{
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    "nbpresent": {
     "id": "a20290f5-2a26-4622-9e8b-ce94cc1dcb1a"
    },
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Estimation of tree height using GEDI dataset -  Clean Data - Perceptron 2 - 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Base on data quality flag select more reilable tree height."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "nbpresent": {
     "id": "8f67df50-3050-47d2-a5d9-4329a61325fa"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**File storing tree hight (cm) obtained by 6 algorithms, with their associate quality flags.**\n",
    "The quality flags can be used to refine and select the best tree height estimation and use it as tree height observation.\n",
    "\n",
    "* a?_95: tree hight (cm) at 95 quintile, for each algorithm  \n",
    "* min_rh_95: minimum value of tree hight (cm) ammong the 6 algorithms  \n",
    "* max_rh_95: maximum value of tree hight (cm) ammong the 6 algorithms  \n",
    "* BEAM: 1-4 coverage beam = lower power (worse) ; 5-8 power beam = higher power (better)  \n",
    "* digital_elev: digital mdoel elevation  \n",
    "* elev_low: elevation of center of lowest mode  \n",
    "* qc_a?: quality_flag for six algorithms quality_flag = 1 (better); = 0 (worse)  \n",
    "* se_a?: sensitivity for six algorithms sensitivity < 0.95 (worse);  sensitivity > 0.95  (beter )  \n",
    "* deg_fg: (degrade_flag) not-degraded 0 (better) ;  degraded > 0 (worse)  \n",
    "* solar_ele: solar elevation. > 0 day (worse); < 0 night (better)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
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       "      <th>qc_a2</th>\n",
       "      <th>qc_a3</th>\n",
       "      <th>qc_a4</th>\n",
       "      <th>qc_a5</th>\n",
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       "      <td>0.990</td>\n",
       "      <td>0.960</td>\n",
       "      <td>0.948</td>\n",
       "      <td>0.994</td>\n",
       "      <td>0.980</td>\n",
       "      <td>0</td>\n",
       "      <td>43.7</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>6.050002</td>\n",
       "      <td>48.602377</td>\n",
       "      <td>380</td>\n",
       "      <td>1336</td>\n",
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       "      <td>362</td>\n",
       "      <td>1336</td>\n",
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       "      <td>0.956</td>\n",
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       "      <td>0.981</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0</td>\n",
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       "      <td>49.588410</td>\n",
       "      <td>666</td>\n",
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       "      <td>1179</td>\n",
       "      <td>1187</td>\n",
       "      <td>761</td>\n",
       "      <td>1833</td>\n",
       "      <td>1833</td>\n",
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       "      <td>0.952</td>\n",
       "      <td>0.979</td>\n",
       "      <td>0.961</td>\n",
       "      <td>0.952</td>\n",
       "      <td>0.986</td>\n",
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       "      <td>0</td>\n",
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       "   ID         X          Y  a1_95  a2_95  a3_95  a4_95  a5_95  a6_95  \\\n",
       "0   1  6.050001  49.727499   3139   3139   3139   3120   3139   3139   \n",
       "1   2  6.050002  49.922155   1022   2303    970    872   5596   1524   \n",
       "2   3  6.050002  48.602377    380   1336    332    362   1336   1340   \n",
       "3   4  6.050009  48.151979   3153   3142   3142   3127   3138   3142   \n",
       "4   5  6.050010  49.588410    666   4221    651     33   5611   2723   \n",
       "5   6  6.050014  48.608456    787   1179   1187    761   1833   1833   \n",
       "\n",
       "   min_rh_95  max_rh_95  BEAM  digital_elev    elev_low  qc_a1  qc_a2  qc_a3  \\\n",
       "0       3120       3139     5         410.0   383.72153      1      1      1   \n",
       "1        872       5596     5         290.0  2374.14110      0      0      0   \n",
       "2        332       1340     4         440.0   435.97781      1      1      1   \n",
       "3       3127       3153     2         450.0   422.00537      1      1      1   \n",
       "4         33       5611     8         370.0  2413.74830      0      0      0   \n",
       "5        761       1833     3         420.0   415.51581      1      1      1   \n",
       "\n",
       "   qc_a4  qc_a5  qc_a6  se_a1  se_a2  se_a3  se_a4  se_a5  se_a6  deg_fg  \\\n",
       "0      1      1      1  0.962  0.984  0.968  0.962  0.989  0.979       0   \n",
       "1      0      0      0  0.948  0.990  0.960  0.948  0.994  0.980       0   \n",
       "2      1      1      1  0.947  0.975  0.956  0.947  0.981  0.968       0   \n",
       "3      1      1      1  0.930  0.970  0.943  0.930  0.978  0.962       0   \n",
       "4      0      0      0  0.941  0.983  0.946  0.941  0.992  0.969       0   \n",
       "5      1      1      1  0.952  0.979  0.961  0.952  0.986  0.975       0   \n",
       "\n",
       "   solar_ele  \n",
       "0       17.7  \n",
       "1       43.7  \n",
       "2        0.2  \n",
       "3      -14.2  \n",
       "4       22.1  \n",
       "5        0.2  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "height_6algorithms = pd.read_csv(\"tree_height/txt/eu_y_x_select_6algorithms_fullTable.txt\", sep=\" \",  index_col=False)\n",
    "pd.set_option('display.max_columns',None)\n",
    "height_6algorithms.head(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "height_6algorithms_sel = height_6algorithms.loc[(height_6algorithms['BEAM'] > 4) \n",
    "                                            &   (height_6algorithms['qc_a1'] == 1)\n",
    "                                            &   (height_6algorithms['qc_a2'] == 1)\n",
    "                                            &   (height_6algorithms['qc_a3'] == 1)    \n",
    "                                            &   (height_6algorithms['qc_a4'] == 1)    \n",
    "                                            &   (height_6algorithms['qc_a5'] == 1)    \n",
    "                                            &   (height_6algorithms['qc_a6'] == 1)\n",
    "                                            &   (height_6algorithms['se_a1'] > 0.95)    \n",
    "                                            &   (height_6algorithms['se_a2'] > 0.95)\n",
    "                                            &   (height_6algorithms['se_a3'] > 0.95)\n",
    "                                            &   (height_6algorithms['se_a4'] > 0.95)\n",
    "                                            &   (height_6algorithms['se_a5'] > 0.95)   \n",
    "                                            &   (height_6algorithms['se_a6'] > 0.95)\n",
    "                                            &   (height_6algorithms['deg_fg'] == 0)  \n",
    "                                            &   (height_6algorithms['solar_ele'] < 0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
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       "      <td>0.992</td>\n",
       "      <td>0.984</td>\n",
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       "      <td>0.975</td>\n",
       "      <td>0.990</td>\n",
       "      <td>0.979</td>\n",
       "      <td>0.975</td>\n",
       "      <td>0.994</td>\n",
       "      <td>0.987</td>\n",
       "      <td>0</td>\n",
       "      <td>-37.3</td>\n",
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       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>6.050046</td>\n",
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       "      <td>1398</td>\n",
       "      <td>2505</td>\n",
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       "      <td>1316</td>\n",
       "      <td>2848</td>\n",
       "      <td>2505</td>\n",
       "      <td>1316</td>\n",
       "      <td>2848</td>\n",
       "      <td>6</td>\n",
       "      <td>340.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <td>0.973</td>\n",
       "      <td>0.994</td>\n",
