5-Chaos/Exercice-polynomes-orthogonaux-cantilever-beam.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice polynômes orthogonaux : application au cas de la déviation verticale de la poutre encastrée\n",
    "\n",
    "## References\n",
    "* http://openturns.github.io/openturns/master/user_manual/_generated/openturns.HermiteFactory.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem statement\n",
    "\n",
    "We consider a cantilever beam defined by its Young’s modulus $E$, its length $L$ and its section modulus $I$. One end is built in a wall and we apply a concentrated bending load $F$ at the other end of the beam, resulting in a vertical deviation $Y$.\n",
    "\n",
    "<img src=\"poutre.png\" width=\"200\">\n",
    "\n",
    "__Inputs__:  $\\left\\{ E, F, L, I \\right\\}$\n",
    "* $E$ : Young modulus (Pa)\n",
    "* $L$ : Length of beam (cm),\n",
    "* $I$ : Moment of inertia (cm^4),\n",
    "* $F$ : Loading (N)\n",
    "\n",
    "|Variable|  Distribution|\n",
    "| ------------- |-------------|\n",
    "|E| Beta(alpha = 0.9, beta = 2.2, a = $2.5\\times 10^7$, $b = 5\\times 10^7$) |\n",
    "|F| Lognormal($\\mu_F=3 \\times 10^4$, $\\sigma_F=9\\times 10^3$, shift=$15\\times 10^3$)|\n",
    "|L| Uniform(min=250.0, max= 260.0)|\n",
    "|I| Beta(alpha = 2.5, beta = 1.5, a = 310, b = 450)|\n",
    "\n",
    "The input variables are supposed to be independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## La classe HermiteFactory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openturns as ot\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La classe `HermiteFactory` permet de créer des polynômes d'Hermite orthonormés par rapport à la densité de probabilité gaussienne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "pofa = ot.HermiteFactory()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La méthode `build` crée un polynôme de degré donné."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "X\n",
      "-0.707107 + 0.707107 * X^2\n",
      "-1.22474 * X + 0.408248 * X^3\n",
      "0.612372 - 1.22474 * X^2 + 0.204124 * X^4\n"
     ]
    }
   ],
   "source": [
    "for k in range(5):\n",
    "    print(pofa.build(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Concentrons-nous sur le polynôme de degré 5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>1.36931 * X - 0.912871 * X^3 + 0.0912871 * X^5</p>"
      ],
      "text/plain": [
       "<openturns.orthogonalbasis.OrthogonalUniVariatePolynomial; proxy of <Swig Object of type 'OT::OrthogonalUniVariatePolynomial *' at 0x7f21f87bc270> >"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk = pofa.build(5)\n",
    "pk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk.getDegree()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'opérateur `()` permet d'évaluer le polynôme en un point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6431676725155"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk(3.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La méthode `getCoefficients` retourne une table des coefficients du polynôme. Le coefficient correspondant au monôme de plus haut degré est le dernier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>[0,1.36931,-0,-0.912871,0,0.0912871]</p>"
      ],
      "text/plain": [
