E18_Kernel Function.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9d22f78e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7803b87d",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_normal = pd.read_csv('./data/normal_training.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fb9c2841",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_faulty = pd.read_csv('./data/faulty_testing.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "aec51d20",
   "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": "3ae041aa",
   "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": "code",
   "execution_count": 6,
   "id": "7155250b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#-std-minmax-robust-norm-pwr\n",
    "x = scl_pick('std', df_train) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6320c1b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "        text-align: right;\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>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>-0.007459</td>\n",
       "      <td>0.343859</td>\n",
       "      <td>0.502126</td>\n",
       "      <td>-1.431359</td>\n",
       "      <td>-0.084087</td>\n",
       "      <td>0.278542</td>\n",
       "      <td>-0.009557</td>\n",
       "      <td>-0.292773</td>\n",
       "      <td>0.510938</td>\n",
       "      <td>0.098431</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.488936</td>\n",
       "      <td>0.000962</td>\n",
       "      <td>1.050090</td>\n",
       "      <td>-0.051818</td>\n",
       "      <td>-0.122736</td>\n",
       "      <td>1.319983</td>\n",
       "      <td>0.471559</td>\n",
       "      <td>-0.720571</td>\n",
       "      <td>0.279630</td>\n",
       "      <td>0.250397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.017875</td>\n",
       "      <td>-0.103316</td>\n",
       "      <td>1.215653</td>\n",
       "      <td>1.035368</td>\n",
       "      <td>-0.866377</td>\n",
       "      <td>1.068875</td>\n",
       "      <td>0.107804</td>\n",
       "      <td>-0.032734</td>\n",
       "      <td>0.510938</td>\n",
       "      <td>-0.071378</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.237481</td>\n",
       "      <td>-0.024152</td>\n",
       "      <td>-1.590601</td>\n",
       "      <td>-0.185906</td>\n",
       "      <td>0.049624</td>\n",
       "      <td>0.089123</td>\n",
       "      <td>-1.227605</td>\n",
       "      <td>-0.760505</td>\n",
       "      <td>0.460598</td>\n",
       "      <td>-0.634866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.007459</td>\n",
       "      <td>-0.075750</td>\n",
       "      <td>-0.821517</td>\n",
       "      <td>1.240929</td>\n",
       "      <td>-0.149278</td>\n",
       "      <td>-1.229449</td>\n",
       "      <td>0.308995</td>\n",
       "      <td>-0.467397</td>\n",
       "      <td>1.023929</td>\n",
       "      <td>-0.120262</td>\n",
       "      <td>...</td>\n",
       "      <td>0.901543</td>\n",
       "      <td>0.004238</td>\n",
       "      <td>0.029987</td>\n",
       "      <td>0.562959</td>\n",
       "      <td>0.098256</td>\n",
       "      <td>0.231510</td>\n",
       "      <td>0.029317</td>\n",
       "      <td>-0.740779</td>\n",
       "      <td>0.173916</td>\n",
       "      <td>1.722067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.029225</td>\n",
       "      <td>-0.045122</td>\n",
       "      <td>0.065220</td>\n",
       "      <td>1.685042</td>\n",
       "      <td>-0.694087</td>\n",
       "      <td>-1.261244</td>\n",
       "      <td>0.476653</td>\n",
       "      <td>0.392438</td>\n",
       "      <td>-0.515042</td>\n",
       "      <td>-0.128838</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.030736</td>\n",
       "      <td>0.025713</td>\n",
       "      <td>-1.110695</td>\n",
       "      <td>0.302375</td>\n",
       "      <td>0.107554</td>\n",
       "      <td>-0.068286</td>\n",
       "      <td>0.381272</td>\n",
       "      <td>-0.649365</td>\n",
       "      <td>0.969458</td>\n",
       "      <td>-0.002535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.550795</td>\n",
       "      <td>0.497001</td>\n",
       "      <td>-0.325151</td>\n",
       "      <td>-0.085064</td>\n",
       "      <td>-0.084087</td>\n",
       "      <td>1.404994</td>\n",
       "      <td>0.124570</td>\n",
       "      <td>0.703725</td>\n",
       "      <td>-0.515042</td>\n",
       "      <td>-0.918704</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.684011</td>\n",
       "      <td>1.507821</td>\n",
       "      <td>-0.418568</td>\n",
       "      <td>-0.532509</td>\n",
       "      <td>-0.688446</td>\n",
       "      <td>1.199804</td>\n",
       "      <td>0.424744</td>\n",
       "      <td>-0.799476</td>\n",
       "      <td>0.725778</td>\n",
       "      <td>0.260288</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>-0.163035</td>\n",
       "      <td>-0.333028</td>\n",
       "      <td>-0.133843</td>\n",
       "      <td>1.615252</td>\n",
       "      <td>-1.429812</td>\n",
       "      <td>-0.130251</td>\n",
       "      <td>0.476653</td>\n",
       "      <td>-0.748315</td>\n",
       "      <td>-0.002052</td>\n",
       "      <td>-1.133966</td>\n",
       "      <td>...</td>\n",
       "      <td>0.391172</td>\n",
       "      <td>-0.360829</td>\n",
       "      <td>-1.326130</td>\n",
       "      <td>0.818484</td>\n",
       "      <td>-0.825761</td>\n",
       "      <td>-1.564979</td>\n",
       "      <td>-0.596009</td>\n",
       "      <td>0.429321</td>\n",
       "      <td>-0.080515</td>\n",
       "      <td>-1.161925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>-0.571599</td>\n",
       "      <td>0.006947</td>\n",
       "      <td>0.515052</td>\n",
       "      <td>-0.010199</td>\n",
       "      <td>-0.163247</td>\n",
       "      <td>0.423891</td>\n",
       "      <td>-0.043088</td>\n",
       "      <td>0.200731</td>\n",
       "      <td>-0.002052</td>\n",
       "      <td>1.501493</td>\n",
       "      <td>...</td>\n",
       "      <td>0.155266</td>\n",
       "      <td>-0.683676</td>\n",
       "      <td>-0.539952</td>\n",
       "      <td>0.201177</td>\n",
       "      <td>2.053568</td>\n",
       "      <td>-0.086248</td>\n",
       "      <td>-1.668594</td>\n",
       "      <td>0.513518</td>\n",
       "      <td>0.424762</td>\n",
       "      <td>-0.464596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>-0.710404</td>\n",
       "      <td>-0.195201</td>\n",
       "      <td>-0.428561</td>\n",
       "      <td>-0.596428</td>\n",
       "      <td>0.060264</td>\n",
       "      <td>0.887190</td>\n",
       "      <td>-0.680190</td>\n",
       "      <td>-0.142824</td>\n",
       "      <td>-0.515042</td>\n",
       "      <td>1.848829</td>\n",
       "      <td>...</td>\n",
       "      <td>1.146522</td>\n",
       "      <td>-0.544637</td>\n",
       "      <td>0.694782</td>\n",
       "      <td>-1.311733</td>\n",
       "      <td>1.699552</td>\n",
       "      <td>0.893150</td>\n",
       "      <td>0.064011</td>\n",
       "      <td>0.524584</td>\n",
       "      <td>0.313673</td>\n",
       "      <td>0.157137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>-0.283998</td>\n",
       "      <td>-0.927219</td>\n",
       "      <td>0.308233</td>\n",
       "      <td>0.592525</td>\n",
       "      <td>0.227898</td>\n",
       "      <td>-0.107540</td>\n",
       "      <td>-0.411937</td>\n",
       "      <td>-0.222544</td>\n",
       "      <td>-1.541023</td>\n",
       "      <td>0.303401</td>\n",
       "      <td>...</td>\n",
       "      <td>1.298499</td>\n",
       "      <td>-0.461651</td>\n",
       "      <td>1.548485</td>\n",
       "      <td>1.273875</td>\n",
       "      <td>-0.392360</td>\n",
       "      <td>-0.127070</td>\n",
       "      <td>0.350758</td>\n",
       "      <td>0.627545</td>\n",
       "      <td>-0.976396</td>\n",
       "      <td>0.780990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>-0.392830</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>1.466421</td>\n",
       "      <td>2.059365</td>\n",
       "      <td>1.452554</td>\n",
       "      <td>1.891003</td>\n",
       "      <td>-0.093386</td>\n",
       "      <td>1.345279</td>\n",
       "      <td>-0.515042</td>\n",
       "      <td>-0.032785</td>\n",
       "      <td>...</td>\n",
       "      <td>0.082680</td>\n",
       "      <td>-0.352458</td>\n",
       "      <td>-1.354265</td>\n",
       "      <td>1.496511</td>\n",
       "      <td>-0.050502</td>\n",
       "      <td>-0.099311</td>\n",
       "      <td>2.401877</td>\n",
       "      <td>0.827693</td>\n",
       "      <td>0.077160</td>\n",
       "      <td>0.661589</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   \\\n",
       "0   -0.007459  0.343859  0.502126 -1.431359 -0.084087  0.278542 -0.009557   \n",
       "1    0.017875 -0.103316  1.215653  1.035368 -0.866377  1.068875  0.107804   \n",
       "2   -0.007459 -0.075750 -0.821517  1.240929 -0.149278 -1.229449  0.308995   \n",
       "3   -0.029225 -0.045122  0.065220  1.685042 -0.694087 -1.261244  0.476653   \n",
       "4    1.550795  0.497001 -0.325151 -0.085064 -0.084087  1.404994  0.124570   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "495 -0.163035 -0.333028 -0.133843  1.615252 -1.429812 -0.130251  0.476653   \n",
       "496 -0.571599  0.006947  0.515052 -0.010199 -0.163247  0.423891 -0.043088   \n",
       "497 -0.710404 -0.195201 -0.428561 -0.596428  0.060264  0.887190 -0.680190   \n",
       "498 -0.283998 -0.927219  0.308233  0.592525  0.227898 -0.107540 -0.411937   \n",
       "499 -0.392830 -1.012978  1.466421  2.059365  1.452554  1.891003 -0.093386   \n",
       "\n",
       "           7         8         9   ...        42        43        44  \\\n",
       "0   -0.292773  0.510938  0.098431  ... -0.488936  0.000962  1.050090   \n",
       "1   -0.032734  0.510938 -0.071378  ... -1.237481 -0.024152 -1.590601   \n",
       "2   -0.467397  1.023929 -0.120262  ...  0.901543  0.004238  0.029987   \n",
       "3    0.392438 -0.515042 -0.128838  ... -0.030736  0.025713 -1.110695   \n",
       "4    0.703725 -0.515042 -0.918704  ... -0.684011  1.507821 -0.418568   \n",
       "..        ...       ...       ...  ...       ...       ...       ...   \n",
       "495 -0.748315 -0.002052 -1.133966  ...  0.391172 -0.360829 -1.326130   \n",
       "496  0.200731 -0.002052  1.501493  ...  0.155266 -0.683676 -0.539952   \n",
       "497 -0.142824 -0.515042  1.848829  ...  1.146522 -0.544637  0.694782   \n",
       "498 -0.222544 -1.541023  0.303401  ...  1.298499 -0.461651  1.548485   \n",
       "499  1.345279 -0.515042 -0.032785  ...  0.082680 -0.352458 -1.354265   \n",
       "\n",
       "           45        46        47        48        49        50        51  \n",
       "0   -0.051818 -0.122736  1.319983  0.471559 -0.720571  0.279630  0.250397  \n",
       "1   -0.185906  0.049624  0.089123 -1.227605 -0.760505  0.460598 -0.634866  \n",
       "2    0.562959  0.098256  0.231510  0.029317 -0.740779  0.173916  1.722067  \n",
       "3    0.302375  0.107554 -0.068286  0.381272 -0.649365  0.969458 -0.002535  \n",
       "4   -0.532509 -0.688446  1.199804  0.424744 -0.799476  0.725778  0.260288  \n",
       "..        ...       ...       ...       ...       ...       ...       ...  \n",
       "495  0.818484 -0.825761 -1.564979 -0.596009  0.429321 -0.080515 -1.161925  \n",
       "496  0.201177  2.053568 -0.086248 -1.668594  0.513518  0.424762 -0.464596  \n",
       "497 -1.311733  1.699552  0.893150  0.064011  0.524584  0.313673  0.157137  \n",
       "498  1.273875 -0.392360 -0.127070  0.350758  0.627545 -0.976396  0.780990  \n",
       "499  1.496511 -0.050502 -0.099311  2.401877  0.827693  0.077160  0.661589  \n",
       "\n",
       "[500 rows x 52 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3f3cf0e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "74c7e039",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 52)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65d387bb",
   "metadata": {},
   "source": [
    "### Trial and Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c10c5eda",
   "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>0.000056</td>\n",
       "      <td>0.118239</td>\n",
       "      <td>0.252131</td>\n",
       "      <td>2.048790</td>\n",
       "      <td>0.007071</td>\n",
       "      <td>0.077586</td>\n",
       "      <td>0.000091</td>\n",
       "      <td>0.085716</td>\n",
       "      <td>0.261058</td>\n",
       "      <td>0.009689</td>\n",
       "      <td>...</td>\n",
       "      <td>0.239058</td>\n",
       "      <td>9.261202e-07</td>\n",
       "      <td>1.102688</td>\n",
       "      <td>0.002685</td>\n",
       "      <td>0.015064</td>\n",
       "      <td>1.742356</td>\n",
       "      <td>0.222368</td>\n",
       "      <td>0.519223</td>\n",
       "      <td>0.078193</td>\n",
       "      <td>0.062699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000320</td>\n",
       "      <td>0.010674</td>\n",
       "      <td>1.477812</td>\n",
       "      <td>1.071988</td>\n",
       "      <td>0.750609</td>\n",
       "      <td>1.142495</td>\n",
       "      <td>0.011622</td>\n",
       "      <td>0.001072</td>\n",
       "      <td>0.261058</td>\n",
       "      <td>0.005095</td>\n",
       "      <td>...</td>\n",
       "      <td>1.531360</td>\n",
       "      <td>5.833173e-04</td>\n",
       "      <td>2.530011</td>\n",
       "      <td>0.034561</td>\n",
       "      <td>0.002463</td>\n",
       "      <td>0.007943</td>\n",
       "      <td>1.507015</td>\n",
       "      <td>0.578368</td>\n",
       "      <td>0.212150</td>\n",
       "      <td>0.403054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000056</td>\n",
       "      <td>0.005738</td>\n",
       "      <td>0.674891</td>\n",
       "      <td>1.539905</td>\n",
       "      <td>0.022284</td>\n",
       "      <td>1.511545</td>\n",
       "      <td>0.095478</td>\n",
       "      <td>0.218460</td>\n",
       "      <td>1.048430</td>\n",
       "      <td>0.014463</td>\n",
       "      <td>...</td>\n",
       "      <td>0.812780</td>\n",
       "      <td>1.796176e-05</td>\n",
       "      <td>0.000899</td>\n",
       "      <td>0.316923</td>\n",
       "      <td>0.009654</td>\n",
       "      <td>0.053597</td>\n",
       "      <td>0.000859</td>\n",
       "      <td>0.548753</td>\n",
