Measuring_the_Z_boson_mass.ipynb

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      "name": "Measuring the Z boson mass.ipynb",
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      "source": [
        "# Measuring the Z boson mass\n",
        "## About the DataSet: Zmumu.csv\n",
        "\n",
        "\n",
        "Sample of $Z$ boson candidates recorded by CMS in 2011 and published at CERN opendata portal. It comes from DoubleMuon dataset with the following selection applied:\n",
        "\n",
        "- Both muons are \"global\" muons\n",
        "- invariant mass sits in range: 60 GeV < $ M_{\\mu\\mu}$ < 120 GeV\n",
        "- |$\\eta$| < 2.1 for both muons\n",
        "- $p_{t}$ > 20 GeV\n",
        "\n",
        "The following columns presented in the CSV file:\n",
        "\n",
        "- `Run`, Event are the run and event numbers, respectively\n",
        "- `pt` is the transverse momentum $p_{t}$ of the muon\n",
        "- `eta` is the pseudorapidity of the muon: $\\eta$\n",
        "- `phi` is the $\\phi$ angle of the muon direction\n",
        "- `Q` is the charge of the muon\n",
        "- `dxy` is the impact parameter in the transverse plane: $d_{xy}$ - how distant is the track from the collision point\n",
        "- `iso` is the track isolation: $I_{track}$ - how many other tracks are there around given track\n",
        "\n",
        "## Link for the Dataset: http://opendata.cern.ch/record/545"
      ]
    },
    {
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      "metadata": {
        "id": "moEek9sMYsjJ"
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      "source": [
        "# Incase you want to upload the file and use it in Colab\n",
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "execution_count": null,
      "outputs": []
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      "source": [
        "!pip install scikit-optimize"
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            "Collecting scikit-optimize\n",
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            "\u001b[?25hRequirement already satisfied: numpy>=1.13.3 in /usr/local/lib/python3.6/dist-packages (from scikit-optimize) (1.18.5)\n",
            "Collecting pyaml>=16.9\n",
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            "Requirement already satisfied: scipy>=0.19.1 in /usr/local/lib/python3.6/dist-packages (from scikit-optimize) (1.4.1)\n",
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            "Installing collected packages: pyaml, scikit-optimize\n",
            "Successfully installed pyaml-20.4.0 scikit-optimize-0.8.1\n"
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    {
      "cell_type": "code",
      "metadata": {
        "id": "T9Tb9Mi_Duea"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from skopt import gp_minimize\n",
        "%matplotlib inline"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BKNDQQ7FDueq"
