Interpolation-and-polynomial-approximation.ipynb

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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from bokeh.io import show, output_notebook\n",
    "from bokeh.plotting import figure\n",
    "from bokeh.layouts import row, gridplot, column\n",
    "\n",
    "output_notebook(hide_banner=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Méthode des différences divisées"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Implémenter une fonction qui prend en entrée des abscisses $x_k$ et des valeurs $f(x_k)$, et qui retourne les coefficients $f[x_0,\\ldots,x_k]$. On pourra utiliser :**\n",
    "\n",
    "$$\n",
    "f[x_0,\\ldots,x_{n+1}]=\\frac{f[x_{1},\\ldots,x_{n+1}]-f[x_0,\\ldots,x_{n}]}{x_{n+1}-x_0}.\n",
    "$$\n",
    "\n",
    "**en remarquant que $f[x_k]=f(x_k)$ pour tout $k$.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_divided_diff_coef(x, y):\n",
    "    \n",
    "    # Voir le commentaire en dessous\n",
    "    \n",
    "    n = len(x)\n",
    "    coef = np.zeros(n)\n",
    "    D = {}\n",
    "    \n",
    "    # Remplissage de D\n",
    "    for k in range(n) :\n",
    "        D[(k,)] = y[k]\n",
    "    for k in range(1,n+1) :\n",
    "        for i in range(0,n-k) :\n",
    "            t = tuple([ j for j in range(i,i+k+1)])\n",
    "            D[t] = ( D[t[1:]] - D[t[:-1]] )/(x[i+k] - x[i])\n",
    "    \n",
    "    # Remplissage de coef\n",
    "    for k in range(n) :\n",
    "        t = tuple([ j for j in range(0,k+1)])\n",
    "        coef[k] = D[t]\n",
    "    \n",
    "    return coef"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "Bien qu il soit possible de calculer les différences divisées de facon récursive avec un code plus court, la récursivité ménera à calculer certains termes plusieurs fois, ce qui encombre la mémoire si on a un grand nombre de points (ce qui sera à priori le cas), et sa complexité est exponentielle. C'est pourquoi j'ai préféré utiliser un dictionnaire où seront stockées les valeurs calculées, ainsi chaque terme sera calculé une seule fois, et la complexité de ma fonction est $O(n^2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Implémenter une fonction qui prend en entrée des abscisses $x_k$ les coefficients $f[x_0,\\ldots,x_k]$ et un vecteurs de points de $[a,b]$, et qui renvoie la valeur de $P_n(f)$ en ces différents points. On pourra utiliser :**\n",
    "\n",
    "$$\n",
    "P_n(f)(x)=\\sum_{k=0}^n f[x_0,\\ldots,x_k] \\Pi_k(x),\\quad \\forall~x\\in[a,b].\n",
    "$$\n",
    "\n",
    "**et un algorithme d'évaluation de type Horner.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_interp(coef, xk, x):\n",
    "    n = len(coef) - 1\n",
    "    p = np.zeros(len(x))\n",
    "    for i in range(len(x)) :\n",
    "        p[i] = coef[-1]\n",
    "        for j in range(1,n+1) :\n",
    "            p[i] = p[i]*(x[i] - xk[n-j]) + coef[n-j]\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Générer aléatoirement des abscisses $x_k\\in[-1,1]$ et des valeurs $y_k\\in\\mathbb{R}$, $0\\leq k\\leq 11$, et utiliser les fonctions construites aux deux questions précédentes pour tracer l'unique polynôme $P_n$ de degré $n$ vérifiant $P_n(x_k)=y_k$ pour tout $k$. Commenter.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "figure gauche : polynôme interpolant des points aléatoires dans [-1,1]\n",
      "figure droite : polynôme interpolant des points aléatoires sur la courbe se sin dans [-5,5]\n"
     ]
    },
    {
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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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al\\u00e9atoires\"},\"renderers\":[{\"id\":\"25917\",\"type\":\"GlyphRenderer\"}]},\"id\":\"25927\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"25836\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_color\":\"orange\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"25929\",\"type\":\"Line\"},{\"attributes\":{\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"25944\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"25930\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"25928\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"25929\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"25930\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"25932\",\"type\":\"CDSView\"}},\"id\":\"25931\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"25941\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"source\":{\"id\":\"25928\",\"type\":\"ColumnDataSource\"}},\"id\":\"25932\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"25940\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"27011\",\"type\":\"Selection\"},{\"attributes\":{\"below\":[{\"id\":\"25891\",\"type\":\"LinearAxis\"}],\"center\":[{\"id\":\"25895\",\"type\":\"Grid\"},{\"id\":\"25900\",\"type\":\"Grid\"},{\"id\":\"25926\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"25896\",\"type\":\"LinearAxis\"}],\"plot_height\":300,\"plot_width\":490,\"renderers\":[{\"id\":\"25917\",\"type\":\"GlyphRenderer\"},{\"id\":\"25931\",\"type\":\"GlyphRenderer\"},{\"id\":\"25946\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"25920\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"25907\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"25883\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"25887\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"25885\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"25889\",\"type\":\"LinearScale\"}},\"id\":\"25882\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"25945\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"25943\",\"type\":\"ColumnDataSource\"}},\"id\":\"25947\",\"type\":\"CDSView\"},{\"attributes\":{\"data_source\":{\"id\":\"25943\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"25944\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"25945\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"25947\",\"type\":\"CDSView\"}},\"id\":\"25946\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null},\"id\":\"25824\",\"type\":\"DataRange1d\"},{\"attributes\":{\"callback\":null},\"id\":\"25822\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"25957\",\"type\":\"Selection\"}],\"root_ids\":[\"25960\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"6eaf51f8-e9d9-4668-8ec6-492e5c1b5a88\",\"roots\":{\"25960\":\"9c0c6724-4211-43ff-abac-a2b237c92644\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "25960"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = -1\n",
    "b = 1\n",
    "\n",
    "n = 10\n",
    "xk = a + (b-a)*np.random.rand(n+1)\n",
    "yk = 11*(np.random.randn(n+1))\n",
    "\n",
    "# points auxquels p sera évalués pour le tracé\n",
    "x = np.linspace(a,b,1000)\n",
    "\n",
    "coef = compute_divided_diff_coef(xk, yk)\n",
    "p = poly_interp(coef, xk, x)\n",
    "\n",
    "# Tracer les points (xk, yk) et le polynome p\n",
    "fig = figure(width=490, height=300)\n",
    "fig.x(xk,yk,size=10, color=\"red\", legend=\"pts aléatoires\")\n",
    "fig.line(x,p, legend=\"polynome p\")\n",
    "\n",
    "\n",
    "#######################################################################################\n",
    "# Approximation de la fonction sinus\n",
    "asin = -5\n",
    "bsin = 5\n",
    "\n",
    "n = 10\n",
    "xk_sin = asin + (bsin-asin)*np.random.rand(n+1)\n",
    "sk = np.sin(xk_sin)\n",
    "xsin = np.linspace(asin,bsin,1000)\n",
    "ysin = np.sin(xsin)\n",
    "coef_sin = compute_divided_diff_coef(xk_sin, sk)\n",
    "psin = poly_interp(coef_sin, xk_sin, xsin)\n",
    "\n",
    "\n",
    "fig2 = figure(width=490, height=300)\n",
    "fig2.x(xk_sin,sk,size=10, color=\"red\", legend=\"pts aléatoires\")\n",
    "fig2.line(xsin,ysin, legend=\"sin\", color=\"orange\")\n",
    "fig2.line(xsin,psin, legend=\"P(sin)\")\n",
    "\n",
    "\n",
