{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1616aV4grSYQ"
      },
      "source": [
        "#Présentation expérimentale de la cinétique de décoloration du bleu de bromophénol\n",
        "\n",
        "## Suivi cinétique\n",
        "\n",
        "Le bleu de bromophénol est fortement coloré, alors que le composé ayant réagi avec les ions hydroxyde est incolore. Cette propriété va être mise à profit pour suivre la cinétique de la réaction grâce au spectrophotomètre.\n",
        "\n",
        "La réaction qui a lieu peut être symbolisée par :\n",
        "\t\t\t\t$ BBPH^{-}   +   HO^{–}    \\to  BBP^{2-} + H_2O$\n",
        "\n",
        "On propose d’écrire la loi de vitesse s’écrit selon $v = k [BBPH^{-}]^{\\alpha} \\cdot [HO^{–}]^{\\beta}$\n",
        "\n",
        "## Rappel de la loi de Beer - Lambert\n",
        "\n",
        "La spectrophotométrie est l'étude de l'interaction entre la matière et le rayonnement.\n",
        "Nous profitons donc du fait que le bleu de bromophénol est une molécule colorée et absorbe dans le visible selon la loi de Beer - Lambert.\n",
        "\n",
        "- L'absorbance d'une solution caractérise son aptitude à absorber une radiation de longueur d'onde donnée. Elle se note $A$ et n'a pas d'unité.\n",
        "\n",
        "- Soit $I_0$ l'intensité lumineuse en entrée de la cuve contenant la solution, soit $I_{sortant}$ celle en sortie de cuve, on écrit : $\\mathrm {A = - log_{10} \\dfrac {I_0}{I_{sortant}}}$\n",
        "\n",
        "- Ici, nous n'avons qu'une seule espèce colorée : le bleu de bromophénol : $\\mathrm {A = \\varepsilon_i(\\lambda) \\ell C_i }$\n",
        "  - la concentration $C_i$ est la concentration molaire de l'espèce colorée $i$,\n",
        "  - $\\ell$ est la longueur de la cuve en $cm$ (souvent $\\ell = 1,0 \\ cm$)\n",
        "  - $\\varepsilon_i( \\lambda)$ est le coefficient d'extinction molaire en $mol^{-1}.L.cm^{-1}$ et dépend de la longueur d'onde de travail $\\lambda$\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2drkOqBZ_0Li"
      },
      "source": [
        "# Etude mathématique\n",
        "\n",
        "## Ordre partiel $0$ supposé par rapport au $BBPH^{-}$ renommé B dans la suite\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { [\\mathsf {\\text {$B$}}] = [\\mathsf {\\text {$B$}}]_0 - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$.\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également $ A = A_0 - \\varepsilon (\\lambda) \\ell k^{'}t$ ou plus simplement $A = f(t)$\n",
        "\n",
        "## Ordre partiel $1$ supposé par rapport au $BBPH^{-}$\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}[\\mathsf {\\text {$B$}}]}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { ln ( \\dfrac {[\\mathsf {\\text {$B$}}]}{[\\mathsf {\\text {$B$}}]_0}) =  - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également $\\mathrm { ln (\\dfrac {[\\mathsf {\\text {$A$}}]}{[\\mathsf {\\text {$A$}}]_0}) =  - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$ ou plus simplement $lnA = f(t)$\n",
        "\n",
        "## Ordre partiel $2$ supposé par rapport au $BBPH^{-}$\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}[\\mathsf {\\text {$B$}}]^{2}}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { ( \\dfrac {1}{[\\mathsf {\\text {$B$}}]}- \\dfrac {1}{[\\mathsf {\\text {$B$}}]_0}) =   \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$.\n",
        "\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également  simplement $1/A = f(t)$ en faisant attention au coefficient de proportionnalité $\\varepsilon (\\lambda) \\ell $\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m7vX_SUAmFO9"
      },
      "source": [
        "# Suivi cinétique de la solution\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "umf_pxxJePH3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 130
        },
        "outputId": "72b76ff6-779c-4f0f-a991-b698697dfbc2"
      },
      "source": [
        "# importation des biliothèques\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import *\n",
        "\n",
        "A = np.array([## à compléter ## ]) # ordre 0\n",
        "\n",
        "time = np.array([## à compléter ##]) # temps en min\n",
        "\n",
        "Z1 = ## à compléter ## # ordre 1  : Python ne connaît pas lnA. Il faut utiliser np.log(A)\n",
        "\n",
        "Z2 = ## à compléter ## # ordre 2\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-18-00c7ff3963f8>\"\u001b[0;36m, line \u001b[0;32m8\u001b[0m\n\u001b[0;31m    time = np.array([## à compléter ##]) # temps en min\u001b[0m\n\u001b[0m         ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique : ordre 0 supposé\n",
        "plt.figure(1)\n",
        "plt.title(r'Tracé de $A$ en fonction du temps ')\n",
        "plt.ylabel(r'$A$')\n",
        "plt.xlabel('temps en min (min)')\n",
        "plt.plot(## à compléter ##)\n",
        "plt.xlim(## à compléter ##)\n",
        "plt.ylim(## à compléter ##)\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "AMIIua2NmF9C"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique ; ordre 1 supposé\n",
        "plt.figure(2)\n",
        "plt.title(r'Tracé de $lnA$ en fonction du temps ')\n",
        "plt.ylabel(r'$lnA$')\n",
        "plt.xlabel('temps en minutes (min)')\n",
        "plt.plot(## à compléter ##)\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "1bBpO74FmFuE",
        "outputId": "5642e008-2934-451a-cee6-a096fca919e5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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vcfPNN7Nt2zaOHDnCY489NvScJ598kp6eHo4cOcKWLVs4++yzufjii3nooYeG2j948CCHDx9O6v0YzcUXX8z999+Pemt4L7300pjz5+TkMHPmzKGa3nvvPWbPns3JJ5/Ma6+9xq9+9auheQsKCnj11VcZGBjg8ccfH3r8hRde4Cc/+QkvvfQSX/va12hubk65DuswPE1NTck/KUTnbUwof8hYDZNkjL/PZIeKWLx4Md/4xjdYsmQJR48e5Q/+4A/Izs7m4Ycf5jOf+czQppovfOELCbd55ZVXcvfdd7NixQr27dvHVVddxbJly1ixYgU333zziKOTrr/+esrKyqiqqmLp0qXceOON9PX18aUvfYmbbrqJ0tJSvv3tb3PbbbcNdQDLly9n7dq1nHPOOdx5553Mnz+fiy66iM997nPU1NSwbNkyrrjiiqGOK1V33nknJ06cYPny5ZSXl3PnnXeOOX9PTw833njj0Oa4devW0dfXx5IlS7jttttiNo/dddddXHrppfzWb/0Wp59+OhAZi+qGG27goYceYv78+dxzzz1cd911Qx3WhI22c2Mq/CSz0/v5559PeN64ILXnpyjl/CFgNSQnqZ3eCUp2p3d5eXnaM6RqvBo2btyod9999ySlmZhklkMqbKe3McYYX7g/rGNY2HkbZpopKipi9+7dQcdI2iYbuWHCbA0jXeyP0ARAU90mbaatifztWIfhWbRo0eS+YJo7mEnP7wOrITnZ2dkcOXIkrZ1GWEdJTYbVMD7VyAWUsrOzk3qebZLyJHvCUsq+8pW0dhqTnt8HVkNyCgsLaWtr4+23305bmwMDA2RkuP090mpIzOAlWpNhHYano6OD2bNnBx1jwlzPD1ZDsmbOnJnU5TUT8cYbb3DWWWeltc3JZjX4x+1uOI0KCgr8fxEfz9uYlPw+sxqC53p+sBr8ZB2GZ3AETV/5eL2NScnvM6sheK7nB6vBT9ZhGGOMSYh1GEGx8zaMMY6xDiMoyW6GsvM8jDEBsw7DE2+c/VAZZ/j00OdPgNUQPNfzg9XgJ5nKZ4quWrVKw7rzKGkiH+wsN8YYn4jILlVdFW+arWF46urqgo4wUhKH4YYyf5KshuC5nh+sBj/ZGoYn9GeHjrOGEfr8CbAagud6frAaUhXaNQwRyReRn4rIPu933FNkRaRfROq9n6f8yNLY2OhHs5PG9fxgNYSB6/nBavBT0N3wbcDPVLUE+Jl3P55uVa30fj7lR5AjR4740Wz6jHMYbujzJ8BqCJ7r+cFq8FPQHcZlwHe8298BPh1glnCzw2qNMQEL+titAlX9tXf7EDDaACrZIrIT