       "      <td>0.986</td>\n",
       "      <td>0</td>\n",
       "      <td>-18.2</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>6.050048</td>\n",
       "      <td>49.050020</td>\n",
       "      <td>984</td>\n",
       "      <td>943</td>\n",
       "      <td>947</td>\n",
       "      <td>958</td>\n",
       "      <td>2617</td>\n",
       "      <td>947</td>\n",
       "      <td>943</td>\n",
       "      <td>2617</td>\n",
       "      <td>6</td>\n",
       "      <td>300.0</td>\n",
       "      <td>291.22598</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.978</td>\n",
       "      <td>0.991</td>\n",
       "      <td>0.982</td>\n",
       "      <td>0.978</td>\n",
       "      <td>0.995</td>\n",
       "      <td>0.988</td>\n",
       "      <td>0</td>\n",
       "      <td>-35.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>6.050049</td>\n",
       "      <td>48.391359</td>\n",
       "      <td>3362</td>\n",
       "      <td>3332</td>\n",
       "      <td>3336</td>\n",
       "      <td>3351</td>\n",
       "      <td>4467</td>\n",
       "      <td>3336</td>\n",
       "      <td>3332</td>\n",
       "      <td>4467</td>\n",
       "      <td>5</td>\n",
       "      <td>530.0</td>\n",
       "      <td>504.78122</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.973</td>\n",
       "      <td>0.988</td>\n",
       "      <td>0.977</td>\n",
       "      <td>0.973</td>\n",
       "      <td>0.992</td>\n",
       "      <td>0.984</td>\n",
       "      <td>0</td>\n",
       "      <td>-5.1</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",
       "      <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>1267207</th>\n",
       "      <td>1267208</td>\n",
       "      <td>9.949829</td>\n",
       "      <td>49.216272</td>\n",
       "      <td>2160</td>\n",
       "      <td>2816</td>\n",
       "      <td>2816</td>\n",
       "      <td>2104</td>\n",
       "      <td>3299</td>\n",
       "      <td>2816</td>\n",
       "      <td>2104</td>\n",
       "      <td>3299</td>\n",
       "      <td>8</td>\n",
       "      <td>420.0</td>\n",
       "      <td>386.44556</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.980</td>\n",
       "      <td>0.993</td>\n",
       "      <td>0.984</td>\n",
       "      <td>0.980</td>\n",
       "      <td>0.995</td>\n",
       "      <td>0.989</td>\n",
       "      <td>0</td>\n",
       "      <td>-16.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267211</th>\n",
       "      <td>1267212</td>\n",
       "      <td>9.949856</td>\n",
       "      <td>49.881190</td>\n",
       "      <td>3190</td>\n",
       "      <td>3179</td>\n",
       "      <td>3179</td>\n",
       "      <td>3171</td>\n",
       "      <td>3822</td>\n",
       "      <td>3179</td>\n",
       "      <td>3171</td>\n",
       "      <td>3822</td>\n",
       "      <td>6</td>\n",
       "      <td>380.0</td>\n",
       "      <td>363.69348</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0.986</td>\n",
       "      <td>0.974</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0.990</td>\n",
       "      <td>0.982</td>\n",
       "      <td>0</td>\n",
       "      <td>-35.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267216</th>\n",
       "      <td>1267217</td>\n",
       "      <td>9.949880</td>\n",
       "      <td>49.873435</td>\n",
       "      <td>2061</td>\n",
       "      <td>2828</td>\n",
       "      <td>2046</td>\n",
       "      <td>2024</td>\n",
       "      <td>2828</td>\n",
       "      <td>2828</td>\n",
       "      <td>2024</td>\n",
       "      <td>2828</td>\n",
       "      <td>7</td>\n",
       "      <td>380.0</td>\n",
       "      <td>361.06812</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.967</td>\n",
       "      <td>0.988</td>\n",
       "      <td>0.974</td>\n",
       "      <td>0.967</td>\n",
       "      <td>0.993</td>\n",
       "      <td>0.983</td>\n",
       "      <td>0</td>\n",
       "      <td>-35.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267227</th>\n",
       "      <td>1267228</td>\n",
       "      <td>9.949958</td>\n",
       "      <td>49.127182</td>\n",
       "      <td>366</td>\n",
       "      <td>2307</td>\n",
       "      <td>1260</td>\n",
       "      <td>355</td>\n",
       "      <td>3531</td>\n",
       "      <td>2719</td>\n",
       "      <td>355</td>\n",
       "      <td>3531</td>\n",
       "      <td>6</td>\n",
       "      <td>500.0</td>\n",
       "      <td>493.52792</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.973</td>\n",
       "      <td>0.989</td>\n",
       "      <td>0.978</td>\n",
       "      <td>0.973</td>\n",
       "      <td>0.993</td>\n",
       "      <td>0.985</td>\n",
       "      <td>0</td>\n",
       "      <td>-36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267237</th>\n",
       "      <td>1267238</td>\n",
       "      <td>9.949999</td>\n",
       "      <td>49.936763</td>\n",
       "      <td>2513</td>\n",
       "      <td>2490</td>\n",
       "      <td>2490</td>\n",
       "      <td>2494</td>\n",
       "      <td>2490</td>\n",
       "      <td>2490</td>\n",
       "      <td>2490</td>\n",
       "      <td>2513</td>\n",
       "      <td>5</td>\n",
       "      <td>360.0</td>\n",
       "      <td>346.54227</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0.988</td>\n",
       "      <td>0.974</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0.993</td>\n",
       "      <td>0.983</td>\n",
       "      <td>0</td>\n",
       "      <td>-32.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>226892 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              ID         X          Y  a1_95  a2_95  a3_95  a4_95  a5_95  \\\n",
       "7              8  6.050019  49.921613   3303   3288   3296   3236   3857   \n",
       "11            12  6.050039  47.995344   2762   2736   2740   2747   3893   \n",
       "14            15  6.050046  49.865317   1398   2505   2509   1316   2848   \n",
       "15            16  6.050048  49.050020    984    943    947    958   2617   \n",
       "16            17  6.050049  48.391359   3362   3332   3336   3351   4467   \n",
       "...          ...       ...        ...    ...    ...    ...    ...    ...   \n",
       "1267207  1267208  9.949829  49.216272   2160   2816   2816   2104   3299   \n",
       "1267211  1267212  9.949856  49.881190   3190   3179   3179   3171   3822   \n",
       "1267216  1267217  9.949880  49.873435   2061   2828   2046   2024   2828   \n",
       "1267227  1267228  9.949958  49.127182    366   2307   1260    355   3531   \n",
       "1267237  1267238  9.949999  49.936763   2513   2490   2490   2494   2490   \n",
       "\n",
       "         a6_95  min_rh_95  max_rh_95  BEAM  digital_elev   elev_low  qc_a1  \\\n",
       "7         3292       3236       3857     7         320.0  297.68533      1   \n",
       "11        2736       2736       3893     5         390.0  368.55121      1   \n",
       "14        2505       1316       2848     6         340.0  330.40564      1   \n",
       "15         947        943       2617     6         300.0  291.22598      1   \n",
       "16        3336       3332       4467     5         530.0  504.78122      1   \n",
       "...        ...        ...        ...   ...           ...        ...    ...   \n",
       "1267207   2816       2104       3299     8         420.0  386.44556      1   \n",
       "1267211   3179       3171       3822     6         380.0  363.69348      1   \n",
       "1267216   2828       2024       2828     7         380.0  361.06812      1   \n",
       "1267227   2719        355       3531     6         500.0  493.52792      1   \n",
       "1267237   2490       2490       2513     5         360.0  346.54227      1   \n",
       "\n",
       "         qc_a2  qc_a3  qc_a4  qc_a5  qc_a6  se_a1  se_a2  se_a3  se_a4  se_a5  \\\n",
       "7            1      1      1      1      1  0.971  0.988  0.976  0.971  0.992   \n",
       "11           1      1      1      1      1  0.975  0.990  0.979  0.975  0.994   \n",
       "14           1      1      1      1      1  0.973  0.990  0.979  0.973  0.994   \n",
