0.19062143, 0.10375337, 0.08398382,\n",
-       "        0.08540681, 0.06744911, 0.05001434, 0.11532449, 0.05467102],\n",
-       "       [0.0654435 , 0.05079065, 0.09036648, 0.04918559, 0.03981358,\n",
-       "        0.04048817, 0.0319751 , 0.02370993, 0.05467102, 0.02591748]])"
+       "array([[ 5.43656281e-02,  4.34834245e-02,  4.19767251e-02,\n",
+       "         1.05636123e-01,  5.20142602e-02,  9.55252408e-02,\n",
+       "        -2.12099538e-04,  9.82940879e-02,  7.77995496e-02,\n",
+       "         9.51475954e-02],\n",
+       "       [ 4.34834245e-02,  3.47794788e-02,  3.35743708e-02,\n",
+       "         8.44912593e-02,  4.16027228e-02,  7.64042419e-02,\n",
+       "        -1.69644214e-04,  7.86188573e-02,  6.22266488e-02,\n",
+       "         7.61021886e-02],\n",
+       "       [ 4.19767251e-02,  3.35743708e-02,  3.24110199e-02,\n",
+       "         8.15636397e-02,  4.01611897e-02,  7.37568371e-02,\n",
+       "        -1.63766047e-04,  7.58947161e-02,  6.00704972e-02,\n",
+       "         7.34652500e-02],\n",
+       "       [ 1.05636123e-01,  8.44912593e-02,  8.15636397e-02,\n",
+       "         2.05258191e-01,  1.01067255e-01,  1.85612057e-01,\n",
+       "        -4.12123867e-04,  1.90992116e-01,  1.51169831e-01,\n",
+       "         1.84878267e-01],\n",
+       "       [ 5.20142602e-02,  4.16027228e-02,  4.01611897e-02,\n",
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+       "         9.10323665e-02],\n",
+       "       [ 9.55252408e-02,  7.64042419e-02,  7.37568371e-02,\n",
+       "         1.85612057e-01,  9.13936784e-02,  1.67846339e-01,\n",
+       "        -3.72677741e-04,  1.72711449e-01,  1.36700724e-01,\n",
+       "         1.67182782e-01],\n",
+       "       [-2.12099538e-04, -1.69644214e-04, -1.63766047e-04,\n",
+       "        -4.12123867e-04, -2.02926021e-04, -3.72677741e-04,\n",
+       "         8.27475294e-07, -3.83479993e-04, -3.03523552e-04,\n",
+       "        -3.71204412e-04],\n",
+       "       [ 9.82940879e-02,  7.86188573e-02,  7.58947161e-02,\n",
+       "         1.90992116e-01,  9.40427701e-02,  1.72711449e-01,\n",
+       "        -3.83479993e-04,  1.77717578e-01,  1.40663063e-01,\n",
+       "         1.72028659e-01],\n",
+       "       [ 7.77995496e-02,  6.22266488e-02,  6.00704972e-02,\n",
+       "         1.51169831e-01,  7.44346411e-02,  1.36700724e-01,\n",
+       "        -3.03523552e-04,  1.40663063e-01,  1.11334498e-01,\n",
+       "         1.36160297e-01],\n",
+       "       [ 9.51475954e-02,  7.61021886e-02,  7.34652500e-02,\n",
