E15_KPCA-FaultDetection_with different scaling technique.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cc5c4d51",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6a945f89",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# import seaborn as sns\n",
    "from sklearn.preprocessing import Normalizer\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.preprocessing import RobustScaler\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.preprocessing import PowerTransformer\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db6e1732",
   "metadata": {},
   "source": [
    "# The Datas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dcac490a",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_normal = pd.read_csv('./data/normal_training.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5cbaef6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_faulty = pd.read_csv('./data/faulty_testing.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "842eb7db",
   "metadata": {},
   "outputs": [],
   "source": [
    "# data preparing\n",
    "df_train = train_normal[(train_normal.simulationRun>=1)].iloc[:500,3:]\n",
    "\n",
    "df_test = train_normal[(train_normal.simulationRun>5)&(train_normal.simulationRun<10)].iloc[:,3:].reset_index(drop=True)\n",
    "# IDV = 1\n",
    "# df_test = test_faulty[(test_faulty.faultNumber==IDV) & \n",
    "#                                (test_faulty.simulationRun==1)].iloc[:,3:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "55e44e93",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>xmeas_1</th>\n",
       "      <th>xmeas_2</th>\n",
       "      <th>xmeas_3</th>\n",
       "      <th>xmeas_4</th>\n",
       "      <th>xmeas_5</th>\n",
       "      <th>xmeas_6</th>\n",
       "      <th>xmeas_7</th>\n",
       "      <th>xmeas_8</th>\n",
       "      <th>xmeas_9</th>\n",
       "      <th>xmeas_10</th>\n",
       "      <th>...</th>\n",
       "      <th>xmv_2</th>\n",
       "      <th>xmv_3</th>\n",
       "      <th>xmv_4</th>\n",
       "      <th>xmv_5</th>\n",
       "      <th>xmv_6</th>\n",
       "      <th>xmv_7</th>\n",
       "      <th>xmv_8</th>\n",
       "      <th>xmv_9</th>\n",
       "      <th>xmv_10</th>\n",
       "      <th>xmv_11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.25038</td>\n",
       "      <td>3674.0</td>\n",
       "      <td>4529.0</td>\n",
       "      <td>9.2320</td>\n",
       "      <td>26.889</td>\n",
       "      <td>42.402</td>\n",
       "      <td>2704.3</td>\n",
       "      <td>74.863</td>\n",
       "      <td>120.41</td>\n",
       "      <td>0.33818</td>\n",
       "      <td>...</td>\n",
       "      <td>53.744</td>\n",
       "      <td>24.657</td>\n",
       "      <td>62.544</td>\n",
       "      <td>22.137</td>\n",
       "      <td>39.935</td>\n",
       "      <td>42.323</td>\n",
       "      <td>47.757</td>\n",
       "      <td>47.510</td>\n",
       "      <td>41.258</td>\n",
       "      <td>18.447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.25109</td>\n",
       "      <td>3659.4</td>\n",
       "      <td>4556.6</td>\n",
       "      <td>9.4264</td>\n",
       "      <td>26.721</td>\n",
       "      <td>42.576</td>\n",
       "      <td>2705.0</td>\n",
       "      <td>75.000</td>\n",
       "      <td>120.41</td>\n",
       "      <td>0.33620</td>\n",
       "      <td>...</td>\n",
       "      <td>53.414</td>\n",
       "      <td>24.588</td>\n",
       "      <td>59.259</td>\n",
       "      <td>22.084</td>\n",
       "      <td>40.176</td>\n",
       "      <td>38.554</td>\n",
       "      <td>43.692</td>\n",
       "      <td>47.427</td>\n",
       "      <td>41.359</td>\n",
       "      <td>17.194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.25038</td>\n",
       "      <td>3660.3</td>\n",
       "      <td>4477.8</td>\n",
       "      <td>9.4426</td>\n",
       "      <td>26.875</td>\n",
       "      <td>42.070</td>\n",
       "      <td>2706.2</td>\n",
       "      <td>74.771</td>\n",
       "      <td>120.42</td>\n",
       "      <td>0.33563</td>\n",
       "      <td>...</td>\n",
       "      <td>54.357</td>\n",
       "      <td>24.666</td>\n",
       "      <td>61.275</td>\n",
       "      <td>22.380</td>\n",
       "      <td>40.244</td>\n",
       "      <td>38.990</td>\n",
       "      <td>46.699</td>\n",
       "      <td>47.468</td>\n",
       "      <td>41.199</td>\n",
       "      <td>20.530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.24977</td>\n",
       "      <td>3661.3</td>\n",
       "      <td>4512.1</td>\n",
       "      <td>9.4776</td>\n",
       "      <td>26.758</td>\n",
       "      <td>42.063</td>\n",
       "      <td>2707.2</td>\n",
       "      <td>75.224</td>\n",
       "      <td>120.39</td>\n",
       "      <td>0.33553</td>\n",
       "      <td>...</td>\n",
       "      <td>53.946</td>\n",
       "      <td>24.725</td>\n",
       "      <td>59.856</td>\n",
       "      <td>22.277</td>\n",
       "      <td>40.257</td>\n",
       "      <td>38.072</td>\n",
       "      <td>47.541</td>\n",
       "      <td>47.658</td>\n",
       "      <td>41.643</td>\n",
       "      <td>18.089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.29405</td>\n",
       "      <td>3679.0</td>\n",
       "      <td>4497.0</td>\n",
       "      <td>9.3381</td>\n",
       "      <td>26.889</td>\n",
       "      <td>42.650</td>\n",
       "      <td>2705.1</td>\n",
       "      <td>75.388</td>\n",
       "      <td>120.39</td>\n",
       "      <td>0.32632</td>\n",
       "      <td>...</td>\n",
       "      <td>53.658</td>\n",
       "      <td>28.797</td>\n",
       "      <td>60.717</td>\n",
       "      <td>21.947</td>\n",
       "      <td>39.144</td>\n",
       "      <td>41.955</td>\n",
       "      <td>47.645</td>\n",
       "      <td>47.346</td>\n",
       "      <td>41.507</td>\n",
       "      <td>18.461</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 52 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   xmeas_1  xmeas_2  xmeas_3  xmeas_4  xmeas_5  xmeas_6  xmeas_7  xmeas_8  \\\n",
       "0  0.25038   3674.0   4529.0   9.2320   26.889   42.402   2704.3   74.863   \n",
       "1  0.25109   3659.4   4556.6   9.4264   26.721   42.576   2705.0   75.000   \n",
       "2  0.25038   3660.3   4477.8   9.4426   26.875   42.070   2706.2   74.771   \n",
       "3  0.24977   3661.3   4512.1   9.4776   26.758   42.063   2707.2   75.224   \n",
       "4  0.29405   3679.0   4497.0   9.3381   26.889   42.650   2705.1   75.388   \n",
       "\n",
       "   xmeas_9  xmeas_10  ...   xmv_2   xmv_3   xmv_4   xmv_5   xmv_6   xmv_7  \\\n",
       "0   120.41   0.33818  ...  53.744  24.657  62.544  22.137  39.935  42.323   \n",
       "1   120.41   0.33620  ...  53.414  24.588  59.259  22.084  40.176  38.554   \n",
       "2   120.42   0.33563  ...  54.357  24.666  61.275  22.380  40.244  38.990   \n",
       "3   120.39   0.33553  ...  53.946  24.725  59.856  22.277  40.257  38.072   \n",
       "4   120.39   0.32632  ...  53.658  28.797  60.717  21.947  39.144  41.955   \n",
       "\n",
       "    xmv_8   xmv_9  xmv_10  xmv_11  \n",
       "0  47.757  47.510  41.258  18.447  \n",
       "1  43.692  47.427  41.359  17.194  \n",
       "2  46.699  47.468  41.199  20.530  \n",
       "3  47.541  47.658  41.643  18.089  \n",
       "4  47.645  47.346  41.507  18.461  \n",
       "\n",
       "[5 rows x 52 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3e5479b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>xmeas_1</th>\n",
       "      <th>xmeas_2</th>\n",
       "      <th>xmeas_3</th>\n",
       "      <th>xmeas_4</th>\n",
       "      <th>xmeas_5</th>\n",
       "      <th>xmeas_6</th>\n",
       "      <th>xmeas_7</th>\n",
       "      <th>xmeas_8</th>\n",
       "      <th>xmeas_9</th>\n",
       "      <th>xmeas_10</th>\n",
       "      <th>...</th>\n",
       "      <th>xmv_2</th>\n",
       "      <th>xmv_3</th>\n",
       "      <th>xmv_4</th>\n",
       "      <th>xmv_5</th>\n",
       "      <th>xmv_6</th>\n",
       "      <th>xmv_7</th>\n",
       "      <th>xmv_8</th>\n",
       "      <th>xmv_9</th>\n",
       "      <th>xmv_10</th>\n",
       "      <th>xmv_11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.25025</td>\n",
       "      <td>3676.1</td>\n",
       "      <td>4518.7</td>\n",
       "      <td>9.3769</td>\n",
       "      <td>26.748</td>\n",
       "      <td>42.130</td>\n",
       "      <td>2704.3</td>\n",
       "      <td>75.375</td>\n",
       "      <td>120.42</td>\n",
       "      <td>0.33850</td>\n",
       "      <td>...</td>\n",
       "      <td>53.867</td>\n",
       "      <td>24.670</td>\n",
       "      <td>62.322</td>\n",
       "      <td>22.375</td>\n",
       "      <td>39.896</td>\n",
       "      <td>36.040</td>\n",
       "      <td>47.321</td>\n",
       "      <td>47.384</td>\n",
       "      <td>41.161</td>\n",
       "      <td>15.931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.25331</td>\n",
       "      <td>3639.9</td>\n",
       "      <td>4487.0</td>\n",
       "      <td>9.3852</td>\n",
       "      <td>27.153</td>\n",
       "      <td>42.877</td>\n",
       "      <td>2704.6</td>\n",
       "      <td>74.702</td>\n",
       "      <td>120.37</td>\n",
       "      <td>0.33614</td>\n",
       "      <td>...</td>\n",
       "      <td>54.247</td>\n",
       "      <td>24.370</td>\n",
       "      <td>59.331</td>\n",
       "      <td>22.425</td>\n",
       "      <td>40.183</td>\n",
       "      <td>38.570</td>\n",
       "      <td>51.266</td>\n",
       "      <td>47.403</td>\n",
       "      <td>40.431</td>\n",
       "      <td>15.211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.25096</td>\n",
       "      <td>3667.0</td>\n",
       "      <td>4481.4</td>\n",
       "      <td>9.3008</td>\n",
       "      <td>26.742</td>\n",
       "      <td>42.349</td>\n",
       "      <td>2706.5</td>\n",
       "      <td>76.107</td>\n",
       "      <td>120.41</td>\n",
       "      <td>0.33515</td>\n",
       "      <td>...</td>\n",
       "      <td>54.313</td>\n",
       "      <td>24.608</td>\n",
       "      <td>60.264</td>\n",
       "      <td>22.032</td>\n",
       "      <td>40.303</td>\n",
       "      <td>40.878</td>\n",
       "      <td>52.589</td>\n",
       "      <td>47.485</td>\n",
       "      <td>42.107</td>\n",
       "      <td>19.123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.24879</td>\n",
       "      <td>3676.8</td>\n",
       "      <td>4536.7</td>\n",
       "      <td>9.3483</td>\n",
       "      <td>26.752</td>\n",
       "      <td>42.211</td>\n",
       "      <td>2706.3</td>\n",
       "      <td>75.858</td>\n",
       "      <td>120.38</td>\n",
       "      <td>0.33705</td>\n",
       "      <td>...</td>\n",
       "      <td>53.651</td>\n",
       "      <td>24.822</td>\n",
       "      <td>61.995</td>\n",
       "      <td>22.102</td>\n",
       "      <td>40.071</td>\n",
       "      <td>40.130</td>\n",
       "      <td>40.554</td>\n",
       "      <td>47.630</td>\n",
       "      <td>41.308</td>\n",
       "      <td>18.192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.23790</td>\n",
       "      <td>3652.6</td>\n",
       "      <td>4492.4</td>\n",
       "      <td>9.2783</td>\n",
       "      <td>27.071</td>\n",
       "      <td>42.767</td>\n",
       "      <td>2704.7</td>\n",
       "      <td>74.040</td>\n",
       "      <td>120.41</td>\n",
       "      <td>0.32679</td>\n",
       "      <td>...</td>\n",
       "      <td>53.430</td>\n",
       "      <td>23.416</td>\n",
       "      <td>60.937</td>\n",
       "      <td>22.235</td>\n",
       "      <td>38.458</td>\n",
       "      <td>39.328</td>\n",
       "      <td>43.594</td>\n",
       "      <td>47.543</td>\n",
       "      <td>41.020</td>\n",
       "      <td>19.733</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 52 columns</p>\n",
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      ],
      "text/plain": [
       "   xmeas_1  xmeas_2  xmeas_3  xmeas_4  xmeas_5  xmeas_6  xmeas_7  xmeas_8  \\\n",
       "0  0.25025   3676.1   4518.7   9.3769   26.748   42.130   2704.3   75.375   \n",
       "1  0.25331   3639.9   4487.0   9.3852   27.153   42.877   2704.6   74.702   \n",
       "2  0.25096   3667.0   4481.4   9.3008   26.742   42.349   2706.5   76.107   \n",
       "3  0.24879   3676.8   4536.7   9.3483   26.752   42.211   2706.3   75.858   \n",
       "4  0.23790   3652.6   4492.4   9.2783   27.071   42.767   2704.7   74.040   \n",
       "\n",
       "   xmeas_9  xmeas_10  ...   xmv_2   xmv_3   xmv_4   xmv_5   xmv_6   xmv_7  \\\n",
       "0   120.42   0.33850  ...  53.867  24.670  62.322  22.375  39.896  36.040   \n",
       "1   120.37   0.33614  ...  54.247  24.370  59.331  22.425  40.183  38.570   \n",
       "2   120.41   0.33515  ...  54.313  24.608  60.264  22.032  40.303  40.878   \n",
       "3   120.38   0.33705  ...  53.651  24.822  61.995  22.102  40.071  40.130   \n",
       "4   120.41   0.32679  ...  53.430  23.416  60.937  22.235  38.458  39.328   \n",
       "\n",
       "    xmv_8   xmv_9  xmv_10  xmv_11  \n",
       "0  47.321  47.384  41.161  15.931  \n",
       "1  51.266  47.403  40.431  15.211  \n",
       "2  52.589  47.485  42.107  19.123  \n",
       "3  40.554  47.630  41.308  18.192  \n",
       "4  43.594  47.543  41.020  19.733  \n",
       "\n",
       "[5 rows x 52 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78d9a669",
   "metadata": {},
   "source": [
    "## Scaling Training Datas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0409589a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def scl_pick(name, data):\n",
    "    \"\"\"\n",
    "    the several option for name:\n",
    "    -std\n",
    "    -minmax\n",
    "    -robust\n",
    "    -norm\n",
    "    -pwr\n",
    "    \"\"\"\n",
    "    if name == 'std':\n",
    "        std_scl = StandardScaler().fit(data)\n",
    "        df_scl = std_scl.transform(data)\n",
    "        df_scl = pd.DataFrame(df_scl)\n",
    "    elif name == 'minmax':\n",
    "        MM_scl = MinMaxScaler().fit(data)\n",
    "        df_scl = MM_scl.transform(data)\n",
    "        df_scl = pd.DataFrame(df_scl)\n",
    "    elif name == 'robust':\n",
    "        rb_scl = RobustScaler().fit(data)\n",
    "        df_scl = rb_scl.transform(data)\n",
    "        df_scl = pd.DataFrame(df_scl)\n",
    "    elif name == 'norm': ##### xxxxxx\n",
    "        df_norm = Normalizer().fit(data)\n",
    "        df_scl = df_norm.transform(data)\n",
    "        df_scl = pd.DataFrame(df_scl)\n",
    "    else:\n",
    "        pt_scl = PowerTransformer().fit(data)\n",
    "        df_scl = pt_scl.transform(data)\n",
    "        df_scl = pd.DataFrame(df_scl)\n",
    "    return df_scl"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5878bef2",
   "metadata": {},
   "source": [
    "### Important Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0698776e",
