Sonic_IEEE_Sensitivity_Analysis.ipynb

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      "cell_type": "markdown",
      "metadata": {
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        "<a href=\"https://colab.research.google.com/github/yohanesnuwara/volve-machine-learning/blob/main/Sonic_IEEE_Sensitivity_Analysis.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "## Sensitivity analysis for sonic log prediction using two-stage evolutionary model"
      ],
      "metadata": {
        "id": "Y6qV9oIPqh34"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_percentage_error\n",
        "\n",
        "%config InlineBackend.figure_format = 'retina'"
      ],
      "metadata": {
        "id": "PJMD1G8XUp62"
      },
      "execution_count": 1,
      "outputs": []
    },
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      "source": [
        "def bias_score(y_actual, y_pred):\n",
        "  d = y_pred - y_actual\n",
        "  b = d.sum() / len(d)\n",
        "  return b\n",
        "\n",
        "def SI_score(y_actual, y_pred):\n",
        "  d = ((y_pred - y_pred.mean()) - (y_actual - y_actual.mean()))\n",
        "  s1 = d.sum()**2 / len(y_actual)\n",
        "  s2 = y_actual.sum() / len(y_actual)\n",
        "  si = np.sqrt(s1 / s2)\n",
        "  return si\n",
        "\n",
        "def MAPE(y_actual, y_pred):\n",
        "  diff = abs((y_pred - y_actual) / y_actual)\n",
        "  sum = np.sum(diff)\n",
        "  mape = sum / len(y_actual)\n",
        "  return mape\n",
        "\n",
        "def R2_score(y_actual, y_pred):\n",
        "  return 1 - (np.sum((y_actual - y_pred)**2) / np.sum((y_actual - y_pred.mean())**2))"
      ],
      "metadata": {
        "id": "aG675pnMegF5"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## DT Sensitivity ANalysis"
      ],
      "metadata": {
        "id": "t8c8IurdxuHy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Read full dataset\n",
        "DT_df = pd.read_csv('/content/DT_Volve_Normalized_Test.csv')\n",
        "\n",
        "# Eliminate NaNs\n",
        "DT_df = DT_df.dropna().reset_index(drop=True)\n",
        "\n",
        "DT_df"
      ],
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        "outputId": "bef2de36-84a8-4a63-e29f-3d2ec58c0776"
      },
      "execution_count": 38,
      "outputs": [
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              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-636ead31-39c8-4358-be30-f5fe990b3d63 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-636ead31-39c8-4358-be30-f5fe990b3d63');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "DT_df.columns"
      ],
      "metadata": {
        "id": "6NJ4DKgVz86Y",
        "outputId": "f166a05e-ba43-42a6-aae4-72d5ae07a23c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['CALI', 'DRHO', 'GR', 'NPHI', 'PEF', 'RACEHM', 'RACELM', 'RHOB', 'ROP',\n",
              "       'RPCEHM', 'RPCELM', 'RT', '0.1', '0.2', '0.3', '0.4', '0.5', '0.6',\n",
              "       '0.7', '0.8', '0.9', 's'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Read full dataset\n",
        "colname = ['CALI', 'DRHO', 'GR', 'NPHI', 'PEF', 'RACEHM', 'RACELM', 'RHOB', 'ROP',\n",
        "       'RPCEHM', 'RPCELM', 'RT', 's']\n",
        "DT_df = pd.read_csv('/content/YOHAN_DT.csv', delimiter=';', names=colname)\n",
        "\n",
        "# Eliminate NaNs\n",
        "DT_df = DT_df.dropna().reset_index(drop=True)\n",
        "\n",
        "DT_df"
      ],
      "metadata": {
        "id": "1HIgcpBUzfgX",
        "outputId": "efcaabee-a90f-4f21-d018-3cfba6f722a4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        }
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          CALI      DRHO        GR      NPHI       PEF    RACEHM    RACELM  \\\n",
              "0     0.422486  0.695652  0.002694  0.183642  0.371982  0.000304  0.000948   \n",
              "1     0.513713  0.690342  0.005553  0.253772  0.415814  0.000272  0.000827   \n",
              "2     0.636258  0.687023  0.009344  0.236626  0.399572  0.000263  0.000825   \n",
              "3     0.513713  0.673747  0.024396  0.435528  0.097053  0.000043  0.000120   \n",
              "4     0.513713  0.693661  0.005355  0.123457  0.422206  0.000560  0.001585   \n",
              "...        ...       ...       ...       ...       ...       ...       ...   \n",
              "4753  0.513713  0.617325  0.007038  0.269204  0.205298  0.003849  0.005270   \n",
              "4754  0.392142  0.672088  0.027770  0.331447  0.058607  0.000060  0.000202   \n",
              "4755  0.513713  0.676402  0.045120  0.239540  0.236818  0.000392  0.001142   \n",
              "4756  0.513713  0.671092  0.045340  0.207819  0.290961  0.000514  0.001449   \n",
              "4757  0.422291  0.673747  0.029863  0.413237  0.074943  0.000061  0.000181   \n",
              "\n",
              "          RHOB       ROP    RPCEHM    RPCELM        RT         s  \n",
              "0     0.540006  0.600484  0.000028  0.009380  0.000028  0.184679  \n",
              "1     0.471851  0.359957  0.000033  0.009105  0.000033  0.266895  \n",
              "2     0.467183  0.205846  0.000030  0.008888  0.000030  0.250278  \n",
              "3     0.178695  0.831873  0.000003  0.001118  0.000003  0.595341  \n",
              "4     0.571749  0.553468  0.000082  0.020309  0.000082  0.169857  \n",
              "...        ...       ...       ...       ...       ...       ...  \n",
              "4753  0.238446  0.449225  0.000516  0.139580  0.000516  0.445725  \n",
              "4754  0.285688  0.831327  0.000006  0.001929  0.000006  0.529950  \n",
              "4755  0.524041  0.573480  0.000043  0.012821  0.000043  0.308876  \n",
              "4756  0.545327  0.537687  0.000044  0.014613  0.000044  0.269403  \n",
              "4757  0.205770  0.782299  0.000004  0.001628  0.000004  0.489493  \n",
              "\n",
              "[4758 rows x 13 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-26bf49cb-decc-4d2f-a509-46bce3b295f1\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
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              "        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>CALI</th>\n",
              "      <th>DRHO</th>\n",
              "      <th>GR</th>\n",
              "      <th>NPHI</th>\n",
              "      <th>PEF</th>\n",
              "      <th>RACEHM</th>\n",
              "      <th>RACELM</th>\n",
              "      <th>RHOB</th>\n",
              "      <th>ROP</th>\n",
              "      <th>RPCEHM</th>\n",
              "      <th>RPCELM</th>\n",
              "      <th>RT</th>\n",
              "      <th>s</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.422486</td>\n",
              "      <td>0.695652</td>\n",
              "      <td>0.002694</td>\n",
              "      <td>0.183642</td>\n",
              "      <td>0.371982</td>\n",
              "      <td>0.000304</td>\n",
              "      <td>0.000948</td>\n",
              "      <td>0.540006</td>\n",
              "      <td>0.600484</td>\n",
              "      <td>0.000028</td>\n",
              "      <td>0.009380</td>\n",
              "      <td>0.000028</td>\n",
              "      <td>0.184679</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.690342</td>\n",
              "      <td>0.005553</td>\n",
              "      <td>0.253772</td>\n",
              "      <td>0.415814</td>\n",
              "      <td>0.000272</td>\n",
              "      <td>0.000827</td>\n",
              "      <td>0.471851</td>\n",
              "      <td>0.359957</td>\n",
              "      <td>0.000033</td>\n",
              "      <td>0.009105</td>\n",
              "      <td>0.000033</td>\n",
              "      <td>0.266895</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.636258</td>\n",
              "      <td>0.687023</td>\n",
              "      <td>0.009344</td>\n",
              "      <td>0.236626</td>\n",
              "      <td>0.399572</td>\n",
              "      <td>0.000263</td>\n",
              "      <td>0.000825</td>\n",
              "      <td>0.467183</td>\n",
              "      <td>0.205846</td>\n",