    "print(\"figure gauche : polynôme interpolant des points aléatoires dans [-1,1]\\nfigure droite : polynôme interpolant des points aléatoires sur la courbe se sin dans [-5,5]\")\n",
    "\n",
    "show(row(fig,fig2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "On remarque qu'au bords de la 1ère figure, le comportement du polynôme n'est pas controlé par les points d'interpolation choisis, il varie très rapidement. C'est le phénomène de Runge.\n",
    "\n",
    "Par contre, sur la 2ème figure, même avec des points aléatoires, le polynôme produit avec une très bonne approximation la fonction sinus. Ceci est dû à la régularité de sin et au fait que toutes des dérivées sont majorées en valeur absolue par 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phénomène de Runge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Considérer la fonction :**\n",
    "\n",
    "$$\n",
    "f(x) =\\frac{1}{0.1 +x^2}\n",
    "$$\n",
    "\n",
    "**sur l'intervalle $[-1,1]$, et tracer le polynôme d'interpolation $P_n(f)$ pour différentes valeurs de $n$ et différents choix de $x_k$, ainsi que l'erreur entre $f$ et $P_n(f)$. Commenter.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1/(0.1+x*x)\n",
    "\n",
    "\n",
    "## Pour pouvoir appliquer f directement aux vecteurs\n",
    "f_vect = np.vectorize(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"b7ab841a-3713-4951-8fe1-5944e243bff3\" data-root-id=\"10949\"></div>\n"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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JHOUIEALer8vRq0fQIedNeyzKR5Awj6R+hqhHEBco66pHBYbQFrZkiUVixlAc5+oPCACGEAiH1/jHX0WQOJzDXm2/RRAzsTi0F6FE0AXYpABXBUSQJHMQf7GrhBAjqq79h+lDkDsJOhCAwMMQGtmRSGIeAlARZpUbb8GB0Dp/Z7zf64EQJd/KnVrcAJA46uMXPNMAEDv/sJQuoj8P6tAix2Nrfg/EEadulII9T/e0rAxvpjxP1zQcIGRvOw/UtqSV3Cw5j8gYklCSQvhP1yYHdT4ldc/uKeF1Y+0yz+ASeD863izP8CB/RbSHqs/aChY/vbjxT/kMgSqdNLRP7IaijXMC9g/iAPJWbak3T/W2e6zBFLhP4CZcoxZiOM/GhgOZdd45T8BqCBM/ibnPyk5d6ZMlug/lWmciDvK6T9nAL9sO8bqPwgZaj+xjes/hM6PvfMj7D/pKqoeSYzsPyeD9gXlyew/dFgNtubf7D+zZVSCV9HsP6G9AXopoew/eeCdSDZS7D8rhSdIPufrP0+TLsHnYus/oHxsVb7H6j976Y6RMhjqP4qAFqOZVuk/UJVWLy2F6D+xxctIC6bnP6ANJ4A2u+Y/iLWQDpbG5T/yusoW9snkP/wD/foHx+M/9+AWxWK/4j+2GdGfg7ThP/Mfel7Op+A/TPelIxw13z9Gb75Q6xvdP8oKSTFBBts/sgjgJyf22D/MUp6Aeu3WP3JcAvHt7dQ/WIx3IQv50j/8Q2U+NBDRP3BPlB1Lac4/QM8fHe7Oyj9wGs8VPFPHP3iGQH7d98M/oJAV4Tu+wD9gL2kgCk+7P2CgQaJcabU/oNPqAN6Zrz+gTbyjuPWkP4AhX4iEz5U/ANQbaC0MZz8A2WCAjLyNPwCCRjTOcJ8/QIqvaw9spz/AczJppouuP9C8ZO+XjLI/sK1ibY+LtT+AN/LmJUS4PyAPmYH1t7o/EBuMuMHovD/wImbycti+P9jxOSKJRMA/sCfpsWL+wD9AIzpi5ZrBP/BGAPM6G8I/OIEr55WAwj9QfLbYL8zCP7AVCuNH/8I/+LuSIyEbwz9QajhQASHDPxAfX2MvEsM/KOQLXfLvwj8Qq8EYkLvCP2hcoTdMdsI/IHdRHmchwj9wbysGHb7BPxCWJyGlTcE/+Kn7zzDRwD/wQtzp6knAPyDnmyrucb8/cK7gYuI+vj8gQ1ae2fy8P+B0R3Pprbs/wMXBGhVUuj/QmAK7TPG4P+Da08xsh7c/IEiimj0Ytj9AyhjYcqW0P3B2DlGrMLM/AGqXrnC7sT+wEwxRN0ewP+CvvHu8qq0/wMYwQF7Oqj9grcu0vPunPyCHGlMWNaU/QC6LrH98oj+AUmTVx6efPwBYN9QKepo/AG5J2/xylT9ASM7Qg5WQPwDcRXFxyIc/AEqOXKaFfT8AlJ6w23hoPwBcx303D1E/AE0cYSb1cz8AjHEkX2mBPwAXz8RbbIg/APbguhQCjz/AmviixZSSP8DnbIQYcZU/QM3+YfEVmD8AVFuAcYOaP0CqfFnquZw/QDfX6tq5nj9ApoKB9kGgP2Bve0h5DKE/QKJGe/G8oT9AHDcw7FOiP+B0XpIG0qI/oAkmlew3oz8AauCsV4ajP0CiAY0NvqM/INif7N7foz/g+9BRpuyjPwDhbeRG5aM/wAm3SKvKoz+AtkuCxJ2jPyBy2N+IX6M/YEvX7/IQoz/AUrF+ALOiP8Cfhp6xRqI/QETYuAfNoT8A/kWqBEehPwBXiOiptaA/wBLHsvcZoD+ArMaY2OmePwDgiYQGj50/gN9kdWklnD8A1Wif6a6aP4Cq+udlLZk/AHKRxLKilz+AoTwumRCWP4Bsv6nVeJQ/AEgDZBfdkj+Adpli/z6RPwDT8o8/QI8/AL1BVvYDjD8AKmQECMyIPwARST84m4U/ABkrgyh0gj8Akv3KrrJ+PwCWXfI/mng/AFI5qHKjcj8AQEnT2KRpPwDwPzomrFw/AOBT89ANOz8AsITne8ZMPwBQBlL3XWE/AMy9j98daz8AnOtOPDZyPwCGFwm5onY/AHJ5HITSej8AvBjlAMR+PwCkrVPrOoE/AIhMjnfzgj8AYiluOouEPwAhQ9LoAYY/ADHLQVZXhz8ARxvzc4uIPwB84cVPnok/AGOzMROQij8A7DMqAmGLPwAz8/l5EYw/AIApFfChjD8AD2nl8BKNPwCtW48eZY0/AMOasy+ZjT8AAakr7q+NPwDPDcQ1qo0/AN6K9PKIjT8AMlyXIU2NPwARa6DL94w/AJRT1QeKjD8AchSH+ASMPwBxN07KaYs/AIQ4yrK5ij8AQ+hk7/WJPwCWfRrEH4k/AFABR3o4iD8ABrV5X0GHPwCiDU/EO4Y/AI3QUfsohT8AWdnjVwqEPwClBC8t4YI/AJOzHs2ugT8AUlJih3SAPwBShvJQZ34/AMgMkfHaez8AuN10d0Z5PwAGVNFdrHY/AMqzoRIPdD8Awu0n9XBxPwAonAKpqG0/ABTCotx2aD8AFJIG21BjPwCwx4akdVw/ANj2FY1xUj8AYMjZQDpBPwCATSrABBA/ABDbdoK/RD8AeI2OqXpTPwA4UBvTSlw/APQO+zhlYj8A4LT7EHpmPwC87Bl0YWo/ABCCDxoZbj8ANpQWeM9wPwCiacyMeHI/AOLwsfcGdD8Akg09AHp1PwCqRbUI0XY/ADiuBY4LeD8Aqu18Jyl5PwAG8XuGKXo/AID3E3YMez8A2p6U2tF7PwAOnwqxeXw/AM7prw4EfT8AtuVNIHF9PwDMgZIpwX0/ALzgWIT0fT8Aal7mnwt+PwB+tBwAB34/ACYFojznfT8A4pP//6x9PwAy9rcGWX0/AHiFVR7sfD8AetxxJGd8PwAWKrcFy3s/AAgi3LwYez8ADlSbUVF6PwAIr6bXdXk/AIL1l22HeD8A7OTeO4d3PwDyz61zdnY/AMJn5U1WdT8ASm4ACih0PwCYBgDt7HI/AGpVWUCmcT8AUB/lUFVwPwAQG6Tb9m0/ANh7NM8zaz8AsHn5HWRoPwAgB/dnimU/AGAevUmpYj8AIH3ytIZfPwBwlChUtlk/AECYu37mUz8AgHMWWThMPwBgU5N4uEA/AACkboFbJT8AACPDqYwnPwBA1hCo7EA/AACF6OO8Sz8AMIz9vCVTPwAAEwsuSFg/APC+VetBXT8AePpVpQdhPwCIQcVpVmM/AGAphaCLZT8AOB3RwaVnPwAIMl5ho2k/AKhrDy+Daz8AkGyT90NtPwCgcuuk5G4/ACDLbR8ycD8AOCWi9eBwPwDAljJ3fnE/AJSihFUKcj8AvGdOUYRyPwBAb5Y67HI/ALSAqPBBcz8A7KT/YYVzPwD0hCWMtnM/AFhYh3vVcz8AyJxAS+JzPwCU1dsk3XM/ALiXCUDGcz8ALCxO4p1zPwDkFqZeZHM/AGTWIRUacz8AlDN5cr9yPwD0fpbvVHI/AGAbGhHbcT8AELvWZlJxPwCQt0aLu3A/ANjv+iIXcD8AcDgHuMtuPwBQEqfaUG0/AJhcPCy/az8A+DBiOhhqPwCQP5KgXWg/AADKxwaRZj8AwCUcILRkPwAow12pyGI/AJC2omfQYD8AsIavTZpdPwBQ1JlwgVk/AAD3gOJZVT8AkF/TUidRPwCAFA/m2kk/AACNaudfQT8AwA7QBsoxPwAAIA2gYew+AIDrt1bNLz8AAD3rb0JAPwAgYdzEdEg/AMDRLLpBUD8AsJ5S4zNUPwBQ2L6YDVg/AHAuhK7LWz8AYIVIFGtfPwAozsZrdGE/AHCC8BIhYz8A8Ph4J7pkPwAouUVjPmY/AHjdOJOsZz8AmJ4QmANpPwDQKjdnQmo/AGg5ggtoaz8AcNbhpXNsPwAo7f1tZG0/AAgiwrI5bj8AaJrX2vJuPwCwWgxlj28/AEz4U3QHcD8A3JXWijhwPwBIWYTaWnA/ABgoVlRucD8AeHHL9XJwPwBgceTIaHA/AIjAEuRPcD8A0DogaihwPwCwkxgU5W8/AJBWv/1cbz8AqJztHrluPwCA2oUc+m0/ADgYBLIgbT8AmB3csC1sPwAIO8b/IWs/ADAs+5n+aT8AUJ5fjsRoPwDI75/+dGc/ACjMPB4RZj8A+FKJMZpkPwB4hJuMEWM/AMC5L5J4YT8AEPL/ZKFfPwDQBSDUNlw/AMD43YC0WD8A0EvfjR1VPwDgLbAudVE/AMD6J0p9Sz8AoMWRfPpDPwAAmQJB0Tg/AIAjh7Y5Iz8AAPQx8moWPwAARxMKyDQ/AAAKzc3uQT8AgGy+CmdJPwDAkGMPY1A/AADZmcECVD8AIGemZo9XPwDAXO7ZBVs/AEA/TgpjXj8AYBRh/tFgPwCQo37nYmI/AAAz99ziYz8AgKgXilBlPwDgby6qqmY/AHDJqgnwZz8AYFsuhx9pPwAACJAUOGo/ANAWz7c4az8AYMr1iyBsPwCQhOrB7mw/AMCtLqGibT8AoJqKiDtuPwAQwqXuuG4/AGCdimIabz8AwKEVjF9vPwAg0k4siG8/APB3rR2Ubz8AUKdFVINvPwCwQt/dVW8/ADBI9uELbz8AEEWkoaVuPwDQ4HJ3I24/AMCFF9eFbT8A8EIYTc1sPwAwFlp++ms/APDkmCcOaz8AEH7JHAlqPwDQE2ZI7Gg/ABC0paq4Zz8AgFefWG9mPwBQNll7EWU/ALAkxU6gYz8AkMyqIB1iPwDwrYBPiWA/AIDAaZLMXT8AQETNE2taPwCApiM18VY/AMAPWx9iUz8AgL37HoJPPwAAX4enIkg/AICUIJGsQD8AAOWMVU0yPwAAkFs3fQk/AADkkDDkJz8AAIMHEAo7PwCAnjA3BUU/AIDNILpyTD8AYEOLYONRPwAgnDlJfVU/AOCufMgDWT8AYJT7oHNcPwCg9KmpyV8/AOCUXmiBYT8A8HBGDw5jPwAgNi5ciWQ/ABD1hPHxZT8AAF7QgkZnPwCASebVhWg/AMBbFcSuaT8AcJc7O8BqPwAwx8k+uWs/AAC4suiYbD8A4FNFal5tPwDgu/AMCW4/AHCf8TKYbj8AMBzoVwtvPwCAkFURYm8/AHDfAQ+cbz8AEL5HG7lvPwAQvkcbuW8/AGDfAQ+cbz8AgJBVEWJvPwAgHOhXC28/AHCf8TKYbj8A8LvwDAluPwDgU0VqXm0/ACC4suiYbD8AIMfJPrlrPwCAlzs7wGo/ANBbFcSuaT8AcEnm1YVoPwAAXtCCRmc/ABD1hPHxZT8AEDYuXIlkPwAAcUYPDmM/APCUXmiBYT8AoPSpqclfPwBglPugc1w/AACvfMgDWT8AQJw5SX1VPwCgQ4tg41E/AMDNILpyTD8AwJ4wNwVFPwAAhAcQCjs/AADlkDDkJz8AAIxbN30JPwCA5IxVTTI/AECUIJGsQD8AwF6HpyJIPwBAvfsegk8/AMAPWx9iUz8AYKYjNfFWPwAgRM0Ta1o/AKDAaZLMXT8A4K2AT4lgPwBgzKogHWI/AKAkxU6gYz8AUDZZexFlPwCAV59Yb2Y/AAC0paq4Zz8AwBNmSOxoPwAAfskcCWo/APDkmCcOaz8AIBZafvprPwDgQhhNzWw/ALCFF9eFbT8AsOBydyNuPwAARaShpW4/ACBI9uELbz8AsELf3VVvPwBAp0VUg28/APB3rR2Ubz8A8NFOLIhvPwDAoRWMX28/AFCdimIabz8AEMKl7rhuPwCwmoqIO24/ALCtLqGibT8AkITqwe5sPwAwyvWLIGw/ALAWz7c4az8A4AeQFDhqPwBgWy6HH2k/AHDJqgnwZz8A0G8uqqpmPwBwqBeKUGU/AAAz99ziYz8AYKN+52JiPwBgFGH+0WA/AAA/TgpjXj8A4Fzu2QVbPwDAZqZmj1c/AODYmcECVD8AoJBjD2NQPwCAbL4KZ0k/AMAJzc3uQT8AAEcTCsg0PwAA+DHyahY/AAAkh7Y5Iz8AQJgCQdE4PwAAxpF8+kM/AKD6J0p9Sz8AIC6wLnVRPwDgS9+NHVU/AMD43YC0WD8A8AUg1DZcPwDQ8f9koV8/AKC5L5J4YT8AiISbjBFjPwDYUokxmmQ/ACjMPB4RZj8A2O+f/nRnPwAonl+OxGg/ADAs+5n+aT8A8DrG/yFrPwCgHdywLWw/AEgYBLIgbT8AcNqFHPptPwConO0euW4/AKhWv/1cbz8AyJMYFOVvPwDwOiBqKHA/AJTAEuRPcD8AcHHkyGhwPwCIccv1cnA/ABQoVlRucD8ASFmE2lpwPwDYldaKOHA/AEj4U3QHcD8A4FoMZY9vPwBwmtfa8m4/ACAiwrI5bj8ACO39bWRtPwBQ1uGlc2w/AHA5ggtoaz8AyCo3Z0JqPwBYnhCYA2k/AHDdOJOsZz8A2LhFYz5mPwAY+XgnumQ/AIiC8BIhYz8AAM7Ga3RhPwAAhUgUa18/AAAuhK7LWz8AMNi+mA1YPwCwnlLjM1Q/AKDRLLpBUD8AgGHcxHRIPwCgPOtvQkA/AADnt1bNLz8AANgMoGHsPgCADtAGyjE/AICLaudfQT8AwBMP5tpJPwBQX9NSJ1E/ADD3gOJZVT8AsNSZcIFZPwBwhq9Nml0/AOi2omfQYD8AKMNdqchiPwCQJRwgtGQ/ANjJxwaRZj8AgD+SoF1oPwAAMWI6GGo/AOBcPCy/az8AyBKn2lBtPwCgOAe4y24/AOjv+iIXcD8AiLdGi7twPwAou9ZmUnE/AHgbGhHbcT8ABH+W71RyPwB0M3lyv3I/AHzWIRUacz8AtBamXmRzPwBQLE7inXM/AMSXCUDGcz8AnNXbJN1zPwDcnEBL4nM/AGhYh3vVcz8AAIUljLZzPwDEpP9hhXM/ANyAqPBBcz8A4G6WOuxyPwCIZ05RhHI/AJSihFUKcj8AwJYyd35xPwBIJaL14HA/AMTLbR8ycD8AmHLrpORuPwDgbJP3Q20/AEBrDy+Daz8ASDJeYaNpPwAIHtHBpWc/ABAqhaCLZT8AWELFaVZjPwCg+lWlB2E/AJDAVetBXT8AMBQLLkhYPwCQjP28JVM/AOCD6OO8Sz8AoNQQqOxAPwAAPcOpjCc/AACvboFbJT8AYFKTeLhAPwBgbxZZOEw/AACYu37mUz8AUJQoVLZZPwBgevK0hl8/AFAevUmpYj8AcAb3Z4plPwCIePkdZGg/ACh8NM8zaz8AZBqk2/ZtPwCYH+VQVXA/AKJVWUCmcT8ALAcA7exyPwBCbQAKKHQ/AFRn5U1WdT8Ams+tc3Z2PwCw5N47h3c/AAr2l22HeD8AQK6m13V5PwAQVJtRUXo/AAoh3LwYez8A7im3Bct7PwCg23EkZ3w/AO6EVR7sfD8AWPa3Bll9PwCikv//rH0/AHgFojznfT8AoLMcAAd+PwAqXeafC34/AAjgWIT0fT8AVoGSKcF9PwCC5E0gcX0/AFzqrw4EfT8APp0KsXl8PwC6nZTa0Xs/AED2E3YMez8A/O57hil6PwC07XwnKXk/AGKtBY4LeD8AXkO1CNF2PwA6DT0AenU/AK7wsfcGdD8ACGvMjHhyPwD6kRZ4z3A/AIB+DxoZbj8A/OkZdGFqPwCUtfsQemY/AEAN+zhlYj8AsEgb00pcPwC4h46pelM/AJDJdoK/RD8AACgqwAQQPwDA2tlAOkE/ALD/FY1xUj8A0NCGpHVcPwAwlgbbUGM/AMDHotx2aD8AkJ8CqahtPwDa8Cf1cHE/ALa2oRIPdD8AIFTRXax2PwDe4HR3Rnk/AAYMkfHaez8AQoryUGd+PwCwUmKHdIA/AGy0Hs2ugT8ApQUvLeGCPwAA2+NXCoQ/AFPRUfsohT8AcQ5PxDuGPwCPtnlfQYc/AE0DR3o4iD8AK38axB+JPwDG52Tv9Yk/AL46yrK5ij8ANTlOymmLPwAxF4f4BIw/AMxV1QeKjD8Axmugy/eMPwAhXZchTY0/AP+L9PKIjT8A9xHENaqNPwBkrCvur40/APCasy+ZjT8AOFyPHmWNPwDOZ+XwEo0/AActFfChjD8A+/f5eRGMPwAaNyoCYYs/ANO2MROQij8AROPFT56JPwBGHPNzi4g/ALHNQVZXhz8AxUjS6AGGPwDSLG46i4Q/APRPjnfzgj8AO7FT6zqBPwCKHOUAxH4/AKiAHITSej8APiEJuaJ2PwAU8k48NnI/APjSj98daz8AoCBS911hPwCAned7xkw/AGBv8tANOz8AeAc6JqxcPwDcLdPYpGk/ADAsqHKjcj8AxFjyP5p4PwCW/squsn4/AOMpgyh0gj8Af0c/OJuFPwBVYQQIzIg/AEhAVvYDjD8Aiu+PP0CPPwBwlmL/PpE/gMgBZBfdkj8AYb2p1XiUP4DDOi6ZEJY/gBqPxLKilz8AwPbnZS2ZP4ACZp/prpo/AL9hdWklnD+AUYeEBo+dP4CKwpjY6Z4/AN7EsvcZoD/AyYboqbWgP0CYRaoER6E/QFTVuAfNoT9Ad4SesUaiP4C0sH4As6I/YODV7/IQoz+gT9XfiF+jP0DrSoLEnaM/wMm1SKvKoz+AwWrkRuWjP0C5zlGm7KM/4ACg7N7foz9A8gCNDb6jPyDv3axXhqM/4Nkhlew3oz9grVmSBtKiP8D0NTDsU6I/wMNEe/G8oT+gSnlIeQyhPyBZgIH2QaA/QM3P6tq5nj9A0ndZ6rmcP4DJVoBxg5o/AN32YfEVmD8AJm+EGHGVP4CA96LFlJI/ACDRuhQCjz8ANsXEW2yIP4DLYSRfaYE/AEUFYSb1cz8A2IZ9Nw9RPwBex7DbeGg/ABm1XKaFfT+AvE9xcciHP0Al19CDlZA/QFxL2/xylT8Aaz3UCnqaP4B5cNXHp58/4CCVrH98oj8A6BpTFjWlP+Bjz7S8+6c/QN81QF7Oqj+gar17vKqtP4BdD1E3R7A/AM6YrnC7sT+w0hBRqzCzPzCBGthypbQ/YJukmj0Ytj/gvdbMbIe3P1CNBbtM8bg/IPzDGhVUuj+AHEhz6a27PzA5WZ7Z/Lw/MKTlYuI+vj9wv50q7nG/PxBY3unqScA/IPz7zzDRwD9IPSkhpU3BP0jJLQYdvsE/yKtTHmchwj/gRqI3THbCP6h5whiQu8I/COgNXfLvwj8otmBjLxLDP6ASO1ABIcM/2NSUIyEbwz+w+Q3jR//CP4CwuNgvzMI/4FAt55WAwj9I8wLzOhvCP/giPGLlmsE/EFrssWL+wD+AqTwiiUTAP/CeZ/Jy2L4/QBSRuMHovD+gTp6B9be6P2AD9+YlRLg/YOdlbY+LtT8wjGbvl4yyP0BGN2mmi64/wAi7aw9spz9AeVU0znCfPwDvgYCMvI0/AATmZy0MZz/AZjSIhM+VP2DhqqO49aQ/4N3SAN6Zrz+gbDeiXGm1P4CMZSAKT7s/AL4Q4Tu+wD+QlD5+3ffDP3D4zBU8U8c/OKsdHe7Oyj9g6ZAdS2nOP3CCYz40ENE/OEF0IQv50j8skQDx7e3UP7TRmoB67dY/wtbeJyf22D/mcUYxQQbbPzJ5u1DrG90/2jekIxw13z8/N3lezqfgP2Ppzp+DtOE/KcgWxWK/4j/T1vr6B8fjPzOgyRb2yeQ/FtKQDpbG5T/knyWANrvmP9jOyUgLpuc/LlhULy2F6D9oJRSjmVbpP3HFjZEyGOo/5NNqVb7H6j9G/CvB52LrP+KHJkg+5+s/FLWaSDZS7D/DIwF6KaHsP+gKVIJX0ew/ZUkMtubf7D9bfvQF5cnsP8VAqB5JjOw/pjWOvfMj7D8AJmo/sY3rPw58vmw7xuo/5hSZiDvK6T+HZXWmTJboP2pjH0z+Juc/LIQLZdd45T9YxnCMWYjjP2ss7rMEUuE/XCXEWbak3T98/IU1zAvYPzjU+Kl00tE/wEZS/vbjxT8AmrAW0h6rP9CGEP3reLM/oI6G1Y+0yz/0qiXU+JXXP2BgSEJJC+E/4C2WV3Cw5j9qAHOBkbzsP+9lsTG+mPE/kDWfulII9T+X9Iwdja34P+PZxFC6iPw/9MSMXPNMAEBUqCp1a3ACQNnrnvN/rgRAMmlVbb8GB0Bbn0YhiHgJ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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"F1100UUX7T8wHtbYczLtP+yxv8DGTe0/UHuGyT5p7T/yQQY03ITtP/JwokGfoO0/TFlHNIi87T9Id2tOl9jtP0C7ENPM9O0/tNXFBSkR7j+chqcqrC3uPznwYYZWSu4/M+0xXihn7j8qaub3IYTuP83C4ZlDoe4/XCIbi42+7j/N5x8TANzuP2sNFXqb+e4/HJS4CGAX7z9U8mIITjXvP6iGCMNlU+8/Hw47g6dx7z9NHiuUE5DvPx+jqUGqru8/n2Ap2GvN7z91eMCkWOzvP7P5lHq4BfA/Wqfji1oV8D/GBtGtEiXwPzOnNgjhNPA/PLJDw8VE8D+uun0HwVTwP1SNwf3SZPA/8gNEz/t08D9R2pKlO4XwP2WFlaqSlfA/rQyOCAGm8D+p5RnqhrbwP5bRMnokx/A/Rr0v5NnX8D9Qo8VTp+jwP3JwCPWM+fA/MOpr9IoK8T/bl8R+oRvxP8etSMHQLPE/9vqQ6Rg+8T8M2Zklek/xP6wexKP0YPE/PRTWkohy8T8Wa/whNoTxPyo3y4D9lfE/HOs+396n8T/aVr1t2rnxP8GoFl3wy/E/OnGG3iDe8T/6qLQjbPDxP8u5tl7SAvI/7IkQwlMV8j8jirWA8CfyP2DGCc6oOvI/Ivni3XxN8j9+oYnkbGDyP90buhZ5c/I/j72lqaGG8j8A8/PS5pnyP9Zgw8hIrfI/ygerwcfA8j9fa7v0Y9TyP3e7f5kd6PI/wAD/5/T78j8WTL0Y6g/zP8bovGT9I/M/yZF/BS848z/7qQc1f0zzP0532S3uYPM/AGH8Knx18z/lMPxnKYrzP7JX6iD2nvM/bzRfkuKz8z/6Xnv57sjzP7T16JMb3vM/Tu7cn2jz8z/JaRhc1gj0P6sL6gdlHvQ/ZFQv4xQ09D///lUu5kn0PwxiXSrZX/Q/0tPXGO519D/hEew7JYz0P+GrVtZ+ovQ/0HFrK/u49D+T5RZ/ms/0P+av3xVd5vQ/yxjoNEP99D9Sg+8hTRT1P97sUyN7K/U/4G8TgM1C9T8Oys1/RFr1PyHmxWrgcfU/EmnjiaGJ9T/qQrQmiKH1PxhDbouUufU/XbDwAsfR9T9T5MXYH+r1P47qJFmfAvY/WyPz0EUb9j8b6sWNEzT2P1Q/5N0ITfY/VHZIECZm9j+e5qF0a3/2P+ugVlvZmPY/5yeFFXCy9j+uLAb1L8z2P+hObkwZ5vY/t+APbywA9z9PrvywaRr3P0nJB2fRNPc/xlfH5mNP9z85Z5aGIWr3PwbDlp0Khfc/0c6ygx+g9z+SZJ+RYLv3P2623SDO1vc/SzS9i2jy9z8idV0tMA74PxQksGElKvg/MfF6hUhG+D8Nhln2mWL4P+x9vxIaf/g/zWH6Ocmb+D8GqDPMp7j4P5i3ciq21fg/O++etvTy+D/6r4HTYxD5P4ZryOQDLvk/ELYGT9VL+T/IW7h32Gn5P+p5Q8UNiPk/Qpv6nnWm+T9M2B5tEMX5P7D64Zje4/k/PKRojOAC+j8+ecyyFiL6P0FOHniBQfo/ClloSSFh+j/jZLCU9oD6PxsK+sgBofo/qOhIVkPB+j/75aKtu+H6P8BtEkFrAvs/sLWog1Ij+z9MBIDpcUT7P2D6vefJZfs/ct+V9FqH+z+38EqHJan7P8iyMhgqy/s/ykW3IGnt+z8ZvFkb4w/8P0BztIOYMvw/M2991olV/D+zt4iRt3j8P7K3yjMinPw/qp5aPcq//D/Lw3QvsOP8P8UKfYzUB/0/K0oB2Dcs/T82s7uW2lD9P9c6lU69df0/8QOohuCa/T9tykHHRMD9P0VP5pnq5f0/DMVRidIL/j8LPXsh/TH+P54Ul+9qWP4/omIZghx//j/WZLhoEqb+P97sbjRNzf4/0Mx+d830/j/8QnPFkxz/P7xkI7OgRP8/Foi01vRs/z/Uq5zHkJX/P/ndpB51vv8/N6DrdaLn/z8PpXO0jAgAQFg0NEptHQBAow1OS3MyAECJNocHn0cAQKtVVs/wXABA3dvj82hyAEA3KwvHB4gAQO67W5vNnQBAtT4axLqzAEB6vEGVz8kAQFyzhGMM4ABAejBOhHH2AECj5sJN/wwBQHdBwha2IwFA2nTnNpY6AUCAiIoGoFEBQDpfwd7TaAFA5rlgGTKAAUCoNf0Qu5cBQCdF7CBvrwFAliRFpU7HAUA0yOH6Wd8BQO/EX3+R9wFA/DIhkfUPAkDpiU2PhigCQOp10tlEQQJAGaZk0TBaAkAsk4DXSnMCQGs+a06TjAJAa+gymQqmAkAzv68bsb8CQHKDhDqH2QJASCQfW43zAkBTUbnjww0DQHACWTsrKANA0vTQycNCA0D4HMH3jV0DQP4Mly6KeANA406O2LiTA0ATsrBgGq8DQO2L1jKvygNAheqmu3fmA0A8uZdodAIEQIrW7aelHgRAXBq96As7BECCTOiap1cEQHYKIS95dARA6ZvnFoGRBEBwtYrEv64EQI4oJ6s1zARAdoCnPuPpBEDTisPzyAcFQMnL/z/nJQVAitysmT5EBUCDs+Z3z2IFQJHVk1KagQVALm9kop+gBUDwVNHg378FQGXqGohb3wVATu5HExP/BUCEKyT+Bh8GQFENP8U3PwZAfxbq5aVfBkAJOjfeUYAGQEcU9yw8oQZArwO3UWXCBkAcIL/MzeMGQEEPEB92BQdAdbVgyl4nB0BpwRtRiEkHQLURXTbzawdA/PLu/Z+OB0BkNUcsj7EHQAkYhEbB1AdAIglp0jb4B0B3OVtW8BsIQMYBXlnuPwhAmRgPYzFkCEA0l6L7uYgIQO7L3quIrQhAhNgX/Z3SCEDwGit5+vcIQMleeqqeHQlA/dXmG4tDCUDO1stYwGkJQIdd+ew+kAlAMFCuZAe3CUAygpJMGt4JQGB2sDF4BQpAS91uoSEtCkDizYkpF1UKQLu2C1hZfQpAgAVGu+ilCkDmgsnhxc4KQMFgXlrx9wpAMPj7s2shC0CzNcB9NUsLQMaw5kZPdQtABW2/nrmfC0AQQqUUdcoLQFTo8zeC9QtA36f9l+EgDED3pgDEk0wMQAfWG0uZeAxAE3ZDvPKkDEBcNzWmoNEMQGzta5ej/gxAytUSHvwrDUDSbvjHqlkNQKDbgCKwhw1Af9KXugy2DUDiEqIcweQNQNhfbtTNEw5AePwlbTNDDkCqpjxx8nIOQPoNYGoLow5AucJm4X7TDkDSmj5eTQQPQAKJ2md3NQ9AJOMfhP1mD0C1FNM34JgPQO25gwYgyw9AoyB4cr39D0CaFUx+XBgQQEDJK5IJMhBAx8HPM+ZLEECoyluh8mUQQM0JFxgvgBBArs1f1JuaEECdAp8RObUQQHZNOwoH0BBA+cmL9wXrEEAxa8oRNgYRQDL8BZCXIRFAb78TqCo9EUAeq4CO71gRQNlAgnbmdBFA/P7mkQ+REUAFagYRa60RQFissCL5yRFA8sod9LnmEUBLbdywrQMSQAw3wILUIBJA/bHPkS4+EkCyxjEEvFsSQLzCGv58eRJAruq4oXGXEkD6liAPmrUSQCPaN2T20xJAKK+hvIbyEkASr6gxSxETQHZMKdpDMBNABZR7ynBPE0A9cVwU0m4TQFh21sZnjhNA5SYq7jGuE0A5xLWTMM4TQHGb3L1j7hNAY9Ttb8sOFEBnwQqqZy8UQL2vDGk4UBRAhDhqpj1xFECaEhxYd5IUQFxlgXDlsxRAF51D3ofVFECVwTmMXvcUQI5PS2FpGRVASpZSQKg7FUAymv4HG14VQEJ+tJLBgBVAj3VwtpujFUD2PqZEqcYVQCQtIQrq6RVAEb3jzl0NFkDlvQZWBDEWQN4MmF3dVBZAnuh4nuh4FkBU3zvMJZ0WQHNbApWUwRZAPNNZoTTmFkBunxiUBQsXQPp9OgoHMBdA58W8mjhVF0DMUXrWmXoXQAEnB0gqoBdAi9+Lc+nFF0DE3aDW1usXQIxQKejxERhA0g8uGDo4GEBXWbjPrl4YQAh2rHBPhRhA9FCkVRusGEApCcrREdMYQE2IsjAy+hhAbCg4tnshGUCJc1We7UgZQLkIAB2HcBlALbIDXkeYGUDhuN2ELcAZQNOCmKw46BlABImn52cQGkCBs8M/ujgaQNopyLUuYRpAHKePQcSJGkAWYdLRebIaQNuSBExO2xpAiLs1jEAEG0BXovBkTy0bQOgxHJ95VhtAMT3d+b1/G0DQQHkqG6kbQFM0OtyP0htANH9TsBr8G0AXJsg9uiUcQB9FUhFtTxxAsuxLrTF5HECLdpmJBqMcQEhplRPqzBxABQH+rdr2HEA5dOSw1iAdQOALnmncSh1A+ia3Gup0HUDfQOj7/Z4dQBYTDToWyR1Am+od9zDzHUBnSStKTB0eQN3sWz9mRx5Ar1Ht13xxHkAkzjYKjpseQGNbr8GXxR5ARib23pfvHkBjAN43jBkfQDrJe5dyQx9Ax+c3vkhtH0DM6+JhDJcfQDJuzS27wB9AEkfjwlLqH0C+F+Vb6AkgQEXygUyZHiBAJfCJ9DozIEA/XlQQzEcgQB2pZFdLXCBAG9SCfLdwIEB34NUtD4UgQBcsABVRmSBASM8913utIEAYAIUVjsEgQAWBqGyG1SBAQiB8dWPpIECkS/vEI/0gQNm8cezFECFAPECmeUgkIUDvlwf3qTchQNp72+voSiFA8LVv3ANeIUBeWU1K+XAhQOkRbrTHgyFAoIdzl22WIUAZ0uBt6aghQLf0VbA5uyFA1VzN1VzNIUDZWNtTUd8hQEN+754V8SFAWPOXKqgCIkCfj8ZpBxQiQDHFF88xJSJAVUMbzSU2IkCYQZ7W4UYiQDBh915kVyJAARFU2qtnIkBaXwe+tnciQAMj2oCDhyJA72NcmxCXIkCb6jeIXKYiQKjbg8RltSJAQUQZ0CrEIkBXeugtqtIiQL0yT2Ti4CJABi5v/dHuIkDKW4WHd/wiQDFTQZXRCSNAXf4cvt4WI0CqVbSenSMjQM4GHdkMMCNABuM9FSs8I0AX7yUB90cjQBnvYlFvUyNArUdXwZJeI0DLDY8TYGkjQA8eFBLWcyNAVRTBjvN9I0A5/JJjt4cjQEGT+XIgkSNAiPUlqC2aI0AGjlf33aIjQAckJ14wqyNAut/P4yOzI0CQIHaZt7ojQKwAbJrqwSNApWFzDLzII0C8X/0fK88jQLEJZxA31SNAtDwzJN/aI0AWhUGtIuAjQMrlAQkB5SNAW2qloHnpI0ByaEvpi+0jQNhXK2Q38SNAiCm7nnv0I0BSCNIyWPcjQHhvx8bM+SNAqIWODdn7I0DTrM3GfP0jQG858r63/iNA4UVAz4n/I0AGmd7d8v8jQAaZ3t3y/yNA4UVAz4n/I0BvOfK+t/4jQNOszcZ8/SNAqIWODdn7I0B4b8fGzPkjQFII0jJY9yNAiCm7nnv0I0DYVytkN/EjQHJoS+mL7SNAWmqloHnpI0DK5QEJAeUjQBaFQa0i4CNAtDwzJN/aI0CxCWcQN9UjQLxf/R8rzyNApWFzDLzII0CsAGya6sEjQJAgdpm3uiNAut/P4yOzI0AHJCdeMKsjQAaOV/fdoiNAiPUlqC2aI0BCk/lyIJEjQDr8kmO3hyNAVRTBjvN9I0APHhQS1nMjQMsNjxNgaSNArkdXwZJeI0Aa72JRb1MjQBbvJQH3RyNABuM9FSs8I0DOBh3ZDDAjQKtVtJ6dIyNAXf4cvt4WI0AxU0GV0QkjQMpbhYd3/CJABi5v/dHuIkC+Mk9k4uAiQFd66C2q0iJAQUQZ0CrEIkCo24PEZbUiQJvqN4hcpiJA8GNcmxCXIkAEI9qAg4ciQFpfB762dyJAARFU2qtnIkAwYfdeZFciQJlBntbhRiJAVUMbzSU2IkAxxRfPMSUiQJ+PxmkHFCJAWPOXKqgCIkBEfu+eFfEhQNhY21NR3yFA1VzN1VzNIUC39FWwObshQBnS4G3pqCFAoodzl22WIUDnEW60x4MhQF5ZTUr5cCFA8LVv3ANeIUDae9vr6EohQPCXB/epNyFAOkCmeUgkIUDZvHHsxRAhQKRL+8Qj/SBAQiB8dWPpIEAGgahshtUgQBYAhRWOwSBASM8913utIEAXLAAVUZkgQHng1S0PhSBAHNSCfLdwIEAcqWRXS1wgQD9eVBDMRyBAJfCJ9DozIEBH8oFMmR4gQL8X5VvoCSBAEEfjwlLqH0Aybs0tu8AfQMzr4mEMlx9Ayec3vkhtH0A+yXuXckMfQGEA3jeMGR9ARib23pfvHkBjW6/Bl8UeQCXONgqOmx5AsFHt13xxHkDc7Fs/ZkceQGdJK0pMHR5Am+od9zDzHUAYEw06FskdQOFA6Pv9nh1A9ya3Gup0HUDgC55p3EodQDl05LDWIB1ACQH+rdr2HEBLaZUT6swcQIt2mYkGoxxAsuxLrTF5HEAfRVIRbU8cQBomyD26JRxAN39TsBr8G0BTNDrcj9IbQNBAeSobqRtAMT3d+b1/G0DqMRyfeVYbQFai8GRPLRtAiLs1jEAEG0DbkgRMTtsaQBZh0tF5shpAH6ePQcSJGkDYKci1LmEaQIGzwz+6OBpABImn52cQGkDTgpisOOgZQOO43YQtwBlAKrIDXkeYGUC5CAAdh3AZQIlzVZ7tSBlAbCg4tnshGUBPiLIwMvoYQCcJytER0xhA9FCkVRusGEAIdqxwT4UYQFdZuM+uXhhA1A8uGDo4GECKUCno8REYQMTdoNbW6xdAi9+Lc+nFF0ABJwdIKqAXQM5RetaZehdA5cW8mjhVF0D6fToKBzAXQG6fGJQFCxdAPtNZoTTmFkB1WwKVlMEWQFLfO8wlnRZAnuh4nuh4FkDeDJhd3VQWQOe9BlYEMRZAE73jzl0NFkAiLSEK6ukVQPY+pkSpxhVAj3VwtpujFUBEfrSSwYAVQDWa/gcbXhVAR5ZSQKg7FUCOT0thaRkVQJXBOYxe9xRAGp1D3ofVFEBdZYFw5bMUQJkSHFh3khRAhDhqpj1xFEC9rwxpOFAUQGnBCqpnLxRAZdTtb8sOFEBwm9y9Y+4TQDnEtZMwzhNA5SYq7jGuE0BbdtbGZ44TQD9xXBTSbhNABZR7ynBPE0B2TCnaQzATQBKvqDFLERNAKa+hvIbyEkAl2jdk9tMSQPqWIA+atRJAruq4oXGXEkC8whr+fHkSQLTGMQS8WxJA/rHPkS4+EkAMN8CC1CASQEtt3LCtAxJA8sod9LnmEUBZrLAi+ckRQANqBhFrrRFA/P7mkQ+REUDZQIJ25nQRQB6rgI7vWBFAcb8TqCo9EUAx/AWQlyERQDFryhE2BhFA+cmL9wXrEEB2TTsKB9AQQJ4CnxE5tRBArM1f1JuaEEDNCRcYL4AQQKjKW6HyZRBAx8HPM+ZLEEBCySuSCTIQQJkVTH5cGBBAoyB4cr39D0DtuYMGIMsPQLUU0zfgmA9AKOMfhP1mD0AAidpndzUPQNKaPl5NBA9AucJm4X7TDkD8DWBqC6MOQK6mPHHycg5AdPwlbTNDDkDYX27UzRMOQOISohzB5A1Ag9KXugy2DUCh24AisIcNQM9u+MeqWQ1AytUSHvwrDUBs7WuXo/4MQF83Naag0QxAFXZDvPKkDEAE1htLmXgMQPemAMSTTAxA36f9l+EgDEBW6PM3gvULQBJCpRR1ygtAAm2/nrmfC0DGsOZGT3ULQLM1wH01SwtAM/j7s2shC0DDYF5a8fcKQOOCyeHFzgpAgAVGu+ilCkC7tgtYWX0KQOTNiSkXVQpATN1uoSEtCkBgdrAxeAUKQDKCkkwa3glAMFCuZAe3CUCJXfnsPpAJQNDWy1jAaQlA/dXmG4tDCUDJXnqqnh0JQPAaK3n69whAh9gX/Z3SCEDry96riK0IQDSXovu5iAhAmRgPYzFkCEDGAV5Z7j8IQHk5W1bwGwhAIAlp0jb4B0AJGIRGwdQHQGQ1RyyPsQdA/PLu/Z+OB0C2EV0282sHQGfBG1GISQdAdbVgyl4nB0BBDxAfdgUHQBwgv8zN4wZAsQO3UWXCBkBFFPcsPKEGQAk6N95RgAZAfxbq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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":{\"id\":\"10933\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"10932\",\"type\":\"UnionRenderers\"}},\"id\":\"10811\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"10825\",\"type\":\"Selection\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"size\":{\"units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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":{\"id\":\"10825\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"10824\",\"type\":\"UnionRenderers\"}},\"id\":\"10806\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data_source\":{\"id\":\"10746\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"10747\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"10748\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"10750\",\"type\":\"CDSView\"}},\"id\":\"10749\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"10738\",\"type\":\"HelpTool\"}],\"root_ids\":[\"10949\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"df3a41b8-df33-4e57-bcd2-aedcd593bad6\",\"roots\":{\"10949\":\"b7ab841a-3713-4951-8fe1-5944e243bff3\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "10949"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# En utilisant les fonctions de la partie précedente, tracer les points (xk, yk) et le polynome p \n",
    "# pour différentes valeurs de n et différents choix de xk (uniforme et Chebyshev).\n",
    "# Tracer également l'erreur entre f et p.\n",
    "\n",
    "a = -1\n",
    "b = 1\n",
    "n = 20\n",
    "x = np.linspace(a,b,1000)\n",
    "y = f_vect(x)\n",
    "\n",
    "##########################################################################################\n",
    "# Points aléatoires sur [a,b]\n",
    "xk_al = a + (b-a)*np.random.rand(n+1)\n",
    "yk_al = f_vect(xk_al)\n",
    "\n",
    "coef_al = compute_divided_diff_coef(xk_al, yk_al)\n",
    "p_al = poly_interp(coef_al, xk_al, x)\n",
    "\n",
    "err_al = abs(p_al - y)\n",
    "\n",
    "fig1 = figure(width=490, height=300)\n",
    "fig1.x(xk_al,yk_al,size=10, color=\"red\", legend=\"pts aléatoires\")\n",
    "fig1.line(x,y, color = \"orange\")\n",
    "fig1.line(x,p_al, legend=\"P(f)\")\n",
    "\n",
    "fig1b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig1b.line(x,err_al, legend=\"|f-P(f)|\")\n",
    "\n",
    "\n",
    "##########################################################################################\n",
    "# Points equidistants sur [a,b]\n",
    "xk_eq = np.linspace(a,b,n)\n",
    "yk_eq = f_vect(xk_eq)\n",
    "\n",
    "coef_eq = compute_divided_diff_coef(xk_eq, yk_eq)\n",
    "p_eq = poly_interp(coef_eq, xk_eq, x)\n",
    "\n",
    "err_eq = abs(p_eq - y)\n",
    "\n",
    "fig2 = figure(width=490, height=300)\n",
    "fig2.x(xk_eq,yk_eq,size=10, color=\"red\", legend=\"pts equidistants\")\n",
    "fig2.line(x,y, color = \"orange\")\n",
    "fig2.line(x,p_eq, legend=\"P(f)\")\n",
    "\n",
    "fig2b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig2b.line(x,err_eq, legend=\"|f-P(f)|\")\n",
    "\n",
    "\n",
    "##########################################################################################\n",
    "# Points de Tchebychef sur [a,b]\n",
    "xk_tbf = np.array([(a + (b-a)/2*(1 + np.cos((2*k+1)/(2*n+1)*np.pi))) for k in range(n+1)])\n",
    "yk_tbf = f_vect(xk_tbf)\n",
    "\n",
    "\n",
    "coef_tbf = compute_divided_diff_coef(xk_tbf, yk_tbf)\n",
    "p_tbf = poly_interp(coef_tbf, xk_tbf, x)\n",
    "\n",
    "err_tbf = abs(p_tbf - y)\n",
    "\n",
    "fig3 = figure(width=490, height=300)\n",
    "fig3.x(xk_tbf,yk_tbf,size=10, color=\"red\", legend=\"pts de Tchebychef\")\n",
    "fig3.line(x,y, color = \"orange\")\n",
    "fig3.line(x,p_tbf, legend=\"P(f)\")\n",
    "\n",
    "fig3b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig3b.line(x,err_tbf, legend=\"|f-P(f)|\")\n",
    "\n",
    "\n",
    "\n",
    "grid = gridplot([[fig1, fig1b], [fig2, fig2b], [fig3, fig3b]])\n",
    "show(grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "La fonction $f$ est lipschitzienne sur $[a,b]$, en effet :\n",
    "$$\\forall x,y \\in [a,b] : |f(x)-f(y)|=\\frac{|0.1+y^2-0.1-x^2|}{(0.1+x^2)(0.1+y^2)}\n",