   "metadata": {},
   "outputs": [],
   "source": [
    "nComponent = 30\n",
    "nSamples = df_train.shape[0]\n",
    "conf_T2 = 0.99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f1711636",
   "metadata": {},
   "outputs": [],
   "source": [
    "#-std-minmax-robust-norm-pwr\n",
    "df_scl = scl_pick('robust', df_train) #robust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bbe9fca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_scl = round(df_scl, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6514ebcd",
   "metadata": {},
   "outputs": [
    {
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       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
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       "      <th>43</th>\n",
       "      <th>44</th>\n",
       "      <th>45</th>\n",
       "      <th>46</th>\n",
       "      <th>47</th>\n",
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       "      <td>-0.0644</td>\n",
       "      <td>0.2363</td>\n",
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       "      <td>-0.2091</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0855</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.3949</td>\n",
       "      <td>0.0221</td>\n",
       "      <td>0.7175</td>\n",
       "      <td>-0.0009</td>\n",
       "      <td>-0.0934</td>\n",
       "      <td>0.9596</td>\n",
       "      <td>0.3379</td>\n",
       "      <td>-0.3292</td>\n",
       "      <td>0.2105</td>\n",
       "      <td>0.1863</td>\n",
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       "      <td>0.0357</td>\n",
       "      <td>-0.0594</td>\n",
       "      <td>0.9697</td>\n",
       "      <td>0.7171</td>\n",
       "      <td>-0.6334</td>\n",
       "      <td>0.8322</td>\n",
       "      <td>0.1289</td>\n",
       "      <td>-0.0122</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.0650</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.9805</td>\n",
       "      <td>0.0026</td>\n",
       "      <td>-1.1996</td>\n",
       "      <td>-0.0989</td>\n",
       "      <td>0.0572</td>\n",
       "      <td>0.0967</td>\n",
       "      <td>-0.8830</td>\n",
       "      <td>-0.3606</td>\n",
       "      <td>0.3495</td>\n",
       "      <td>-0.4568</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0161</td>\n",
       "      <td>-0.0366</td>\n",
       "      <td>-0.5464</td>\n",
       "      <td>0.8615</td>\n",
       "      <td>-0.1118</td>\n",
       "      <td>-0.9007</td>\n",
       "      <td>0.2633</td>\n",
       "      <td>-0.3412</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.1083</td>\n",
       "      <td>...</td>\n",
       "      <td>0.6930</td>\n",
       "      <td>0.0247</td>\n",
       "      <td>-0.0231</td>\n",
       "      <td>0.4485</td>\n",
       "      <td>0.0997</td>\n",
       "      <td>0.1966</td>\n",
       "      <td>0.0201</td>\n",
       "      <td>-0.3451</td>\n",
       "      <td>0.1293</td>\n",
       "      <td>1.2555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.0007</td>\n",
       "      <td>-0.0114</td>\n",
       "      <td>0.1135</td>\n",
       "      <td>1.1733</td>\n",
       "      <td>-0.5080</td>\n",
       "      <td>-0.9247</td>\n",
       "      <td>0.3754</td>\n",
       "      <td>0.3096</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.1159</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0364</td>\n",
       "      <td>0.0414</td>\n",
       "      <td>-0.8512</td>\n",
       "      <td>0.2580</td>\n",
       "      <td>0.1078</td>\n",
       "      <td>-0.0136</td>\n",
       "      <td>0.2730</td>\n",
       "      <td>-0.2734</td>\n",
       "      <td>0.7403</td>\n",
       "      <td>0.0026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.2188</td>\n",
       "      <td>0.4359</td>\n",
       "      <td>-0.1770</td>\n",
       "      <td>-0.0695</td>\n",
       "      <td>-0.0644</td>\n",
       "      <td>1.0856</td>\n",
       "      <td>0.1401</td>\n",
       "      <td>0.5453</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.8159</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.5475</td>\n",
       "      <td>1.1956</td>\n",
       "      <td>-0.3487</td>\n",
       "      <td>-0.3523</td>\n",
       "      <td>-0.5878</td>\n",
       "      <td>0.8754</td>\n",
       "      <td>0.3042</td>\n",
       "      <td>-0.3911</td>\n",
       "      <td>0.5531</td>\n",
       "      <td>0.1935</td>\n",
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       "       0       1       2       3       4       5       6       7    8   \\\n",
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       "2  0.0161 -0.0366 -0.5464  0.8615 -0.1118 -0.9007  0.2633 -0.3412  1.0   \n",
       "3 -0.0007 -0.0114  0.1135  1.1733 -0.5080 -0.9247  0.3754  0.3096 -0.5   \n",
       "4  1.2188  0.4359 -0.1770 -0.0695 -0.0644  1.0856  0.1401  0.5453 -0.5   \n",
       "\n",
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       "3 -0.1159  ... -0.0364  0.0414 -0.8512  0.2580  0.1078 -0.0136  0.2730   \n",
       "4 -0.8159  ... -0.5475  1.1956 -0.3487 -0.3523 -0.5878  0.8754  0.3042   \n",
       "\n",
       "       49      50      51  \n",
       "0 -0.3292  0.2105  0.1863  \n",
       "1 -0.3606  0.3495 -0.4568  \n",
       "2 -0.3451  0.1293  1.2555  \n",
       "3 -0.2734  0.7403  0.0026  \n",
       "4 -0.3911  0.5531  0.1935  \n",
       "\n",
       "[5 rows x 52 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scl.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8751e7c0",
   "metadata": {},
   "source": [
    "## Training Centraling kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "502e8ce2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/605243457.py:3: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  K = np.matmul(A, A.T)\n"
     ]
    }
   ],
   "source": [
    "# training proccess\n",
    "A = df_scl\n",
    "K = np.matmul(A, A.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f1a062b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = round(K, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a9a35c58",
   "metadata": {},
   "outputs": [
    {
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       "      <td>-2.1675</td>\n",
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       "      <td>2.2867</td>\n",
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       "      <td>-0.5181</td>\n",
       "      <td>8.4373</td>\n",
       "      <td>-1.0766</td>\n",
       "      <td>2.7443</td>\n",
       "      <td>1.0491</td>\n",
       "      <td>-0.8767</td>\n",
       "      <td>2.8401</td>\n",
       "      <td>2.2830</td>\n",
       "      <td>-2.2442</td>\n",
       "      <td>1.4829</td>\n",
       "      <td>...</td>\n",
       "      <td>0.8801</td>\n",
       "      <td>1.1952</td>\n",
       "      <td>-2.2143</td>\n",
       "      <td>0.1188</td>\n",
       "      <td>-0.1430</td>\n",
       "      <td>4.1460</td>\n",
       "      <td>2.9184</td>\n",
       "      <td>-3.2018</td>\n",
       "      <td>-4.9446</td>\n",
       "      <td>-0.3601</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.0321</td>\n",
       "      <td>-1.0766</td>\n",
       "      <td>14.7987</td>\n",
       "      <td>9.2876</td>\n",
       "      <td>-0.5506</td>\n",
       "      <td>2.3805</td>\n",
       "      <td>1.0183</td>\n",
       "      <td>5.3368</td>\n",
       "      <td>-4.7893</td>\n",
       "      <td>2.2260</td>\n",
       "      <td>...</td>\n",
       "      <td>3.3381</td>\n",
       "      <td>3.8664</td>\n",
       "      <td>4.9688</td>\n",
       "      <td>-3.2767</td>\n",
       "      <td>2.9033</td>\n",
       "      <td>-1.3023</td>\n",
       "      <td>-0.6163</td>\n",
       "      <td>-1.8032</td>\n",
       "      <td>-1.2647</td>\n",
       "      <td>-2.2529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.7792</td>\n",
       "      <td>2.7443</td>\n",
       "      <td>9.2876</td>\n",
       "      <td>15.2941</td>\n",
       "      <td>-0.6093</td>\n",
       "      <td>0.4360</td>\n",
       "      <td>3.8382</td>\n",
       "      <td>3.8612</td>\n",
       "      <td>-3.8954</td>\n",
       "      <td>-1.1527</td>\n",
       "      <td>...</td>\n",
       "      <td>2.2427</td>\n",
       "      <td>2.5750</td>\n",
       "      <td>4.1539</td>\n",
       "      <td>0.7523</td>\n",
       "      <td>1.0522</td>\n",
       "      <td>3.6037</td>\n",
       "      <td>0.1213</td>\n",
       "      <td>-4.2110</td>\n",
       "      <td>-3.9486</td>\n",
       "      <td>0.7484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.2119</td>\n",
       "      <td>1.0491</td>\n",
       "      <td>-0.5506</td>\n",
       "      <td>-0.6093</td>\n",
       "      <td>22.2775</td>\n",
       "      <td>19.1028</td>\n",
       "      <td>-1.1796</td>\n",
       "      <td>-3.3707</td>\n",
       "      <td>2.6894</td>\n",
       "      <td>1.6580</td>\n",
       "      <td>...</td>\n",
       "      <td>1.1942</td>\n",
       "      <td>3.1520</td>\n",
       "      <td>-4.8655</td>\n",
       "      <td>-0.4547</td>\n",
       "      <td>0.8588</td>\n",
       "      <td>-1.0321</td>\n",
       "      <td>-0.5124</td>\n",
       "      <td>3.5905</td>\n",
       "      <td>-2.1945</td>\n",
       "      <td>1.3274</td>\n",
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       "      0       1        2        3        4        5       6       7       8    \\\n",
       "0  5.5913 -0.5181  -0.0321  -1.7792   3.2119   0.8766 -0.4944  0.4639 -0.8014   \n",
       "1 -0.5181  8.4373  -1.0766   2.7443   1.0491  -0.8767  2.8401  2.2830 -2.2442   \n",
       "2 -0.0321 -1.0766  14.7987   9.2876  -0.5506   2.3805  1.0183  5.3368 -4.7893   \n",
       "3 -1.7792  2.7443   9.2876  15.2941  -0.6093   0.4360  3.8382  3.8612 -3.8954   \n",
       "4  3.2119  1.0491  -0.5506  -0.6093  22.2775  19.1028 -1.1796 -3.3707  2.6894   \n",
       "\n",
       "      9    ...     490     491     492     493     494     495     496  \\\n",
       "0  0.9281  ...  0.4599  2.5594 -5.1953  2.0894 -2.1675 -5.6556 -1.6185   \n",
       "1  1.4829  ...  0.8801  1.1952 -2.2143  0.1188 -0.1430  4.1460  2.9184   \n",
       "2  2.2260  ...  3.3381  3.8664  4.9688 -3.2767  2.9033 -1.3023 -0.6163   \n",
       "3 -1.1527  ...  2.2427  2.5750  4.1539  0.7523  1.0522  3.6037  0.1213   \n",
       "4  1.6580  ...  1.1942  3.1520 -4.8655 -0.4547  0.8588 -1.0321 -0.5124   \n",
       "\n",
       "      497     498     499  \n",
       "0  2.2867 -1.0814 -0.9864  \n",
       "1 -3.2018 -4.9446 -0.3601  \n",
       "2 -1.8032 -1.2647 -2.2529  \n",
       "3 -4.2110 -3.9486  0.7484  \n",
       "4  3.5905 -2.1945  1.3274  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = pd.DataFrame(K)\n",
    "K.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4b7e0729",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = (len(df_scl),len(df_scl))\n",
    "unit = np.ones(s)/len(df_scl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "58548df2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#######\n",
    "unit = pd.DataFrame(unit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6af65b98",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
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       "      <th>491</th>\n",
       "      <th>492</th>\n",
       "      <th>493</th>\n",
       "      <th>494</th>\n",
       "      <th>495</th>\n",
       "      <th>496</th>\n",
       "      <th>497</th>\n",
       "      <th>498</th>\n",
       "      <th>499</th>\n",
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       "      <th>0</th>\n",
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       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0      1      2      3      4      5      6      7      8      9    ...  \\\n",
       "0  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  ...   \n",
       "1  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  ...   \n",
       "2  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  ...   \n",
       "3  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  ...   \n",
       "4  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  ...   \n",
       "\n",
       "     490    491    492    493    494    495    496    497    498    499  \n",
       "0  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  \n",
       "1  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  \n",
       "2  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  \n",
       "3  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  \n",
       "4  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unit.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e4e716e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_c = K-unit@K-K@unit+unit@K@unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7316c4a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "K_c = round(K_c, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dfe32064",
   "metadata": {},
   "outputs": [
    {
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       "      <td>-4.0425</td>\n",
       "      <td>2.7730</td>\n",
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       "      <td>5.3160</td>\n",
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       "      <td>3.1137</td>\n",
       "      <td>-1.2229</td>\n",
       "      <td>-0.7912</td>\n",
       "      <td>-1.8973</td>\n",
       "      <td>-1.4601</td>\n",
       "      <td>-2.6703</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.3735</td>\n",
       "      <td>3.0396</td>\n",
       "      <td>9.6506</td>\n",
       "      <td>15.6192</td>\n",
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       "      <td>-4.3429</td>\n",
       "      <td>-4.1818</td>\n",
       "      <td>0.2932</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.7195</td>\n",
       "      <td>1.4463</td>\n",
       "      <td>-0.0857</td>\n",
       "      <td>-0.1823</td>\n",
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       "      <td>-0.5172</td>\n",
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       "      <td>3.5003</td>\n",
       "      <td>2.2691</td>\n",
       "      <td>...</td>\n",
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       "      0       1        2        3        4        5       6       7       8    \\\n",
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       "3 -1.3735  3.0396   9.6506  15.6192  -0.1823   0.9754  4.3988  4.3660 -3.1864   \n",
       "4  3.7195  1.4463  -0.0857  -0.1823  22.8064  19.7441 -0.5172 -2.7640  3.5003   \n",
       "\n",
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       "2  2.7730  ...  3.2576  3.7961  5.3160 -3.1991  3.1137 -1.2229 -0.7912   \n",
       "3 -0.6435  ...  2.1244  2.4669  4.4633  0.7921  1.2248  3.6453 -0.0915   \n",
       "4  2.2691  ...  1.1778  3.1458 -4.4542 -0.3130  1.1333 -0.8886 -0.6233   \n",