       "      <td>0.030247</td>\n",
       "      <td>2.965515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000854</td>\n",
       "      <td>0.002036</td>\n",
       "      <td>0.004254</td>\n",
       "      <td>2.839365</td>\n",
       "      <td>0.481756</td>\n",
       "      <td>1.590737</td>\n",
       "      <td>0.227198</td>\n",
       "      <td>0.154007</td>\n",
       "      <td>0.265268</td>\n",
       "      <td>0.016599</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000945</td>\n",
       "      <td>6.611424e-04</td>\n",
       "      <td>1.233642</td>\n",
       "      <td>0.091430</td>\n",
       "      <td>0.011568</td>\n",
       "      <td>0.004663</td>\n",
       "      <td>0.145368</td>\n",
       "      <td>0.421674</td>\n",
       "      <td>0.939849</td>\n",
       "      <td>0.000006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.404964</td>\n",
       "      <td>0.247010</td>\n",
       "      <td>0.105723</td>\n",
       "      <td>0.007236</td>\n",
       "      <td>0.007071</td>\n",
       "      <td>1.974008</td>\n",
       "      <td>0.015518</td>\n",
       "      <td>0.495228</td>\n",
       "      <td>0.265268</td>\n",
       "      <td>0.844018</td>\n",
       "      <td>...</td>\n",
       "      <td>0.467872</td>\n",
       "      <td>2.273525e+00</td>\n",
       "      <td>0.175199</td>\n",
       "      <td>0.283566</td>\n",
       "      <td>0.473958</td>\n",
       "      <td>1.439529</td>\n",
       "      <td>0.180407</td>\n",
       "      <td>0.639162</td>\n",
       "      <td>0.526754</td>\n",
       "      <td>0.067750</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>0.026580</td>\n",
       "      <td>0.110908</td>\n",
       "      <td>0.017914</td>\n",
       "      <td>2.609040</td>\n",
       "      <td>2.044362</td>\n",
       "      <td>0.016965</td>\n",
       "      <td>0.227198</td>\n",
       "      <td>0.559975</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>1.285880</td>\n",
       "      <td>...</td>\n",
       "      <td>0.153015</td>\n",
       "      <td>1.301978e-01</td>\n",
       "      <td>1.758620</td>\n",
       "      <td>0.669917</td>\n",
       "      <td>0.681881</td>\n",
       "      <td>2.449158</td>\n",
       "      <td>0.355227</td>\n",
       "      <td>0.184316</td>\n",
       "      <td>0.006483</td>\n",
       "      <td>1.350071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>0.326725</td>\n",
       "      <td>0.000048</td>\n",
       "      <td>0.265279</td>\n",
       "      <td>0.000104</td>\n",
       "      <td>0.026650</td>\n",
       "      <td>0.179684</td>\n",
       "      <td>0.001857</td>\n",
       "      <td>0.040293</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>2.254483</td>\n",
       "      <td>...</td>\n",
       "      <td>0.024108</td>\n",
       "      <td>4.674124e-01</td>\n",
       "      <td>0.291548</td>\n",
       "      <td>0.040472</td>\n",
       "      <td>4.217142</td>\n",
       "      <td>0.007439</td>\n",
       "      <td>2.784206</td>\n",
       "      <td>0.263700</td>\n",
       "      <td>0.180423</td>\n",
       "      <td>0.215849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>0.504674</td>\n",
       "      <td>0.038103</td>\n",
       "      <td>0.183664</td>\n",
       "      <td>0.355726</td>\n",
       "      <td>0.003632</td>\n",
       "      <td>0.787105</td>\n",
       "      <td>0.462659</td>\n",
       "      <td>0.020399</td>\n",
       "      <td>0.265268</td>\n",
       "      <td>3.418168</td>\n",
       "      <td>...</td>\n",
       "      <td>1.314512</td>\n",
       "      <td>2.966295e-01</td>\n",
       "      <td>0.482722</td>\n",
       "      <td>1.720645</td>\n",
       "      <td>2.888478</td>\n",
       "      <td>0.797717</td>\n",
       "      <td>0.004097</td>\n",
       "      <td>0.275188</td>\n",
       "      <td>0.098391</td>\n",
       "      <td>0.024692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>0.080655</td>\n",
       "      <td>0.859735</td>\n",
       "      <td>0.095008</td>\n",
       "      <td>0.351086</td>\n",
       "      <td>0.051937</td>\n",
       "      <td>0.011565</td>\n",
       "      <td>0.169692</td>\n",
       "      <td>0.049526</td>\n",
       "      <td>2.374751</td>\n",
       "      <td>0.092052</td>\n",
       "      <td>...</td>\n",
       "      <td>1.686099</td>\n",
       "      <td>2.131213e-01</td>\n",
       "      <td>2.397805</td>\n",
       "      <td>1.622758</td>\n",
       "      <td>0.153946</td>\n",
       "      <td>0.016147</td>\n",
       "      <td>0.123031</td>\n",
       "      <td>0.393812</td>\n",
       "      <td>0.953349</td>\n",
       "      <td>0.609945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>0.154315</td>\n",
       "      <td>1.026125</td>\n",
       "      <td>2.150391</td>\n",
       "      <td>4.240984</td>\n",
       "      <td>2.109914</td>\n",
       "      <td>3.575894</td>\n",
       "      <td>0.008721</td>\n",
       "      <td>1.809776</td>\n",
       "      <td>0.265268</td>\n",
       "      <td>0.001075</td>\n",
       "      <td>...</td>\n",
       "      <td>0.006836</td>\n",
       "      <td>1.242266e-01</td>\n",
       "      <td>1.834034</td>\n",
       "      <td>2.239545</td>\n",
       "      <td>0.002550</td>\n",
       "      <td>0.009863</td>\n",
       "      <td>5.769015</td>\n",
       "      <td>0.685076</td>\n",
       "      <td>0.005954</td>\n",
       "      <td>0.437700</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   \\\n",
       "0    0.000056  0.118239  0.252131  2.048790  0.007071  0.077586  0.000091   \n",
       "1    0.000320  0.010674  1.477812  1.071988  0.750609  1.142495  0.011622   \n",
       "2    0.000056  0.005738  0.674891  1.539905  0.022284  1.511545  0.095478   \n",
       "3    0.000854  0.002036  0.004254  2.839365  0.481756  1.590737  0.227198   \n",
       "4    2.404964  0.247010  0.105723  0.007236  0.007071  1.974008  0.015518   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "495  0.026580  0.110908  0.017914  2.609040  2.044362  0.016965  0.227198   \n",
       "496  0.326725  0.000048  0.265279  0.000104  0.026650  0.179684  0.001857   \n",
       "497  0.504674  0.038103  0.183664  0.355726  0.003632  0.787105  0.462659   \n",
       "498  0.080655  0.859735  0.095008  0.351086  0.051937  0.011565  0.169692   \n",
       "499  0.154315  1.026125  2.150391  4.240984  2.109914  3.575894  0.008721   \n",
       "\n",
       "           7         8         9   ...        42            43        44  \\\n",
       "0    0.085716  0.261058  0.009689  ...  0.239058  9.261202e-07  1.102688   \n",
       "1    0.001072  0.261058  0.005095  ...  1.531360  5.833173e-04  2.530011   \n",
       "2    0.218460  1.048430  0.014463  ...  0.812780  1.796176e-05  0.000899   \n",
       "3    0.154007  0.265268  0.016599  ...  0.000945  6.611424e-04  1.233642   \n",
       "4    0.495228  0.265268  0.844018  ...  0.467872  2.273525e+00  0.175199   \n",
       "..        ...       ...       ...  ...       ...           ...       ...   \n",
       "495  0.559975  0.000004  1.285880  ...  0.153015  1.301978e-01  1.758620   \n",
       "496  0.040293  0.000004  2.254483  ...  0.024108  4.674124e-01  0.291548   \n",
       "497  0.020399  0.265268  3.418168  ...  1.314512  2.966295e-01  0.482722   \n",
       "498  0.049526  2.374751  0.092052  ...  1.686099  2.131213e-01  2.397805   \n",
       "499  1.809776  0.265268  0.001075  ...  0.006836  1.242266e-01  1.834034   \n",
       "\n",
       "           45        46        47        48        49        50        51  \n",
       "0    0.002685  0.015064  1.742356  0.222368  0.519223  0.078193  0.062699  \n",
       "1    0.034561  0.002463  0.007943  1.507015  0.578368  0.212150  0.403054  \n",
       "2    0.316923  0.009654  0.053597  0.000859  0.548753  0.030247  2.965515  \n",
       "3    0.091430  0.011568  0.004663  0.145368  0.421674  0.939849  0.000006  \n",
       "4    0.283566  0.473958  1.439529  0.180407  0.639162  0.526754  0.067750  \n",
       "..        ...       ...       ...       ...       ...       ...       ...  \n",
       "495  0.669917  0.681881  2.449158  0.355227  0.184316  0.006483  1.350071  \n",
       "496  0.040472  4.217142  0.007439  2.784206  0.263700  0.180423  0.215849  \n",
       "497  1.720645  2.888478  0.797717  0.004097  0.275188  0.098391  0.024692  \n",
       "498  1.622758  0.153946  0.016147  0.123031  0.393812  0.953349  0.609945  \n",
       "499  2.239545  0.002550  0.009863  5.769015  0.685076  0.005954  0.437700  \n",
       "\n",
       "[500 rows x 52 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2968cb85",
   "metadata": {},
   "outputs": [],
   "source": [
    "sx = np.power(x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ca2234bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.frame.DataFrame"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(sx)\n",
    "# need to change into numpy.ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "50cc169c",
   "metadata": {},
   "outputs": [],
   "source": [
    "sx = sx.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e82e983d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(sx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "74560f68",
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.matrix.sum(sx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6e2d82ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install pydist2\n",
    "# pip.main(['install', 'pydist2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1f46ed90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting pydist2\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  Cache entry deserialization failed, entry ignored\n",
      "  Could not find a version that satisfies the requirement pydist2 (from versions: )\n",
      "No matching distribution found for pydist2\n",
      "You are using pip version 21.3.1, however version 22.3.1 is available.\n",
      "You should consider upgrading via the 'python -m pip install --upgrade pip' command.\n"
     ]
    }
   ],
   "source": [
    "# pip --upgrade \n",
    "!pip install pydist2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a2aa40e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import pdist2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e500e958",
   "metadata": {},
   "outputs": [],
   "source": [
    "### POLYNOMIAL\n",
    "poly = 0.1*x*x.T+0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "172fd6ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 500)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "11757a8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.power(poly,2)\n",
    "# i will continue in spyder "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5110c658",
   "metadata": {},
   "source": [
    "## Linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "05fdd7d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "lin = x@x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e709d940",
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
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       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
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       "      <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",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>11.254634</td>\n",
       "      <td>-1.006097</td>\n",
       "      <td>0.067399</td>\n",
       "      <td>-2.911136</td>\n",
       "      <td>7.180838</td>\n",
       "      <td>2.800996</td>\n",
       "      <td>0.005696</td>\n",
       "      <td>1.450963</td>\n",
       "      <td>0.406271</td>\n",
       "      <td>1.580191</td>\n",
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       "      <td>0.593039</td>\n",
       "      <td>3.850171</td>\n",
       "      <td>-9.136394</td>\n",
       "      <td>4.291930</td>\n",
       "      <td>-3.399547</td>\n",
       "      <td>-10.671728</td>\n",
       "      <td>-3.103647</td>\n",
       "      <td>5.082999</td>\n",
       "      <td>-1.139681</td>\n",
       "      <td>-2.065223</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.006097</td>\n",
       "      <td>15.648105</td>\n",
       "      <td>-1.643850</td>\n",
       "      <td>5.655817</td>\n",
       "      <td>2.590303</td>\n",
       "      <td>-0.440812</td>\n",
       "      <td>6.002199</td>\n",
       "      <td>4.606890</td>\n",
       "      <td>-2.434063</td>\n",
       "      <td>2.604167</td>\n",
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       "      <td>0.910302</td>\n",
       "      <td>1.025712</td>\n",
       "      <td>-2.711872</td>\n",
       "      <td>0.154117</td>\n",
       "      <td>0.319368</td>\n",
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       "      <td>-5.636426</td>\n",
       "      <td>-8.433953</td>\n",
       "      <td>-1.243001</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.067399</td>\n",
       "      <td>-1.643850</td>\n",
       "      <td>26.753057</td>\n",
       "      <td>17.878376</td>\n",
       "      <td>-0.314381</td>\n",
       "      <td>5.125456</td>\n",
       "      <td>3.053187</td>\n",
       "      <td>9.695625</td>\n",
       "      <td>-6.101215</td>\n",
       "      <td>3.928392</td>\n",
       "      <td>...</td>\n",
       "      <td>6.034873</td>\n",
       "      <td>5.882331</td>\n",
       "      <td>9.457952</td>\n",
       "      <td>-6.591729</td>\n",
       "      <td>5.767018</td>\n",
       "      <td>-1.737426</td>\n",
       "      <td>-1.248601</td>\n",
       "      <td>-3.118928</td>\n",
       "      <td>-1.144356</td>\n",
       "      <td>-3.652338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.911136</td>\n",
       "      <td>5.655817</td>\n",
       "      <td>17.878376</td>\n",
       "      <td>28.075591</td>\n",
       "      <td>-1.217920</td>\n",
       "      <td>1.028497</td>\n",
       "      <td>7.369408</td>\n",
       "      <td>7.878824</td>\n",
       "      <td>-6.396740</td>\n",
       "      <td>-0.043967</td>\n",
       "      <td>...</td>\n",
       "      <td>4.392604</td>\n",
       "      <td>5.631827</td>\n",
       "      <td>7.720344</td>\n",
       "      <td>0.811632</td>\n",
       "      <td>2.467457</td>\n",
       "      <td>7.440443</td>\n",
       "      <td>0.087824</td>\n",
       "      <td>-8.028105</td>\n",
       "      <td>-7.513966</td>\n",
       "      <td>1.320220</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.180838</td>\n",