    "=\\frac{|x+y||x-y|}{(0.1+x^2)(0.1+y^2)} \\leq \\frac{2max(|a|,|b|)}{0.1^2}|x-y| $$\n",
    "\n",
    "Le résultat de la 2ème question de l'exercice 3 nous assure l'existence d'une constante $C_f$ telle que\n",
    "$$||P_n(f) - f||_{\\infty} \\leq C_f\\frac{1+\\Lambda_n}{\\sqrt{n}} $$\n",
    "\n",
    "* Pour des points equidistants : $\\Lambda_n \\sim \\frac{2^{n+1}}{en\\ln(n)}$, et donc rien ne garantit la convergence de $(P_n(f))_n$ vers $f$.  \n",
    "* Pour des points de Tchebychef : $\\Lambda_n \\sim \\frac{2}{\\pi}\\ln(n)$, on a donc convergence vers 0 de $\\frac{1+\\Lambda_n}{\\sqrt{n}}$, et par suite $(P_n(f))_n$ converge vers $f$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interpolation de Hermite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Implémenter la méthode et tester sur l'exemple suivant :**\n",
    "\n",
    "$$\n",
    "f(x) =\\frac{1}{0.1 +x^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implémenter la méthode\n",
    "# la fonction interp_Hermite retourne le vecteur des valeurs du polynome évalué aux points de x\n",
    "\n",
    "def denom2_dl(xk) :\n",
    "    denom = np.ones(len(xk))\n",
    "    dl = np.zeros(len(xk))\n",
    "    for j in range(len(xk)) :\n",
    "        for i in range(len(xk)) :\n",
    "            if i!=j :\n",
    "                denom[j]*=(xk[j]-xk[i])\n",
    "                dl[j]+=1/(xk[j]-xk[i])\n",
    "    return denom*denom, dl\n",
    "\n",
    "def scinde_carre(xk,k,x) :\n",
    "    S = np.ones(len(x))\n",
    "    for j in range(len(xk)) :\n",
    "        if k!=j : S*= (x-xk[j])\n",
    "    return S*S\n",
    "\n",
    "def interp_Hermite(xk,yk,dyk,x) :\n",
    "    denom2,dl = denom2_dl(xk)\n",
    "    Q = np.zeros(len(x))\n",
    "    H0 = np.zeros(len(x))\n",
    "    H1 = np.zeros(len(x))\n",
    "    for k in range(len(xk)) :\n",
    "        scinde2 = scinde_carre(xk,k,x)\n",
    "        l2 = scinde2/denom2[k]\n",
    "        H0 = (1-2*dl[k]*(x-xk[k]))*l2\n",
    "        H1 = (x-xk[k])*l2\n",
    "        Q += yk[k]*H0 + dyk[k]*H1\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1/(0.1+x*x)\n",
    "\n",
    "def df(x) :\n",
    "    return -2*x/((0.1 +x*x)**2)\n",
    "\n",
    "## Pour pouvoir appliquer f et df directement aux vecteurs\n",
    "f_vect = np.vectorize(f)\n",
    "df_vect = np.vectorize(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"4a1cb784-bcab-489a-8ca0-c3e402cdba49\" data-root-id=\"12409\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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9wYia+1jcG/wBT5rBtMwb+oEGmqgQrBv5AM2afnyMC/dAhJpU2HwL9cBLmis0XAv0AAKaAZBMC/UPgxO/+Ev78g8BE2ywG/v+jn8TCXfr6/uN/RK2P7vb+A17EmL3i9v1DPkSH79Ly/IMdxHMdxvL/ovlEXk+67v7i2MRJfa7u/gK4RDSvour9QpvEH92S6vyCe0QLD4bm/6JWx/Y5eub+4jZH4Wtu4v4CFcfMmWLi/UH1R7vLUt78gdTHpvlG3v+hsEeSKzra/uGTx3lZLtr+AXNHZIsi1v1BUsdTuRLW/IEyRz7rBtL/oQ3HKhj60v7g7UcVSu7O/gDMxwB44s79QKxG76rSyvyAj8bW2MbK/6BrRsIKusb+4ErGrTiuxv4AKkaYaqLC/UAJxoeYksL8w9KE4ZUOvv9DjYS79PK6/cNMhJJU2rb8Aw+EZLTCsv6CyoQ/FKau/MKJhBV0jqr/QkSH79Bypv3CB4fCMFqi/AHGh5iQQp7+gYGHcvAmmvzBQIdJUA6W/0D/hx+z8o79wL6G9hPaivwAfYbMc8KG/oA4hqbTpoL9g/ME9mcafv6DbQSnJuZ2/4LrBFPmsm78AmkEAKaCZv0B5wetYk5e/YFhB14iGlb+gN8HCuHmTv+AWQa7obJG/AOyBMzHAjr+AqoEKkaaKv8BogeHwjIa/QCeBuFBzgr8AywEfYbN8vwBIAc0ggHS/AIoB9sCZaL8ABgGkgGZQvwAIAaSAZlA/AIoB9sCZaD8ASAHNIIB0PwDLAR9hs3w/ACeBuFBzgj8AaYHh8IyGP4CqgQqRpoo/AOyBMzHAjj/AFkGu6GyRP4A3wcK4eZM/gFhB14iGlT9AecHrWJOXPwCaQQApoJk/wLrBFPmsmz+A20EpybmdP4D8wT2Zxp8/oA4hqbTpoD8AH2GzHPChP2Avob2E9qI/wD/hx+z8oz9AUCHSVAOlP6BgYdy8CaY/AHGh5iQQpz9ggeHwjBaoP8CRIfv0HKk/QKJhBV0jqj+gsqEPxSmrPwDD4RktMKw/YNMhJJU2rT/A42Eu/TyuP0D0oThlQ68/UAJxoeYksD+ACpGmGqiwP7ASsatOK7E/4BrRsIKusT8gI/G1tjGyP1ArEbvqtLI/gDMxwB44sz+wO1HFUruzP+BDccqGPrQ/IEyRz7rBtD9QVLHU7kS1P4Bc0dkiyLU/sGTx3lZLtj/gbBHkis62PyB1Mem+Ubc/UH1R7vLUtz+AhXHzJli4P7CNkfha27g/8JWx/Y5euT8gntECw+G5P1Cm8Qf3ZLo/gK4RDSvouj+wtjESX2u7P/C+UReT7rs/IMdxHMdxvD9Qz5Eh+/S8P4DXsSYveL0/sN/RK2P7vT/w5/Ewl36+PyDwETbLAb8/UPgxO/+Evz9AACmgGQTAP1gEuaKzRcA/eAhJpU2HwD+QDNmn58jAP6gQaaqBCsE/wBT5rBtMwT/YGImvtY3BP/gcGbJPz8E/ECGptOkQwj8oJTm3g1LCP0ApybkdlMI/WC1ZvLfVwj94Mem+URfDP5A1ecHrWMM/qDkJxIWawz/APZnGH9zDP9hBKcm5HcQ/+EW5y1NfxD8QSknO7aDEPyhO2dCH4sQ/QFJp0yEkxT9YVvnVu2XFP3haidhVp8U/kF4Z2+/oxT+oYqndiSrGP8BmOeAjbMY/2GrJ4r2txj/4blnlV+/GPxBz6efxMMc/KHd56otyxz9AewntJbTHP1h/me+/9cc/eIMp8lk3yD+Qh7n083jIP6iLSfeNusg/wI/Z+Sf8yD/Yk2n8wT3JP/iX+f5bf8k/EJyJAfbAyT8ooBkEkALKP0CkqQYqRMo/WKg5CcSFyj94rMkLXsfKP5CwWQ74CMs/qLTpEJJKyz/AuHkTLIzLP+C8CRbGzcs/+MCZGGAPzD8QxSkb+lDMPyjJuR2Uksw/QM1JIC7UzD9g0dkiyBXNP3jVaSViV80/kNn5J/yYzT+o3YkqltrNP8DhGS0wHM4/4OWpL8pdzj/46TkyZJ/OPxDuyTT+4M4/KPJZN5gizz9A9uk5MmTPP2D6eTzMpc8/eP4JP2bnzz9IAc0ggBTQP1QDFSJNNdA/YAVdIxpW0D9wB6Uk53bQP3wJ7SW0l9A/iAs1J4G40D+UDX0oTtnQP6APxSkb+tA/sBENK+ga0T+8E1UstTvRP8gVnS2CXNE/1BflLk990T/gGS0wHJ7RP/AbdTHpvtE//B29Mrbf0T8IIAU0gwDSPxQiTTVQIdI/ICSVNh1C0j8wJt036mLSPzwoJTm3g9I/SCptOoSk0j9ULLU7UcXSP2Au/Twe5tI/cDBFPusG0z98Mo0/uCfTP4g01UCFSNM/lDYdQlJp0z+gOGVDH4rTP7A6rUTsqtM/vDz1RbnL0z/IPj1HhuzTP9RAhUhTDdQ/4ELNSSAu1D/wRBVL7U7UP/xGXUy6b9Q/CEmlTYeQ1D8US+1OVLHUPyBNNVAh0tQ/ME99Ue7y1D88UcVSuxPVP0hTDVSINNU/VFVVVVVV1T9gV51WInbVP3BZ5VfvltU/fFstWby31T+IXXVaidjVP5RfvVtW+dU/oGEFXSMa1j+wY01e8DrWP7xllV+9W9Y/yGfdYIp81j/UaSViV53WP+RrbWMkvtY/8G21ZPHe1j/8b/1lvv/WPwhyRWeLINc/FHSNaFhB1z8kdtVpJWLXPzB4HWvygtc/PHplbL+j1z9IfK1tjMTXP1R+9W5Z5dc/ZIA9cCYG2D9wgoVx8ybYP3yEzXLAR9g/iIYVdI1o2D+UiF11WonYP6SKpXYnqtg/sIztd/TK2D+8jjV5wevYP8iQfXqODNk/1JLFe1st2T/klA19KE7ZP/CWVX71btk//Jidf8KP2T8Im+WAj7DZPxSdLYJc0dk/JJ91gyny2T8wob2E9hLaPzyjBYbDM9o/SKVNh5BU2j9Up5WIXXXaP2Sp3Ykqlto/cKsli/e22j98rW2MxNfaP4ivtY2R+No/lLH9jl4Z2z+ks0WQKzrbP7C1jZH4Wts/vLfVksV72z/IuR2UkpzbP9S7ZZVfvds/5L2tlize2z/wv/WX+f7bP/zBPZnGH9w/CMSFmpNA3D8Uxs2bYGHcPyTIFZ0tgtw/MMpdnvqi3D88zKWfx8PcP0jO7aCU5Nw/VNA1omEF3T9k0n2jLibdP3DUxaT7Rt0/fNYNpshn3T+I2FWnlYjdP5Tanahiqd0/pNzlqS/K3T+w3i2r/OrdP7zgdazJC94/yOK9rZYs3j/Y5AWvY03eP+TmTbAwbt4/8OiVsf2O3j/86t2yyq/ePwjtJbSX0N4/GO9ttWTx3j8k8bW2MRLfPzDz/bf+Mt8/PPVFuctT3z9I9426mHTfP1j51btlld8/ZPsdvTK23z9w/WW+/9bfP3z/rb/M998/xAB74EwM4D/MAR9hsxzgP9ICw+EZLeA/2ANnYoA94D/eBAvj5k3gP+QFr2NNXuA/7AZT5LNu4D/yB/dkGn/gP/gIm+WAj+A//gk/Zuef4D8EC+PmTbDgPwwMh2e0wOA/Eg0r6BrR4D8YDs9ogeHgPx4Pc+nn8eA/JBAXak4C4T8sEbvqtBLhPzISX2sbI+E/OBMD7IEz4T8+FKds6EPhP0QVS+1OVOE/TBbvbbVk4T9SF5PuG3XhP1gYN2+CheE/Xhnb7+iV4T9kGn9wT6bhP2wbI/G1tuE/chzHcRzH4T94HWvygtfhP34eD3Pp5+E/hB+z80/44T+MIFd0tgjiP5Ih+/QcGeI/mCKfdYMp4j+eI0P26TniP6Qk53ZQSuI/rCWL97Za4j+yJi94HWviP7gn0/iDe+I/vih3eeqL4j/EKRv6UJziP8wqv3q3rOI/0itj+x294j/YLAd8hM3iP94tq/zq3eI/5C5PfVHu4j/sL/P9t/7iP/Iwl34eD+M/+DE7/4Qf4z/+Mt9/6y/jPwQ0gwBSQOM/DDUngbhQ4z8SNssBH2HjPxg3b4KFceM/HjgTA+yB4z8mObeDUpLjPyw6WwS5ouM/Mjv/hB+z4z84PKMFhsPjPz49R4bs0+M/Rj7rBlPk4z9MP4+HufTjP1JAMwggBeQ/WEHXiIYV5D9eQnsJ7SXkP2ZDH4pTNuQ/bETDCrpG5D9yRWeLIFfkP3hGCwyHZ+Q/fkevjO135D+GSFMNVIjkP4xJ9426mOQ/kkqbDiGp5D+YSz+Ph7nkP55M4w/uyeQ/pk2HkFTa5D+sTisRu+rkP7JPz5Eh++Q/uFBzEogL5T++UReT7hvlP8ZSuxNVLOU/zFNflLs85T/SVAMVIk3lP9hVp5WIXeU/3lZLFu9t5T/mV++WVX7lP+xYkxe8juU/8lk3mCKf5T/4WtsYia/lP/5bf5nvv+U/Bl0jGlbQ5T8MXseavODlPxJfaxsj8eU/GGAPnIkB5j8eYbMc8BHmPyZiV51WIuY/LGP7Hb0y5j8yZJ+eI0PmPzhlQx+KU+Y/Pmbnn/Bj5j9GZ4sgV3TmP0xoL6G9hOY/UmnTISSV5j9YaneiiqXmP15rGyPxteY/Zmy/o1fG5j9sbWMkvtbmP3JuB6Uk5+Y/eG+rJYv35j9+cE+m8QfnP4Zx8yZYGOc/jHKXp74o5z+SczsoJTnnP5h036iLSec/oHWDKfJZ5z+mdieqWGrnP6x3yyq/euc/snhvqyWL5z+4eRMsjJvnP8B6t6zyq+c/xntbLVm85z/MfP+tv8znP9J9oy4m3ec/2H5Hr4zt5z/gf+sv8/3nP+aAj7BZDug/7IEzMcAe6D/ygtexJi/oP/iDezKNP+g/AIUfs/NP6D8GhsMzWmDoPwyHZ7TAcOg/EogLNSeB6D8Yia+1jZHoPyCKUzb0oeg/Jov3tlqy6D8sjJs3wcLoPzKNP7gn0+g/OI7jOI7j6D9Aj4e59PPoP0aQKzpbBOk/TJHPusEU6T9SknM7KCXpP1iTF7yONek/YJS7PPVF6T9mlV+9W1bpP2yWAz7CZuk/cpenvih36T94mEs/j4fpP4CZ77/1l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RP8gVnS2CXNE/1BflLk990T/gGS0wHJ7RP/AbdTHpvtE//B29Mrbf0T8IIAU0gwDSPxQiTTVQIdI/ICSVNh1C0j8wJt036mLSPzwoJTm3g9I/SCptOoSk0j9ULLU7UcXSP2Au/Twe5tI/cDBFPusG0z98Mo0/uCfTP4g01UCFSNM/lDYdQlJp0z+gOGVDH4rTP7A6rUTsqtM/vDz1RbnL0z/IPj1HhuzTP9RAhUhTDdQ/4ELNSSAu1D/wRBVL7U7UP/xGXUy6b9Q/CEmlTYeQ1D8US+1OVLHUPyBNNVAh0tQ/ME99Ue7y1D88UcVSuxPVP0hTDVSINNU/VFVVVVVV1T9gV51WInbVP3BZ5VfvltU/fFstWby31T+IXXVaidjVP5RfvVtW+dU/oGEFXSMa1j+wY01e8DrWP7xllV+9W9Y/yGfdYIp81j/UaSViV53WP+RrbWMkvtY/8G21ZPHe1j/8b/1lvv/WPwhyRWeLINc/FHSNaFhB1z8kdtVpJWLXPzB4HWvygtc/PHplbL+j1z9IfK1tjMTXP1R+9W5Z5dc/ZIA9cCYG2D9wgoVx8ybYP3yEzXLAR9g/iIYVdI1o2D+UiF11WonYP6SKpXYnqtg/sIztd/TK2D+8jjV5wevYP8iQfXqODNk/1JLFe1st2T/klA19KE7ZP/CWVX71btk//Jidf8KP2T8Im+WAj7DZPxSdLYJc0dk/JJ91gyny2T8wob2E9hLaPzyjBYbDM9o/SKVNh5BU2j9Up5WIXXXaP2Sp3Ykqlto/cKsli/e22j98rW2MxNfaP4ivtY2R+No/lLH9jl4Z2z+ks0WQKzrbP7C1jZH4Wts/vLfVksV72z/IuR2UkpzbP9S7ZZVfvds/5L2tlize2z/wv/WX+f7bP/zBPZnGH9w/CMSFmpNA3D8Uxs2bYGHcPyTIFZ0tgtw/MMpdnvqi3D88zKWfx8PcP0jO7aCU5Nw/VNA1omEF3T9k0n2jLibdP3DUxaT7Rt0/fNYNpshn3T+I2FWnlYjdP5Tanahiqd0/pNzlqS/K3T+w3i2r/OrdP7zgdazJC94/yOK9rZYs3j/Y5AWvY03eP+TmTbAwbt4/8OiVsf2O3j/86t2yyq/ePwjtJbSX0N4/GO9ttWTx3j8k8bW2MRLfPzDz/bf+Mt8/PPVFuctT3z9I9426mHTfP1j51btlld8/ZPsdvTK23z9w/WW+/9bfP3z/rb/M998/xAB74EwM4D/MAR9hsxzgP9ICw+EZLeA/2ANnYoA94D/eBAvj5k3gP+QFr2NNXuA/7AZT5LNu4D/yB/dkGn/gP/gIm+WAj+A//gk/Zuef4D8EC+PmTbDgPwwMh2e0wOA/Eg0r6BrR4D8YDs9ogeHgPx4Pc+nn8eA/JBAXak4C4T8sEbvqtBLhPzISX2sbI+E/OBMD7IEz4T8+FKds6EPhP0QVS+1OVOE/TBbvbbVk4T9SF5PuG3XhP1gYN2+CheE/Xhnb7+iV4T9kGn9wT6bhP2wbI/G1tuE/chzHcRzH4T94HWvygtfhP34eD3Pp5+E/hB+z80/44T+MIFd0tgjiP5Ih+/QcGeI/mCKfdYMp4j+eI0P26TniP6Qk53ZQSuI/rCWL97Za4j+yJi94HWviP7gn0/iDe+I/vih3eeqL4j/EKRv6UJziP8wqv3q3rOI/0itj+x294j/YLAd8hM3iP94tq/zq3eI/5C5PfVHu4j/sL/P9t/7iP/Iwl34eD+M/+DE7/4Qf4z/+Mt9/6y/jPwQ0gwBSQOM/DDUngbhQ4z8SNssBH2HjPxg3b4KFceM/HjgTA+yB4z8mObeDUpLjPyw6WwS5ouM/Mjv/hB+z4z84PKMFhsPjPz49R4bs0+M/Rj7rBlPk4z9MP4+HufTjP1JAMwggBeQ/WEHXiIYV5D9eQnsJ7SXkP2ZDH4pTNuQ/bETDCrpG5D9yRWeLIFfkP3hGCwyHZ+Q/fkevjO135D+GSFMNVIjkP4xJ9426mOQ/kkqbDiGp5D+YSz+Ph7nkP55M4w/uyeQ/pk2HkFTa5D+sTisRu+rkP7JPz5Eh++Q/uFBzEogL5T++UReT7hvlP8ZSuxNVLOU/zFNflLs85T/SVAMVIk3lP9hVp5WIXeU/3lZLFu9t5T/mV++WVX7lP+xYkxe8juU/8lk3mCKf5T/4WtsYia/lP/5bf5nvv+U/Bl0jGlbQ5T8MXseavODlPxJfaxsj8eU/GGAPnIkB5j8eYbMc8BHmPyZiV51WIuY/LGP7Hb0y5j8yZJ+eI0PmPzhlQx+KU+Y/Pmbnn/Bj5j9GZ4sgV3TmP0xoL6G9hOY/UmnTISSV5j9YaneiiqXmP15rGyPxteY/Zmy/o1fG5j9sbWMkvtbmP3JuB6Uk5+Y/eG+rJYv35j9+cE+m8QfnP4Zx8yZYGOc/jHKXp74o5z+SczsoJTnnP5h036iLSec/oHWDKfJZ5z+mdieqWGrnP6x3yyq/euc/snhvqyWL5z+4eRMsjJvnP8B6t6zyq+c/xntbLVm85z/MfP+tv8znP9J9oy4m3ec/2H5Hr4zt5z/gf+sv8/3nP+aAj7BZDug/7IEzMcAe6D/ygtexJi/oP/iDezKNP+g/AIUfs/NP6D8GhsMzWmDoPwyHZ7TAcOg/EogLNSeB6D8Yia+1jZHoPyCKUzb0oeg/Jov3tlqy6D8sjJs3wcLoPzKNP7gn0+g/OI7jOI7j6D9Aj4e59PPoP0aQKzpbBOk/TJHPusEU6T9SknM7KCXpP1iTF7yONek/YJS7PPVF6T9mlV+9W1bpP2yWAz7CZuk/cpenvih36T94mEs/j4fpP4CZ77/1l+k/hpqTQFyo6T+MmzfBwrjpP5Kc20Epyek/mJ1/wo/Z6T+gniND9unpP6afx8Nc+uk/rKBrRMMK6j+yoQ/FKRvqP7iis0WQK+o/wKNXxvY76j/GpPtGXUzqP8yln8fDXOo/0qZDSCpt6j/Yp+fIkH3qP+Coi0n3jeo/5qkvyl2e6j/sqtNKxK7qP/Krd8sqv+o/+KwbTJHP6j8Arr/M99/qPwavY01e8Oo/DLAHzsQA6z8SsatOKxHrPxiyT8+RIes/ILPzT/gx6z8mtJfQXkLrPyy1O1HFUus/Mrbf0Stj6z84t4NSknPrP0C4J9P4g+s/RrnLU1+U6z9Mum/UxaTrP1K7E1Ustes/Wry31ZLF6z9gvVtW+dXrP2a+/9Zf5us/bL+jV8b26z9ywEfYLAfsP3rB61iTF+w/gMKP2fkn7D+GwzNaYDjsP4zE19rGSOw/ksV7Wy1Z7D+axh/ck2nsP6DHw1z6eew/pshn3WCK7D+syQtex5rsP7LKr94tq+w/ustTX5S77D/AzPff+svsP8bNm2Bh3Ow/zM4/4cfs7D/Sz+NhLv3sP9rQh+KUDe0/4NErY/sd7T/m0s/jYS7tP+zTc2TIPu0/8tQX5S5P7T/61btllV/tPwDXX+b7b+0/BtgDZ2KA7T8M2afnyJDtPxLaS2gvoe0/Gtvv6JWx7T8g3JNp/MHtPybdN+pi0u0/LN7basni7T8y33/rL/PtPzrgI2yWA+4/QOHH7PwT7j9G4mttYyTuP0zjD+7JNO4/UuSzbjBF7j9a5VfvllXuP2Dm+2/9Ze4/Zuef8GN27j9s6ENxyobuP3Lp5/Ewl+4/euqLcpen7j+A6y/z/bfuP4bs03NkyO4/jO139MrY7j+S7ht1MenuP5rvv/WX+e4/oPBjdv4J7z+m8Qf3ZBrvP6zyq3fLKu8/svNP+DE77z+69PN4mEvvP8D1l/n+W+8/xvY7emVs7z/M99/6y3zvP9T4g3syje8/2vkn/Jid7z/g+st8/63vP+b7b/1lvu8/7PwTfszO7z/0/bf+Mt/vP/r+W3+Z7+8/AAAAAAAA8D8=\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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elZoomTool\"},{\"attributes\":{\"overlay\":{\"id\":\"12307\",\"type\":\"BoxAnnotation\"}},\"id\":\"12285\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"formatter\":{\"id\":\"12237\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"12206\",\"type\":\"BasicTicker\"}},\"id\":\"12205\",\"type\":\"LinearAxis\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"12283\",\"type\":\"PanTool\"},{\"id\":\"12284\",\"type\":\"WheelZoomTool\"},{\"id\":\"12285\",\"type\":\"BoxZoomTool\"},{\"id\":\"12286\",\"type\":\"SaveTool\"},{\"id\":\"12287\",\"type\":\"ResetTool\"},{\"id\":\"12288\",\"type\":\"HelpTool\"}]},\"id\":\"12289\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"12286\",\"type\":\"SaveTool\"},{\"attributes\":{\"text\":\"\"},\"id\":\"12233\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"12287\",\"type\":\"ResetTool\"},{\"attributes\":{\"callback\":null},\"id\":\"12197\",\"type\":\"DataRange1d\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"12307\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"12288\",\"type\":\"HelpTool\"},{\"attributes\":{\"callback\":null},\"id\":\"12199\",\"type\":\"DataRange1d\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"12211\",\"type\":\"BasicTicker\"}},\"id\":\"12214\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"12201\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"12203\",\"type\":\"LinearScale\"},{\"attributes\":{\"source\":{\"id\":\"12296\",\"type\":\"ColumnDataSource\"}},\"id\":\"12300\",\"type\":\"CDSView\"},{\"attributes\":{\"ticker\":{\"id\":\"12206\",\"type\":\"BasicTicker\"}},\"id\":\"12209\",\"type\":\"Grid\"},{\"attributes\":{\"ticker\":null},\"id\":\"12303\",\"type\":\"LogTickFormatter\"},{\"attributes\":{\"items\":[{\"id\":\"12309\",\"type\":\"LegendItem\"}]},\"id\":\"12308\",\"type\":\"Legend\"},{\"attributes\":{},\"id\":\"12206\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"12305\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"12330\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"12211\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data_source\":{\"id\":\"12228\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"12229\",\"type\":\"X\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"12230\",\"type\":\"X\"},\"selection_glyph\":null,\"view\":{\"id\":\"12232\",\"type\":\"CDSView\"}},\"id\":\"12231\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"formatter\":{\"id\":\"12303\",\"type\":\"LogTickFormatter\"},\"ticker\":{\"id\":\"12279\",\"type\":\"LogTicker\"}},\"id\":\"12278\",\"type\":\"LogAxis\"},{\"attributes\":{},\"id\":\"12331\",\"type\":\"Selection\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"size\":{\"units\":\"screen\",\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"12229\",\"type\":\"X\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"size\":{\"units\":\"screen\",\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"12230\",\"type\":\"X\"},{\"attributes\":{},\"id\":\"12320\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"12215\",\"type\":\"PanTool\"},{\"id\":\"12216\",\"type\":\"WheelZoomTool\"},{\"id\":\"12217\",\"type\":\"BoxZoomTool\"},{\"id\":\"12218\",\"type\":\"SaveTool\"},{\"id\":\"12219\",\"type\":\"ResetTool\"},{\"id\":\"12220\",\"type\":\"HelpTool\"}]},\"id\":\"12221\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"12321\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"12215\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"12354\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"12355\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"12216\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"12345\",\"type\":\"Selection\"},{\"attributes\":{\"overlay\":{\"id\":\"12239\",\"type\":\"BoxAnnotation\"}},\"id\":\"12217\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"AAAAAAAA8L/6/lt/me/vv/P9t/4y3++/7fwTfszO77/m+2/9Zb7vv+D6y3z/re+/2vkn/Jid77/T+IN7Mo3vv8333/rLfO+/xvY7emVs77/A9Zf5/lvvv7r083iYS++/s/NP+DE777+t8qt3yyrvv6bxB/dkGu+/oPBjdv4J77+a77/1l/nuv5PuG3Ux6e6/je139MrY7r+G7NNzZMjuv4DrL/P9t+6/euqLcpen7r9z6efxMJfuv23oQ3HKhu6/Zuef8GN27r9g5vtv/WXuv1nlV++WVe6/U+SzbjBF7r9N4w/uyTTuv0bia21jJO6/QOHH7PwT7r854CNslgPuvzPff+sv8+2/Ld7ba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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