       "\n",
       "      497     498     499  \n",
       "0  2.2354 -1.2340 -1.3610  \n",
       "1 -3.3636 -5.2077 -0.8452  \n",
       "2 -1.8973 -1.4601 -2.6703  \n",
       "3 -4.3429 -4.1818  0.2932  \n",
       "4  3.5605 -2.3258  0.9741  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_c.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8965afd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute Eigenvalues and Eigenvector\n",
    "eigvls, eigvct = np.linalg.eig(K_c) # K_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ac3d6d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvls = eigvls.real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6a9c0e8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvct = eigvct.real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "40be854e",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvct = pd.DataFrame(eigvct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6b88f7b2",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.019549</td>\n",
       "      <td>-0.017527</td>\n",
       "      <td>0.018272</td>\n",
       "      <td>0.030785</td>\n",
       "      <td>-0.038309</td>\n",
       "      <td>-0.041388</td>\n",
       "      <td>0.002467</td>\n",
       "      <td>0.017669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.011395</td>\n",
       "      <td>-0.006786</td>\n",
       "      <td>0.028961</td>\n",
       "      <td>0.010722</td>\n",
       "      <td>-0.052895</td>\n",
       "      <td>0.076471</td>\n",
       "      <td>-0.020368</td>\n",
       "      <td>-0.004152</td>\n",
       "      <td>-0.030626</td>\n",
       "      <td>-0.006206</td>\n",
       "      <td>...</td>\n",
       "      <td>0.007225</td>\n",
       "      <td>-0.127517</td>\n",
       "      <td>-0.016280</td>\n",
       "      <td>0.045200</td>\n",
       "      <td>-0.027218</td>\n",
       "      <td>0.003760</td>\n",
       "      <td>0.034619</td>\n",
       "      <td>-0.098265</td>\n",
       "      <td>0.079002</td>\n",
       "      <td>-0.000123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.012333</td>\n",
       "      <td>-0.006654</td>\n",
       "      <td>0.013331</td>\n",
       "      <td>0.010824</td>\n",
       "      <td>-0.011701</td>\n",
       "      <td>0.021689</td>\n",
       "      <td>-0.019219</td>\n",
       "      <td>0.004695</td>\n",
       "      <td>-0.030004</td>\n",
       "      <td>-0.042697</td>\n",
       "      <td>...</td>\n",
       "      <td>0.008745</td>\n",
       "      <td>-0.009585</td>\n",
       "      <td>0.047978</td>\n",
       "      <td>0.002866</td>\n",
       "      <td>0.011574</td>\n",
       "      <td>-0.002350</td>\n",
       "      <td>0.038762</td>\n",
       "      <td>0.004171</td>\n",
       "      <td>-0.009867</td>\n",
       "      <td>0.083360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.021066</td>\n",
       "      <td>-0.041475</td>\n",
       "      <td>0.023546</td>\n",
       "      <td>-0.018461</td>\n",
       "      <td>-0.003416</td>\n",
       "      <td>-0.007622</td>\n",
       "      <td>0.064725</td>\n",
       "      <td>0.044008</td>\n",
       "      <td>0.078418</td>\n",
       "      <td>0.026605</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.060330</td>\n",
       "      <td>-0.062348</td>\n",
       "      <td>-0.060533</td>\n",
       "      <td>-0.017727</td>\n",
       "      <td>-0.014991</td>\n",
       "      <td>0.009408</td>\n",
       "      <td>-0.023725</td>\n",
       "      <td>0.040339</td>\n",
       "      <td>-0.038722</td>\n",
       "      <td>-0.057778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0         1         2         3         4         5         6    \\\n",
       "0  0.009236 -0.021278  0.005735  0.011204 -0.023953  0.029021  0.046297   \n",
       "1  0.011884 -0.005083  0.018300  0.017497  0.041126  0.007411  0.007932   \n",
       "2  0.011395 -0.006786  0.028961  0.010722 -0.052895  0.076471 -0.020368   \n",
       "3  0.012333 -0.006654  0.013331  0.010824 -0.011701  0.021689 -0.019219   \n",
       "4  0.021066 -0.041475  0.023546 -0.018461 -0.003416 -0.007622  0.064725   \n",
       "\n",
       "        7         8         9    ...       490       491       492       493  \\\n",
       "0  0.033948  0.005682  0.011180  ... -0.004083  0.002088  0.008445 -0.002345   \n",
       "1 -0.025720 -0.032851 -0.039360  ... -0.050372  0.059584  0.019549 -0.017527   \n",
       "2 -0.004152 -0.030626 -0.006206  ...  0.007225 -0.127517 -0.016280  0.045200   \n",
       "3  0.004695 -0.030004 -0.042697  ...  0.008745 -0.009585  0.047978  0.002866   \n",
       "4  0.044008  0.078418  0.026605  ... -0.060330 -0.062348 -0.060533 -0.017727   \n",
       "\n",
       "        494       495       496       497       498       499  \n",
       "0 -0.022687 -0.001617  0.014499  0.005549 -0.005895 -0.000162  \n",
       "1  0.018272  0.030785 -0.038309 -0.041388  0.002467  0.017669  \n",
       "2 -0.027218  0.003760  0.034619 -0.098265  0.079002 -0.000123  \n",
       "3  0.011574 -0.002350  0.038762  0.004171 -0.009867  0.083360  \n",
       "4 -0.014991  0.009408 -0.023725  0.040339 -0.038722 -0.057778  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvct.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c036e77f",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvls = pd.DataFrame(eigvls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "862b9af6",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigvls = round(eigvls, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a3acc649",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "           0\n",
       "0  1921.3774\n",
       "1  1410.1365\n",
       "2   944.6365\n",
       "3   672.1728\n",
       "4   600.9824"
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     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "eigvls.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ffb3770f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/485419572.py:2: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  score_train = np.matmul(K_c, eigvct.iloc[:,:nComponent])\n"
     ]
    }
   ],
   "source": [
    "# score matrix\n",
    "score_train = np.matmul(K_c, eigvct.iloc[:,:nComponent])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a266c42a",
   "metadata": {},
   "outputs": [],
   "source": [
    "score_train = round(score_train, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c9918600",
   "metadata": {},
   "outputs": [],
   "source": [
    "score_train = pd.DataFrame(score_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9adebfef",
   "metadata": {},
   "outputs": [
    {
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       "      <th>1</th>\n",
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       "      <th>5</th>\n",
       "      <th>6</th>\n",
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       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>20</th>\n",
       "      <th>21</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
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       "      <th>27</th>\n",
       "      <th>28</th>\n",
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       "  <tbody>\n",
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       "      <td>17.7458</td>\n",
       "      <td>-30.0055</td>\n",
       "      <td>5.4171</td>\n",
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       "      <td>-14.3954</td>\n",
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       "      <td>2.5294</td>\n",
       "      <td>4.3637</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.5907</td>\n",
       "      <td>-0.4157</td>\n",
       "      <td>-5.4953</td>\n",
       "      <td>-1.4942</td>\n",
       "      <td>9.1448</td>\n",
       "      <td>1.2217</td>\n",
       "      <td>-6.8822</td>\n",
       "      <td>-4.3992</td>\n",
       "      <td>0.6889</td>\n",
       "      <td>1.7966</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22.8329</td>\n",
       "      <td>-7.1675</td>\n",
       "      <td>17.2871</td>\n",
       "      <td>11.7613</td>\n",
       "      <td>24.7162</td>\n",
       "      <td>4.0289</td>\n",
       "      <td>4.1191</td>\n",
       "      <td>-12.3480</td>\n",
       "      <td>-14.6240</td>\n",
       "      <td>-15.3624</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0386</td>\n",
       "      <td>-13.6558</td>\n",
       "      <td>-18.6220</td>\n",
       "      <td>5.3272</td>\n",
       "      <td>7.4403</td>\n",
       "      <td>-8.5118</td>\n",
       "      <td>-2.5032</td>\n",
       "      <td>-3.0257</td>\n",
       "      <td>6.5024</td>\n",
       "      <td>-4.3455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.8944</td>\n",
       "      <td>-9.5691</td>\n",
       "      <td>27.3574</td>\n",
       "      <td>7.2072</td>\n",
       "      <td>-31.7887</td>\n",
       "      <td>41.5753</td>\n",
       "      <td>-10.5776</td>\n",
       "      <td>-1.9936</td>\n",
       "      <td>-13.6333</td>\n",
       "      <td>-2.4222</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.2301</td>\n",
       "      <td>-5.5057</td>\n",
       "      <td>11.8704</td>\n",
       "      <td>-4.5879</td>\n",
       "      <td>6.7174</td>\n",
       "      <td>9.5517</td>\n",
       "      <td>3.6126</td>\n",
       "      <td>9.0552</td>\n",
       "      <td>-0.8659</td>\n",
       "      <td>-7.1914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.6968</td>\n",
       "      <td>-9.3829</td>\n",
       "      <td>12.5928</td>\n",
       "      <td>7.2753</td>\n",
       "      <td>-7.0319</td>\n",
       "      <td>11.7918</td>\n",
       "      <td>-9.9808</td>\n",
       "      <td>2.2540</td>\n",
       "      <td>-13.3564</td>\n",
       "      <td>-16.6648</td>\n",
       "      <td>...</td>\n",
       "      <td>13.8022</td>\n",
       "      <td>-10.8031</td>\n",
       "      <td>-0.6166</td>\n",
       "      <td>-0.9344</td>\n",
       "      <td>7.9909</td>\n",
       "      <td>-5.3804</td>\n",
       "      <td>10.2828</td>\n",
       "      <td>7.6218</td>\n",
       "      <td>2.0802</td>\n",
       "      <td>-15.2408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40.4765</td>\n",
       "      <td>-58.4853</td>\n",
       "      <td>22.2424</td>\n",
       "      <td>-12.4089</td>\n",
       "      <td>-2.0527</td>\n",
       "      <td>-4.1439</td>\n",
       "      <td>33.6134</td>\n",
       "      <td>21.1279</td>\n",
       "      <td>34.9080</td>\n",
       "      <td>10.3841</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.6188</td>\n",
       "      <td>3.0055</td>\n",
       "      <td>-20.6460</td>\n",
       "      <td>-8.8553</td>\n",
       "      <td>14.7104</td>\n",
       "      <td>-1.0128</td>\n",
       "      <td>5.3660</td>\n",
       "      <td>6.4512</td>\n",
       "      <td>5.8764</td>\n",
       "      <td>4.6926</td>\n",
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       "    <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>495</th>\n",
       "      <td>27.0726</td>\n",
       "      <td>42.8030</td>\n",
       "      <td>14.3472</td>\n",
       "      <td>-38.1975</td>\n",
       "      <td>27.5071</td>\n",
       "      <td>-38.2344</td>\n",
       "      <td>-27.2509</td>\n",
       "      <td>-15.5867</td>\n",
       "      <td>-16.9413</td>\n",
       "      <td>-32.3274</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.7909</td>\n",
       "      <td>-16.9814</td>\n",
       "      <td>-6.1089</td>\n",
       "      <td>-15.2438</td>\n",
       "      <td>4.5453</td>\n",
       "      <td>-11.3974</td>\n",
       "      <td>2.4034</td>\n",
       "      <td>-3.7956</td>\n",
       "      <td>0.6598</td>\n",
       "      <td>0.8366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>-7.1370</td>\n",
       "      <td>57.9582</td>\n",
       "      <td>-5.5602</td>\n",
       "      <td>60.6203</td>\n",
       "      <td>20.3735</td>\n",
       "      <td>9.7057</td>\n",
       "      <td>-8.4340</td>\n",
       "      <td>-13.7278</td>\n",
       "      <td>-2.3845</td>\n",
       "      <td>-8.3749</td>\n",
       "      <td>...</td>\n",
       "      <td>-8.1215</td>\n",
       "      <td>-0.6654</td>\n",
       "      <td>-9.9196</td>\n",
       "      <td>0.7744</td>\n",
       "      <td>-6.4997</td>\n",
       "      <td>-7.0170</td>\n",
       "      <td>-5.3486</td>\n",
       "      <td>8.0728</td>\n",
       "      <td>5.5051</td>\n",
       "      <td>2.7157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>-30.9725</td>\n",
       "      <td>32.4778</td>\n",
       "      <td>-35.1369</td>\n",
       "      <td>61.8014</td>\n",
       "      <td>-9.7260</td>\n",
       "      <td>9.3474</td>\n",
       "      <td>14.3196</td>\n",
       "      <td>22.7212</td>\n",
       "      <td>24.6479</td>\n",
       "      <td>-3.3800</td>\n",
       "      <td>...</td>\n",
       "      <td>-22.8585</td>\n",
       "      <td>-3.1391</td>\n",
       "      <td>0.8206</td>\n",
       "      <td>-10.7785</td>\n",
       "      <td>-2.4633</td>\n",
       "      <td>2.1168</td>\n",
       "      <td>-3.8778</td>\n",
       "      <td>6.2852</td>\n",
       "      <td>-1.3274</td>\n",
       "      <td>10.7542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>-2.7114</td>\n",
       "      <td>11.7059</td>\n",
       "      <td>-47.7749</td>\n",
       "      <td>-11.9804</td>\n",
       "      <td>-24.7132</td>\n",
       "      <td>-14.0636</td>\n",
       "      <td>-7.3654</td>\n",
       "      <td>-7.9999</td>\n",
       "      <td>24.0331</td>\n",
       "      <td>-11.1785</td>\n",
       "      <td>...</td>\n",
       "      <td>-15.5151</td>\n",
       "      <td>3.9924</td>\n",
       "      <td>7.1600</td>\n",
       "      <td>-4.4879</td>\n",
       "      <td>-5.8517</td>\n",
       "      <td>17.1668</td>\n",
       "      <td>-3.1917</td>\n",
       "      <td>6.0705</td>\n",
       "      <td>-7.0828</td>\n",
       "      <td>-14.5067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>12.8255</td>\n",
       "      <td>15.8016</td>\n",
       "      <td>-23.1540</td>\n",
       "      <td>-17.2449</td>\n",
       "      <td>-53.7857</td>\n",
       "      <td>-41.8481</td>\n",
       "      <td>4.7096</td>\n",
       "      <td>20.9024</td>\n",
       "      <td>5.2301</td>\n",
       "      <td>-11.0618</td>\n",
       "      <td>...</td>\n",
       "      <td>-10.2071</td>\n",
       "      <td>-4.9992</td>\n",
       "      <td>-20.8515</td>\n",
       "      <td>4.2788</td>\n",
       "      <td>-7.1391</td>\n",
       "      <td>7.0395</td>\n",
       "      <td>1.6674</td>\n",
       "      <td>-2.3099</td>\n",
       "      <td>-4.2075</td>\n",
       "      <td>-13.7562</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0        1        2        3        4        5        6        7   \\\n",