              "      <td>0.000030</td>\n",
              "      <td>0.008888</td>\n",
              "      <td>0.000030</td>\n",
              "      <td>0.250278</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.673747</td>\n",
              "      <td>0.024396</td>\n",
              "      <td>0.435528</td>\n",
              "      <td>0.097053</td>\n",
              "      <td>0.000043</td>\n",
              "      <td>0.000120</td>\n",
              "      <td>0.178695</td>\n",
              "      <td>0.831873</td>\n",
              "      <td>0.000003</td>\n",
              "      <td>0.001118</td>\n",
              "      <td>0.000003</td>\n",
              "      <td>0.595341</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.693661</td>\n",
              "      <td>0.005355</td>\n",
              "      <td>0.123457</td>\n",
              "      <td>0.422206</td>\n",
              "      <td>0.000560</td>\n",
              "      <td>0.001585</td>\n",
              "      <td>0.571749</td>\n",
              "      <td>0.553468</td>\n",
              "      <td>0.000082</td>\n",
              "      <td>0.020309</td>\n",
              "      <td>0.000082</td>\n",
              "      <td>0.169857</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",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4753</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.617325</td>\n",
              "      <td>0.007038</td>\n",
              "      <td>0.269204</td>\n",
              "      <td>0.205298</td>\n",
              "      <td>0.003849</td>\n",
              "      <td>0.005270</td>\n",
              "      <td>0.238446</td>\n",
              "      <td>0.449225</td>\n",
              "      <td>0.000516</td>\n",
              "      <td>0.139580</td>\n",
              "      <td>0.000516</td>\n",
              "      <td>0.445725</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4754</th>\n",
              "      <td>0.392142</td>\n",
              "      <td>0.672088</td>\n",
              "      <td>0.027770</td>\n",
              "      <td>0.331447</td>\n",
              "      <td>0.058607</td>\n",
              "      <td>0.000060</td>\n",
              "      <td>0.000202</td>\n",
              "      <td>0.285688</td>\n",
              "      <td>0.831327</td>\n",
              "      <td>0.000006</td>\n",
              "      <td>0.001929</td>\n",
              "      <td>0.000006</td>\n",
              "      <td>0.529950</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4755</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.676402</td>\n",
              "      <td>0.045120</td>\n",
              "      <td>0.239540</td>\n",
              "      <td>0.236818</td>\n",
              "      <td>0.000392</td>\n",
              "      <td>0.001142</td>\n",
              "      <td>0.524041</td>\n",
              "      <td>0.573480</td>\n",
              "      <td>0.000043</td>\n",
              "      <td>0.012821</td>\n",
              "      <td>0.000043</td>\n",
              "      <td>0.308876</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4756</th>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.671092</td>\n",
              "      <td>0.045340</td>\n",
              "      <td>0.207819</td>\n",
              "      <td>0.290961</td>\n",
              "      <td>0.000514</td>\n",
              "      <td>0.001449</td>\n",
              "      <td>0.545327</td>\n",
              "      <td>0.537687</td>\n",
              "      <td>0.000044</td>\n",
              "      <td>0.014613</td>\n",
              "      <td>0.000044</td>\n",
              "      <td>0.269403</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4757</th>\n",
              "      <td>0.422291</td>\n",
              "      <td>0.673747</td>\n",
              "      <td>0.029863</td>\n",
              "      <td>0.413237</td>\n",
              "      <td>0.074943</td>\n",
              "      <td>0.000061</td>\n",
              "      <td>0.000181</td>\n",
              "      <td>0.205770</td>\n",
              "      <td>0.782299</td>\n",
              "      <td>0.000004</td>\n",
              "      <td>0.001628</td>\n",
              "      <td>0.000004</td>\n",
              "      <td>0.489493</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>4758 rows × 13 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-26bf49cb-decc-4d2f-a509-46bce3b295f1')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-26bf49cb-decc-4d2f-a509-46bce3b295f1 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-26bf49cb-decc-4d2f-a509-46bce3b295f1');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def DT_extended_elimination(df1_transf, term=[1,1,1,1,1,1,1,1]):\n",
        "  a,b,c,d,e,f,g,h = term\n",
        "\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)\n",
        "\n",
        "  # Weights\n",
        "  w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = 0.5031,\t1.4726,\t0.6406,\t1.5049,\t1.1661,\t0.3136,\t1.4603,\t1.0598,\t1.6055,\t0.8324,\t-1.1867,\t1.0798,\t1.7063,\t3.0303,\t-1.2994,\t0.1373,\t1.1493,\t0.0133,\t0.7760,\t0.5400\n",
        "\n",
        "  # Equation\n",
        "  a=a*w1*(CALI)*np.sqrt(w2*GR)*(w3*ROP)**2*np.tan(w4*ROP)\n",
        "  b=b*w5*NPHI/np.sign(RPCELM) \n",
        "  c=c*-np.sqrt(w6*ROP)*np.log1p(w7*0.4)*np.log1p(w8*PEF) \n",
        "  d=d*-w19*abs(NPHI)*np.log1p(w9*PEF)*np.tan(w10*NPHI) \n",
        "  e=e*-w11*(w12*0.1)**2 \n",
        "  f=f*w13*(w14*0.4)**2*np.cos(w15*RPCELM)**2*np.tan(w16*RPCELM) \n",
        "  g=g*w17*0.1003*np.tan(w18*NPHI) \n",
        "  h=h*0.1003*w20\n",
        "\n",
        "  DT1 = a+b+c+d+e+f+g+h\n",
        "  return DT1"
      ],
      "metadata": {
        "id": "zlk-F61qwo6r"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def DT_extended(df1_transf):\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)\n",
        "\n",
        "  # Weights\n",
        "  w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = \\\n",
        "  0.5031,\t1.4726,\t0.6406,\t1.5049,\t1.1661,\t0.3136,\t1.4603,\t1.0598,\t1.6055,\t\\\n",
        "  0.8324,\t-1.1867,\t1.0798,\t1.7063,\t3.0303,\t-1.2994,\t0.1373,\t1.1493,\t0.0133,\t\\\n",
        "  0.7760,\t0.5400\n",
        "\n",
        "  # DT_ext = w1 * CALI * np.sqrt(w2 * GR) * (w3 * ROP)**2 * np.tan(w4 * ROP) + \\\n",
        "  # w5 * NPHI / np.sign(RPCELM) - np.sqrt(w6 * ROP) * np.log1p(w7 * 0.4) * np.log1p(w8 * PEF) - \\\n",
        "  # abs(w19 * (NPHI)) * np.log1p(w9 * PEF) * np.log1p(w10 * NPHI) - \\\n",
        "  # w11 * w12 * 0.1000**2 + \\\n",
        "  # w13 * w14 * 0.4000**2 * np.cos(w15 * RPCELM)**2 * np.tan(w16 * RPCELM) + \\\n",
        "  # w17 * 0.1003 * np.tan(w18 * NPHI) + 0.1003 * w20\n",
        "\n",
        "  DT_ext = \\\n",
        "  (w1 * CALI * np.sqrt(w2 * GR) * (w3 * ROP)**2 * np.tan(w4 * ROP)) + \\\n",
        "  (w5 * NPHI / np.sign(RPCELM)) - \\\n",
        "  (np.sqrt(w6 * ROP) * np.log1p(w7 * 0.4) * np.log1p(w8 * PEF)) - \\\n",
        "  (abs(w19 * (NPHI)) * np.log1p(w9 * PEF) * np.log1p(w10 * NPHI)) - \\\n",
        "  (w11 * w12 * 0.1000**2) + \\\n",
        "  (w13 * w14 * (0.4000**2) * (np.cos(w15 * RPCELM)**2) * np.tan(w16 * RPCELM)) + \\\n",
        "  (w17 * 0.1003 * np.tan(w18 * NPHI)) + \\\n",
        "  (0.1003 * w20)  \n",
        "\n",
        "  return DT_ext"
      ],
      "metadata": {
        "id": "68piXOETwcfu"
      },
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "DT_ext = DT_extended(DT_df)\n",
        "\n",
        "print(mean_absolute_percentage_error(DT_df['s'], DT_ext)) # skelarn\n",
        "print(MAPE(DT_df['s'], DT_ext))\n",
        "print(R2_score(DT_df['s'], DT_ext))"
      ],
      "metadata": {
        "id": "Qtu8pMaJ0Kqy",
        "outputId": "db8ab55c-8e5f-476d-d6e5-619d45f6a200",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.25535711771871955\n",
            "0.25535711771871955\n",
            "0.8293877263291289\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# f=np.full(4,1)\n",
        "\n",
        "# def identity_matrix(n_terms):\n",
        "#   f=np.full(n_terms,1)\n",
        "#   x=[]\n",
        "#   for i in range(n_terms):\n",
        "#     f_copy = f.copy()\n",
