cost_function.ipynb

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    "colab": {
      "name": "execution",
      "provenance": [],
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "yamjLYP18nhk",
        "outputId": "90c3507e-5d4e-4dfd-9179-0025cd6451a9"
      },
      "source": [
        "from brownian import BrownianMotion\n",
        "from activebrownianparticles import Vicsek\n",
        "import tij\n",
        "import ballisticwithstop as bws\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import tkinter as tk\n",
        "from animate import MovementAnimation as Ma\n",
        "import plotly.graph_objects as go\n",
        "\n",
        "\n",
        "'''\n",
        "Brownian model\n",
        "'''\n",
        "br = BrownianMotion(0.2, 20, 1, 100, 10000, 2000)\n",
        "brownian_tij = br.total_movement()\n",
        "timeline_array = tij.timeline(brownian_tij, 20)\n",
        "quantities_brown = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "'''\n",
        "Ballistic with stop low density (100 * pi / 10000 * 100 = 3.14%)\n",
        "'''\n",
        "\n",
        "\n",
        "bs = bws.BallStop(0.09951822671326738, 20, 1, 100, 10000, 2000)\n",
        "ballistic_tij = bs.total_movement()\n",
        "timeline_array = tij.timeline(ballistic_tij, 20)\n",
        "quantities_ball = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "\n",
        "'''\n",
        "Ballistic with stop and Brownian low density (100 * pi / 10000 * 100 = 3.14%)\n",
        "'''\n",
        "bsb = bws.BallStop(0.09364401458527466, 20, 1, 100, 10000, 2000, brownian=True)\n",
        "ball_brownian_tij = bsb.total_movement()\n",
        "timeline_array = tij.timeline(ball_brownian_tij, 20)\n",
        "quantities_ball_brown = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "bsb = bws.BallStop(1, 20, 1, 100, 10000, 2000, brownian=True)\n",
        "ball_brownian_tij = bsb.total_movement()\n",
        "timeline_array = tij.timeline(ball_brownian_tij, 20)\n",
        "quantities_ball_brown_1 = tij.quantities_calculator(timeline_array)\n",
        "'''\n",
        "Vicsek model\n",
        "'''\n",
        "vi = Vicsek(0.0730330481871587, 20, 1, 100, 10000, 2000, 1, stop=False)\n",
        "vi_tij = vi.total_movement()\n",
        "timeline_array = tij.timeline(vi_tij, 20)\n",
        "quantities_vicsek = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "'''\n",
        "Vicsek model with stop\n",
        "'''\n",
        "vi = Vicsek(0.017126453046216707, 20, 1, 100, 10000, 2000, 1, stop=True)\n",
        "vi_tij = vi.total_movement()\n",
        "timeline_array = tij.timeline(vi_tij, 20)\n",
        "quantities_vicsek_stop = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "\n",
        "pt = 'tij_InVS15_1.dat'\n",
        "tij_array = tij.conversion(pt)\n",
        "timeline_array = tij.timeline(tij_array, 20)\n",
        "quantities_in1 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "pt = 'tij_InVS15_2.dat'\n",
        "tij_array = tij.conversion(pt)\n",
        "timeline_array = tij.timeline(tij_array, 20)\n",
        "quantities_in2 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "pt = 'tij_conf1.dat'\n",
        "tij_array = tij.conversion(pt)\n",
        "timeline_array = tij.timeline(tij_array, 20)\n",
        "quantities_conf1 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "pt = 'tij_conf2.dat'\n",
        "tij_array = tij.conversion(pt)\n",
        "timeline_array = tij.timeline(tij_array, 20)\n",
        "quantities_conf2 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "quantities_array = [quantities_brown, quantities_conf1, quantities_conf2]\n",
        "label_array = ['brownian', 'conf1', 'conf2', 'in1', 'in2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_ball, quantities_conf1, quantities_conf2]\n",
        "label_array = ['ball', 'conf1', 'conf2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_ball_brown, quantities_conf1, quantities_conf2]\n",
        "label_array = ['ball-brown', 'conf1', 'conf2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_ball_brown_1, quantities_conf1, quantities_conf2]\n",
        "label_array = ['ball-brown', 'conf1', 'conf2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_vicsek, quantities_conf1, quantities_conf2]\n",
        "label_array = ['vicsek', 'conf1', 'conf2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_vicsek_stop, quantities_conf1, quantities_conf2]\n",
        "label_array = ['vicsek_stop', 'conf1', 'conf2']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "'''\n",