       "15           1      1      1      1      1  0.978  0.991  0.982  0.978  0.995   \n",
       "16           1      1      1      1      1  0.973  0.988  0.977  0.973  0.992   \n",
       "...        ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
       "1267207      1      1      1      1      1  0.980  0.993  0.984  0.980  0.995   \n",
       "1267211      1      1      1      1      1  0.968  0.986  0.974  0.968  0.990   \n",
       "1267216      1      1      1      1      1  0.967  0.988  0.974  0.967  0.993   \n",
       "1267227      1      1      1      1      1  0.973  0.989  0.978  0.973  0.993   \n",
       "1267237      1      1      1      1      1  0.968  0.988  0.974  0.968  0.993   \n",
       "\n",
       "         se_a6  deg_fg  solar_ele  \n",
       "7        0.984       0      -33.9  \n",
       "11       0.987       0      -37.3  \n",
       "14       0.986       0      -18.2  \n",
       "15       0.988       0      -35.4  \n",
       "16       0.984       0       -5.1  \n",
       "...        ...     ...        ...  \n",
       "1267207  0.989       0      -16.9  \n",
       "1267211  0.982       0      -35.1  \n",
       "1267216  0.983       0      -35.1  \n",
       "1267227  0.985       0      -36.0  \n",
       "1267237  0.983       0      -32.2  \n",
       "\n",
       "[226892 rows x 28 columns]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "height_6algorithms_sel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean height excluidng the maximum and minimum values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "height_sel =  pd.DataFrame({'ID' : height_6algorithms_sel['ID'] , \n",
    "                            'hm_sel': (height_6algorithms_sel['a1_95'] + height_6algorithms_sel['a2_95'] + height_6algorithms_sel['a3_95'] + height_6algorithms_sel['a4_95'] \n",
    "                             + height_6algorithms_sel['a5_95'] + height_6algorithms_sel['a6_95'] - height_6algorithms_sel['min_rh_95'] - height_6algorithms_sel['max_rh_95']) / 400 } )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>1267207</th>\n",
       "      <td>1267208</td>\n",
       "      <td>26.5200</td>\n",
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       "    <tr>\n",
       "      <th>1267211</th>\n",
       "      <td>1267212</td>\n",
       "      <td>31.8175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267216</th>\n",
       "      <td>1267217</td>\n",
       "      <td>24.4075</td>\n",
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       "    <tr>\n",
       "      <th>1267227</th>\n",
       "      <td>1267228</td>\n",
       "      <td>16.6300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1267237</th>\n",
       "      <td>1267238</td>\n",
       "      <td>24.9100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>226892 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              ID   hm_sel\n",
       "7              8  32.9475\n",
       "11            12  27.4625\n",
       "14            15  22.2925\n",
       "15            16   9.5900\n",
       "16            17  33.4625\n",
       "...          ...      ...\n",
       "1267207  1267208  26.5200\n",
       "1267211  1267212  31.8175\n",
       "1267216  1267217  24.4075\n",
       "1267227  1267228  16.6300\n",
       "1267237  1267238  24.9100\n",
       "\n",
       "[226892 rows x 2 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "height_sel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import raw data, extracted predictors and show the data distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>ID</th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>h</th>\n",
       "      <th>BLDFIE_WeigAver</th>\n",
       "      <th>CECSOL_WeigAver</th>\n",
       "      <th>CHELSA_bio18</th>\n",
       "      <th>CHELSA_bio4</th>\n",
       "      <th>convergence</th>\n",
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       "      <th>eastness</th>\n",
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       "      <td>276.871094</td>\n",
       "      <td>46.444092</td>\n",
       "      <td>347.665405</td>\n",
       "      <td>0.042500</td>\n",
       "      <td>9</td>\n",
       "      <td>780403</td>\n",
       "      <td>19.798992</td>\n",
       "      <td>440.672211</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>6.050002</td>\n",
       "      <td>49.922155</td>\n",
       "      <td>1454.75</td>\n",
       "      <td>1491</td>\n",
       "      <td>12</td>\n",
       "      <td>1993</td>\n",
       "      <td>5912</td>\n",
       "      <td>33.274361</td>\n",
       "      <td>-208915344</td>\n",
       "      <td>-1.755341</td>\n",
       "      <td>0.269112</td>\n",
       "      <td>267.511688</td>\n",
       "      <td>19</td>\n",
       "      <td>-49.526367</td>\n",
       "      <td>19.552734</td>\n",
       "      <td>-130.541748</td>\n",
       "      <td>0.182780</td>\n",
       "      <td>16</td>\n",
       "      <td>772777</td>\n",
       "      <td>20.889412</td>\n",
       "      <td>457.756195</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>6.050002</td>\n",
       "      <td>48.602377</td>\n",
       "      <td>853.50</td>\n",
       "      <td>1521</td>\n",
       "      <td>17</td>\n",
       "      <td>2124</td>\n",
       "      <td>5983</td>\n",
       "      <td>0.045293</td>\n",
       "      <td>-137479792</td>\n",
       "      <td>1.908780</td>\n",
       "      <td>-0.016055</td>\n",
       "      <td>389.751160</td>\n",
       "      <td>21</td>\n",
       "      <td>93.257324</td>\n",
       "      <td>50.743652</td>\n",
       "      <td>384.522461</td>\n",
       "      <td>0.036253</td>\n",
       "      <td>14</td>\n",
       "      <td>898820</td>\n",
       "      <td>20.695877</td>\n",
       "      <td>481.879700</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>6.050009</td>\n",
       "      <td>48.151979</td>\n",
       "      <td>3141.00</td>\n",
       "      <td>1526</td>\n",
       "      <td>16</td>\n",
       "      <td>2569</td>\n",
       "      <td>6130</td>\n",
       "      <td>-33.654274</td>\n",
       "      <td>-267223072</td>\n",
       "      <td>0.965787</td>\n",
       "      <td>0.067767</td>\n",
       "      <td>380.207703</td>\n",
       "      <td>27</td>\n",
       "      <td>542.401367</td>\n",
       "      <td>202.264160</td>\n",
       "      <td>386.156738</td>\n",
       "      <td>0.005139</td>\n",
       "      <td>15</td>\n",
       "      <td>831824</td>\n",
       "      <td>19.375000</td>\n",
       "      <td>479.410278</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>6.050010</td>\n",
       "      <td>49.588410</td>\n",
       "      <td>2065.25</td>\n",
       "      <td>1547</td>\n",
       "      <td>14</td>\n",
       "      <td>2108</td>\n",
       "      <td>5923</td>\n",
       "      <td>27.493824</td>\n",
       "      <td>-107809368</td>\n",
       "      <td>-0.162624</td>\n",
       "      <td>0.014065</td>\n",
       "      <td>308.042786</td>\n",
       "      <td>25</td>\n",
       "      <td>136.048340</td>\n",
       "      <td>146.835205</td>\n",
       "      <td>198.127441</td>\n",
       "      <td>0.028847</td>\n",
       "      <td>17</td>\n",
       "      <td>796962</td>\n",
       "      <td>18.777500</td>\n",
       "      <td>457.880066</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>6.050014</td>\n",
       "      <td>48.608456</td>\n",
       "      <td>1246.50</td>\n",
       "      <td>1515</td>\n",
       "      <td>19</td>\n",
       "      <td>2124</td>\n",
       "      <td>6010</td>\n",
       "      <td>-1.602039</td>\n",
       "      <td>17384282</td>\n",
       "      <td>1.447979</td>\n",
       "      <td>-0.018912</td>\n",
       "      <td>364.527100</td>\n",
       "      <td>18</td>\n",
       "      <td>221.339844</td>\n",
       "      <td>247.387207</td>\n",
       "      <td>480.387939</td>\n",
       "      <td>0.042747</td>\n",
       "      <td>14</td>\n",
       "      <td>897945</td>\n",
       "      <td>19.398880</td>\n",
       "      <td>474.331329</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>6.050016</td>\n",