      },
      "source": [
        "## Read dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ltNiHr6Dues",
        "outputId": "cfa0c4ff-2dd2-4e45-ee25-d30f97f9d493",
        "colab": {
          "base_uri": "https://localhost:8080/",
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        }
      },
      "source": [
        "df = pd.read_csv('./Zmumu.csv')\n",
        "df.shape"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 14)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u9MBw9wyDue2"
      },
      "source": [
        "Let's calculate the invariant mass $M$ of the two muons using the formula\n",
        "\n",
        "$M = \\sqrt{2p_{t}^{1}p_{t}^{2}(\\cosh(\\eta_{1}-\\eta_{2}) - \\cos(\\phi_{1}-\\phi_{2}))}$"
      ]
    },
    {
      "cell_type": "code",
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        "id": "oOiM9GPwDue4",
        "outputId": "04bb5552-cfdc-47d0-a3e8-25014036f7d3",
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      },
      "source": [
        "df['M'] = np.sqrt(2 * df['pt1'] * df['pt2'] * (np.cosh(df['eta1'] - df['eta2']) - np.cos(df['phi1'] - df['phi2'])))\n",
        "df.head(2)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Run</th>\n",
              "      <th>Event</th>\n",
              "      <th>pt1</th>\n",
              "      <th>eta1</th>\n",
              "      <th>phi1</th>\n",
              "      <th>Q1</th>\n",
              "      <th>dxy1</th>\n",
              "      <th>iso1</th>\n",
              "      <th>pt2</th>\n",
              "      <th>eta2</th>\n",
              "      <th>phi2</th>\n",
              "      <th>Q2</th>\n",
              "      <th>dxy2</th>\n",
              "      <th>iso2</th>\n",
              "      <th>M</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>165617</td>\n",
              "      <td>74969122</td>\n",
              "      <td>54.7055</td>\n",
              "      <td>-0.4324</td>\n",
              "      <td>2.5742</td>\n",
              "      <td>1</td>\n",
              "      <td>-0.0745</td>\n",
              "      <td>0.4999</td>\n",
              "      <td>34.2464</td>\n",
              "      <td>-0.9885</td>\n",
              "      <td>-0.4987</td>\n",
              "      <td>-1</td>\n",
              "      <td>0.0712</td>\n",
              "      <td>3.4221</td>\n",
              "      <td>89.885919</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>165617</td>\n",
              "      <td>75138253</td>\n",
              "      <td>24.5872</td>\n",
              "      <td>-2.0522</td>\n",
              "      <td>2.8666</td>\n",
              "      <td>-1</td>\n",
              "      <td>-0.0554</td>\n",
              "      <td>0.0000</td>\n",
              "      <td>28.5389</td>\n",
              "      <td>0.3852</td>\n",
              "      <td>-1.9912</td>\n",