        "Execution\n",
        "'''\n",
        "'''\n",
        "quantities_array = [quantities_brown, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['brownian', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_ball, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['ballistic', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_ball_brown, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['ball-brown', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_vicsek, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['vicsek', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "\n",
        "quantities_array = [quantities_vicsek_stop, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['vicsek-stop', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')\n",
        "'''\n",
        "'''\n",
        "tij.make_hist(quantities_ball, \"Ballistic motion with stop\", scale='log')\n",
        "tij.make_hist(quantities_ball_brown, \"Ballistic and Brownian motion with stop\", scale='semi_log')\n",
        "tij.make_hist(quantities_brown, \"Brownian motion\", scale='semi_log')\n",
        "tij.make_hist(quantities_vicsek, \"Vicsek motion\", scale='semi_log')\n",
        "tij.make_hist(quantities_vicsek_stop, \"Vicsek motion with stop\", scale='semi_log')\n",
        "\n",
        "\n",
        "quantities_array = [quantities_brown, quantities_conf1, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['brownian', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='semi_log')\n",
        "\n",
        "quantities_array = [quantities_ball, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['ballistic', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='semi_log')\n",
        "\n",
        "quantities_array = [quantities_ball_brown, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['ball-brown', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='semi_log')\n",
        "\n",
        "quantities_array = [quantities_vicsek, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['vicsek', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='semi_log')\n",
        "\n",
        "quantities_array = [quantities_vicsek_stop, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\n",
        "label_array = ['vicsek-stop', 'conf', 'inv', 'lh', 'hosp']\n",
        "tij.compare_quantities(quantities_array, label_array'star-triangle-up' , scale='semi_log')\n",
        "'''\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
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              "                            \n",
              "var gd = document.getElementById('d3863526-7ef7-47ba-b596-c57d31c251ba');\n",
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              "            Plotly.purge(gd);\n",
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              "        if (!display || display === 'none') {{\n",
              "            console.log([gd, 'removed!']);\n",
              "            Plotly.purge(gd);\n",
              "            observer.disconnect();\n",
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              "if (notebookContainer) {{\n",
              "    x.observe(notebookContainer, {childList: true});\n",
              "}}\n",
              "\n",
              "// Listen for the clearing of the current output cell\n",
              "var outputEl = gd.closest('.output');\n",
              "if (outputEl) {{\n",
              "    x.observe(outputEl, {childList: true});\n",
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            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'\\ntij.make_hist(quantities_ball, \"Ballistic motion with stop\", scale=\\'log\\')\\ntij.make_hist(quantities_ball_brown, \"Ballistic and Brownian motion with stop\", scale=\\'semi_log\\')\\ntij.make_hist(quantities_brown, \"Brownian motion\", scale=\\'semi_log\\')\\ntij.make_hist(quantities_vicsek, \"Vicsek motion\", scale=\\'semi_log\\')\\ntij.make_hist(quantities_vicsek_stop, \"Vicsek motion with stop\", scale=\\'semi_log\\')\\n\\n\\nquantities_array = [quantities_brown, quantities_conf1, quantities_inv, quantities_lh, quantities_hosp]\\nlabel_array = [\\'brownian\\', \\'conf\\', \\'inv\\', \\'lh\\', \\'hosp\\']\\ntij.compare_quantities(quantities_array, label_array, scale=\\'semi_log\\')\\n\\nquantities_array = [quantities_ball, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\\nlabel_array = [\\'ballistic\\', \\'conf\\', \\'inv\\', \\'lh\\', \\'hosp\\']\\ntij.compare_quantities(quantities_array, label_array, scale=\\'semi_log\\')\\n\\nquantities_array = [quantities_ball_brown, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\\nlabel_array = [\\'ball-brown\\', \\'conf\\', \\'inv\\', \\'lh\\', \\'hosp\\']\\ntij.compare_quantities(quantities_array, label_array, scale=\\'semi_log\\')\\n\\nquantities_array = [quantities_vicsek, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\\nlabel_array = [\\'vicsek\\', \\'conf\\', \\'inv\\', \\'lh\\', \\'hosp\\']\\ntij.compare_quantities(quantities_array, label_array, scale=\\'semi_log\\')\\n\\nquantities_array = [quantities_vicsek_stop, quantities_conf, quantities_inv, quantities_lh, quantities_hosp]\\nlabel_array = [\\'vicsek-stop\\', \\'conf\\', \\'inv\\', \\'lh\\', \\'hosp\\']\\ntij.compare_quantities(quantities_array, label_array\\'star-triangle-up\\' , scale=\\'semi_log\\')\\n'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8VRmJifypZL0"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "87sXIv9PG-8v"
      },
      "source": [
        "import tij\n",
        "import numpy as np\n",
        "from brownian import BrownianMotion\n",
        "import tkinter as tk\n",
        "from animate import MovementAnimation as Ma\n",
        "import ballisticwithstop as bws\n",
        "import activebrownianparticles as abp\n",
        "import common_calc as cc\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize\n",
        "import hyperopt as ho\n",
        "import plotly.graph_objects as go\n",
        "\n",
        "def remove_duplicates(ar1, ar2):\n",
        "    set1 = set(ar1)\n",
        "    set2 = set(ar2)\n",
        "    duplicates = set2 - set1\n",
        "    return np.array(list(set1) + list(duplicates))\n",
        "\n",
        "\n",
        "def cost_function(v):\n",
        "    mod = bws.BallStop(v, 20, 1, 100, 10000, 2000)\n",
        "    vi_tij = mod.total_movement()\n",
        "    timeline_array = tij.timeline(vi_tij, 20)\n",
        "    quantities_mod = tij.quantities_calculator(timeline_array)\n",
        "    pt = 'tij_conf1.dat'\n",
        "    tij_array = tij.conversion(pt)\n",
        "    timeline_array = tij.timeline(tij_array, 20)\n",
        "    quantities_conf1 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "    data1 = quantities_mod[2]\n",
        "    data2 = quantities_conf1[2]\n",
        "    min_data, max_data = np.min([np.min(data1), np.min(data2)]), np.max([np.max(data1), np.max(data2)])\n",
        "    max_min_data, min_max_data = np.max([np.min(data1), np.min(data2)]), np.min([np.max(data1), np.max(data2)])\n",
        "    counts1, bins1 = np.histogram(data1, bins=np.logspace(np.log10(min_data-0.5), np.log10(max_data+0.5)), density=True)\n",
        "    counts2, bins2 = np.histogram(data2, bins=np.logspace(np.log10(min_data-0.5), np.log10(max_data+0.5)), density=True)\n",
        "    bins1 = (bins1[1:] + bins1[:-1]) / 2\n",
        "    bins2 = (bins2[1:] + bins2[:-1]) / 2\n",
        "    index1 = np.where(np.logical_and(counts1 != 0, bins1 <= min_max_data))[0]\n",
        "    index2 = np.where(np.logical_and(counts2 != 0, bins2 <= min_max_data))[0]\n",
        "    index_max = np.where(bins1 > min_max_data)[0]\n",
        "\n",
        "    index = np.concatenate((remove_duplicates(index1, index2), index_max))\n",
        "\n",
        "    counts1, counts2 = counts1[index], counts2[index]\n",
        "    if min_max_data == np.max(data1):\n",
        "        counts1 = np.where(counts1 == 0, 1, counts1)\n",
        "        counts2 = np.where(counts2 == 0, 1, counts2)\n",
        "        counts1, counts2 = np.log10(counts1), np.log10(counts2)\n",
        "        null_index = np.where(counts1 == 0)[0]\n",
        "        index = np.where(counts1 != 0)[0]\n",
        "        difference  = counts1 - counts2\n",
        "        mse = np.sqrt(np.mean((difference[index]) ** 2))\n",
        "        difference[null_index] = [i*3*mse for i in range(null_index.size)]\n",
        "        mse = np.sqrt(np.mean(difference ** 2))\n",
        "\n",
        "    else:\n",
        "        counts1 = np.where(counts1 == 0, 1, counts1)\n",
        "        counts2 = np.where(counts2 == 0, 1, counts2)\n",
        "        counts1, counts2 = np.log10(counts1), np.log10(counts2)\n",
        "        null_index = np.where(counts2 == 0)[0]\n",
        "        index = np.where(counts2 != 0)[0]\n",
        "        difference  = counts1 - counts2\n",
        "        mse = np.sqrt(np.mean((difference[index]) ** 2))\n",
        "        difference[null_index] = [i*3*mse for i in range(null_index.size)]\n",