       "0    17.7458 -30.0055   5.4171   7.5312 -14.3954  15.7779  24.0434  16.2982   \n",
       "1    22.8329  -7.1675  17.2871  11.7613  24.7162   4.0289   4.1191 -12.3480   \n",
       "2    21.8944  -9.5691  27.3574   7.2072 -31.7887  41.5753 -10.5776  -1.9936   \n",
       "3    23.6968  -9.3829  12.5928   7.2753  -7.0319  11.7918  -9.9808   2.2540   \n",
       "4    40.4765 -58.4853  22.2424 -12.4089  -2.0527  -4.1439  33.6134  21.1279   \n",
       "..       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "495  27.0726  42.8030  14.3472 -38.1975  27.5071 -38.2344 -27.2509 -15.5867   \n",
       "496  -7.1370  57.9582  -5.5602  60.6203  20.3735   9.7057  -8.4340 -13.7278   \n",
       "497 -30.9725  32.4778 -35.1369  61.8014  -9.7260   9.3474  14.3196  22.7212   \n",
       "498  -2.7114  11.7059 -47.7749 -11.9804 -24.7132 -14.0636  -7.3654  -7.9999   \n",
       "499  12.8255  15.8016 -23.1540 -17.2449 -53.7857 -41.8481   4.7096  20.9024   \n",
       "\n",
       "          8        9   ...       20       21       22       23       24  \\\n",
       "0     2.5294   4.3637  ...  -1.5907  -0.4157  -5.4953  -1.4942   9.1448   \n",
       "1   -14.6240 -15.3624  ...  10.0386 -13.6558 -18.6220   5.3272   7.4403   \n",
       "2   -13.6333  -2.4222  ...  -1.2301  -5.5057  11.8704  -4.5879   6.7174   \n",
       "3   -13.3564 -16.6648  ...  13.8022 -10.8031  -0.6166  -0.9344   7.9909   \n",
       "4    34.9080  10.3841  ...  -3.6188   3.0055 -20.6460  -8.8553  14.7104   \n",
       "..       ...      ...  ...      ...      ...      ...      ...      ...   \n",
       "495 -16.9413 -32.3274  ...  -3.7909 -16.9814  -6.1089 -15.2438   4.5453   \n",
       "496  -2.3845  -8.3749  ...  -8.1215  -0.6654  -9.9196   0.7744  -6.4997   \n",
       "497  24.6479  -3.3800  ... -22.8585  -3.1391   0.8206 -10.7785  -2.4633   \n",
       "498  24.0331 -11.1785  ... -15.5151   3.9924   7.1600  -4.4879  -5.8517   \n",
       "499   5.2301 -11.0618  ... -10.2071  -4.9992 -20.8515   4.2788  -7.1391   \n",
       "\n",
       "          25       26      27      28       29  \n",
       "0     1.2217  -6.8822 -4.3992  0.6889   1.7966  \n",
       "1    -8.5118  -2.5032 -3.0257  6.5024  -4.3455  \n",
       "2     9.5517   3.6126  9.0552 -0.8659  -7.1914  \n",
       "3    -5.3804  10.2828  7.6218  2.0802 -15.2408  \n",
       "4    -1.0128   5.3660  6.4512  5.8764   4.6926  \n",
       "..       ...      ...     ...     ...      ...  \n",
       "495 -11.3974   2.4034 -3.7956  0.6598   0.8366  \n",
       "496  -7.0170  -5.3486  8.0728  5.5051   2.7157  \n",
       "497   2.1168  -3.8778  6.2852 -1.3274  10.7542  \n",
       "498  17.1668  -3.1917  6.0705 -7.0828 -14.5067  \n",
       "499   7.0395   1.6674 -2.3099 -4.2075 -13.7562  \n",
       "\n",
       "[500 rows x 30 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4fa1ea5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "### T2 training Process\n",
    "a = eigvls.iloc[:nComponent,:]\n",
    "b = np.zeros((nComponent, nComponent), int)\n",
    "np.fill_diagonal(b, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "6ae0de4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 30)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "bd50c081",
   "metadata": {},
   "outputs": [],
   "source": [
    "# b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "95ff782e",
   "metadata": {},
   "outputs": [],
   "source": [
    "invegvldiag = np.linalg.inv(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "bfa3516d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 30)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invegvldiag.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4a3b1415",
   "metadata": {},
   "outputs": [],
   "source": [
    "# invegvldiag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "787a9e89",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_train = score_train@invegvldiag@score_train.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "31eabdc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_train = round(T2_train, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "32aa8d30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 500)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "8deb723e",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>490</th>\n",
       "      <th>491</th>\n",
       "      <th>492</th>\n",
       "      <th>493</th>\n",
       "      <th>494</th>\n",
       "      <th>495</th>\n",
       "      <th>496</th>\n",
       "      <th>497</th>\n",
       "      <th>498</th>\n",
       "      <th>499</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.6215</td>\n",
       "      <td>-0.1358</td>\n",
       "      <td>0.2967</td>\n",
       "      <td>-1.6340</td>\n",
       "      <td>3.8314</td>\n",
       "      <td>1.4188</td>\n",
       "      <td>0.3360</td>\n",
       "      <td>1.0265</td>\n",
       "      <td>-0.1748</td>\n",
       "      <td>1.3205</td>\n",
       "      <td>...</td>\n",
       "      <td>0.2918</td>\n",
       "      <td>2.4409</td>\n",
       "      <td>-4.3866</td>\n",
       "      <td>1.9797</td>\n",
       "      <td>-1.2659</td>\n",
       "      <td>-4.8973</td>\n",
       "      <td>-1.7909</td>\n",
       "      <td>2.1817</td>\n",
       "      <td>-0.5211</td>\n",
       "      <td>-0.7904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.1358</td>\n",
       "      <td>8.3294</td>\n",
       "      <td>-0.5362</td>\n",
       "      <td>3.0729</td>\n",
       "      <td>1.1910</td>\n",
       "      <td>-0.5511</td>\n",
       "      <td>2.9722</td>\n",
       "      <td>2.8504</td>\n",
       "      <td>-1.3782</td>\n",
       "      <td>1.9027</td>\n",
       "      <td>...</td>\n",
       "      <td>0.3685</td>\n",
       "      <td>0.9065</td>\n",
       "      <td>-1.8591</td>\n",
       "      <td>-0.1526</td>\n",
       "      <td>-0.1744</td>\n",
       "      <td>4.3626</td>\n",
       "      <td>2.7380</td>\n",
       "      <td>-3.5046</td>\n",
       "      <td>-5.4472</td>\n",
       "      <td>-1.0819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2967</td>\n",
       "      <td>-0.5362</td>\n",
       "      <td>14.2507</td>\n",
       "      <td>9.3734</td>\n",
       "      <td>0.3498</td>\n",
       "      <td>3.4656</td>\n",
       "      <td>1.4760</td>\n",
       "      <td>5.2431</td>\n",
       "      <td>-4.2729</td>\n",
       "      <td>2.3194</td>\n",
       "      <td>...</td>\n",
       "      <td>3.7859</td>\n",
       "      <td>4.4076</td>\n",
       "      <td>5.8761</td>\n",
       "      <td>-2.5385</td>\n",
       "      <td>3.4110</td>\n",
       "      <td>-0.8821</td>\n",
       "      <td>-0.3758</td>\n",
       "      <td>-1.4732</td>\n",
       "      <td>-0.9215</td>\n",
       "      <td>-1.6780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.6340</td>\n",
       "      <td>3.0729</td>\n",
       "      <td>9.3734</td>\n",
       "      <td>13.3947</td>\n",
       "      <td>-0.3649</td>\n",
       "      <td>1.0971</td>\n",
       "      <td>2.7150</td>\n",
       "      <td>3.2923</td>\n",
       "      <td>-4.5591</td>\n",
       "      <td>-1.4339</td>\n",
       "      <td>...</td>\n",
       "      <td>2.2146</td>\n",
       "      <td>2.0745</td>\n",
       "      <td>3.4769</td>\n",
       "      <td>0.5485</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>3.8468</td>\n",
       "      <td>-0.4617</td>\n",
       "      <td>-5.0390</td>\n",
       "      <td>-3.5172</td>\n",
       "      <td>0.5722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.8314</td>\n",
       "      <td>1.1910</td>\n",
       "      <td>0.3498</td>\n",
       "      <td>-0.3649</td>\n",
       "      <td>21.2046</td>\n",
       "      <td>19.0875</td>\n",
       "      <td>-0.1688</td>\n",
       "      <td>-1.4045</td>\n",
       "      <td>2.7573</td>\n",
       "      <td>1.8885</td>\n",
       "      <td>...</td>\n",
       "      <td>1.2727</td>\n",
       "      <td>2.9817</td>\n",
       "      <td>-5.2212</td>\n",
       "      <td>-0.7091</td>\n",
       "      <td>0.6875</td>\n",
       "      <td>-1.0816</td>\n",
       "      <td>-1.1507</td>\n",
       "      <td>3.1489</td>\n",
       "      <td>-2.5003</td>\n",
       "      <td>0.6222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      0       1        2        3        4        5       6       7       8    \\\n",
       "0  5.6215 -0.1358   0.2967  -1.6340   3.8314   1.4188  0.3360  1.0265 -0.1748   \n",
       "1 -0.1358  8.3294  -0.5362   3.0729   1.1910  -0.5511  2.9722  2.8504 -1.3782   \n",
       "2  0.2967 -0.5362  14.2507   9.3734   0.3498   3.4656  1.4760  5.2431 -4.2729   \n",
       "3 -1.6340  3.0729   9.3734  13.3947  -0.3649   1.0971  2.7150  3.2923 -4.5591   \n",
       "4  3.8314  1.1910   0.3498  -0.3649  21.2046  19.0875 -0.1688 -1.4045  2.7573   \n",
       "\n",
       "      9    ...     490     491     492     493     494     495     496  \\\n",
       "0  1.3205  ...  0.2918  2.4409 -4.3866  1.9797 -1.2659 -4.8973 -1.7909   \n",
       "1  1.9027  ...  0.3685  0.9065 -1.8591 -0.1526 -0.1744  4.3626  2.7380   \n",
       "2  2.3194  ...  3.7859  4.4076  5.8761 -2.5385  3.4110 -0.8821 -0.3758   \n",
       "3 -1.4339  ...  2.2146  2.0745  3.4769  0.5485  0.9067  3.8468 -0.4617   \n",
       "4  1.8885  ...  1.2727  2.9817 -5.2212 -0.7091  0.6875 -1.0816 -1.1507   \n",
       "\n",
       "      497     498     499  \n",
       "0  2.1817 -0.5211 -0.7904  \n",
       "1 -3.5046 -5.4472 -1.0819  \n",
       "2 -1.4732 -0.9215 -1.6780  \n",
       "3 -5.0390 -3.5172  0.5722  \n",
       "4  3.1489 -2.5003  0.6222  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "7a70bdf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# here the data is from training data \n",
    "# or with using same data\n",
    "T2_tfinal = np.diag(T2_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a0756384",
   "metadata": {},
   "outputs": [],
   "source": [
    "# T2_tfinal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "4f3eca0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "### T2 limit\n",
    "# im using 16 component\n",
    "# nComponent = 30\n",
    "# nSamples = df_train.shape[0]\n",
    "# conf_T2 = 0.99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2d32dde3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import f\n",
    "F = f.ppf(conf_T2, nComponent, nSamples-nComponent)\n",
    "T2_trlim = ((nComponent*(nSamples**2-1))/(nSamples*(nSamples-nComponent)))*F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "3ae540ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.46204002064628"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2_trlim\n",
    "# conf_T2 = 0.95, T2_trlim = 47.3464294521146\n",
    "# conf_T2 = 0.99, T2_trlim = 55.46204002064628"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "ac4aa121",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the result\n",
    "plt.semilogy(T2_tfinal,'.')\n",
    "plt.axhline(T2_trlim, ls='--',c='r')\n",
    "plt.title('$T^2$ statistic')\n",
    "plt.show()\n",
    "# in this scatter plot the data has been use is\n",
    "# training data it self "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "37f1c8ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(T2_tfinal)\n",
    "plt.axhline(T2_trlim, ls='--',c='r')\n",
    "plt.title('$T^2$ statistic')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "ddbbab14",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T2: 0.0\n"
     ]
    }
   ],
   "source": [
    "print(f'T2: {(T2_tfinal>T2_trlim).sum()/T2_tfinal.shape[0]}')\n",
    "# ofcourse 100% because we using train and test in the same dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d62062",
   "metadata": {},
   "source": [
    "## Scaling Testing Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "7a38c201",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_ts = scl_pick('robust', df_test) ##robust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "31dea5c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_ts = round(X_ts, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "f76d024e",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>42</th>\n",
       "      <th>43</th>\n",
       "      <th>44</th>\n",
       "      <th>45</th>\n",
       "      <th>46</th>\n",
       "      <th>47</th>\n",
       "      <th>48</th>\n",
       "      <th>49</th>\n",
       "      <th>50</th>\n",
       "      <th>51</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.0035</td>\n",
       "      <td>0.2900</td>\n",
       "      <td>0.1990</td>\n",
       "      <td>0.2481</td>\n",
       "      <td>-0.5098</td>\n",
       "      <td>-0.7039</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.5041</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0688</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.1912</td>\n",
       "      <td>0.0131</td>\n",
       "      <td>0.6219</td>\n",
       "      <td>0.2366</td>\n",
       "      <td>-0.0824</td>\n",
       "      <td>-0.4930</td>\n",
       "      <td>0.2882</td>\n",
       "      <td>-0.2027</td>\n",
       "      <td>0.0826</td>\n",
       "      <td>-1.1132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0710</td>\n",
       "      <td>-0.4876</td>\n",
       "      <td>-0.4046</td>\n",
       "      <td>0.3168</td>\n",
       "      <td>0.8713</td>\n",
       "      <td>1.7533</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>-0.4091</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>-0.0671</td>\n",
       "      <td>...</td>\n",
       "      <td>0.3923</td>\n",
       "      <td>-0.0602</td>\n",
       "      <td>-1.1702</td>\n",
       "      <td>0.3165</td>\n",
       "      <td>0.0543</td>\n",
       "      <td>0.1219</td>\n",
       "      <td>1.4972</td>\n",
       "      <td>-0.1974</td>\n",
       "      <td>-0.9478</td>\n",
       "      <td>-1.4795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0138</td>\n",
       "      <td>0.0945</td>\n",
       "      <td>-0.5112</td>\n",
       "      <td>-0.3813</td>\n",
       "      <td>-0.5303</td>\n",
       "      <td>0.0164</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.4973</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.1240</td>\n",
       "      <td>...</td>\n",
       "      <td>0.4937</td>\n",
       "      <td>-0.0021</td>\n",
       "      <td>-0.6111</td>\n",
       "      <td>-0.3118</td>\n",
       "      <td>0.1115</td>\n",
       "      <td>0.6827</td>\n",
       "      <td>1.9027</td>\n",
       "      <td>-0.1746</td>\n",
       "      <td>1.4178</td>\n",
       "      <td>0.5108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.0391</td>\n",
       "      <td>0.3050</td>\n",
       "      <td>0.5416</td>\n",
       "      <td>0.0116</td>\n",
       "      <td>-0.4962</td>\n",
       "      <td>-0.4375</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1.1594</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-0.0147</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.5228</td>\n",