       "class=Point name=Unnamed dimension=6 values=[0,1.36931,-0,-0.912871,0,0.0912871]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk.getCoefficients()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme chaque polynôme retourné est une fonction, la méthode `draw` permet de les dessiner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "class=Graph name=Orthonormal Hermite polynomials implementation=class=GraphImplementation name=Orthonormal Hermite polynomials title=Orthonormal Hermite polynomials xTitle=x yTitle=y axes=ON grid=ON legendposition=bottomright legendFontSize=1 drawables=[class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=P0 data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=50 dimension=2 data=[[-3,1],[-2.88,1],[-2.76,1],[-2.64,1],[-2.52,1],[-2.4,1],[-2.28,1],[-2.16,1],[-2.04,1],[-1.92,1],[-1.8,1],[-1.68,1],[-1.56,1],[-1.44,1],[-1.32,1],[-1.2,1],[-1.08,1],[-0.96,1],[-0.84,1],[-0.72,1],[-0.6,1],[-0.48,1],[-0.36,1],[-0.24,1],[-0.12,1],[0,1],[0.12,1],[0.24,1],[0.36,1],[0.48,1],[0.6,1],[0.72,1],[0.84,1],[0.96,1],[1.08,1],[1.2,1],[1.32,1],[1.44,1],[1.56,1],[1.68,1],[1.8,1],[1.92,1],[2.04,1],[2.16,1],[2.28,1],[2.4,1],[2.52,1],[2.64,1],[2.76,1],[2.88,1]] color=#1f77b4 fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2,class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=P1 data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=50 dimension=2 data=[[-3,-3],[-2.88,-2.88],[-2.76,-2.76],[-2.64,-2.64],[-2.52,-2.52],[-2.4,-2.4],[-2.28,-2.28],[-2.16,-2.16],[-2.04,-2.04],[-1.92,-1.92],[-1.8,-1.8],[-1.68,-1.68],[-1.56,-1.56],[-1.44,-1.44],[-1.32,-1.32],[-1.2,-1.2],[-1.08,-1.08],[-0.96,-0.96],[-0.84,-0.84],[-0.72,-0.72],[-0.6,-0.6],[-0.48,-0.48],[-0.36,-0.36],[-0.24,-0.24],[-0.12,-0.12],[0,0],[0.12,0.12],[0.24,0.24],[0.36,0.36],[0.48,0.48],[0.6,0.6],[0.72,0.72],[0.84,0.84],[0.96,0.96],[1.08,1.08],[1.2,1.2],[1.32,1.32],[1.44,1.44],[1.56,1.56],[1.68,1.68],[1.8,1.8],[1.92,1.92],[2.04,2.04],[2.16,2.16],[2.28,2.28],[2.4,2.4],[2.52,2.52],[2.64,2.64],[2.76,2.76],[2.88,2.88]] color=#ff7f0e fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2,class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=P2 data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=50 dimension=2 data=[[-3,5.65685],[-2.88,5.15792],[-2.76,4.67935],[-2.64,4.22114],[-2.52,3.7833],[-2.4,3.36583],[-2.28,2.96872],[-2.16,2.59197],[-2.04,2.23559],[-1.92,1.89957],[-1.8,1.58392],[-1.68,1.28863],[-1.56,1.01371],[-1.44,0.75915],[-1.32,0.524956],[-1.2,0.311127],[-1.08,0.117663],[-0.96,-0.0554372],[-0.84,-0.208172],[-0.72,-0.340543],[-0.6,-0.452548],[-0.48,-0.544189],[-0.36,-0.615466],[-0.24,-0.666377],[-0.12,-0.696924],[0,-0.707107],[0.12,-0.696924],[0.24,-0.666377],[0.36,-0.615466],[0.48,-0.544189],[0.6,-0.452548],[0.72,-0.340543],[0.84,-0.208172],[0.96,-0.0554372],[1.08,0.117663],[1.2,0.311127],[1.32,0.524956],[1.44,0.75915],[1.56,1.01371],[1.68,1.28863],[1.8,1.58392],[1.92,1.89957],[2.04,2.23559],[2.16,2.59197],[2.28,2.96872],[2.4,3.36583],[2.52,3.7833],[2.64,4.22114],[2.76,4.67935],[2.88,5.15792]] color=#2ca02c fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2,class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=P3 data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=50 dimension=2 data=[[-3,-7.34847],[-2.88,-6.22492],[-2.76,-5.20295],[-2.64,-4.27834],[-2.52,-3.44684],[-2.4,-2.70424],[-2.28,-2.04628],[-2.16,-1.46875],[-2.04,-0.967411],[-1.92,-0.538026],[-1.8,-0.176363],[-1.68,0.121808],[-1.56,0.360722],[-1.44,0.54461],[-1.32,0.677705],[-1.2,0.764241],[-1.08,0.808449],[-0.96,0.814563],[-0.84,0.786815],[-0.72,0.729438],[-0.6,0.646665],[-0.48,0.542729],[-0.36,0.421861],[-0.24,0.288295],[-0.12,0.146264],[0,-0],[0.12,-0.146264],[0.24,-0.288295],[0.36,-0.421861],[0.48,-0.542729],[0.6,-0.646665],[0.72,-0.729438],[0.84,-0.786815],[0.96,-0.814563],[1.08,-0.808449],[1.2,-0.764241],[1.32,-0.677705],[1.44,-0.54461],[1.56,-0.360722],[1.68,-0.121808],[1.8,0.176363],[1.92,0.538026],[2.04,0.967411],[2.16,1.46875],[2.28,2.04628],[2.4,2.70424],[2.52,3.44684],[2.64,4.27834],[2.76,5.20295],[2.88,6.22492]] color=#d62728 fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2,class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=P4 data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=50 dimension=2 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      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degreemax = 5\n",