        "        mse = np.sqrt(np.mean(difference ** 2))\n",
        "\n",
        "    return mse\n",
        "\n",
        "\n",
        "def total_cost_function(v):\n",
        "    mod = BrownianMotion(v, 20, 1, 100, 10000, 2000)\n",
        "    vi_tij = mod.total_movement()\n",
        "    timeline_array = tij.timeline(vi_tij, 20)\n",
        "    quantities_mod = tij.quantities_calculator(timeline_array)\n",
        "    pt = 'tij_conf1.dat'\n",
        "    tij_array = tij.conversion(pt)\n",
        "    timeline_array = tij.timeline(tij_array, 20)\n",
        "    quantities_conf1 = tij.quantities_calculator(timeline_array)\n",
        "    total_mse = 0 \n",
        "    for i in range(3):\n",
        "\n",
        "        data1 = quantities_mod[i]\n",
        "        data2 = quantities_conf1[i]\n",
        "        min_data, max_data = np.min([np.min(data1), np.min(data2)]), np.max([np.max(data1), np.max(data2)])\n",
        "        max_min_data, min_max_data = np.max([np.min(data1), np.min(data2)]), np.min([np.max(data1), np.max(data2)])\n",
        "        counts1, bins1 = np.histogram(data1, bins=np.logspace(np.log10(min_data-0.5), np.log10(max_data+0.5)), density=True)\n",
        "        counts2, bins2 = np.histogram(data2, bins=np.logspace(np.log10(min_data-0.5), np.log10(max_data+0.5)), density=True)\n",
        "        bins1 = (bins1[1:] + bins1[:-1]) / 2\n",
        "        bins2 = (bins2[1:] + bins2[:-1]) / 2\n",
        "        index1 = np.where(np.logical_and(counts1 != 0, bins1 <= min_max_data))[0]\n",
        "        index2 = np.where(np.logical_and(counts2 != 0, bins2 <= min_max_data))[0]\n",
        "        index_max = np.where(bins1 > min_max_data)[0]\n",
        "\n",
        "        index = np.concatenate((remove_duplicates(index1, index2), index_max))\n",
        "\n",
        "        counts1, counts2 = counts1[index], counts2[index]\n",
        "        if min_max_data == np.max(data1):\n",
        "            counts1 = np.where(counts1 == 0, 1, counts1)\n",
        "            counts2 = np.where(counts2 == 0, 1, counts2)\n",
        "            counts1, counts2 = np.log10(counts1), np.log10(counts2)\n",
        "            null_index = np.where(counts1 == 0)[0]\n",
        "            index = np.where(counts1 != 0)[0]\n",
        "            difference  = counts1 - counts2\n",
        "            mse = np.sqrt(np.mean((difference[index]) ** 2))\n",
        "            difference[null_index] = [i*3*mse for i in range(null_index.size)]\n",
        "            mse = np.sqrt(np.mean(difference ** 2))\n",
        "\n",
        "        else:\n",
        "            counts1 = np.where(counts1 == 0, 1, counts1)\n",
        "            counts2 = np.where(counts2 == 0, 1, counts2)\n",
        "            counts1, counts2 = np.log10(counts1), np.log10(counts2)\n",
        "            null_index = np.where(counts2 == 0)[0]\n",
        "            index = np.where(counts2 != 0)[0]\n",
        "            difference  = counts1 - counts2\n",
        "            mse = np.sqrt(np.mean((difference[index]) ** 2))\n",
        "            difference[null_index] = [i*3*mse for i in range(null_index.size)]\n",
        "            mse = np.sqrt(np.mean(difference ** 2))\n",
        "\n",
        "        total_mse += mse\n",
        "\n",
        "    return total_mse\n",
        "\n",
        "\n",
        "def evaluations(bounds, evals, distrib_index):\n",
        "  tpe_algo = ho.tpe.suggest\n",
        "  tpe_trials = ho.Trials()\n",
        "  space = ho.hp.uniform('x', bounds[0], bounds[1])\n",
        "  tpe_best = ho.fmin(fn=cost_function, space=space, \n",
        "                  algo=tpe_algo, trials=tpe_trials, \n",
        "                  max_evals=evals)\n",
        "  results = tpe_trials.trials\n",
        "  results_array = np.empty((evals, 2))\n",
        "  for i, elt in enumerate(results):\n",
        "      loss = elt['result']['loss']\n",
        "      diff = elt['misc']['vals']['x'][0]\n",
        "      results_array[i] = [diff, loss]\n",
        "  return results_array\n",
        "\n",
        "def total_evaluations(bounds, evals):\n",
        "  tpe_algo = ho.tpe.suggest\n",
        "  tpe_trials = ho.Trials()\n",
        "  space = ho.hp.uniform('x', bounds[0], bounds[1])\n",
        "  tpe_best = ho.fmin(fn=total_cost_function, space=space, \n",
        "                  algo=tpe_algo, trials=tpe_trials, \n",
        "                  max_evals=evals)\n",
        "  results = tpe_trials.trials\n",