       "      <td>2.590303</td>\n",
       "      <td>-0.314381</td>\n",
       "      <td>-1.217920</td>\n",
       "      <td>40.463249</td>\n",
       "      <td>34.783786</td>\n",
       "      <td>-1.699829</td>\n",
       "      <td>-4.665480</td>\n",
       "      <td>5.307867</td>\n",
       "      <td>4.026851</td>\n",
       "      <td>...</td>\n",
       "      <td>2.648738</td>\n",
       "      <td>6.922856</td>\n",
       "      <td>-7.399262</td>\n",
       "      <td>0.624002</td>\n",
       "      <td>1.256144</td>\n",
       "      <td>-2.809074</td>\n",
       "      <td>-0.029658</td>\n",
       "      <td>7.971182</td>\n",
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       "      <td>-0.148896</td>\n",
       "      <td>3.515290</td>\n",
       "      <td>8.046493</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.764045</td>\n",
       "      <td>-4.210899</td>\n",
       "      <td>3.461888</td>\n",
       "      <td>-6.719312</td>\n",
       "      <td>18.034202</td>\n",
       "      <td>40.463401</td>\n",
       "      <td>7.860271</td>\n",
       "      <td>-8.157611</td>\n",
       "      <td>4.955096</td>\n",
       "      <td>8.035931</td>\n",
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       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>-3.103647</td>\n",
       "      <td>5.372732</td>\n",
       "      <td>-1.248601</td>\n",
       "      <td>0.087824</td>\n",
       "      <td>-0.029658</td>\n",
       "      <td>-1.633637</td>\n",
       "      <td>-1.137229</td>\n",
       "      <td>0.502417</td>\n",
       "      <td>-8.135956</td>\n",
       "      <td>-5.761141</td>\n",
       "      <td>...</td>\n",
       "      <td>2.461151</td>\n",
       "      <td>2.056640</td>\n",
       "      <td>3.404392</td>\n",
       "      <td>-1.032472</td>\n",
       "      <td>-0.650834</td>\n",
       "      <td>7.860271</td>\n",
       "      <td>29.333470</td>\n",
       "      <td>19.186341</td>\n",
       "      <td>0.828928</td>\n",
       "      <td>-3.457594</td>\n",
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       "      <th>497</th>\n",
       "      <td>5.082999</td>\n",
       "      <td>-5.636426</td>\n",
       "      <td>-3.118928</td>\n",
       "      <td>-8.028105</td>\n",
       "      <td>7.971182</td>\n",
       "      <td>2.713818</td>\n",
       "      <td>-6.155890</td>\n",
       "      <td>-6.842317</td>\n",
       "      <td>-4.205185</td>\n",
       "      <td>-12.150855</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.619284</td>\n",
       "      <td>4.995748</td>\n",
       "      <td>6.710797</td>\n",
       "      <td>11.294084</td>\n",
       "      <td>-6.044172</td>\n",
       "      <td>-8.157611</td>\n",
       "      <td>19.186341</td>\n",
       "      <td>36.603012</td>\n",
       "      <td>9.409031</td>\n",
       "      <td>3.965179</td>\n",
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       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>-1.139681</td>\n",
       "      <td>-8.433953</td>\n",
       "      <td>-1.144356</td>\n",
       "      <td>-7.513966</td>\n",
       "      <td>-3.672549</td>\n",
       "      <td>-1.293656</td>\n",
       "      <td>-4.383462</td>\n",
       "      <td>-4.969577</td>\n",
       "      <td>2.194989</td>\n",
       "      <td>-4.847208</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.139085</td>\n",
       "      <td>-8.862680</td>\n",
       "      <td>6.183725</td>\n",
       "      <td>-2.552092</td>\n",
       "      <td>6.351287</td>\n",
       "      <td>4.955096</td>\n",
       "      <td>0.828928</td>\n",
       "      <td>9.409031</td>\n",
       "      <td>33.992203</td>\n",
       "      <td>24.623654</td>\n",
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       "      <th>499</th>\n",
       "      <td>-2.065223</td>\n",
       "      <td>-1.243001</td>\n",
       "      <td>-3.652338</td>\n",
       "      <td>1.320220</td>\n",
       "      <td>2.661713</td>\n",
       "      <td>-1.027238</td>\n",
       "      <td>-6.002098</td>\n",
       "      <td>-8.532572</td>\n",
       "      <td>-2.822009</td>\n",
       "      <td>-5.131042</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.927922</td>\n",
       "      <td>-2.104777</td>\n",
       "      <td>-0.786033</td>\n",
       "      <td>1.265762</td>\n",
       "      <td>1.118703</td>\n",
       "      <td>8.035931</td>\n",
       "      <td>-3.457594</td>\n",
       "      <td>3.965179</td>\n",
       "      <td>24.623654</td>\n",
       "      <td>51.905131</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1          2          3          4          5    \\\n",
       "0    11.254634  -1.006097   0.067399  -2.911136   7.180838   2.800996   \n",
       "1    -1.006097  15.648105  -1.643850   5.655817   2.590303  -0.440812   \n",
       "2     0.067399  -1.643850  26.753057  17.878376  -0.314381   5.125456   \n",
       "3    -2.911136   5.655817  17.878376  28.075591  -1.217920   1.028497   \n",
       "4     7.180838   2.590303  -0.314381  -1.217920  40.463249  34.783786   \n",
       "..         ...        ...        ...        ...        ...        ...   \n",
       "495 -10.671728   8.139373  -1.737426   7.440443  -2.809074  -4.698697   \n",
       "496  -3.103647   5.372732  -1.248601   0.087824  -0.029658  -1.633637   \n",
       "497   5.082999  -5.636426  -3.118928  -8.028105   7.971182   2.713818   \n",
       "498  -1.139681  -8.433953  -1.144356  -7.513966  -3.672549  -1.293656   \n",
       "499  -2.065223  -1.243001  -3.652338   1.320220   2.661713  -1.027238   \n",
       "\n",
       "          6         7         8          9    ...       490       491  \\\n",
       "0    0.005696  1.450963  0.406271   1.580191  ...  0.593039  3.850171   \n",
       "1    6.002199  4.606890 -2.434063   2.604167  ...  0.910302  1.025712   \n",
       "2    3.053187  9.695625 -6.101215   3.928392  ...  6.034873  5.882331   \n",
       "3    7.369408  7.878824 -6.396740  -0.043967  ...  4.392604  5.631827   \n",
       "4   -1.699829 -4.665480  5.307867   4.026851  ...  2.648738  6.922856   \n",
       "..        ...       ...       ...        ...  ...       ...       ...   \n",
       "495  1.355132 -0.148896  3.515290   8.046493  ... -0.764045 -4.210899   \n",
       "496 -1.137229  0.502417 -8.135956  -5.761141  ...  2.461151  2.056640   \n",
       "497 -6.155890 -6.842317 -4.205185 -12.150855  ... -2.619284  4.995748   \n",
       "498 -4.383462 -4.969577  2.194989  -4.847208  ... -4.139085 -8.862680   \n",
       "499 -6.002098 -8.532572 -2.822009  -5.131042  ... -2.927922 -2.104777   \n",
       "\n",
       "          492        493        494        495        496        497  \\\n",
       "0   -9.136394   4.291930  -3.399547 -10.671728  -3.103647   5.082999   \n",
       "1   -2.711872   0.154117   0.319368   8.139373   5.372732  -5.636426   \n",
       "2    9.457952  -6.591729   5.767018  -1.737426  -1.248601  -3.118928   \n",
       "3    7.720344   0.811632   2.467457   7.440443   0.087824  -8.028105   \n",
       "4   -7.399262   0.624002   1.256144  -2.809074  -0.029658   7.971182   \n",
       "..        ...        ...        ...        ...        ...        ...   \n",
       "495  3.461888  -6.719312  18.034202  40.463401   7.860271  -8.157611   \n",
       "496  3.404392  -1.032472  -0.650834   7.860271  29.333470  19.186341   \n",
       "497  6.710797  11.294084  -6.044172  -8.157611  19.186341  36.603012   \n",
       "498  6.183725  -2.552092   6.351287   4.955096   0.828928   9.409031   \n",
       "499 -0.786033   1.265762   1.118703   8.035931  -3.457594   3.965179   \n",
       "\n",
       "           498        499  \n",
       "0    -1.139681  -2.065223  \n",
       "1    -8.433953  -1.243001  \n",
       "2    -1.144356  -3.652338  \n",
       "3    -7.513966   1.320220  \n",
       "4    -3.672549   2.661713  \n",
       "..         ...        ...  \n",
       "495   4.955096   8.035931  \n",
       "496   0.828928  -3.457594  \n",
       "497   9.409031   3.965179  \n",
       "498  33.992203  24.623654  \n",
       "499  24.623654  51.905131  \n",
       "\n",
       "[500 rows x 500 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "ccc7ed72",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>1</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>...</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-4.882423e-13</td>\n",
       "      <td>-4.331895e-13</td>\n",
       "      <td>-9.015935e-13</td>\n",
       "      <td>4.594938e-13</td>\n",
       "      <td>5.265974e-13</td>\n",
       "      <td>3.231548e-13</td>\n",
       "      <td>4.129106e-13</td>\n",
       "      <td>-9.868018e-13</td>\n",
       "      <td>1.271275e-12</td>\n",
       "      <td>-1.953765e-12</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.745573e-13</td>\n",
       "      <td>-1.921222e-12</td>\n",
       "      <td>3.376499e-13</td>\n",
       "      <td>-2.477236e-13</td>\n",
       "      <td>-8.975576e-14</td>\n",
       "      <td>1.234355e-13</td>\n",
       "      <td>8.111556e-14</td>\n",
       "      <td>2.979732e-13</td>\n",
       "      <td>1.228614e-12</td>\n",
       "      <td>4.305321e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.716524e+00</td>\n",
       "      <td>4.778649e+00</td>\n",
       "      <td>6.338038e+00</td>\n",
       "      <td>5.651331e+00</td>\n",
       "      <td>8.554545e+00</td>\n",
       "      <td>9.754645e+00</td>\n",
       "      <td>5.573037e+00</td>\n",
       "      <td>6.049014e+00</td>\n",
       "      <td>7.569132e+00</td>\n",
       "      <td>1.008295e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>7.993475e+00</td>\n",
       "      <td>9.196392e+00</td>\n",
       "      <td>8.720044e+00</td>\n",
       "      <td>1.061736e+01</td>\n",
       "      <td>7.633776e+00</td>\n",
       "      <td>8.500852e+00</td>\n",
       "      <td>7.238600e+00</td>\n",
       "      <td>7.614222e+00</td>\n",
       "      <td>6.203727e+00</td>\n",
       "      <td>8.544686e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.583659e+01</td>\n",
       "      <td>-1.687460e+01</td>\n",
       "      <td>-1.642913e+01</td>\n",
       "      <td>-1.530054e+01</td>\n",
       "      <td>-3.442024e+01</td>\n",
       "      <td>-3.172695e+01</td>\n",
       "      <td>-1.545492e+01</td>\n",
       "      <td>-1.899654e+01</td>\n",
       "      <td>-1.810157e+01</td>\n",
       "      <td>-2.842067e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.505040e+01</td>\n",
       "      <td>-2.298760e+01</td>\n",
       "      <td>-2.468787e+01</td>\n",
       "      <td>-3.567952e+01</td>\n",
       "      <td>-2.424828e+01</td>\n",
       "      <td>-2.504012e+01</td>\n",
       "      <td>-1.976989e+01</td>\n",
       "      <td>-2.541813e+01</td>\n",
       "      <td>-1.965804e+01</td>\n",
       "      <td>-3.084648e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-3.008397e+00</td>\n",
       "      <td>-3.057855e+00</td>\n",
       "      <td>-3.969573e+00</td>\n",
       "      <td>-3.902961e+00</td>\n",
       "      <td>-5.385980e+00</td>\n",
       "      <td>-5.801977e+00</td>\n",
       "      <td>-3.510588e+00</td>\n",
       "      <td>-3.922582e+00</td>\n",
       "      <td>-5.057770e+00</td>\n",
       "      <td>-7.201864e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>-4.905231e+00</td>\n",
       "      <td>-6.303238e+00</td>\n",
       "      <td>-5.589354e+00</td>\n",
       "      <td>-6.736356e+00</td>\n",
       "      <td>-4.846433e+00</td>\n",
       "      <td>-5.262711e+00</td>\n",
       "      <td>-4.699101e+00</td>\n",
       "      <td>-5.278079e+00</td>\n",
       "      <td>-4.239495e+00</td>\n",
       "      <td>-5.585520e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.325165e-03</td>\n",
       "      <td>-1.413585e-01</td>\n",
       "      <td>-2.523802e-01</td>\n",
       "      <td>-8.621058e-03</td>\n",
       "      <td>4.627394e-02</td>\n",
       "      <td>1.081094e-01</td>\n",
       "      <td>-1.812943e-01</td>\n",
       "      <td>9.187919e-02</td>\n",
       "      <td>-3.250027e-01</td>\n",
       "      <td>2.442891e-01</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.678317e-02</td>\n",
       "      <td>3.996536e-01</td>\n",
       "      <td>-4.203533e-01</td>\n",
       "      <td>-1.308644e-01</td>\n",
       "      <td>-4.648557e-01</td>\n",
       "      <td>-5.321977e-01</td>\n",
       "      <td>-8.581737e-02</td>\n",
       "      <td>3.204284e-01</td>\n",
       "      <td>-4.339646e-03</td>\n",
       "      <td>5.841747e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.211763e+00</td>\n",
       "      <td>3.597435e+00</td>\n",
       "      <td>3.942971e+00</td>\n",
       "      <td>3.662164e+00</td>\n",
       "      <td>5.231904e+00</td>\n",
       "      <td>6.651532e+00</td>\n",
       "      <td>3.576924e+00</td>\n",
       "      <td>3.628681e+00</td>\n",
       "      <td>4.594958e+00</td>\n",
       "      <td>6.551037e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>4.842445e+00</td>\n",
       "      <td>5.660645e+00</td>\n",
       "      <td>5.393087e+00</td>\n",
       "      <td>5.708735e+00</td>\n",
       "      <td>4.982327e+00</td>\n",
       "      <td>5.677667e+00</td>\n",
       "      <td>4.547684e+00</td>\n",
       "      <td>4.603735e+00</td>\n",
       "      <td>4.218490e+00</td>\n",
       "      <td>4.721765e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.468455e+01</td>\n",
       "      <td>1.565211e+01</td>\n",
       "      <td>2.675306e+01</td>\n",
       "      <td>2.807559e+01</td>\n",
       "      <td>4.046325e+01</td>\n",
       "      <td>6.019564e+01</td>\n",
       "      <td>2.828130e+01</td>\n",
       "      <td>3.144206e+01</td>\n",
       "      <td>4.585478e+01</td>\n",
       "      <td>5.270524e+01</td>\n",
       "      <td>...</td>\n",
       "      <td>4.135756e+01</td>\n",
       "      <td>4.666928e+01</td>\n",
       "      <td>5.914190e+01</td>\n",
       "      <td>6.539987e+01</td>\n",
       "      <td>4.117686e+01</td>\n",
       "      <td>4.046340e+01</td>\n",
       "      <td>2.933347e+01</td>\n",
       "      <td>3.660301e+01</td>\n",
       "      <td>3.399220e+01</td>\n",
       "      <td>5.190513e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                0             1             2             3             4    \\\n",