        "#     f_copy[i] = 0\n",
        "#     x.append(list(f_copy))\n",
        "#   return x\n",
        "\n",
        "# np.dot(identity_matrix(8), [9,8,3,4,5,6,7,1])\n",
        "# np.dot([9,8,3,4,5,6,7,1], identity_matrix(8))"
      ],
      "metadata": {
        "id": "XVl_79fP31Io"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# def DT_extended_sensitivity_analysis(df1_transf, term=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]):\n",
        "#   a1,a2,a3,a4,b,c1,c2,c3,d1,d2,d3,e1,e2,f1,f2,f3,f4,g1,g2,h = term\n",
        "\n",
        "#   GR = df1_transf['GR'].astype(float)\n",
        "#   RHOB = df1_transf['RHOB'].astype(float)\n",
        "#   NPHI = df1_transf['NPHI'].astype(float)\n",
        "#   RACELM = df1_transf['RACELM'].astype(float)\n",
        "#   PEF = df1_transf['NPHI'].astype(float)\n",
        "#   RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "#   CALI = df1_transf['CALI'].astype(float)\n",
        "#   ROP = df1_transf['ROP'].astype(float)\n",
        "#   DRHO = df1_transf['DRHO'].astype(float)\n",
        "\n",
        "#   # Weights\n",
        "#   w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = 0.5031,\t1.4726,\t0.6406,\t1.5049,\t1.1661,\t0.3136,\t1.4603,\t1.0598,\t1.6055,\t0.8324,\t-1.1867,\t1.0798,\t1.7063,\t3.0303,\t-1.2994,\t0.1373,\t1.1493,\t0.0133,\t0.7760,\t0.5400\n",
        "\n",
        "#   # Equation\n",
        "#   a1=(w1*(CALI))**a1\n",
        "#   a2=(np.sqrt(w2*GR))**a2\n",
        "#   a3=((w3*ROP)**2)**a3\n",
        "#   a4=(np.tan(w4*ROP))**a4\n",
        "#   b=(w5*NPHI/np.sign(RPCELM))**b\n",
        "#   c1=(-np.sqrt(w6*ROP))**c1\n",
        "#   c2=(np.log1p(w7*0.4))**c2\n",
        "#   c3=(np.log1p(w8*PEF))**c3 \n",
        "#   d1=(-w19*abs(NPHI))**d1\n",
        "#   d2=(np.log1p(w9*PEF))**d2\n",
        "#   d3=(np.tan(w10*NPHI))**d3 \n",
        "#   e1=(-w11)**e1 \n",
        "#   e2=((w12*0.1)**2)**e2\n",
        "#   f1=(w13)**f1\n",
        "#   f2=((w14*0.4)**2)**f2\n",
        "#   f3=(np.cos(w15*RPCELM)**2)**f3\n",
        "#   f4=(np.tan(w16*RPCELM))**f4 \n",
        "#   g1=(w17*0.1003)**g1\n",
        "#   g2=(np.tan(w18*NPHI))**g2 \n",
        "#   h=(0.1003*w20)**h\n",
        "\n",
        "#   DT1 = (a1*a2*a3*a4)+b+(c1*c2*c3)+(d1*d2*d3)+(e1*e2)+(f1*f2*f3*f4)+(g1*g2)+h\n",
        "#   return DT1"
      ],
      "metadata": {
        "id": "9jvTVUZ-w5MY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# a=pd.DataFrame(DT_df.iloc[:,1]).pow(3)\n",
        "# b=pd.DataFrame(DT_df.iloc[:,1]).pow(3)\n",
        "# np.prod([a,b])"
      ],
      "metadata": {
        "id": "WZtj6WXcLyZD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# from itertools import accumulate\n",
        "# x=pd.DataFrame([9,9,1])\n",
        "# y=pd.DataFrame([9,9,1])\n",
        "# z=pd.DataFrame([9,9,1])\n",
        "# l=[x,y,z]\n",
        "# out = [*accumulate(l, lambda a, b: a*b)]\n",
        "\n",
        "# # out"
      ],
      "metadata": {
        "id": "ltKtj0l4NzTZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# def augment(x_list):\n",
        "#   # x_list = [i.values for i in x_list]\n",
        "#   n_terms = len(x_list)\n",
        "#   f=np.full(n_terms,1)\n",
        "#   dt_aug=[]\n",
        "#   for i in range(n_terms):\n",
        "#     f_copy = f.copy()\n",
        "#     f_copy[i] = 0\n",
        "#     replace_with_one = [a.pow(b) for a, b in zip(x_list, f_copy)]\n",
        "#     # replace_with_one = [i**j for i, j in zip(x_list, f_copy)]\n",
        "#     aug = np.prod(replace_with_one)\n",
        "#     print()\n",
        "#     # dt_aug.append(aug)\n",
        "#   # return dt_aug\n",
        "#   # return x_list\n",
        "  \n",
        "# # augment([7,8,9,1])"
      ],
      "metadata": {
        "id": "R-YMiIQLFYZA"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def DT_extended_augment(df1_transf, term=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]):\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)\n",
        "\n",
        "  # Weights\n",
        "  w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = 0.5031,\t1.4726,\t0.6406,\t1.5049,\t1.1661,\t0.3136,\t1.4603,\t1.0598,\t1.6055,\t0.8324,\t-1.1867,\t1.0798,\t1.7063,\t3.0303,\t-1.2994,\t0.1373,\t1.1493,\t0.0133,\t0.7760,\t0.5400\n",
        "\n",
        "  # Equation\n",
        "  ax=a*w1*(CALI)*np.sqrt(w2*GR)*(w3*ROP)**2*np.tan(w4*ROP)\n",
        "  bx=b*w5*NPHI/np.sign(RPCELM) \n",
        "  cx=c*-np.sqrt(w6*ROP)*np.log1p(w7*0.4)*np.log1p(w8*PEF) \n",
        "  dx=d*-w19*abs(NPHI)*np.log1p(w9*PEF)*np.tan(w10*NPHI) \n",
        "  ex=e*-w11*(w12*0.1)**2 \n",
        "  fx=f*w13*(w14*0.4)**2*np.cos(w15*RPCELM)**2*np.tan(w16*RPCELM) \n",
        "  gx=g*w17*0.1003*np.tan(w18*NPHI) \n",
        "  hx=h*0.1003*w20\n",
        "\n",
        "  DT_incomplete = ax+bx+cx+dx+ex+fx+gx+hx\n",
        "\n",
        "  if a==0:\n",
        "    a1=w1*(CALI)\n",
        "    a2=np.sqrt(w2*GR)\n",
        "    a3=(w3*ROP)**2\n",
        "    a4=np.tan(w4*ROP)    \n",
        "    x_list =[a1,a2,a3,a4]\n",
        "    # x_list = [i.values for i in x_list]\n",
        "  if b==0:\n",
        "    b1=w5*NPHI\n",
        "    b2=1/np.sign(RPCELM) \n",
        "    x_list = [b1,b2]\n",
        "  if c==0:\n",
        "    c1=-np.sqrt(w6*ROP)*np.log1p(w7*0.4)\n",
        "    c2=np.log1p(w8*PEF) \n",
        "    x_list = [c1,c2]\n",
        "  if d==0:\n",
        "    d1=-w19*abs(NPHI)\n",
        "    d2=np.log1p(w9*PEF)\n",
        "    d3=np.tan(w10*NPHI) \n",
        "    x_list = [d1,d2,d3]\n",
        "  if e==0:\n",
        "    e1 = -w11*(w12*0.1)**2\n",
        "    x_list = [DT_incomplete]\n",
        "  if f==0:\n",
        "    # f1=w13*(w14*0.4)**2\n",
        "    f2=np.cos(w15*RPCELM)**2\n",
        "    f3=np.tan(w16*RPCELM)\n",
        "    x_list = [f2,f3]\n",
        "  if g==0:\n",
        "    g1=w17*0.1003*np.tan(w18*NPHI) \n",
        "    x_list = [g1]\n",
        "  if h==0:\n",
        "    h1=0.1003*w20\n",
        "    x_list = [DT_incomplete]\n",
        "\n",
        "  DT_augment_part = augment(x_list)\n",
        "  # n_terms = len(x_list)\n",
        "  # M_identity = identity_matrix(n_terms) # make identity matrix\n",
        "  # DT_augment_part = np.dot(M_identity, x_list)\n",
        "  # DT_augment_part = np.sum(DT_augment_part)\n",
        "  # DT1 = DT_incomplete + DT_augment_part\n",
        "\n",
        "  return DT_augment_part"
      ],
      "metadata": {
        "id": "8nZATJFezBmB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def squared_error(ys_orig,ys_line):\n",
        "    return sum((ys_line - ys_orig) * (ys_line - ys_orig))\n",
        "\n",
        "def r2_score2(ys_orig,ys_line):\n",
        "    y_mean_line = [np.mean(ys_orig) for y in ys_orig]\n",
        "    squared_error_regr = squared_error(ys_orig, ys_line)\n",
        "    squared_error_y_mean = squared_error(ys_orig, y_mean_line)\n",
        "    return 1 - (squared_error_regr/squared_error_y_mean)"
      ],
      "metadata": {
        "id": "oEtmtjLlXevR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "term = np.full(8,1)\n",
        "\n",
        "# Sensitivity analysis of whole eqn\n",
        "DT_full_pred = DT_extended_elimination(DT_df, term=term)\n",
        "DT_actu = DT_df['s']\n",
        "r2 = R2_score(DT_actu, DT_full_pred)\n",
        "mape = mean_absolute_percentage_error(DT_actu, DT_full_pred)\n",
        "bias = bias_score(DT_actu, DT_full_pred)\n",
        "si = SI_score(DT_actu, DT_full_pred)\n",
        "# print(r2, mape, bias, si)\n",
        "\n",
        "full_sens_df = pd.DataFrame({'Term': ['Full'], 'Method': 'Full', 'R2': [r2], 'MAPE': [mape], 'Bias': [bias], 'SI': [si]})\n",
        "\n",
        "eqn = [  \n",
        "  'w1*(CALI)*np.sqrt(w2*GR)*(w3*ROP)**2*np.tan(w4*ROP)',\n",
        "  'w5*NPHI/np.sign(RPCELM)',\n",
        "  '-np.sqrt(w6*ROP)*np.log1p(w7*0.4)*np.log1p(w8*PEF)', \n",
        "  '-w19*abs(NPHI)*np.log1p(w9*PEF)*np.tan(w10*NPHI)', \n",
        "  '-w11*(w12*0.1)**2', \n",
        "  'w13*(w14*0.4)**2*np.cos(w15*RPCELM)**2*np.tan(w16*RPCELM)', \n",
        "  'w17*0.1003*np.tan(w18*NPHI)', \n",
        "  '0.1003*w20'\n",
        "]\n",
        "\n",
        "R2 = []\n",
        "MAPE = []\n",
        "Bias = []\n",
        "SI = []\n",
        "\n",
        "for i in range(len(term)):\n",
        "  t = term.copy()\n",
        "  t[i] = 0\n",
        "\n",
        "  DT_pred = DT_extended_elimination(DT_df, term=t)\n",
        "  DT_actu = DT_df['s']\n",
        "  r2 = R2_score(DT_actu, DT_pred)\n",
        "  mse = mean_squared_error(DT_actu, DT_pred)\n",
        "  mape = mean_absolute_percentage_error(DT_actu, DT_pred)\n",
        "  rmse = np.sqrt(mse)\n",
        "  bias = bias_score(DT_actu, DT_pred)\n",
        "  si = SI_score(DT_actu, DT_pred)\n",
        "\n",
        "  R2.append(r2)\n",
        "  MAPE.append(mape)\n",
        "  Bias.append(bias)\n",
        "  SI.append(si)\n",
        "\n",
        "method = np.full(8, 'Elim')\n",
        "sens_df = pd.DataFrame({'Term': eqn, 'Method': method, 'R2': R2, 'MAPE': MAPE, 'Bias': Bias, 'SI': SI})\n",
        "result_df = pd.concat((full_sens_df, sens_df))\n",
        "\n",
        "result_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "id": "d-KjQVOrxGOa",
        "outputId": "9e164306-a8cb-46a3-e04d-03abc0681049"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                                                Term Method        R2  \\\n",
              "0                                               Full   Full  0.728661   \n",
              "0  w1*(CALI)*np.sqrt(w2*GR)*(w3*ROP)**2*np.tan(w4...   Elim  0.515961   \n",
              "1                            w5*NPHI/np.sign(RPCELM)   Elim -0.291319   \n",
              "2  -np.sqrt(w6*ROP)*np.log1p(w7*0.4)*np.log1p(w8*...   Elim  0.789513   \n",
              "3   -w19*abs(NPHI)*np.log1p(w9*PEF)*np.tan(w10*NPHI)   Elim  0.789997   \n",
              "4                                  -w11*(w12*0.1)**2   Elim  0.714659   \n",
              "5  w13*(w14*0.4)**2*np.cos(w15*RPCELM)**2*np.tan(...   Elim  0.722418   \n",
              "6                        w17*0.1003*np.tan(w18*NPHI)   Elim  0.727127   \n",
              "7                                         0.1003*w20   Elim  0.636623   \n",
              "\n",
              "       MAPE      Bias            SI  \n",
              "0  0.161783 -0.015863  0.000000e+00  \n",
              "0  0.166971 -0.034540  2.478388e-15  \n",
              "1  0.976638 -0.386358  6.836933e-16  \n",
              "2  0.227093  0.037873  0.000000e+00  \n",
              "3  0.178550  0.045114  3.931236e-15  \n",
              "4  0.154263 -0.029699  4.529468e-15  \n",
              "5  0.156858 -0.020262  2.905696e-15  \n",
              "6  0.161598 -0.016350  4.273083e-15  \n",
              "7  0.197614 -0.070025  1.111002e-15  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-1c7ad755-d854-4763-b575-f7050218f466\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Term</th>\n",
              "      <th>Method</th>\n",
              "      <th>R2</th>\n",
              "      <th>MAPE</th>\n",
              "      <th>Bias</th>\n",
              "      <th>SI</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Full</td>\n",
              "      <td>Full</td>\n",
              "      <td>0.728661</td>\n",
              "      <td>0.161783</td>\n",
              "      <td>-0.015863</td>\n",
              "      <td>0.000000e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>w1*(CALI)*np.sqrt(w2*GR)*(w3*ROP)**2*np.tan(w4...</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.515961</td>\n",
              "      <td>0.166971</td>\n",
              "      <td>-0.034540</td>\n",
              "      <td>2.478388e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>w5*NPHI/np.sign(RPCELM)</td>\n",
              "      <td>Elim</td>\n",
              "      <td>-0.291319</td>\n",
              "      <td>0.976638</td>\n",
              "      <td>-0.386358</td>\n",
              "      <td>6.836933e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-np.sqrt(w6*ROP)*np.log1p(w7*0.4)*np.log1p(w8*...</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.789513</td>\n",
              "      <td>0.227093</td>\n",
              "      <td>0.037873</td>\n",
              "      <td>0.000000e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-w19*abs(NPHI)*np.log1p(w9*PEF)*np.tan(w10*NPHI)</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.789997</td>\n",
              "      <td>0.178550</td>\n",
              "      <td>0.045114</td>\n",
              "      <td>3.931236e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-w11*(w12*0.1)**2</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.714659</td>\n",
              "      <td>0.154263</td>\n",
              "      <td>-0.029699</td>\n",
              "      <td>4.529468e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>w13*(w14*0.4)**2*np.cos(w15*RPCELM)**2*np.tan(...</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.722418</td>\n",
              "      <td>0.156858</td>\n",
              "      <td>-0.020262</td>\n",
              "      <td>2.905696e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>w17*0.1003*np.tan(w18*NPHI)</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.727127</td>\n",
              "      <td>0.161598</td>\n",
              "      <td>-0.016350</td>\n",
              "      <td>4.273083e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.1003*w20</td>\n",
              "      <td>Elim</td>\n",
              "      <td>0.636623</td>\n",
              "      <td>0.197614</td>\n",
              "      <td>-0.070025</td>\n",
              "      <td>1.111002e-15</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "term = np.full(20,1)\n",
        "\n",
        "# Sensitivity analysis of whole eqn\n",
        "DT_full_pred = DT_extended_sensitivity_analysis(DT_df, term=term)\n",
        "DT_actu = DT_df['s']\n",
        "r2 = r2_score(DT_actu, DT_full_pred)\n",
        "mape = mean_absolute_percentage_error(DT_actu, DT_full_pred)\n",
        "bias = bias_score(DT_actu, DT_full_pred)\n",
        "si = SI_score(DT_actu, DT_full_pred)\n",
        "# print(r2, mape, bias, si)\n",
        "\n",
        "full_sens_df = pd.DataFrame({'Term': ['Full'], 'R2': [r2], 'MAPE': [mape], 'Bias': [bias], 'SI': [si]})\n",
        "\n",
        "\n",
        "eqn = [\n",
        "  'w1*(CALI)',\n",
        "  'np.sqrt(w2*GR)',\n",
        "  '(w3*ROP)**2',\n",
        "  'np.tan(w4*ROP)',\n",
        "  'w5*NPHI/np.sign(RPCELM)',\n",
        "  '-np.sqrt(w6*ROP)',\n",
        "  'np.log1p(w7*0.4)',\n",
        "  'np.log1p(w8*PEF)',\n",
        "  '-w19*abs(NPHI)',\n",
        "  'np.log1p(w9*PEF)',\n",
        "  'np.tan(w10*NPHI)',\n",
        "  '-w11',\n",
        "  '(w12*0.1)**2',\n",
        "  'w13',\n",
        "  '(w14*0.4)**2',\n",
        "  'np.cos(w15*RPCELM)**2',\n",
        "  'np.tan(w16*RPCELM)',\n",
        "  'w17*0.1003',\n",
        "  'np.tan(w18*NPHI)',\n",
        "  '0.1003*w20'\n",
        "]\n",
        "\n",
        "R2 = []\n",
        "MAPE = []\n",
        "Bias = []\n",
        "SI = []\n",
        "\n",
        "for i in range(len(term)):\n",
        "  t = term.copy()\n",
        "  t[i] = 0\n",
        "\n",
        "  DT_pred = DT_extended_sensitivity_analysis(DT_df, term=t)\n",
        "  DT_actu = DT_df['s']\n",
        "  r2 = r2_score(DT_actu, DT_pred)\n",
        "  mse = mean_squared_error(DT_actu, DT_pred)\n",
        "  mape = mean_absolute_percentage_error(DT_actu, DT_pred)\n",
        "  rmse = np.sqrt(mse)\n",
        "  bias = bias_score(DT_actu, DT_pred)\n",
        "  si = SI_score(DT_actu, DT_pred)\n",
        "\n",
        "  R2.append(r2)\n",
        "  MAPE.append(mape)\n",
        "  Bias.append(bias)\n",
        "  SI.append(si)\n",
        "\n",
        "sens_df = pd.DataFrame({'Term': eqn, 'R2': R2, 'MAPE': MAPE, 'Bias': Bias, 'SI': SI})\n",
        "result_df = pd.concat((full_sens_df, sens_df))\n",
        "\n",
        "result_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 707
        },
        "id": "HFCDncaco6Ws",
        "outputId": "3a585fe8-bf31-48ea-9a69-86221a149241"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                       Term          R2         MAPE      Bias            SI\n",