       "      <td>0.0502</td>\n",
       "      <td>0.4260</td>\n",
       "      <td>-0.1998</td>\n",
       "      <td>0.0010</td>\n",
       "      <td>0.5010</td>\n",
       "      <td>-1.7856</td>\n",
       "      <td>-0.1343</td>\n",
       "      <td>0.2900</td>\n",
       "      <td>0.0371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.3046</td>\n",
       "      <td>-0.2148</td>\n",
       "      <td>-0.3018</td>\n",
       "      <td>-0.5674</td>\n",
       "      <td>0.5916</td>\n",
       "      <td>1.3914</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>-1.3073</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.6052</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.8622</td>\n",
       "      <td>-0.2934</td>\n",
       "      <td>-0.2079</td>\n",
       "      <td>0.0128</td>\n",
       "      <td>-0.7678</td>\n",
       "      <td>0.3061</td>\n",
       "      <td>-0.8540</td>\n",
       "      <td>-0.1585</td>\n",
       "      <td>-0.1164</td>\n",
       "      <td>0.8212</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>1995</th>\n",
       "      <td>0.1022</td>\n",
       "      <td>-0.6079</td>\n",
       "      <td>0.1475</td>\n",
       "      <td>0.2911</td>\n",
       "      <td>0.9906</td>\n",
       "      <td>-0.6480</td>\n",
       "      <td>-0.70</td>\n",
       "      <td>0.1024</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-0.2247</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.6917</td>\n",
       "      <td>0.0839</td>\n",
       "      <td>0.9946</td>\n",
       "      <td>-0.3645</td>\n",
       "      <td>-0.1701</td>\n",
       "      <td>0.2733</td>\n",
       "      <td>0.0670</td>\n",
       "      <td>0.8173</td>\n",
       "      <td>-0.2378</td>\n",
       "      <td>0.0524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>1.3977</td>\n",
       "      <td>0.3845</td>\n",
       "      <td>0.8025</td>\n",
       "      <td>0.4946</td>\n",
       "      <td>-1.0827</td>\n",
       "      <td>-0.0033</td>\n",
       "      <td>-0.45</td>\n",
       "      <td>-0.2707</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5925</td>\n",
       "      <td>...</td>\n",
       "      <td>0.2572</td>\n",
       "      <td>1.3698</td>\n",
       "      <td>-0.5045</td>\n",
       "      <td>-1.4836</td>\n",
       "      <td>0.4694</td>\n",
       "      <td>-0.7950</td>\n",
       "      <td>-0.5996</td>\n",
       "      <td>0.8090</td>\n",
       "      <td>0.7544</td>\n",
       "      <td>-1.2058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>1.3719</td>\n",
       "      <td>-0.0945</td>\n",
       "      <td>-0.1666</td>\n",
       "      <td>1.7022</td>\n",
       "      <td>0.7383</td>\n",
       "      <td>1.0658</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>0.2693</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4446</td>\n",
       "      <td>...</td>\n",
       "      <td>1.1923</td>\n",
       "      <td>1.3954</td>\n",
       "      <td>-1.1156</td>\n",
       "      <td>-1.5028</td>\n",
       "      <td>0.6191</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>0.9379</td>\n",
       "      <td>0.8298</td>\n",
       "      <td>-0.8095</td>\n",
       "      <td>0.3160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>0.1098</td>\n",
       "      <td>0.5435</td>\n",
       "      <td>0.5702</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>-0.1108</td>\n",
       "      <td>0.9276</td>\n",
       "      <td>-0.35</td>\n",
       "      <td>0.3901</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0498</td>\n",
       "      <td>...</td>\n",
       "      <td>0.2541</td>\n",
       "      <td>0.1318</td>\n",
       "      <td>-0.2199</td>\n",
       "      <td>-0.7242</td>\n",
       "      <td>-0.0105</td>\n",
       "      <td>1.1902</td>\n",
       "      <td>-0.2594</td>\n",
       "      <td>0.9071</td>\n",
       "      <td>0.6175</td>\n",
       "      <td>-1.1473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>0.1303</td>\n",
       "      <td>0.0430</td>\n",
       "      <td>-0.0733</td>\n",
       "      <td>0.2465</td>\n",
       "      <td>1.2293</td>\n",
       "      <td>1.3750</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.1594</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0555</td>\n",
       "      <td>...</td>\n",
       "      <td>0.8760</td>\n",
       "      <td>0.1116</td>\n",
       "      <td>0.6435</td>\n",
       "      <td>-1.1607</td>\n",
       "      <td>-0.0162</td>\n",
       "      <td>-0.4217</td>\n",
       "      <td>0.6223</td>\n",
       "      <td>0.9035</td>\n",
       "      <td>-1.3063</td>\n",
       "      <td>0.5103</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 52 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0       1       2       3       4       5     6       7    8   \\\n",
       "0    -0.0035  0.2900  0.1990  0.2481 -0.5098 -0.7039 -0.18  0.5041  1.0   \n",
       "1     0.0710 -0.4876 -0.4046  0.3168  0.8713  1.7533 -0.15 -0.4091 -1.5   \n",
       "2     0.0138  0.0945 -0.5112 -0.3813 -0.5303  0.0164  0.04  1.4973  0.5   \n",
       "3    -0.0391  0.3050  0.5416  0.0116 -0.4962 -0.4375  0.02  1.1594 -1.0   \n",
       "4    -0.3046 -0.2148 -0.3018 -0.5674  0.5916  1.3914 -0.14 -1.3073  0.5   \n",
       "...      ...     ...     ...     ...     ...     ...   ...     ...  ...   \n",
       "1995  0.1022 -0.6079  0.1475  0.2911  0.9906 -0.6480 -0.70  0.1024 -1.0   \n",
       "1996  1.3977  0.3845  0.8025  0.4946 -1.0827 -0.0033 -0.45 -0.2707  0.5   \n",
       "1997  1.3719 -0.0945 -0.1666  1.7022  0.7383  1.0658 -0.43  0.2693  0.0   \n",
       "1998  0.1098  0.5435  0.5702  0.9222 -0.1108  0.9276 -0.35  0.3901  2.0   \n",
       "1999  0.1303  0.0430 -0.0733  0.2465  1.2293  1.3750 -0.44 -0.1594  0.5   \n",
       "\n",
       "          9   ...      42      43      44      45      46      47      48  \\\n",
       "0     0.0688  ... -0.1912  0.0131  0.6219  0.2366 -0.0824 -0.4930  0.2882   \n",
       "1    -0.0671  ...  0.3923 -0.0602 -1.1702  0.3165  0.0543  0.1219  1.4972   \n",
       "2    -0.1240  ...  0.4937 -0.0021 -0.6111 -0.3118  0.1115  0.6827  1.9027   \n",
       "3    -0.0147  ... -0.5228  0.0502  0.4260 -0.1998  0.0010  0.5010 -1.7856   \n",
       "4    -0.6052  ... -0.8622 -0.2934 -0.2079  0.0128 -0.7678  0.3061 -0.8540   \n",
       "...      ...  ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "1995 -0.2247  ... -0.6917  0.0839  0.9946 -0.3645 -0.1701  0.2733  0.0670   \n",
       "1996  0.5925  ...  0.2572  1.3698 -0.5045 -1.4836  0.4694 -0.7950 -0.5996   \n",
       "1997  0.4446  ...  1.1923  1.3954 -1.1156 -1.5028  0.6191  0.7112  0.9379   \n",
       "1998  0.0498  ...  0.2541  0.1318 -0.2199 -0.7242 -0.0105  1.1902 -0.2594   \n",
       "1999  0.0555  ...  0.8760  0.1116  0.6435 -1.1607 -0.0162 -0.4217  0.6223   \n",
       "\n",
       "          49      50      51  \n",
       "0    -0.2027  0.0826 -1.1132  \n",
       "1    -0.1974 -0.9478 -1.4795  \n",
       "2    -0.1746  1.4178  0.5108  \n",
       "3    -0.1343  0.2900  0.0371  \n",
       "4    -0.1585 -0.1164  0.8212  \n",
       "...      ...     ...     ...  \n",
       "1995  0.8173 -0.2378  0.0524  \n",
       "1996  0.8090  0.7544 -1.2058  \n",
       "1997  0.8298 -0.8095  0.3160  \n",
       "1998  0.9071  0.6175 -1.1473  \n",
       "1999  0.9035 -1.3063  0.5103  \n",
       "\n",
       "[2000 rows x 52 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "309e002d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>42</th>\n",
       "      <th>43</th>\n",
       "      <th>44</th>\n",
       "      <th>45</th>\n",
       "      <th>46</th>\n",
       "      <th>47</th>\n",
       "      <th>48</th>\n",
       "      <th>49</th>\n",
       "      <th>50</th>\n",
       "      <th>51</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0161</td>\n",
       "      <td>0.3095</td>\n",
       "      <td>0.4387</td>\n",
       "      <td>-1.0147</td>\n",
       "      <td>-0.0644</td>\n",
       "      <td>0.2363</td>\n",
       "      <td>0.0504</td>\n",
       "      <td>-0.2091</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0855</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.3949</td>\n",
       "      <td>0.0221</td>\n",
       "      <td>0.7175</td>\n",
       "      <td>-0.0009</td>\n",
       "      <td>-0.0934</td>\n",
       "      <td>0.9596</td>\n",
       "      <td>0.3379</td>\n",
       "      <td>-0.3292</td>\n",
       "      <td>0.2105</td>\n",
       "      <td>0.1863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0357</td>\n",
       "      <td>-0.0594</td>\n",
       "      <td>0.9697</td>\n",
       "      <td>0.7171</td>\n",
       "      <td>-0.6334</td>\n",
       "      <td>0.8322</td>\n",
       "      <td>0.1289</td>\n",
       "      <td>-0.0122</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.0650</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.9805</td>\n",
       "      <td>0.0026</td>\n",
       "      <td>-1.1996</td>\n",
       "      <td>-0.0989</td>\n",
       "      <td>0.0572</td>\n",
       "      <td>0.0967</td>\n",
       "      <td>-0.8830</td>\n",
       "      <td>-0.3606</td>\n",
       "      <td>0.3495</td>\n",
       "      <td>-0.4568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0161</td>\n",
       "      <td>-0.0366</td>\n",
       "      <td>-0.5464</td>\n",
       "      <td>0.8615</td>\n",
       "      <td>-0.1118</td>\n",
       "      <td>-0.9007</td>\n",
       "      <td>0.2633</td>\n",
       "      <td>-0.3412</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.1083</td>\n",
       "      <td>...</td>\n",
       "      <td>0.6930</td>\n",
       "      <td>0.0247</td>\n",
       "      <td>-0.0231</td>\n",
       "      <td>0.4485</td>\n",
       "      <td>0.0997</td>\n",
       "      <td>0.1966</td>\n",
       "      <td>0.0201</td>\n",
       "      <td>-0.3451</td>\n",
       "      <td>0.1293</td>\n",
       "      <td>1.2555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.0007</td>\n",
       "      <td>-0.0114</td>\n",
       "      <td>0.1135</td>\n",
       "      <td>1.1733</td>\n",
       "      <td>-0.5080</td>\n",
       "      <td>-0.9247</td>\n",
       "      <td>0.3754</td>\n",
       "      <td>0.3096</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.1159</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0364</td>\n",
       "      <td>0.0414</td>\n",
       "      <td>-0.8512</td>\n",
       "      <td>0.2580</td>\n",
       "      <td>0.1078</td>\n",
       "      <td>-0.0136</td>\n",
       "      <td>0.2730</td>\n",
       "      <td>-0.2734</td>\n",
       "      <td>0.7403</td>\n",
       "      <td>0.0026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.2188</td>\n",
       "      <td>0.4359</td>\n",
       "      <td>-0.1770</td>\n",
       "      <td>-0.0695</td>\n",
       "      <td>-0.0644</td>\n",
       "      <td>1.0856</td>\n",
       "      <td>0.1401</td>\n",
       "      <td>0.5453</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.8159</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.5475</td>\n",
       "      <td>1.1956</td>\n",
       "      <td>-0.3487</td>\n",
       "      <td>-0.3523</td>\n",
       "      <td>-0.5878</td>\n",
       "      <td>0.8754</td>\n",
       "      <td>0.3042</td>\n",
       "      <td>-0.3911</td>\n",
       "      <td>0.5531</td>\n",
       "      <td>0.1935</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>495</th>\n",
       "      <td>-0.1040</td>\n",
       "      <td>-0.2489</td>\n",
       "      <td>-0.0346</td>\n",
       "      <td>1.1243</td>\n",
       "      <td>-1.0432</td>\n",
       "      <td>-0.0719</td>\n",
       "      <td>0.3754</td>\n",
       "      <td>-0.5539</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.0067</td>\n",
       "      <td>...</td>\n",
       "      <td>0.2937</td>\n",
       "      <td>-0.2596</td>\n",
       "      <td>-1.0076</td>\n",
       "      <td>0.6352</td>\n",
       "      <td>-0.7078</td>\n",
       "      <td>-1.0629</td>\n",
       "      <td>-0.4292</td>\n",
       "      <td>0.5726</td>\n",
       "      <td>-0.0660</td>\n",
       "      <td>-0.8397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>-0.4193</td>\n",
       "      <td>0.0316</td>\n",
       "      <td>0.4483</td>\n",
       "      <td>-0.0169</td>\n",
       "      <td>-0.1219</td>\n",
       "      <td>0.3459</td>\n",
       "      <td>0.0280</td>\n",
       "      <td>0.1645</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.3289</td>\n",
       "      <td>...</td>\n",
       "      <td>0.1091</td>\n",
       "      <td>-0.5111</td>\n",
       "      <td>-0.4368</td>\n",
       "      <td>0.1840</td>\n",
       "      <td>1.8084</td>\n",
       "      <td>-0.0262</td>\n",
       "      <td>-1.1999</td>\n",
       "      <td>0.6387</td>\n",
       "      <td>0.3220</td>\n",
       "      <td>-0.3331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>-0.5264</td>\n",
       "      <td>-0.1352</td>\n",
       "      <td>-0.2540</td>\n",
       "      <td>-0.4285</td>\n",
       "      <td>0.0406</td>\n",
       "      <td>0.6952</td>\n",
       "      <td>-0.3978</td>\n",
       "      <td>-0.0955</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1.6367</td>\n",
       "      <td>...</td>\n",
       "      <td>0.8846</td>\n",
       "      <td>-0.4028</td>\n",
       "      <td>0.4596</td>\n",
       "      <td>-0.9219</td>\n",
       "      <td>1.4991</td>\n",
       "      <td>0.6604</td>\n",
       "      <td>0.0451</td>\n",
       "      <td>0.6474</td>\n",
       "      <td>0.2367</td>\n",
       "      <td>0.1186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>-0.1973</td>\n",
       "      <td>-0.7391</td>\n",
       "      <td>0.2944</td>\n",
       "      <td>0.4062</td>\n",
       "      <td>0.1626</td>\n",
       "      <td>-0.0548</td>\n",
       "      <td>-0.2185</td>\n",
       "      <td>-0.1559</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>0.2671</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0035</td>\n",
       "      <td>-0.3382</td>\n",
       "      <td>1.0794</td>\n",
       "      <td>0.9681</td>\n",
       "      <td>-0.3291</td>\n",
       "      <td>-0.0548</td>\n",
       "      <td>0.2511</td>\n",
       "      <td>0.7281</td>\n",
       "      <td>-0.7540</td>\n",
       "      <td>0.5718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>-0.2813</td>\n",
       "      <td>-0.8099</td>\n",
       "      <td>1.1563</td>\n",
       "      <td>1.4361</td>\n",
       "      <td>1.0533</td>\n",
       "      <td>1.4521</td>\n",
       "      <td>-0.0056</td>\n",
       "      <td>1.0309</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.0308</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0524</td>\n",
       "      <td>-0.2531</td>\n",
       "      <td>-1.0280</td>\n",
       "      <td>1.1308</td>\n",
