Singular Value Decomposition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "95c325a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "from sklearn import linear_model\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.decomposition import PCA,TruncatedSVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ce5ebc29",
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Time &amp; Date</th>\n",
       "      <th>T/D Activity</th>\n",
       "      <th>Job Time</th>\n",
       "      <th>Trt Time</th>\n",
       "      <th>Stg Time</th>\n",
       "      <th>Stg Pump Time</th>\n",
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       "      <th>Stg Pmp Lft Ann</th>\n",
       "      <th>% Job Complete</th>\n",
       "      <th>...</th>\n",
       "      <th>BHA ConTen</th>\n",
       "      <th>CT-JP ConTen</th>\n",
       "      <th>Max OD Growth</th>\n",
       "      <th>Depth of Max SF</th>\n",
       "      <th>Drag In COF</th>\n",
       "      <th>Drag Out COF</th>\n",
       "      <th>Drag Avg COF</th>\n",
       "      <th>Treating Pr LOR</th>\n",
       "      <th>Ann Pr @WH LOR</th>\n",
       "      <th>cpatToolfaceTar</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>12.20018</td>\n",
       "      <td>12.200184</td>\n",
       "      <td>12.20018</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>15.50704</td>\n",
       "      <td>15.507041</td>\n",
       "      <td>15.50704</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.797165</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>16.50711</td>\n",
       "      <td>16.507106</td>\n",
       "      <td>16.50711</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-5.668681</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>17.50775</td>\n",
       "      <td>17.507745</td>\n",
       "      <td>17.50775</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-6.362158</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>38286</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>38299.53000</td>\n",
       "      <td>38299.531400</td>\n",
       "      <td>38299.53000</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>38287</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>38300.53000</td>\n",
       "      <td>38300.531280</td>\n",
       "      <td>38300.53000</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>38288</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>38301.53000</td>\n",
       "      <td>38301.531430</td>\n",
       "      <td>38301.53000</td>\n",
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       "    <tr>\n",
       "      <th>38289</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>38302.53000</td>\n",
       "      <td>38302.531320</td>\n",
       "      <td>38302.53000</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>38290</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>38303.53000</td>\n",
       "      <td>38303.531070</td>\n",
       "      <td>38303.53000</td>\n",
       "      <td>0</td>\n",
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       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
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       "<p>38291 rows × 428 columns</p>\n",
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      "text/plain": [
       "          Time & Date T/D Activity     Job Time      Trt Time     Stg Time  \\\n",
       "0       5/4/2018 9:08         None      0.00000      0.000000      0.00000   \n",
       "1       5/4/2018 9:08         None     12.20018     12.200184     12.20018   \n",
       "2       5/4/2018 9:08         None     15.50704     15.507041     15.50704   \n",
       "3       5/4/2018 9:08         None     16.50711     16.507106     16.50711   \n",
       "4       5/4/2018 9:08         None     17.50775     17.507745     17.50775   \n",
       "...               ...          ...          ...           ...          ...   \n",
       "38286  5/4/2018 19:46         None  38299.53000  38299.531400  38299.53000   \n",
       "38287  5/4/2018 19:46         None  38300.53000  38300.531280  38300.53000   \n",
       "38288  5/4/2018 19:46         None  38301.53000  38301.531430  38301.53000   \n",
       "38289  5/4/2018 19:46         None  38302.53000  38302.531320  38302.53000   \n",
       "38290  5/4/2018 19:46         None  38303.53000  38303.531070  38303.53000   \n",
       "\n",
       "       Stg Pump Time  Stg Pump Left  Stg Pmp Tim Ann  Stg Pmp Lft Ann  \\\n",
       "0                  0              0                0                0   \n",
       "1                  0              0                0                0   \n",
       "2                  0              0                0                0   \n",
       "3                  0              0                0                0   \n",