              "      <td>1</td>\n",
              "      <td>0.0515</td>\n",
              "      <td>0.0000</td>\n",
              "      <td>88.812177</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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            ],
            "text/plain": [
              "      Run     Event      pt1    eta1  ...  Q2    dxy2    iso2          M\n",
              "0  165617  74969122  54.7055 -0.4324  ...  -1  0.0712  3.4221  89.885919\n",
              "1  165617  75138253  24.5872 -2.0522  ...   1  0.0515  0.0000  88.812177\n",
              "\n",
              "[2 rows x 15 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gQs80jWcDufA"
      },
      "source": [
        "# Model\n",
        "\n",
        "The distribution of the Z boson mass has the form of a normal distribution, in addition there is a noise. The distribution of the noise has an exponential form. Thus, the resulting model, it is a result of a superposition of two distributions - normal and polinomial"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "inket7KbDufC"
      },
      "source": [
        "Let's plot the distribution of Z boson mass"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3T1Q_WzXDufD"
      },
      "source": [
        "def plot_mass(mass, bins_count=100):\n",
        "    y, x = np.histogram(mass, bins=bins_count, density=False)\n",
        "    err = np.sqrt(y)\n",
        "\n",
        "    fig = plt.figure(figsize=(15,7))\n",
        "    plt.title('Z mass', fontsize=20)\n",
        "    plt.xlabel(\"$m_{\\mu\\mu}$ [GeV]\", fontsize=20)\n",
        "    plt.ylabel(\"Number of events\", fontsize=20)\n",
        "    plt.errorbar(x[:-1], y, yerr=err, fmt='o', color='red', ecolor='grey', capthick=0.5, zorder=1, label=\"data\")\n",
        "    return y, x"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c6rQxef0DufM",
        "outputId": "1978f9e5-3103-44d6-f7c3-8a83f3bf6745",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 479
        }
      },
      "source": [
        "plot_mass(df.M);"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h2Zd2kg6DufV"
      },
      "source": [
        "\n",
        "```\n",
        "# This is formatted as code\n",
        "```\n",
        "\n",
        "## Now Let's Clean up dataset a bit\n",
        "- Charge of muons should be opposite\n",
        "- $I_{track}$ < 3 and $d_{xy}$ < 0.2 cm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pq1rnW3tDufW"
      },
      "source": [
        "\n",
        "df['df_sign'] = df.Q1*df.Q2\n",
        "iso_cap = 3\n",
        "dxy_cap = 0.2\n",
        "df_isolation = df[(df.df_sign == -1) & (df.iso1 < iso_cap) & (df.iso2 < iso_cap) & (df.dxy1 < dxy_cap) & (df.dxy2 < dxy_cap)]\n",
        "# df = df"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "swm20Bt5Dufc",
        "outputId": "c62f521e-6626-4eae-962c-e4aa356788a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        }