       "      <td>-0.0303</td>\n",
       "      <td>-0.0354</td>\n",
       "      <td>1.7249</td>\n",
       "      <td>0.8851</td>\n",
       "      <td>0.0550</td>\n",
       "      <td>0.4851</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 52 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         0       1       2       3       4       5       6       7    8   \\\n",
       "0    0.0161  0.3095  0.4387 -1.0147 -0.0644  0.2363  0.0504 -0.2091  0.5   \n",
       "1    0.0357 -0.0594  0.9697  0.7171 -0.6334  0.8322  0.1289 -0.0122  0.5   \n",
       "2    0.0161 -0.0366 -0.5464  0.8615 -0.1118 -0.9007  0.2633 -0.3412  1.0   \n",
       "3   -0.0007 -0.0114  0.1135  1.1733 -0.5080 -0.9247  0.3754  0.3096 -0.5   \n",
       "4    1.2188  0.4359 -0.1770 -0.0695 -0.0644  1.0856  0.1401  0.5453 -0.5   \n",
       "..      ...     ...     ...     ...     ...     ...     ...     ...  ...   \n",
       "495 -0.1040 -0.2489 -0.0346  1.1243 -1.0432 -0.0719  0.3754 -0.5539  0.0   \n",
       "496 -0.4193  0.0316  0.4483 -0.0169 -0.1219  0.3459  0.0280  0.1645  0.0   \n",
       "497 -0.5264 -0.1352 -0.2540 -0.4285  0.0406  0.6952 -0.3978 -0.0955 -0.5   \n",
       "498 -0.1973 -0.7391  0.2944  0.4062  0.1626 -0.0548 -0.2185 -0.1559 -1.5   \n",
       "499 -0.2813 -0.8099  1.1563  1.4361  1.0533  1.4521 -0.0056  1.0309 -0.5   \n",
       "\n",
       "         9   ...      42      43      44      45      46      47      48  \\\n",
       "0    0.0855  ... -0.3949  0.0221  0.7175 -0.0009 -0.0934  0.9596  0.3379   \n",
       "1   -0.0650  ... -0.9805  0.0026 -1.1996 -0.0989  0.0572  0.0967 -0.8830   \n",
       "2   -0.1083  ...  0.6930  0.0247 -0.0231  0.4485  0.0997  0.1966  0.0201   \n",
       "3   -0.1159  ... -0.0364  0.0414 -0.8512  0.2580  0.1078 -0.0136  0.2730   \n",
       "4   -0.8159  ... -0.5475  1.1956 -0.3487 -0.3523 -0.5878  0.8754  0.3042   \n",
       "..      ...  ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "495 -1.0067  ...  0.2937 -0.2596 -1.0076  0.6352 -0.7078 -1.0629 -0.4292   \n",
       "496  1.3289  ...  0.1091 -0.5111 -0.4368  0.1840  1.8084 -0.0262 -1.1999   \n",
       "497  1.6367  ...  0.8846 -0.4028  0.4596 -0.9219  1.4991  0.6604  0.0451   \n",
       "498  0.2671  ...  1.0035 -0.3382  1.0794  0.9681 -0.3291 -0.0548  0.2511   \n",
       "499 -0.0308  ...  0.0524 -0.2531 -1.0280  1.1308 -0.0303 -0.0354  1.7249   \n",
       "\n",
       "         49      50      51  \n",
       "0   -0.3292  0.2105  0.1863  \n",
       "1   -0.3606  0.3495 -0.4568  \n",
       "2   -0.3451  0.1293  1.2555  \n",
       "3   -0.2734  0.7403  0.0026  \n",
       "4   -0.3911  0.5531  0.1935  \n",
       "..      ...     ...     ...  \n",
       "495  0.5726 -0.0660 -0.8397  \n",
       "496  0.6387  0.3220 -0.3331  \n",
       "497  0.6474  0.2367  0.1186  \n",
       "498  0.7281 -0.7540  0.5718  \n",
       "499  0.8851  0.0550  0.4851  \n",
       "\n",
       "[500 rows x 52 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scl"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "417c9e03",
   "metadata": {},
   "source": [
    "## Testing Process using Normal Dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "96cba9ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/1694315934.py:3: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  Kt = np.matmul(X_ts, df_scl.T)\n"
     ]
    }
   ],
   "source": [
    "# linear kernel\n",
    "# Kt = np.matmul(X_ts, df_train.T)\n",
    "Kt = np.matmul(X_ts, df_scl.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "45bbb38a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 500)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Kt.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "85177e07",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Kt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "7ce3418a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# centralize the kernel\n",
    "st = (len(X_ts),len(df_train)) # 2000 or 960\n",
    "unit_t = np.ones(st)/len(df_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "2acab630",
   "metadata": {},
   "outputs": [],
   "source": [
    "#######\n",
    "unit_t = pd.DataFrame(unit_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "35663c99",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0      1      2      3      4      5      6      7      8      9    \\\n",
       "0     0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1     0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "2     0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "3     0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "4     0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "...     ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "1995  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1996  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1997  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1998  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1999  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "\n",
       "      ...    490    491    492    493    494    495    496    497    498  \\\n",
       "0     ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1     ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "2     ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "3     ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "4     ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "...   ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "1995  ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1996  ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1997  ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1998  ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "1999  ...  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002  0.002   \n",
       "\n",
       "        499  \n",
       "0     0.002  \n",
       "1     0.002  \n",
       "2     0.002  \n",
       "3     0.002  \n",
       "4     0.002  \n",
       "...     ...  \n",
       "1995  0.002  \n",
       "1996  0.002  \n",
       "1997  0.002  \n",
       "1998  0.002  \n",
       "1999  0.002  \n",
       "\n",
       "[2000 rows x 500 columns]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unit_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "0ff59d4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "Kt_c = Kt-unit_t@K-Kt@unit+unit_t@K@unit\n",
    "# the result are NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "472b1026",
   "metadata": {},
   "outputs": [],
   "source": [
    "Kt_c = round(Kt_c, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "21f69d83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>490</th>\n",
       "      <th>491</th>\n",
       "      <th>492</th>\n",
       "      <th>493</th>\n",
       "      <th>494</th>\n",
       "      <th>495</th>\n",
       "      <th>496</th>\n",
       "      <th>497</th>\n",
       "      <th>498</th>\n",
       "      <th>499</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0188</td>\n",
       "      <td>1.0215</td>\n",
       "      <td>-1.4660</td>\n",
       "      <td>1.5186</td>\n",
       "      <td>-1.3545</td>\n",
       "      <td>-1.3153</td>\n",
       "      <td>2.2159</td>\n",
       "      <td>0.8179</td>\n",
       "      <td>-1.2094</td>\n",
       "      <td>1.0922</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.3923</td>\n",
       "      <td>1.1752</td>\n",
       "      <td>0.8051</td>\n",
       "      <td>4.3029</td>\n",
       "      <td>-2.9390</td>\n",
       "      <td>2.0600</td>\n",
       "      <td>-1.1568</td>\n",
       "      <td>-1.1731</td>\n",
       "      <td>-2.5431</td>\n",
       "      <td>-1.4404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.7846</td>\n",
       "      <td>0.1073</td>\n",
       "      <td>-5.3418</td>\n",
       "      <td>0.7921</td>\n",
       "      <td>3.0303</td>\n",
       "      <td>0.1664</td>\n",
       "      <td>-0.2565</td>\n",
       "      <td>-1.8078</td>\n",
       "      <td>4.0919</td>\n",
       "      <td>-5.7388</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.1305</td>\n",
       "      <td>-2.3121</td>\n",
       "      <td>-1.5139</td>\n",
       "      <td>8.7844</td>\n",
       "      <td>-1.8246</td>\n",
       "      <td>2.1515</td>\n",
       "      <td>-3.0177</td>\n",
       "      <td>1.0513</td>\n",
       "      <td>1.4741</td>\n",
       "      <td>8.9313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.4853</td>\n",
       "      <td>-2.5587</td>\n",
       "      <td>6.3826</td>\n",
       "      <td>6.9272</td>\n",
       "      <td>2.3324</td>\n",
       "      <td>0.2460</td>\n",
       "      <td>0.4835</td>\n",
       "      <td>-1.8794</td>\n",
       "      <td>-5.1252</td>\n",
       "      <td>2.2843</td>\n",
       "      <td>...</td>\n",
       "      <td>0.9189</td>\n",
       "      <td>3.3676</td>\n",
       "      <td>0.9715</td>\n",
       "      <td>5.1658</td>\n",
       "      <td>0.4749</td>\n",
       "      <td>-3.0521</td>\n",
       "      <td>-4.1536</td>\n",
       "      <td>-0.4385</td>\n",
       "      <td>-3.2656</td>\n",
       "      <td>5.1107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1781</td>\n",
       "      <td>4.3833</td>\n",
       "      <td>2.5297</td>\n",
       "      <td>6.5030</td>\n",
       "      <td>-1.6825</td>\n",
       "      <td>-4.8087</td>\n",
       "      <td>5.0954</td>\n",
       "      <td>5.1175</td>\n",
       "      <td>0.6024</td>\n",
       "      <td>-4.8725</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.2584</td>\n",
       "      <td>-6.2486</td>\n",
       "      <td>3.1835</td>\n",
       "      <td>-0.7552</td>\n",
       "      <td>-0.6708</td>\n",
       "      <td>1.6339</td>\n",
       "      <td>3.3172</td>\n",
       "      <td>-2.3688</td>\n",
       "      <td>-2.9202</td>\n",
       "      <td>-6.6667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.2427</td>\n",
       "      <td>2.8768</td>\n",
       "      <td>-0.0979</td>\n",
       "      <td>-3.6247</td>\n",
       "      <td>6.1552</td>\n",
       "      <td>4.3584</td>\n",
       "      <td>-0.1796</td>\n",
       "      <td>4.5197</td>\n",
       "      <td>1.0541</td>\n",
       "      <td>0.5470</td>\n",
       "      <td>...</td>\n",
       "      <td>3.5367</td>\n",
       "      <td>1.3653</td>\n",
       "      <td>-3.3016</td>\n",
       "      <td>-5.1878</td>\n",
       "      <td>4.5571</td>\n",
       "      <td>1.4794</td>\n",
       "      <td>0.3545</td>\n",
       "      <td>0.0060</td>\n",
       "      <td>-1.4157</td>\n",
       "      <td>-2.0946</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>1995</th>\n",
       "      <td>-1.0256</td>\n",
       "      <td>-3.2267</td>\n",
       "      <td>-0.2242</td>\n",
       "      <td>0.5043</td>\n",
       "      <td>-0.4823</td>\n",
       "      <td>-0.6418</td>\n",
       "      <td>-0.1367</td>\n",
       "      <td>-0.2541</td>\n",
       "      <td>0.8641</td>\n",
       "      <td>-5.3823</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.2141</td>\n",
       "      <td>-1.6204</td>\n",
       "      <td>-3.5746</td>\n",
       "      <td>-4.8739</td>\n",
       "      <td>1.3321</td>\n",
       "      <td>-0.2140</td>\n",
       "      <td>-2.5051</td>\n",
       "      <td>-0.8088</td>\n",
       "      <td>4.6130</td>\n",
       "      <td>2.4314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>-4.0628</td>\n",
       "      <td>3.7545</td>\n",
       "      <td>-3.9482</td>\n",
       "      <td>0.8835</td>\n",
       "      <td>0.0119</td>\n",
       "      <td>-2.0839</td>\n",
       "      <td>-0.7814</td>\n",
       "      <td>-3.6789</td>\n",
       "      <td>-0.7329</td>\n",
       "      <td>2.8000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0765</td>\n",
       "      <td>3.2842</td>\n",
       "      <td>8.9108</td>\n",
       "      <td>8.8197</td>\n",
       "      <td>-0.6913</td>\n",
       "      <td>7.5614</td>\n",
       "      <td>4.0697</td>\n",
       "      <td>-0.6031</td>\n",
       "      <td>-2.2064</td>\n",
       "      <td>-2.0541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>-2.0520</td>\n",
       "      <td>-2.1996</td>\n",
       "      <td>-0.2109</td>\n",
       "      <td>-0.5470</td>\n",
       "      <td>6.1712</td>\n",
       "      <td>4.2556</td>\n",
       "      <td>-7.5386</td>\n",
       "      <td>-4.8411</td>\n",
       "      <td>2.7267</td>\n",
       "      <td>-1.1218</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.7387</td>\n",
       "      <td>3.1020</td>\n",
       "      <td>10.6645</td>\n",
       "      <td>9.3399</td>\n",
       "      <td>-1.6697</td>\n",
       "      <td>-1.2467</td>\n",
       "      <td>-0.8042</td>\n",
       "      <td>6.1580</td>\n",
       "      <td>4.1240</td>\n",
       "      <td>11.3016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>0.5303</td>\n",
       "      <td>2.4416</td>\n",
       "      <td>0.3342</td>\n",
       "      <td>-1.5051</td>\n",
       "      <td>3.1487</td>\n",
       "      <td>0.9427</td>\n",
       "      <td>0.4626</td>\n",
       "      <td>2.2181</td>\n",
       "      <td>-13.7182</td>\n",
       "      <td>-3.6946</td>\n",
       "      <td>...</td>\n",
       "      <td>2.4626</td>\n",
       "      <td>11.0562</td>\n",
       "      <td>-8.0311</td>\n",
       "      <td>2.3554</td>\n",
       "      <td>-4.5367</td>\n",
       "      <td>-4.2883</td>\n",
       "      <td>5.9011</td>\n",
       "      <td>4.9918</td>\n",
       "      <td>-5.2968</td>\n",
       "      <td>-2.6332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>-1.7974</td>\n",
       "      <td>-4.1785</td>\n",
       "      <td>2.0359</td>\n",
       "      <td>-1.9460</td>\n",
       "      <td>-0.4948</td>\n",
       "      <td>-3.8470</td>\n",
       "      <td>-0.6106</td>\n",
       "      <td>1.7065</td>\n",
       "      <td>-6.0516</td>\n",
       "      <td>-10.1299</td>\n",
       "      <td>...</td>\n",
       "      <td>4.8326</td>\n",
       "      <td>4.0642</td>\n",
       "      <td>-5.2377</td>\n",
       "      <td>-5.9469</td>\n",
       "      <td>-6.8350</td>\n",
       "      <td>-4.6508</td>\n",
       "      <td>0.0214</td>\n",
       "      <td>3.8915</td>\n",
       "      <td>0.8824</td>\n",
       "      <td>2.7988</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         0       1       2       3       4       5       6       7        8    \\\n",
       "0     1.0188  1.0215 -1.4660  1.5186 -1.3545 -1.3153  2.2159  0.8179  -1.2094   \n",
       "1    -0.7846  0.1073 -5.3418  0.7921  3.0303  0.1664 -0.2565 -1.8078   4.0919   \n",
       "2     2.4853 -2.5587  6.3826  6.9272  2.3324  0.2460  0.4835 -1.8794  -5.1252   \n",
       "3     0.1781  4.3833  2.5297  6.5030 -1.6825 -4.8087  5.0954  5.1175   0.6024   \n",
       "4     2.2427  2.8768 -0.0979 -3.6247  6.1552  4.3584 -0.1796  4.5197   1.0541   \n",