6APuUtUnRmtQRG4EbgSYP38+W7ZsiZk+b948iouLaWpqory8nG3btgHQ1dU1NG9NTQ3Nzc0UFhbS3t5Oa2trTBsLFiygsLCQ5uZmSktL2b59+4gcq1evpqmpieLiYtra2jh48GDM9IULF1JQUEBbWxvFxcXU1taOaOO8886jsbGR0tJSmpubOXToUMz0oqIi8vPzaW9vZ2BgIKbWokce4c1rr2XNmjU0NDRQXl5OU1PTiIvaL1q0iLy8PDo6OigoKBgxJMGMGTNYvXo1dXV1VFZW0tjYOOLbT0lJCVlZWXR1dZGfnz9ih11WVhY1NTXs2rWLlStX0tDQwNGjR2PmWbx4MSdOnODAgQPk5eXR0NAQMz0nJ4fq6uqhNurq6jh27FjMPGVlZfT39zMwMEBWVtaIi/vk5uayatWqoTZ27txJV1dXzDxLly6lt7eXjIwMMjMz2bNnT8z0WbNmUVVVNdTGjh076O7uHpre1dXF0aNH6ezsJDs7m/7+fvbu3RvTxuzZs6moqBhqo7a2lt7e3ph5qqqq6OjoIDc3l97eXvbt2xczfc6cOZSXl1NfX09VVRXbt2+nr68vZp5Vq1bR3t5Ofn4+nZ2d7N+/P2b63LlzKS0tpbGxkYqKCrZu3RrzOQCorq6mra2NgoICOjo6aGlpiWljtM9TtMn+PA3/LAxK5vNUWFjIjh07YqaLyKR9nvr6+mhpaUnp85SZmUlPT8+EP09xjXbt1nT9AM8Bu+P8XAa8O2zeo6O0scD7vQhoAc5K5LUn9ZreARuRP+BrjE+E68tA1f0aXM+vajWkijGu6e37GoaqXjjaNBFpF5HTVfXXInI6cDjefKp60Pu9X0S2ACuAN9KZs6SkJJ3NTTrX84PVEAau5werwU9B78N4Ctjg3d4APDl8BhGZLSJZ3u3TgHOBPcPnS1VWVla6m5xUWVlZvg6fPhlcXwbgfg2u5werwU9Bdxh3Ab8jIvuAC737iMgqEXnQm2cJsFNEGoDniezDSHuHMXxbtmu6urp8HT59Mri+DMD9GlzPD1aDnwLd6a2qR4AL4jy+E7jeu/1LYJnfWfLz8/1+CV+5nh+shjBwPT9YDX4Keg0jNMJ6Kn6iRuR3cPh015cBuF+D6/nBavCTdRhTlSOboYwx7rAOw3zAOhljzBiswzAfGOeaG8aY6c06DE9YD2NLlOv5wWoIA9fzg9XgJxvefLrbtCn+msXGjbaJyphpKLTDm4fJrl27go6QkgnnD9G5G64vA3C/Btfzg9XgJ1vDMB+wy8AaM+3ZGkYCho/m6Jq05A/43A3XlwG4X4Pr+cFq8JN1GJ7hwwO7Ji35A95n4foyAPdrcD0/WA1+sg7DTJztFDdmWrEOw0ycnbdhzLRiHYYxxpiEWIfhWbx4cdARUjJp+X285obrywDcr8H1/GA1+Cnoa3qHRmZmZtARUjJp+Tdt+qBzSPNhuK4vA3C/Btfzg9XgJ1vD8PT09AQdISWu5werIQxczw9Wg5+sw/Dk5eUFHSElgeRP83kbri8DcL8G1/OD1eAn6zA8YT1RJlGB5E/zYbWuLwNwvwbX84PV4CfrMMzksfM2jHGadRhm8th5G8Y4zToMY4wxCbEOw5OTkxN0hJSENn8S522EtoYkuF6D6/nBavCTDW9uJo8Nn25M6Nnw5gkI6wVLEuV6frAawsD1/GA1+MnWMMzkiT5L3BgTSraGkYC6urqgI6TEifzjdBYjanCwc3FiOYzB9fxgNfjJOgzPsWPHgo6QEtfzQ5waHDwM1/Xl4Hp+sBr8ZB2GMcaYhFiHYcLFx+HTjTGpseHNTbj4OHy6MSY1tobhKSsrCzpCSlzPD1ZDGLieH6wGP1mH4env7w86Qkpczw9xakjz8OmTwfXl4Hp+sBr8ZB2GZ2BgIOgIKXE9P8SpwcH9Fq4vB9fzg9XgJ+swPFlZWUFHSInr+SENNYSgg3F9ObieH6wGP1mH4dm9e3fQEVLien5IQw0hOG/D9eXgen6wGvxkHYYxxpiEWIdh3GbnbRgzaQLtMETkMyLSKCIDIhJ3sCtvvnUisldEXheR2yYzowm5TZsi52oMnq8xeNs6DGPSLug1jN3A5cC20WYQkUzgG8AngDLgsyKS9oOUc3Nz093kpHI9P1gNYeB6frAa/BSK4c1FZAvwZVUdMRa5iNQAm1T1Yu/+7QCq+vfjtWvDm08zNny6MSkba3hzF4YGWQC0Rt1vA6pHm1lEbgRuBJg/fz5btmyJmT5v3jyKi4tpamqivLycbdsiKzfHjx/n5JNPBqCmpobm5mYKCwtpb2+ntbU1po0FCxZQWFhIc3MzpaWlbN++fUSO1atX09TURHFxMW1tbRw8eDBm+sKFCykoKKCtrY3i4mJqa2tHtHHeeefR2NhIaWkpzc3NHDp0KGZ6UVER+fn5tLe309HRQXd39/D3gjVr1tDQ0EB5eTlNTU0cPnw4Zp5FixaRl5dHR0cHBQUFDO9gZ8yYwerVq6mrq6OyspLGxkaOHDkSM09JSQlZWVl0dXWRn58/YmjmrKwsampq2LVrFytXrqShoYGjR4/GzLN48WL279/PwoULycvLo6GhIWZ6Tk4O1dXVQ23U1dWNGNGz7A//kP5f/5qBgQGysrJGHGmSm5vLqlWrhtrYuXMnXV1dMfMsXbqU3t5eMjIyyMzMZM+ePTHTZ82aRVVV1VAbO3bsiHnfjx8/Tk1NDZ2dnWRnZ9Pf38/evXtj2pg9ezYVFRVDbdTW1tLb2xszT1VVFR0dHeTm5tLb28u+fftips+ZM4fy8nLq6+upqqpi+/bt9PX1xcyzatUq2tvbyc/Pp7Ozk/3798dMnzt3LqWlpTQ2NlJRUcHWrVt5//33hz4HANXV1bS1tVFQUEBHRwctLS0xbYz2eYo22Z+nY8eOcfz48RFtJPN5KiwsZMeOHTHTJ/Pz9OabbzJ//vyUPk+ZmZn09PRM+PMUj+9rGCLyHDAvzqQ7VPVJb54tjL6GcQWwTlWv9+5fDVSr6hfHe21bwzDjsrUSY2IEegElVb1QVZfG+XkywSYOAguj7hd6j6WV6x2L6/khoBrSfO6G68vB9fxgNfgp6J3eiXgRKBGRYhE5CbgSeCrdLzJ804RrXM8PVkMYuJ4frAY/BX1Y7e+KSBtQAzwtIs96j88XkWcAVLUP+CLwLPAq8O+q2hhUZjMF2LkbxkxIoDu9VfVx4PE4j78FXBJ1/xngmUmMZqYyu+aGMRPiwiYpY4wxIWAdhmfp0qVBR0iJ6/khoBrSfM0N15eD6/nBavCTdRie4cfBu8b1/BBQDWneb+H6cnA9P1gNfrIOw5OR4fZb4Xp+cKSGcToYJ2oYg+v5wWrwUzhTBSAzMzPoCClxPT84UsM45204UcMYXM8PVoOfrMPwDB8CwjWu5werIQxczw9Wg5+swzBmPHbehjGAG4MPGhMsO2/DGMDWMIwxxiTIOgzPrFmzgo6QEtfzgyM1jHPehhM1jMH1/GA1+CkUF1Dyiw1vbowxyQl0eHNX7Nq1K+gIKXE9P0zRGhzbMT4ll4GDwlqDrWEY4yfbSW4c49sahoh8KJXnh8nwyzG6xvX8YDWEgev5wWrwU0IdhoicIiIfE5HrROQeEXlWRA4CLf7GmzzDr4ftGtfzwxSqweHzNqbMMnBcWGsY9zwMEWkBZgJ7gNeIXMTos0Clqh4e46nGTE923oaZohJZw/gPoAP4lqr+kar+E9BrnYUxxkwv43YYqvpHwKXAJSLyooh8ArCvTMYkIs3X2zAmSAntw1DVN1X1GuAa4AZgnois9THXpKuoqAg6Qkpczw9TtIZk91sEvJ9jSi4DB4W1hqSOklLVRlW9HFgL3CEiW/2JNfk6OzuDjpAS1/OD1QCMO3y632wZhENYa5jQ4IOqugO4UEQuSHOewGRnZwcdISWu5werIQxczw9Wg58SXsMQkY+LyLe9w2qvFZGVwHYfs02q/v7+oCOkxPX8MI1rCNFhuNN2GYRMWGtIZpPUQ0SOmPoVsAj4S6DRj1BB2Lt3b9ARUuJ6fpjGNWzaFDn0dvDw28HbAXQY03YZhExYa0hmk9SbqvqEd/uHfoQxxhgTXsmsYWwTkS+JDK43G2PSzg7DNSGWzBpGGbAM+DMR2QXUA/WqamsbxqSLA8OHmOlr3DUMEXlURP4U+CegBigmsv9iH1Dtb7zJM3v27KAjpMT1/GA1TEiaOxhbBuEQ1hrGHd5cRD4OVET9zCIynlQDIV/DsOHNzZRnY1WZNEtpeHNV/bmq3quq16jqCmAxcDuRTuPs9EYNTlgvWJIo1/OD1RAGrucHq8FPdgElY1yzaVP8M8I3brR9ICZldonWBNTW1gYdISWu5werIWE+nrdhyyAcwlqDdRie3t7eoCOkxPX8YDWEgev5wWrwk3UYxrjMztswk8g6DGNcZvsszCSyDsMYY0xCrMPwVFVVBR0hJa7nB6thUoyzRhL6/AmwGvxjHYano6Mj6AgpcT0/WA2TYpwLNIU+fwKsBv8E2mGIyGdEpFFEBkQk7nG/3nwtIvKKiNSLiC8nVuTm5vrR7KRxPT9YDWHgen6wGvwU9BrGbuByYFsC865V1crRTihJVVgPY0uU6/nBavBNEhdoCmX+JFkN/gm0w1DVV1U1FFcK2bdvX9ARUuJ6frAafJPEiX6hzJ8kq8E/Qa9hJEqBzSKyS0RuDDqMMcZMR8lcD2NCROQ5YF6cSXeo6pMJNrNaVQ+KyFzgpyLymqrG3YzldSg3AsyfP58tW7bETJ83bx7FxcU0NTVRXl7Otm2RZrq6uobmrVVMQg0AABRoSURBVKmpobm5mcLCQtrb22ltbY1pY8GCBRQWFtLc3ExpaSnbt4+8tPnq1atpamqiuLiYtrY2Dh48GDN94cKFFBQU0NbWRnFxcdyhAM477zwaGxspLS2lubmZQ4cOxUwvKioiPz+f9vZ2BgYGRtQqIqxZs4aGhgbKy8tpamri8OHDMfMsWrSIvLw8Ojo6KCgoYPjYWzNmzGD16tXU1dVRWVlJY2MjR44ciZmnpKSErKwsurq6yM/Pp66uLmZ6VlYWNTU17Nq1i5UrV9LQ0MDRo0dj5lm8eDEnTpzgwIED5OXl0dDQEDM9JyeH6urqoTbq6uo4duxYzDxlZWX09/czMDBAVlYWu3fvjpmem5vLqlWrhtrYuXMnXV1dMfMsXbqU3t5eMjIyyMzMZM+ePTHTZ82aRVVV1VAbO3bsoLu7e2h6V1cXR48epbOzk+zsbPr7+0dcbnP27NlUVFQMtVFbWztiE0RVVRUdHR3k5ubS29s74hvnnDlzKC8vp76+nqqqKrZv305fX1/MPKtWraK9vZ38/Hw6OzvZv38/RRs20OL9ncydO5fS0lIaGxupqKhg69atMZ8DgOrqatra2igoKKCjo4OWlpaY1xjt8xRtsj9P8T4LkNznqbCwkB07dsRMn8zPU19fHy0tLSl9njIzM+np6Znw5ykuVQ38B9gCrEpw3k3AlxOZd+XKlZqo559/PuF5w8j1/KpWQxi4nl/VakgVsFNH+Z8a+k1SInKKiOQN3gYuIrKzPK3mzJmT7iYnlev5wWoIg7j5HTub3PVlAOGtIdDhzUXkd4H7gQ8D7xK5INPFIjIfeFBVLxGRRcDj3lNmAN9X1b9NpP1khjcfGBggIyP0/eeoXM8PVkMYxM3v2EWaXF8GEGwNoR3eXFUfV9VCVc1S1QJVvdh7/C1VvcS7vV9VK7yf8kQ7i2TV19f70eykcT0/WA1h4Hp+sBr8ZBdQMsaMZBdpmrZCu4YRJvGOzHCJ6/nBagiDofw+XqTJb64vAwhvDdZheIYfkuga1/OD1RAGrucHq8FP1mEYY8ZmF2kyHuswjDFjS3YzlAObrczEWIdhjEmvcYZQN+6yo6Q8XV1doR1SOBGu5werIQzSkj/g8zZcXwYQbA12lFQC2tvbg46QEtfzg9UQBhPOn8QQ6n5zfRlAeGvwffBBV+Tn5wcdISWu5werIQwmnH/Tpg86h4DXMFxfBhDeGmwNw9PZ2Rl0hJS4nh+shjBwPT9YDX6yDsOzf//+oCOkxPX8YDWEQVryB3wYruvLAMJbg3UYxpj0ssNqpyzrMIwxxiTEOgxjjDEJsQ7DM3fu3KAjpMT1/GA1hEEg+dO8Ccv1ZQDhrcFO3PP09fUxY4a7Rxm7nh+shjAIJH+aD8N1fRlAsDXYiXsJaGxsDDpCSlzPD1ZDGLieH6wGP9kahjFm8tkFmkLL1jASsHXr1qAjpMT1/GA1hMGk5ffxAk2uLwMIbw3WYXhcX9NyPT9YDWHgen6wGvxkHYYxJlh2gSZnWIdhjAmWXaDJGdZhGGPcYhdoCowdJeXp7u4mJyfH50T+cT0/WA1h4ET+cc7bcKKGcQRZgx0llYC2tragI6TE9fxgNYRBaPMncYGm0NaQhLDW4PbpkGlUUFAQdISUuJ4frIYwCG3+JC7QFNoakhDWGmwNw9PR0RF0hJS4nh+shjBwPT9YDX6yDsPT0tISdISUuJ4frIYwcCL/OIfhOlHDOMJag3UYxhi32GG1gbEOwxhjTEKswzDGTG22RpI21mF45s2bF3SElLieH6yGMHA9P8SpwcET/cK6HKzD8BQXFwcdISWu5werIQxczw9Wg5+sw/A0NTUFHSElrucHqyEMXM8PXg1JnOgXRmFdDjY0iGdgYICMDHf7T9fzg9UQBq7nhzg1pPkSsJMhyOVgQ4MkYNu2bUFHSInr+cFqCAPX84PV4CfrMIwxU5tdbyNtrMMwxkxtjuy3cEGgHYaI3C0ir4nIyyLyuIh8aJT51onIXhF5XURum+ycxphpxDqYUQW9hvFTYKmqLgeagNuHzyAimcA3gE8AZcBnRaRsUlMaY6YPB8/bmCyhOUpKRH4XuEJV1w97