       "      <td>48.571401</td>\n",
       "      <td>2938.75</td>\n",
       "      <td>1520</td>\n",
       "      <td>19</td>\n",
       "      <td>2169</td>\n",
       "      <td>6147</td>\n",
       "      <td>27.856503</td>\n",
       "      <td>-66516432</td>\n",
       "      <td>-1.073956</td>\n",
       "      <td>0.002280</td>\n",
       "      <td>254.679596</td>\n",
       "      <td>19</td>\n",
       "      <td>125.250488</td>\n",
       "      <td>87.865234</td>\n",
       "      <td>160.696777</td>\n",
       "      <td>0.037254</td>\n",
       "      <td>11</td>\n",
       "      <td>908426</td>\n",
       "      <td>20.170450</td>\n",
       "      <td>476.414520</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>6.050019</td>\n",
       "      <td>49.921613</td>\n",
       "      <td>3294.75</td>\n",
       "      <td>1490</td>\n",
       "      <td>12</td>\n",
       "      <td>1995</td>\n",
       "      <td>5912</td>\n",
       "      <td>22.102139</td>\n",
       "      <td>-297770784</td>\n",
       "      <td>-1.402633</td>\n",
       "      <td>0.309765</td>\n",
       "      <td>294.927765</td>\n",
       "      <td>26</td>\n",
       "      <td>-86.729492</td>\n",
       "      <td>-145.584229</td>\n",
       "      <td>-190.062988</td>\n",
       "      <td>0.222435</td>\n",
       "      <td>15</td>\n",
       "      <td>772784</td>\n",
       "      <td>20.855963</td>\n",
       "      <td>457.195404</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>6.050020</td>\n",
       "      <td>48.822645</td>\n",
       "      <td>1623.50</td>\n",
       "      <td>1554</td>\n",
       "      <td>18</td>\n",
       "      <td>1973</td>\n",
       "      <td>6138</td>\n",
       "      <td>18.496584</td>\n",
       "      <td>-25336536</td>\n",
       "      <td>-0.800016</td>\n",
       "      <td>0.010370</td>\n",
       "      <td>240.493759</td>\n",
       "      <td>22</td>\n",
       "      <td>-51.470703</td>\n",
       "      <td>-245.886719</td>\n",
       "      <td>172.074707</td>\n",
       "      <td>0.004428</td>\n",
       "      <td>8</td>\n",
       "      <td>839132</td>\n",
       "      <td>21.812290</td>\n",
       "      <td>496.231110</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>6.050024</td>\n",
       "      <td>49.847522</td>\n",
       "      <td>1400.00</td>\n",
       "      <td>1521</td>\n",
       "      <td>15</td>\n",
       "      <td>2187</td>\n",
       "      <td>5886</td>\n",
       "      <td>-5.660453</td>\n",
       "      <td>-278652608</td>\n",
       "      <td>1.477951</td>\n",
       "      <td>-0.068720</td>\n",
       "      <td>376.671143</td>\n",
       "      <td>12</td>\n",
       "      <td>277.297363</td>\n",
       "      <td>273.141846</td>\n",
       "      <td>-138.895996</td>\n",
       "      <td>0.098817</td>\n",
       "      <td>13</td>\n",
       "      <td>768873</td>\n",
       "      <td>21.137711</td>\n",
       "      <td>466.976685</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ID         X          Y        h  BLDFIE_WeigAver  CECSOL_WeigAver  \\\n",
       "0   1  6.050001  49.727499  3139.00             1540               13   \n",
       "1   2  6.050002  49.922155  1454.75             1491               12   \n",
       "2   3  6.050002  48.602377   853.50             1521               17   \n",
       "3   4  6.050009  48.151979  3141.00             1526               16   \n",
       "4   5  6.050010  49.588410  2065.25             1547               14   \n",
       "5   6  6.050014  48.608456  1246.50             1515               19   \n",
       "6   7  6.050016  48.571401  2938.75             1520               19   \n",
       "7   8  6.050019  49.921613  3294.75             1490               12   \n",
       "8   9  6.050020  48.822645  1623.50             1554               18   \n",
       "9  10  6.050024  49.847522  1400.00             1521               15   \n",
       "\n",
       "   CHELSA_bio18  CHELSA_bio4  convergence        cti  devmagnitude  eastness  \\\n",
       "0          2113         5893   -10.486560 -238043120      1.158417  0.069094   \n",
       "1          1993         5912    33.274361 -208915344     -1.755341  0.269112   \n",
       "2          2124         5983     0.045293 -137479792      1.908780 -0.016055   \n",
       "3          2569         6130   -33.654274 -267223072      0.965787  0.067767   \n",
       "4          2108         5923    27.493824 -107809368     -0.162624  0.014065   \n",
       "5          2124         6010    -1.602039   17384282      1.447979 -0.018912   \n",
       "6          2169         6147    27.856503  -66516432     -1.073956  0.002280   \n",
       "7          1995         5912    22.102139 -297770784     -1.402633  0.309765   \n",
       "8          1973         6138    18.496584  -25336536     -0.800016  0.010370   \n",
       "9          2187         5886    -5.660453 -278652608      1.477951 -0.068720   \n",
       "\n",
       "         elev  forestheight  glad_ard_SVVI_max  glad_ard_SVVI_med  \\\n",
       "0  353.983124            23         276.871094          46.444092   \n",
       "1  267.511688            19         -49.526367          19.552734   \n",
       "2  389.751160            21          93.257324          50.743652   \n",
       "3  380.207703            27         542.401367         202.264160   \n",
       "4  308.042786            25         136.048340         146.835205   \n",
       "5  364.527100            18         221.339844         247.387207   \n",
       "6  254.679596            19         125.250488          87.865234   \n",
       "7  294.927765            26         -86.729492        -145.584229   \n",
       "8  240.493759            22         -51.470703        -245.886719   \n",
       "9  376.671143            12         277.297363         273.141846   \n",
       "\n",
       "   glad_ard_SVVI_min  northness  ORCDRC_WeigAver  outlet_dist_dw_basin  \\\n",
       "0         347.665405   0.042500                9                780403   \n",
       "1        -130.541748   0.182780               16                772777   \n",
       "2         384.522461   0.036253               14                898820   \n",
       "3         386.156738   0.005139               15                831824   \n",
       "4         198.127441   0.028847               17                796962   \n",
       "5         480.387939   0.042747               14                897945   \n",
       "6         160.696777   0.037254               11                908426   \n",
       "7        -190.062988   0.222435               15                772784   \n",
       "8         172.074707   0.004428                8                839132   \n",
       "9        -138.895996   0.098817               13                768873   \n",
       "\n",
       "   SBIO3_Isothermality_5_15cm  SBIO4_Temperature_Seasonality_5_15cm  treecover  \n",
       "0                   19.798992                            440.672211         85  \n",
       "1                   20.889412                            457.756195         85  \n",
       "2                   20.695877                            481.879700         62  \n",
       "3                   19.375000                            479.410278         85  \n",
       "4                   18.777500                            457.880066         85  \n",
       "5                   19.398880                            474.331329         62  \n",
       "6                   20.170450                            476.414520         96  \n",
       "7                   20.855963                            457.195404         86  \n",
       "8                   21.812290                            496.231110         64  \n",
       "9                   21.137711                            466.976685         70  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors = pd.read_csv(\"tree_height/txt/eu_x_y_height_predictors_select.txt\", sep=\" \",  index_col=False)\n",
    "pd.set_option('display.max_columns',None)\n",
    "# change column name\n",