+       "         1.84878267e-01,  9.10323665e-02,  1.67182782e-01,\n",
+       "        -3.71204412e-04,  1.72028659e-01,  1.36160297e-01,\n",
+       "         1.66521849e-01]])"
       ]
      },
-     "execution_count": 59,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2280,7 +2328,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 62,
    "id": "db976c33",
    "metadata": {},
    "outputs": [
@@ -2313,63 +2361,63 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>5.805660</td>\n",
-       "      <td>10.829947</td>\n",
-       "      <td>10.936833</td>\n",
+       "      <td>3.446640</td>\n",
+       "      <td>8.385673</td>\n",
+       "      <td>6.665600</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
-       "      <td>4.505769</td>\n",
-       "      <td>7.700637</td>\n",
-       "      <td>8.488068</td>\n",
+       "      <td>2.756737</td>\n",
+       "      <td>6.352920</td>\n",
+       "      <td>5.331367</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
-       "      <td>8.016641</td>\n",
-       "      <td>15.834128</td>\n",
-       "      <td>15.101928</td>\n",
+       "      <td>2.661216</td>\n",
+       "      <td>4.678290</td>\n",
+       "      <td>5.146635</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
-       "      <td>4.363379</td>\n",
-       "      <td>7.800512</td>\n",
-       "      <td>8.219831</td>\n",
+       "      <td>6.697058</td>\n",
+       "      <td>12.212893</td>\n",
+       "      <td>12.951714</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
-       "      <td>3.531965</td>\n",
-       "      <td>5.616152</td>\n",
-       "      <td>6.653594</td>\n",
+       "      <td>3.297570</td>\n",
+       "      <td>5.771224</td>\n",
+       "      <td>6.377306</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
-       "      <td>3.591809</td>\n",
-       "      <td>6.293603</td>\n",
-       "      <td>6.766330</td>\n",
+       "      <td>6.056054</td>\n",
+       "      <td>11.692736</td>\n",
+       "      <td>11.712051</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
-       "      <td>2.836593</td>\n",
-       "      <td>5.717766</td>\n",
-       "      <td>5.343637</td>\n",
+       "      <td>-0.013447</td>\n",
+       "      <td>-0.743050</td>\n",
+       "      <td>-0.026005</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
-       "      <td>2.103368</td>\n",
-       "      <td>3.913067</td>\n",
-       "      <td>3.962372</td>\n",
+       "      <td>6.231591</td>\n",
+       "      <td>12.346966</td>\n",
+       "      <td>12.051531</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