       "4                  0              0                0                0   \n",
       "...              ...            ...              ...              ...   \n",
       "38286              0              0                0                0   \n",
       "38287              0              0                0                0   \n",
       "38288              0              0                0                0   \n",
       "38289              0              0                0                0   \n",
       "38290              0              0                0                0   \n",
       "\n",
       "       % Job Complete  ...  BHA ConTen  CT-JP ConTen  Max OD Growth  \\\n",
       "0                   0  ...           0             0       0.000000   \n",
       "1                   0  ...           0             0       0.000046   \n",
       "2                   0  ...           0             0       0.000046   \n",
       "3                   0  ...           0             0       0.000046   \n",
       "4                   0  ...           0             0       0.000046   \n",
       "...               ...  ...         ...           ...            ...   \n",
       "38286               0  ...           0             0       0.000045   \n",
       "38287               0  ...           0             0       0.000045   \n",
       "38288               0  ...           0             0       0.000045   \n",
       "38289               0  ...           0             0       0.000045   \n",
       "38290               0  ...           0             0       0.000045   \n",
       "\n",
       "       Depth of Max SF  Drag In COF  Drag Out COF  Drag Avg COF  \\\n",
       "0                    0            0             0             0   \n",
       "1                    0            0             0             0   \n",
       "2                    0            0             0             0   \n",
       "3                    0            0             0             0   \n",
       "4                    0            0             0             0   \n",
       "...                ...          ...           ...           ...   \n",
       "38286                0            0             0             0   \n",
       "38287                0            0             0             0   \n",
       "38288                0            0             0             0   \n",
       "38289                0            0             0             0   \n",
       "38290                0            0             0             0   \n",
       "\n",
       "       Treating Pr LOR  Ann Pr @WH LOR  cpatToolfaceTar  \n",
       "0             0.000000          -237.6                0  \n",
       "1             0.000000          -237.6                0  \n",
       "2            -4.797165          -237.6                0  \n",
       "3            -5.668681          -237.6                0  \n",
       "4            -6.362158          -237.6                0  \n",
       "...                ...             ...              ...  \n",
       "38286      -237.600000          -237.6                0  \n",
       "38287      -237.600000          -237.6                0  \n",
       "38288      -237.600000          -237.6                0  \n",
       "38289      -237.600000          -237.6                0  \n",
       "38290      -237.600000          -237.6                0  \n",
       "\n",
       "[38291 rows x 428 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"sensordata1hz.csv\")\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a8d13bf3",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>-4.797165</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.50711</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-5.668681</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.50775</td>\n",
       "      <td>17.507745</td>\n",
       "      <td>17.50775</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-6.362158</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38286</th>\n",
       "      <td>38299.53000</td>\n",
       "      <td>38299.531400</td>\n",
       "      <td>38299.53000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38287</th>\n",
       "      <td>38300.53000</td>\n",
       "      <td>38300.531280</td>\n",
       "      <td>38300.53000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38288</th>\n",
       "      <td>38301.53000</td>\n",
       "      <td>38301.531430</td>\n",
       "      <td>38301.53000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38289</th>\n",
       "      <td>38302.53000</td>\n",
       "      <td>38302.531320</td>\n",
       "      <td>38302.53000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38290</th>\n",