vAbYpKoXe/dvB1DVvx+vzWSOkurt7SUrKyvp3GHhen6wGsLA9fyQhhpCcFRVkMthrKOkwnQ9jOuAH8R5fAHQGnW/DagerRERuRG4EWD+/Pls2bIlZvq8efMoLi6mqamJ8vLyoaMRenp6yM7OBqCmpobm5mYKCwtpb2+ntbU1po0FCxZQWFhIc3MzpaWlbN++fUSO1atX09TURHFxMW1tbRw8eDBm+sKFCykoKKCtrY3i4mJqa2tHtHHeeefR2NhIaWkpzc3NHDp0KGZ6UVER+fn5tLe309PTw5EjR4a/F6xZs4aGhgbKy8tpamri8OHDMfMsWrSIvLw8Ojo6KCgoYHgHO2PGDFavXk1dXR2VlZU0NjaOeJ2SkhKysrLo6uoiPz+furq6mOlZWVnU1NSwa9cuVq5cSUNDA0ePHo2ZZ/Hixbz11lt8+MMfJi8vj4aGhpjpOTk5VFdXD7VRV1fHsWPHYuYpKyujv7+fgYEBsrKy2L17d8z03NxcVq1aNdTGzp076erqipln6dKl9Pb2kpGRQWZmJnv27ImZPmvWLKqqqoba2LFjB93d3UPTe3p6qK6uprOzk+zsbPr7+9m7d29MG7Nnz6aiomKojdraWnp7e2PmqaqqoqOjg9zcXHp7e9m3b1/M9Dlz5lBeXk59fT1VVVVs376dvr6+mHlWrVpFe3s7+fn5dHZ2sn///pjpc+fOpbS0lMbGRioqKti6dSvd3d1DnwOA6upq2traKCgooKOjY8QoqqN9nqJN9uepr6+Pd955Z0QbY32eih55hKLvfOeDmb3zN1o2bKDlmmu8hybv8zS43FL5PGVmZtLT0zPhz1M8vq9hiMhzQLzz3O9Q1Se9ee4AVgGX67BAInIFsE5Vr/fuXw1Uq+oXx3vtZNYwurq6yM3NTWjeMHI9P1gNYeB6fkhDDSFYwwhyOQS6hqGqF441XUSuAS4FLhjeWXgOAguj7hd6j6VVe3u70x8U1/OD1RAGrucHq8FPQR8ltQ64FfiUqh4fZbYXgRIRKRaRk4ArgafSnWX4arJrXM8PVkMYuJ4f0lBDCM7bCOtyCPooqa8DecBPRaReRP4FQETmi8gzAKraB3wReBZ4Ffh3VW0MKrAxZoqbyGG10+RQ3EB3eqvqR0Z5/C3gkqj7zwDPTFYuY4xJyle+Mi06jaDXMIwxxjjCOgzPggULgo6QEtfzg9UQBq7nh0mswcch1MO6HEJz4p4fkjmstru7m5ycHJ8T+cf1/GA1hIHr+SGgGtJ8KG6Qy8GGN09Ac3Nz0BFS4np+sBrCwPX8YDX4yToMT2lpadARUuJ6frAawsD1/BBQDWk+FDesy8E6DE+84Qhc4np+sBrCwPX8EFANaT5CKqzLwToMY4wxCbEOwxhjJpuj52xYh2GMMZPN0WtuWIdhjDEmIXYehqevr48ZM8J0eZDkuJ4frIYwcD0/hLiGTZvir1ls3DhiE1WQNdh5GAloamoKOkJKXM8PVkMYuJ4fQlzDpk2Rk/sGv6QP3o6zPyOsNViH4SkuLg46Qkpczw9WQxi4nh+sBj9Zh+Fpa2sLOkJKXM8PVkMYuJ4fHKlhnBP9wlqDdRie4dcIdo3r+cFqCAPX84MjNYxzWG1Ya7AOwxhjwi4k521Yh2GMMWEXkvM2rMMwxhiTEOswPAsXLgw6Qkpczw9WQxi4nh+mUA0+XqBpouzEPU9XVxe5ubk+J/KP6/nBaggD1/PDFK0hzRdoGouduJeAsB7GlijX84PVEAau5werwU/WYXjCeqJMolzPD1ZDGLieH6ZoDWm+QNNEWYfhqa2tDTpCSlzPD1ZDGLieH6ZoDcnut/BpP4d1GMYYM9X4dBiudRjGGGMSYh2GMcZMBZNwGG4IB403xhiTtE2bPugcfDoM187D8AwMDJCR4e4Kl+v5wWoIA9fzg9UApNRh2HkYCWhsbAw6Qkpczw9WQxi4nh+sBsC3w3BtDcPT29tLVlaWz4n843p+sBrCwPX8YDWkytYwEtDc3Bx0hJS4nh+shjBwPT9YDX6yDsNz6NChoCOkxPX8YDWEgev5wWrwk3UYxhhjEmIdhjHGmIRYh2GMMSYhU/ooKRF5G3gzwdlPA97xMY7fXM8PVkMYuJ4frIZUnamqH443YUp3GMkQkZ2jHUrmAtfzg9UQBq7nB6vBT7ZJyhhjTEKswzDGGJMQ6zA+8M2gA6TI9fxgNYSB6/nBavCN7cMwxhiTEFvDMMYYkxDrMIwxxiRk2ncYIrJORPaKyOsiclvQeZIlIgtF5HkR2SMijSLyx0FnmggRyRSRl0TkP4POMhEi8iEReUxEXhORV0WkJuhMyRKRL3l/Q7tF5P+KSHbQmcYjIg+JyGER2R31WL6I/FRE9nm/ZweZcTyj1HC397f0sog8LiIfCjLjoGndYYhIJvAN4BNAGfBZESkLNlXS+oD/paplwDnATQ7WAPDHwKtBh0jB/wH+S1U/ClTgWC0isgC4GVilqkuBTODKYFMl5BFg3bDHbgN+pqolwM+8+2H2CCNr+CmwVFWXA03A7ZMdKp5p3WEAHwNeV9X9qvob4N+AywLOlBRV/bWq1nm3O4n8o1oQbKrkiEgh8EngwaCzTISInAqcB3wbQFV/o6rvBptqQmYAOSIyAzgZeCvgPONS1W1Ax7CHLwO+493+DvDpSQ2VpHg1qOpmVe3z7v4KKJz0YHFM9w5jAdAadb8Nx/7ZRhORImAFsCPYJEn738CtwEDQQSaoGHgbeNjbrPagiJwSdKhkqOpB4GvAAeDXwHuqujnYVBNWoKq/9m4fAgqCDJMG1wE/CToEWIcxZYhILvAj4E9U9VjQeRIlIpcCh1V1V9BZUjADqAL+WVVXAO8T/s0gMbzt/JcR6fzmA6eIyFXBpkqdRs4bcPbcARG5g8hm5+8FnQWswzgILIy6X+g95hQRmUmks/ieqv446DxJOhf4lIi0ENkk+HER+ddgIyWtDWhT1cE1u8eIdCAuuRBoVtW3VfUE8GPgtwLONFHtInI6gPf7cMB5JkRErgEuBdZrSE6Ym+4dxotAiYgUi8hJRHbyPRVwpqSIiBDZdv6qqv5j0HmSpaq3q2qhqhYRef9/rqpOfbNV1UNAq4gs9h66ANgTYKSJOACcIyIne39TF+DYjvsoTwEbvNsbgCcDzDIhIrKOyGbaT6nq8aDzDJrWHYa3U+mLwLNEPhz/rqqNwaZK2rnA1US+mdd7P5cEHWoa+iPgeyLyMlAJ/F3AeZLirR09BtQBrxD53xDK4Smiicj/BWqBxSLSJiK/D9wF/I6I7COy5nRXkBnHM0oNXwfygJ96n+l/CTSkx4YGMcYYk5BpvYZhjDEmcdZhGGOMSYh1GMYYYxJiHYYxxpiEWIdhjDEmIdZhmFDwRnv9w6BzTBYR+YKIfD6F5/95GrP8SbJZROSXCczzbyJSMvFkJmzssFoTCt44WP/pjZRqxiEiXaqam4Z2ZhA596IqarC7tBCRNcBVqnpDOts1wbE1DBMWdwFneScp3Q0gIreIyIveNQG+4j1W5F0n4BERaRKR74nIhSLyC+/6Bx/z5tskIo+KSK33+A3e46eLyDbvdXaLyG8PDyIiK0Vkq4jsEpFno4aZ2CIiXxWRF7zXjvfc873nPiki+0XkLhFZ7z3nFRE5Kyrfl8dqV0SuEZGvR7X9n177dxEZVbZeRL7nTbvKe369iDwgkeuLZHrv027vtb8U533/OFA32Fl4We4VkZ0Sua7H2SLyY+89/JuoLF1R9W6RD64F8j3vTHGA/wdc6HVKZgqwDsOExW3AG6paqaq3iMhFQAmRIegrgZUicp4370eAe4CPej+fA1YDXwaiN9UsJ/IPsQb4SxGZ7837rKpWErluRX10CImMy3U/cIWqrgQeAv42apYZqvox4E+AjaPUUgF8AVhC5Cz8Uu85DxI5IzyeRNoFQFVvA7q992q9iCwBfg8416urH1hP5H1boKpLVXUZ8HCc5s4Fhg/8+BtVXQX8C5FhNW4ClgLXiMicOG2s8HKXAYu8NlHVAeB17/0wU4D1/CasLvJ+XvLu5xLpQA4QGSTvFQARaSRysRwVkVeAoqg2nlTVbqBbRJ4n0vm8CDzkdQxPqGpMhwEsJvLP8afeF+VMIsN9Dxoc3HHXsNeK9uLg8Noi8gYwOEz4K8DaUZ6TSLujuQBYCbzoZc4hMuDefwCLROR+4OmoHNFOZ+SYUYPjqb0CNEbVsp/IYJ1Hhs3/gqq2efPUe/m3e9MOExn91uXRiI3HOgwTVgL8vao+EPNgZF9Hb9RDA1H3B4j9mx6+g05VdZu3pvJJ4BER+UdV/e6w121U1dEusTr4Wv2M/vlJNN947fYRuxVgtEumCvAdVR1xVTYRqQAuJrLG8z+IXFshWnecdqPzDq8lXv7oeYa/L9nea5gpwDZJmbDoJDLY2qBngeskcp0PRGSBiMxNss3LRCTb24xyPpFv4GcC7ar6LSKbiIYPQ74X+LB41+QWkZkiUp58OWnRAlSKSIaILCSyhjTohLeWBJHLkF4x+P5I5JrWZ4rIaUCGqv4I+AviD7n+KpFNfH4pBXaPO5dxgq1hmFBQ1SPejuvdwE+8/RhLgFpvM0sXcBWRb7CJehl4HjgN+GtVfUtENgC3iMgJr82Yw0lV9TcicgVwn0QuvTqDyBUBgxjF+BdAM5Gh0l8lcjTToG8CL4tInbcf4y+AzSKSAZwgst+hm8hVAAe/GMa7LvRPgEf9CC8iBUT2tRzyo30z+eywWjMlicgmoEtVvxZ0lrATkceBW1V1X5rb/RJwTFW/nc52TXBsk5Qx5jYiO7/T7V3gOz60awJiaxjGGGMSYmsYxhhjEmIdhjHGmIRYh2GMMSYh1mEYY4xJiHUYxhhjEvL/AduHTxC/PvIDAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique : ordre 2 supposé\n",
        "plt.figure(5)\n",
        "plt.title(r'Tracé de $1/A$ en fonction du temps ')\n",
        "plt.ylabel(r'$1/A$')\n",
        "plt.xlabel('temps en minutes (min)')\n",
        "plt.plot(## à compléter ##)\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 130
        },
        "id": "XbN8vXtZmFbx",
        "outputId": "6a6ba717-116a-48fe-e9fd-64bc459cde8c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-17-701ce34401e9>\"\u001b[0;36m, line \u001b[0;32m8\u001b[0m\n\u001b[0;31m    plt.legend()\u001b[0m\n\u001b[0m      ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Régression linéaire sur la courbe sélectionnée"
      ],
      "metadata": {
        "id": "iOi7rKQspdvX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p1 = np.polyfit(## à compléter ##)                      #Régression linéaire de lnA en fonction de t\n",
        "\n",
        "delta_A =(2/100)*A # demi - étendue du spectrophotomètre donné par le constructeur\n",
        "u_A = delta_A/np.sqrt(3) # incertitude - type par rapport à l'absorbance\n",
        "u_Z1=u_A/A # incertitude - type par rapport au calcul du ln : axe des Y\n",
        "\n",
        "modele1=(\"ln A = \"+ format(p1[0], \"#.3e\")+\"x t +\"+ format(p1[1], \"#.3g\"))   # on fabrique l'écriture de l'équation de la droite de régression\n",
        "plt.plot(time,np.polyval(p1,time),color='green',label=modele1)\n",
        "\n",
        "plt.plot(time, np.polyval(p1,time))\n",
        "plt.errorbar(time, Z1, yerr=u_Z1, fmt='.r')   #On ajoute les barres d'incertitude\n",
        "plt.xlabel('t/min')\n",
        "plt.ylabel('ln A' )\n",
        "plt.title('Évolution de $lnA$ en fonction de t')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()\n",
        "\n",
        "print(\"kapp =\",## à compléter ##,'min^-1')                   #Affichage de kapp, l'opposé de la pente de la droite de régression\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "id": "tulzewUAp_S4",