        "  results_array = np.empty((evals, 2))\n",
        "  for i, elt in enumerate(results):\n",
        "      loss = elt['result']['loss']\n",
        "      diff = elt['misc']['vals']['x'][0]\n",
        "      results_array[i] = [diff, loss]\n",
        "  return results_array\n",
        "\n",
        "def plot_error(results_array, distribution_type, x_label, tit):\n",
        "    fig = go.Figure()\n",
        "    fig.add_trace(go.Scatter(x=results_array[:, 0], y=results_array[:, 1], name=distribution_type, mode='markers')) \n",
        "    error_min = np.min(results_array[:, 1])\n",
        "    error_max = np.max(results_array[:, 1])\n",
        "    index = np.where(results_array[:, 1] == error_min)[0]\n",
        "    x_min = results_array[index[0], 0]\n",
        "    fig.add_trace(go.Scatter(x=[x_min]*2, y=[error_min-0.1, error_max+0.1], name='min', mode='lines'))\n",
        "    fig.update_layout(\n",
        "    title=tit,\n",
        "    xaxis_title=x_label,\n",
        "    yaxis_title=\"RMSE\")\n",
        "    fig.show()\n",
        "    return x_min\n",
        "\n",
        "def plot_distributions(v_array, distrib_index, x_label, y_label):\n",
        "    fig = go.Figure()\n",
        "    fig.update_xaxes(title_text=x_label, type='log')\n",
        "    fig.update_yaxes(title_text=y_label, type='log')\n",
        "    pt = 'tij_conf1.dat'\n",
        "    tij_array = tij.conversion(pt)\n",
        "    timeline_array = tij.timeline(tij_array, 20)\n",
        "    quantities_conf1 = tij.quantities_calculator(timeline_array)\n",
        "    data_exp = quantities_conf1[distrib_index]\n",
        "    counts, bins = np.histogram(data_exp, bins=np.logspace(np.log10(np.min(data_exp-0.5)), np.log10(np.max(data_exp+0.5))), density=True)\n",
        "    bins = np.array([(elt + bins[i+1])/2 for i, elt in enumerate(bins[:-1])])\n",
        "    non_null_index = np.where(counts != 0)[0]\n",
        "    bins, counts = bins[non_null_index], counts[non_null_index]\n",
        "    fig.add_trace(go.Scatter(x=bins, y=counts, name='conf1', mode='markers')) \n",
        "\n",
        "    for elt in v_array:\n",
        "        mod = bws.BallStop(elt, 20, 1, 100, 10000, 2000)\n",
        "        tij_array = mod.total_movement()\n",
        "        timeline_array = tij.timeline(tij_array, 20)\n",
        "        quantities_mod = tij.quantities_calculator(timeline_array)\n",
        "        \n",
        "        data = quantities_mod[distrib_index]\n",
        "        counts, bins = np.histogram(data, bins=np.logspace(np.log10(np.min(data-0.5)), np.log10(np.max(data+0.5))), density=True)\n",
        "        bins = np.array([(elt + bins[i+1])/2 for i, elt in enumerate(bins[:-1])])\n",
        "        non_null_index = np.where(counts != 0)[0]\n",
        "        bins, counts = bins[non_null_index], counts[non_null_index]\n",
        "        fig.add_trace(go.Scatter(x=bins, y=counts, name=str(elt), mode='lines'))\n",
        "      \n",
        "    fig.show()\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OjhNYZwyxAZk"
      },
      "source": [
        "# **Mouvement Brownien**\n",
        "\n",
        "Pour ce modèle, il n'y a qu'un seul paramètre à modifier: le coefficient de diffusion. Le coefficient de diffusion fois le temps d'itération est égale à la variance de la loi normale.\n",
        "\n",
        "# Intercontact duration\n",
        "On trace en premier lieu le RMSE entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps d'intercontact."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "VGI0F75syA_-",
        "outputId": "ecc2b0ec-bf2c-4d49-9d70-763fea885850"
      },
      "source": [
        "results = evaluations([0, 100], 100, 1)\n",
        "diff_min = plot_error(results, 'intercontact', 'Diffusion coefficient', 'RMSE in function of D (intercontact distribution)')\n",
        "print('The diffusion coefficient that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [02:56<00:00,  1.77s/it, best loss: 0.184482441432111]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "The diffusion coefficient that minimizes the RMSE is 0.06702306092152951\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqPLuKEB5-E1"
      },
      "source": [
        "Le code précédent nous donne un coefficient de diffusion optimal de quelques dizièmes. Cela nous pousse à refaire un test avec une borne max inférieure."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "ZZF4ctO26Jfe",
        "outputId": "2715c8e0-40c2-4ada-f97b-575e01e7d36e"
      },
      "source": [