    "palette = ot.Drawable.BuildDefaultPalette(degreemax)\n",
    "graph = ot.Graph(\"Orthonormal Hermite polynomials\", \"x\", \"y\", True, \"bottomright\")\n",
    "for k in range(degreemax):\n",
    "    pk = pofa.build(k)\n",
    "    curve = pk.draw(-3.0, 3.0, 50)\n",
    "    curve.setLegends([\"P%d\" % (k)])\n",
    "    graph.add(curve)\n",
    "graph.setColors(palette)  # Add colors\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Les polynômes sont orthonormés pour la densité\n",
    "\n",
    "Dans OpenTURNS, les polynômes sont orthonormés pour la densité de probabilité. Par conséquent, ils ne sont généralement pas moniques, c'est à dire que le coefficient associé au monôme de plus haut degré n'est pas toujours égal à 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linearSample(xmin, xmax, npoints):\n",
    "    \"\"\"Returns a sample created from a regular grid\n",
    "    from xmin to xmax with npoints points.\"\"\"\n",
    "    step = (xmax - xmin) / (npoints - 1)\n",
    "    rg = ot.RegularGrid(xmin, step, npoints)\n",
    "    vertices = rg.getVertices()\n",
    "    return vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans la boucle `for` suivante, on considère les polynômes d'Hermite de degré 0 à 5. Pour chaque degré, on affiche le coefficient du monôme de plus grand exposant, son inverse ainsi que le facteur $\\frac{1}{\\sqrt{k!}}$. On observe que les deux sont égaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Leading coefficient:\n",
      "OT = 1.0000, ref. = 1.0000\n",
      "OT = 1.0000, ref. = 1.0000\n",
      "OT = 0.7071, ref. = 0.7071\n",
      "OT = 0.4082, ref. = 0.4082\n",
      "OT = 0.2041, ref. = 0.2041\n"
     ]
    }
   ],
   "source": [
    "print(\"Leading coefficient:\")\n",
    "for k in range(degreemax):\n",
    "    pk = pofa.build(k)\n",
    "    leadingCoeffOT = pk.getCoefficients()[-1]\n",
    "    leadingCoeffReference = 1.0 / np.sqrt(math.factorial(k))\n",
    "    print(f\"OT = {leadingCoeffOT:.4f}, ref. = {leadingCoeffReference:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## La récurrence à trois termes\n",
    "\n",
    "La méthode `getRecurrenceCoefficients` permet d'obtenir les coefficients de la récurrence à trois termes permettant d'évaluer les polynômes:\n",
    "$$\n",
    "P_{n+1}(x) = (a_{0,n} x + a_{1,n}) P_n(x) + a_{2,n} P_{n-1}(x)\n",
    "$$\n",
    "pour $n\\neq 0$ et tout $x\\in\\mathbb{R}$. En d'autres termes, la méthode `getRecurrenceCoefficients(n)` retourne les coefficients $(a_{0,n},a_{1,n},a_{2,n})$ permettant de calculer $P_{n+1}$ en fonction de $P_n$ et $P_{n-1}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1,0,0]\n",
      "[0.707107,0,-0.707107]\n",
      "[0.57735,0,-0.816497]\n",
      "[0.5,0,-0.866025]\n",
      "[0.447214,0,-0.894427]\n"
     ]
    }
   ],
   "source": [
    "for n in range(5):\n",
    "    print(pofa.getRecurrenceCoefficients(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Définir des polynômes univariés de manière automatique\n",
    "\n",
    "Dans cette partie, on montre comment définir des polynômes univariés dans le cas de la poutre encastrée. Nous voyons comment créer la famille de polynômes orthogonaux associé à une variable aléatoire. Nous analysons la mesure associée à une famille de polynômes orthogonaux et montrons comment dessiner les polynômes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour commencer, on définit une variable aléatoire de loi uniforme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_L = ot.Uniform(250.0, 260.0)  # in cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puis on crée le polynôme univarié associé à cette variable avec la classe `StandardPolynomialFactory`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1</p>"
      ],
      "text/plain": [