       "count  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean  -4.882423e-13 -4.331895e-13 -9.015935e-13  4.594938e-13  5.265974e-13   \n",
       "std    4.716524e+00  4.778649e+00  6.338038e+00  5.651331e+00  8.554545e+00   \n",
       "min   -1.583659e+01 -1.687460e+01 -1.642913e+01 -1.530054e+01 -3.442024e+01   \n",
       "25%   -3.008397e+00 -3.057855e+00 -3.969573e+00 -3.902961e+00 -5.385980e+00   \n",
       "50%    5.325165e-03 -1.413585e-01 -2.523802e-01 -8.621058e-03  4.627394e-02   \n",
       "75%    3.211763e+00  3.597435e+00  3.942971e+00  3.662164e+00  5.231904e+00   \n",
       "max    1.468455e+01  1.565211e+01  2.675306e+01  2.807559e+01  4.046325e+01   \n",
       "\n",
       "                5             6             7             8             9    \\\n",
       "count  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean   3.231548e-13  4.129106e-13 -9.868018e-13  1.271275e-12 -1.953765e-12   \n",
       "std    9.754645e+00  5.573037e+00  6.049014e+00  7.569132e+00  1.008295e+01   \n",
       "min   -3.172695e+01 -1.545492e+01 -1.899654e+01 -1.810157e+01 -2.842067e+01   \n",
       "25%   -5.801977e+00 -3.510588e+00 -3.922582e+00 -5.057770e+00 -7.201864e+00   \n",
       "50%    1.081094e-01 -1.812943e-01  9.187919e-02 -3.250027e-01  2.442891e-01   \n",
       "75%    6.651532e+00  3.576924e+00  3.628681e+00  4.594958e+00  6.551037e+00   \n",
       "max    6.019564e+01  2.828130e+01  3.144206e+01  4.585478e+01  5.270524e+01   \n",
       "\n",
       "       ...           490           491           492           493  \\\n",
       "count  ...  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean   ... -4.745573e-13 -1.921222e-12  3.376499e-13 -2.477236e-13   \n",
       "std    ...  7.993475e+00  9.196392e+00  8.720044e+00  1.061736e+01   \n",
       "min    ... -2.505040e+01 -2.298760e+01 -2.468787e+01 -3.567952e+01   \n",
       "25%    ... -4.905231e+00 -6.303238e+00 -5.589354e+00 -6.736356e+00   \n",
       "50%    ... -1.678317e-02  3.996536e-01 -4.203533e-01 -1.308644e-01   \n",
       "75%    ...  4.842445e+00  5.660645e+00  5.393087e+00  5.708735e+00   \n",
       "max    ...  4.135756e+01  4.666928e+01  5.914190e+01  6.539987e+01   \n",
       "\n",
       "                494           495           496           497           498  \\\n",
       "count  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean  -8.975576e-14  1.234355e-13  8.111556e-14  2.979732e-13  1.228614e-12   \n",
       "std    7.633776e+00  8.500852e+00  7.238600e+00  7.614222e+00  6.203727e+00   \n",
       "min   -2.424828e+01 -2.504012e+01 -1.976989e+01 -2.541813e+01 -1.965804e+01   \n",
       "25%   -4.846433e+00 -5.262711e+00 -4.699101e+00 -5.278079e+00 -4.239495e+00   \n",
       "50%   -4.648557e-01 -5.321977e-01 -8.581737e-02  3.204284e-01 -4.339646e-03   \n",
       "75%    4.982327e+00  5.677667e+00  4.547684e+00  4.603735e+00  4.218490e+00   \n",
       "max    4.117686e+01  4.046340e+01  2.933347e+01  3.660301e+01  3.399220e+01   \n",
       "\n",
       "                499  \n",
       "count  5.000000e+02  \n",
       "mean   4.305321e-13  \n",
       "std    8.544686e+00  \n",
       "min   -3.084648e+01  \n",
       "25%   -5.585520e+00  \n",
       "50%    5.841747e-02  \n",
       "75%    4.721765e+00  \n",
       "max    5.190513e+01  \n",
       "\n",
       "[8 rows x 500 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bdd2a562",
   "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.hist(lin)\n",
    "plt.title('Linear')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5646ca3",
   "metadata": {},
   "source": [
    "## Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f5138156",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import pairwise_distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "423f4abd",
   "metadata": {},
   "outputs": [],
   "source": [
    "pdist_gs = pairwise_distances(x, x, metric='sqeuclidean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9179bed0",
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.1\n",
    "gaus = np.exp(-gamma*pdist_gs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "6e752312",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.00000000e+00, 5.54932851e-02, 2.26569364e-02, ...,\n",
       "        2.30713244e-02, 8.62905812e-03, 1.19570302e-03],\n",
       "       [5.54932851e-02, 1.00000000e+00, 1.03695024e-02, ...,\n",
       "        1.74256530e-03, 1.29295960e-03, 9.08310915e-04],\n",
       "       [2.26569364e-02, 1.03695024e-02, 1.00000000e+00, ...,\n",
       "        9.49673322e-04, 1.83007699e-03, 1.84790770e-04],\n",
       "       ...,\n",
       "       [2.30713244e-02, 1.74256530e-03, 9.49673322e-04, ...,\n",
       "        1.00000000e+00, 5.64087945e-03, 3.16629433e-04],\n",
       "       [8.62905812e-03, 1.29295960e-03, 1.83007699e-03, ...,\n",
       "        5.64087945e-03, 1.00000000e+00, 2.56041057e-02],\n",
       "       [1.19570302e-03, 9.08310915e-04, 1.84790770e-04, ...,\n",
       "        3.16629433e-04, 2.56041057e-02, 1.00000000e+00]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "c125c38a",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauss = pd.DataFrame(gaus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0409579a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\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>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>1.000000</td>\n",
       "      <td>0.055493</td>\n",
       "      <td>0.022657</td>\n",
       "      <td>0.010941</td>\n",
       "      <td>0.023858</td>\n",
       "      <td>0.001381</td>\n",
       "      <td>0.019208</td>\n",
       "      <td>0.018695</td>\n",
       "      <td>0.003590</td>\n",
       "      <td>0.002288</td>\n",
       "      <td>...</td>\n",
       "      <td>0.005842</td>\n",
       "      <td>0.006589</td>\n",
       "      <td>0.000141</td>\n",
       "      <td>0.001106</td>\n",
       "      <td>0.002677</td>\n",
       "      <td>0.000671</td>\n",
       "      <td>0.009283</td>\n",
       "      <td>0.023071</td>\n",
       "      <td>0.008629</td>\n",
       "      <td>0.001196</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>1.000000</td>\n",
       "      <td>0.010370</td>\n",
       "      <td>0.039117</td>\n",
       "      <td>0.006139</td>\n",
       "      <td>0.000465</td>\n",
       "      <td>0.041069</td>\n",
       "      <td>0.022649</td>\n",
       "      <td>0.001311</td>\n",
       "      <td>0.001810</td>\n",
       "      <td>...</td>\n",
       "      <td>0.004012</td>\n",
       "      <td>0.002414</td>\n",
       "      <td>0.000328</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>0.003630</td>\n",
       "      <td>0.018625</td>\n",
       "      <td>0.032595</td>\n",
       "      <td>0.001743</td>\n",
       "      <td>0.001293</td>\n",
       "      <td>0.000908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.022657</td>\n",
       "      <td>0.010370</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.148497</td>\n",
       "      <td>0.001131</td>\n",
       "      <td>0.000467</td>\n",
       "      <td>0.007500</td>\n",
       "      <td>0.020643</td>\n",
       "      <td>0.000207</td>\n",
       "      <td>0.000777</td>\n",
       "      <td>...</td>\n",
       "      <td>0.003683</td>\n",
       "      <td>0.002100</td>\n",
       "      <td>0.001233</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.003554</td>\n",
       "      <td>0.000851</td>\n",
       "      <td>0.002856</td>\n",
       "      <td>0.000950</td>\n",
       "      <td>0.001830</td>\n",
       "      <td>0.000185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.010941</td>\n",
       "      <td>0.039117</td>\n",
       "      <td>0.148497</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000827</td>\n",
       "      <td>0.000180</td>\n",
       "      <td>0.015579</td>\n",
       "      <td>0.012576</td>\n",
       "      <td>0.000171</td>\n",
       "      <td>0.000308</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002323</td>\n",
       "      <td>0.001750</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000103</td>\n",
       "      <td>0.001610</td>\n",
       "      <td>0.004674</td>\n",
       "      <td>0.003269</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>0.000449</td>\n",
       "      <td>0.000438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.023858</td>\n",
       "      <td>0.006139</td>\n",
       "      <td>0.001131</td>\n",
       "      <td>0.000827</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.044640</td>\n",
       "      <td>0.000736</td>\n",
       "      <td>0.000296</td>\n",
       "      <td>0.000516</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000475</td>\n",
       "      <td>0.000656</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.000366</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000925</td>\n",
       "      <td>0.002215</td>\n",
       "      <td>0.000280</td>\n",
       "      <td>0.000166</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>0.000671</td>\n",
       "      <td>0.018625</td>\n",
       "      <td>0.000851</td>\n",
       "      <td>0.004674</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>0.001356</td>\n",
       "      <td>0.000732</td>\n",
       "      <td>0.000360</td>\n",
       "      <td>0.000449</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000240</td>\n",
       "      <td>0.000071</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>0.010492</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.004482</td>\n",
       "      <td>0.000088</td>\n",
       "      <td>0.001573</td>\n",
       "      <td>0.000486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>0.009283</td>\n",
       "      <td>0.032595</td>\n",
       "      <td>0.002856</td>\n",
       "      <td>0.003269</td>\n",
       "      <td>0.000925</td>\n",
       "      <td>0.000093</td>\n",
       "      <td>0.002506</td>\n",
       "      <td>0.002536</td>\n",
       "      <td>0.000107</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001392</td>\n",
       "      <td>0.000755</td>\n",
       "      <td>0.000284</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.000761</td>\n",
       "      <td>0.004482</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.063521</td>\n",
       "      <td>0.002098</td>\n",
       "      <td>0.000148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>0.023071</td>\n",
       "      <td>0.001743</td>\n",
       "      <td>0.000950</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>0.002215</td>\n",
       "      <td>0.000108</td>\n",
       "      <td>0.000444</td>\n",
       "      <td>0.000282</td>\n",
       "      <td>0.000113</td>\n",
       "      <td>0.000012</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>0.000657</td>\n",
       "      <td>0.000266</td>\n",
       "      <td>0.000356</td>\n",
       "      <td>0.000125</td>\n",
       "      <td>0.000088</td>\n",
       "      <td>0.063521</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.005641</td>\n",
       "      <td>0.000317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>0.008629</td>\n",
       "      <td>0.001293</td>\n",
       "      <td>0.001830</td>\n",
       "      <td>0.000449</td>\n",
       "      <td>0.000280</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.000822</td>\n",
       "      <td>0.000533</td>\n",
       "      <td>0.000528</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000233</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000311</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>0.001937</td>\n",
       "      <td>0.001573</td>\n",
       "      <td>0.002098</td>\n",
       "      <td>0.005641</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.025604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>0.001196</td>\n",
       "      <td>0.000908</td>\n",
       "      <td>0.000185</td>\n",
       "      <td>0.000438</td>\n",
       "      <td>0.000166</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>0.000099</td>\n",
       "      <td>0.000044</td>\n",
       "      <td>0.000032</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000050</td>\n",
       "      <td>0.000034</td>\n",
       "      <td>0.000013</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>0.000113</td>\n",
       "      <td>0.000486</td>\n",
       "      <td>0.000148</td>\n",
       "      <td>0.000317</td>\n",
       "      <td>0.025604</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6    \\\n",
       "0    1.000000  0.055493  0.022657  0.010941  0.023858  0.001381  0.019208   \n",
       "1    0.055493  1.000000  0.010370  0.039117  0.006139  0.000465  0.041069   \n",
       "2    0.022657  0.010370  1.000000  0.148497  0.001131  0.000467  0.007500   \n",
       "3    0.010941  0.039117  0.148497  1.000000  0.000827  0.000180  0.015579   \n",
       "4    0.023858  0.006139  0.001131  0.000827  1.000000  0.044640  0.000736   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "495  0.000671  0.018625  0.000851  0.004674  0.000174  0.000017  0.001356   \n",
       "496  0.009283  0.032595  0.002856  0.003269  0.000925  0.000093  0.002506   \n",
       "497  0.023071  0.001743  0.000950  0.000312  0.002215  0.000108  0.000444   \n",
       "498  0.008629  0.001293  0.001830  0.000449  0.000280  0.000063  0.000822   \n",
       "499  0.001196  0.000908  0.000185  0.000438  0.000166  0.000011  0.000099   \n",
       "\n",
       "          7         8         9    ...       490       491       492  \\\n",
       "0    0.018695  0.003590  0.002288  ...  0.005842  0.006589  0.000141   \n",
       "1    0.022649  0.001311  0.001810  ...  0.004012  0.002414  0.000328   \n",
       "2    0.020643  0.000207  0.000777  ...  0.003683  0.002100  0.001233   \n",
       "3    0.012576  0.000171  0.000308  ...  0.002323  0.001750  0.000763   \n",
       "4    0.000296  0.000516  0.000201  ...  0.000475  0.000656  0.000011   \n",
       "..        ...       ...       ...  ...       ...       ...       ...   \n",
       "495  0.000732  0.000360  0.000449  ...  0.000240  0.000071  0.000094   \n",
       "496  0.002536  0.000107  0.000086  ...  0.001392  0.000755  0.000284   \n",
       "497  0.000282  0.000113  0.000012  ...  0.000244  0.000657  0.000266   \n",
       "498  0.000533  0.000528  0.000065  ...  0.000233  0.000053  0.000311   \n",
       "499  0.000044  0.000032  0.000010  ...  0.000050  0.000034  0.000013   \n",