      },
      "source": [
        "plot_mass(df.M)\n",
        "df.shape"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 16)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vzgZyZCnMRJc",
        "outputId": "e8689832-b5b6-41d5-bb07-2679c6bcb39a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        }
      },
      "source": [
        "df=df_isolation\n",
        "plot_mass(df.M)\n",
        "df.shape\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(8819, 16)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EzgDgwjQDufp"
      },
      "source": [
        "### Let's define parametrised model\n",
        "it should represent mixture of 1) Gaussian signal and 2) background that for the simplicity we consider to be flat over mass. So it gives the following set of parameters:\n",
        "\n",
        "- m0 - center of the Gaussian\n",
        "- sigma - standard deviation of the Gaussian\n",
        "- ampl - height of the peak\n",
        "- bck - height of the background \n",
        "\n",
        "finding those parameters is called _fitting_ model into the data. It will be the goal for the rest of the exercise. For simplicity sake we'll stick with old good binned fit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RwDRxjSYDufq"
      },
      "source": [
        "def model_predict(params, X):\n",
        "    m0, sigma, ampl, bck = params\n",
        "    return bck + ampl / (sigma * np.sqrt(2 * np.pi)) * np.exp((-1) * (X - m0)**2 / (2 * sigma**2))"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fUD5OaaODufx"
      },
      "source": [
        "def model_loss(params, X, y):\n",
        "#     y, x = np.histogram(mass, bins=bins_count, density=False)\n",
        "#     residuals = model_predict(params, (x[1:] + x[:-1])/2) - y \n",
        "    residuals = y - model_predict(params, X)\n",
        "    return np.sum(residuals**2) / len(residuals)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1YrFcrUODuf4"
      },
      "source": [
        "def plot_mass_with_model(params, mass, bins_count=100):\n",
        "    y, X = plot_mass(mass, bins_count=bins_count)\n",
        "    X = (X[1:] + X[:-1]) / 2\n",
        "    error = model_loss(params, X, y)\n",
        "    plt.plot(X, model_predict(params, X), color='blue', linewidth=3.0, zorder=2, label=\"fit, loss=%.2f\" % error)\n",
        "    plt.legend(fontsize='x-large')"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "caoDVxMADuf_"
      },
      "source": [
        "## Here you can fit model parameters by hand"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "blzojC0CDugB",
        "outputId": "301d820c-d828-474f-eea0-fba8bfa1e07e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 479
        }
      },
      "source": [
        "plot_mass_with_model((91, 2.0440499861850895, 3940 , 22), df.M)"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zQQkHDBpDugI"