        "outputId": "a0a17080-79e2-4df1-b226-ed10dfd088d7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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jxukjYs5WkPwrV67UiIgIrVChglarVk0jIyNPv9amTZsz2jZu3Fi3bNmSp/fPmDFDg4ODtU2bNqdva9euVVXVtWvX6pVXXqlRUVEaGRmpb775ZrZ9mDt3rjZv3lybNGmiY8eOPf38K6+8ohERERoUFKR169bVwYMHq9fr1W7duumcOXNUVTU+Pl5btWqlp06dOiPv1q1btXXr1tqmTRtdtmxZjr+XvBz15PV69S9/+Ys2adJEW7VqpatWrTrdh6y/uxEjRmhERISKiEZEROizzz57+v2PPvqoXnLJJdqqVSudNWuWqqp+88032rp1a42KitLWrVvr5MmTs51/fo96Es3hiIlA1r59ey2ugYu8Xi//N/9zZixP5tKkJHru+Jw+48ZwQdduBUxbODZYS/HbsmULl1xySa5tAv06Q4GeH6wP+ZHd37SIrFbV9tm1t01P+eRyuRh7w62siKnCrNmj6f/jj4RcdwMfT3rF6WjGGFMsrFAUUPiaDYR5PASrl5B0D7/MWoP7hYkkHvrd6WjGGFOkrFAUVEwM+I4SCQorx74Otdm7vz4xExYxeu4nRXaii/EPpXETrSmbCvK3bIWioDLPuxg3Dlm0iJcm/IeX7qpDSMhxZi4Po834N4jf/bPTKU0RCAsL4+DBg1YsTMBTzRiPIiwsLF/vs/MoCiPLeRcAt0Z14IZLohk8ayZxm+vSZ+JarmnzHZNvv5vgAp61a5xXr149kpKSTl9GIjvJycn5/ufzJ4GeH6wPeZU5wl1+WKEoYmEhocwccC9xiT8x9L3FLFrfkEu2vsUrt3fghsi2TsczBZB5UlNuYmNjads2cD/fQM8P1ofiZJueiknnxhezafQw+nQ8TmrKhTz47i6e6NuHlKZN7DLmxpiAYoWiGLlcLl7o3Y+Fj15Jt+PL+eecrwhK3Imna1crFsaYgGGFogRcVCucdyJqUM6TSrAqpKYx+bnx7D1yyOloxhhzXlYoSkpMDC6XCwU8wUHMr9oZ97/nMfabL5xOZowxubJCUVJ8h9PKuHGELV3KbX+7gqCgZN5aHETb8RNJ+G33+adhjDEOsKOeSlKWw2nvAnq3bs/AmTNYuTWcG15Zwc3tlvPqrXfYmBfGGL9iSyQHVQgtx0f33s/Uwc0JCzvIV/FViBw7mSU7EpyOZowxp1mh8ANXN29FwtNDubH9n5w6WZ1Bb22j37S3SW7XFprY4bTGGGdZofATwUFBTOx7N1893JFqF+4lbdFhdEMC3sRE6NbNioUxxjFWKPxM6/AGrB05nL+GbCAkPR0X4ElJ4fiC+U5HM8aUUVYo/NTVQx7EJeARIc0VzIBELy/Gfu10LGNMGeRIoRCRaiKyUES2+35WzaFduois893K1gkHbjeuqCiCGzXi2zdeZG39xrw630uHCRPZcWCf0+mMMWWIU2sUI4FFqtocWOR7nJ1Tqhrtu+U+OnpptHYt/PILN98/nA1P30mbpnv4/WAE3V6IZcScD23MC2NMiXCqUPQCpvvuTwd6O5QjYFQOK8+cIUN5Y0BDQssd5aMVFWk9bhKbD9uIesaY4iVODMYiIn+q6oW++wIcznx8VjsPsA7wAONV9fNcpjkUGApQu3btdrNnz85TluPHj1OpUqX8d8JBaV4Pr25cx/p9jQChZZ1f+HtUW0JcgXn+ZCB+BmcL9D4Een6wPhRW165dV6tq++xeK7ZCISLfAnWyeWk0MD1rYRCRw6p6zn4KEYlQ1T0i0gRYDHRT1fMOG9e+fXuNj4/PU87Y2FhiYmLy1NbfxO/+mbvf/pKU5OYEl9vD20uncdWvv8HMmWcMqOTvAvkzyBTofQj0/GB9KCwRybFQFNtXUFW9JpdAv4tIXVXdJyJ1gT9ymMYe389fRCQWaAvY+KI+7es35Y0uUXx78jBbPtxHh+9Wk56ehqtbN2TRooAqFsYY/+XUPoovgIG++wOBOWc3EJGqIlLOd78G0AnYXGIJA4TL5WLcTX14u2EqIelpBKmSnpzCD9PfcjqaMaaUcKpQjAeuFZHtwDW+x4hIexHJXMJdAsSLyHpgCRn7KKxQ5KDaDTcRLIJXIC0omP+cuIROL05k16Gcx3k2xpi8cGTvp6oeBLpl83w8cL/v/vdA6xKOFrjcboiKwnXkCKlvvcnJrTtI2hVOlwkLGdAljH92721XpTXGFIgtOUoT33kXVa6+hvkPDuPFO+sQHHKCGUvLET3+DdbtSXQ6oTEmAFmhKMX6tOlAwjMDuSLyd44crUuv1+IZOnsGnvR0p6MZYwKIFYpSLiwklPcH3MfMByKpUHE/36yrRuSYKSz4ab3T0YwxAcIKRRnRufHFJIwexq0dj5GSUpWh0xLp/dabnGh3qY15YYzJlRWKMsTlcvFi7ztY8Ghnalbbg2vpUVwbNtmYF8aYXFmhKIMurhVB/BPDeaTcRkLSPafHvDg6f57T0YwxfsgKRRl21eBhBImcHvNiYKIwbuGXTscyxviZwLyKnCkabjcSF0dwbCzf1q7K+sQQ1i5y8fGaicwY2JOWdeo7ndAY4wesUJR1bje43fQANqQkM3DmDOK3RXDDKyvo2X45r9xyh52oZ0wZZ0sAc1qlcmF8ct8Q3r6vKWFhh/hyVRVajp3M0p/tyinGlGVWKMw5rrmoNQlPD+H6doc5ebIGA6b8RL9pb3MyNcXpaMYYB1ihMNkKDgrijdvu4YuHO1D1wn38+FMdWo2ZwcKrO9t5F8aUMVYoTK7ahDdk3cjhDIpJo82uJDovX0X6zp2onXdhTJlhhcLkyT969GZqI88ZY17ETX3T6VjGmBJghcLk2YXX35hlzIsgXjzVkg7/nciOA/ucjmaMKUZWKEzeud0QF4fruXGkL5xP2pWV+f1APbq9EMuIOR/i9XqdTmiMKQZWKEz+uN0wahSVYq7my6EP8Hr/eoSGHuWjFRVpPW4SP+7a7nRCY0wRs0JhCuXmlu1IeGYwMVEHOH68Nre/sYGBM6eR6vE4Hc0YU0SsUJhCCw0OZtpdA/nwwSgqV/qdpRtrEjnmHeZsioeYmIybMSZgWaEwRebyhs3Z8NQw+nU6SVpqZR5+bw+P16hB8u5f7VBaYwKYFQpTpFwuF/+++TYWP9aVa44vY8ycLwlO3Ela165WLIwJUFYoTLFoWqMOb0fUoJwnlWBVJDWNSWOf59fDB5yOZozJJysUpvjExOByuVDAExzEgmqduXLCAv4x/3Onkxlj8sEKhSk+vvMuZNw4wpYu5c7HuhAcfJJpsSG0eX4i6/YkOp3QGJMHNh6FKV6+8S4AbgduimzL4Fnv8f2WuvR6LZ4ebeO4rWa4sxmNMbmyNQpToiqElmPWwMG8O+RiKlQ4wIK11XhgyRYWbt3gdDRjTA6sUBhHXNU0koSnH6DnZUdJS6vJ/VN/4da3p3CyXVu7jLkxfsYKhXGMy+Xi1T53MqZzCDWq7oHYI8iGBLyJiWCXMTfGb1ihMI5rWKkaq58czsOhGwlJ9+ACPCkpHJv/tdPRjDFYoTB+JOb+YQSJ4BEhzRXMgET496K5Tscypsyzo56M/3C7kbg4gmNj+aZWFdbtLMfahfDh6onMGNCLyDr1nE5oTJlkhcL4F9/htDcAG1OS6T9jBmt2RHD9K9/R+zIvL/Xuh8tlK8LGlCT7jzN+q1K5MD67fwhvDmpMubDDzFl5AS2fm8zyn7c4Hc2YMsUKhfF73S9uw+anh9C97SFOnqjBPVO2cOf0d0hOS3U6mjFlghUKExCCg4KY3K8/cx5qT5UL9rFiS21ajpnOoq6d7LwLY4qZFQoTUKIjGrNu5IMMvCqVqJ17uCIunvSdO1E778KYYuNIoRCR20QkQUS8ItI+l3Y9RGSriOwQkZElmdH4L5fLxT+vv4WpjTyEpKcRpEp6cgrfT53idDRjSiWn1ig2AbcCy3JqICJBwETgeiASuFNEIksmngkEF15/I8EieAXSgoL476lIOr4wkZ8P/OZ0NGNKFUcKhapuUdWt52nWAdihqr+oaiowG+hV/OlMwPBdxtz13DjSF84npXNl9u2vx9UvLGHUVx/j9XqdTmhMqeDP+ygigN1ZHif5njPm/3O7YdQoKsVczdwHHuDVeyIICT3GrLjytHn+DVb9usPphMYEPFHV4pmwyLdAnWxeGq2qc3xtYoHHVTU+m/f3BXqo6v2+x/2By1X1rznMbygwFKB27drtZs+enaecx48fp1KlSnlq648CPT8UfR/SvB5e2rCOTb81AiCq7k4eaR1NiKv4zi8N9M8h0POD9aGwunbtulpVs99nrKqO3YBYoH0Or7mBBVkejwJG5WW67dq107xasmRJntv6o0DPr1p8ffg+catGjpmoDZ/8Spv93yT9MmF1scxHNfA/h0DPr2p9KCwgXnNYpvrzpqdVQHMRaSwiocAdwBcOZzIBxN3oIjY+NYzbrzhJauoFDH/3V3q+OZnj7S+1cy+MyQenDo+9RUSSyFhrmCsiC3zPh4vIPABV9QB/BRYAW4APVTXBibwmcLlcLv7T8zYWPRZD7Rp7CF5+jKD1m2zMC2Pywamjnj5T1XqqWk5Va6tqd9/ze1X1hizt5qnqRaraVFWfcyKrKR2a1ajLyseH8/fyCWeMeXHk63lORzPG7/nzpidjilzne4eeMebFoJ0u/rVgjtOxjPFrdplxU7ZkGfNiSd3qrP/ZxdolwXy6diLTB9xEm/CGTic0xu9YoTBlj2/Mi2uBTakp3Pf+e6z4qS49X/2RG9ot57Vb7yQ4KMjplMb4Ddv0ZMq0CqHlmD1oMNPub0H5Cgf5enVVWo6dwrfbNjodzRi/YYXCGKBrs5ZsfvoBbr7sCMnJ1Rj8zg76vvMWx1OSnY5mjOOsUBjj43K5eK3PXcx7xE31qnuJ31aXqLHv8U23znbehSnTrFAYc5aWdeqz5snhDOmWTptdu7ly2Sob88KUaVYojMnB6Gt7Mr2x94wxL5a9PdnpWMaUOCsUxuTigh43nDHmxcsprWg/YSI//bHH6WjGlBgrFMbkJsuYF96F3+C96gL2H4yg+0tx/P3z2TbmhSkT7DwKY87Hd95FReDzmBjm/7SOh2f/wKc/1Gf+xkm8ec/VTic0plgVaI1CREKKOogxgaLHxdFsfmYI10Yf5MSJmtw9eTPPr11Fclqq09GMKRZ5LhSSoZuIvE3GaHPGlFnBQUFMuWMAn/21HRdcsI+tv0fScsx0Plm/Etq2tcNpTaly3kIhIh1F5FVgFzAHWAZcXNzBjAkEl9ZrwvqRDxLTZAeetIq8999YkjdtQu0y5qYUybFQiMg4EdkOPAdsANoC+1V1uqoeLqmAxvg7l8vFoIvasGzEtVx3KI7gdC8CeFNSIDbW6XjGFFpuaxT3A78DbwAzVPUgUDwDbBtTCjSsVpMHnx6FusAjLlJcwQzZe4DEQ787Hc2YQsntqKe6wLXAncDLIrIEKC8iwb7R54wxZ3O7CVkex6lvFvDUiZN84+rMNxMWcXencoy94RZcLjsi3QSeHAuFqqYD84H5IlIOuAkoD+wRkUWqelcJZTQmsLjdlHe7eQm4csNKnvhkHe/HVeHLDW8wtX8P2tdv6nRCY/IlT19vVDVFVT9R1b5AczIKiDHmPG6N6sCmpwfRueUfHD1ahz4T13LfrOmkemyl3ASOfK8Hq+pRVX23OMIYUxqFhYTyXv97mfVAKypW+oPF62vQcuzbzNu8NqOBHU5r/JxtMDWmhFzRuAWbnhpGX/cJUlOq8OC7u3hi5JPohg1gh9MaP2aFwpgS5HK5+G+v21n4aBdqV99DjRW/ka6+gwlTU+1wWuOX8nStJxG5AmiUtb1tfjKm4C6qFc7KEcN5v3wKad/PgvR0PC4XR9u1pZbT4Yw5y3kLhYjMAJoC64B039MKWKEwppDu+uvfOTR9Ju+HhPFV016siT3AEL7g6et6Oh3NmNPyskbRHohUVTvZzphiUG3VagYD5Vd/x/rPt/DW4qp8smYi7w64mdbhDZyOZ0ye9lFsAuoUdxBjyrq72nVi0zP96dBiH4f+DOemV39g+MczbcwL47i8FIoawGYRWSAiX2TeijuYMWVRhdByfHjv/Uwd3Jyw8geZG38hkWMns2RHgtPRTBmWl01P/yjuEMaYM1tOsoYAABRmSURBVF3dvBUJT1/Cw5/OZu7q6gx6axuXt1jBtLv7U+HyjnDkCMycmTGokjHF7LyFQlWXlkQQY8yZgoOC+N9td7Ox068MePdLVm5tRP8H/sEHGzcQnO7NOO9i0SIrFqbY5XaZ8WMicjSb2zEROVqSIY0py1qHN2DtyOHc19VDh8SfwbfLQu28C1NCcrsoYOWSDGKMyd3/de/FH1IOz3efQTqkSRCfVS6HXZ3TFDc7M9uYAFLruh6ELVvG2gfu4+67H+OppBZcNmEi2/7Y63Q0U4pZoTAm0LjdXPbGFKa+MZqoJkn8cTCCa19axuNzPrRDaU2xsEJhTICqUr4iXwx9gIkDGhBa7ggfr6hI63GT+D5xq9PRTCljhcKYAHdT5KUkPD2Yq9sc4PjxWtw5eRP3zJhKclqq09FMKWGFwphSIDQ4mHfuHMgnw9tyQeXfiEuoRaux0/h84yob78IUmhUKY0qR9vWbsn7Ug9zVOZm01EpM/88SkjdtQm28C1MIjhQKEblNRBJExCsi7XNpt1NENorIOhGJL8mMxgQql8vFuJv6EDuiG9cdjCM43YsA