       "class=StandardDistributionPolynomialFactory hasSpecificFamily=true specificFamily=class=OrthogonalUniVariatePolynomialFamily implementation=class=LegendreFactory measure=class=Uniform name=Uniform dimension=1 a=-1 b=1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factory_L = ot.StandardDistributionPolynomialFactory(dist_L)\n",
    "factory_L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe que les polynômes orthogonaux associés à la loi uniforme sont les polynômes de Legendre.\n",
    "\n",
    "Pour générer le polynôme de degré zéro associée à cette famille, on utilise la méthode `build`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>1</p>"
      ],
      "text/plain": [
       "<openturns.orthogonalbasis.OrthogonalUniVariatePolynomial; proxy of <Swig Object of type 'OT::OrthogonalUniVariatePolynomial *' at 0x7f21f87bc810> >"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P0 = factory_L.build(0)\n",
    "P0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour toute famille de polynômes orthogonaux, le polynôme de degré zéro est toujours égal à 1. Observons les polynômes de degrés 0 à 5 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1.73205 * X\n",
      "-1.11803 + 3.3541 * X^2\n",
      "-3.96863 * X + 6.61438 * X^3\n",
      "1.125 - 11.25 * X^2 + 13.125 * X^4\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    Pi = factory_L.build(i)\n",
    "    print(Pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour toute famille de polynômes orthogonaux, on *standardise* la densité de probabilité pour obtenir une famille dont les paramètres sont constants : dans OpenTURNS, on nomme cette distribution la *mesure*. La méthode `getMeasure` permet de l'obtenir :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>Uniform(a = -1, b = 1)</p>"
      ],
      "text/plain": [
       "class=Uniform name=Uniform dimension=1 a=-1 b=1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measure = factory_L.getMeasure()\n",
    "measure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme cette distribution est uniforme, on peut facilement obtenir les bornes associées avec la methode `getRange`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "Lrange = measure.getRange()\n",
    "Lmin = Lrange.getLowerBound()[0]\n",
    "Lmax = Lrange.getUpperBound()[0]\n",
    "print(Lmin)\n",
    "print(Lmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On souhaite ensuite dessiner le polynôme orthogonal de degré 6 : on utilise la méthode `draw`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "class=Graph name=Unnamed implementation=class=GraphImplementation name=Unnamed title=Polynôme pour L de degré 6 xTitle=x yTitle=y axes=ON grid=ON legendposition=topright legendFontSize=1 drawables=[class=Drawable name=Unnamed implementation=class=Curve name=Unnamed derived from class=DrawableImplementation name=Unnamed legend=Unnamed data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=100 dimension=2 data=[[-1,3.60555],[-0.98,2.23671],[-0.96,1.13595],[-0.94,0.270866],[-0.92,-0.388448],[-0.9,-0.86953],[-0.88,-1.19765],[-0.86,-1.39592],[-0.84,-1.4854],[-0.82,-1.48522],[-0.8,-1.41264],[-0.78,-1.2832],[-0.76,-1.11077],[-0.74,-0.907701],[-0.72,-0.684851],[-0.7,-0.451726],[-0.68,-0.216546],[-0.66,0.013666],[-0.64,0.233002],[-0.62,0.436586],[-0.6,0.620501],[-0.58,0.781707],[-0.56,0.917974],[-0.54,1.02781],[-0.52,1.11038],[-0.5,1.16547],[-0.48,1.19338],[-0.46,1.19492],[-0.44,1.17129],[-0.42,1.12406],[-0.4,1.05511],[-0.38,0.966591],[-0.36,0.860836],[-0.34,0.740353],[-0.32,0.607765],[-0.3,0.465769],[-0.28,0.317097],[-0.26,0.164477],[-0.24,0.0106027],[-0.22,-0.141905],[-0.2,-0.290521],[-0.18,-0.43285],[-0.16,-0.566649],[-0.14,-0.689848],[-0.12,-0.800574],[-0.1,-0.897167],[-0.08,-0.978195],[-0.06,-1.04247],[-0.04,-1.08906],[-0.02,-1.11728],[0,-1.12673],[0.02,-1.11728],[0.04,-