       "      <td>38303.53000</td>\n",
       "      <td>38303.531070</td>\n",
       "      <td>38303.53000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-237.600000</td>\n",
       "      <td>-237.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>38291 rows × 423 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Job Time      Trt Time     Stg Time  Stg Pump Time  Stg Pump Left  \\\n",
       "0          0.00000      0.000000      0.00000              0              0   \n",
       "1         12.20018     12.200184     12.20018              0              0   \n",
       "2         15.50704     15.507041     15.50704              0              0   \n",
       "3         16.50711     16.507106     16.50711              0              0   \n",
       "4         17.50775     17.507745     17.50775              0              0   \n",
       "...            ...           ...          ...            ...            ...   \n",
       "38286  38299.53000  38299.531400  38299.53000              0              0   \n",
       "38287  38300.53000  38300.531280  38300.53000              0              0   \n",
       "38288  38301.53000  38301.531430  38301.53000              0              0   \n",
       "38289  38302.53000  38302.531320  38302.53000              0              0   \n",
       "38290  38303.53000  38303.531070  38303.53000              0              0   \n",
       "\n",
       "       Stg Pmp Tim Ann  Stg Pmp Lft Ann  % Job Complete  % Trt Complete  \\\n",
       "0                    0                0               0               0   \n",
       "1                    0                0               0               0   \n",
       "2                    0                0               0               0   \n",
       "3                    0                0               0               0   \n",
       "4                    0                0               0               0   \n",
       "...                ...              ...             ...             ...   \n",
       "38286                0                0               0               0   \n",
       "38287                0                0               0               0   \n",
       "38288                0                0               0               0   \n",
       "38289                0                0               0               0   \n",
       "38290                0                0               0               0   \n",
       "\n",
       "       % Stg Complete  ...  BHA ConTen  CT-JP ConTen  Max OD Growth  \\\n",
       "0                   0  ...           0             0       0.000000   \n",
       "1                   0  ...           0             0       0.000046   \n",
       "2                   0  ...           0             0       0.000046   \n",
       "3                   0  ...           0             0       0.000046   \n",
       "4                   0  ...           0             0       0.000046   \n",
       "...               ...  ...         ...           ...            ...   \n",
       "38286               0  ...           0             0       0.000045   \n",
       "38287               0  ...           0             0       0.000045   \n",
       "38288               0  ...           0             0       0.000045   \n",
       "38289               0  ...           0             0       0.000045   \n",
       "38290               0  ...           0             0       0.000045   \n",
       "\n",
       "       Depth of Max SF  Drag In COF  Drag Out COF  Drag Avg COF  \\\n",
       "0                    0            0             0             0   \n",
       "1                    0            0             0             0   \n",
       "2                    0            0             0             0   \n",
       "3                    0            0             0             0   \n",
       "4                    0            0             0             0   \n",
       "...                ...          ...           ...           ...   \n",
       "38286                0            0             0             0   \n",
       "38287                0            0             0             0   \n",
       "38288                0            0             0             0   \n",
       "38289                0            0             0             0   \n",
       "38290                0            0             0             0   \n",
       "\n",
       "       Treating Pr LOR  Ann Pr @WH LOR  cpatToolfaceTar  \n",
       "0             0.000000          -237.6                0  \n",
       "1             0.000000          -237.6                0  \n",
       "2            -4.797165          -237.6                0  \n",
       "3            -5.668681          -237.6                0  \n",