              "0                      Full    0.760772    57.179434 -0.011290  1.829509e-15\n",
              "0                 w1*(CALI)    0.689338    58.685963  0.025329  2.744264e-14\n",
              "1            np.sqrt(w2*GR)    0.627299    71.107194  0.037963  1.683149e-14\n",
              "2               (w3*ROP)**2    0.763749    63.100538  0.035872  8.598694e-15\n",
              "3            np.tan(w4*ROP)    0.728000    57.245889 -0.016607  1.207476e-14\n",
              "4   w5*NPHI/np.sign(RPCELM)  -15.008930   583.677906  0.696112  5.634889e-14\n",
              "5          -np.sqrt(w6*ROP)    0.321886    59.368014  0.137439  1.262361e-14\n",
              "6          np.log1p(w7*0.4)    0.518369    56.559520 -0.062337  1.317247e-14\n",
              "7          np.log1p(w8*PEF)    0.101726    38.146693 -0.154611  1.829509e-16\n",
              "8            -w19*abs(NPHI)    0.273518    57.351667  0.109069  1.500198e-14\n",
              "9          np.log1p(w9*PEF)    0.617952    57.171089 -0.039615  3.293117e-15\n",
              "10         np.tan(w10*NPHI)    0.451416    57.175060 -0.063563  1.317247e-14\n",
              "11                     -w11    0.759184    56.028341 -0.013467  8.964596e-15\n",
              "12             (w12*0.1)**2  -38.976590   679.525817  1.161573  1.646558e-14\n",
              "13                      w13    0.762454    49.781734 -0.013848  1.774624e-14\n",
              "14             (w14*0.4)**2    0.762171    51.471693 -0.013264  7.318038e-16\n",
              "15    np.cos(w15*RPCELM)**2    0.760166    57.485838 -0.011058  1.280657e-14\n",
              "16       np.tan(w16*RPCELM) -181.044360  1347.437116  2.483869  1.408722e-13\n",
              "17               w17*0.1003    0.768882    57.213893 -0.008337  2.122231e-14\n",
              "18         np.tan(w18*NPHI)    0.447548   118.238914  0.103600  1.829509e-15\n",
              "19               0.1003*w20  -24.960150   559.033656  0.934548  3.988330e-14"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-9a951a54-1c48-49f8-a2f2-1ccb2907bb8b\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Term</th>\n",
              "      <th>R2</th>\n",
              "      <th>MAPE</th>\n",
              "      <th>Bias</th>\n",
              "      <th>SI</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Full</td>\n",
              "      <td>0.760772</td>\n",
              "      <td>57.179434</td>\n",
              "      <td>-0.011290</td>\n",
              "      <td>1.829509e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>w1*(CALI)</td>\n",
              "      <td>0.689338</td>\n",
              "      <td>58.685963</td>\n",
              "      <td>0.025329</td>\n",
              "      <td>2.744264e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>np.sqrt(w2*GR)</td>\n",
              "      <td>0.627299</td>\n",
              "      <td>71.107194</td>\n",
              "      <td>0.037963</td>\n",
              "      <td>1.683149e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>(w3*ROP)**2</td>\n",
              "      <td>0.763749</td>\n",
              "      <td>63.100538</td>\n",
              "      <td>0.035872</td>\n",
              "      <td>8.598694e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>np.tan(w4*ROP)</td>\n",
              "      <td>0.728000</td>\n",
              "      <td>57.245889</td>\n",
              "      <td>-0.016607</td>\n",
              "      <td>1.207476e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>w5*NPHI/np.sign(RPCELM)</td>\n",
              "      <td>-15.008930</td>\n",
              "      <td>583.677906</td>\n",
              "      <td>0.696112</td>\n",
              "      <td>5.634889e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>-np.sqrt(w6*ROP)</td>\n",
              "      <td>0.321886</td>\n",
              "      <td>59.368014</td>\n",
              "      <td>0.137439</td>\n",
              "      <td>1.262361e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>np.log1p(w7*0.4)</td>\n",
              "      <td>0.518369</td>\n",
              "      <td>56.559520</td>\n",
              "      <td>-0.062337</td>\n",
              "      <td>1.317247e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>np.log1p(w8*PEF)</td>\n",
              "      <td>0.101726</td>\n",
              "      <td>38.146693</td>\n",
              "      <td>-0.154611</td>\n",
              "      <td>1.829509e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>-w19*abs(NPHI)</td>\n",
              "      <td>0.273518</td>\n",
              "      <td>57.351667</td>\n",
              "      <td>0.109069</td>\n",
              "      <td>1.500198e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>np.log1p(w9*PEF)</td>\n",
              "      <td>0.617952</td>\n",
              "      <td>57.171089</td>\n",
              "      <td>-0.039615</td>\n",
              "      <td>3.293117e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>np.tan(w10*NPHI)</td>\n",
              "      <td>0.451416</td>\n",
              "      <td>57.175060</td>\n",
              "      <td>-0.063563</td>\n",
              "      <td>1.317247e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>-w11</td>\n",
              "      <td>0.759184</td>\n",
              "      <td>56.028341</td>\n",
              "      <td>-0.013467</td>\n",
              "      <td>8.964596e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>(w12*0.1)**2</td>\n",
              "      <td>-38.976590</td>\n",
              "      <td>679.525817</td>\n",
              "      <td>1.161573</td>\n",
              "      <td>1.646558e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>w13</td>\n",
              "      <td>0.762454</td>\n",
              "      <td>49.781734</td>\n",
              "      <td>-0.013848</td>\n",
              "      <td>1.774624e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>(w14*0.4)**2</td>\n",
              "      <td>0.762171</td>\n",
              "      <td>51.471693</td>\n",
              "      <td>-0.013264</td>\n",
              "      <td>7.318038e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>np.cos(w15*RPCELM)**2</td>\n",
              "      <td>0.760166</td>\n",
              "      <td>57.485838</td>\n",
              "      <td>-0.011058</td>\n",
              "      <td>1.280657e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>np.tan(w16*RPCELM)</td>\n",
              "      <td>-181.044360</td>\n",
              "      <td>1347.437116</td>\n",
              "      <td>2.483869</td>\n",
              "      <td>1.408722e-13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>w17*0.1003</td>\n",
              "      <td>0.768882</td>\n",
              "      <td>57.213893</td>\n",
              "      <td>-0.008337</td>\n",
              "      <td>2.122231e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>np.tan(w18*NPHI)</td>\n",
              "      <td>0.447548</td>\n",
              "      <td>118.238914</td>\n",
              "      <td>0.103600</td>\n",
              "      <td>1.829509e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>0.1003*w20</td>\n",
              "      <td>-24.960150</td>\n",
              "      <td>559.033656</td>\n",
              "      <td>0.934548</td>\n",
              "      <td>3.988330e-14</td>\n",
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          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "DT_full_pred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dxEbvXZirQ-e",
        "outputId": "a914f238-33c3-40df-ce23-a2abc6cc9947"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0        0.225824\n",
              "1        0.221100\n",
              "2        0.214766\n",
              "3        0.206913\n",
              "4        0.199056\n",
              "           ...   \n",
              "19026    0.253004\n",
              "19027    0.255000\n",
              "19028    0.260492\n",
              "19029    0.257543\n",
              "19030    0.260601\n",
              "Length: 19031, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## DTS Sensitivity Analysis"
      ],
      "metadata": {