1.08906],[0.06,-1.04247],[0.08,-0.978195],[0.1,-0.897167],[0.12,-0.800574],[0.14,-0.689848],[0.16,-0.566649],[0.18,-0.43285],[0.2,-0.290521],[0.22,-0.141905],[0.24,0.0106027],[0.26,0.164477],[0.28,0.317097],[0.3,0.465769],[0.32,0.607765],[0.34,0.740353],[0.36,0.860836],[0.38,0.966591],[0.4,1.05511],[0.42,1.12406],[0.44,1.17129],[0.46,1.19492],[0.48,1.19338],[0.5,1.16547],[0.52,1.11038],[0.54,1.02781],[0.56,0.917974],[0.58,0.781707],[0.6,0.620501],[0.62,0.436586],[0.64,0.233002],[0.66,0.013666],[0.68,-0.216546],[0.7,-0.451726],[0.72,-0.684851],[0.74,-0.907701],[0.76,-1.11077],[0.78,-1.2832],[0.8,-1.41264],[0.82,-1.48522],[0.84,-1.4854],[0.86,-1.39592],[0.88,-1.19765],[0.9,-0.86953],[0.92,-0.388448],[0.94,0.270866],[0.96,1.13595],[0.98,2.23671]] color=red fillStyle=solid lineStyle=solid pointStyle=none lineWidth=2]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P6 = factory_L.build(6)\n",
    "graph = P6.draw(Lmin, Lmax, 100)\n",
    "graph.setTitle(\"Polynôme pour L de degré 6\")\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 1 : vérifier la récurrence à trois termes pour les polynômes d'Hermite\n",
    "\n",
    "Si $\\{P_n\\}_{n\\geq 0}$ est une famille de polynômes orthonormaux, alors :\n",
    "\n",
    "$$\n",
    "P_{n+1}(x) = (a_{0,n} x + a_{1, n}) P_n(x) + a_{2,n} P_{n - 1}(x),\n",
    "$$\n",
    "\n",
    "pour $n\\geq 0$ et tout point $x\\in  \\mathbb{R}$ où $a_{0,n}$, $a_{1,n}$ et $a_{2,n}$ sont des coefficients.\n",
    "\n",
    "L'objectif de cet exercice est de vérifier la récurrence à trois termes.\n",
    "\n",
    "La fonction `evalPolynomialFactory` suivante utilise la formule de récurrence à trois termes pour évaluer les polynômes d'Hermite. \n",
    "- Dans une boucle `for`, elle appele la méthode `getRecurrenceCoefficients` pour obtenir les coefficients de la récurrence $(a_{0,n},a_{1,n},a_{2,n})$. \n",
    "- Puis elle utilise la formule de récurrence pour calculer $P_{n+1}$ en fonction de $P_n$ et $P_{n-1}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evalPolynomialFactory(x, polyfact, degree):\n",
    "    \"\"\"\n",
    "    Evaluates the orthogonal polynomial with given degree.\n",
    "\n",
    "    The code uses the three-term recurrence:\n",
    "\n",
    "        P{n+1}(x) = (a0n * x + a1n) * P{n}(x) + a2n * P{n-1}(x)\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : float\n",
    "        The point where the polynomial must be evaluated.\n",
    "    polyfact : ot.OrthogonalUniVariatePolynomial()\n",
    "        A family of orthonormal polynomials.\n",
    "    degree : int\n",
    "        The polynomial degree.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    p : float\n",
    "        The polynomial value at point x.\n",
    "\n",
    "    \"\"\"\n",
    "    if degree == 0:\n",
    "        p = 1.0\n",
    "    else:\n",
    "        pp = 0.0  # Previous : P{n-1}\n",
    "        pc = 1.0  # Current : Pn\n",
    "        for n in range(degree):\n",
    "            # Evalue P{n+1}(x) en fonction de Pn et P{n-1}\n",
    "            a0, a1, a2 = polyfact.getRecurrenceCoefficients(n)\n",
    "            p = (a0 * x + a1) * pc + a2 * pp\n",
    "            pp = pc\n",
    "            pc = p\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Valider la fonction `evalPolynomialFactory` en comparant ses sorties avec celles du polynôme.\n",
    "\n",
    "- En utilisant la fonction `linearSample`, créer la variable `x` contenant une liste de `npoints = 5` abscisses régulièrement réparties entre -3 et 3. \n",
    "- Puis, réaliser une boucle `for` sur les degrés $k$ de 0 à 5. \n",
    "- Pour chaque degré `k`, créer le polynôme `pk` de degré `k`, puis réaliser une boucle sur les indices `i` des abscisses.\n",
    "- Pour chaque abscisse, évaluer le polynôme `pk` avec son opérateur `()` et comparer avec la valeur de la fonction `evalPolynomialFactory`.\n",