       "...      ...     ...     ...     ...     ...     ...     ...     ...      ...   \n",
       "1995 -1.0256 -3.2267 -0.2242  0.5043 -0.4823 -0.6418 -0.1367 -0.2541   0.8641   \n",
       "1996 -4.0628  3.7545 -3.9482  0.8835  0.0119 -2.0839 -0.7814 -3.6789  -0.7329   \n",
       "1997 -2.0520 -2.1996 -0.2109 -0.5470  6.1712  4.2556 -7.5386 -4.8411   2.7267   \n",
       "1998  0.5303  2.4416  0.3342 -1.5051  3.1487  0.9427  0.4626  2.2181 -13.7182   \n",
       "1999 -1.7974 -4.1785  2.0359 -1.9460 -0.4948 -3.8470 -0.6106  1.7065  -6.0516   \n",
       "\n",
       "          9    ...     490      491      492     493     494     495     496  \\\n",
       "0      1.0922  ... -3.3923   1.1752   0.8051  4.3029 -2.9390  2.0600 -1.1568   \n",
       "1     -5.7388  ... -1.1305  -2.3121  -1.5139  8.7844 -1.8246  2.1515 -3.0177   \n",
       "2      2.2843  ...  0.9189   3.3676   0.9715  5.1658  0.4749 -3.0521 -4.1536   \n",
       "3     -4.8725  ... -3.2584  -6.2486   3.1835 -0.7552 -0.6708  1.6339  3.3172   \n",
       "4      0.5470  ...  3.5367   1.3653  -3.3016 -5.1878  4.5571  1.4794  0.3545   \n",
       "...       ...  ...     ...      ...      ...     ...     ...     ...     ...   \n",
       "1995  -5.3823  ... -0.2141  -1.6204  -3.5746 -4.8739  1.3321 -0.2140 -2.5051   \n",
       "1996   2.8000  ...  0.0765   3.2842   8.9108  8.8197 -0.6913  7.5614  4.0697   \n",
       "1997  -1.1218  ... -1.7387   3.1020  10.6645  9.3399 -1.6697 -1.2467 -0.8042   \n",
       "1998  -3.6946  ...  2.4626  11.0562  -8.0311  2.3554 -4.5367 -4.2883  5.9011   \n",
       "1999 -10.1299  ...  4.8326   4.0642  -5.2377 -5.9469 -6.8350 -4.6508  0.0214   \n",
       "\n",
       "         497     498      499  \n",
       "0    -1.1731 -2.5431  -1.4404  \n",
       "1     1.0513  1.4741   8.9313  \n",
       "2    -0.4385 -3.2656   5.1107  \n",
       "3    -2.3688 -2.9202  -6.6667  \n",
       "4     0.0060 -1.4157  -2.0946  \n",
       "...      ...     ...      ...  \n",
       "1995 -0.8088  4.6130   2.4314  \n",
       "1996 -0.6031 -2.2064  -2.0541  \n",
       "1997  6.1580  4.1240  11.3016  \n",
       "1998  4.9918 -5.2968  -2.6332  \n",
       "1999  3.8915  0.8824   2.7988  \n",
       "\n",
       "[2000 rows x 500 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Kt_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "e6184f90",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/2005656394.py:1: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  score_test = np.matmul(Kt_c, eigvct.iloc[:,:nComponent])\n"
     ]
    }
   ],
   "source": [
    "score_test = np.matmul(Kt_c, eigvct.iloc[:,:nComponent])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "1ecab55a",
   "metadata": {},
   "outputs": [],
   "source": [
    "score_test = round(score_test, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "ed40b816",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>20</th>\n",
       "      <th>21</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
       "      <th>24</th>\n",
       "      <th>25</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "      <th>28</th>\n",
       "      <th>29</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.2522</td>\n",
       "      <td>-16.5604</td>\n",
       "      <td>6.9500</td>\n",
       "      <td>12.1403</td>\n",
       "      <td>24.1203</td>\n",
       "      <td>-24.2168</td>\n",
       "      <td>-0.7119</td>\n",
       "      <td>14.2208</td>\n",
       "      <td>-10.7054</td>\n",
       "      <td>-1.2672</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0266</td>\n",
       "      <td>-1.8248</td>\n",
       "      <td>-2.1109</td>\n",
       "      <td>-5.2978</td>\n",
       "      <td>8.1373</td>\n",
       "      <td>-2.8136</td>\n",
       "      <td>-1.5360</td>\n",
       "      <td>-2.5067</td>\n",
       "      <td>-1.9525</td>\n",
       "      <td>1.2615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-3.1338</td>\n",
       "      <td>-25.9309</td>\n",
       "      <td>-34.1928</td>\n",
       "      <td>-1.3121</td>\n",
       "      <td>-3.1725</td>\n",
       "      <td>-60.7121</td>\n",
       "      <td>28.0195</td>\n",
       "      <td>25.1383</td>\n",
       "      <td>8.9503</td>\n",
       "      <td>-14.6828</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.1672</td>\n",
       "      <td>-11.2750</td>\n",
       "      <td>1.3392</td>\n",
       "      <td>-1.4573</td>\n",
       "      <td>-9.9254</td>\n",
       "      <td>-0.6956</td>\n",
       "      <td>6.6704</td>\n",
       "      <td>2.4412</td>\n",
       "      <td>-0.9473</td>\n",
       "      <td>-3.3949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-12.1051</td>\n",
       "      <td>-18.0488</td>\n",
       "      <td>28.9146</td>\n",
       "      <td>-0.1250</td>\n",
       "      <td>-49.1862</td>\n",
       "      <td>5.2862</td>\n",
       "      <td>8.3648</td>\n",
       "      <td>41.6174</td>\n",
       "      <td>-22.6251</td>\n",
       "      <td>7.4831</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.7763</td>\n",
       "      <td>-12.1778</td>\n",
       "      <td>-1.0279</td>\n",
       "      <td>-1.4643</td>\n",
       "      <td>-4.8413</td>\n",
       "      <td>-9.6694</td>\n",
       "      <td>15.0042</td>\n",
       "      <td>-7.7464</td>\n",
       "      <td>-12.2579</td>\n",
       "      <td>-13.6094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-8.1831</td>\n",
       "      <td>-8.8509</td>\n",
       "      <td>-14.5989</td>\n",
       "      <td>9.5084</td>\n",
       "      <td>32.8458</td>\n",
       "      <td>46.9232</td>\n",
       "      <td>-8.9680</td>\n",
       "      <td>-29.2560</td>\n",
       "      <td>-0.6895</td>\n",
       "      <td>0.3762</td>\n",
       "      <td>...</td>\n",
       "      <td>4.1892</td>\n",
       "      <td>-11.6515</td>\n",
       "      <td>-5.7436</td>\n",
       "      <td>2.6249</td>\n",
       "      <td>17.4862</td>\n",
       "      <td>-12.8371</td>\n",
       "      <td>3.3065</td>\n",
       "      <td>-13.1430</td>\n",
       "      <td>-6.4301</td>\n",
       "      <td>-15.7539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>19.6697</td>\n",
       "      <td>-2.9693</td>\n",
       "      <td>23.5209</td>\n",
       "      <td>-19.7780</td>\n",
       "      <td>-1.5467</td>\n",
       "      <td>31.9657</td>\n",
       "      <td>5.6242</td>\n",
       "      <td>-5.8701</td>\n",
       "      <td>15.3834</td>\n",
       "      <td>-7.4251</td>\n",
       "      <td>...</td>\n",
       "      <td>-19.2280</td>\n",
       "      <td>-6.6392</td>\n",
       "      <td>-13.1211</td>\n",
       "      <td>0.6643</td>\n",
       "      <td>15.9505</td>\n",
       "      <td>3.0048</td>\n",
       "      <td>-1.7123</td>\n",
       "      <td>4.5291</td>\n",
       "      <td>2.9316</td>\n",
       "      <td>9.0924</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>1995</th>\n",
       "      <td>-70.3000</td>\n",
       "      <td>-10.1117</td>\n",
       "      <td>-26.3532</td>\n",
       "      <td>-23.5399</td>\n",
       "      <td>2.7131</td>\n",
       "      <td>10.5514</td>\n",
       "      <td>2.9892</td>\n",
       "      <td>2.3767</td>\n",
       "      <td>-2.3587</td>\n",
       "      <td>1.9600</td>\n",
       "      <td>...</td>\n",
       "      <td>0.6129</td>\n",
       "      <td>14.5502</td>\n",
       "      <td>-2.1388</td>\n",
       "      <td>-5.5382</td>\n",
       "      <td>0.5804</td>\n",
       "      <td>23.5635</td>\n",
       "      <td>8.5027</td>\n",
       "      <td>-10.5010</td>\n",
       "      <td>21.8863</td>\n",
       "      <td>-6.3508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>-80.4047</td>\n",
       "      <td>15.5018</td>\n",
       "      <td>51.6190</td>\n",
       "      <td>18.6623</td>\n",
       "      <td>45.8489</td>\n",
       "      <td>-29.3822</td>\n",
       "      <td>-0.5561</td>\n",
       "      <td>-20.0772</td>\n",
       "      <td>-3.3920</td>\n",
       "      <td>-9.8103</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.3183</td>\n",
       "      <td>-15.6505</td>\n",
       "      <td>-3.7298</td>\n",
       "      <td>-0.4109</td>\n",
       "      <td>9.2879</td>\n",
       "      <td>8.5998</td>\n",
       "      <td>4.6877</td>\n",
       "      <td>-11.2148</td>\n",
       "      <td>15.4550</td>\n",
       "      <td>-6.8248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>-73.7599</td>\n",
       "      <td>0.3587</td>\n",
       "      <td>23.5028</td>\n",
       "      <td>5.7171</td>\n",
       "      <td>-23.8187</td>\n",
       "      <td>-13.7779</td>\n",
       "      <td>33.3891</td>\n",
       "      <td>9.6680</td>\n",
       "      <td>28.4560</td>\n",
       "      <td>-7.5115</td>\n",
       "      <td>...</td>\n",
       "      <td>-8.3134</td>\n",
       "      <td>-18.2702</td>\n",
       "      <td>2.4819</td>\n",
       "      <td>-3.3934</td>\n",
       "      <td>-4.9926</td>\n",
       "      <td>22.4112</td>\n",
       "      <td>12.7142</td>\n",
       "      <td>-7.5693</td>\n",
       "      <td>7.2985</td>\n",
       "      <td>-3.4525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>-50.3724</td>\n",
       "      <td>7.7406</td>\n",
       "      <td>38.3425</td>\n",
       "      <td>23.0753</td>\n",
       "      <td>43.0044</td>\n",
       "      <td>14.3275</td>\n",
       "      <td>33.2000</td>\n",
       "      <td>38.9186</td>\n",
       "      <td>-27.6553</td>\n",
       "      <td>2.3268</td>\n",
       "      <td>...</td>\n",
       "      <td>12.8052</td>\n",
       "      <td>8.6977</td>\n",
       "      <td>5.3972</td>\n",
       "      <td>12.7110</td>\n",
       "      <td>-4.4248</td>\n",
       "      <td>3.9366</td>\n",
       "      <td>-8.8082</td>\n",
       "      <td>8.2996</td>\n",
       "      <td>-3.4439</td>\n",
       "      <td>1.2343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>-65.7138</td>\n",
       "      <td>-10.0785</td>\n",
       "      <td>8.3813</td>\n",
       "      <td>1.0576</td>\n",
       "      <td>-16.8991</td>\n",
       "      <td>-5.4478</td>\n",
       "      <td>-17.0304</td>\n",
       "      <td>15.2046</td>\n",
       "      <td>4.4585</td>\n",
       "      <td>17.5410</td>\n",
       "      <td>...</td>\n",
       "      <td>1.2919</td>\n",
       "      <td>5.6576</td>\n",
       "      <td>13.3295</td>\n",
       "      <td>1.9645</td>\n",
       "      <td>0.5388</td>\n",
       "      <td>10.5374</td>\n",
       "      <td>-6.0169</td>\n",
       "      <td>9.5329</td>\n",
       "      <td>-3.9815</td>\n",
       "      <td>9.3287</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0        1        2        3        4        5        6        7   \\\n",
       "0      6.2522 -16.5604   6.9500  12.1403  24.1203 -24.2168  -0.7119  14.2208   \n",
       "1     -3.1338 -25.9309 -34.1928  -1.3121  -3.1725 -60.7121  28.0195  25.1383   \n",
       "2    -12.1051 -18.0488  28.9146  -0.1250 -49.1862   5.2862   8.3648  41.6174   \n",
       "3     -8.1831  -8.8509 -14.5989   9.5084  32.8458  46.9232  -8.9680 -29.2560   \n",
       "4     19.6697  -2.9693  23.5209 -19.7780  -1.5467  31.9657   5.6242  -5.8701   \n",
       "...       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "1995 -70.3000 -10.1117 -26.3532 -23.5399   2.7131  10.5514   2.9892   2.3767   \n",
       "1996 -80.4047  15.5018  51.6190  18.6623  45.8489 -29.3822  -0.5561 -20.0772   \n",
       "1997 -73.7599   0.3587  23.5028   5.7171 -23.8187 -13.7779  33.3891   9.6680   \n",
       "1998 -50.3724   7.7406  38.3425  23.0753  43.0044  14.3275  33.2000  38.9186   \n",
       "1999 -65.7138 -10.0785   8.3813   1.0576 -16.8991  -5.4478 -17.0304  15.2046   \n",
       "\n",
       "           8        9   ...       20       21       22       23       24  \\\n",
       "0    -10.7054  -1.2672  ...  -0.0266  -1.8248  -2.1109  -5.2978   8.1373   \n",
       "1      8.9503 -14.6828  ...  -0.1672 -11.2750   1.3392  -1.4573  -9.9254   \n",
       "2    -22.6251   7.4831  ...  -1.7763 -12.1778  -1.0279  -1.4643  -4.8413   \n",
       "3     -0.6895   0.3762  ...   4.1892 -11.6515  -5.7436   2.6249  17.4862   \n",
       "4     15.3834  -7.4251  ... -19.2280  -6.6392 -13.1211   0.6643  15.9505   \n",
       "...       ...      ...  ...      ...      ...      ...      ...      ...   \n",
       "1995  -2.3587   1.9600  ...   0.6129  14.5502  -2.1388  -5.5382   0.5804   \n",
       "1996  -3.3920  -9.8103  ...  -2.3183 -15.6505  -3.7298  -0.4109   9.2879   \n",
       "1997  28.4560  -7.5115  ...  -8.3134 -18.2702   2.4819  -3.3934  -4.9926   \n",
       "1998 -27.6553   2.3268  ...  12.8052   8.6977   5.3972  12.7110  -4.4248   \n",
       "1999   4.4585  17.5410  ...   1.2919   5.6576  13.3295   1.9645   0.5388   \n",
       "\n",
       "           25       26       27       28       29  \n",
       "0     -2.8136  -1.5360  -2.5067  -1.9525   1.2615  \n",
       "1     -0.6956   6.6704   2.4412  -0.9473  -3.3949  \n",
       "2     -9.6694  15.0042  -7.7464 -12.2579 -13.6094  \n",
       "3    -12.8371   3.3065 -13.1430  -6.4301 -15.7539  \n",
       "4      3.0048  -1.7123   4.5291   2.9316   9.0924  \n",
       "...       ...      ...      ...      ...      ...  \n",
       "1995  23.5635   8.5027 -10.5010  21.8863  -6.3508  \n",
       "1996   8.5998   4.6877 -11.2148  15.4550  -6.8248  \n",
       "1997  22.4112  12.7142  -7.5693   7.2985  -3.4525  \n",
       "1998   3.9366  -8.8082   8.2996  -3.4439   1.2343  \n",
       "1999  10.5374  -6.0169   9.5329  -3.9815   9.3287  \n",
       "\n",
       "[2000 rows x 30 columns]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "2af4ca18",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test = score_test@invegvldiag@score_test.T\n",
    "T2_test_final = np.diag(T2_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "e7161a7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test = round(T2_test, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "dd11361f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>1990</th>\n",
       "      <th>1991</th>\n",
       "      <th>1992</th>\n",
       "      <th>1993</th>\n",
       "      <th>1994</th>\n",
       "      <th>1995</th>\n",
       "      <th>1996</th>\n",
       "      <th>1997</th>\n",
       "      <th>1998</th>\n",
       "      <th>1999</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.3780</td>\n",
       "      <td>0.6880</td>\n",
       "      <td>0.1578</td>\n",
       "      <td>-0.2273</td>\n",
       "      <td>-2.5936</td>\n",
       "      <td>1.8312</td>\n",
       "      <td>3.2244</td>\n",
       "      <td>3.1650</td>\n",
       "      <td>0.3623</td>\n",
       "      <td>-1.0284</td>\n",
       "      <td>...</td>\n",
       "      <td>2.1278</td>\n",
       "      <td>1.1235</td>\n",
       "      <td>1.1816</td>\n",
       "      <td>-2.4504</td>\n",
       "      <td>2.5620</td>\n",