       "\n",
       "          493       494       495       496       497       498       499  \n",
       "0    0.001106  0.002677  0.000671  0.009283  0.023071  0.008629  0.001196  \n",
       "1    0.000312  0.003630  0.018625  0.032595  0.001743  0.001293  0.000908  \n",
       "2    0.000027  0.003554  0.000851  0.002856  0.000950  0.001830  0.000185  \n",
       "3    0.000103  0.001610  0.004674  0.003269  0.000312  0.000449  0.000438  \n",
       "4    0.000029  0.000366  0.000174  0.000925  0.002215  0.000280  0.000166  \n",
       "..        ...       ...       ...       ...       ...       ...       ...  \n",
       "495  0.000007  0.010492  1.000000  0.004482  0.000088  0.001573  0.000486  \n",
       "496  0.000063  0.000761  0.004482  1.000000  0.063521  0.002098  0.000148  \n",
       "497  0.000356  0.000125  0.000088  0.063521  1.000000  0.005641  0.000317  \n",
       "498  0.000029  0.001937  0.001573  0.002098  0.005641  1.000000  0.025604  \n",
       "499  0.000010  0.000113  0.000486  0.000148  0.000317  0.025604  1.000000  \n",
       "\n",
       "[500 rows x 500 columns]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "afb23443",
   "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>count</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>...</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "      <td>5.000000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.007643</td>\n",
       "      <td>0.006147</td>\n",
       "      <td>3.770046e-03</td>\n",
       "      <td>0.003548</td>\n",
       "      <td>2.697924e-03</td>\n",
       "      <td>2.183755e-03</td>\n",
       "      <td>3.704658e-03</td>\n",
       "      <td>3.338726e-03</td>\n",
       "      <td>2.304868e-03</td>\n",
       "      <td>2.230997e-03</td>\n",
       "      <td>...</td>\n",
       "      <td>2.709166e-03</td>\n",
       "      <td>2.584722e-03</td>\n",
       "      <td>2.101332e-03</td>\n",
       "      <td>2.075025e-03</td>\n",
       "      <td>2.410592e-03</td>\n",
       "      <td>2.546248e-03</td>\n",
       "      <td>0.003263</td>\n",
       "      <td>2.703533e-03</td>\n",
       "      <td>2.663017e-03</td>\n",
       "      <td>2.204626e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.045408</td>\n",
       "      <td>0.045235</td>\n",
       "      <td>4.524165e-02</td>\n",
       "      <td>0.045228</td>\n",
       "      <td>4.477803e-02</td>\n",
       "      <td>4.475828e-02</td>\n",
       "      <td>4.509647e-02</td>\n",
       "      <td>4.504931e-02</td>\n",
       "      <td>4.471494e-02</td>\n",
       "      <td>4.471741e-02</td>\n",
       "      <td>...</td>\n",
       "      <td>4.511977e-02</td>\n",
       "      <td>4.512131e-02</td>\n",
       "      <td>4.471812e-02</td>\n",
       "      <td>4.471872e-02</td>\n",
       "      <td>4.471439e-02</td>\n",
       "      <td>4.472333e-02</td>\n",
       "      <td>0.044828</td>\n",
       "      <td>4.480229e-02</td>\n",
       "      <td>4.472082e-02</td>\n",
       "      <td>4.472793e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>3.973569e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>2.235932e-09</td>\n",
       "      <td>5.326324e-10</td>\n",
       "      <td>4.237044e-07</td>\n",
       "      <td>2.895562e-07</td>\n",
       "      <td>5.710573e-08</td>\n",
       "      <td>5.066626e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>8.128776e-08</td>\n",
       "      <td>7.879990e-08</td>\n",
       "      <td>1.669235e-08</td>\n",
       "      <td>7.191638e-10</td>\n",
       "      <td>1.044258e-07</td>\n",
       "      <td>3.388486e-08</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>1.476683e-07</td>\n",
       "      <td>1.552464e-07</td>\n",
       "      <td>2.762215e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000634</td>\n",
       "      <td>0.000366</td>\n",
       "      <td>1.072895e-04</td>\n",
       "      <td>0.000112</td>\n",
       "      <td>2.541412e-05</td>\n",
       "      <td>2.907894e-06</td>\n",
       "      <td>9.785189e-05</td>\n",
       "      <td>6.527118e-05</td>\n",
       "      <td>1.428376e-05</td>\n",
       "      <td>6.311115e-06</td>\n",
       "      <td>...</td>\n",
       "      <td>2.466922e-05</td>\n",
       "      <td>1.131402e-05</td>\n",
       "      <td>3.538816e-06</td>\n",
       "      <td>1.697858e-06</td>\n",
       "      <td>2.895548e-05</td>\n",
       "      <td>2.358221e-05</td>\n",
       "      <td>0.000085</td>\n",
       "      <td>4.782000e-05</td>\n",
       "      <td>6.271186e-05</td>\n",
       "      <td>7.060556e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.001964</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>4.584289e-04</td>\n",
       "      <td>0.000370</td>\n",
       "      <td>1.169568e-04</td>\n",
       "      <td>1.727896e-05</td>\n",
       "      <td>3.891686e-04</td>\n",
       "      <td>2.583178e-04</td>\n",
       "      <td>6.407775e-05</td>\n",
       "      <td>3.076068e-05</td>\n",
       "      <td>...</td>\n",
       "      <td>1.084518e-04</td>\n",
       "      <td>6.159171e-05</td>\n",
       "      <td>1.612817e-05</td>\n",
       "      <td>1.017123e-05</td>\n",
       "      <td>8.543799e-05</td>\n",
       "      <td>1.072869e-04</td>\n",
       "      <td>0.000309</td>\n",
       "      <td>1.496967e-04</td>\n",
       "      <td>2.077336e-04</td>\n",
       "      <td>3.549803e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.006859</td>\n",
       "      <td>0.003877</td>\n",
       "      <td>1.450206e-03</td>\n",
       "      <td>0.001215</td>\n",
       "      <td>4.568765e-04</td>\n",
       "      <td>7.682962e-05</td>\n",
       "      <td>1.143710e-03</td>\n",
       "      <td>9.197712e-04</td>\n",
       "      <td>2.296619e-04</td>\n",
       "      <td>1.510149e-04</td>\n",
       "      <td>...</td>\n",
       "      <td>3.359013e-04</td>\n",
       "      <td>2.424878e-04</td>\n",
       "      <td>7.155696e-05</td>\n",
       "      <td>4.269831e-05</td>\n",
       "      <td>3.452386e-04</td>\n",
       "      <td>4.224034e-04</td>\n",
       "      <td>0.001108</td>\n",
       "      <td>5.130982e-04</td>\n",
       "      <td>5.946243e-04</td>\n",
       "      <td>1.598879e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              0           1             2           3             4    \\\n",
       "count  500.000000  500.000000  5.000000e+02  500.000000  5.000000e+02   \n",
       "mean     0.007643    0.006147  3.770046e-03    0.003548  2.697924e-03   \n",
       "std      0.045408    0.045235  4.524165e-02    0.045228  4.477803e-02   \n",
       "min      0.000002    0.000004  3.973569e-07    0.000001  2.235932e-09   \n",
       "25%      0.000634    0.000366  1.072895e-04    0.000112  2.541412e-05   \n",
       "50%      0.001964    0.001200  4.584289e-04    0.000370  1.169568e-04   \n",
       "75%      0.006859    0.003877  1.450206e-03    0.001215  4.568765e-04   \n",
       "max      1.000000    1.000000  1.000000e+00    1.000000  1.000000e+00   \n",
       "\n",
       "                5             6             7             8             9    \\\n",
       "count  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean   2.183755e-03  3.704658e-03  3.338726e-03  2.304868e-03  2.230997e-03   \n",
       "std    4.475828e-02  4.509647e-02  4.504931e-02  4.471494e-02  4.471741e-02   \n",
       "min    5.326324e-10  4.237044e-07  2.895562e-07  5.710573e-08  5.066626e-09   \n",
       "25%    2.907894e-06  9.785189e-05  6.527118e-05  1.428376e-05  6.311115e-06   \n",
       "50%    1.727896e-05  3.891686e-04  2.583178e-04  6.407775e-05  3.076068e-05   \n",
       "75%    7.682962e-05  1.143710e-03  9.197712e-04  2.296619e-04  1.510149e-04   \n",
       "max    1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "\n",
       "       ...           490           491           492           493  \\\n",
       "count  ...  5.000000e+02  5.000000e+02  5.000000e+02  5.000000e+02   \n",
       "mean   ...  2.709166e-03  2.584722e-03  2.101332e-03  2.075025e-03   \n",
       "std    ...  4.511977e-02  4.512131e-02  4.471812e-02  4.471872e-02   \n",
       "min    ...  8.128776e-08  7.879990e-08  1.669235e-08  7.191638e-10   \n",
       "25%    ...  2.466922e-05  1.131402e-05  3.538816e-06  1.697858e-06   \n",
       "50%    ...  1.084518e-04  6.159171e-05  1.612817e-05  1.017123e-05   \n",
       "75%    ...  3.359013e-04  2.424878e-04  7.155696e-05  4.269831e-05   \n",
       "max    ...  1.000000e+00  1.000000e+00  1.000000e+00  1.000000e+00   \n",
       "\n",
       "                494           495         496           497           498  \\\n",
       "count  5.000000e+02  5.000000e+02  500.000000  5.000000e+02  5.000000e+02   \n",
       "mean   2.410592e-03  2.546248e-03    0.003263  2.703533e-03  2.663017e-03   \n",
       "std    4.471439e-02  4.472333e-02    0.044828  4.480229e-02  4.472082e-02   \n",
       "min    1.044258e-07  3.388486e-08    0.000001  1.476683e-07  1.552464e-07   \n",
       "25%    2.895548e-05  2.358221e-05    0.000085  4.782000e-05  6.271186e-05   \n",
       "50%    8.543799e-05  1.072869e-04    0.000309  1.496967e-04  2.077336e-04   \n",
       "75%    3.452386e-04  4.224034e-04    0.001108  5.130982e-04  5.946243e-04   \n",
       "max    1.000000e+00  1.000000e+00    1.000000  1.000000e+00  1.000000e+00   \n",
       "\n",
       "                499  \n",
       "count  5.000000e+02  \n",
       "mean   2.204626e-03  \n",
       "std    4.472793e-02  \n",
       "min    2.762215e-09  \n",
       "25%    7.060556e-06  \n",
       "50%    3.549803e-05  \n",
       "75%    1.598879e-04  \n",
       "max    1.000000e+00  \n",
       "\n",
       "[8 rows x 500 columns]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauss.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "87eaf79a",
   "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.hist(gaus)\n",
    "plt.title('Gaussian')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e91a7b6",
   "metadata": {},
   "source": [
    "## Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4ee641c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "offset = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "36fe6455",
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = gamma*x@x.T+offset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "57d824b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "powr = np.power(poly,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "6f155ffd",
   "metadata": {},
   "outputs": [],
   "source": [
    "fpoly = poly+powr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "34e55aa6",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.533255</td>\n",
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       "      <td>0.672923</td>\n",
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       "      <td>4.984201</td>\n",
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       "      <td>1.909614</td>\n",
       "      <td>-0.237873</td>\n",
       "      <td>0.547162</td>\n",
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       "      <td>0.967684</td>\n",
       "      <td>0.934251</td>\n",
       "      <td>1.840324</td>\n",
       "      <td>-0.224664</td>\n",
       "      <td>0.909287</td>\n",
       "      <td>-0.143556</td>\n",
       "      <td>-0.109270</td>\n",
       "      <td>-0.214616</td>\n",
       "      <td>-0.101340</td>\n",
       "      <td>-0.231838</td>\n",
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       "      <th>3</th>\n",
       "      <td>-0.206366</td>\n",
       "      <td>0.885464</td>\n",
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       "      <td>10.689947</td>\n",
       "      <td>-0.106959</td>\n",
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       "      <td>1.280023</td>\n",
       "      <td>1.408641</td>\n",
       "      <td>-0.230491</td>\n",
       "      <td>-0.004377</td>\n",
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       "      <td>0.632210</td>\n",
       "      <td>0.880358</td>\n",
       "      <td>1.368072</td>\n",
       "      <td>0.087751</td>\n",
       "      <td>0.307629</td>\n",
       "      <td>1.297646</td>\n",
       "      <td>0.008860</td>\n",
       "      <td>-0.158306</td>\n",
       "      <td>-0.186800</td>\n",
       "      <td>0.149452</td>\n",
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       "      <th>4</th>\n",
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       "      <td>0.326127</td>\n",
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       "      <td>-0.106959</td>\n",
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       "      <td>-0.248881</td>\n",
       "      <td>0.812521</td>\n",
       "      <td>0.564840</td>\n",
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       "      <td>0.335032</td>\n",
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       "      <td>1.403866</td>\n",
       "      <td>-0.150295</td>\n",
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       "      <th>496</th>\n",
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       "      <td>0.052766</td>\n",
       "      <td>-0.151658</td>\n",
       "      <td>-0.244207</td>\n",
       "      <td>...</td>\n",
       "      <td>0.306688</td>\n",
       "      <td>0.247962</td>\n",
       "      <td>0.456338</td>\n",
       "      <td>-0.092587</td>\n",
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       "      <td>-0.243683</td>\n",
       "      <td>0.261347</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.193322</td>\n",
       "      <td>0.749150</td>\n",
       "      <td>1.121428</td>\n",
       "      <td>2.404972</td>\n",
       "      <td>-0.239097</td>\n",
       "      <td>-0.150295</td>\n",
       "      <td>5.599791</td>\n",
       "      <td>17.058106</td>\n",
       "      <td>1.826202</td>\n",
       "      <td>0.553744</td>\n",
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       "      <th>498</th>\n",
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       "      <td>-0.101340</td>\n",
       "      <td>-0.186800</td>\n",
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       "      <td>-0.112630</td>\n",
       "      <td>-0.246199</td>\n",
       "      <td>-0.249991</td>\n",
       "      <td>0.267679</td>\n",
       "      <td>-0.249767</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.242588</td>\n",
       "      <td>-0.100797</td>\n",