3pQUO+/CFIhTaxSbgFuBZXlo21VVo1U1x4JijDlX42q1efCZUahL8IiLFFcwQ/cdYNeh/U5HMwEmTwMXFTVV3QIgIk7M3piyw+0mZPlyTnyzgKePn2RBUGcWTFjIgC5h/LN7b1wu2/pszk+cHGZCRGKBx1U1281KIpIIHCZjoKTJqvpmLtMaCgwFqF27drvZs2fnKcPx48epVKlSPpP7j0DPD9aHkrR8XyLvJKSgnvqEhW3jsbb1aV6lRsDkz431oXC6du26OqctN8VWKETkW7Ifx2K0qs7xtYkl90IRoap7RKQWsBB4SFXPu7mqffv2Gh+ft10asbGxxMTE5KmtPwr0/GB9KGnJaakMnjWTuM1VgHSuiz5Fv1oRXHN1N6ejFUogfQY5cbIPIpJjoSi2TU+qek0RTGOP7+cfIvIZ0IG87dcwxuQgLCSUmQPuJS7xJ4a8t5iF6xqyOOQn/hdeg+4Xt3E6nvFDfruBUkQqikjlzPvAdWTsBDfGFIHOjS8mYfQwbu14jLS06gydlkjvt97kWPIpp6MZP+PU4bG3iEgS4AbmisgC3/PhIjLP16w2ECci64GVwFxVne9EXmNKK5fLxYu972Bs53LUrL6HdTsiiHrufeZ162wn6ZnTnDrq6TPgs2ye3wvc4Lv/C2DrwcaUgAaVqhI/4hYmLJ7H99N20XXZKjzpabi6dcNlgyOVeX676ckYU/JGXH0DM5oIoelpBKviTU5hyZQ3nI5lHGaFwhhzhkrdexAkglcgLSiI19KiuPTfE9n8W5LT0YxDHNn0ZIzxY243xMXhio1Fr3Dj+nkHB7dV5/pXvqNn+3ReueUOO1GvjLFP2xhzLrcbRo2iwlUxfHzf/bx9XzPCwg7z5aoqtBw7maU/b3Y6oSlBViiMMed1zUWtSXh6CNe3O8zJk9UZMOUn7pj2NidTUzIa2KXMSzUrFMaYPAkOCuKN2+7hi4cvp+qF+/jhpzq0Hvsui6ZPgQ0bwC5lXmpZoTDG5Eub8IasGzmce2PS8HgqEP/OctIzLwWUmmqXMi+FrFAYYwrk2R69WT6iO4lta5IaFIJHXKQFB0OAX2/JnMuOejLGFFiDqjWY9PILfB7ZiG2zlvJDvY4kfbeG95s3olmNuk7HM0XE1iiMMYXWe+hDPDBvOmlXVub3A/Xo9kIsT3zxEV6v1+lopghYoTDGFIkq5Svy5dAHeL1/PUJDj/Lh9xVoPW4SP+7a7nQ0U0hWKIwxRermlu1IeGYwMVEHOH68Nre/sYEB700j1eNxOpopICsUxpgiFxoczLS7BvLhg1FUrvw7yzbVJHLMO8zZlLcBxYx/sUJhjCk2lzdszoZRw+jX6SRpqZV5+L093Dh5MkdOnXA6mskHKxTGmGLlcrn49823sfixrtSpkURCYj3uHTKGH9tE2sl5AcIKhTGmRDStUYcfHx/OvxtsY+YHL9Ju41aSr7qKfQvmnf/NxlF2HoUxpkT1O5KMetIQAA+8+/x0TnpTeLZ7L7sqrZ+yT8UYU7JiYpDMghAawqomjZm+NJTo8W+wbk+is9lMtqxQGGNKlm+8C8aNI3jJEt6b/C/cl/zOkaN16fVaPA98MANPerrTKU0WViiMMSXPN94FbjdhIaHMGngf7w25hAoVD7BgbTUix05h4dYNTqc0PlYojDF+4cqml5Aw+gF6dThKSnJV7p/6C7e+PYXjKclORyvzrFAYY/yGy+XilVvv5OtHOlGj2h7WbA8nauxM5nXrbAMjOcgKhTHG70TWqcfqJ4bzwDVKm1276LpsFek7d6I2MJIjrFAYY/zWqGtu4t3GEJqeRpAq6ckpLH1rktOxyhwrFMYYv1a5x/UEieAVSAsK4pXU1rT7z0Q2/5bkdLQyw064M8b4N9/htK7YWPQKN+zYzoHtNbn+le/o1d7Ly7f0sxP1ipkVCmOM/3O7we2mAvDpVTEs+Gk9D32wgi9W1Wfh5sm8eVeM0wlLNSvDxpiA0/3iNmx+egjd2x7i5Ika3DNlC+PWrCI5LdXpaKWSFQpjTEAKDgpicr/+zHmoPVUu2Me2PyJpOWY6H63/0elopY4VCmNMQIuOaMy6kQ/StckOPJ4KPD7rdx657XZONLPzLoqKFQpjTMBzuVwMvKgNyx6/ju6nljL+8zmU+2UnaV27WrEoAlYojDGlRsNqNXmzTg3KeVIJVkVS0/jfmOf5+cBvTkcLaFYojDGlS0wMLpcLBTzBQSys3omrX1jCk19+hNfrdTpdQLJCYYwpXdxuiIpCGjcmbOlSBj3ZjZDQY3zwXQWinp/Eql93OJ0w4FihMMaUPmvXwi+/gNtNr1bt2fzMfXRptZ9jx2rT93/rGfT+dFI9HqdTBgwrFMaYUi80OJh37xnE7GGtqVTpd2I31KDlmLf5avMap6MFBEcKhYhMEJGfRGSDiHwmIhfm0K6HiGwVkR0iMrKkcxpjShd3o4vY+NQwbnOfIDX1Aoa/u5ub35zMkVMnnI7m15xao1gItFLVKGAbMOrsBiISBEwErgcigTtFJLJEUxpjSh2Xy8WEXrez6LEYatdIYuMv9Yh+7kPeXLHY6Wh+y5FCoarfqGrmBsIfgHrZNOsA7FDVX1Q1FZgN9CqpjMaY0q1ZjbqsfHw4j1wfRNtd2/lz5HSG/e0xkv486HQ0v+MPFwW8D/ggm+cjgN1ZHicBl5dIImNMmfFoaBX+9v6/8aqS+n0Idx2qTPRd0Tzbo7fT0fxGsRUKEfkWqJPNS6NVdY6vzWjAA8wsgvkNBYYC1K5dm9jY2Dy97/jx43lu648CPT9YH/xBoOeHgvehwcyZNPZ6CQJCvR7cu9fzv9jLmP3jizzetgFNL6hR5Flz4refg6o6cgMGASuACjm87gYWZHk8ChiVl2m3a9dO82rJkiV5buuPAj2/qvXBHwR6ftVC9OH771VdLlVQLV9eTy2N1X5T39IGT36iDZ78QId9OEPTPJ4izZoTJz8HIF5zWKY6ddRTD+AJoKeqnsyh2SqguYg0FpFQ4A7gi5LKaIwpI3wDIzFuHCxaRFiXq5g9aDDT7m9B+QoH+Xp1VVqOncK32zY6ndQxTh319DpQGVgoIutEZBKAiISLyDwAzdjZ/VdgAbAF+FBVExzKa4wpzdxuGDUq46dP12Yt2fz0A9x82RGSk6sx+J0d9H3nLY6nJDsY1BlOHfXUTFXrq2q07zbM9/xeVb0hS7t5qnqRqjZV1eecyGqMKbtcLhev9bmLeY+4qV51L/Hb6hI19j3ei4+Dtm2hSdm4lLmdmW2MMefRsk591jw5nKHdvKSnl+OTV1aQvGkTmpgI3bqV+mJhhcIYY/LoqWtvZsWTN3L9n3EEp3sRID0lBfzxSKUiZIXCGGPyIbxKNYY+NRJc4BEXqa5g7t1zgG1/7HU6WrHxhxPujDEmsLjdBC+PI+Xbhfzz5EkWa0cWv7SMPpfDf3vejstVur6DW6EwxpiCcLsp53YzHoj5aR0Pz/6BT3+oz/yNk3jrnm5c0biF0wmLTOkqe8YY44AeF0ez+ZkhXBd9iBMnanLn5E3c/e5UktNSnY5WJKxQGGNMEQgOCuLNO/rz2V/bUeWC3/hucy1ajZnGJ+tXOh2t0KxQGGNMEbq0XhPWjXyQ/lelkJZWib/P+o3r35jE4ZPHnY5WYFYojDGmiLlcLsZcfyvLRlxLRK3dbNlVn8FDn2NFm5YBec6FFQpjjCkmDavV5Pu/D+eFRj8z84MXuGzjTyRfdRV7F8x1Olq+WKEwxphi1ufwCcI8aQSrl2BPOjOef5fRcz/B6/U6HS1PrFAYY0xxi4lBMs+tCA0hvkkjZi4Po834N4jf/bOz2fLACoUxxhS3LJcyD16yhBmTx3Blqz84erQOfSau5b5Z00n1eM4/HYfYCXfGGFMS3O7TlzEPA2bccy/fJ27l/pmLWLy+IS23vs39keWJcTRk9myNwhhjHHJF4xZsemoYfd0nSE2pwv/WXEDPNydzLPmU09HOYIXCGGMc5HK5+G+v21n4aBcuqLiDDb/UI2rsLN7+MdbpaKdZoTDGGD9wUa1wXruyPQ91d6HeYOa+Hs/kTl3445v5TkezQmGMMf7ksa7Xs+bqurw/exSDV3xH5Rt7MfXl/ziayQqFMcb4mWqr4gnzeAhWLyHpHvZ/lkDb8RPZuPdXR/JYoTDGGH8TEwO+8y6CwspxpHM4h/4M56ZXf2D4xzNL/EQ9KxTGGONvspx3IYsW8dxzzzN1cHPKVzjI3PgLuWTMZBZv31RicaxQGGOMP3K7YdSo0+deXN28FZuffoCb2h8h+VR17n17O7dPfYuTqSnFHsUKhTHGBAiXy8Xrfe/iq4c7Uu3CvazcWpdWY2Ywa833xTvfYp26McaYItc6vAFrRw7n/qvTSU8PY+SHB3jo9n4cb9a0WC5jboXCGGMC1NPX9WTFkzdwY/Iy/vPZ54T9koh261bkxcIKhTHGBLDwKtX4X+3qlPOkEqyKpKZCbGyRzsMKhTHGBLqYGFynL2MemnF4bRGyq8caY0ygyzycNjY2o0j4jpQqKlYojDGmNMhyGfOiZpuejDHG5MoKhTHGmFxZoTDGGJMrKxTGGGNyZYXCGGNMrqxQGGOMyZUVCmOMMbmyQmGMMSZXoqpOZyhyIrIf2JXH5jWAA8UYp7gFen6wPviDQM8P1ofCaqiqNbN7oVQWivwQkXhVbe90joIK9PxgffAHgZ4frA/FyTY9GWOMyZUVCmOMMbmyQgFvOh2gkAI9P1gf/EGg5wfrQ7Ep8/sojDHG5M7WKIwxxuTKCoUxxphcldlCISI9RGSriOwQkZFO58kvEakvIktEZLOIJIjII05nKggRCRKRtSLyldNZCkJELhSRj0XkJxHZIiLFM3JMMRKRR31/Q5tEZJaIhDmd6XxE5B0R+UNENmV5rpqILBSR7b6fVZ3MeD459GGC729pg4h8JiIXOpkxU5ksFCISBEwErgcigTtFJNLZVPnmAR5T1UigIzA8APsA8AiwxekQhfAKMF9VLwbaEGB9EZEI4GGgvaq2AoKAO5xNlSfTgB5nPTcSWKSqzYFFvsf+bBrn9mEh0EpVo4BtwKiSDpWdMlkogA7ADlX9RVVTgdlAL4cz5Yuq7lPVNb77x8hYQEU4myp/RKQecCPwltNZCkJEqgBdgLcBVDVVVf90NlWBBAPlRSQYqADsdTjPeanqMuDQWU/3Aqb77k8HepdoqHzKrg+q+o2qenwPfwDqlXiwbJTVQhEB7M7yOIkAW8hmJSKNgLbAj84mybeXgScAr9NBCqgxsB+Y6tt89paIVHQ6VH6o6h7gv8CvwD7giKp+42yqAqutqvt8938DajsZpgjcB3ztdAgou4Wi1BCRSsAnwN9U9ajTefJKRG4C/lDV1U5nKYRg4FLgDVVtC5zA/zd3nMG3Hb8XGUUvHKgoIvc4m6rwNOO4/4A99l9ERpOxeXmm01mg7BaKPUD9LI/r+Z4LKCISQkaRmKmqnzqdJ586AT1FZCcZm/6uFpH3nI2Ub0lAkqpmrsl9TEbhCCTXAImqul9V04BPgSsczlRQv4tIXQDfzz8czlMgIjIIuAm4W/3kRLeyWihWAc1FpLGIhJKx8+4LhzPli4gIGdvGt6jqi07nyS9VHaWq9VS1ERm//8WqGlDfZFX1N2C3iLTwPdUN2OxgpIL4FegoIhV8f1PdCLAd8ll8AQz03R8IzHEwS4GISA8yNsf2VNWTTufJVCYLhW9n0V+BBWT8U3yoqgnOpsq3TkB/Mr6Jr/PdbnA6VBn0EDBTRDYA0cA4h/Pki29t6GNgDbCRjGWCX15GIisRmQWsAFqISJKIDAbGA9eKyHYy1pTGO5nxfHLow+tAZWCh7396kqMhfewSHsYYY3JVJtcojDHG5J0VCmOMMbmyQmGMMSZXViiMMcbkygqFMcaYXFmhMKaAfFeO/ctZz33tu4ZVXt4fLiIfF086Y4qOHR5rTAH5rrH1le+qq4hIeWCpqnZwMpcxRc3WKIwpuPFAU9+JUROAGCAWQER2isjzvtfiReRSEVkgIj+LyDBfm0aZYxGIyCAR+VRE5vvGU/iPQ30y5hzBTgcwJoCNJGPsgGgAEXkV+DzL67+qarSIvETG2AOdgDBgE5DdGbfRZFwFOAXYKiKvqerubNoZU6JsjcKYotMJiMvyOPP6YRuBH1X1mKruB1JyGLlskaoeUdVkMq4Z1bB44xqTN1YojCkCItIE2O0bCCtTiu+nN8v9zMfZrc1nbZOeQxtjSpwVCmMK7hgZF3CDjGF15zuYxZhiY99YjCkgVT0oIt/5dkjvA4Y4ncmY4mCHxxpTSCJSDvhOVds7ncWY4mCFwhhjTK5sH4UxxphcWaEwxhiTKysUxhhjcmWFwhhjTK6sUBhjjMmVFQpjjDG5+n+CzKNKoT9FNAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "kapp = 0.17119422182738273 min^-1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pour s'assurer efficacement que la droite de régression passe par les barres d'incertitude, on peut tracer :\n",
        "- les résidus avec les barres d'incertitude ;\n",
        "- les résidus normalisés directement.\n",
        "\n",
        "Notre critère de décision est le dépassement, en valeur absolue, de la valeur 2 pour l'écart normalisé."