        "id": "hVct2yUHxnKY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Read full dataset\n",
        "DT_df = pd.read_csv('/content/DTS_Volve_Normalized_Test.csv')\n",
        "\n",
        "# Eliminate NaNs\n",
        "DT_df = DT_df.dropna().reset_index(drop=True)\n",
        "\n",
        "DT_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "vjPKXSiixgB9",
        "outputId": "9c150522-a4ff-41ce-9040-10b5cbaf9cf5"
      },
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "        no   no.1      CALI      DRHO        GR      NPHI       PEF    RACEHM  \\\n",
              "0        0   6087  0.513713  0.683704  0.003333  0.065158  0.453014  0.000982   \n",
              "1        1  17495  0.422486  0.657816  0.006920  0.174040  0.367026  0.000393   \n",
              "2        2  21986  0.513713  0.681713  0.050135  0.409294  0.262679  0.000140   \n",
              "3        3   5822  0.558452  0.700299  0.001654  0.178326  0.416548  0.000403   \n",
              "4        4  22071  0.604746  0.559243  0.020566  0.179698  0.245840  0.000201   \n",
              "...    ...    ...       ...       ...       ...       ...       ...       ...   \n",
              "4738  4738   3625  0.361992  0.687023  0.024749  0.411523  0.072219  0.000058   \n",
              "4739  4739   1077  0.491150  0.669101  0.024610  0.231653  0.155839  0.000401   \n",
              "4740  4740   9462  0.605135  0.700299  0.009035  0.147462  0.386998  0.000540   \n",
              "4741  4741   8153  0.513713  0.713575  0.004100  0.140604  0.427341  0.000451   \n",
              "4742  4742  15902  0.422680  0.742449  0.003308  0.155521  0.373187  0.000346   \n",
              "\n",
              "        RACELM      RHOB  ...  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  \\\n",
              "0     0.002137  0.603492  ...    0    0    0    0    0    0    0    0    0   \n",
              "1     0.001173  0.520213  ...    0    0    0    0    0    0    0    0    0   \n",
              "2     0.000308  0.483895  ...    0    0    0    0    0    0    0    0    0   \n",
              "3     0.001256  0.497993  ...    0    0    0    0    0    0    0    0    0   \n",
              "4     0.000341  0.468210  ...    0    0    0    0    0    0    0    0    0   \n",
              "...        ...       ...  ...  ...  ...  ...  ...  ...  ...  ...  ...  ...   \n",
              "4738  0.000236  0.205770  ...    0    0    0    0    0    0    0    0    0   \n",
              "4739  0.001245  0.419755  ...    0    0    0    0    0    0    0    0    0   \n",
              "4740  0.001602  0.550275  ...    0    0    0    0    0    0    0    0    0   \n",
              "4741  0.001304  0.549342  ...    0    0    0    0    0    0    0    0    0   \n",
              "4742  0.000944  0.523481  ...    0    0    0    0    0    0    0    0    0   \n",
              "\n",
              "             s  \n",
              "0     0.110481  \n",
              "1     0.164048  \n",
              "2     0.231630  \n",
              "3     0.161428  \n",
              "4     0.136263  \n",
              "...        ...  \n",
              "4738  0.390767  \n",
              "4739  0.166683  \n",
              "4740  0.128690  \n",
              "4741  0.134240  \n",
              "4742  0.156662  \n",
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              "      <th></th>\n",
              "      <th>no</th>\n",
              "      <th>no.1</th>\n",
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              "      <td>0.065158</td>\n",
              "      <td>0.453014</td>\n",
              "      <td>0.000982</td>\n",
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              "      <td>0.657816</td>\n",
              "      <td>0.006920</td>\n",
              "      <td>0.174040</td>\n",
              "      <td>0.367026</td>\n",
              "      <td>0.000393</td>\n",
              "      <td>0.001173</td>\n",
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              "      <td>21986</td>\n",
              "      <td>0.513713</td>\n",
              "      <td>0.681713</td>\n",
              "      <td>0.050135</td>\n",
              "      <td>0.409294</td>\n",
              "      <td>0.262679</td>\n",
              "      <td>0.000140</td>\n",
              "      <td>0.000308</td>\n",
              "      <td>0.483895</td>\n",
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              "      <td>0</td>\n",
              "      <td>0.231630</td>\n",
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              "      <th>3</th>\n",
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              "      <td>0.700299</td>\n",
              "      <td>0.001654</td>\n",
              "      <td>0.178326</td>\n",
              "      <td>0.416548</td>\n",
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              "      <td>0.020566</td>\n",
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              "      <td>0.245840</td>\n",
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              "      <td>0.000944</td>\n",
              "      <td>0.523481</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
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              "      <td>0.156662</td>\n",
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              "<p>4743 rows × 24 columns</p>\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  </div>\n",
              "  "
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          },
          "metadata": {},
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Read full dataset\n",
        "colname = ['CALI', 'DRHO', 'GR', 'NPHI', 'PEF', 'RACEHM', 'RACELM', 'RHOB', 'ROP',\n",
        "       'RPCEHM', 'RPCELM', 'RT', 's']\n",
        "DT_df = pd.read_csv('/content/YOHAN_DTS.csv', delimiter=';', names=colname)\n",
        "\n",
        "# Eliminate NaNs\n",
        "DT_df = DT_df.dropna().reset_index(drop=True)\n",
        "\n",
        "DT_df"
      ],
      "metadata": {
        "id": "4fTcZVO28F74",
        "outputId": "f08e3ffa-36bf-469a-9b94-ad829215b898",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        }
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          CALI      DRHO        GR      NPHI       PEF    RACEHM    RACELM  \\\n",
              "0     0.513713  0.683704  0.003333  0.065158  0.453014  0.000982  0.002137   \n",
              "1     0.422486  0.657816  0.006920  0.174040  0.367026  0.000393  0.001173   \n",
              "2     0.513713  0.681713  0.050135  0.409294  0.262679  0.000140  0.000308   \n",
              "3     0.558452  0.700299  0.001654  0.178326  0.416548  0.000403  0.001256   \n",
              "4     0.604746  0.559243  0.020566  0.179698  0.245840  0.000201  0.000341   \n",
              "...        ...       ...       ...       ...       ...       ...       ...   \n",
              "4738  0.361992  0.687023  0.024749  0.411523  0.072219  0.000058  0.000236   \n",
              "4739  0.491150  0.669101  0.024610  0.231653  0.155839  0.000401  0.001245   \n",
              "4740  0.605135  0.700299  0.009035  0.147462  0.386998  0.000540  0.001602   \n",
              "4741  0.513713  0.713575  0.004100  0.140604  0.427341  0.000451  0.001304   \n",
              "4742  0.422680  0.742449  0.003308  0.155521  0.373187  0.000346  0.000944   \n",
              "\n",
              "          RHOB       ROP    RPCEHM    RPCELM        RT         s  \n",
              "0     0.603492  0.507436  0.000164  0.038381  0.000164  0.110481  \n",
              "1     0.520213  0.650159  0.000043  0.012648  0.000043  0.164048  \n",
              "2     0.483895  0.645181  0.000026  0.005820  0.000026  0.231630  \n",
              "3     0.497993  0.451818  0.000042  0.012916  0.000042  0.161428  \n",
              "4     0.468210  0.538693  0.000052  0.008725  0.000052  0.136263  \n",
              "...        ...       ...       ...       ...       ...       ...  \n",
              "4738  0.205770  0.782818  0.000003  0.001727  0.000003  0.390767  \n",
              "4739  0.419755  0.676867  0.000039  0.012610  0.000039  0.166683  \n",
              "4740  0.550275  0.527870  0.000069  0.018800  0.000069  0.128690  \n",