    "\n",
    "Pour vous aider, vous pouvez vous inspirer du squelette suivant, dans lequel vous remplacerez les sections *TODO* par du code Python valide.\n",
    "\n",
    "```python\n",
    "npoints = 5\n",
    "x = linearSample(-3.0, 3.0, npoints)\n",
    "for k in range(5):\n",
    "    print(\"Degree = %d\" % (k))\n",
    "    pk = pofa.build(TODO)\n",
    "    for i in range(npoints):\n",
    "        y = evalPolynomialFactory(TODO)\n",
    "        ytrue = TODO\n",
    "        print(\"x=%f, y=%f, True y = %f\" % (x[i,0 ], y, ytrue))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 2 : vérification de l'orthornormalité des polynômes\n",
    "\n",
    "L'objectif de cet exercice est d'observer l'orthonormalité des polynômes par rapport à la densité de probabilité associée. \n",
    "\n",
    "On souhaite vérifier que le produit scalaire \n",
    "$$\n",
    "\\left\\langle P_j, P_k \\right\\rangle = \\int_\\mathbb{R} P_j(x) P_k(x) f(x) dx \n",
    "$$\n",
    "satisfait l'égalité :\n",
    "$$\n",
    "\\left\\langle P_j, P_k \\right\\rangle = \\delta_{jk}\n",
    "$$\n",
    "pour $j,k= 0,...,5$ où $\\delta_{jk}$ est le symbole de Kronecker.\n",
    "\n",
    "Pour cela, nous définissons la fonction `integrandPiJPiKF` qui évalue la fonction $P_j(x) P_k(x) f(x)$ pour tout $x\\in\\mathbb{R}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrandPiJPiKF(x):\n",
    "    \"\"\"\n",
    "    Evaluates pj(x) * pk(x) * f(x) for the Gaussian PDF at point x.\n",
    "\n",
    "    This function is the integrand to consider when\n",
    "    we want to check that the polynomials are orthogonal.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : ot.Point(1)\n",
    "        The point.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    y : list(float)\n",
    "        The integrand value.\n",
    "\n",
    "    \"\"\"\n",
    "    pdf = gaussianRandomVariable.computePDF(x)\n",
    "    yf = hermitePolynomialJ(x[0]) * hermitePolynomialK(x[0]) * pdf\n",
    "    return [yf]\n",
    "\n",
    "\n",
    "gaussianRandomVariable = ot.Normal()\n",
    "integrandPiJPiKFPy = ot.PythonFunction(1, 1, integrandPiJPiKF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour évaluer l'intégrale, nous proposons d'utiliser la règle de Gauss-Kronrod implémentée dans la classe `GaussKronrodRule`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "gkr = ot.GaussKronrodRule(ot.GaussKronrodRule.G11K23)\n",
    "algo = ot.GaussKronrod(1000, 1e-16, gkr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il est nécessaire de fixer des bornes finies pour évaluer l'intégrale. Nous savons que la densité de probabilité de la loi gaussienne centrée et réduite est numériquement égale à zéro en dehors de l'intervalle [-38,38]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "  <tr><td></td><th>v0</th></tr>\n",
       "  <tr><th>0</th><td>1.097221e-314</td></tr>\n",
       "  <tr><th>1</th><td>2.120007e-298</td></tr>\n",
       "  <tr><th>2</th><td>2.120007e-298</td></tr>\n",
       "  <tr><th>3</th><td>1.097221e-314</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=4 dimension=1 data=[[1.09722e-314],[2.12001e-298],[2.12001e-298],[1.09722e-314]]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussianRandomVariable.computePDF(ot.Sample([[x] for x in [-38.0, -37.0, 37.0, 38.0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C'est pour cette raisons que nous fixons ainsi les bornes de l'intervalle d'intégration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "bounds = ot.Interval(-38.0, 38.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le produit scalaire peut alors être calculé avec les instructions :\n",
    "```python\n",
    "hermitePolynomialJ = pofa.build(j)\n",
    "hermitePolynomialK = pofa.build(k)\n",