      ],
      "metadata": {
        "id": "LeFRvW5upJbn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Tracé des résidus\n",
        "\n",
        "plt.figure(3)\n",
        "plt.title(\"Résidus\")\n",
        "plt.ylabel('lnA - modèle affine')\n",
        "plt.xlabel('temps en (s)')\n",
        "plt.errorbar(time,Z1-np.polyval(p1,time), yerr = u_Z1, fmt = 'ro',label=\"Résidus\")\n",
        "plt.plot((np.min(time), np.max(time)), (0, 0) )\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Tracé des résidus normalisés z\n",
        "plt.figure(4)\n",
        "plt.title('Résidus normalisés')\n",
        "z = (Z1-np.polyval(p1,time))/(u_Z1)\n",
        "plt.plot(time, z,'bo')\n",
        "plt.xlabel('temps en (s)')\n",
        "plt.ylabel('Résidus normalisés de $lnA$' )\n",
        "plt.plot((np.min(time), np.max(time)), (0, 0) )\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "c4uUW7KAn3k6",
        "outputId": "4c3db82e-4f1c-476c-8024-0c7ab29708a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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Va4Eagns1DgE3xBEsCStXrkw6Ql58zw9WQ1yiDArlYv6orIb45NqNyNeAHwMtBHsWZ4Cm8DFtFBcXJx0hL77nB6shLlEGhXIxf1RWQ3xy3dP4R0CBdwM/EJHnROQ7IrJVRN4eX7ypdf78+aQj5MX3/GA1xCXKoFAu5o/KaohPTnsaqvpD4IfDr0WkBHgZsAa4nmlyJVV5eXnSEfLie36wGuKydWv2OQ249KBQLuaPymqIz6QGYVLVAVV9SlUfUNU7Ch0qKa7eTJMr3/OD1RCXKINCuZg/KqshPs6M3Ccit4jIQRF5VkTuHGf+e0XkZyKyL3y8P4mcxvhq82Y4cgSGhoKvdtWUmYy8R+4rBBEpBu4FbgY6gCdF5CFVPTBq0X9W1Q9OeUBjjDFA9L6nRETeJSIfD19fF3ZcmK/rgWdV9bCqXgC+DmwqwHqNMcYUUNQ9jc8CQ8BrgT8HeoF/BV6VZ44lwPGM1x1AwzjL/ZqIbATagI+o6vHRC4jIFmALwOLFi9m+fXvW/EWLFlFTU0NbWxt1dXXs3LlzZN7Zs2fZvn07GzZsoL29naqqKjo7Ozl+PPttlixZQlVVFe3t7dTW1rJr164xQRsbG2lra6OmpoaOjg5OnDiRNX/p0qVUVlbS0dFBTU0Nu3fvHrOOjRs30traSm1tLe3t7Zw6dSprfnV1NRUVFXR2dlJVVTWSP+NnwY033khLSwt1dXW0tbVx+nT2uFnLly+nvLycrq4uKisrGd0rcElJCY2NjTQ3N7N27VpaW1s5c+ZM1jIrVqwglUrR19dHRUUFzc3NWfNTqRQbNmygqamJdevW0dLSMqZfnZUrV45cYtjd3T3meO6cOXNoaGgYWUdzczM9PT1Zy6xatYrBwUGGhoZIpVLs378/a35ZWRnr168fWcfevXvp6+vLWmb16tWk02mKioooLi7mwIHsnd158+ZRX18/so49e/bQ39+ftUxxcTHHjh1j9uzZDA4OcvDgwaz58+fPZ82aNSPr2L17N+l0OmuZ+vp6urq6KCsrI51Oc+jQoaz5CxYsoK6ujn379lFfX8+uXbsYGBjIWmb9+vV0dnZSUVFBb28vhw8fzpq/cOFCamtraW1tZc2aNezYsQNVzfo9amhooKOjg8rKSrq6ujhy5EjWOib6PA1L4vM0+rMA0T9Pe/bsyZo/1Z8nVaWnpyevz9P58+cpLy+f1OfpUiJ1jS4izapaLyI/VtVXhtNaVHVNzisZf723Abeo6vvD1+8GGjIPRYnIAqBPVdMi8t+Bd6jqaydar3WNbowx0RWsa3TgYnj+QcMVX0Ow55GvE8DSjNdV4bQRqnpGVYf/HfsisK4A75vF1UFPcuV7frAaXOB7frAa4hR1T2Mz8A6gHvgKcBvwsXz7ngrv+2gDXkfQWDwJ/IaqtmYsc62qngyfvw34E1WdsAsT29MwxpjoCranoarbgD8G/hI4Cby1EJ0VquoA8EHgUeBp4F9UtVVE/lxE3hIu9mERaRWRFuDDBMPOFtToY4e+8T0/WA0u8D0/WA1xinzJrao+AzxT6CCq+gjwyKhpH894/lHgo4V+30y5nghyle/5wWpwge/5wWqIU64dFv7BRPNV9W8KE8cYY4zLct3TGO4EZSXB5bUPha9vBX5U6FDGGGPclGuHhZ8EEJGdQL2q9oav72aajA9ujDHm8qJeclsJXMh4fSGcNi2sWrUq6Qh58T0/WA0u8D0/WA1xitpofBX4kYjcHe5l7AHuL3SopAwODiYdIS++5werwQW+54eprSGusddd3Q6Rrp5S1a0i8l3gl8NJ71PVHxc+VjKGhgpxn2JyfM8PVoMLfM8PU1dDnGOvu7odJnPJbTPg5gXEeUqlUklHyIvv+cFqcIHv+WHqapho7PV8Gw1Xt4Mz42m4YHQHd77xPT9YDS7wPT9MXQ1Rxl6PytXtYI2GMcZMUpSx16eLqONpvF1EysPnHxORB0WkPp5oxhjjtq1bg7HWM11q7PXpIuqexp+paq+INAI3AV8CPlf4WMYY474oY69PF1FPhA9fA/YrwH2q+rCI/EWBMyWmrKws6Qh58T0/WA0u8D0/TG0NmzfH00i4uh2ido3+HYKuy18PvBLoB36U7yBMcbGu0WeObduCK1aOHQuOJ2/dOr3/2zMmToUchOnXCbovf72qPg9UAHfkmc8Zrg56kivf88Pkahi+Vv7oUVB98Vr5Qt1kFZXv28H3/GA1xCnqnoYA7wJqVPXPReQ6YJGqOtlpoe1pzAzV1UFDMdqyZTBqSGtjTA7y2tMQkcZwiFeAzwI3ALeHr3uBewuS0gG+NzC+54fJ1RDntfKT4ft28D0/WA1xyuXw1BAvXiHVoKofAM4DqGo3cEVM2aZcX19f0hHy4nt+mFwNrl0r7/t28D0/WA1xumyjoaqPE+xhAFwM9zoUQESuIWhUjCmoKJ3AzcRr5Y1JSk4nwlV1X/j0M8A3gYUishXYBXwqpmxmhop6YnsmXitvTFKi9nK7TUSagNeFkzaFY4YbUzCT6QQurmvljTHZIncjApxQ1XsJLrf91HTqRmT16tVJR8iL7/khqMG1E9tR+b4dfM8PVkOc8ulG5LVMs25E0ul00hHy4nL+XM9RpNNp505sR+XydsiF7/nBaohT1EYjsxuRL6jqw0yjq6eKivzu9NfV/FHOURQVFXl/YtvV7ZAr3/OD1RCnqKlOiMj/Ad4BPCIiqUmsw1nFxcWXX8hhruaf6BzFaMXFxd6f2HZ1O+TK9/xgNcRpst2IvGE6diNy4MCBpCPkxdX8Uc5RDNeweXNwN/fQUPDVlwYD3N0OufI9P1gNcYrUaKjqOVV9UFUPha9Pqur34olmpgsXz1FEuQ/EGPOinBoNEdkVfu0VkZ6MR6+I9MQb0fj+B861cxSudXDoKt9/70w8cr25rzH8Wq6q8zIe5ao6L96IM9t0+APn2jmKKOdYZqrp8Htn4jFtTmIXwrx57rV/Uf7AuZh/WK7nKKaihrjvA3F5O+Ri3rx53jesvm8DcLeGnLpGF5Fegv6mZJzZ6urexnToGr2oKPhPbzSR4A+wic66Ur88+72b2fIehCnjsFT5OA8nG4zJcHHQkygnkacyf1zHu6eihsmeY8m1Zhd/j6Joampy8uKFKHzfBuBwDaoa6QHMB64HNg4/oq5jqh7r1q1T3z3wgGppqWrwf1/wKC0NplumyXvgAdVly1RFgq+Xyz4dao5iptVrsgF79VJtwKVmjLswvB94CugGHiMYI/yHUdYxlY+ojcYTTzwRafmpkusfuKnKv2xZ9h+T4ceyZfmv29VtEKVmV2vI1XD+qA2rS3zfBqrJ1jBRoxGpl1vg94BXAU+o6mtE5KVMo67R+/v7k44wrlx7cJ2q/HGeSHZ1G0Sp2dUacjWc3+eeg33fBuBuDVGvnjqvqucBRCSlQbfoKwsfy7jM9+PdkzETazZmPFEbjQ4RuQr4FvB9Efk2MM51KGY6c+1mvakwE2s2ZjxRuxF5m6o+r6p3A39G0DX6WwsRRERuEZGDIvKsiNw5zvyUiPxzOH+PiFQX4n1NdK7drDcVZmLNxownp/s0Yg8RjDveBtwMdABPArer6oGMZf4H8ApV/R0ReSfwNlV9x0TrjXqfRnd3N/Pnz59MCU7wPT9YDS7wPT9YDfma6D6NSCfCRWQ9cBewLPN7VfUVeSUMLuF9VlUPh+/zdWATkNnN4ybg7vD5N4B/EBHRArZ6vb29Ixvpk//WyoGf+tWtVjqdJpVKJR0jL1ZD8nzPD1YDwKrF8/jErXUFTBSIevXUNoKu0J8CCnlf6BLgeMbrDqDhUsuo6oCIvAAsAH6euZCIbAG2ACxevJjt27dnrWTRokXU1NTQ1tZGXV0dO3fuHJk3MDDA4cOH2bBhA91d3QwOwsWLFzh/PnsErVQqRSqV4vz588yZM4cXXnhhTEFXXnkl/f39zJ49m3Q6PWYUrtmzU8yadQXpdJo5c2bzwgtjG6irrrqKs2fPUlo6h/7+81y4cGHUOmYza9YsLly4QCqV4ty5c1lXXIjAlVdexdmzfZSWzqW/v3/MOubMmUNxcTEDAxeZNesKent7s+aLCFdeeSV9fX2UlZVx9uxZLl68mLVMaekcRIoYHBxk1qxZY9ZRVFTEvHnz6OvrpaysnLNn+7h4cWDUOkoREQYGBiguLqavry9rfnFxEeXlL66jr6+PgYHsdcydOze8NFwRKeLs2bOj1lFMeXn5yDp6e3sZHBwcZx1DgCAiY9ZRUlJCWVlZxjp6GBzM/ijMnp0inU5TVFSEqnJuVH8cs2aVMHfui+vo6elhaNRt1uXl5Vy8eJHi4mJUhzh3rn/UOmYxd+7cke3ywgsvMPr/p2AdFygpmcXg4OCYq3GuuOIK5syZw7lzZ5k7t4wXXnie4cvwh5edN28e6XSaK664gosXL3L+/Plx1jGbc+f6mTt3Ls8//zyjXXnlPPr7z5NKpabs8zT6swDRP089Pdmfyan+PA0MDFBSUjLpz1P/uX6OHTtGeXk5LS0tY3I2NDTQ1NTEunXraG5uHlPvpUQ6PCUiuzTsvLCQROQ24BZVfX/4+t1Ag6p+MGOZ/eEyHeHr58Jlfj7eOiH64amTJ09y7bXXTrKK5PmeH6wGF/ieH6yGfOXdjUiGT4jIF0XkdhH51eFHATKeAJZmvK4Kp427jIiUAFcCZwrw3iMOHjxYyNVNOd/zg9XgAt/zg9UQp6iNxvuAtcAtwK3h480FyPEksEJEakTkCuCdwEOjlnkIeE/4/DaCO9GTP4tvjDEOiXsclKjnNF6lqgW/mS88R/FBgqFki4Evq2qriPw5we3sDxFc3vs1EXkW6CJoWIwxxoSGx0EZPo02PA4KFO7y8KiNxuMisirzUthCUdVHgEdGTft4xvPzwNsL/b7GGDNdTDQOSlKNxg3APhFpB9IE42toAS65dYLv13X7nh+sBhf4nh9mbg1xDzAGEa6eEhEBfplxug1RVSe7EpkOgzAZY0yuCjXAWEGungpPOt+rqkdHP3KP4jZnBz3J0XD+yZwIi/vkWa583wbgfw0u558pA2HB5GqYkj7SLtVn+ngP4CsEJ8MTHysjl8d0GIQpqskMnmMD7hgf2O9pbgoxDgoFHITpGWAAeA74CcGd4T+Jso6pfERtNB5//PFIy7vm8ccfn9QASXEOqhSV79tA1f8aXM0f5ffU1RqiSLKGiRqNqCfC31CwXRwHje6awDfpdHpSJ8Km4uRZrnzfBuB/Da7mj/J76moNUbhaQ9Su0Y8CV/HijX1X6TQ6pzEdTGawIBtgyPjAfk/dEKnREJHfI+i0cGH4eEBEPhRHMDM5kzkRZgMMGR/Y76kbonYj8t8IOgn8uAY33t0A/HbhY5nJmsxgQTbAkPGB/Z66IWovt08RXD01PE74bOBJVX15TPnyEvU+jZ6eHubNmxdjonj5nh+sBhf4nh+shnwVspfbfwT2iMjdIvJJ4Angy/kGdEVXV1fSEfLie36wGlzge36wGuIU6eopVf0bEdkONAIKvE9VfxxHsCSUlZUlHSEvvucHq8EFvucHqyFOUU+Ep4CXAmXAfOBWEfn4xN/lD1cvccuV7/nBanCB7/nBaohT1MNT3yYYq3sAOJvxmBYOHTqUdIS8+J4frAYX+J4frIY4Rb25r0pVb4kliTHGGOdF3dN4XEScvFLKGGNM/KLuaTQC752u42kYY4yZWNRG442xpHDEggULko6QF9/zg9XgAt/zg9UQp0g39/km6s19Q0NDFBVFPWLnDt/zg9XgAt/zg9WQr0Le3Det7du3L+kIefE9P1gNLvA9P1gNcbI9DWOMMVlsTyNHu3btSjpCXnzPD1aDC3zPD1ZDnKLeEf52ESkPn39MRB4Ukfp4ok29gYGBpCPkxff8YDW4wPf8YDXEKeqexp+paq+INAI3AV8CPlf4WMaYmWDbNqiuhqKi4Ou2bUknMpcTtdEYDL/+CnCfqj4MXFHYSMaYmWDbNtiyBY4eDUb7Pno0eG0Nh9uiNhonROT/AO8EHgk7MLTzIsaYyO66C86dy5527lww3bgr6iBMpcAtwFOqekhErgVerqrfiytgPqJePdXX1+dsd8S58D0/WA0umKr8RUXBHsZoIsEIXRYAABV3SURBVDA0lN+6fd8GkGwNhbx66o+A1cDtYZfov00w5Ou00NnZmXSEvPieH6wGF0xV/uuuizY9Ct+3AbhbQ9RGI7M79EGCbkWqC5wpMRUVFUlHyIvv+cFqcMFU5d+6FUpLs6eVlgbT8+X7NgB3a4jUaKjq/854bAVeDSyPJVkCent7k46QF9/zg9XggqnKv3kz3HcfLFsWHJJatix4vXlz/uv2fRuAuzXkexK7FKgqRBAXHD58OOkIefE9P1gNLpjK/Js3