    "predictors = predictors.rename({'dev-magnitude':'devmagnitude'} , axis='columns')\n",
    "predictors.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Merge the new height with the predictors table, using the ID as Primary Key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors_hm_sel = pd.merge( predictors ,  height_sel , left_on='ID' ,  right_on='ID' ,  how='right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>ID</th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>h</th>\n",
       "      <th>BLDFIE_WeigAver</th>\n",
       "      <th>CECSOL_WeigAver</th>\n",
       "      <th>CHELSA_bio18</th>\n",
       "      <th>CHELSA_bio4</th>\n",
       "      <th>convergence</th>\n",
       "      <th>cti</th>\n",
       "      <th>devmagnitude</th>\n",
       "      <th>eastness</th>\n",
       "      <th>elev</th>\n",
       "      <th>forestheight</th>\n",
       "      <th>glad_ard_SVVI_max</th>\n",
       "      <th>glad_ard_SVVI_med</th>\n",
       "      <th>glad_ard_SVVI_min</th>\n",
       "      <th>northness</th>\n",
       "      <th>ORCDRC_WeigAver</th>\n",
       "      <th>outlet_dist_dw_basin</th>\n",
       "      <th>SBIO3_Isothermality_5_15cm</th>\n",
       "      <th>SBIO4_Temperature_Seasonality_5_15cm</th>\n",
       "      <th>treecover</th>\n",
       "      <th>hm_sel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>6.050019</td>\n",
       "      <td>49.921613</td>\n",
       "      <td>3294.75</td>\n",
       "      <td>1490</td>\n",
       "      <td>12</td>\n",
       "      <td>1995</td>\n",
       "      <td>5912</td>\n",
       "      <td>22.102139</td>\n",
       "      <td>-297770784</td>\n",
       "      <td>-1.402633</td>\n",
       "      <td>0.309765</td>\n",
       "      <td>294.927765</td>\n",
       "      <td>26</td>\n",
       "      <td>-86.729492</td>\n",
       "      <td>-145.584229</td>\n",
       "      <td>-190.062988</td>\n",
       "      <td>0.222435</td>\n",
       "      <td>15</td>\n",
       "      <td>772784</td>\n",
       "      <td>20.855963</td>\n",
       "      <td>457.195404</td>\n",
       "      <td>86</td>\n",
       "      <td>32.9475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12</td>\n",
       "      <td>6.050039</td>\n",
       "      <td>47.995344</td>\n",
       "      <td>2746.25</td>\n",
       "      <td>1523</td>\n",
       "      <td>12</td>\n",
       "      <td>2612</td>\n",
       "      <td>6181</td>\n",
       "      <td>3.549103</td>\n",
       "      <td>-71279992</td>\n",
       "      <td>0.507727</td>\n",
       "      <td>-0.021408</td>\n",
       "      <td>322.920227</td>\n",
       "      <td>26</td>\n",
       "      <td>660.006104</td>\n",
       "      <td>92.722168</td>\n",
       "      <td>190.979736</td>\n",
       "      <td>-0.034787</td>\n",
       "      <td>16</td>\n",
       "      <td>784807</td>\n",
       "      <td>20.798000</td>\n",
       "      <td>460.501221</td>\n",
       "      <td>97</td>\n",
       "      <td>27.4625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15</td>\n",
       "      <td>6.050046</td>\n",
       "      <td>49.865317</td>\n",
       "      <td>2229.25</td>\n",
       "      <td>1517</td>\n",
       "      <td>13</td>\n",
       "      <td>2191</td>\n",
       "      <td>5901</td>\n",
       "      <td>31.054762</td>\n",
       "      <td>-186807440</td>\n",
       "      <td>-1.375050</td>\n",
       "      <td>-0.126880</td>\n",
       "      <td>291.412537</td>\n",
       "      <td>7</td>\n",
       "      <td>1028.385498</td>\n",
       "      <td>915.806396</td>\n",
       "      <td>841.586182</td>\n",
       "      <td>0.024677</td>\n",
       "      <td>16</td>\n",
       "      <td>766444</td>\n",
       "      <td>19.941267</td>\n",
       "      <td>454.185089</td>\n",
       "      <td>54</td>\n",
       "      <td>22.2925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16</td>\n",
       "      <td>6.050048</td>\n",
       "      <td>49.050020</td>\n",
       "      <td>959.00</td>\n",
       "      <td>1526</td>\n",
       "      <td>14</td>\n",
       "      <td>2081</td>\n",
       "      <td>6100</td>\n",
       "      <td>9.933455</td>\n",
       "      <td>-183562672</td>\n",
       "      <td>-0.382834</td>\n",
       "      <td>0.086874</td>\n",
       "      <td>246.288010</td>\n",
       "      <td>24</td>\n",
       "      <td>-12.283691</td>\n",
       "      <td>-58.179199</td>\n",
       "      <td>174.205566</td>\n",
       "      <td>0.094175</td>\n",
       "      <td>10</td>\n",
       "      <td>805730</td>\n",
       "      <td>19.849365</td>\n",
       "      <td>470.946533</td>\n",
       "      <td>78</td>\n",
       "      <td>9.5900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17</td>\n",
       "      <td>6.050049</td>\n",
       "      <td>48.391359</td>\n",
       "      <td>3346.25</td>\n",
       "      <td>1489</td>\n",
       "      <td>19</td>\n",
       "      <td>2486</td>\n",
       "      <td>5966</td>\n",
       "      <td>-6.957157</td>\n",
       "      <td>-273522688</td>\n",
       "      <td>2.989759</td>\n",
       "      <td>0.214769</td>\n",
       "      <td>474.409088</td>\n",
       "      <td>24</td>\n",
       "      <td>125.583008</td>\n",
       "      <td>6.154297</td>\n",
       "      <td>128.129150</td>\n",
       "      <td>0.017164</td>\n",
       "      <td>15</td>\n",
       "      <td>950190</td>\n",
       "      <td>21.179420</td>\n",
       "      <td>491.398376</td>\n",
       "      <td>85</td>\n",
       "      <td>33.4625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>19</td>\n",
       "      <td>6.050053</td>\n",
       "      <td>49.877876</td>\n",
       "      <td>529.00</td>\n",
       "      <td>1531</td>\n",
       "      <td>12</td>\n",
       "      <td>2184</td>\n",
       "      <td>5915</td>\n",
       "      <td>-24.278454</td>\n",
       "      <td>-377335296</td>\n",
       "      <td>0.265329</td>\n",
       "      <td>-0.248356</td>\n",
       "      <td>335.534760</td>\n",
       "      <td>25</td>\n",
       "      <td>593.601074</td>\n",
       "      <td>228.712402</td>\n",
       "      <td>315.298340</td>\n",
       "      <td>-0.127365</td>\n",
       "      <td>17</td>\n",
       "      <td>764713</td>\n",
       "      <td>19.760756</td>\n",
       "      <td>448.580811</td>\n",
       "      <td>96</td>\n",
       "      <td>5.2900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ID         X          Y        h  BLDFIE_WeigAver  CECSOL_WeigAver  \\\n",
       "0   8  6.050019  49.921613  3294.75             1490               12   \n",
       "1  12  6.050039  47.995344  2746.25             1523               12   \n",
       "2  15  6.050046  49.865317  2229.25             1517               13   \n",
       "3  16  6.050048  49.050020   959.00             1526               14   \n",
       "4  17  6.050049  48.391359  3346.25             1489               19   \n",
       "5  19  6.050053  49.877876   529.00             1531               12   \n",
       "\n",
       "   CHELSA_bio18  CHELSA_bio4  convergence        cti  devmagnitude  eastness  \\\n",
       "0          1995         5912    22.102139 -297770784     -1.402633  0.309765   \n",
       "1          2612         6181     3.549103  -71279992      0.507727 -0.021408   \n",
       "2          2191         5901    31.054762 -186807440     -1.375050 -0.126880   \n",
       "3          2081         6100     9.933455 -183562672     -0.382834  0.086874   \n",
       "4          2486         5966    -6.957157 -273522688      2.989759  0.214769   \n",
       "5          2184         5915   -24.278454 -377335296      0.265329 -0.248356   \n",
       "\n",
       "         elev  forestheight  glad_ard_SVVI_max  glad_ard_SVVI_med  \\\n",
       "0  294.927765            26         -86.729492        -145.584229   \n",
       "1  322.920227            26         660.006104          92.722168   \n",
       "2  291.412537             7        1028.385498         915.806396   \n",
       "3  246.288010            24         -12.283691         -58.179199   \n",
       "4  474.409088            24         125.583008           6.154297   \n",