    "pscalJK = algo.integrate(integrandPiJPiKFPy, bounds)[0]\n",
    "```\n",
    "\n",
    "Réaliser une boucle sur les indices `j` et `k` entre 0 et 5 et évaluer le produit scalaire : qu'observez-vous ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 3 : orthonormalisation d'une densité de probabilité\n",
    "\n",
    "La classe `AdaptiveStieltjesAlgorithm` propose un algorithme pour générer la base orthonormale associée à une densité de probabilité donnée. Sur le principe, cette classe réalise l'algorithme de Gram-Schmidt pour générer la base orthonormale à partir de la base canonique. L'implémentation repose en fait sur un algorithme plus précis sur le plan numérique, en particulier pour les polynômes de dégré élevés.\n",
    "\n",
    "L'objectif de cet exercice est de comparer les polynômes obtenus par la classe `AdaptiveStieltjesAlgorithm` pour la loi uniforme avec les polynômes de Legendre.\n",
    "\n",
    "* Dans un premier temps, on utilise l'algorithme d'orthonormalisation.\n",
    "  * Créer la variable `measure` contenant une variable uniforme standard.\n",
    "  * Utiliser la classe `AdaptiveStieltjesAlgorithm` pour créer un algorithme d'orthonormalisation `algo`.\n",
    "  * Utiliser la classe `StandardDistributionPolynomialFactory` pour créer la variable `pofa` sur cet algorithme.\n",
    "  * Utiliser la méthode `build` pour afficher les polynômes de degrés 0 à 4 correspondants.\n",
    "* Dans un second temps, on utilise les polynômes de Legendre.\n",
    "  * Utiliser la classe `LegendreFactory` pour créer la variable `lefa`.\n",
    "  * Utiliser la variable `lefa` pour afficher les polynômes de Legendre de degrés 0 à 4 correspondants.\n",
    "* Comparer les deux résultats : qu'observez-vous ?\n",
    "\n",
    "TODO : étendre l'exercice en utilisant l'algorithme de Gram-Schmidt. Constater son échec lorsque le degré polynomial augmente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 4 : polynômes orthogonaux pour une variable gaussienne\n",
    "\n",
    "* Créer la famille de polynômes orthogonaux associés à une variable $X$ de loi normale de moyenne 12 et d'écart-type 3.4 :\n",
    "```python\n",
    "N = ot.Normal(12.0, 3.4)\n",
    "```\n",
    "* Quelle est la famille de polynômes orthogonaux associés à cette variable ?\n",
    "* Afficher les polynômes de degrés 0 à 5 associés.\n",
    "* Quelle est la mesure standard associée ?\n",
    "* On souhaite dessiner le polynôme de degré 6 associé à cette mesure : pourquoi ne peut-on pas utiliser la méthode `getRange` pour déterminer les bornes ? \n",
    "* Utiliser la méthode `computeBilateralConfidenceInterval` pour déterminer l'intervalle de confiance à 95% : en déduire des bornes pour dessiner le polynôme.\n",
    "* Dessiner le polynôme de degré 6 associé à cette mesure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 5 : polynômes orthogonaux pour la variable F\n",
    "\n",
    "* Créer la famille de polynômes orthogonaux associés à la variable $F$ :\n",
    "```python\n",
    "F_para = ot.LogNormalMuSigma(3.0e4, 9.0e3, 15.0e3)  # in N\n",
    "dist_F = ot.ParametrizedDistribution(F_para)\n",
    "```\n",
    "* Quelle est la famille de polynômes orthogonaux associés à cette variable ?\n",
    "* Afficher les polynômes de degrés 0 à 5 associés.\n",
    "* Quelle est la mesure standard associée ?\n",
    "* On souhaite dessiner le polynôme de degré 6 associé à cette mesure : pourquoi ne peut-on pas utiliser la méthode `getRange` pour déterminer les bornes ? \n",
    "* Utiliser la méthode `computeBilateralConfidenceInterval` pour déterminer l'intervalle de confiance à 95% : en déduire des bornes pour dessiner le polynôme.\n",
    "* Dessiner le polynôme de degré 6 associé à cette mesure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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