       "4            -6.362158          -237.6                0  \n",
       "...                ...             ...              ...  \n",
       "38286      -237.600000          -237.6                0  \n",
       "38287      -237.600000          -237.6                0  \n",
       "38288      -237.600000          -237.6                0  \n",
       "38289      -237.600000          -237.6                0  \n",
       "38290      -237.600000          -237.6                0  \n",
       "\n",
       "[38291 rows x 423 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_data = data.select_dtypes(include=[np.number])\n",
    "numeric_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "96f038b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time &amp; Date</th>\n",
       "      <th>T/D Activity</th>\n",
       "      <th>Plan 1 Stg Mode</th>\n",
       "      <th>Time BH Inj Tbg</th>\n",
       "      <th>Time BH Inj Ann</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5/4/2018 9:08</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38286</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38287</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38288</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38289</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38290</th>\n",
       "      <td>5/4/2018 19:46</td>\n",
       "      <td>None</td>\n",
       "      <td>Unknown</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "      <td>1/1/1970 0:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>38291 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Time & Date T/D Activity Plan 1 Stg Mode Time BH Inj Tbg  \\\n",
       "0       5/4/2018 9:08         None         Unknown   1/1/1970 0:00   \n",
       "1       5/4/2018 9:08         None         Unknown   1/1/1970 0:00   \n",
       "2       5/4/2018 9:08         None         Unknown   1/1/1970 0:00   \n",
       "3       5/4/2018 9:08         None         Unknown   1/1/1970 0:00   \n",
       "4       5/4/2018 9:08         None         Unknown   1/1/1970 0:00   \n",
       "...               ...          ...             ...             ...   \n",
       "38286  5/4/2018 19:46         None         Unknown   1/1/1970 0:00   \n",
       "38287  5/4/2018 19:46         None         Unknown   1/1/1970 0:00   \n",
       "38288  5/4/2018 19:46         None         Unknown   1/1/1970 0:00   \n",
       "38289  5/4/2018 19:46         None         Unknown   1/1/1970 0:00   \n",
       "38290  5/4/2018 19:46         None         Unknown   1/1/1970 0:00   \n",
       "\n",
       "      Time BH Inj Ann  \n",
       "0       1/1/1970 0:00  \n",
       "1       1/1/1970 0:00  \n",
       "2       1/1/1970 0:00  \n",
       "3       1/1/1970 0:00  \n",
       "4       1/1/1970 0:00  \n",
       "...               ...  \n",
       "38286   1/1/1970 0:00  \n",
       "38287   1/1/1970 0:00  \n",
       "38288   1/1/1970 0:00  \n",
       "38289   1/1/1970 0:00  \n",
       "38290   1/1/1970 0:00  \n",
       "\n",
       "[38291 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "non_numeric_columns = data.select_dtypes(exclude=[np.number])\n",
    "non_numeric_columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b42e22ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         0.00000000e+00, -2.37600000e+02,  0.00000000e+00],\n",
       "       [ 1.22001800e+01,  1.22001836e+01,  1.22001800e+01, ...,\n",
       "         0.00000000e+00, -2.37600000e+02,  0.00000000e+00],\n",
       "       [ 1.55070400e+01,  1.55070410e+01,  1.55070400e+01, ...,\n",
       "        -4.79716499e+00, -2.37600000e+02,  0.00000000e+00],\n",
       "       ...,\n",
       "       [ 3.83015300e+04,  3.83015314e+04,  3.83015300e+04, ...,\n",
       "        -2.37600000e+02, -2.37600000e+02,  0.00000000e+00],\n",
       "       [ 3.83025300e+04,  3.83025313e+04,  3.83025300e+04, ...,\n",
       "        -2.37600000e+02, -2.37600000e+02,  0.00000000e+00],\n",
       "       [ 3.83035300e+04,  3.83035311e+04,  3.83035300e+04, ...,\n",
       "        -2.37600000e+02, -2.37600000e+02,  0.00000000e+00]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = numeric_data.to_numpy()\n",
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a9f7870c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform SVD on the data matrix\n",
    "U, S, V = np.linalg.svd(dataset, full_matrices=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58b2fd0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(38291, 423)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "03498fc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(423,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dc4d97b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(423, 423)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2af619b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.25332783e-03  1.75968332e-03 -9.92904991e-03 ...  6.89211298e-16\n",