       "5  335.534760            25         593.601074         228.712402   \n",
       "\n",
       "   glad_ard_SVVI_min  northness  ORCDRC_WeigAver  outlet_dist_dw_basin  \\\n",
       "0        -190.062988   0.222435               15                772784   \n",
       "1         190.979736  -0.034787               16                784807   \n",
       "2         841.586182   0.024677               16                766444   \n",
       "3         174.205566   0.094175               10                805730   \n",
       "4         128.129150   0.017164               15                950190   \n",
       "5         315.298340  -0.127365               17                764713   \n",
       "\n",
       "   SBIO3_Isothermality_5_15cm  SBIO4_Temperature_Seasonality_5_15cm  \\\n",
       "0                   20.855963                            457.195404   \n",
       "1                   20.798000                            460.501221   \n",
       "2                   19.941267                            454.185089   \n",
       "3                   19.849365                            470.946533   \n",
       "4                   21.179420                            491.398376   \n",
       "5                   19.760756                            448.580811   \n",
       "\n",
       "   treecover   hm_sel  \n",
       "0         86  32.9475  \n",
       "1         97  27.4625  \n",
       "2         54  22.2925  \n",
       "3         78   9.5900  \n",
       "4         85  33.4625  \n",
       "5         96   5.2900  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors_hm_sel.head(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors_hm_sel = predictors_hm_sel.loc[(predictors['h'] < 5000) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>h</th>\n",
       "      <th>BLDFIE_WeigAver</th>\n",
       "      <th>CECSOL_WeigAver</th>\n",
       "      <th>CHELSA_bio18</th>\n",
       "      <th>CHELSA_bio4</th>\n",
       "      <th>convergence</th>\n",
       "      <th>cti</th>\n",
       "      <th>devmagnitude</th>\n",
       "      <th>eastness</th>\n",
       "      <th>elev</th>\n",
       "      <th>forestheight</th>\n",
       "      <th>glad_ard_SVVI_max</th>\n",
       "      <th>glad_ard_SVVI_med</th>\n",
       "      <th>glad_ard_SVVI_min</th>\n",
       "      <th>northness</th>\n",
       "      <th>ORCDRC_WeigAver</th>\n",
       "      <th>outlet_dist_dw_basin</th>\n",
       "      <th>SBIO3_Isothermality_5_15cm</th>\n",
       "      <th>SBIO4_Temperature_Seasonality_5_15cm</th>\n",
       "      <th>treecover</th>\n",
       "      <th>hm_sel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12</td>\n",
       "      <td>6.050039</td>\n",
       "      <td>47.995344</td>\n",
       "      <td>2746.25</td>\n",
       "      <td>1523</td>\n",
       "      <td>12</td>\n",
       "      <td>2612</td>\n",
       "      <td>6181</td>\n",
       "      <td>3.549103</td>\n",
       "      <td>-71279992</td>\n",
       "      <td>0.507727</td>\n",
       "      <td>-0.021408</td>\n",
       "      <td>322.920227</td>\n",
       "      <td>26</td>\n",
       "      <td>660.006104</td>\n",
       "      <td>92.722168</td>\n",
       "      <td>190.979736</td>\n",
       "      <td>-0.034787</td>\n",
       "      <td>16</td>\n",
       "      <td>784807</td>\n",
       "      <td>20.798000</td>\n",
       "      <td>460.501221</td>\n",
       "      <td>97</td>\n",
       "      <td>27.4625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15</td>\n",
       "      <td>6.050046</td>\n",
       "      <td>49.865317</td>\n",
       "      <td>2229.25</td>\n",
       "      <td>1517</td>\n",
       "      <td>13</td>\n",
       "      <td>2191</td>\n",
       "      <td>5901</td>\n",
       "      <td>31.054762</td>\n",
       "      <td>-186807440</td>\n",
       "      <td>-1.375050</td>\n",
       "      <td>-0.126880</td>\n",
       "      <td>291.412537</td>\n",
       "      <td>7</td>\n",
       "      <td>1028.385498</td>\n",
       "      <td>915.806396</td>\n",
       "      <td>841.586182</td>\n",
       "      <td>0.024677</td>\n",
       "      <td>16</td>\n",
       "      <td>766444</td>\n",
       "      <td>19.941267</td>\n",
       "      <td>454.185089</td>\n",
       "      <td>54</td>\n",
       "      <td>22.2925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>19</td>\n",
       "      <td>6.050053</td>\n",
       "      <td>49.877876</td>\n",
       "      <td>529.00</td>\n",
       "      <td>1531</td>\n",
       "      <td>12</td>\n",
       "      <td>2184</td>\n",
       "      <td>5915</td>\n",
       "      <td>-24.278454</td>\n",
       "      <td>-377335296</td>\n",
       "      <td>0.265329</td>\n",
       "      <td>-0.248356</td>\n",
       "      <td>335.534760</td>\n",
       "      <td>25</td>\n",
       "      <td>593.601074</td>\n",
       "      <td>228.712402</td>\n",
       "      <td>315.298340</td>\n",
       "      <td>-0.127365</td>\n",
       "      <td>17</td>\n",
       "      <td>764713</td>\n",
       "      <td>19.760756</td>\n",
       "      <td>448.580811</td>\n",
       "      <td>96</td>\n",
       "      <td>5.2900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>27</td>\n",
       "      <td>6.050083</td>\n",
       "      <td>49.281439</td>\n",
       "      <td>3921.25</td>\n",
       "      <td>1488</td>\n",
       "      <td>13</td>\n",
       "      <td>2345</td>\n",
       "      <td>5915</td>\n",
       "      <td>3.646593</td>\n",
       "      <td>-223499248</td>\n",
       "      <td>0.383314</td>\n",
       "      <td>0.062349</td>\n",
       "      <td>309.142609</td>\n",
       "      <td>25</td>\n",
       "      <td>862.362305</td>\n",
       "      <td>263.612793</td>\n",
       "      <td>249.693115</td>\n",
       "      <td>-0.068810</td>\n",
       "      <td>16</td>\n",
       "      <td>781120</td>\n",
       "      <td>17.538614</td>\n",
       "      <td>463.280243</td>\n",
       "      <td>100</td>\n",
       "      <td>39.2125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>35</td>\n",
       "      <td>6.050119</td>\n",
       "      <td>49.928610</td>\n",
       "      <td>1765.00</td>\n",
       "      <td>1510</td>\n",
       "      <td>13</td>\n",
       "      <td>1976</td>\n",
       "      <td>5917</td>\n",
       "      <td>-2.138205</td>\n",
       "      <td>-393005696</td>\n",
       "      <td>-1.467515</td>\n",
       "      <td>-0.316702</td>\n",
       "      <td>301.649567</td>\n",
       "      <td>20</td>\n",
       "      <td>248.561035</td>\n",
       "      <td>164.831299</td>\n",
       "      <td>237.283447</td>\n",
       "      <td>-0.144407</td>\n",
       "      <td>19</td>\n",
       "      <td>773647</td>\n",
       "      <td>21.324263</td>\n",
       "      <td>465.046478</td>\n",
       "      <td>87</td>\n",
       "      <td>17.6500</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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226876</th>\n",
       "      <td>1267176</td>\n",
       "      <td>9.949637</td>\n",
       "      <td>49.887471</td>\n",
       "      <td>3266.50</td>\n",
       "      <td>1558</td>\n",
       "      <td>14</td>\n",
       "      <td>2074</td>\n",
       "      <td>6484</td>\n",
       "      <td>4.993805</td>\n",
       "      <td>-196691680</td>\n",
       "      <td>1.260540</td>\n",
       "      <td>0.044238</td>\n",
       "      <td>328.019165</td>\n",
       "      <td>26</td>\n",
       "      <td>-144.124023</td>\n",
       "      <td>-145.522949</td>\n",
       "      <td>-14.317627</td>\n",
       "      <td>0.020914</td>\n",
       "      <td>7</td>\n",
       "      <td>857229</td>\n",
       "      <td>17.376682</td>\n",
       "      <td>463.421387</td>\n",
       "      <td>98</td>\n",
       "      <td>32.6650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226878</th>\n",
       "      <td>1267180</td>\n",
       "      <td>9.949658</td>\n",
       "      <td>49.856387</td>\n",
       "      <td>497.00</td>\n",
       "      <td>1515</td>\n",
       "      <td>17</td>\n",
       "      <td>1956</td>\n",
       "      <td>6561</td>\n",