        "results = evaluations([0, 0.2], 100, 1)\n",
        "diff_min = plot_error(results, 'intercontact', 'Diffusion coefficient', 'RMSE in function of D (intercontact distribution)')\n",
        "\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [02:18<00:00,  1.39s/it, best loss: 0.16716618438207417]\n"
          ],
          "name": "stdout"
        },
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          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.0986123792640833\n"
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        "Nous représentons maintenant la distribution d'intercontact avec le coefficient de diffusion idéale. On voit que le minimum n'est pas parfaitement défini (variation infime). On prend d idéal égal à 0.1. Pour comparer nous représentons d=0.01 et d=10. On remarque ci-dessous que c'est bien pour d=0.1 que la courbe de la modélisation \"fit\" le mieux les données expérimentales. Au contraire pour d>0.1, la courbe passe \"au dessus\" puis \"en dessous\" de la courbe expérimentales pour un temps égale à 1000s. C'est exactement l'inverse pour d<0.1. "
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      "source": [
        "plot_distributions([0.001, 0.1, 40], 1, \"Intercontact duration\", \"Distribution of intercontact duration\")"
      ],
      "execution_count": null,
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1PxZfDd9FUR6"
      },
      "source": [
        "# Contact duration\n",
        "\n",
        "On trace maintenant le RMSE entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps de contact."
      ]
    },
    {
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        "id": "vRRiZdf2GbPC",
        "outputId": "a9f20dc3-2467-4b03-b1af-6d9fc192612f"
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      "source": [
        "results = evaluations([0, 100], 100, 0)\n",
        "diff_min = plot_error(results, 'contact', 'Diffusion coefficient', 'RMSE in function of D (contact time distribution)')\n",
        "\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [03:12<00:00,  1.93s/it, best loss: 7.282057057014629]\n"
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          },
          "metadata": {
            "tags": []
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        },
        {
          "output_type": "stream",
          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.011018411051982764\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u9OPSDERHRMh"
      },
      "source": [
        "On remarque une chute de l'erreur lorsque la valeur du coefficient de diffusion diminue en dessous d'environ 1 unité. On refait donc un calcul pour obtenir plus précisément le mininum."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "U3T2dONuHFgN",
        "outputId": "120f3482-970a-475f-d014-b41174a18d77"
      },
      "source": [
        "results = evaluations([0, 0.1], 100, 0)\n",
        "diff_min = plot_error(results, 'contact', 'Diffusion coefficient', 'RMSE in function of D (contact time distribution)')\n",
        "\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [02:15<00:00,  1.35s/it, best loss: 1.253264427636464]\n"
          ],
          "name": "stdout"
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          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.0016164945298515832\n"
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      "source": [
        "On trouve que la valeur optimale du coefficient de diffusion est environ égal à environ 0.001. Effectivment on remarque que pour des coefficients de diffusion élevés, la courbe est \"petite\" et ne reproduit pas la majorité des données. C'est logique, plus le coefficient de diffusion est élevé, plus la particule est véloce et donc la probabilité que deux particules restent ensemble est faible. On voit que pour des valeurs très faible, l'erreur est très élevée. Celà est dû à \"l'allongement\" de la courbe. Les durées de contacts sont trop élevées."
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      "source": [
        "plot_distributions([0.00001, 0.0016, 1], 0, \"contact duration\", \"Distribution of contact duration\")"
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      "execution_count": null,
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      "metadata": {
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      "source": [
        "# Number of contacts\n",
        "\n",
        "On trace maintenant le RMSE entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps de contact."