       "      <td>1.000757</td>\n",
       "      <td>-0.190077</td>\n",
       "      <td>1.038517</td>\n",
       "      <td>0.741039</td>\n",
       "      <td>0.089764</td>\n",
       "      <td>1.826202</td>\n",
       "      <td>14.953919</td>\n",
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       "      <th>499</th>\n",
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       "      <td>0.337018</td>\n",
       "      <td>-0.092172</td>\n",
       "      <td>-0.239958</td>\n",
       "      <td>-0.125209</td>\n",
       "      <td>-0.202564</td>\n",
       "      <td>-0.249828</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.207065</td>\n",
       "      <td>-0.166177</td>\n",
       "      <td>-0.072425</td>\n",
       "      <td>0.142598</td>\n",
       "      <td>0.124385</td>\n",
       "      <td>1.449355</td>\n",
       "      <td>-0.226210</td>\n",
       "      <td>0.553744</td>\n",
       "      <td>8.525609</td>\n",
       "      <td>32.131939</td>\n",
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       "<p>500 rows × 500 columns</p>\n",
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       "          0         1         2          3          4          5         6    \\\n",
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       "1   -0.090487  4.013442 -0.137363   0.885464   0.326127  -0.042138  0.960484   \n",
       "2    0.006785 -0.137363  9.832566   4.984201  -0.030450   0.775249  0.398538   \n",
       "3   -0.206366  0.885464  4.984201  10.689947  -0.106959   0.113428  1.280023   \n",
       "4    1.233728  0.326127 -0.030450  -0.106959  20.419070  15.577496 -0.141089   \n",
       "..        ...       ...       ...        ...        ...        ...       ...   \n",
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       "499 -0.163871 -0.108850 -0.231838   0.149452   0.337018  -0.092172 -0.239958   \n",
       "\n",
       "          7         8         9    ...       490       491       492  \\\n",
       "0    0.166149  0.042278  0.182989  ...  0.062821  0.533255 -0.078902   \n",
       "1    0.672923 -0.184160  0.328234  ...  0.099317  0.113092 -0.197645   \n",
       "2    1.909614 -0.237873  0.547162  ...  0.967684  0.934251  1.840324   \n",
       "3    1.408641 -0.230491 -0.004377  ...  0.632210  0.880358  1.368072   \n",
       "4   -0.248881  0.812521  0.564840  ...  0.335032  1.171545 -0.192435   \n",
       "..        ...       ...       ...  ...       ...       ...       ...   \n",
       "495 -0.014668  0.475102  1.452110  ... -0.070567 -0.243773  0.466035   \n",
       "496  0.052766 -0.151658 -0.244207  ...  0.306688  0.247962  0.456338   \n",
       "497 -0.216059 -0.243683  0.261347  ... -0.193322  0.749150  1.121428   \n",
       "498 -0.249991  0.267679 -0.249767  ... -0.242588 -0.100797  1.000757   \n",
       "499 -0.125209 -0.202564 -0.249828  ... -0.207065 -0.166177 -0.072425   \n",
       "\n",
       "          493       494        495        496        497        498        499  \n",
       "0    0.613400 -0.224386   0.071685  -0.214038   0.766669  -0.100979  -0.163871  \n",
       "1    0.015649  0.032957   1.476431   0.825936  -0.245950  -0.132080  -0.108850  \n",
       "2   -0.224664  0.909287  -0.143556  -0.109270  -0.214616  -0.101340  -0.231838  \n",
       "3    0.087751  0.307629   1.297646   0.008860  -0.158306  -0.186800   0.149452  \n",
       "4    0.066294  0.141393  -0.201998  -0.002957   1.432516  -0.232379   0.337018  \n",
       "..        ...       ...        ...        ...        ...        ...        ...  \n",
       "495 -0.220440  5.055745  20.419208   1.403866  -0.150295   0.741039   1.449355  \n",
       "496 -0.092587 -0.060848   1.403866  11.537871   5.599791   0.089764  -0.226210  \n",
       "497  2.404972 -0.239097  -0.150295   5.599791  17.058106   1.826202   0.553744  \n",
       "498 -0.190077  1.038517   0.741039   0.089764   1.826202  14.953919   8.525609  \n",
       "499  0.142598  0.124385   1.449355  -0.226210   0.553744   8.525609  32.131939  \n",
       "\n",
       "[500 rows x 500 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "8a85e3f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>count</th>\n",
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       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
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       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
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       "      <td>500.000000</td>\n",
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       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
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       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.222011</td>\n",
       "      <td>0.227898</td>\n",
       "      <td>0.400904</td>\n",
       "      <td>0.318737</td>\n",
       "      <td>0.730339</td>\n",
       "      <td>0.949628</td>\n",
       "      <td>0.309966</td>\n",
       "      <td>0.365174</td>\n",
       "      <td>0.571772</td>\n",
       "      <td>1.014625</td>\n",
       "      <td>...</td>\n",
       "      <td>0.637679</td>\n",
       "      <td>0.844045</td>\n",
       "      <td>0.758871</td>\n",
       "      <td>1.125029</td>\n",
       "      <td>0.581580</td>\n",
       "      <td>0.721200</td>\n",
       "      <td>0.522925</td>\n",
       "      <td>0.578604</td>\n",
       "      <td>0.384093</td>\n",
       "      <td>0.728656</td>\n",
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       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.530682</td>\n",
       "      <td>0.585550</td>\n",
       "      <td>0.952406</td>\n",
       "      <td>0.824955</td>\n",
       "      <td>1.665588</td>\n",
       "      <td>2.395340</td>\n",
       "      <td>0.854970</td>\n",
       "      <td>0.942982</td>\n",
       "      <td>1.613761</td>\n",
       "      <td>2.165067</td>\n",
       "      <td>...</td>\n",
       "      <td>1.588066</td>\n",
       "      <td>1.951483</td>\n",
       "      <td>2.274054</td>\n",
       "      <td>2.904321</td>\n",
       "      <td>1.438850</td>\n",
       "      <td>1.526570</td>\n",
       "      <td>1.265990</td>\n",
       "      <td>1.337572</td>\n",
       "      <td>1.048933</td>\n",
       "      <td>1.923816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.249997</td>\n",
       "      <td>-0.249998</td>\n",
       "      <td>-0.249912</td>\n",
       "      <td>-0.249998</td>\n",
       "      <td>-0.249908</td>\n",
       "      <td>-0.249999</td>\n",
       "      <td>-0.249998</td>\n",
       "      <td>-0.249994</td>\n",
       "      <td>-0.250000</td>\n",
       "      <td>-0.250000</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.249992</td>\n",
       "      <td>-0.249999</td>\n",
       "      <td>-0.249996</td>\n",
       "      <td>-0.249998</td>\n",
       "      <td>-0.250000</td>\n",
       "      <td>-0.249996</td>\n",
       "      <td>-0.249998</td>\n",
       "      <td>-0.249994</td>\n",
       "      <td>-0.250000</td>\n",
       "      <td>-0.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.176779</td>\n",
       "      <td>-0.184469</td>\n",
       "      <td>-0.173881</td>\n",
       "      <td>-0.176964</td>\n",
       "      <td>-0.141147</td>\n",
       "      <td>-0.129112</td>\n",
       "      <td>-0.186116</td>\n",
       "      <td>-0.169173</td>\n",
       "      <td>-0.175927</td>\n",
       "      <td>-0.111915</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.153756</td>\n",
       "      <td>-0.115549</td>\n",
       "      <td>-0.162483</td>\n",
       "      <td>-0.130779</td>\n",
       "      <td>-0.182547</td>\n",
       "      <td>-0.165821</td>\n",
       "      <td>-0.179325</td>\n",
       "      <td>-0.158530</td>\n",
       "      <td>-0.181674</td>\n",
       "      <td>-0.153066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.017997</td>\n",
       "      <td>0.009263</td>\n",
       "      <td>0.032598</td>\n",
       "      <td>0.028375</td>\n",
       "      <td>0.204184</td>\n",
       "      <td>0.282699</td>\n",
       "      <td>0.023049</td>\n",
       "      <td>0.052997</td>\n",
       "      <td>0.079547</td>\n",
       "      <td>0.376883</td>\n",
       "      <td>...</td>\n",
       "      <td>0.147937</td>\n",
       "      <td>0.246634</td>\n",
       "      <td>0.190500</td>\n",
       "      <td>0.269738</td>\n",
       "      <td>0.091276</td>\n",
       "      <td>0.210233</td>\n",
       "      <td>0.091973</td>\n",
       "      <td>0.116188</td>\n",
       "      <td>0.069942</td>\n",
       "      <td>0.198612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.438795</td>\n",
       "      <td>0.495984</td>\n",
       "      <td>0.579916</td>\n",
       "      <td>0.513235</td>\n",
       "      <td>0.954651</td>\n",
       "      <td>1.343130</td>\n",
       "      <td>0.487042</td>\n",
       "      <td>0.527531</td>\n",
       "      <td>0.731709</td>\n",
       "      <td>1.326681</td>\n",
       "      <td>...</td>\n",
       "      <td>0.852241</td>\n",
       "      <td>1.133046</td>\n",
       "      <td>0.940777</td>\n",
       "      <td>1.385621</td>\n",
       "      <td>0.860188</td>\n",
       "      <td>1.014257</td>\n",
       "      <td>0.746480</td>\n",
       "      <td>0.784059</td>\n",
       "      <td>0.615388</td>\n",
       "      <td>0.847324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.624813</td>\n",
       "      <td>4.015095</td>\n",
       "      <td>9.832566</td>\n",
       "      <td>10.689947</td>\n",
       "      <td>20.419070</td>\n",
       "      <td>42.254721</td>\n",
       "      <td>10.826448</td>\n",
       "      <td>13.030235</td>\n",
       "      <td>25.612084</td>\n",
       "      <td>33.048951</td>\n",
       "      <td>...</td>\n",
       "      <td>21.240230</td>\n",
       "      <td>26.447141</td>\n",
       "      <td>40.891832</td>\n",
       "      <td>49.311418</td>\n",
       "      <td>21.073020</td>\n",
       "      <td>20.419208</td>\n",
       "      <td>11.537871</td>\n",
       "      <td>17.058106</td>\n",
       "      <td>14.953919</td>\n",
       "      <td>32.131939</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              0           1           2           3           4           5    \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean     0.222011    0.227898    0.400904    0.318737    0.730339    0.949628   \n",
       "std      0.530682    0.585550    0.952406    0.824955    1.665588    2.395340   \n",
       "min     -0.249997   -0.249998   -0.249912   -0.249998   -0.249908   -0.249999   \n",
       "25%     -0.176779   -0.184469   -0.173881   -0.176964   -0.141147   -0.129112   \n",
       "50%      0.017997    0.009263    0.032598    0.028375    0.204184    0.282699   \n",
       "75%      0.438795    0.495984    0.579916    0.513235    0.954651    1.343130   \n",
       "max      3.624813    4.015095    9.832566   10.689947   20.419070   42.254721   \n",
       "\n",
       "              6           7           8           9    ...         490  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  ...  500.000000   \n",
       "mean     0.309966    0.365174    0.571772    1.014625  ...    0.637679   \n",
       "std      0.854970    0.942982    1.613761    2.165067  ...    1.588066   \n",
       "min     -0.249998   -0.249994   -0.250000   -0.250000  ...   -0.249992   \n",
       "25%     -0.186116   -0.169173   -0.175927   -0.111915  ...   -0.153756   \n",
       "50%      0.023049    0.052997    0.079547    0.376883  ...    0.147937   \n",
       "75%      0.487042    0.527531    0.731709    1.326681  ...    0.852241   \n",
       "max     10.826448   13.030235   25.612084   33.048951  ...   21.240230   \n",
       "\n",
       "              491         492         493         494         495         496  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean     0.844045    0.758871    1.125029    0.581580    0.721200    0.522925   \n",
       "std      1.951483    2.274054    2.904321    1.438850    1.526570    1.265990   \n",
       "min     -0.249999   -0.249996   -0.249998   -0.250000   -0.249996   -0.249998   \n",
       "25%     -0.115549   -0.162483   -0.130779   -0.182547   -0.165821   -0.179325   \n",
       "50%      0.246634    0.190500    0.269738    0.091276    0.210233    0.091973   \n",
       "75%      1.133046    0.940777    1.385621    0.860188    1.014257    0.746480   \n",
       "max     26.447141   40.891832   49.311418   21.073020   20.419208   11.537871   \n",
       "\n",
       "              497         498         499  \n",
       "count  500.000000  500.000000  500.000000  \n",
       "mean     0.578604    0.384093    0.728656  \n",
       "std      1.337572    1.048933    1.923816  \n",
       "min     -0.249994   -0.250000   -0.250000  \n",
       "25%     -0.158530   -0.181674   -0.153066  \n",
       "50%      0.116188    0.069942    0.198612  \n",
       "75%      0.784059    0.615388    0.847324  \n",
       "max     17.058106   14.953919   32.131939  \n",
       "\n",
       "[8 rows x 500 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d678d819",
   "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.hist(fpoly)\n",
    "plt.title('Ploynomial')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fbdcc67",
   "metadata": {},
   "source": [
    "## Sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "36386e13",
   "metadata": {},
   "outputs": [],
   "source": [
    "sig = gamma*x@x.T+offset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "bec622c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "fsig = np.tanh(sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "b99ed827",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\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>490</th>\n",
       "      <th>491</th>\n",
       "      <th>492</th>\n",
       "      <th>493</th>\n",
       "      <th>494</th>\n",
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       "      <th>497</th>\n",
       "      <th>498</th>\n",
       "      <th>499</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>0.006740</td>\n",
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       "      <td>0.615721</td>\n",
       "      <td>0.272997</td>\n",
       "      <td>0.000570</td>\n",
       "      <td>0.144087</td>\n",
       "      <td>0.040605</td>\n",
       "      <td>0.156717</td>\n",
       "      <td>...</td>\n",