w5EjwTmMI0cK02CA/9sA3K0hUi+3IvIUwdjgAMXANcD/LHQoY4wxboraNfqbM54PAJ2q6uZti8YYYwoup0ZDRP5ggnmo6t8ULpIxxhhX5bqnUR5+XQm8CngofH0r8KNCh0rKwoULk46QF9/zg9XgAt/zg9UQp6g39+0EfkVVe8PX5cDDqroxpnx5iXpz38DAACUlUY/YBd0e3HUXHDsWXGO+dWvhTuhFMdn8LrEakud7frAa8lXIm/sqgQsZry+E0yZNRCpE5Psicij8Ov8Syw2KyL7w8dB4y+SrtbU18ve41H/OZPK7xmpInu/5wWqIU9Q9jbuAXwe+GU56K/DPqvqXkw4g8tdAl6reIyJ3AvNV9U/GWa5PVSPdUz8VgzBVVwcNxWjLlgWXEBpjjG8KtqcR3tD3W0B3+HhfPg1GaBPwlfD5VwgaokTs2LEj8vccOxZtOsTXHfRk8rvGakie7/nBaohT5ANmqtoENBUwQ6Wqngyfn+LSh7tmi8hegkt971HVb423kIhsAbYALF68mO3bt2fNX7RoETU1NbS1tVFXV8fOnTtH5vX19bF9+3Y2bNhAe3s7VVVVdHZ2cvz48ax1LFmyhKqqKtrb21m69GUcOyZjcixdqhw48DQ1NTV0dHRw4sQJAH7wg4V8+tMrSaeLgeHDWcrTTz/NTTedzlrHxo0baW1tpba2lvb2dk6dOpU1v7q6moqKCjo7O6mqqqK3tzerXhHhxhtvpKWlhbq6Otra2jh9Ovs9li9fTnl5OV1dXVRWVjJ6z6ykpITGxkaam5tZu3Ytra2tnDlzJmuZFStWkEql6Ovro6Kigubm5qz5qVSKDRs20NTUxLp162hpaaG7uztrmZUrV1JcXEw6naa7u5uWlpas+XPmzKGhoWFkHc3NzfT09GQts2rVKgYHBxkaGiKVSrF///6s+WVlZaxfv35kHXv37qWvry9rmdWrV5NOpykqKqK4uJgDBw5kzZ83bx719fUj69izZw/9/f1ZywwMDHDs2DFmz57N4OAgBw8ezJo/f/581qxZM7KO3bt3k06ns5apr6+nq6uLsrIy0uk0hw4dypq/YMEC6urq2LdvH/X19ezatWvMoD3r16+ns7OTiooKent7x9wstnDhQmpra2ltbWXNmjXs2LEDVR35HAA0NDTQ0dFBZWUlXV1dHBm1+zzR52lYlM9TbW3tuCPWNTY20tbWNubzNGzp0qVUVlbS0dFBTU3NyGfhBz9YyBe/uJzTp1MsXQq/+7vH+chHKnP6PO3Zsydr/lR/ntLpND09PXl9ns6fP095efmkPk+XpKqXfQC7wq+9QE/GoxfoyeH7fwDsH+exCXh+1LLdl1jHkvDrcuAI8JLLve+6des0isceeyzS8qqqDzygWlqqGpzRCB6lpcH08Sxblr3s8GPZsshvPcZk8rvGakie7/lVgxqifjZdk+R2APbqJf6u5rSnoaqN4dfyyy17ie+/6VLzRKRTRK5V1ZNhV+unx1tOVU+EXw+LyHbglcBzk8lTSMNXSeV69dRkDmcZY6KbaLyOJK5unC4KMUb4K/PM8BDwnvD5e4Bvj/O+88MBnxCRq4FfAg6MXi4pUfrPibM7aGPMi+wftHgUYozwz+eZ4R7gZhE5FK7zHgARWS8iXwyXeRmwV0RagMcIzmkUvNFoaGgo9CrHiLM76KnIHzerIXm+54egBt//QXN1OyQ+RriqnlHV16nqClW9SVW7wul7VfX94fPHVfXlqrom/PqlfN7zUjo6OuJYbZY4u4OeivxxsxqS53t+CGqI8x+0qeDqdoh69dTwGOE3A3813cYIr6zM6z7FnG3eHM8x1anKHyerIXm+54eghqjnG13j6naI+gf/14FHgTeo6vNABXBHwVMlpKurK+kIefE9P1gNLvA9P7xYQ1zjdUyF4Rriuq9rsqLe3HdOVR9U1UPh65Oq+r14ok290deg+8b3/GA1uMD3/DB9anCpm6JhUa+eEhF5l4h8PHx9nYhcH080Y4yZ2Sa6bDgpl200RKRRRIrDl58FNgC3h697gXtjymaMMTOai5cN57KnMQR8LnzeoKofAM4DqGo3eV49ZYwxZnwuXjZ82UZDVR8n2MMAuBjudSiAiFxD0KhMC4sWLUo6Ql58zw9Wgwt8zw/TpwYXLxvO6ZyGqu4Ln36GoFv0hSKyFdgFfCqmbFOupqYm6Qh58T0/WA0u8D0/TJ8a4ryva7KiXj21Dfhj4C+BnwK3MY0OT7W1tSUdIS++5werwQW+54fpVYNrlw3nNAiTiMwDPgAsIegr6vvAB4E/BFpUdVOcIScr6iBMQ0NDFBX5e6+i7/nBanCB7/nBashXIQZh+hqwEngKeD9B/0+3AW91tcGYjPHGAvCJ7/nBanCB7/nBaohTrt2ILFfVlwOEnQieBK5T1fOxJTPGGOOcXPc0Lg4/UdVBoMMaDGOMmXly3dNYIyLDYwEKMCd8LYCq6rxY0hljjHFKriP3FV9+KWOMMdNdTldP+Srq1VPpdJpUKhVjonj5nh+sBhf4nh+shnwV4uqpGaG9vT3pCHnxPT9YDS7wPT9YDXGyRiNDVVVV0hHy4nt+sBpc4Ht+sBriZI1Ghs7OzqQj5MX3/GA1uMD3/GA1xMkajQzHjx9POkJefM8PVoMLfM8PVkOcrNEwxhiTM2s0jDHG5MwaDWOMMTmzRiPDkiVLko6QF9/zg9XgAt/zg9UQJ2s0Mrh6iVuufM8PVoMLfM8PVkOcrNHI4OrNNLnyPT9YDS7wPT9YDXGybkQyDAwMUFKSax+O7vE9P1gNLvA9P1gN+bJuRHK0a9eupCPkxff8YDW4wPf84HYN27ZBdTUUFQVft20bfzlXa/C7KTbGGI9s2wZbtsC5c8Hro0eD15D82N+5sj0NY4yZInfd9WKDMezcuWC6L6zRMMaYKXLsWLTpLrJGwxhjpsh110Wb7iK7eiqD71dc+J4frAYX+J4f3K1h9DkNgNJSuO++sec07OopD7S1tSUdIS++5werwQW+5wd3a9i8OWggli0DkeDreA0GuFuD7Wlk6O/vZ86cOTEmipfv+cFqcIHv+cFqyJftaeSoo6Mj6Qh58T0/WA0u8D0/WA1xSrzREJG3i0iriAyJyLgtW7jcLSJyUESeFZE748hy4sSJOFY7ZXzPD1aDC3zPD1ZDnBJvNID9wK8COy+1gIgUA/cCbwRWAbeLyKqpiWeMMWZY4pcXqOrTACIy0WLXA8+q6uFw2a8Dm4ADsQc0xhgzIvFGI0dLgMwBczuAhvEWFJEtwBaAxYsXs3379qz5ixYtoqamhra2Nurq6ti588UdnL6+PrZv386GDRtob2+nqqqKzs7OMWP1LlmyhKqqKtrb26mtrR23j5jGxkba2tqoqamho6NjzK7m0qVLqayspKOjg5qaGnbv3j1mHRs3bqS1tZXa2lra29s5depU1vzq6moqKiro7OykqqpqJH/Gz4Ibb7yRlpYW6urqaGtr4/Tp01nrWL58OeXl5XR1dVFZWcnoCwdKSkpobGykubmZtWvX0traypkzZ7KWWbFiBalUir6+PioqKmhubs6an0ql2LBhA01NTaxbt46Wlha6u7uzllm5ciXFxcVcuHCB7u5uWlpasubPmTOHhoaGkXU0NzfT09OTtcyqVasYHBxkaGiIVCrF/v37s+aXlZWxfv36kXXs3buXvr6+rGVWr15NOp2mqKiI4uJiDhzI/r9k3rx51NfXj6xjz5499Pf3Zy0zMDDAsWPHmD17NoODgxw8eDBr/vz581mzZs3IOnbv3k06nc5apr6+nq6uLsrKykin0xw6dChr/oIFC6irq2Pfvn3U19eza9cuBgYGspZZv349nZ2dVFRU0Nvby+HDh7PmL1y4kNraWlpbW1mzZg07duxAVbN+jxoaGujo6KCyspKuri6OHDmStY6JPk/Dkvg8jf4sQPTP0549e7LmT/Xn6cKFC/T09OT1eTp//jzl5eWT+jxdypRcPSUiPwAWjTPrLlX9drjMduCPVHXM5U4ichtwi6q+P3z9bqBBVT840ftGvXrqueee4yUveUnOy7vG9/xgNbjA9/xgNeQr8aunVPUmVV09zuPbOa7iBLA043VVOK2gKisrgdx7oXTNcH6fWQ3J8z0/WA1xcuFEeC6eBFaISI2IXAG8E3io0G/S0dExcsfm0aOg+mIvlD40HK5eoheF1ZA83/OD1RCnxG/uE5G3AX8PXAM8D+xT1TeIyGLgi6r6pnC5NwF/CxQDX1bVrZdbd9TDU+l0mpUrUxw9OnbesmUw6nCuc9LpNKlUKukYebEakud7frAa8pX44amJqOo3VbVKVVOqWqmqbwin/3S4wQhfP6Kqtar6klwajMnYvXu3171Qjncy3TdWQ/J8zw+Tr8GlQ9OubofEGw3XTIdeKI0x0fl8aHoqWaMxytatQa+TmUpLg+nGmOlrOgyQNBWs0RglSi+Uxpjpw+dD01PJl5v7ptTmzdZIGDPTXHcd414EY4emsyV+9VScol49NTQ0RFGRvztfvucHq8EFvueHydUQZYCkqZDkdnD66imXtLa2Jh0hL77nB6vBBb7nh8nV4NqhaVe3g+1pZPD92m7f84PV4ALf84PVkC/b08hRe3t70hHy4nt+sBpc4Ht+sBriZI1GhtG9XvrG9/xgNbjA9/xgNcTJGg1jjDE5s0bDGGNMzqzRMMYYk7NpffWUiPwMGOd2nUu6Gvh5THGmgu/5wWpwge/5wWrI1zJVvWa8GdO60YhKRPZe6jIzH/ieH6wGF/ieH6yGONnhKWOMMTmzRsMYY0zOrNHIdl/SAfLke36wGlzge36wGmJj5zSMMcbkzPY0jDHG5MwaDWOMMTmzRgMQkVtE5KCIPCsidyadJyoRWSoij4nIARFpFZHfSzrTZIhIsYj8WES+k3SWyRCRq0TkGyLyjIg8LSIbks4UlYh8JPwd2i8i/yQis5POdDki8mUROS0i+zOmVYjI90XkUPh1fpIZJ3KJ/P8r/D36iYh8U0SuSjJjphnfaIhIMXAv8EZgFXC7iKxKNlVkA8Afquoq4AbgAx7WAPB7wNNJh8jD3wH/rqovBdbgWS0isgT4MLBeVVcDxcA7k02Vk/uBW0ZNuxP4D1VdAfxH+NpV9zM2//eB1ar6CqAN+OhUh7qUGd9oANcDz6rqYVW9AHwd2JRwpkhU9aSqNofPewn+WC1JNlU0IlIF/ArwxaSzTIaIXAlsBL4EoKoXVPX5ZFNNSgkwR0RKgFLgpwnnuSxV3Ql0jZq8CfhK+PwrwFunNFQE4+VX1e+p6kD48gmgasqDXYI1GsEf1+MZrzvw7A9uJhGpBl4J7Ek2SWR/C/wxMJR0kEmqAX4G/GN4iO2LIjI36VBRqOoJ4NPAMeAk8IKqfi/ZVJNWqaonw+engMokw+Tpt4DvJh1imDUa04iIlAH/Cvy+qvYknSdXIvJm4LSqNiWdJQ8lQD3wOVV9JXAWtw+JjBEe999E0AAuBuaKyLuSTZU/De4r8PLeAhG5i+Dw87akswyzRgNOAEszXleF07wiIrMIGoxtqvpg0nki+iXgLSJyhODw4GtF5IFkI0XWAXSo6vAe3jcIGhGf3AS0q+rPVPUi8CDwiwlnmqxOEbkWIPx6OuE8kYnIe4E3A5vVoRvqrNGAJ4EVIlIjIlcQnPh7KOFMkYiIEBxLf1pV/ybpPFGp6kdVtUpVqwl+/j9UVa/+w1XVU8BxEVkZTnodcCDBSJNxDLhBRErD36nX4dnJ/AwPAe8Jn78H+HaCWSITkVsIDte+RVXPJZ0n04xvNMKTTR8EHiX4gPyLqrYmmyqyXwLeTfAf+r7w8aakQ81AHwK2ichPgLXApxLOE0m4l/QNoBl4iuDvg5NdWWQSkX8CdgMrRaRDRP4bcA9ws4gcItiDuifJjBO5RP5/AMqB74ef588nGjKDdSNijDEmZzN+T8MYY0zurNEwxhiTM2s0jDHG5MwaDWOMMTmzRsMYY0zOrNEwM1bYK+3/SDpHIYjItRP1DiwiV4jIzrBPKWMmzRoNM5NdBUyLRgP4A+ALl5oZdsb5H8A7piyRmZas0TAz2T3AS8Kbp/4XgIjcISJPhuMYfDKcVh2ObXC/iLSJyDYRuUlE/iscr+H6cLm7ReRrIrI7nP7b4fRrw//y94XjVPzy6CAisk5EdohIk4g8mtEFxnYR+SsR+VH43mO+N/RrwL+H31MXLr8vrGNFuMy3gM0F/PmZGch2Vc1MdifBmAVrAUTk9cAKgu7yBXhIRDYSdK/xC8DbCXocfRL4DaAReAvwp7zY9fYrCMY0mQv8WEQeBm4HHlXVreH4LaWZIcJ+w/4e2KSqPxORdwBbw/cCKFHV68O7/D9BcIdz5vfXAN2qmg4n/Q7wd6q6Lewapzicvh941aR/WsZgjYYxmV4fPn4cvi4jaESOEXTk9xSAiLQSDPCjIvIUUJ2xjm+raj/QLyKPETRATwJfDhuHb6nqvlHvuxJYTdBlBAR/5E9mzB/ugLJp1HsNu5agW/Zhu4G7wjFKHlTVQwCqOigiF0SkPBx3xZjI7PCUMS8S4C9VdW34+AVV/VI4L52x3FDG6yGy//ka3S+PhoPsbCToPfl+EfnNcd63NeN9X66qr8+YP/xeg4z/j14/MDIsq6r+X4I9oH7gERF5bcayKeD8OOswJifWaJiZrJegU7hhjwK/FY5LgogsEZGFEde5SURmi8gC4NXAkyKyDOhU1S8QjEw4usv0g8A1Eo4pLiKzRKQuwnu2kbEHIiLLgcOq+hmC3l1fEU5fAPw87PbcmEmxw1NmxlLVM+HJ7P3Ad1X1DhF5GbA7PEzUB7yL4D/8XP0EeAy4GvifqvpTEXkPcIeIXAzXmbWnoaoXROQ24DPhsLElBCMZ5tTbsqqeFZHnROQXVPVZ4NeBd4fvd4oXe9t9DfBwhFqMGcN6uTWmQETkbqBPVT+dwHu/DVinqh+bYJkHgTtVtW3qkpnpxvY0jJkGVPWb4eGncYVXUX3LGgyTL9vTMMYYkzM7EW6MMSZn1mgYY4zJmTUaxhhjcmaNhjHGmJxZo2GMMSZn/x/lbUt4vAlB/QAAAABJRU5ErkJggg==\n"
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    {
      "cell_type": "markdown",
      "source": [
        "On valide le résultat si, sur le graphe des résidus normalisés, les points représentés sont inférieurs à 2. Cela signifie qu'il y a moins de deux incertitudes types entre le modèle affine et les points expérimentaux.\n",
        "Si ce n'est pas le cas, il est possible que :\n",