      },
      "source": [
        "## ... but you can do it automatically of course"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vef2uOwTDugK"
      },
      "source": [
        "Setting up a scikit optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jNPMJ5nADugL"
      },
      "source": [
        "from tqdm import tqdm\n",
        "from skopt import Optimizer\n",
        "# 91, 2.0, 3160 , 21\n",
        "search_space = [(90.0, 92.0), # m0 range\n",
        "    (2.0, 2.5), # sigma range\n",
        "    (3000, 5000), # amplitude range\n",
        "    (20, 30) # bck range\n",
        "    ]\n",
        "y, X = np.histogram(df.M, bins=120, density=False)\n",
        "X = (X[1:] + X[:-1]) / 2\n",
        "opt = Optimizer(search_space, base_estimator=\"GP\", acq_func=\"EI\", acq_optimizer=\"lbfgs\")"
      ],
      "execution_count": 104,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9fUVjtMxDugR"
      },
      "source": [
        "Running it for a while. You can re-run this cell several times"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tV6Y3OU_DugS",
        "outputId": "70ce4798-dca4-4d13-d6d5-656d70a5d2d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "from skopt.utils import create_result\n",
        "for i in tqdm(range(50)):\n",
        "    next_x = opt.ask()\n",
        "    f_val = model_loss(next_x, X, y)\n",
        "    opt.tell(next_x, f_val)\n",
        "    \n",
        "res = create_result(Xi=opt.Xi, yi=opt.yi, space=opt.space,\n",
        "                         rng=opt.rng, models=opt.models)"
      ],
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 50/50 [00:10<00:00,  4.58it/s]\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rrCm-2qcDugZ"
      },
      "source": [
        "## A bit of search history"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dgMI4DNdDugc",
        "outputId": "29538705-4d5a-4f8c-aaf1-913ba8540822",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        }
      },
      "source": [
        "import skopt.plots\n",
        "skopt.plots.plot_convergence(res)\n",
        "print (list(zip([\"m0\", \"sigma\", \"ampl\", \"bck\"], res.x)))"
      ],
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[('m0', 90.9069965426124), ('sigma', 2.148663208070879), ('ampl', 3377), ('bck', 24)]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1xSFpG1AauBYQSjZoUJruTRnqTGnNKj/LYVafeg0cETGqPwpiA4cfAjSrb17k0DIrdVWtcleVWV3K0lXV1QaiERHuqqozzeNHM3RoAxs372DHzlZGdLMVrZnVpl5bHBExKiJGp187vxw06tCgQWLy4clixqu8xLpZ3cnUVSVprKRTJJ1WeuVVMCu2yRM9QG5Wr/r8HIek9wGXkiz18SBwKslDfafnUzQrsileXt2sbmVpcVwKvApYGRGvB14JbM6lVFZ4HTOr3FVlVm+yBI7nI+J5AEmNEbEcOC6fYlnRTfazHGZ1K8uSI6vT7V1/SrK+1CZgZT7FsqKbMrG0Su4m9u0LBg3qatKdmdWiPgeOiHhTeniFpLuAQ0gWIbQ6NGrEMMYe0sSmLTtZv3Ebhx/mCXZm9eKAHgCMiP+JiIXpFq5Wp0oD5N6bw6y+ZNnI6aa0q6r0fqykG/Iplg0Epe4qz6wyqy9ZWhwnpqviAhARm0hmVlmd6hgg98wqs3qSJXAMktS++YKkQynAnuVWPV4l