       "      <td>0.059234</td>\n",
       "      <td>0.367057</td>\n",
       "      <td>-0.722874</td>\n",
       "      <td>0.404647</td>\n",
       "      <td>-0.327437</td>\n",
       "      <td>-0.788394</td>\n",
       "      <td>-0.300769</td>\n",
       "      <td>0.468619</td>\n",
       "      <td>-0.113477</td>\n",
       "      <td>-0.203635</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.100272</td>\n",
       "      <td>0.916196</td>\n",
       "      <td>-0.162920</td>\n",
       "      <td>0.512107</td>\n",
       "      <td>0.253388</td>\n",
       "      <td>-0.044053</td>\n",
       "      <td>0.537206</td>\n",
       "      <td>0.430646</td>\n",
       "      <td>-0.238711</td>\n",
       "      <td>0.254685</td>\n",
       "      <td>...</td>\n",
       "      <td>0.090780</td>\n",
       "      <td>0.102213</td>\n",
       "      <td>-0.264729</td>\n",
       "      <td>0.015411</td>\n",
       "      <td>0.031926</td>\n",
       "      <td>0.671757</td>\n",
       "      <td>0.490921</td>\n",
       "      <td>-0.510675</td>\n",
       "      <td>-0.687603</td>\n",
       "      <td>-0.123664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.006740</td>\n",
       "      <td>-0.162920</td>\n",
       "      <td>0.990554</td>\n",
       "      <td>0.945532</td>\n",
       "      <td>-0.031428</td>\n",
       "      <td>0.471926</td>\n",
       "      <td>0.296172</td>\n",
       "      <td>0.748512</td>\n",
       "      <td>-0.544213</td>\n",
       "      <td>0.373805</td>\n",
       "      <td>...</td>\n",
       "      <td>0.539526</td>\n",
       "      <td>0.528624</td>\n",
       "      <td>0.737874</td>\n",
       "      <td>-0.577813</td>\n",
       "      <td>0.520264</td>\n",
       "      <td>-0.172015</td>\n",
       "      <td>-0.124215</td>\n",
       "      <td>-0.302158</td>\n",
       "      <td>-0.113939</td>\n",
       "      <td>-0.349816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.283159</td>\n",
       "      <td>0.512107</td>\n",
       "      <td>0.945532</td>\n",
       "      <td>0.992742</td>\n",
       "      <td>-0.121193</td>\n",
       "      <td>0.102489</td>\n",
       "      <td>0.627293</td>\n",
       "      <td>0.657208</td>\n",
       "      <td>-0.564678</td>\n",
       "      <td>-0.004397</td>\n",
       "      <td>...</td>\n",
       "      <td>0.413031</td>\n",
       "      <td>0.510335</td>\n",
       "      <td>0.648111</td>\n",
       "      <td>0.080985</td>\n",
       "      <td>0.241857</td>\n",
       "      <td>0.631582</td>\n",
       "      <td>0.008782</td>\n",
       "      <td>-0.665605</td>\n",
       "      <td>-0.635981</td>\n",
       "      <td>0.131260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.615721</td>\n",
       "      <td>0.253388</td>\n",
       "      <td>-0.031428</td>\n",
       "      <td>-0.121193</td>\n",
       "      <td>0.999389</td>\n",
       "      <td>0.998097</td>\n",
       "      <td>-0.168364</td>\n",
       "      <td>-0.435406</td>\n",
       "      <td>0.485982</td>\n",
       "      <td>0.382244</td>\n",
       "      <td>...</td>\n",
       "      <td>0.258848</td>\n",
       "      <td>0.599448</td>\n",
       "      <td>-0.629101</td>\n",
       "      <td>0.062319</td>\n",
       "      <td>0.124958</td>\n",
       "      <td>-0.273745</td>\n",
       "      <td>-0.002966</td>\n",
       "      <td>0.662423</td>\n",
       "      <td>-0.351588</td>\n",
       "      <td>0.260059</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",
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       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>-0.788394</td>\n",
       "      <td>0.671757</td>\n",
       "      <td>-0.172015</td>\n",
       "      <td>0.631582</td>\n",
       "      <td>-0.273745</td>\n",
       "      <td>-0.438094</td>\n",
       "      <td>0.134690</td>\n",
       "      <td>-0.014888</td>\n",
       "      <td>0.337731</td>\n",
       "      <td>0.666628</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.076256</td>\n",
       "      <td>-0.397848</td>\n",
       "      <td>0.332991</td>\n",
       "      <td>-0.586249</td>\n",
       "      <td>0.947159</td>\n",
       "      <td>0.999389</td>\n",
       "      <td>0.656153</td>\n",
       "      <td>-0.672756</td>\n",
       "      <td>0.458578</td>\n",
       "      <td>0.666041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>-0.300769</td>\n",
       "      <td>0.490921</td>\n",
       "      <td>-0.124215</td>\n",
       "      <td>0.008782</td>\n",
       "      <td>-0.002966</td>\n",
       "      <td>-0.161926</td>\n",
       "      <td>-0.113235</td>\n",
       "      <td>0.050199</td>\n",
       "      <td>-0.671569</td>\n",
       "      <td>-0.519835</td>\n",
       "      <td>...</td>\n",
       "      <td>0.241263</td>\n",
       "      <td>0.202812</td>\n",
       "      <td>0.327869</td>\n",
       "      <td>-0.102882</td>\n",
       "      <td>-0.064992</td>\n",
       "      <td>0.656153</td>\n",
       "      <td>0.994352</td>\n",
       "      <td>0.957805</td>\n",
       "      <td>0.082703</td>\n",
       "      <td>-0.332609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>0.468619</td>\n",
       "      <td>-0.510675</td>\n",
       "      <td>-0.302158</td>\n",
       "      <td>-0.665605</td>\n",
       "      <td>0.662423</td>\n",
       "      <td>0.264910</td>\n",
       "      <td>-0.548049</td>\n",
       "      <td>-0.594264</td>\n",
       "      <td>-0.397367</td>\n",
       "      <td>-0.838198</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.256098</td>\n",
       "      <td>0.461783</td>\n",
       "      <td>0.585690</td>\n",
       "      <td>0.810817</td>\n",
       "      <td>-0.540185</td>\n",
       "      <td>-0.672756</td>\n",
       "      <td>0.957805</td>\n",
       "      <td>0.998677</td>\n",
       "      <td>0.735637</td>\n",
       "      <td>0.376966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>-0.113477</td>\n",
       "      <td>-0.687603</td>\n",
       "      <td>-0.113939</td>\n",
       "      <td>-0.635981</td>\n",
       "      <td>-0.351588</td>\n",
       "      <td>-0.128649</td>\n",
       "      <td>-0.412273</td>\n",
       "      <td>-0.459721</td>\n",
       "      <td>0.216040</td>\n",
       "      <td>-0.450016</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.391786</td>\n",
       "      <td>-0.709546</td>\n",
       "      <td>0.549994</td>\n",
       "      <td>-0.249809</td>\n",
       "      <td>0.561574</td>\n",
       "      <td>0.458578</td>\n",
       "      <td>0.082703</td>\n",
       "      <td>0.735637</td>\n",
       "      <td>0.997771</td>\n",
       "      <td>0.985575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>-0.203635</td>\n",
       "      <td>-0.123664</td>\n",
       "      <td>-0.349816</td>\n",
       "      <td>0.131260</td>\n",
       "      <td>0.260059</td>\n",
       "      <td>-0.102364</td>\n",
       "      <td>-0.537199</td>\n",
       "      <td>-0.692767</td>\n",
       "      <td>-0.274941</td>\n",
       "      <td>-0.472360</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.284703</td>\n",
       "      <td>-0.207424</td>\n",
       "      <td>-0.078442</td>\n",
       "      <td>0.125905</td>\n",
       "      <td>0.111406</td>\n",
       "      <td>0.666041</td>\n",
       "      <td>-0.332609</td>\n",
       "      <td>0.376966</td>\n",
       "      <td>0.985575</td>\n",
       "      <td>0.999938</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6    \\\n",
       "0    0.809461 -0.100272  0.006740 -0.283159  0.615721  0.272997  0.000570   \n",
       "1   -0.100272  0.916196 -0.162920  0.512107  0.253388 -0.044053  0.537206   \n",
       "2    0.006740 -0.162920  0.990554  0.945532 -0.031428  0.471926  0.296172   \n",
       "3   -0.283159  0.512107  0.945532  0.992742 -0.121193  0.102489  0.627293   \n",
       "4    0.615721  0.253388 -0.031428 -0.121193  0.999389  0.998097 -0.168364   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "495 -0.788394  0.671757 -0.172015  0.631582 -0.273745 -0.438094  0.134690   \n",
       "496 -0.300769  0.490921 -0.124215  0.008782 -0.002966 -0.161926 -0.113235   \n",
       "497  0.468619 -0.510675 -0.302158 -0.665605  0.662423  0.264910 -0.548049   \n",
       "498 -0.113477 -0.687603 -0.113939 -0.635981 -0.351588 -0.128649 -0.412273   \n",
       "499 -0.203635 -0.123664 -0.349816  0.131260  0.260059 -0.102364 -0.537199   \n",
       "\n",
       "          7         8         9    ...       490       491       492  \\\n",
       "0    0.144087  0.040605  0.156717  ...  0.059234  0.367057 -0.722874   \n",
       "1    0.430646 -0.238711  0.254685  ...  0.090780  0.102213 -0.264729   \n",
       "2    0.748512 -0.544213  0.373805  ...  0.539526  0.528624  0.737874   \n",
       "3    0.657208 -0.564678 -0.004397  ...  0.413031  0.510335  0.648111   \n",
       "4   -0.435406  0.485982  0.382244  ...  0.258848  0.599448 -0.629101   \n",
       "..        ...       ...       ...  ...       ...       ...       ...   \n",
       "495 -0.014888  0.337731  0.666628  ... -0.076256 -0.397848  0.332991   \n",
       "496  0.050199 -0.671569 -0.519835  ...  0.241263  0.202812  0.327869   \n",
       "497 -0.594264 -0.397367 -0.838198  ... -0.256098  0.461783  0.585690   \n",
       "498 -0.459721  0.216040 -0.450016  ... -0.391786 -0.709546  0.549994   \n",
       "499 -0.692767 -0.274941 -0.472360  ... -0.284703 -0.207424 -0.078442   \n",
       "\n",
       "          493       494       495       496       497       498       499  \n",
       "0    0.404647 -0.327437 -0.788394 -0.300769  0.468619 -0.113477 -0.203635  \n",
       "1    0.015411  0.031926  0.671757  0.490921 -0.510675 -0.687603 -0.123664  \n",
       "2   -0.577813  0.520264 -0.172015 -0.124215 -0.302158 -0.113939 -0.349816  \n",
       "3    0.080985  0.241857  0.631582  0.008782 -0.665605 -0.635981  0.131260  \n",
       "4    0.062319  0.124958 -0.273745 -0.002966  0.662423 -0.351588  0.260059  \n",
       "..        ...       ...       ...       ...       ...       ...       ...  \n",
       "495 -0.586249  0.947159  0.999389  0.656153 -0.672756  0.458578  0.666041  \n",
       "496 -0.102882 -0.064992  0.656153  0.994352  0.957805  0.082703 -0.332609  \n",
       "497  0.810817 -0.540185 -0.672756  0.957805  0.998677  0.735637  0.376966  \n",
       "498 -0.249809  0.561574  0.458578  0.082703  0.735637  0.997771  0.985575  \n",
       "499  0.125905  0.111406  0.666041 -0.332609  0.376966  0.985575  0.999938  \n",
       "\n",
       "[500 rows x 500 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fsig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "11cd8680",
   "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",
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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>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>count</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.003731</td>\n",
       "      <td>-0.000365</td>\n",
       "      <td>-0.005999</td>\n",
       "      <td>-0.002587</td>\n",
       "      <td>0.000425</td>\n",
       "      <td>0.002289</td>\n",
       "      <td>-0.005517</td>\n",
       "      <td>-0.001081</td>\n",
       "      <td>-0.016101</td>\n",
       "      <td>-0.005375</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000614</td>\n",
       "      <td>-0.002959</td>\n",
       "      <td>-0.011315</td>\n",
       "      <td>-0.013321</td>\n",
       "      <td>-0.009317</td>\n",
       "      <td>-0.003756</td>\n",
       "      <td>-0.009283</td>\n",
       "      <td>-0.002067</td>\n",
       "      <td>-0.003130</td>\n",
       "      <td>-0.005893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.399509</td>\n",
       "      <td>0.402509</td>\n",
       "      <td>0.483539</td>\n",
       "      <td>0.452010</td>\n",
       "      <td>0.565446</td>\n",
       "      <td>0.610792</td>\n",
       "      <td>0.442541</td>\n",
       "      <td>0.464827</td>\n",
       "      <td>0.529995</td>\n",
       "      <td>0.632379</td>\n",
       "      <td>...</td>\n",
       "      <td>0.540321</td>\n",
       "      <td>0.590600</td>\n",
       "      <td>0.569476</td>\n",
       "      <td>0.622941</td>\n",
       "      <td>0.538040</td>\n",
       "      <td>0.573844</td>\n",
       "      <td>0.518277</td>\n",
       "      <td>0.532513</td>\n",
       "      <td>0.476441</td>\n",
       "      <td>0.564447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.919171</td>\n",
       "      <td>-0.933823</td>\n",
       "      <td>-0.927879</td>\n",
       "      <td>-0.910434</td>\n",
       "      <td>-0.997954</td>\n",
       "      <td>-0.996497</td>\n",
       "      <td>-0.913039</td>\n",
       "      <td>-0.956208</td>\n",
       "      <td>-0.947848</td>\n",
       "      <td>-0.993224</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.986748</td>\n",
       "      <td>-0.980047</td>\n",
       "      <td>-0.985758</td>\n",
       "      <td>-0.998409</td>\n",
       "      <td>-0.984460</td>\n",
       "      <td>-0.986721</td>\n",
       "      <td>-0.962365</td>\n",
       "      <td>-0.987682</td>\n",
       "      <td>-0.961530</td>\n",
       "      <td>-0.995823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.292080</td>\n",
       "      <td>-0.296598</td>\n",
       "      <td>-0.377342</td>\n",
       "      <td>-0.371615</td>\n",
       "      <td>-0.491926</td>\n",
       "      <td>-0.522809</td>\n",
       "      <td>-0.337314</td>\n",
       "      <td>-0.373304</td>\n",
       "      <td>-0.466646</td>\n",
       "      <td>-0.617025</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.454631</td>\n",
       "      <td>-0.558275</td>\n",
       "      <td>-0.507184</td>\n",
       "      <td>-0.587363</td>\n",
       "      <td>-0.449954</td>\n",
       "      <td>-0.482523</td>\n",
       "      <td>-0.438126</td>\n",
       "      <td>-0.483698</td>\n",
       "      <td>-0.400250</td>\n",
       "      <td>-0.506898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000533</td>\n",
       "      <td>-0.014135</td>\n",
       "      <td>-0.025233</td>\n",
       "      <td>-0.000862</td>\n",
       "      <td>0.004627</td>\n",
       "      <td>0.010810</td>\n",
       "      <td>-0.018127</td>\n",
       "      <td>0.009188</td>\n",
       "      <td>-0.032489</td>\n",
       "      <td>0.024424</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001678</td>\n",