-       "      <td>4.850006</td>\n",
-       "      <td>10.235146</td>\n",
-       "      <td>9.136549</td>\n",
+       "      <td>4.932291</td>\n",
+       "      <td>8.789199</td>\n",
+       "      <td>9.538759</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9</th>\n",
-       "      <td>2.299206</td>\n",
-       "      <td>3.985440</td>\n",
-       "      <td>4.331296</td>\n",
+       "      <td>6.032112</td>\n",
+       "      <td>11.899764</td>\n",
+       "      <td>11.665749</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
@@ -2377,19 +2425,19 @@
       ],
       "text/plain": [
        "          x          y          p\n",
-       "0  5.805660  10.829947  10.936833\n",
-       "1  4.505769   7.700637   8.488068\n",
-       "2  8.016641  15.834128  15.101928\n",
-       "3  4.363379   7.800512   8.219831\n",
-       "4  3.531965   5.616152   6.653594\n",
-       "5  3.591809   6.293603   6.766330\n",
-       "6  2.836593   5.717766   5.343637\n",
-       "7  2.103368   3.913067   3.962372\n",
-       "8  4.850006  10.235146   9.136549\n",
-       "9  2.299206   3.985440   4.331296"
+       "0  3.446640   8.385673   6.665600\n",
+       "1  2.756737   6.352920   5.331367\n",
+       "2  2.661216   4.678290   5.146635\n",
+       "3  6.697058  12.212893  12.951714\n",
+       "4  3.297570   5.771224   6.377306\n",
+       "5  6.056054  11.692736  11.712051\n",
+       "6 -0.013447  -0.743050  -0.026005\n",
+       "7  6.231591  12.346966  12.051531\n",
+       "8  4.932291   8.789199   9.538759\n",
+       "9  6.032112  11.899764  11.665749"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 62,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2401,7 +2449,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 63,
    "id": "9aab4539",
    "metadata": {},
    "outputs": [
@@ -2411,13 +2459,13 @@
        "<Axes: xlabel='x', ylabel='p'>"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 63,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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19xKtULKjxSkeQFIRSWAQlfYSrbJkR4tTPICkIpLAIHK5XPJ4PLIfFy273S6PxzM4R7lyigeQNEQSGGRer1fu46LldrvlHaxoHTvFIxCQ/vjHrv/Z2Ni1DqBfbLFYLDaQNzj2cpvNlpSBki0SicjhcCgcDquwsNDqcZDDgsGgQqHQ4J8nCeAEibYg4S3JJ554QpMmTdKwYcM0bNgwTZo0SY8//niib2f04Ycf6oYbbtDIkSM1fPhwXXDBBdqxY0fS/w4w2JxOp6qqqggkkEESuuLOPffco2XLlmnBggWaPn26JGnbtm2644479MEHH+inP/1pUoZra2vTjBkzdOWVV2r9+vU688wzFQwGVcRuIwBACiS0u/XMM8/Uww8/fMLJ0F6vVwsWLNDHH3+clOHuuusu/eUvf9Grr76a8HuwuxUAkNLdrUePHlVFRcUJ61OmTNHnn3+eyFue1CuvvKKKigpde+21GjVqlC6