              "4741  0.549342  0.412936  0.000059  0.015727  0.000059  0.134240  \n",
              "4742  0.523481  0.620167  0.000038  0.011078  0.000038  0.156662  \n",
              "\n",
              "[4743 rows x 13 columns]"
            ],
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CALI</th>\n",
              "      <th>DRHO</th>\n",
              "      <th>GR</th>\n",
              "      <th>NPHI</th>\n",
              "      <th>PEF</th>\n",
              "      <th>RACEHM</th>\n",
              "      <th>RACELM</th>\n",
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              "      <th>4740</th>\n",
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              "<p>4743 rows × 13 columns</p>\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-50010485-48ba-46d6-8692-775543d8becf button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-50010485-48ba-46d6-8692-775543d8becf');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "min(DT_df['s'])"
      ],
      "metadata": {
        "id": "tpcIwehdxdRO",
        "outputId": "e931eb20-84f2-4f2f-eb44-f9a521b4003b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1e-08"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def DTS_extended(df1_transf):\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)  \n",
        "  DTS_ext = 1.1573 * (0.6216)**RPCELM * PEF**GR * abs(NPHI) * np.cos(CALI)**CALI * np.cos(CALI)**(RPCELM**PEF) * np.cos(GR) * np.cos(NPHI)**GR * np.cos(RHOB)**NPHI * np.cos(RHOB)**(NPHI**(GR**NPHI)) * np.sign(GR) * np.sign(ROP)\n",
        "  return DTS_ext  "
      ],
      "metadata": {
        "id": "D8SKlt9tkYD3"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def DTS_extended(df1_transf):\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)  \n",
        "  \n",
        "  w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = \\\n",
        "  0.9218,\t0.9069,\t-0.4394,\t1.0982,\t1.0988,\t-0.5895,\t1.6804,\t1.5166,\t\\\n",
        "  2.6716,\t1.3256,\t0.0374,\t1.2709,\t1.7112,\t-0.4737,\t-1.2486,\t1.0312,\\\n",
        "  3.3366,\t6.7381,\t1.4668,\t1.343123104\n",
        "\n",
        "  # w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = \\\n",
        "  # 0.9692,\t-0.7301,\t0.7516,\t1.4647,\t0.9964,\t0.1425,\t1.8056,\t39.0119,\t\\\n",
        "  # -1.5550,\t2.3382,\t1.5743,\t0.5369,\t1.1624,\t-1.4585,\t-0.8881,\t1.3855,\t\\\n",
        "  # 0.4326,\t0.8925,\t2.7454,\t1.288151188  \n",
        "  \n",
        "  DTS_ext = \\\n",
        "  w1 * 1.1573 * (w8 * 0.6216)**(w2 * RPCELM) * (w3 * PEF**GR) * \\\n",
        "  abs(w4 * NPHI) * np.cos(w5 * CALI)**(w6 * CALI) * \\\n",
        "  np.cos(w9 * CALI)**((w10 * RPCELM)**(w11 * PEF)) * np.cos(w12 * GR) \\\n",
        "  * np.cos(w13 * NPHI)**(w19 * GR) * np.cos(w14 * RHOB)**(w15 * NPHI) * \\\n",
        "  np.cos(w16 * RHOB)**((w7 * NPHI)**(w17 * GR)**(w18 * NPHI)) \\\n",
        "  * np.sign(GR) * np.sign(ROP)\n",
        "\n",
        "  DTS_ext = \\\n",
        "  w1*1.1572*(w2*0.6216)**(w3*RPCELM)*(w4*PEF**GR)*abs(w5*NPHI)*\\\n",
        "  (np.cos(w6*CALI)**(w7*CALI))*np.cos(w8*CALI)**((w9*RPCELM)**(w10*PEF))*\\\n",
        "  np.cos(w11*GR)*(np.cos(w12*NPHI)**(w13*GR))*np.cos(w14*RHOB)**(w15*NPHI)*\\\n",
        "  np.cos(w16*RHOB)**(w17*NPHI**((w18*GR)**(w19*NPHI)))*np.sign(GR)*np.sign(ROP)\n",
        "\n",
        "  return DTS_ext"
      ],
      "metadata": {
        "id": "FQk47HNPsS9H"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "DTS_ext = DTS_extended(DT_df) \n",
        "\n",
        "print(mean_absolute_percentage_error(DT_df['s'], DTS_ext)) # skelarn\n",
        "print(MAPE(DT_df['s'], DTS_ext))\n",
        "print(R2_score(DT_df['s'], DTS_ext))"
      ],
      "metadata": {
        "id": "EAlF8M-RlZMu",
        "outputId": "a02ebb5e-a688-4be0-bbaa-a3656367374c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 387
        }
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-84-82fa57ea2472>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mDTS_ext\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDTS_extended\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDT_df\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmean_absolute_percentage_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDT_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mDTS_ext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# skelarn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mMAPE\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDT_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mDTS_ext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR2_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDT_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m's'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mDTS_ext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36minner_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     63\u001b[0m             \u001b[0mextra_args\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mextra_args\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m             \u001b[0;31m# extra_args > 0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/sklearn/metrics/_regression.py\u001b[0m in \u001b[0;36mmean_absolute_percentage_error\u001b[0;34m(y_true, y_pred, sample_weight, multioutput)\u001b[0m\n\u001b[1;32m    359\u001b[0m     \u001b[0;36m112589990684262.48\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    360\u001b[0m     \"\"\"\n\u001b[0;32m--> 361\u001b[0;31m     y_type, y_true, y_pred, multioutput = _check_reg_targets(\n\u001b[0m\u001b[1;32m    362\u001b[0m         \u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmultioutput\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    363\u001b[0m     )\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/sklearn/metrics/_regression.py\u001b[0m in \u001b[0;36m_check_reg_targets\u001b[0;34m(y_true, y_pred, multioutput, dtype)\u001b[0m\n\u001b[1;32m     94\u001b[0m     \u001b[0mcheck_consistent_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m     \u001b[0my_true\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_true\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mensure_2d\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 96\u001b[0;31m     \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mensure_2d\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     97\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0my_true\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, accept_large_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, estimator)\u001b[0m\n\u001b[1;32m    798\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    799\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mforce_all_finite\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 800\u001b[0;31m             \u001b[0m_assert_all_finite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mallow_nan\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mforce_all_finite\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"allow-nan\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    801\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    802\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mensure_min_samples\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.8/dist-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36m_assert_all_finite\u001b[0;34m(X, allow_nan, msg_dtype)\u001b[0m\n\u001b[1;32m    112\u001b[0m         ):\n\u001b[1;32m    113\u001b[0m             \u001b[0mtype_err\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"infinity\"\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mallow_nan\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m\"NaN, infinity\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m             raise ValueError(\n\u001b[0m\u001b[1;32m    115\u001b[0m                 msg_err.format(\n\u001b[1;32m    116\u001b[0m                     \u001b[0mtype_err\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmsg_dtype\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mmsg_dtype\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: Input contains NaN, infinity or a value too large for dtype('float64')."