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       "    }, 10, root)\n",
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      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "12409"
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Tracer les points (xk, yk) et le polynome d'interpolation de Hermite h, \n",
    "# comparer avec le polynome d'interpolation de Lagrange p\n",
    "a = -1\n",
    "b = 1\n",
    "n = 15\n",
    "x = np.linspace(a,b,1000)\n",
    "y = f_vect(x)\n",
    "xk = np.linspace(a,b,n)\n",
    "yk = f_vect(xk)\n",
    "dyk = df_vect(xk)\n",
    "xkT = np.array([(a + (b-a)/2*(1 + np.cos((2*k+1)/(2*n+1)*np.pi))) for k in range(n+1)])\n",
    "ykT = f_vect(xkT)\n",
    "dykT = df_vect(xkT)\n",
    "\n",
    "#################################################################################\n",
    "# Interpolation de Hermite avec points equidistants\n",
    "QE = interp_Hermite(xk,yk,dyk,x)\n",
    "errQE = abs(QE - y)\n",
    "\n",
    "fig1 = figure(width=490, height=300)\n",
    "fig1.x(xk,yk,size=10, color=\"red\", legend=\"pts equidistants\")\n",
    "fig1.line(x,y, color=\"orange\")\n",
    "fig1.line(x,QE, legend=\"Q(f)\")\n",
    "\n",
    "fig1b = figure(width=490, height=300,y_axis_type=\"log\")\n",
    "fig1b.line(x,errQE, legend=\"|f-Q(f)|\")\n",
    "\n",
    "\n",
    "#################################################################################\n",
    "# Interpolation de Lagrange avec points equidistants\n",
    "coefE = compute_divided_diff_coef(xk, yk)\n",
    "PE = poly_interp(coefE, xk, x)\n",
    "\n",
    "errPE = abs(PE - y)\n",
    "\n",
    "fig2 = figure(width=490, height=300)\n",
    "fig2.x(xk,yk,size=10, color=\"red\", legend=\"pts equidistants\")\n",
    "fig2.line(x,y, color = \"orange\")\n",
    "fig2.line(x,PE, legend=\"P(f)\")\n",
    "\n",
    "fig2b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig2b.line(x,errPE, legend=\"|f-P(f)|\")\n",
    "\n",
    "#################################################################################\n",
    "# Interpolation de Hermite avec points de Tchebychef\n",
    "QT = interp_Hermite(xkT,ykT,dykT,x)\n",
    "errQT = abs(QT - y)\n",
    "\n",
    "fig3 = figure(width=490, height=300)\n",
    "fig3.x(xkT,ykT,size=10, color=\"red\", legend=\"pts de Tchebychef\")\n",
    "fig3.line(x,y, color=\"orange\")\n",
    "fig3.line(x,QT, legend=\"Q(f)\")\n",
    "\n",
    "fig3b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig3b.line(x,errQT, legend=\"|f-Q(f)|\")\n",
    "\n",
    "\n",
    "#################################################################################\n",
    "# Interpolation de Lagrange avec points de Tchebychef\n",
    "coefT = compute_divided_diff_coef(xkT, ykT)\n",
    "PT = poly_interp(coefT, xkT, x)\n",
    "\n",
    "errPT = abs(PT - y)\n",
    "\n",
    "fig4 = figure(width=490, height=300)\n",
    "fig4.x(xkT,ykT,size=10, color=\"red\", legend=\"pts de Tchebychef\")\n",
    "fig4.line(x,y, color = \"orange\")\n",
    "fig4.line(x,PT, legend=\"P(f)\")\n",
    "\n",
    "fig4b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig4b.line(x,errPT, legend=\"|f-P(f)|\")\n",
    "\n",
    "#################################################################################\n",
    "\n",
    "grid = gridplot([[fig1,fig1b],[fig2,fig2b],[fig3,fig3b],[fig4,fig4b]])\n",
    "show(grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "L'approximation par les polynômes de Hermite est meilleure que celle par les polnômes de Lagrange.    \n",
    "En testant avec des petites valeurs de $n$, on remarque que le polynôme d'Hermite s'approche plus de la fonction $f$. Ce qui est normal puisqu'on utilise plus d'informations. Toutefois, pour $n\\geq 15$, le phénomène de Runge aux bords est plus viloent pour les polynômes d'Hermite lorsqu'on choisit une subdivision par des points equidistants.\n",
    "\n",
    "La majoration de l'erreur entre $f$ et $Q(f)$ établie dans la question 3 du $1^{er}$ exercice de la PC3 montre que les points de Tchebychef donneront encore une fois la meilleure approximation parmi toutes les subdivisions de $[a,b]$ de taille $n$ :\n",
    "$$ ||f-Q_n(f)|| \\leq \\frac{||\\Pi_{n+1}||_{\\infty}}{(2n+2)!}||f^{(2n+2)}||_{\\infty}$$  \n",
    "\n",
    "car les points de Tchebychef minimisent la quantité $||\\Pi_{n+1}||_{\\infty}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Krigeage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**On considère les 13 points $(x_k,y_k)$ suivants :**\n",
    "\n",
    "$$(-3,0.5),\\ (-2.5,0),\\ (-2,2),\\ (-1.5,1.5),\\ (-1,4),\\ (-0.5,2),\\ (0,1.5),\\ (0.5,3),\\ (1,0),\\ (1.5,2),\\ (2,1),\\ (2.5,2.5),\\ (3,3)$$\n",
    "\n",
    "**Implémenter $G$, $A$ et $Y$, puis résoudre le système linéaire et tracer la fonction $u$ obtenue pour $g(x)=x$ et $g(x)=x^3$. Comparer avec le polynôme d'interpolation de Lagrange. Commenter les résultats obtenus.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return x**3\n",
    "\n",
    "g_vect = np.vectorize(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "xk = np.linspace(-3,3,13)\n",
    "yk = np.array([0.5,0,2,1.5,4,2,1.5,3,0,2,1,2.5,3])\n",
    "x = np.linspace(-3,3,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":{\"id\":\"13609\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"13608\",\"type\":\"UnionRenderers\"}},\"id\":\"13580\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"13609\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"13608\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"source\":{\"id\":\"13595\",\"type\":\"ColumnDataSource\"}},\"id\":\"13599\",\"type\":\"CDSView\"},{\"attributes\":{\"label\":{\"value\":\"P(x)\"},\"renderers\":[{\"id\":\"13598\",\"type\":\"GlyphRenderer\"}]},\"id\":\"13611\",\"type\":\"LegendItem\"},{\"attributes\":{\"below\":[{\"id\":\"13621\",\"type\":\"LinearAxis\"}],\"center\":[{\"id\":\"13625\",\"type\":\"Grid\"},{\"id\":\"13630\",\"type\":\"Grid\"},{\"id\":\"13656\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"13626\",\"type\":\"LogAxis\"}],\"plot_height\":300,\"plot_width\":490,\"renderers\":[{\"id\":\"13647\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"13649\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"13637\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"13613\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"13617\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"13615\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"13619\",\"type\":\"LogScale\"}},\"id\":\"13612\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"13558\",\"type\":\"HelpTool\"},{\"attributes\":{\"callback\":null},\"id\":\"13613\",\"type\":\"DataRange1d\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"13646\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"13554\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"13645\",\"type\":\"Line\"},{\"attributes\":{\"formatter\":{\"id\":\"13653\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"13622\",\"type\":\"BasicTicker\"}},\"id\":\"13621\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"13619\",\"type\":\"LogScale\"},{\"attributes\":{\"callback\":null},\"id\":\"13615\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"13617\",\"type\":\"LinearScale\"},{\"attributes\":{\"ticker\":{\"id\":\"13622\",\"type\":\"BasicTicker\"}},\"id\":\"13625\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"13622\",\"type\":\"BasicTicker\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"13627\",\"type\":\"LogTicker\"}},\"id\":\"13630\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"13544\",\"type\":\"BasicTicker\"},{\"attributes\":{\"formatter\":{\"id\":\"13575\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"13544\",\"type\":\"BasicTicker\"}},\"id\":\"13543\",\"type\":\"LinearAxis\"},{\"attributes\":{\"formatter\":{\"id\":\"13651\",\"type\":\"LogTickFormatter\"},\"ticker\":{\"id\":\"13627\",\"type\":\"LogTicker\"}},\"id\":\"13626\",\"type\":\"LogAxis\"},{\"attributes\":{\"num_minor_ticks\":10},\"id\":\"13627\",\"type\":\"LogTicker\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"AAAAAAAACMAAAAAAAAAEwAAAAAAAAADAAAAAAAAA+L8AAAAAAADwvwAAAAAAAOC/AAAAAAAAAAAAAAAAAADgPwAAAAAAAPA/AAAAAAAA+D8AAAAAAAAAQAAAAAAAAARAAAAAAAAACEA=\",\"dtype\":\"float64\",\"shape\":[13]},\"y\":{\"__ndarray__\":\"AAAAAAAA4D8AAAAAAAAAAAAAAAAAAABAAAAAAAAA+D8AAAAAAAAQQAAAAAAAAABAAAAAAAAA+D8AAAAAAAAIQAAAAAAAAAAAAAAAAAAAAEAAAAAAAADwPwAAAAAAAARAAAAAAAAACEA=\",\"dtype\":\"float64\",\"shape\":[13]}},\"selected\":{\"id\":\"13592\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"13591\",\"type\":\"UnionRenderers\"}},\"id\":\"13566\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"13553\",\"type\":\"PanTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"size\":{\"units\":\"screen\",\"value\":10},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"13568\",\"type\":\"X\"},{\"attributes\":{},\"id\":\"13631\",\"type\":\"PanTool\"},{\"attributes\":{\"data_source\":{\"id\":\"13566\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"13567\",\"type\":\"X\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"13568\",\"type\":\"X\"},\"selection_glyph\":null,\"view\":{\"id\":\"13570\",\"type\":\"CDSView\"}},\"id\":\"13569\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"13634\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"13632\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"overlay\":{\"id\":\"13655\",\"type\":\"BoxAnnotation\"}},\"id\":\"13633\",\"type\":\"BoxZoomTool\"}],\"root_ids\":[\"13658\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"cfe53fc2-0066-4666-9dd7-0b4cb8493a0a\",\"roots\":{\"13658\":\"e51f70e1-14b0-4082-adba-9c21e67f709f\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "13658"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.ones((13,2))\n",
    "for i in range(13) :\n",
    "    A[i][1] = xk[i]\n",
    "# ... \n",
    "\n",
    "G = np.zeros((13,13))\n",
    "for i in range (13) :\n",
    "    G[i][i] = g(0)\n",
    "    for j in range(i) :\n",
    "        G[i][j] = G[j][i] = g(abs(xk[i]-xk[j]))\n",
    "# ...\n",
    "\n",
    "M = np.concatenate((np.concatenate((G,np.transpose(A))),np.concatenate((A,np.zeros((2,2))))),axis=1)\n",
    "\n",
    "Y = np.hstack(( yk, np.array([0,0]) ))\n",
    "# ...\n",
    "\n",
    "# Résolution de M S = Y\n",
    "S = np.linalg.solve(M,Y)\n",
    "\n",
    "# Evaluation de la fonction de krigeage u en un vecteur de points x\n",
    "def u_kri(x, S, xk):\n",
    "    u = S[-2] + S[-1]*x\n",
    "    for k in range(len(xk)) :\n",
    "        u += S[k]*g_vect(abs(x-xk[k]))\n",
    "    return u\n",
    "\n",
    "# Fonction de krigeage\n",
    "u = u_kri(x, S, xk)\n",
    "\n",
    "fig = figure(width=490, height=300)\n",
    "fig.x(xk,yk,size=10, color=\"red\", legend=\"pts d'interpolation\")\n",
    "fig.line(x,u, legend=\"u(x)\")\n",
    "\n",
    "# Polynôme de Lagrange\n",
    "coef = compute_divided_diff_coef(xk, yk)\n",
    "p = poly_interp(coef, xk, x)\n",
    "fig.line(x,p, color=\"orange\", legend=\"P(x)\")\n",
    "\n",
    "# Erreur\n",
    "err = abs(p-u)\n",
    "fig2 = figure(width=490, height=300,y_axis_type=\"log\")\n",
    "fig2.line(x,err, legend=\"|P(x)-u(x)|\")\n",
    "\n",
    "show(row(fig,fig2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "La fonction de krigeage obtenue est plus régulière pour $g(x)=x^3$ (courbe lisse) que pour $g(x)=x$ (courbe par lignes brisées).  \n",
    "Ensuite, pour comparer la fonction de krigeage avec le polynôme de Lagrange, j'ai tracé à droite la courbe de l'erreur entre les deux : les deux fonctions sont assez proches sur l'intervalle $[-1.4, 1]$, mais aux bords, le phénomène de Runge fait que le polynôme $P$ varie très rapidement, alors que $u$ ne s'éloigne pas des points d'interpolation.  \n",
    "Ceci nous laisse penser que pour une fonction ayant des variations lentes, comme $f(x) = \\frac{1}{0.1 + x^2}$, la fonction de krigeage fournirait une meilleure approximation que le polynôme de Lagrange en interpolant aux mêmes points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1/(0.1+x*x)\n",
    "\n",
    "\n",
    "## Pour pouvoir appliquer f directement aux vecteurs\n",
    "f_vect = np.vectorize(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"fc7cac50-be84-4a11-beb3-09df8104b92b\" data-root-id=\"22163\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":{\"id\":\"21949\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"21948\",\"type\":\"UnionRenderers\"}},\"id\":\"21930\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"21930\",\"type\":\"ColumnDataSource\"}},\"id\":\"21934\",\"type\":\"CDSView\"},{\"attributes\":{\"data_source\":{\"id\":\"21930\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"21931\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"21932\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"21934\",\"type\":\"CDSView\"}},\"id\":\"21933\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"22008\",\"type\":\"BasicTicker\"}],\"root_ids\":[\"22163\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"b8e57a1f-62c2-4c31-ab98-f954b0ef857f\",\"roots\":{\"22163\":\"fc7cac50-be84-4a11-beb3-09df8104b92b\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "22163"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = -1\n",
    "b = 1\n",
    "n = 20\n",
    "x = np.linspace(a,b,1000)\n",
    "y = f_vect(x)\n",
    "\n",
    "## Choisir ici le type de subdivision : \n",
    "\n",
    "#xk = a + (b-a)*np.random.rand(n)\n",
    "#xk = np.linspace(a,b,n)\n",
    "xk = np.array([(a + (b-a)/2*(1 + np.cos((2*k+1)/(2*n+1)*np.pi))) for k in range(n+1)])\n",
    "yk = f_vect(xk)\n",
    "\n",
    "#################################################################################\n",
    "# Polynôme de Lagrange\n",
    "coef = compute_divided_diff_coef(xk, yk)\n",
    "p = poly_interp(coef, xk, x)\n",
    "errp = abs(p - y)\n",
    "\n",
    "fig1 = figure(width=490, height=300)\n",
    "fig1.x(xk,yk,size=10, color=\"red\", legend=\"pts d'interpolation\")\n",
    "fig1.line(x,y, color = \"orange\")\n",
    "fig1.line(x,p, legend=\"P(f)\")\n",
    "\n",
    "fig1b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig1b.line(x,errp, legend=\"|f-P(f)|\")\n",
    "\n",
    "#################################################################################\n",
    "# Fonction de krigeage\n",
    "A = np.ones((len(xk),2))\n",
    "for i in range(len(xk)) :\n",
    "    A[i][1] = xk[i]\n",
    "\n",
    "G = np.zeros((len(xk),len(xk)))\n",
    "for i in range (len(xk)) :\n",
    "    G[i][i] = g(0)\n",
    "    for j in range(i) :\n",
    "        G[i][j] = G[j][i] = g(abs(xk[i]-xk[j]))\n",
    "\n",
    "M = np.concatenate((np.concatenate((G,np.transpose(A))),np.concatenate((A,np.zeros((2,2))))),axis=1)\n",
    "Y = np.hstack(( yk, np.array([0,0]) ))\n",
    "S = np.linalg.solve(M,Y)\n",
    "\n",
    "u = u_kri(x, S, xk)\n",
    "erru = abs(u-y)\n",
    "fig2 = figure(width=490, height=300)\n",
    "fig2.x(xk,yk,size=10, color=\"red\", legend=\"pts d'interpolation\")\n",
    "fig2.line(x,y, color = \"orange\")\n",
    "fig2.line(x,u, legend=\"u(f)\")\n",
    "\n",
    "fig2b = figure(width=490, height=300, y_axis_type=\"log\")\n",
    "fig2b.line(x,erru, legend=\"|f-u(f)|\")\n",
    "\n",
    "#################################################################################\n",
    "\n",
    "grid = gridplot([[fig1,fig1b],[fig2,fig2b]])\n",
    "show(grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Commentaire :**  \n",
    "En testant les 2 méthodes d'interpolation (avec $g(x)=x^3$ pour le krigeage), avec différents types de subdivisions de l'intervalle $[a,b]$, on remarque que la fonction de krigeage donne une meilleure approximation de $f(x)$, même en choisissant une subdivision par les points de Tchebychef."
   ]
  }
 ],
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