16w+ZfnFfxVwt6Qfpu/fRhebLVn9cFeVWX3KMqvqu5KW0vGk+JsjYlk+xbKB4MgJhzB48CDWbdjG8617GNY4pNpFMrN+kKmrKQ0UDhYGQEPDYCY2j+Gpp59j1dpNHDt1QrWLZGb9wPtx2EFxd5VZ/XHgsIPS8SyHZ1aZ1Yssq+OeDswhWdjwUeBh4NGIaM2pbDYAOHCY1Z8sYxw3AB8FhgAnAucBLwVenEO5bIBY++wWAH61eBkPLlvN3DkzmH3aNBYtXsZ1C5awfuNWJowb3Z4O9HjOzIovS+BYGRE/TY9/2GNOqwuLFi/j+wuXtr9ft2Er865dxCPL13Bby2O0trbtl14y79pFXZ5z8DAbGLIEjsWS/hH4akREXgWygeO6BUto3d22X1praxu3/uqhF+RtbW1j3jVJgOjqM9ctWOLAYTZAZAkc04ATgE9Juo9kF8AHI8Ktjzq1fuPWTPk7B4xy6zZsdReW2QCR5QHAtwBIGk5HEHk17raqWxPGjWbdhhcGD0l01SgdM3o4AJu37uryel+8+hftn3MXlllxZZ6OGxG7IuK+iLgxIj6eR6FsYJg7ZwaNjfv/7dHY2MB5s0/sMv2S97yeS97z+hecG5xuAtU52JS6sMysWLxIoR2wUkugq+6lE46f2GO3U+dzX/zabXQ1cJa1O8zM8ufAYQdl9mnTuuxK6i69u3PXLVjSZbfXhHHeWdCsaPrUVaXE5LwLY/Vr7pwZNA59YffW3DkzqlQiM+tOnwJHOv32tgO9iaQbJK2X9GhZ2qGSbpf0x/Tr2DRdkq6WtELSw5JOKvvMBWn+P0q64EDLY8Uz+7RpfOqDs9vfTxg/ik99YLYHxs0KKMvg+P2SXnWA97kROKtT2qeBOyLiWOCO9D3A2cCx6esi4Bpo3zjqcpKZXKcAl5dvLGUD3+zTpjH2kCYAvvUv73TQMCuoLIHj1cA9kv6UtgQekfRwXz4YEYuBzsunngvclB7fRLKESSn9u5G4Bxgj6QjgDcDtEfFcum3t7bwwGNkAN2L4UAB27PISaGZFlWVw/A0VvndzRKxNj58BmtPjicCqsnyr07Tu0l9A0kUkrRWam5tpaWnpsSDbt2/vNU+tKlrd9+3dDcCvf303E5tH5HafotW7v7je9SWvemcJHE+RrI57TER8QdIU4HBg5cEWIiJCUsWWMYmI+cB8gOnTp8fMmTN7zN/S0kJveWpV0er+4zvX8fSzOzl+2gmcfMKU3O5TtHr3F9e7vuRV7yxdVd8EXgOcn77fBnzjIO69Lu2CIv26Pk1fA5TP4JqUpnWXbjVkRFPaVbXTXVVmRZVpjCMiLgaeB0jHGYYexL0XAqWZURcAPytLf1c6u+pUYEvapfUrYLaksemg+Ow0zWrIiOGNAOzYtbvKJTGz7mTpqtojaTAkD/hKOgzY15cPSroZmAmMl7SaZHbUvwC3SLqQpLvr79LstwFvBFYAO4H3AETEc5K+CPw+zfeFiPB+pTWmyS0Os8LLEjiuBm4FJki6Engr8M99+WBEnN/NqVld5A3g4m6ucwPJhlJWo9pnVe10i8OsqLKsjrsgXU59FiDgvIh4PLeSWV0a0VTqqnKLw6yosuw5Pi8iPgUs7yLNrCKa0hbHTrc4zAory+D4mV2knV2pgphB+QOADhxmRdVri0PSB4EPAcd0elJ8FPCbvApm9am9q8qD42aF1ZeuqjcC5wBPAP+7LH2bZzVZpZWe49jpFodZYfUlcLwI2EMSOLaSDIwDycKDDh5WSR2D4w4cZkXVl8BxLcnqtUcD91EWOEie6Tgmh3JZneqYjuuuKrOi6nVwPCKujoiXAN+JiGMi4uiyl4OGVZS7qsyKL8tzHB9Ml/o4FhhWlr44j4JZfWoqLTni6bhmhZXlOY73AZeSLC74IHAqcDdwej5Fs3o0dMhgGhoGsadtL7v3tDF0SJbFDcysP2R5juNS4FXAyoh4PfBKYHMupbK6JaljoUO3OswKKUvgeD4ingeQ1BgRy4Hj8imW1bP2p8c9zmFWSFn6AVZLGgP8FLhd0iYqsImTWWelAfLtnlllVkhZBsfflB5eIeku4BDgl7mUyupaR1eVA4dZER3QyGNE/E+lC2JW4im5ZsWWZYzDrF80eU8Os0Jz4LDC8Z4cZsWWOXBIGpFuIWuWixFNbnGYFVmvgUPSIEnvkPRzSetJNnJaK2mZpC9LenH+xbR6Uhoc9xiHWTH1pcVxF8kKuZ8BDo+IyRExAZgB3APMk/TOHMtodaajxeGuKrMi6susqjMiYk/nxHQ59R8DP5Y0pOIls7rlXQDNiq0vq+PuAZD0NUnqKY9ZJTSlg+Ped9ysmLIMjm8DFkoaASDpDZK8daxVXEeLw11VZkWU5cnxz0l6B9AiaTewHfh0biWzutU+xuGuKrNCyrKs+izg/cAO4AjgvRHxRF4Fs/rl1XHNii1LV9VngX+OiJnAW4EfSPJeHFZxTe1LjriryqyIsnRVnV52/Iiks0lmVf1VHgWz+lUa49juFodZIfXlAcDuZlKtBWb1lMfsQAxrHMKgQWL37jb27Nlb7eKYWSd9egBQ0kckTSlPlDQUeI2km4ALcimd1SVJHZs5Pe9Wh1nR9CVwnAXsBW6W9HS61MifgT8C5wNfjYgbcyyj1aH2Kbl+etyscPoyxjEvIi6VdCOwBxgP7IoI7zduuRnZ1Mg6tnlKrlkB9aXFcVr69dcRsSci1lYyaEj6R0mPSXpU0s2Shkk6WtK9klZI+kHaLYakxvT9ivT81EqVw4rFT4+bFVdfAscdku4GDpf0XkknS2qsxM0lTQQuAaZHxMuAwcDbgXnAVyLixcAm4ML0IxcCm9L0r6T5rAb56XGz4urLWlUfB95JMs5xNPDPwKNpK+EHFShDAzBcUgPQBKwFTgd+lJ6/CTgvPT43fU96fpZndNUm78lhVlx9eo4jIv4k6YyI+EMpTdJI4GUHc/OIWCPp34CngF3AIuA+YHNEtKXZVgMT0+OJwKr0s22StgDjgA3l15V0EXARQHNzMy0tLT2WY/v27b3mqVVFrfuWzRsBeOChRxmyd13Fr1/UeufN9a4vedW7zw8AAivTtaqmdvrcPQd6c0ljSVoRRwObgR+SzOI6KBExH5gPMH369Jg5c2aP+VtaWugtT60qat0fXdnC0sc2MGnSUcyceUrFr1/UeufN9a4vedU7S+D4GbCFpEVQqY7nM4C/RMSzAJJ+ArwWGCOpIW11TALWpPnXAJOB1WnX1iHAxgqVxQrEe3KYFVeWwDEpIg66NdDJU8CpkppIuqpmAUtJdh18K/B9kocLf5bmX5i+vzs9f2dERIXLZAUwoskLHZoVVZZFDn8r6YRK3jwi7iUZ5L4feCQtz3zgU8BlklaQjGFcn37kemBcmn4ZXta9ZrU/Oe5ZVWaFk6XFMQN4t6S/kHRVCYiIOPFgChARlwOXd0r+M/CCju2IeB5428HczwYGz6oyK64sgePs3Eph1kn7nhwe4zArnCzLqq/MsyBm5ZqavFaVWVH1ZVn1JenXbZK2pl9Lr635F9HqUccih25xmBVNry2OiJiRfh2Vf3HMEiNLs6o8OG5WOFn2HJ8O/BOdHgA82MFxs66UpuPu9BiHWeFkGRxfAHyCZNrsvnyKY5YY1jgECXY9v4e9e/cxeHCWmeNmlqcsgePZiFiYW0nMygwalOwCuGPnbnY+v5tRI4ZVu0hmlsoSOC6X9G3gDsqWHImIn1S8VGYkU3J37NzNjp0OHGZFkiVwvAc4HhhCR1dVAA4clgs/PW5WTFkCx6si4rjcSmLWiZ8eNyumrGtVTcutJGad+Olxs2LK0uI4FXiw0mtVmXXHT4+bFVOWwFHpJdXNejSifYzDLQ6zIvFaVVZY3pPDrJj8VJUVVscugO6qMisSBw4rrCbPqjIrJAcOK6z2WVUeHDcrFAcOK6z25zg8OG5WKA4cVljtK+S6q8qsUBw4rLA8OG5WTA4cVlhecsSsmBw4rLCahnszJ7MicuCwwuoYHHdXlVmROHBYYTUN61hyZN++qHJpzKzEgcMKa/DgQQwfNoQIeL51T7WLY2YpBw4rtNJmTn4I0Kw4HDis0Lwnh1nxOHBYoXlKrlnxOHBYoXnfcbPiceCwQistO7LdYxxmheHAYYU20l1VZoVT9cAhaYykH0laLulxSa+RdKik2yX9Mf06Ns0rSVdLWiHpYUknVbv8li8/PW5WPFUPHMDXgF9GxPHAy4HHgU8Dd0TEscAd6XuAs4Fj09dFwDX9X1zrTx2D4+6qMiuKqgYOSYcApwHXA0TE7ojYDJwL3JRmuwk4Lz0+F/huJO4Bxkg6op+Lbf2oY4VctzjMiqLaLY6jgWeB70h6QNK3JY0AmiNibZrnGaA5PZ4IrCr7/Oo0zWpUU1NpF0AHDrOiaCjA/U8CPhIR90r6Gh3dUgBEREjKtFCRpItIurJobm6mpaWlx/zbt2/vNU+tKnrdVz65EYAnV66qaDmLXu+8uN71Ja96VztwrAZWR8S96fsfkQSOdZKOiIi1aVfU+vT8GmBy2ecnpWn7iYj5wHyA6dOnx8yZM3ssREtLC73lqVVFr/vQUX/ih7/6CyNGjqloOYte77y43vUlr3pXtasqIp4BVkk6Lk2aBSwDFgIXpGkXAD9LjxcC70pnV50KbCnr0rIa5CVHzIqn2i0OgI8ACyQNBf4MvIckoN0i6UJgJfB3ad7bgDcCK4CdaV6rYU3prKqdnlVlVhhVDxwR8SAwvYtTs7rIG8DFuRfKCsOzqsyKp9qzqsx6VFpyxIHDrDgcOKzQ2ncB3NlK0uA0s2pz4LBCGzJkMEOHNrB3X9C6u63axTEzHDhsACgtdOgVcs2KwYHDCq99oUM/PW5WCA4cVnjtCx16MyezQnDgsMJrn5LrFodZIThwWOH56XGzYnHgsMLz0+NmxeLAYYXnp8fNisWBwwpvhPfkMCsUBw4rvKbhnlVlViQOHFZ4I9rHONziMCsCBw4rPM+qMisWBw4rvPYHAD2ryqwQHDis8EpjHDvd4jArBAcOK7yR3pPDrFAcOKzwStNxt+9wV5VZEVR961iz3vzuwScBWLt+C2+ZO5+5c2Yw+7RpLFq8jOsWLGH9xq1MGDe613Sg/dy6DVtpvvkPB3ytvtzjYK+Vx71d79qsX1/rXSmq9V3Vpk+fHkuXLu0xT0tLCzNnzuyfAhVM0eu+aPEy5l2zaL9NnBqHNjDrtcdxx2+e6HP6hy+YCcDXb2o56GtV8x6+t/9dD+hajQ186gOzMwUPSfdFxPQuzzlwFP+XZ56KXve3zJ3Pug1bq10MswGvefxofnzdRX3O31Pg8BiHFdr6jQ4aZpVQyf9LDhxWaBPGje4yfdAgZUpvHj+a5vGVuVY17+F79/+9a6V+3f1fOhAOHFZoc+fMoLFx/zkcjY0NnHvmiZnS586ZUbFrVfMevnf/37tW6jd3zgwqZfAVV1xRsYsV0fz586+46KKe+/WefPJJpk6d2j8FKpii1/1FRx3GEYeNZvmf1rFzVyvN40dz6Xtfzz+8+dRM6bNPm7bftXbsPPBr9fUeB3OtvO7tetdm/fpS76yzqj7/+c+vvZi5QdEAAAcJSURBVOKKK+Z3dc6D4xR/gDhP9Vp317u+uN7ZeXDczMwqxoHDzMwyceAwM7NMHDjMzCwTBw4zM8uk5mdVSXoWWNlLtvHAhn4oThHVa91d7/riemd3VEQc1tWJmg8cfSFpaXfTzmpdvdbd9a4vrndluavKzMwyceAwM7NMHDgSXT5WXyfqte6ud31xvSvIYxxmZpaJWxxmZpaJA4eZmWVS94FD0lmSnpC0QtKnq12evEi6QdJ6SY+WpR0q6XZJf0y/jq1mGfMgabKkuyQtk/SYpEvT9Jquu6Rhkn4n6aG03p9P04+WdG/68/4DSUOrXdY8SBos6QFJ/5W+r5d6PynpEUkPSlqaplX8Z72uA4ekwcA3gLOBacD5krItWj9w3Aic1Snt08AdEXEscEf6vta0AR+LiGnAqcDF6b9xrde9FTg9Il4OvAI4S9KpwDzgKxHxYmATcGEVy5inS4HHy97XS70BXh8Rryh7fqPiP+t1HTiAU4AVEfHniNgNfB84t8plykVELAae65R8LnBTenwTcF6/FqofRMTaiLg/Pd5G8stkIjVe90hsT98OSV8BnA78KE2vuXoDSJoE/A3w7fS9qIN696DiP+v1HjgmAqvK3q9O0+pFc0SsTY+fAZqrWZi8SZoKvBK4lzqoe9pd8yCwHrgd+BOwOSLa0iy1+vP+VeCTwL70/Tjqo96Q/HGwSNJ9kkpbn1b8Z72h9yxWDyIiJNXs3GxJI4EfAx+NiK3JH6GJWq17ROwFXiFpDHArcHyVi5Q7SecA6yPiPkkzq12eKpgREWskTQBul7S8/GSlftbrvcWxBphc9n5SmlYv1kk6AiD9ur7K5cmFpCEkQWNBRPwkTa6LugNExGbgLuA1wBhJpT8Ya/Hn/bXA30p6kqTr+XTga9R+vQGIiDXp1/UkfyycQg4/6/UeOH4PHJvOuBgKvB1YWOUy9aeFwAXp8QXAz6pYllyk/dvXA49HxL+Xnarpuks6LG1pIGk4cCbJ+M5dwFvTbDVX74j4TERMioipJP+f74yIOdR4vQEkjZA0qnQMzAYeJYef9bp/clzSG0n6RAcDN0TElVUuUi4k3QzMJFlmeR1wOfBT4BZgCsnS838XEZ0H0Ac0STOAXwOP0NHn/U8k4xw1W3dJJ5IMhA4m+QPxloj4gqRjSP4SPxR4AHhnRLRWr6T5SbuqPh4R59RDvdM63pq+bQC+FxFXShpHhX/W6z5wmJlZNvXeVWVmZhk5cJiZWSYOHGZmlokDh5mZZeLAYWZmmThwmJlZJg4cZmaWiQOH1RxJIemqsvcfl3RFBa47tXw/kzxJukTS45IWHOR1tnd1bHYwHDisFrUCb5Y0vtoFKadEX//PfQg4M10uw6xQHDisFrUB84F/LE/s3GIotUTS9OWSbpT0B0kLJJ0h6TfprmmnlF2mIT3/uKQfSWpKr/XOdMe9ByVdl24SVrrnE5K+S7Ju0OROZbpM0qPp66Np2rXAMcAvJO1Xh/T8uyQ9rGR3v/9I036aLqX9WNly2l1K1zT6efr5RyX9fRd5fiLpS5IWS3pK0hk9XdPqiwOH1apvAHMkHdLH/C8GriJZevx44B3ADODjJGtblRwHfDMiXgJsBT4k6SXA3wOvjYhXAHuB8pbCselnXhoRK0uJkk4G3gO8mmR3wvdLemVEfAB4mmQnt6+UF1LSS4HP0bG736XpqfdGxMnAdOCSdH2i7pwFPB0RL4+IlwG/7CLPCSR7WJyW3sMtH2vnwGE1KSK2At8FLunjR/4SEY9ExD7gMZKtNoNkccSpZflWRcRv0uP/JAkus4CTgd+nGyfNImkxlKyMiHu6uOcM4NaI2JHu1vcT4K97KefpwA8jYkNaz9JidZdIegi4h6RVc2wP13gEOFPSPEl/HRFbyk+mrahDgFLQGgJs7qVcVke8kZPVsq8C9wPfSd+3sf8fS8PKjstXSt1X9n4f+/8/6bwqaAACboqIz3RTjh0ZypxZugrsGcBrImKnpBb2r9t+IuIPkk4C3gh8SdIdEfGFsizTgPvSjaAATiTpZjMD3OKwGpb+NX4LcGGatA6YIGmcpEbgnAO47BRJr0mP3wEsAe4A3pruuoakQyUd1Ydr/Ro4T1JTun/Cm9K0ntwJvK3UFSXpUJLWwaY0aBxP0u3VLUlHAjsj4j+BLwMndcpyAvBg2fsTgYf7UB+rE25xWK27CvgwQETskfQF4HckO8At7+mD3XgCuFjSDcAy4Jr0F/bnSPZ6HgTsAS4m2fugWxFxv6Qb0/IAfDsiHujlM49JuhL4H0l7SfaWmAt8QNLjafm66hYrdwLwZUn70rJ+sIvz95a9fxlucVgZ78dhZmaZuKvKzMwyceAwM7NMHDjMzCwTBw4zM8vEgcPMzDJx4DAzs0wcOMzMLJP/D4rdyo+APbWiAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PNlBT9xFDugg"
      },
      "source": [
        "# even more details on the search space\n",
        "skopt.plots.plot_objective(res, dimensions=['m0', 'sigma', 'ampl', 'bck'])\n"
      ],
      "execution_count": 107,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5oa6f6zCDugn"
      },
      "source": [
        "Let's see how well the prediction fits the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fs0X6I7xDugo",
        "outputId": "3dba69ad-27f4-4e9e-efa9-9242e8251951",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 479
        }
      },
      "source": [
        "plot_mass_with_model(res.x, df.M, bins_count=120)"
      ],
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}