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot([0,1],[0,1], c='r')\n",
        "plt.scatter(DT_df['s'], DTS_ext)"
      ],
      "metadata": {
        "id": "zPFd196ywaNx",
        "outputId": "32eab61a-d954-4135-fcd7-b707338e91e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f4d8ebb0520>"
            ]
          },
          "metadata": {},
          "execution_count": 79
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 372,
              "height": 248
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def DTS_extended_sensitivity_analysis(df1_transf, term=[1,1,1,1,1,1,1,1,1,1,1,1]):\n",
        "  a,b,c,d,e,f,g,h,i,j,k,l = term\n",
        "\n",
        "  GR = df1_transf['GR'].astype(float)\n",
        "  RHOB = df1_transf['RHOB'].astype(float)\n",
        "  NPHI = df1_transf['NPHI'].astype(float)\n",
        "  RACELM = df1_transf['RACELM'].astype(float)\n",
        "  PEF = df1_transf['NPHI'].astype(float)\n",
        "  RPCELM = df1_transf['RPCELM'].astype(float)\n",
        "  CALI = df1_transf['CALI'].astype(float)\n",
        "  ROP = df1_transf['ROP'].astype(float)\n",
        "  DRHO = df1_transf['DRHO'].astype(float)\n",
        "\n",
        "  # Weights\n",
        "  w1,w2,w3,w4,w5,w6,w7,w8,w9,w10,w11,w12,w13,w14,w15,w16,w17,w18,w19,w20 = 0.9692,\t-0.7301,\t0.7516,\t1.4647,\t0.9964,\t0.1425,\t1.8056,\t39.0119,\t-1.5550,\t2.3382,\t1.5743,\t0.5369,\t1.1624,\t-1.4585,\t-0.8881,\t1.3855,\t0.4326,\t0.8925,\t2.7454,\t1.288151188\n",
        "\n",
        "  a=(w1*1.1572840756852)**a\n",
        "  b=((w20*0.621609968270664)**(w2*RPCELM))**b\n",
        "  c=((w3*PEF**GR))**c\n",
        "  d=(abs(w4*NPHI))**d\n",
        "  e=((np.cos(w5*CALI)**(w6*CALI)))**e\n",
        "  f=(np.cos(w9*CALI)**((w10*RPCELM)**(w11*PEF)))**f\n",
        "  g=(np.cos(w12*GR))**g\n",
        "  h=((np.cos(w13*NPHI)**(w19*GR)))**h\n",
        "  i=(np.cos(w14*RHOB)**(w15*NPHI))**i\n",
        "  j=(np.cos(w16*RHOB)**(w7*NPHI**((w17*GR)**(w18*NPHI))))**j\n",
        "  k=(np.sign(GR))**k\n",
        "  l=(np.sign(ROP))**l\n",
        "\n",
        "  DTS1 = a*b*c*d*e*f*g*h*i*j*k*l\n",
        "  return DTS1"
      ],
      "metadata": {
        "id": "u_oHXJogf3GZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "term = np.full(12,1)\n",
        "\n",
        "# Sensitivity analysis of whole eqn\n",
        "DT_full_pred = DTS_extended_sensitivity_analysis(DT_df, term=term)\n",
        "DT_actu = DT_df['s']\n",
        "r2 = r2_score(DT_actu, DT_full_pred)\n",
        "mape = mean_absolute_percentage_error(DT_actu, DT_full_pred)\n",
        "bias = bias_score(DT_actu, DT_full_pred)\n",
        "si = SI_score(DT_actu, DT_full_pred)\n",
        "# print(r2, mape, bias, si)\n",
        "\n",
        "full_sens_df = pd.DataFrame({'Term': ['Full'], 'R2': [r2], 'MAPE': [mape], 'Bias': [bias], 'SI': [si]})\n",
        "\n",
        "\n",
        "eqn = [\n",
        "  'w1*1.1572840756852',\n",
        "  '(w20*0.621609968270664)**(w2*RPCELM)',\n",
        "  '(w3*PEF**GR)',\n",
        "  'abs(w4*NPHI)',\n",
        "  '(np.cos(w5*CALI)**(w6*CALI))',\n",
        "  'np.cos(w9*CALI)**((w10*RPCELM)**(w11*PEF))',\n",
        "  'np.cos(w12*GR)',\n",
        "  '(np.cos(w13*NPHI)**(w19*GR))',\n",
        "  'np.cos(w14*RHOB)**(w15*NPHI)',\n",
        "  'np.cos(w16*RHOB)**(w7*NPHI**((w17*GR)**(w18*NPHI)))',\n",
        "  'np.sign(GR)',\n",
        "  'np.sign(ROP)'\n",
        "]\n",
        "\n",
        "R2 = []\n",
        "MAPE = []\n",
        "Bias = []\n",
        "SI = []\n",
        "\n",
        "for i in range(len(term)):\n",
        "  t = term.copy()\n",
        "  t[i] = 0\n",
        "\n",
        "  DT_pred = DTS_extended_sensitivity_analysis(DT_df, term=t)\n",
        "  DT_actu = DT_df['s']\n",
        "  r2 = r2_score(DT_actu, DT_pred)\n",
        "  mse = mean_squared_error(DT_actu, DT_pred)\n",
        "  mape = mean_absolute_percentage_error(DT_actu, DT_pred)\n",
        "  rmse = np.sqrt(mse)\n",
        "  bias = bias_score(DT_actu, DT_pred)\n",
        "  si = SI_score(DT_actu, DT_pred)\n",
        "\n",
        "  R2.append(r2)\n",
        "  MAPE.append(mape)\n",
        "  Bias.append(bias)\n",
        "  SI.append(si)\n",
        "\n",
        "sens_df = pd.DataFrame({'Term': eqn, 'R2': R2, 'MAPE': MAPE, 'Bias': Bias, 'SI': SI})\n",
        "result_df = pd.concat((full_sens_df, sens_df))\n",
        "\n",
        "result_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "CX0-7YSLmtDJ",
        "outputId": "8663430e-8907-4c8a-dc94-9c1e505f2fca"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                                                 Term        R2         MAPE  \\\n",
              "0                                                Full  0.621762   898.835540   \n",
              "0                                  w1*1.1572840756852  0.678259   801.377573   \n",
              "1                (w20*0.621609968270664)**(w2*RPCELM)  0.622949   888.088185   \n",
              "2                                        (w3*PEF**GR) -0.457679  1303.087970   \n",
              "3                                        abs(w4*NPHI) -7.924871  9672.303910   \n",
              "4                        (np.cos(w5*CALI)**(w6*CALI))  0.612982   913.996162   \n",
              "5          np.cos(w9*CALI)**((w10*RPCELM)**(w11*PEF))  0.595602  1401.594672   \n",
              "6                                      np.cos(w12*GR)  0.619674   898.961199   \n",
              "7                        (np.cos(w13*NPHI)**(w19*GR))  0.425557   899.062584   \n",
              "8                        np.cos(w14*RHOB)**(w15*NPHI)  0.640464   870.015314   \n",
              "9   np.cos(w16*RHOB)**(w7*NPHI**((w17*GR)**(w18*NP... -0.029197   999.584666   \n",
              "10                                        np.sign(GR)  0.621762   898.835540   \n",
              "11                                       np.sign(ROP)  0.621762   898.835540   \n",
              "\n",
              "        Bias            SI  \n",
              "0   0.010707  1.144660e-14  \n",
              "0  -0.015086  7.455174e-15  \n",
              "1   0.010212  5.249742e-15  \n",
              "2   0.101812  1.233960e-14  \n",
              "3   0.373912  1.495094e-14  \n",
              "4   0.013191  5.466226e-15  \n",
              "5   0.030110  6.386284e-15  \n",
              "6   0.010927  3.436687e-15  \n",
              "7   0.019802  2.164842e-16  \n",
              "8  -0.001384  3.355505e-15  \n",
              "9   0.067741  1.074303e-14  \n",
              "10  0.010707  1.144660e-14  \n",
              "11  0.010707  1.144660e-14  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-0c3c470a-ad8b-4ae2-b2c6-bd33a912b26d\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Term</th>\n",
              "      <th>R2</th>\n",
              "      <th>MAPE</th>\n",
              "      <th>Bias</th>\n",
              "      <th>SI</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Full</td>\n",
              "      <td>0.621762</td>\n",
              "      <td>898.835540</td>\n",
              "      <td>0.010707</td>\n",
              "      <td>1.144660e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>w1*1.1572840756852</td>\n",
              "      <td>0.678259</td>\n",
              "      <td>801.377573</td>\n",
              "      <td>-0.015086</td>\n",
              "      <td>7.455174e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>(w20*0.621609968270664)**(w2*RPCELM)</td>\n",
              "      <td>0.622949</td>\n",
              "      <td>888.088185</td>\n",
              "      <td>0.010212</td>\n",
              "      <td>5.249742e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>(w3*PEF**GR)</td>\n",
              "      <td>-0.457679</td>\n",
              "      <td>1303.087970</td>\n",
              "      <td>0.101812</td>\n",
              "      <td>1.233960e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>abs(w4*NPHI)</td>\n",
              "      <td>-7.924871</td>\n",
              "      <td>9672.303910</td>\n",
              "      <td>0.373912</td>\n",
              "      <td>1.495094e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>(np.cos(w5*CALI)**(w6*CALI))</td>\n",
              "      <td>0.612982</td>\n",
              "      <td>913.996162</td>\n",
              "      <td>0.013191</td>\n",
              "      <td>5.466226e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>np.cos(w9*CALI)**((w10*RPCELM)**(w11*PEF))</td>\n",
              "      <td>0.595602</td>\n",
              "      <td>1401.594672</td>\n",
              "      <td>0.030110</td>\n",
              "      <td>6.386284e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>np.cos(w12*GR)</td>\n",
              "      <td>0.619674</td>\n",
              "      <td>898.961199</td>\n",
              "      <td>0.010927</td>\n",
              "      <td>3.436687e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>(np.cos(w13*NPHI)**(w19*GR))</td>\n",
              "      <td>0.425557</td>\n",
              "      <td>899.062584</td>\n",
              "      <td>0.019802</td>\n",
              "      <td>2.164842e-16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>np.cos(w14*RHOB)**(w15*NPHI)</td>\n",
              "      <td>0.640464</td>\n",
              "      <td>870.015314</td>\n",
              "      <td>-0.001384</td>\n",
              "      <td>3.355505e-15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>np.cos(w16*RHOB)**(w7*NPHI**((w17*GR)**(w18*NP...</td>\n",
              "      <td>-0.029197</td>\n",
              "      <td>999.584666</td>\n",
              "      <td>0.067741</td>\n",
              "      <td>1.074303e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>np.sign(GR)</td>\n",
              "      <td>0.621762</td>\n",
              "      <td>898.835540</td>\n",
              "      <td>0.010707</td>\n",
              "      <td>1.144660e-14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>np.sign(ROP)</td>\n",
              "      <td>0.621762</td>\n",
              "      <td>898.835540</td>\n",
              "      <td>0.010707</td>\n",
              "      <td>1.144660e-14</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 141
        }
      ]
    }
  ]
}