      ]
    },
    {
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          "height": 579
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        "id": "ACslHJt-KJvq",
        "outputId": "aa1da5c3-1096-4419-d6e5-a8bfa5bcf8df"
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      "source": [
        "results = evaluations([0, 100], 100, 2)\n",
        "diff_min = plot_error(results, 'number of contact', 'Diffusion coefficient', 'RMSE in function of D (number of contact distribution)')\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [03:00<00:00,  1.81s/it, best loss: 5.0968275567178525]\n"
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.12561229169129717\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBhzGsQGTNc6"
      },
      "source": [
        "Comme la courbe d'erreur pour les durées de contacts, on remarque une chute de l'erreur lorsque la valeur du coefficient de diffusion diminue en dessous d'environ 1 unité. On refait donc un calcul pour obtenir plus précisément le mininum."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "uMbUI1yvzqSy",
        "outputId": "9e7c9fb6-49bf-4c3f-fc86-685d1c12f5de"
      },
      "source": [
        "results = evaluations([0, 0.1], 100, 2)\n",
        "plot_error(results, 'number of contact', 'Diffusion coefficient', 'RMSE in function of D (number of contact distribution)')\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [02:19<00:00,  1.40s/it, best loss: 2.916960488036236]\n"
          ],
          "name": "stdout"
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          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.0986123792640833\n"
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        "On trouve que la valeur optimale du coefficient de diffusion est environ égal à environ 0.09. Effectivement on remarque que pour des coefficients de diffusion élevés, la courbe est \"petite\" et ne reproduit pas la majorité des données. C'est logique, plus le coefficient de diffusion est élevé, plus la particule est véloce et donc la probabilité que deux particules restent proches et aient des contacts proches l'un de l'autre en termes de temps est faible. On voit que pour des valeurs très faible, la courbe s'éloigne vraiment de la courbe expérimentale."
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        "outputId": "15c00d7b-c78d-4707-e021-4ba792c9f489"
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      "source": [
        "plot_distributions([0.001, 0.16, 1], 2, \"number of contacts\", \"Distribution of number of contacts\")"
      ],
      "execution_count": null,
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          "metadata": {
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7_tckyXSMIog"
      },
      "source": [
        "# Total optimization\n",
        "\n",
        "Maintenant, nous optimisons le coefficient de diffusion pour la totalité des variables. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "uLUiaF_NOfiI",
        "outputId": "8516dc57-2fc1-4fca-f226-79dbb81bfefd"
      },
      "source": [
        "results = total_evaluations([0, 100], 100)\n",
        "diff_min = plot_error(results, 'total', 'Diffusion coefficient', 'RMSE in function of D (total optimization)')\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [03:00<00:00,  1.80s/it, best loss: 22.911681692014135]\n"
          ],
          "name": "stdout"
        },
        {
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          },
          "metadata": {
            "tags": []
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        },
        {
          "output_type": "stream",
          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.04268682500806131\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BjE4FH8DXVjA"
      },
      "source": [
        "Le code précédent nous donne un coefficient de diffusion optimal de quelques dizièmes. Cela nous pousse à refaire un test avec une borne max inférieure.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "id": "ZIiyzTFwTODb",
        "outputId": "890ff7c7-b0b0-45b7-fbde-e4af62825f6f"
      },
      "source": [
        "results = total_evaluations([0, 0.1], 100)\n",
        "diff_min = plot_error(results, 'total', 'Diffusion coefficient', 'RMSE in function of D (total optimization)')\n",
        "print('The coefficient of diffusion that minimizes the RMSE is ' + str(diff_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 100/100 [02:20<00:00,  1.41s/it, best loss: 9.221185242182708]\n"
          ],
          "name": "stdout"
        },
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          "metadata": {
            "tags": []
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        },
        {
          "output_type": "stream",
          "text": [
            "The coefficient of diffusion that minimizes the RMSE is 0.0013618859805056699\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b0mRvrgaX1zp"
      },
      "source": [
        "On trouve que le coefficient de diffusion qui minimise la fonction coût est environ égal à 0.001. En traçant l'ensemble des courbes, on remarque que les coubres fittent bien les données. Reste une question: est-ce que les coûts ont les même poids pour toutes les distributions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "lTDwrnGUUR3w",
        "outputId": "aa834c8b-cd02-423c-ee58-3017ecd2f263"
      },
      "source": [
        "br = BrownianMotion(0.001, 20, 1, 100, 10000, 2000)\n",
        "brownian_tij = br.total_movement()\n",
        "timeline_array = tij.timeline(brownian_tij, 20)\n",
        "quantities_brown = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "pt = 'tij_conf1.dat'\n",