      "   5.26495051e-17  2.40449483e-11]\n",
      " [-4.76663877e-03  5.40715122e-03  3.13169377e-03 ...  5.21281326e-04\n",
      "  -7.98595719e-05 -1.03094276e-03]\n",
      " [-4.76684994e-03  5.40438102e-03  3.13289617e-03 ...  1.65744053e-03\n",
      "   4.40037638e-04  3.76235568e-01]\n",
      " ...\n",
      " [-4.79056964e-03  5.52298851e-03  4.22883784e-03 ...  2.73350002e-03\n",
      "  -2.73904667e-05 -9.61735610e-04]\n",
      " [-4.79063570e-03  5.52296731e-03  4.23149408e-03 ...  1.57058907e-03\n",
      "   4.23761100e-05  6.65531373e-04]\n",
      " [-4.79072057e-03  5.52294010e-03  4.23490841e-03 ...  1.46610213e-03\n",
      "  -1.91459302e-05 -2.01842286e-03]]\n"
     ]
    }
   ],
   "source": [
    "print(U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7287e71f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.40341025e+08 9.94161612e+07 2.09507069e+07 1.14853441e+07\n",
      " 3.30249589e+06 9.19198064e+05 5.73897013e+05 1.80907012e+05\n",
      " 1.25428496e+05 8.16918664e+04 7.74243481e+04 3.98137622e+04\n",
      " 3.38291315e+04 1.63745642e+03 8.15626485e+01 8.84871866e+00\n",
      " 5.64319697e+00 2.71131032e+00 1.99408556e+00 1.74164492e+00\n",
      " 1.34540668e+00 8.37855177e-01 4.08774174e-01 8.13395136e-02\n",
      " 3.43409275e-02 2.07738708e-02 7.36587708e-03 6.90372669e-05\n",
      " 3.57546417e-06 7.18694121e-08 5.52764487e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 3.85348098e-08 3.85348098e-08\n",
      " 3.85348098e-08 3.85348098e-08 2.21476503e-08]\n"
     ]
    }
   ],
   "source": [
    "print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "32d268d4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-8.60608421e-003 -8.60608418e-003 -8.60608421e-003 ...  3.92430771e-007\n",
      "   1.05268085e-004  0.00000000e+000]\n",
      " [-4.26807188e-003 -4.26807189e-003 -4.26807188e-003 ... -8.41251999e-005\n",
      "  -3.51066631e-005  0.00000000e+000]\n",
      " [-1.91216803e-002 -1.91216802e-002 -1.91216803e-002 ...  4.87875682e-005\n",
      "   3.98875288e-005  0.00000000e+000]\n",
      " ...\n",
      " [ 0.00000000e+000 -8.62435908e-164 -7.96787002e-164 ...  3.12229628e-165\n",
      "   1.66279388e-160  0.00000000e+000]\n",
      " [ 0.00000000e+000  0.00000000e+000  0.00000000e+000 ...  0.00000000e+000\n",
      "   0.00000000e+000  1.00000000e+000]\n",
      " [ 0.00000000e+000 -1.96433410e-008  1.96433666e-008 ...  4.38112056e-015\n",
      "   1.41829379e-004  0.00000000e+000]]\n"
     ]
    }
   ],
   "source": [
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "adc64efc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def error_k(k, U, S, V, data_matrix):\n",
    "    truncated_U = U[:, :k]\n",
    "    truncated_S = np.diag(S[:k])\n",
    "    truncated_V = V[:k, :]\n",
    "\n",
    "    approximated_matrix = np.dot(np.dot(truncated_U, truncated_S), truncated_V)\n",
    "        \n",
    "    # Calculate Frobenius error\n",
    "    error = np.linalg.norm(data_matrix - approximated_matrix, 'fro')\n",
    "\n",
    "    return error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "d242d398",
   "metadata": {},
   "outputs": [],
   "source": [
    "k_values = []\n",
    "frobenius_errors = []\n",
    "frobenius_errors_percentage = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c648e6be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102306221.61590478\n",
      "Frobenius Error Percentage for k = 1: 22.63064294882566\n",
      "24145183.182718616\n",
      "Frobenius Error Percentage for k = 2: 5.341034112212262\n",
      "12002406.095035007\n",
      "Frobenius Error Percentage for k = 3: 2.6549916766872275\n",
      "3484913.4773482247\n",
      "Frobenius Error Percentage for k = 4: 0.7708801221250208\n",
      "1112718.6713624625\n",
      "Frobenius Error Percentage for k = 5: 0.24613888145176874\n",
      "627070.778147581\n",
      "Frobenius Error Percentage for k = 6: 0.13871116203644454\n",
      "252705.3209974733\n",
      "Frobenius Error Percentage for k = 7: 0.05589966866563589\n",
      "176444.4166502394\n",
      "Frobenius Error Percentage for k = 8: 0.03903037890028604\n",
      "124098.04410749678\n",
      "Frobenius Error Percentage for k = 9: 0.027451102019857745\n",
      "93417.14784536386\n",
      "Frobenius Error Percentage for k = 10: 0.0206643358027937\n",
      "52270.774231112606\n",
      "Frobenius Error Percentage for k = 11: 0.011562554159453843\n",
      "33868.83790693593\n",
      "Frobenius Error Percentage for k = 12: 0.0074919546989150165\n",
      "1639.5252938284516\n",
      "Frobenius Error Percentage for k = 13: 0.00036267111563850345\n",
      "82.3386878823325\n",
      "Frobenius Error Percentage for k = 14: 1.8213725586853062e-05\n",
      "11.278027301103208\n",
      "Frobenius Error Percentage for k = 15: 2.494755499588268e-06\n",
      "6.99243004727574\n",
      "Frobenius Error Percentage for k = 16: 1.5467601602827301e-06\n",
      "4.128971534820582\n",
      "Frobenius Error Percentage for k = 17: 9.133489544868762e-07\n",
      "3.1140331179450738\n",
      "Frobenius Error Percentage for k = 18: 6.888395496376871e-07\n",
      "2.3918246265697802\n",
      "Frobenius Error Percentage for k = 19: 5.290834542138345e-07\n",
      "1.639359024355522\n",
      "Frobenius Error Percentage for k = 20: 3.626343360075512e-07\n",
      "0.9366850471757693\n",
      "Frobenius Error Percentage for k = 21: 2.0719937187909296e-07\n",
      "0.41878106453230735\n",
      "Frobenius Error Percentage for k = 22: 9.263644571628285e-08\n",
      "0.09100126598303651\n",
      "Frobenius Error Percentage for k = 23: 2.0129930768873703e-08\n",
      "0.04080580765603924\n",
      "Frobenius Error Percentage for k = 24: 9.026446766544617e-09\n",
      "0.02204120311792716\n",
      "Frobenius Error Percentage for k = 25: 4.875623300771052e-09\n",
      "0.0073662017238005995\n",
      "Frobenius Error Percentage for k = 26: 1.6294403064382114e-09\n",
      "6.915719407892501e-05\n",
      "Frobenius Error Percentage for k = 27: 1.529791386899858e-11\n",
      "4.0710215822123455e-06\n",
      "Frobenius Error Percentage for k = 28: 9.005301379411725e-13\n",
      "1.946605284272999e-06\n",
      "Frobenius Error Percentage for k = 29: 4.3059873050605295e-13\n"
     ]
    }
   ],
   "source": [
    "# Calculate Frobenius error percentage for a range of k values\n",
    "for k in range(1, 30, 1):\n",
    "    current_error = error_k(k, U, S, V, dataset)\n",
    "    error_percentage = (current_error / np.linalg.norm(dataset, 'fro')) * 100\n",
    "    k_values.append(k)\n",
    "    frobenius_errors.append(current_error)\n",
    "    frobenius_errors_percentage.append(error_percentage)\n",
    "    print(current_error)\n",
    "    print(f\"Frobenius Error Percentage for k = {k}: {error_percentage}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "6a6760db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frobenius Error Percentage for k = 1: 22.63%\n",
      "Frobenius Error Percentage for k = 2: 5.34%\n",
      "Minimum k ensuring error < 0.15: 2\n"
     ]
    }
   ],
   "source": [
    "# Find the minimum k ensuring the error is < 0.1 as soon as possible\n",
    "for k in range(1,30,1):\n",
    "    current_error = error_k(k, U, S, V, dataset)\n",
    "    error_percentage = (current_error / np.linalg.norm(dataset, 'fro')) * 100\n",
    "    \n",
    "    print(f\"Frobenius Error Percentage for k = {k}: {error_percentage:.2f}%\")\n",
    "\n",
    "    # Check if the error is less than 15%\n",
    "    if error_percentage < 15:\n",
    "        print(f\"Minimum k ensuring error < 0.15: {k}\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "30461555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Frobenius error vs. k\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(k_values, frobenius_errors_percentage, marker='o', linestyle='-')\n",
    "plt.title('Frobenius Error Percentage vs. Rank (k)')\n",
    "plt.xlabel('Rank (k)')\n",
    "plt.ylabel('Frobenius Error')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "d3f08948",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 551891.66362728,  174940.96077587],\n",
       "       [2098946.60286877,  537558.21788663],\n",
       "       [2099039.58848571,  537282.81464749],\n",
       "       ...,\n",
       "       [2109484.34661452,  549074.31564646],\n",
       "       [2109513.43446997,  549072.2079776 ],\n",
       "       [2109550.80789787,  549069.50307456]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a TruncatedSVD instance with the optimal k\n",
    "svd = TruncatedSVD(n_components = k)\n",
    "\n",
    "# Fit the SVD to your data and transform it to get the truncated matrix\n",
    "truncated_matrix = svd.fit_transform(dataset)\n",
    "truncated_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "21518681",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(38291, 2)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "truncated_matrix.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "ce5d4d65",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the truncated matrix to a CSV file\n",
    "np.savetxt(\"truncated_data.csv\", truncated_matrix, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a6f050b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
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