       "      <td>34.034641</td>\n",
       "      <td>-126274136</td>\n",
       "      <td>-0.959000</td>\n",
       "      <td>0.047194</td>\n",
       "      <td>260.889069</td>\n",
       "      <td>0</td>\n",
       "      <td>681.798340</td>\n",
       "      <td>657.745605</td>\n",
       "      <td>642.011475</td>\n",
       "      <td>0.050846</td>\n",
       "      <td>5</td>\n",
       "      <td>857225</td>\n",
       "      <td>21.177349</td>\n",
       "      <td>573.086243</td>\n",
       "      <td>12</td>\n",
       "      <td>4.9700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226879</th>\n",
       "      <td>1267184</td>\n",
       "      <td>9.949688</td>\n",
       "      <td>49.362831</td>\n",
       "      <td>2344.00</td>\n",
       "      <td>1517</td>\n",
       "      <td>15</td>\n",
       "      <td>2264</td>\n",
       "      <td>6499</td>\n",
       "      <td>9.173168</td>\n",
       "      <td>160967872</td>\n",
       "      <td>0.645957</td>\n",
       "      <td>-0.011381</td>\n",
       "      <td>447.678040</td>\n",
       "      <td>23</td>\n",
       "      <td>282.119385</td>\n",
       "      <td>79.830811</td>\n",
       "      <td>10.140381</td>\n",
       "      <td>0.014716</td>\n",
       "      <td>7</td>\n",
       "      <td>824157</td>\n",
       "      <td>18.283070</td>\n",
       "      <td>471.167419</td>\n",
       "      <td>89</td>\n",
       "      <td>23.4400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226881</th>\n",
       "      <td>1267189</td>\n",
       "      <td>9.949701</td>\n",
       "      <td>49.114458</td>\n",
       "      <td>2014.50</td>\n",
       "      <td>1529</td>\n",
       "      <td>12</td>\n",
       "      <td>2608</td>\n",
       "      <td>6632</td>\n",
       "      <td>27.137199</td>\n",
       "      <td>104082784</td>\n",
       "      <td>-0.481382</td>\n",
       "      <td>-0.012974</td>\n",
       "      <td>447.814392</td>\n",
       "      <td>21</td>\n",
       "      <td>187.934082</td>\n",
       "      <td>90.763672</td>\n",
       "      <td>168.527100</td>\n",
       "      <td>0.045602</td>\n",
       "      <td>18</td>\n",
       "      <td>907894</td>\n",
       "      <td>18.010750</td>\n",
       "      <td>473.227966</td>\n",
       "      <td>72</td>\n",
       "      <td>20.1450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226882</th>\n",
       "      <td>1267192</td>\n",
       "      <td>9.949731</td>\n",
       "      <td>49.893196</td>\n",
       "      <td>2891.00</td>\n",
       "      <td>1566</td>\n",
       "      <td>15</td>\n",
       "      <td>2088</td>\n",
       "      <td>6482</td>\n",
       "      <td>-36.581142</td>\n",
       "      <td>-219142496</td>\n",
       "      <td>1.348770</td>\n",
       "      <td>0.060537</td>\n",
       "      <td>331.815918</td>\n",
       "      <td>21</td>\n",
       "      <td>-68.830078</td>\n",
       "      <td>-160.909668</td>\n",
       "      <td>11.658203</td>\n",
       "      <td>-0.046048</td>\n",
       "      <td>11</td>\n",
       "      <td>857705</td>\n",
       "      <td>16.320225</td>\n",
       "      <td>450.409271</td>\n",
       "      <td>75</td>\n",
       "      <td>28.9100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>116199 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             ID         X          Y        h  BLDFIE_WeigAver  \\\n",
       "1            12  6.050039  47.995344  2746.25             1523   \n",
       "2            15  6.050046  49.865317  2229.25             1517   \n",
       "5            19  6.050053  49.877876   529.00             1531   \n",
       "8            27  6.050083  49.281439  3921.25             1488   \n",
       "9            35  6.050119  49.928610  1765.00             1510   \n",
       "...         ...       ...        ...      ...              ...   \n",
       "226876  1267176  9.949637  49.887471  3266.50             1558   \n",
       "226878  1267180  9.949658  49.856387   497.00             1515   \n",
       "226879  1267184  9.949688  49.362831  2344.00             1517   \n",
       "226881  1267189  9.949701  49.114458  2014.50             1529   \n",
       "226882  1267192  9.949731  49.893196  2891.00             1566   \n",
       "\n",
       "        CECSOL_WeigAver  CHELSA_bio18  CHELSA_bio4  convergence        cti  \\\n",
       "1                    12          2612         6181     3.549103  -71279992   \n",
       "2                    13          2191         5901    31.054762 -186807440   \n",
       "5                    12          2184         5915   -24.278454 -377335296   \n",
       "8                    13          2345         5915     3.646593 -223499248   \n",
       "9                    13          1976         5917    -2.138205 -393005696   \n",
       "...                 ...           ...          ...          ...        ...   \n",
       "226876               14          2074         6484     4.993805 -196691680   \n",
       "226878               17          1956         6561    34.034641 -126274136   \n",
       "226879               15          2264         6499     9.173168  160967872   \n",
       "226881               12          2608         6632    27.137199  104082784   \n",
       "226882               15          2088         6482   -36.581142 -219142496   \n",
       "\n",
       "        devmagnitude  eastness        elev  forestheight  glad_ard_SVVI_max  \\\n",
       "1           0.507727 -0.021408  322.920227            26         660.006104   \n",
       "2          -1.375050 -0.126880  291.412537             7        1028.385498   \n",
       "5           0.265329 -0.248356  335.534760            25         593.601074   \n",
       "8           0.383314  0.062349  309.142609            25         862.362305   \n",
       "9          -1.467515 -0.316702  301.649567            20         248.561035   \n",
       "...              ...       ...         ...           ...                ...   \n",
       "226876      1.260540  0.044238  328.019165            26        -144.124023   \n",
       "226878     -0.959000  0.047194  260.889069             0         681.798340   \n",
       "226879      0.645957 -0.011381  447.678040            23         282.119385   \n",
       "226881     -0.481382 -0.012974  447.814392            21         187.934082   \n",
       "226882      1.348770  0.060537  331.815918            21         -68.830078   \n",
       "\n",
       "        glad_ard_SVVI_med  glad_ard_SVVI_min  northness  ORCDRC_WeigAver  \\\n",
       "1               92.722168         190.979736  -0.034787               16   \n",
       "2              915.806396         841.586182   0.024677               16   \n",
       "5              228.712402         315.298340  -0.127365               17   \n",
       "8              263.612793         249.693115  -0.068810               16   \n",
       "9              164.831299         237.283447  -0.144407               19   \n",
       "...                   ...                ...        ...              ...   \n",
       "226876        -145.522949         -14.317627   0.020914                7   \n",
       "226878         657.745605         642.011475   0.050846                5   \n",
       "226879          79.830811          10.140381   0.014716                7   \n",
       "226881          90.763672         168.527100   0.045602               18   \n",
       "226882        -160.909668          11.658203  -0.046048               11   \n",
       "\n",
       "        outlet_dist_dw_basin  SBIO3_Isothermality_5_15cm  \\\n",
       "1                     784807                   20.798000   \n",
       "2                     766444                   19.941267   \n",
       "5                     764713                   19.760756   \n",
       "8                     781120                   17.538614   \n",
       "9                     773647                   21.324263   \n",
       "...                      ...                         ...   \n",
       "226876                857229                   17.376682   \n",
       "226878                857225                   21.177349   \n",