++GI99thjPb6mo6NDkUgk7gEAQCISiuR3vvMdNTQ0nLC+cuVKzZ07d8BDHfPee++poaFBTqdTPp9Pt956qxYuXKhVq1YZX1NfXy+Hw9H9KCkpSdo8AIDcktDu1gULFujpp59WSUmJvvKVr0iS3nzzTX3wwQe68cYbdcopp3T/7rJlyxIeLi8vTxUVFXr99de71xYuXKjt27dr27ZtJ31NR0eHOjo6un+ORCIqKSlhdysA5LBEd7cmdODOO++8o0suuUTSfy+7dcYZZ+iMM87QO++80/17Az0tZOzYsTrvvPPi1s4991z97ne/M74mPz9f+fn5A/q7QDZI2a25gCyWUCQ3bdqU7DlOasaMGdqzZ0/cWiAQ0Pjx41Py94FM1NraqtraWvm+cD9Jj8cjr9fLkeFAP6X1FXfuuOMOvfHGG3rwwQcVCoW0evVqrVy5UnV1dVaPBqStlN6aC8hyA77izmBbt26dlixZomAwqIkTJ2rx4sW65ZZb+vx6TgFBLgkEAiovL+/xeXa9Ihel9DvJVLrmmmt0zTXXWD0GkBH6cmsuIgn0XVrvbgXQPym/NReQ5YgkkEUsuTUXkMWIJJBlUn5rLiCLpf13kgD6p6ioSI2NjdyaC0gCIglkKafTSRyBAWJ3KwAABmxJAqkSCEjNzVJZmcQWHpAR2JIEBltrq1RZKZWXS9XVksvV9XNbm9WTAegFkQQGW22tdNxl4uT3S1wmDkh7RBIYTIGA5PNJ0Wj8ejTatR4MWjMXgD4hksBg6uUycQqFUjMHgIRw4A4wGI4dpHPclW9OwGXigLRGJIFkam3t+g7yC/dy1MiRXQfpdHb+d81ul9xujnIF0hy7W4FkOtlBOp98Ih1/s2O3W+IycUDaY0sSSJZjB+kcLxqV/v1v6U9/kj7/nPMkgQxCJIFk6e0gnc8/l6qqUjMLgKRgdyuQLL3cy5GDdIDMQySBZHG5JI/nxCNa7faudXaxAhmHSALJ5PV2HZTzRRykA2QsvpMEkqmoSGps7LqSTijEQTpAhiOSwGBwOokjkAXY3QoAgAGRBADAgN2twCAIBAJqbm5WWVmZnOx2BTIWW5JAErW2tqqyslLl5eWqrq6Wy+VSZWWl2rjBMpCRiCSQRLW1tfIfd+1Wv9+vGm6wDGQkIgkkSSAQkM/nU/S4GyxHo1H5fD4FucEykHGIJJAkzb1cuzXEDZaBjEMkgSQp7eXarWVcuxXIOEQSSBKXyyWPxyP7cddutdvt8ng8HOUKZCAiCSSR1+uV+7hrt7rdbnm5diuQkThPEkiioqIiNTY2KhgMKhQKcZ4kkOGIJDAInE4ncQSyALtbAQAwIJIAABgQSQAADIgkAAAGRBIAAAMiCQCAAZEEAMAgoyL50EMPyWazadGiRVaPAgDIARkTye3bt+vRRx/VhRdeaPUoAIAckRGRPHz4sObOnavHHntMRUVFVo8DAMgRGRHJuro6zZw584QLR59MR0eHIpFI3AMAgESk/bVbn3/+eTU1NWn79u19+v36+nrdd999gzwVACAXpPWWZEtLi26//XY999xzGjZsWJ9es2TJEoXD4e5HS0vLIE8JAMhWtlgsFrN6CJO1a9fqm9/8ZtxNbKPRqGw2m4YMGaKOjo4TbnB7vEgkIofDoXA4rMLCwsEeGQCQhhJtQVrvbr3qqqu0e/fuuLX58+frnHPO0Z133tlrIAEAGIi0jmRBQYEmTZoUt3bqqadq5MiRJ6wDAJBsaf2dJAAAVkrrLcmT2bx5s9UjAAByBFuSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMEjrSNbX1+vSSy9VQUGBRo0apTlz5mjPnj1WjwUAyBFpHcktW7aorq5Ob7zxhjZs2KCjR4/q6quvVnt7u9WjAQBygC0Wi8WsHqKvPvroI40aNUpbtmzRV7/61T69JhKJyOFwKBwOq7CwcJAnBACko0RbMHQQZ0q6cDgsSRoxYoTxdzo6OtTR0dH9cyQSGfS5AADZKa13t35RZ2enFi1apBkzZmjSpEnG36uvr5fD4eh+lJSUpHBKAEA2yZjdrbfeeqvWr1+v1157TWeffbbx9062JVlSUsLuVgDIYVm9u/W2227TunXrtHXr1h4DKUn5+fnKz89P0WQAgGyW1pGMxWJasGCB1qxZo82bN2vixIlWjwQAyCFpHcm6ujqtXr1aL7/8sgoKCrR//35JksPh0PDhwy2eDgCQ7dL6O0mbzXbS9SeffFI33XRTn96DU0AAAFn5nWQa9xsAkAMy5hQQAABSjUgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgEFGRHLFihWaMGGChg0bpmnTpumtt96yeiQAQA5I+0i+8MILWrx4sZYuXaqmpiZNnjxZHo9HBw8eTO0ggYC0fr0UDKb27wIALJP2kVy2bJluueUWzZ8/X+edd54eeeQRfelLX9Jvf/vb1AzQ2ipVVkrl5VJ1teRydf3c1paavw8AsExaR/LIkSPauXOn3G5399qQIUPkdru1bdu2k76mo6NDkUgk7jEgtbWS3x+/5vdLNTUDe18AQNpL60h+/PHHikajGj16dNz66NGjtX///pO+pr6+Xg6Ho/tRUlKS+ACBgOTzSdFo/Ho02rXOrlcAyGppHclELFmyROFwuPvR0tKS+Js1N/f8fCiU+HsDANLeUKsH6MkZZ5whu92uAwcOxK0fOHBAY8aMOelr8vPzlZ+fn5wBSkt7fr6sLDl/BwCQltJ6SzIvL09TpkzRxo0bu9c6Ozu1ceNGTZ8+ffAHcLkkj0ey2+PX7faudadz8GcAAFgmrSMpSYsXL9Zjjz2mVatW6e9//7tuvfVWtbe3a/78+akZwOuVvnDgkKSun73e1Px9AIBl0np3qyRdf/31+uijj3TPPfdo//79uuiii9TY2HjCwTyDpqhIamzsOkgnFOraxcoWJADkBFssFotZPcRgikQicjgcCofDKiwstHocAIAFEm1B2u9uBQDAKkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAzS/oo76SIQCKi5uVllZWVycsUdAMgJbEn2orW1VZWVlSovL1d1dbVcLpcqKyvV1tZm9WgAgEFGJHtRW1srv98ft+b3+1VTU2PRRACAVCGSPQgEAvL5fIpGo3Hr0WhUPp9PwWDQoskAAKlAJHvQ3Nzc4/OhUChFkwAArEAke1BaWtrj82VlZSmaBABgBSLZA5fLJY/HI7vdHrdut9vl8Xg4yhUAshyR7IXX65Xb7Y5bc7vd8nq9Fk0EAEgVzpPsRVFRkRobGxUMBhUKhThPEgByCJHsI6fTSRwBIMewuxUAAAMiCQCAAZEEAMCASAIAYEAkAQAwIJIAABgQSQAADIgkAAAGRBIAAAMiCQCAAZEEAMAg66/dGovFJEmRSMTiSQAAVjnWgGNN6Kusj+ShQ4ckSSUlJRZPAgCw2qFDh+RwOPr8+7ZYf7OaYTo7O7Vv3z4VFBTIZrMl/D6RSEQlJSVqaWlRYWFhEie0TrZ9pmz7PFL2faZs+zxS9n2mbPs80n8/07vvvqvy8nINGdL3bxqzfktyyJAhOvvss5P2foWFhVnzH5xjsu0zZdvnkbLvM2Xb55Gy7zNl2+eRpLPOOqtfgZQ4cAcAACMiCQCAAZHso/z8fC1dulT5+flWj5I02faZsu3zSNn3mbLt80jZ95my7fNIA/tMWX/gDgAAiWJLEgAAAyIJAIABkQQAwIBIAgBgQCT7aMWKFZowYYKGDRumadOm6a233rJ6pIRt3bpVs2bNUnFxsWw2m9auXWv1SANSX1+vSy+9VAUFBRo1apTmzJmjPXv2WD1WwhoaGnThhRd2n8w9ffp0rV+/3uqxkuqhhx6SzWbTokWLrB4lIffee69sNlvc45xzzrF6rAH78MMPdcMNN2jkyJEaPny4LrjgAu3YscPqsRIyYcKEE/4Z2Ww21dXV9et9iGQfvPDCC1q8eLGWLl2qpqYmTZ48WR6PRwcPHrR6tIS0t7dr8uTJWrFihdWjJMWWLVtUV1enN954Qxs2bNDRo0d19dVXq7293erREnL22WfroYce0s6dO7Vjxw59/etf1+zZs/W3v/3N6tGSYvv27Xr00Ud14YUXWj3KgJx//vn617/+1f147bXXrB5pQNra2jRjxgydcsopWr9+vd5991396le/UlFRkdWjJWT79u1x/3w2bNggSbr22mv790Yx9Grq1Kmxurq67p+j0WisuLg4Vl9fb+FUySEptmbNGqvHSKqDBw/GJMW2bNli9ShJU1RUFHv88cetHmPADh06FHM6nbENGzbErrjiitjtt99u9UgJWbp0aWzy5MlWj5FUd955Z+zyyy+3eoxBc/vtt8dKS0tjnZ2d/XodW5K9OHLkiHbu3Cm32929NmTIELndbm3bts3CyWASDoclSSNGjLB4koGLRqN6/vnn1d7erunTp1s9zoDV1dVp5syZcf99ylTBYFDFxcX68pe/rLlz5+qDDz6weqQBeeWVV1RRUaFrr71Wo0aN0sUXX6zHHnvM6rGS4siRI3r22Wd188039/tGF0SyFx9//LGi0ahGjx4dtz569Gjt37/foqlg0tnZqUWLFmnGjBmaNGmS1eMkbPfu3TrttNOUn5+vH/zgB1qzZo3OO+88q8cakOeff15NTU2qr6+3epQBmzZtmp566ik1NjaqoaFBe/fu1f/8z/9035ovE7333ntqaGiQ0+mUz+fTrbfeqoULF2rVqlVWjzZga9eu1SeffKKbbrqp36/N+ruAILfU1dXpnXfeyfjvh8rLy7Vr1y6Fw2G99NJLmjdvnrZs2ZKxoWxpadHtt9+uDRs2aNiwYVaPM2BVVVXd//uFF16oadOmafz48XrxxRf13e9+18LJEtfZ2amKigo9+OCDkqSLL75Y77zzjh555BHNmzfP4ukG5oknnlBVVZWKi4v7/Vq2JHtxxhlnyG6368CBA3HrBw4c0JgxYyyaCidz2223ad26ddq0aVNSb49mhby8PJWVlWnKlCmqr6/X5MmT9etf/9rqsRK2c+dOHTx4UJdccomGDh2qoUOHasuWLXr44Yc1dOhQRaNRq0cckNNPP10ul0uhUMjqURI2duzYE/4l7Nxzz8343cjvv/++/H6/vve97yX0eiLZi7y8PE2ZMkUbN27sXuvs7NTGjRuz4juibBCLxXTbbbdpzZo1+vOf/6yJEydaPVLSdXZ2qqOjw+oxEnbVVVdp9+7d2rVrV/ejoqJCc+fO1a5du2S3260ecUAOHz6s5uZmjR071upREjZjxowTTp0KBAIaP368RRMlx5NPPqlRo0Zp5syZCb2e3a19sHjxYs2bN08VFRWaOnWqli9frvb2ds2fP9/q0RJy+PDhuH/j3bt3r3bt2qURI0Zo3LhxFk6WmLq6Oq1evVovv/yyCgoKur8rdjgcGj58uMXT9d+SJUtUVVWlcePG6dChQ1q9erU2b94sn89n9WgJKygoOOE74lNPPVUjR47MyO+Of/jDH2rWrFkaP3689u3bp6VLl8put6umpsbq0RJ2xx136LLLLtODDz6o6667Tm+99ZZWrlyplStXWj1awjo7O/Xkk09q3rx5Gjo0wdwNzsG22ec3v/lNbNy4cbG8vLzY1KlTY2+88YbVIyVs06ZNMUknPObNm2f1aAk52WeRFHvyySetHi0hN998c2z8+PGxvLy82Jlnnhm76qqrYn/605+sHivpMvkUkOuvvz42duzYWF5eXuyss86KXX/99bFQKGT1WAP2hz/8ITZp0qRYfn5+7JxzzomtXLnS6pEGxOfzxSTF9uzZk/B7cKssAAAM+E4SAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBLLURx99pDFjxnTfH1CSXn/9deXl5cXd1QaAGdduBbLYH//4R82ZM0evv/66ysvLddFFF2n27NlatmyZ1aMBGYFIAlmurq5Ofr9fFRUV2r17t7Zv3678/HyrxwIyApEEstx//vMfTZo0SS0tLdq5c6cuuOACq0cCMgbfSQJZrrm5Wfv27VNnZ6f++c9/Wj0OkFHYkgSy2JEjRzR16lRddNFFKi8v1/Lly7V7926NGjXK6tGAjEAkgSz2ox/9SC+99JLefvttnXbaabriiivkcDi0bt06q0cDMgK7W4EstXnzZi1fvlzPPPOMCgsLNWTIED3zzDN69dVX1dDQYPV4QEZgSxIAAAO2JAEAMCCSAAAYEEkAAAyIJAAABkQSAAADIgkAgAGRBADAgEgCAGBAJAEAMCCSAAAYEEkAAAyIJAAABv8HhjICqw9ac+gAAAAASUVORK5CYII=",
       "text/plain": [
        "<Figure size 500x500 with 1 Axes>"
       ]
@@ -2444,7 +2492,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 64,
    "id": "bfd1ce1d",
    "metadata": {},
    "outputs": [
@@ -2494,7 +2542,7 @@
        "y   8  12"
       ]
      },
-     "execution_count": 62,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2509,7 +2557,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 65,
    "id": "cae18757",
    "metadata": {},
    "outputs": [
@@ -2519,7 +2567,7 @@
        "5.0"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2531,17 +2579,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 66,
    "id": "1e096c19",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "2.0278336399647197"
+       "2.520550690531145"
       ]
      },
-     "execution_count": 64,
+     "execution_count": 66,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2562,7 +2610,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 67,
    "id": "6758c077",
    "metadata": {
     "scrolled": true
@@ -2571,10 +2619,10 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.image.AxesImage at 0x7f22571371c0>"
+       "<matplotlib.image.AxesImage at 0x7f02ea29ee20>"
       ]
      },
-     "execution_count": 65,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     },
-- 
GitLab