       "      <td>-1.7547</td>\n",
       "      <td>3.3849</td>\n",
       "      <td>-3.6565</td>\n",
       "      <td>0.0311</td>\n",
       "      <td>-3.4829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.6880</td>\n",
       "      <td>18.3059</td>\n",
       "      <td>1.9875</td>\n",
       "      <td>-6.3078</td>\n",
       "      <td>-1.1269</td>\n",
       "      <td>0.2721</td>\n",
       "      <td>3.2803</td>\n",
       "      <td>9.1337</td>\n",
       "      <td>-0.2132</td>\n",
       "      <td>-0.7841</td>\n",
       "      <td>...</td>\n",
       "      <td>3.8107</td>\n",
       "      <td>-0.0785</td>\n",
       "      <td>5.1059</td>\n",
       "      <td>-1.4989</td>\n",
       "      <td>4.9471</td>\n",
       "      <td>0.2417</td>\n",
       "      <td>-0.8612</td>\n",
       "      <td>7.7133</td>\n",
       "      <td>-0.6726</td>\n",
       "      <td>2.9671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.1578</td>\n",
       "      <td>1.9875</td>\n",
       "      <td>18.5998</td>\n",
       "      <td>-0.6262</td>\n",
       "      <td>-3.5579</td>\n",
       "      <td>-0.8053</td>\n",
       "      <td>1.8637</td>\n",
       "      <td>1.0370</td>\n",
       "      <td>1.8990</td>\n",
       "      <td>2.0365</td>\n",
       "      <td>...</td>\n",
       "      <td>3.9093</td>\n",
       "      <td>4.6479</td>\n",
       "      <td>0.8723</td>\n",
       "      <td>-1.6522</td>\n",
       "      <td>0.0938</td>\n",
       "      <td>-1.5430</td>\n",
       "      <td>-0.7306</td>\n",
       "      <td>6.3608</td>\n",
       "      <td>1.8135</td>\n",
       "      <td>1.2642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.2273</td>\n",
       "      <td>-6.3078</td>\n",
       "      <td>-0.6262</td>\n",
       "      <td>16.1562</td>\n",
       "      <td>2.0521</td>\n",
       "      <td>0.6347</td>\n",
       "      <td>0.6708</td>\n",
       "      <td>1.1892</td>\n",
       "      <td>4.7466</td>\n",
       "      <td>4.2468</td>\n",
       "      <td>...</td>\n",
       "      <td>3.8137</td>\n",
       "      <td>-1.7973</td>\n",
       "      <td>-2.9693</td>\n",
       "      <td>5.7548</td>\n",
       "      <td>-3.9527</td>\n",
       "      <td>0.8693</td>\n",
       "      <td>3.0835</td>\n",
       "      <td>-4.1575</td>\n",
       "      <td>-2.3772</td>\n",
       "      <td>-4.1168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.5936</td>\n",
       "      <td>-1.1269</td>\n",
       "      <td>-3.5579</td>\n",
       "      <td>2.0521</td>\n",
       "      <td>14.5520</td>\n",
       "      <td>6.3029</td>\n",
       "      <td>-0.2222</td>\n",
       "      <td>-0.3224</td>\n",
       "      <td>-2.6195</td>\n",
       "      <td>0.1934</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.5129</td>\n",
       "      <td>-1.3693</td>\n",
       "      <td>-0.2569</td>\n",
       "      <td>5.7449</td>\n",
       "      <td>-5.1481</td>\n",
       "      <td>-0.8773</td>\n",
       "      <td>-2.4159</td>\n",
       "      <td>0.1442</td>\n",
       "      <td>-3.3054</td>\n",
       "      <td>-1.4296</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>1995</th>\n",
       "      <td>-1.7547</td>\n",
       "      <td>0.2417</td>\n",
       "      <td>-1.5430</td>\n",
       "      <td>0.8693</td>\n",
       "      <td>-0.8773</td>\n",
       "      <td>-1.0918</td>\n",
       "      <td>-1.1636</td>\n",
       "      <td>1.6964</td>\n",
       "      <td>4.5328</td>\n",
       "      <td>3.9936</td>\n",
       "      <td>...</td>\n",
       "      <td>2.9319</td>\n",
       "      <td>3.2765</td>\n",
       "      <td>1.4918</td>\n",
       "      <td>3.3734</td>\n",
       "      <td>12.6722</td>\n",
       "      <td>14.7518</td>\n",
       "      <td>4.7755</td>\n",
       "      <td>6.6148</td>\n",
       "      <td>0.2220</td>\n",
       "      <td>4.0947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996</th>\n",
       "      <td>3.3849</td>\n",
       "      <td>-0.8612</td>\n",
       "      <td>-0.7306</td>\n",
       "      <td>3.0835</td>\n",
       "      <td>-2.4159</td>\n",
       "      <td>1.3395</td>\n",
       "      <td>6.0768</td>\n",
       "      <td>3.0426</td>\n",
       "      <td>-0.5697</td>\n",
       "      <td>-1.8718</td>\n",
       "      <td>...</td>\n",
       "      <td>5.9243</td>\n",
       "      <td>2.8919</td>\n",
       "      <td>3.4920</td>\n",
       "      <td>1.6906</td>\n",
       "      <td>9.2680</td>\n",
       "      <td>4.7755</td>\n",
       "      <td>22.9637</td>\n",
       "      <td>11.8630</td>\n",
       "      <td>4.6943</td>\n",
       "      <td>-0.4756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997</th>\n",
       "      <td>-3.6565</td>\n",
       "      <td>7.7133</td>\n",
       "      <td>6.3608</td>\n",
       "      <td>-4.1575</td>\n",
       "      <td>0.1442</td>\n",
       "      <td>2.0325</td>\n",
       "      <td>1.1915</td>\n",
       "      <td>3.5711</td>\n",
       "      <td>-2.1864</td>\n",
       "      <td>-2.5468</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.9656</td>\n",
       "      <td>2.4971</td>\n",
       "      <td>2.5665</td>\n",
       "      <td>3.7581</td>\n",
       "      <td>9.2089</td>\n",
       "      <td>6.6148</td>\n",
       "      <td>11.8630</td>\n",
       "      <td>26.4048</td>\n",
       "      <td>3.4100</td>\n",
       "      <td>6.0895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998</th>\n",
       "      <td>0.0311</td>\n",
       "      <td>-0.6726</td>\n",
       "      <td>1.8135</td>\n",
       "      <td>-2.3772</td>\n",
       "      <td>-3.3054</td>\n",
       "      <td>-0.1337</td>\n",
       "      <td>5.8349</td>\n",
       "      <td>0.3028</td>\n",
       "      <td>-0.2407</td>\n",
       "      <td>-1.4305</td>\n",
       "      <td>...</td>\n",
       "      <td>2.9707</td>\n",
       "      <td>1.0674</td>\n",
       "      <td>4.9789</td>\n",
       "      <td>5.6069</td>\n",
       "      <td>0.6794</td>\n",
       "      <td>0.2220</td>\n",
       "      <td>4.6943</td>\n",
       "      <td>3.4100</td>\n",
       "      <td>22.2915</td>\n",
       "      <td>5.5033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999</th>\n",
       "      <td>-3.4829</td>\n",
       "      <td>2.9671</td>\n",
       "      <td>1.2642</td>\n",
       "      <td>-4.1168</td>\n",
       "      <td>-1.4296</td>\n",
       "      <td>-6.9613</td>\n",
       "      <td>-2.0074</td>\n",
       "      <td>1.4034</td>\n",
       "      <td>-4.1240</td>\n",
       "      <td>-2.4204</td>\n",
       "      <td>...</td>\n",
       "      <td>1.7265</td>\n",
       "      <td>3.4757</td>\n",
       "      <td>4.2405</td>\n",
       "      <td>1.1607</td>\n",
       "      <td>5.4248</td>\n",
       "      <td>4.0947</td>\n",
       "      <td>-0.4756</td>\n",
       "      <td>6.0895</td>\n",
       "      <td>5.5033</td>\n",
       "      <td>14.0200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2000 rows × 2000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0        1        2        3        4       5       6       7     \\\n",
       "0     6.3780   0.6880   0.1578  -0.2273  -2.5936  1.8312  3.2244  3.1650   \n",
       "1     0.6880  18.3059   1.9875  -6.3078  -1.1269  0.2721  3.2803  9.1337   \n",
       "2     0.1578   1.9875  18.5998  -0.6262  -3.5579 -0.8053  1.8637  1.0370   \n",
       "3    -0.2273  -6.3078  -0.6262  16.1562   2.0521  0.6347  0.6708  1.1892   \n",
       "4    -2.5936  -1.1269  -3.5579   2.0521  14.5520  6.3029 -0.2222 -0.3224   \n",
       "...      ...      ...      ...      ...      ...     ...     ...     ...   \n",
       "1995 -1.7547   0.2417  -1.5430   0.8693  -0.8773 -1.0918 -1.1636  1.6964   \n",
       "1996  3.3849  -0.8612  -0.7306   3.0835  -2.4159  1.3395  6.0768  3.0426   \n",
       "1997 -3.6565   7.7133   6.3608  -4.1575   0.1442  2.0325  1.1915  3.5711   \n",
       "1998  0.0311  -0.6726   1.8135  -2.3772  -3.3054 -0.1337  5.8349  0.3028   \n",
       "1999 -3.4829   2.9671   1.2642  -4.1168  -1.4296 -6.9613 -2.0074  1.4034   \n",
       "\n",
       "        8       9     ...    1990    1991    1992    1993     1994     1995  \\\n",
       "0     0.3623 -1.0284  ...  2.1278  1.1235  1.1816 -2.4504   2.5620  -1.7547   \n",
       "1    -0.2132 -0.7841  ...  3.8107 -0.0785  5.1059 -1.4989   4.9471   0.2417   \n",
       "2     1.8990  2.0365  ...  3.9093  4.6479  0.8723 -1.6522   0.0938  -1.5430   \n",
       "3     4.7466  4.2468  ...  3.8137 -1.7973 -2.9693  5.7548  -3.9527   0.8693   \n",
       "4    -2.6195  0.1934  ... -2.5129 -1.3693 -0.2569  5.7449  -5.1481  -0.8773   \n",
       "...      ...     ...  ...     ...     ...     ...     ...      ...      ...   \n",
       "1995  4.5328  3.9936  ...  2.9319  3.2765  1.4918  3.3734  12.6722  14.7518   \n",
       "1996 -0.5697 -1.8718  ...  5.9243  2.8919  3.4920  1.6906   9.2680   4.7755   \n",
       "1997 -2.1864 -2.5468  ... -1.9656  2.4971  2.5665  3.7581   9.2089   6.6148   \n",
       "1998 -0.2407 -1.4305  ...  2.9707  1.0674  4.9789  5.6069   0.6794   0.2220   \n",
       "1999 -4.1240 -2.4204  ...  1.7265  3.4757  4.2405  1.1607   5.4248   4.0947   \n",
       "\n",
       "         1996     1997     1998     1999  \n",
       "0      3.3849  -3.6565   0.0311  -3.4829  \n",
       "1     -0.8612   7.7133  -0.6726   2.9671  \n",
       "2     -0.7306   6.3608   1.8135   1.2642  \n",
       "3      3.0835  -4.1575  -2.3772  -4.1168  \n",
       "4     -2.4159   0.1442  -3.3054  -1.4296  \n",
       "...       ...      ...      ...      ...  \n",
       "1995   4.7755   6.6148   0.2220   4.0947  \n",
       "1996  22.9637  11.8630   4.6943  -0.4756  \n",
       "1997  11.8630  26.4048   3.4100   6.0895  \n",
       "1998   4.6943   3.4100  22.2915   5.5033  \n",
       "1999  -0.4756   6.0895   5.5033  14.0200  \n",
       "\n",
       "[2000 rows x 2000 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "1f13e237",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test_final = np.diag(T2_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "e3e320ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000,)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2_test_final.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "aade7a76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "plt.semilogy(T2_test_final,'.')\n",
    "plt.axhline(T2_trlim, ls='--',c='r')\n",
    "plt.title('$T^2$ statistic')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a6c7681c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(T2_test_final)\n",
    "plt.axhline(T2_trlim, ls='--',c='r')\n",
    "plt.title('$T^2$ statistic')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "dc1ad8c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T2: 0.0145\n"
     ]
    }
   ],
   "source": [
    "print(f'T2: {(T2_test_final>T2_trlim).sum()/T2_test_final.shape[0]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a5c1a20",
   "metadata": {},
   "source": [
    "## Testing Process using Faulty Dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "b534f3c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "## STEPs\n",
    "# 1-standardize the data\n",
    "# 2-linear kernel\n",
    "# 3-Centralize the kernel\n",
    "# 4-Score faulty\n",
    "# 5-T2 faulty"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81905c3b",
   "metadata": {},
   "source": [
    "### The Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "ebc9f01d",
   "metadata": {},
   "outputs": [],
   "source": [
    "IDV = 1\n",
    "df_test = test_faulty[(test_faulty.faultNumber==IDV) & \n",
    "                               (test_faulty.simulationRun==1)].iloc[:,3:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "de4d9426",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scaling the data\n",
    "X_ts = scl_pick('std', df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "7fd230f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/512610052.py:1: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  Kt = np.matmul(X_ts, df_scl.T)\n"
     ]
    }
   ],
   "source": [
    "Kt = np.matmul(X_ts, df_scl.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b66ba62f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# centralize the kernel\n",
    "st = (len(X_ts),len(df_train)) # 2000 or 960\n",
    "unit_t = np.ones(st)/len(df_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "4126fcfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#######\n",
    "unit_t = pd.DataFrame(unit_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "99f90ba6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Kt_c = Kt-unit_t@K-Kt@unit+unit_t@K@unit\n",
    "# the result are NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "772b0de2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Kt_c = round(Kt_c, 4)\n",
    "# Kt_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "7ed9703e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\m477a\\AppData\\Local\\Temp/ipykernel_22448/3252352834.py:1: FutureWarning: Calling a ufunc on non-aligned DataFrames (or DataFrame/Series combination). Currently, the indices are ignored and the result takes the index/columns of the first DataFrame. In the future , the DataFrames/Series will be aligned before applying the ufunc.\n",
      "Convert one of the arguments to a NumPy array (eg 'ufunc(df1, np.asarray(df2)') to keep the current behaviour, or align manually (eg 'df1, df2 = df1.align(df2)') before passing to the ufunc to obtain the future behaviour and silence this warning.\n",
      "  score_test = np.matmul(Kt_c, eigvct.iloc[:,:nComponent])\n"
     ]
    }
   ],
   "source": [
    "score_test = np.matmul(Kt_c, eigvct.iloc[:,:nComponent])\n",
    "score_test = round(score_test, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "e6ef5ed1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# score_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "04ee9b8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test = score_test@invegvldiag@score_test.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "46a9f406",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test = round(T2_test, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "8625b5c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2_test_final = np.diag(T2_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "baf91161",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "plt.semilogy(T2_test_final,'.')\n",
    "plt.axhline(T2_trlim, ls='--',c='r')\n",
    "plt.axvline(160, c='k')\n",
    "plt.title('$T^2$ statistic')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "a3535532",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T2: 0.2225\n"
     ]
    }
   ],
   "source": [
    "print(f'T2: {(T2_test_final[160:]>T2_trlim).sum()/T2_test_final[160:].shape[0]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df4acba6",
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}