       "      <td>0.039944</td>\n",
       "      <td>-0.042011</td>\n",
       "      <td>-0.013086</td>\n",
       "      <td>-0.046452</td>\n",
       "      <td>-0.053169</td>\n",
       "      <td>-0.008582</td>\n",
       "      <td>0.032032</td>\n",
       "      <td>-0.000434</td>\n",
       "      <td>0.005842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.310570</td>\n",
       "      <td>0.344988</td>\n",
       "      <td>0.375059</td>\n",
       "      <td>0.350676</td>\n",
       "      <td>0.480157</td>\n",
       "      <td>0.581782</td>\n",
       "      <td>0.343180</td>\n",
       "      <td>0.347738</td>\n",
       "      <td>0.429673</td>\n",
       "      <td>0.575096</td>\n",
       "      <td>...</td>\n",
       "      <td>0.449633</td>\n",
       "      <td>0.512463</td>\n",
       "      <td>0.492464</td>\n",
       "      <td>0.516000</td>\n",
       "      <td>0.460726</td>\n",
       "      <td>0.513717</td>\n",
       "      <td>0.425810</td>\n",
       "      <td>0.430388</td>\n",
       "      <td>0.398487</td>\n",
       "      <td>0.439952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.899282</td>\n",
       "      <td>0.916261</td>\n",
       "      <td>0.990554</td>\n",
       "      <td>0.992742</td>\n",
       "      <td>0.999389</td>\n",
       "      <td>0.999988</td>\n",
       "      <td>0.993033</td>\n",
       "      <td>0.996291</td>\n",
       "      <td>0.999792</td>\n",
       "      <td>0.999947</td>\n",
       "      <td>...</td>\n",
       "      <td>0.999489</td>\n",
       "      <td>0.999823</td>\n",
       "      <td>0.999985</td>\n",
       "      <td>0.999996</td>\n",
       "      <td>0.999470</td>\n",
       "      <td>0.999389</td>\n",
       "      <td>0.994352</td>\n",
       "      <td>0.998677</td>\n",
       "      <td>0.997771</td>\n",
       "      <td>0.999938</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              0           1           2           3           4           5    \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean     0.003731   -0.000365   -0.005999   -0.002587    0.000425    0.002289   \n",
       "std      0.399509    0.402509    0.483539    0.452010    0.565446    0.610792   \n",
       "min     -0.919171   -0.933823   -0.927879   -0.910434   -0.997954   -0.996497   \n",
       "25%     -0.292080   -0.296598   -0.377342   -0.371615   -0.491926   -0.522809   \n",
       "50%      0.000533   -0.014135   -0.025233   -0.000862    0.004627    0.010810   \n",
       "75%      0.310570    0.344988    0.375059    0.350676    0.480157    0.581782   \n",
       "max      0.899282    0.916261    0.990554    0.992742    0.999389    0.999988   \n",
       "\n",
       "              6           7           8           9    ...         490  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  ...  500.000000   \n",
       "mean    -0.005517   -0.001081   -0.016101   -0.005375  ...    0.000614   \n",
       "std      0.442541    0.464827    0.529995    0.632379  ...    0.540321   \n",
       "min     -0.913039   -0.956208   -0.947848   -0.993224  ...   -0.986748   \n",
       "25%     -0.337314   -0.373304   -0.466646   -0.617025  ...   -0.454631   \n",
       "50%     -0.018127    0.009188   -0.032489    0.024424  ...   -0.001678   \n",
       "75%      0.343180    0.347738    0.429673    0.575096  ...    0.449633   \n",
       "max      0.993033    0.996291    0.999792    0.999947  ...    0.999489   \n",
       "\n",
       "              491         492         493         494         495         496  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean    -0.002959   -0.011315   -0.013321   -0.009317   -0.003756   -0.009283   \n",
       "std      0.590600    0.569476    0.622941    0.538040    0.573844    0.518277   \n",
       "min     -0.980047   -0.985758   -0.998409   -0.984460   -0.986721   -0.962365   \n",
       "25%     -0.558275   -0.507184   -0.587363   -0.449954   -0.482523   -0.438126   \n",
       "50%      0.039944   -0.042011   -0.013086   -0.046452   -0.053169   -0.008582   \n",
       "75%      0.512463    0.492464    0.516000    0.460726    0.513717    0.425810   \n",
       "max      0.999823    0.999985    0.999996    0.999470    0.999389    0.994352   \n",
       "\n",
       "              497         498         499  \n",
       "count  500.000000  500.000000  500.000000  \n",
       "mean    -0.002067   -0.003130   -0.005893  \n",
       "std      0.532513    0.476441    0.564447  \n",
       "min     -0.987682   -0.961530   -0.995823  \n",
       "25%     -0.483698   -0.400250   -0.506898  \n",
       "50%      0.032032   -0.000434    0.005842  \n",
       "75%      0.430388    0.398487    0.439952  \n",
       "max      0.998677    0.997771    0.999938  \n",
       "\n",
       "[8 rows x 500 columns]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fsig.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4ec4b66c",
   "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.hist(fsig)\n",
    "plt.title('Sigmoid')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01bafa9b",
   "metadata": {},
   "source": [
    "## Laplacian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "bb212550",
   "metadata": {},
   "outputs": [],
   "source": [
    "pdist_lap = pairwise_distances(x, x, metric='cityblock')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4d6c19be",
   "metadata": {},
   "outputs": [],
   "source": [
    "lap = np.exp(-gamma*pdist_lap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "43bdf363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.12385963, 0.04270939, ..., 0.02676804, 0.02127469,\n",
       "        0.01226559],\n",
       "       [0.12385963, 1.        , 0.04111156, ..., 0.00918331, 0.00989429,\n",
       "        0.01388459],\n",
       "       [0.04270939, 0.04111156, 1.        , ..., 0.00814666, 0.00979866,\n",
       "        0.00472473],\n",
       "       ...,\n",
       "       [0.02676804, 0.00918331, 0.00814666, ..., 1.        , 0.02491408,\n",
       "        0.00782337],\n",
       "       [0.02127469, 0.00989429, 0.00979866, ..., 0.02491408, 1.        ,\n",
       "        0.09064378],\n",
       "       [0.01226559, 0.01388459, 0.00472473, ..., 0.00782337, 0.09064378,\n",
       "        1.        ]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "709f9682",
   "metadata": {},
   "outputs": [],
   "source": [
    "lapc = pd.DataFrame(lap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "319efb95",
   "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>count</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.015349</td>\n",
       "      <td>0.013499</td>\n",
       "      <td>0.010068</td>\n",
       "      <td>0.009632</td>\n",
       "      <td>0.007772</td>\n",
       "      <td>0.005336</td>\n",
       "      <td>0.009788</td>\n",
       "      <td>0.009057</td>\n",
       "      <td>0.006531</td>\n",
       "      <td>0.005760</td>\n",
       "      <td>...</td>\n",
       "      <td>0.006997</td>\n",
       "      <td>0.006444</td>\n",
       "      <td>0.005039</td>\n",
       "      <td>0.004592</td>\n",
       "      <td>0.006661</td>\n",
       "      <td>0.006687</td>\n",
       "      <td>0.008961</td>\n",
       "      <td>0.007559</td>\n",
       "      <td>0.007845</td>\n",
       "      <td>0.005677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.045332</td>\n",
       "      <td>0.045302</td>\n",
       "      <td>0.045405</td>\n",
       "      <td>0.045392</td>\n",
       "      <td>0.044881</td>\n",
       "      <td>0.044821</td>\n",
       "      <td>0.045187</td>\n",
       "      <td>0.045136</td>\n",
       "      <td>0.044722</td>\n",
       "      <td>0.044748</td>\n",
       "      <td>...</td>\n",
       "      <td>0.045108</td>\n",
       "      <td>0.045104</td>\n",
       "      <td>0.044664</td>\n",
       "      <td>0.044673</td>\n",
       "      <td>0.044665</td>\n",
       "      <td>0.044674</td>\n",
       "      <td>0.044872</td>\n",
       "      <td>0.044834</td>\n",
       "      <td>0.044770</td>\n",
       "      <td>0.044790</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.001116</td>\n",
       "      <td>0.001134</td>\n",
       "      <td>0.000735</td>\n",
       "      <td>0.000913</td>\n",
       "      <td>0.000261</td>\n",
       "      <td>0.000271</td>\n",
       "      <td>0.001019</td>\n",
       "      <td>0.000809</td>\n",
       "      <td>0.000359</td>\n",
       "      <td>0.000273</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000323</td>\n",
       "      <td>0.000373</td>\n",
       "      <td>0.000372</td>\n",
       "      <td>0.000203</td>\n",
       "      <td>0.000526</td>\n",
       "      <td>0.000354</td>\n",
       "      <td>0.001000</td>\n",
       "      <td>0.000649</td>\n",
       "      <td>0.000598</td>\n",
       "      <td>0.000282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.006919</td>\n",
       "      <td>0.005758</td>\n",
       "      <td>0.003911</td>\n",
       "      <td>0.003840</td>\n",
       "      <td>0.002560</td>\n",
       "      <td>0.001458</td>\n",
       "      <td>0.003855</td>\n",
       "      <td>0.003445</td>\n",
       "      <td>0.002171</td>\n",
       "      <td>0.001688</td>\n",
       "      <td>...</td>\n",
       "      <td>0.002450</td>\n",
       "      <td>0.002014</td>\n",
       "      <td>0.001488</td>\n",
       "      <td>0.001266</td>\n",
       "      <td>0.002555</td>\n",
       "      <td>0.002279</td>\n",
       "      <td>0.003457</td>\n",
       "      <td>0.002824</td>\n",
       "      <td>0.003248</td>\n",
       "      <td>0.001853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.010391</td>\n",
       "      <td>0.008897</td>\n",
       "      <td>0.006302</td>\n",
       "      <td>0.005868</td>\n",
       "      <td>0.004514</td>\n",
       "      <td>0.002463</td>\n",
       "      <td>0.006016</td>\n",
       "      <td>0.005261</td>\n",
       "      <td>0.003593</td>\n",
       "      <td>0.002764</td>\n",
       "      <td>...</td>\n",
       "      <td>0.003850</td>\n",
       "      <td>0.003267</td>\n",
       "      <td>0.002453</td>\n",
       "      <td>0.002095</td>\n",
       "      <td>0.003671</td>\n",
       "      <td>0.003709</td>\n",
       "      <td>0.005440</td>\n",
       "      <td>0.004367</td>\n",
       "      <td>0.004845</td>\n",
       "      <td>0.002965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.017569</td>\n",
       "      <td>0.014048</td>\n",
       "      <td>0.009938</td>\n",
       "      <td>0.009462</td>\n",
       "      <td>0.007233</td>\n",
       "      <td>0.004259</td>\n",
       "      <td>0.009410</td>\n",
       "      <td>0.008770</td>\n",
       "      <td>0.005695</td>\n",
       "      <td>0.004673</td>\n",
       "      <td>...</td>\n",
       "      <td>0.005923</td>\n",
       "      <td>0.005745</td>\n",
       "      <td>0.003767</td>\n",
       "      <td>0.003303</td>\n",
       "      <td>0.005581</td>\n",
       "      <td>0.005990</td>\n",
       "      <td>0.008572</td>\n",
       "      <td>0.006820</td>\n",
       "      <td>0.007098</td>\n",
       "      <td>0.004469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              0           1           2           3           4           5    \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean     0.015349    0.013499    0.010068    0.009632    0.007772    0.005336   \n",
       "std      0.045332    0.045302    0.045405    0.045392    0.044881    0.044821   \n",
       "min      0.001116    0.001134    0.000735    0.000913    0.000261    0.000271   \n",
       "25%      0.006919    0.005758    0.003911    0.003840    0.002560    0.001458   \n",
       "50%      0.010391    0.008897    0.006302    0.005868    0.004514    0.002463   \n",
       "75%      0.017569    0.014048    0.009938    0.009462    0.007233    0.004259   \n",
       "max      1.000000    1.000000    1.000000    1.000000    1.000000    1.000000   \n",
       "\n",
       "              6           7           8           9    ...         490  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  ...  500.000000   \n",
       "mean     0.009788    0.009057    0.006531    0.005760  ...    0.006997   \n",
       "std      0.045187    0.045136    0.044722    0.044748  ...    0.045108   \n",
       "min      0.001019    0.000809    0.000359    0.000273  ...    0.000323   \n",
       "25%      0.003855    0.003445    0.002171    0.001688  ...    0.002450   \n",
       "50%      0.006016    0.005261    0.003593    0.002764  ...    0.003850   \n",
       "75%      0.009410    0.008770    0.005695    0.004673  ...    0.005923   \n",
       "max      1.000000    1.000000    1.000000    1.000000  ...    1.000000   \n",
       "\n",
       "              491         492         493         494         495         496  \\\n",
       "count  500.000000  500.000000  500.000000  500.000000  500.000000  500.000000   \n",
       "mean     0.006444    0.005039    0.004592    0.006661    0.006687    0.008961   \n",
       "std      0.045104    0.044664    0.044673    0.044665    0.044674    0.044872   \n",
       "min      0.000373    0.000372    0.000203    0.000526    0.000354    0.001000   \n",
       "25%      0.002014    0.001488    0.001266    0.002555    0.002279    0.003457   \n",
       "50%      0.003267    0.002453    0.002095    0.003671    0.003709    0.005440   \n",
       "75%      0.005745    0.003767    0.003303    0.005581    0.005990    0.008572   \n",
       "max      1.000000    1.000000    1.000000    1.000000    1.000000    1.000000   \n",
       "\n",
       "              497         498         499  \n",
       "count  500.000000  500.000000  500.000000  \n",
       "mean     0.007559    0.007845    0.005677  \n",
       "std      0.044834    0.044770    0.044790  \n",
       "min      0.000649    0.000598    0.000282  \n",
       "25%      0.002824    0.003248    0.001853  \n",
       "50%      0.004367    0.004845    0.002965  \n",
       "75%      0.006820    0.007098    0.004469  \n",
       "max      1.000000    1.000000    1.000000  \n",
       "\n",
       "[8 rows x 500 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lapc.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "55b5c8ad",
   "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.hist(lap)\n",
    "plt.title('Laplacian')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff66cd14",
   "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
}