        "* le modèle d'ordre choisi ne permette pas de décrire correctement ces résultats expérimentaux et la loi est autre ;\n",
        "* certaines incertitudes aient été sous-estimées ;\n",
        "* une erreur de manipulation ait été commise."
      ],
      "metadata": {
        "id": "lLYPsViKud3c"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YqU_FcdQyGhq"
      },
      "source": [
        "# Méthode de MC pour la régression linéaire\n",
        "# Méthode de Monte Carlo\n",
        "Une autre méthode (appelée Monte-Carlo) consiste à réaliser un grand nombre d'expériences virtuelles, en faisant varier les paramètres qu'on sait ne pas être connus de manière certaine. Pour simuler un résultat de mesure (l’ensemble des valeurs raisonnablement attribuables à une grandeur), on génère un ensemble de valeurs aléatoires. Selon les cas, pour modéliser les grandeurs mal connues, on choisit une distribution de probabilité  ou uniforme :\n",
        "- normale (gaussienne) si on a des raisons de connaître l'écart-type de la distribution ;\n",
        "- uniforme si on ne pense que connaitre l'étendue de la distribution.\n",
        "\n",
        "### Nombres aléatoires\n",
        "\n",
        "On utilise le sous-module `random` de la bibliothèque Numpy :\n",
        "1. dans sa version la plus simple, l' expression  `rd.uniform(x-a, x+a, N)` permet de créer un array de $N$ valeurs tirées aléatoirement entre $x−a$ et $x+a$ et issues d'une distribution uniforme (autrement dit rectangulaire) ; ici `x`et `a` sont des scalaires ;\n",
        "2. l' expression  `X + rd.uniform(-a, +a, N)` permet de rajouter à `X`, un scalaire __ou un `array`__, un array de $N$ valeurs tirées aléatoirement entre $−a$ et $+a$, issues d'une distribution uniforme ; cette expression permet de gérer le cas où on a un ensemble de différentes valeurs mesurées, auxquelles on rajoute des variables aléatoires uniformes ayant toute la même étendue `a` ;\n",
        "3. l' expression  `X + A * rd.uniform(-1, +1, N)`  permet de gérer le cas où on a un ensemble de différentes valeurs mesurées, auxquelles on rajoute des variables aléatoires uniforme de __différentes__ étendues, contenues dans un array `A` ; ainsi peut-on prendre en compte le fait que la « précision » varie en fonction de la valeur de la lecture à l'appareil.\n",
        "\n",
        "4. l'expression `rd.normal(loc=0.0, scale=1.0, size=None)` crée un array de taille `size` qu’on peut préciser (si on ne le précise pas on obtient un scalaire), contenant des valeurs tirées aléatoirement issues d’une distribution gaussienne d’espérance `loc` et d’écart-type `scale`.\n",
        "    - C’est ce qu’on utlise habituellement si on a un processus qu’on peut raisonnablement penser comme Gaussien, par exemple en application du théorème de la limite centrale (un processus additif de nombreuses variables aléatoires).\n",
        "    - On fait souvent **l’hypothèse gaussienne lorsqu’on souhaite modéliser un résultat de mesurage dont on ne connait pas la distribution exacte, mais dont on connait une estimation de l’espérance et de l’écart-type** (la valeur mesurée et l’incertitude-type, en termes métrologiques).\n",
        "    \n",
        "### Détermination de l'incertitude - type des paramètres de la droite de régression\n",
        "\n",
        "* Le résultat d'une mesure est l'ensemble des valeurs raisonnablement attribuables à la grandeur mesurée. On caractérise cet ensemble par la valeur mesurée (parfois une moyenne), et l'écart-type expérimental ; ce dernier est par définition l'incertitude-type associée à la valeur mesurée.\n",
        "\n",
        "* L'idée pour estimer l'incertitude-type associée à la pente de la droite   consiste à simuler *in silico* le résultat de $N$ expériences virtuelles. Pour cela on  ajoute aux observations de la grandeur portée en $Y$ des valeurs aléatoires dont l'écart-type est égal à l'incertitude-type qu'on a évalué lors de l'expérience. On fait la même chose pour la grandeur portée en $X$.\n",
        "\n",
        "* Pour chaque graphe de $Y$ en fonction de $X$, on fait une régression linéaire et on obtient une valeur la pente. L'ensemble des valeurs de la pente  représente l'ensemble de des valeurs raisonnablement attribuables à cette pente, donc le résultat de la mesure.\n",
        "\n",
        "* On la caractérise par :\n",
        "    * sa valeur moyenne, autrement dit la valeur mesurée ;\n",
        "    * son écart-type, autrement dit l'incertitude-type.\n",
        "\n",
        "* Bien entendu, pour chaque graphe on peut récupérer également l'ordonnée à l'origine (oo) dont on peut calculer la moyenne et l'écart-type."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "3aAIDln7yCuT",
        "outputId": "732b9b0a-3c3b-4e91-a31b-8adf31111cc1"
      },
      "source": [
        "\n",
        "from numpy import random as rd\n",
        "# importation des biliothèques\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import *\n",
        "\n",
        "A = np.array([0.815, 0.753, .691, .639, .585, .537, .494, .454, .417, .383, .351, .322, .298, .274, .252, .230, .210, .195, .176, .162, .148, .135, .126, .114, .105, .097 ])\n",
        "\n",
        "time = np.array([0.17, 0.67, 1.17, 1.67, 2.17, 2.67, 3.17, 3.67, 4.17, 4.67, 5.17, 5.67, 6.17, 6.67, 7.17, 7.67, 8.17, 8.67, 9.17, 9.67, 10.17, 10.67, 11.17, 11.67, 12.17, 12.67])\n",
        "\n",
        "#Proposition des valeurs des précisions :\n",
        "p_time = 0.2/(2*60) # demi - étendue du déclenchement et arrêt du chronomètre\n",
        "delta_A=(2/100)*A # demi - étendue de l'absorbance donnée par le constructeur\n",
        "\n",
        "\n",
        "# Paramètres\n",
        "N_sim = 20000     # Nombre d'itérations souhaitées\n",
        "N = len(time)        # Nombre de données de notre expérience\n",
        "p1_sim=np.zeros(N_sim)\n",
        "\n",
        "\n",
        "for i in range(0, N_sim):   # Création d'une boucle for permettant de générer les N_sim expériences virtuelles\n",
        "\n",
        "    time_sim = time + rd.uniform(-p_time, p_time, N)                 # Génère les N valeurs aléatoires de pH selon une loi rectangulaire\n",
        "\n",
        "    A1_sim = A + delta_A*rd.uniform(-1, 1, N)        # Si on connaissait une précision, on génererait les N valeurs aléatoires de A selon une loi rectangulaire\n",
        "\n",
        "    Z1_sim = np.log(A1_sim)\n",
        "\n",
        "    p1_sim [i]= np.polyfit(time_sim, Z1_sim, 1)[0]\n",
        "\n",
        "\n",
        "plt.figure(2)\n",
        "plt.title('Pour 20 000 iterations')\n",
        "plt.hist(-p1_sim, bins='rice', color='brown', label = \"$k'_{1}$\") # tracé d'un histogramme\n",
        "plt.xlabel(r\"$k'_{1}$ \")\n",
        "plt.ylabel('effectif')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print(\"k'1 = \", format(np.average(-p1_sim), \"#.5g\"), 'min^-1')\n",
        "print(\"u(k'1) = \", format(np.std(-p1_sim, ddof=1), \"#.3g\"), 'min^-1')\n",
        "\n",
        "print(\"k'1 = \", format(np.average(-p1_sim), \"#.4e\"), 'min^-1')\n",
        "print(\"u(k'1) = \", format(np.std(-p1_sim, ddof=1), \"#.3g\"), 'min^-1')\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "k'1 =  0.17120 min^-1\n",
            "u(k'1) =  0.000604 min^-1\n",
            "k'1 =  1.7120e-01 min^-1\n",
            "u(k'1) =  0.000604 min^-1\n"
          ]
        }
      ]
    }
  ]
}