        "tij_array = tij.conversion(pt)\n",
        "timeline_array = tij.timeline(tij_array, 20)\n",
        "quantities_conf1 = tij.quantities_calculator(timeline_array)\n",
        "\n",
        "quantities_array = [quantities_brown, quantities_conf1]\n",
        "label_array = ['brownian', 'conf1']\n",
        "tij.compare_quantities(quantities_array, label_array, scale='log')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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      "source": [
        "# **Ballistic with stop**\n",
        "\n",
        "Pour ce modèle, il n'y a qu'un seul paramètre à modifier: la vitesse des particules.\n",
        "\n",
        "# Intercontact duration\n",
        "On trace en premier lieu le RMSE entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps d'intercontact. Ici nous prenons une borne max déjà assez faible car si la vitesse est trop importante, le risque d'avoir une interpénétration de deux particules est trop important. Le système devient figé dans ce cas. "
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        "outputId": "08171dc3-5f9d-446d-8934-543894a3e30a"
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      "source": [
        "results = evaluations([0, 1.5], 50, 1)\n",
        "speed_min = plot_error(results, 'intercontact', 'Speed', 'RMSE in function of D (intercontact distribution)')\n",
        "\n",
        "print('The speed that minimizes the cost function is ' + str(speed_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 50/50 [20:05<00:00, 24.11s/it, best loss: 0.3973172677023746]\n"
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          "text": [
            "The speed that minimizes the cost function is 0.21275000609164885\n"
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        "Nous représentons maintenant la distribution d'intercontact avec le coefficient de diffusion idéale. On voit que le minimum n'est pas parfaitement défini (variation infime). On prend d idéal égal à 0.3. Pour comparer nous représentons d=0.03 et d=1.5. On remarque ci-dessous que c'est bien pour d=0.3 que la courbe de la modélisation \"fit\" le mieux les données expérimentales. Au contraire pour d>0.1, la courbe passe \"au dessus\" puis \"en dessous\" de la courbe expérimentales pour un temps égale à 1000s. C'est exactement l'inverse pour d<0.1. "
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        "plot_distributions([0.001, 0.6, 1], 1, \"Intercontact duration\", \"Distribution of intercontact duration\")"
      ],
      "execution_count": null,
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      "cell_type": "markdown",
      "metadata": {
        "id": "KRoeZ4Kl7N-g"
      },
      "source": [
        "# Contact duration\n",
        "\n",
        "On trace maintenant la fonction coût entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps de contact."
      ]
    },
    {
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        "id": "Z3s-jdMzqnDD",
        "outputId": "53f83624-0843-473f-f305-7cab93f2bc07"
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      "source": [
        "results = evaluations([0, 1.5], 50, 0)\n",
        "speed_min = plot_error(results, 'contact', 'Speed', 'RMSE in function of D (contact distribution)')\n",
        "\n",
        "print('The speed that minimizes the cost function is ' + str(speed_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 50/50 [18:05<00:00, 21.71s/it, best loss: 0.5248150110401554]\n"
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          "text": [
            "The speed that minimizes the cost function is 1.213111551101835\n"
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      "source": [
        "Le graphe précédent nous donne aucune information sur une valeur optimale de la vitesse. Celà semble logique, la forme des distributions est différente."
      ]
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      "source": [
        "plot_distributions([0.01, 1.2, 2], 0, \"contact duration\", \"Distribution of contact duration\")"
      ],
      "execution_count": null,
      "outputs": [
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QCDMfKME7cYk"
      },
      "source": [
        "# Number of contacts\n",
        "\n",
        "On trace maintenant le RMSE entre les données expérimentales (conf1) et les données du modèle (en fonction de du coefficient de diffusion) pour la distribution du temps de contact."
      ]
    },
    {
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        "id": "k4Nfgy_O2Oiq",
        "outputId": "ed8bab1a-9cd8-41e8-9127-925332449f34"
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      "source": [
        "results = evaluations([0, 1.5], 50, 2)\n",
        "speed_min = plot_error(results, 'number', 'Speed', 'RMSE in function of D (number of contact distribution)')\n",
        "\n",
        "print('The speed that minimizes the cost function is ' + str(speed_min))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 50/50 [19:05<00:00, 22.91s/it, best loss: 18.581467811280262]\n"
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          "text": [
            "The speed that minimizes the cost function is 0.14836931213028473\n"
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      "source": [
        "Le graphe précédent nous donne aucune information sur une valeur optimale de la vitesse. Celà semble logique, la forme des distributions est différente."
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        "plot_distributions([0.01, 0.1, 2], 0, \"number of contacts\", \"Distribution of number of contacts\")"
      ],
      "execution_count": null,
      "outputs": [
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