       "226879                824157                   18.283070   \n",
       "226881                907894                   18.010750   \n",
       "226882                857705                   16.320225   \n",
       "\n",
       "        SBIO4_Temperature_Seasonality_5_15cm  treecover   hm_sel  \n",
       "1                                 460.501221         97  27.4625  \n",
       "2                                 454.185089         54  22.2925  \n",
       "5                                 448.580811         96   5.2900  \n",
       "8                                 463.280243        100  39.2125  \n",
       "9                                 465.046478         87  17.6500  \n",
       "...                                      ...        ...      ...  \n",
       "226876                            463.421387         98  32.6650  \n",
       "226878                            573.086243         12   4.9700  \n",
       "226879                            471.167419         89  23.4400  \n",
       "226881                            473.227966         72  20.1450  \n",
       "226882                            450.409271         75  28.9100  \n",
       "\n",
       "[116199 rows x 24 columns]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors_hm_sel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>hm_sel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.050039</td>\n",
       "      <td>47.995344</td>\n",
       "      <td>27.4625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6.050046</td>\n",
       "      <td>49.865317</td>\n",
       "      <td>22.2925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.050053</td>\n",
       "      <td>49.877876</td>\n",
       "      <td>5.2900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.050083</td>\n",
       "      <td>49.281439</td>\n",
       "      <td>39.2125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6.050119</td>\n",
       "      <td>49.928610</td>\n",
       "      <td>17.6500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226876</th>\n",
       "      <td>9.949637</td>\n",
       "      <td>49.887471</td>\n",
       "      <td>32.6650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226878</th>\n",
       "      <td>9.949658</td>\n",
       "      <td>49.856387</td>\n",
       "      <td>4.9700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226879</th>\n",
       "      <td>9.949688</td>\n",
       "      <td>49.362831</td>\n",
       "      <td>23.4400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226881</th>\n",
       "      <td>9.949701</td>\n",
       "      <td>49.114458</td>\n",
       "      <td>20.1450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226882</th>\n",
       "      <td>9.949731</td>\n",
       "      <td>49.893196</td>\n",
       "      <td>28.9100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>116199 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               X          Y   hm_sel\n",
       "1       6.050039  47.995344  27.4625\n",
       "2       6.050046  49.865317  22.2925\n",
       "5       6.050053  49.877876   5.2900\n",
       "8       6.050083  49.281439  39.2125\n",
       "9       6.050119  49.928610  17.6500\n",
       "...          ...        ...      ...\n",
       "226876  9.949637  49.887471  32.6650\n",
       "226878  9.949658  49.856387   4.9700\n",
       "226879  9.949688  49.362831  23.4400\n",
       "226881  9.949701  49.114458  20.1450\n",
       "226882  9.949731  49.893196  28.9100\n",
       "\n",
       "[116199 rows x 3 columns]"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_y_hm_sel = predictors_hm_sel[[\"X\",\"Y\",\"hm_sel\"]]\n",
    "x_y_hm_sel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Normalize the data\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler()\n",
    "data = scaler.fit_transform(x_y_hm_sel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.4490e+03, 2.5580e+03, 2.3750e+03, 2.2710e+03, 2.7280e+03,\n",
       "        3.3330e+03, 4.4110e+03, 5.5060e+03, 6.5250e+03, 7.5690e+03,\n",
       "        8.9780e+03, 1.0236e+04, 1.1240e+04, 1.0795e+04, 9.7710e+03,\n",
       "        7.9490e+03, 5.6670e+03, 3.7270e+03, 2.4290e+03, 1.4340e+03,\n",
       "        8.8400e+02, 4.8700e+02, 2.8500e+02, 1.5300e+02, 1.0600e+02,\n",
       "        6.5000e+01, 4.1000e+01, 2.4000e+01, 2.9000e+01, 2.2000e+01,\n",
       "        1.6000e+01, 2.0000e+01, 1.5000e+01, 1.2000e+01, 1.5000e+01,\n",
       "        5.0000e+00, 9.0000e+00, 8.0000e+00, 7.0000e+00, 7.0000e+00,\n",
       "        7.0000e+00, 3.0000e+00, 2.0000e+00, 7.0000e+00, 4.0000e+00,\n",
       "        2.0000e+00, 4.0000e+00, 6.0000e+00, 1.0000e+00, 2.0000e+00]),\n",
       " array([0.  , 0.02, 0.04, 0.06, 0.08, 0.1 , 0.12, 0.14, 0.16, 0.18, 0.2 ,\n",
       "        0.22, 0.24, 0.26, 0.28, 0.3 , 0.32, 0.34, 0.36, 0.38, 0.4 , 0.42,\n",
       "        0.44, 0.46, 0.48, 0.5 , 0.52, 0.54, 0.56, 0.58, 0.6 , 0.62, 0.64,\n",
       "        0.66, 0.68, 0.7 , 0.72, 0.74, 0.76, 0.78, 0.8 , 0.82, 0.84, 0.86,\n",
       "        0.88, 0.9 , 0.92, 0.94, 0.96, 0.98, 1.  ]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Inspect the ranges \n",
    "fig,ax = plt.subplots(1,3,figsize=(15,5))\n",
    "ax[0].hist(data[:,0],50)\n",
    "ax[1].hist(data[:,1],50)\n",
    "ax[2].hist(data[:,2],50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train.shape: torch.Size([81339, 2]), X_test.shape: torch.Size([34860, 2]), y_train.shape: torch.Size([81339]), y_test.shape: torch.Size([34860])\n"
     ]
    }
   ],
   "source": [
    "#Split the data\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[:,:2], data[:,2], test_size=0.30, random_state=0)\n",
    "X_train = torch.FloatTensor(X_train)\n",
    "y_train = torch.FloatTensor(y_train)\n",
    "X_test = torch.FloatTensor(X_test)\n",
    "y_test = torch.FloatTensor(y_test)\n",
    "print('X_train.shape: {}, X_test.shape: {}, y_train.shape: {}, y_test.shape: {}'.format(X_train.shape, X_test.shape, y_train.shape, y_test.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron(torch.nn.Module):\n",
    "    def __init__(self,input_size, output_size, use_activation_fn=False):\n",
    "        super(Perceptron, self).__init__()\n",
    "        self.fc = nn.Linear(input_size,output_size) # Initializes weights with uniform distribution centered in zero\n",
    "        self.activation_fn = nn.ReLU() # instead of Heaviside step fn\n",
    "        self.use_activation_fn = use_activation_fn # If we want to use an activation function\n",
    "    def forward(self, x):\n",
    "        output = self.fc(x)\n",
    "        if self.use_activation_fn:\n",
    "            output = self.activation_fn(output) # To add the non-linearity. Try training you Perceptron with and without the non-linearity\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create percetron\n",
    "model = Perceptron(input_size=2, output_size=1 , use_activation_fn=True)\n",
    "criterion = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.train()\n",
    "epoch = 5000\n",
    "all_loss=[]\n",
    "for epoch in range(epoch):\n",
    "    optimizer.zero_grad()\n",
    "    # Forward pass\n",
    "    y_pred = model(X_train)\n",
    "    # Compute Loss\n",
    "    loss = criterion(y_pred.squeeze(), y_train)\n",
    "   \n",
    "    # Backward pass\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    all_loss.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f72adb26430>]"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(all_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss after Training 0.009606563486158848\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(X_test)\n",
    "    after_train = criterion(y_pred.squeeze(), y_test) \n",
    "    print('Test loss after Training' , after_train.item())\n",
    "\n",
    "    y_pred = y_pred.detach().numpy().squeeze()\n",
    "    slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "    fig,ax=plt.subplots()\n",
    "    ax.scatter(y_pred, y_test)\n",
    "    ax.set_xlabel('Prediction')\n",
    "    ax.set_ylabel('True')\n",
    "    ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}