{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP 1 : chapitres 1 et 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapitre 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Étudier les points critiques de la fonction $f(x) = x^3 - 3x^2 + 2x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Math, Markdown # Affichage de formules mathématiques amelioré"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "\n",
    "# Définition des symboles\n",
    "x, y = sp.symbols('x y', real=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} y + 2 x - y^{3}$"
      ],
      "text/plain": [
       "x**2*y + 2*x - y**3"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La fonction\n",
    "f = lambda a,b : 2*a-b**3+a**2*b\n",
    "f(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 x y + 2$"
      ],
      "text/plain": [
       "2*x*y + 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} - 3 y^{2}$"
      ],
      "text/plain": [
       "x**2 - 3*y**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Le gradient\n",
    "df_dx = sp.diff(f(x,y),x)\n",
    "df_dy = sp.diff(f(x,y),y)\n",
    "display(df_dx)\n",
    "display(df_dy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 x y + 2\\\\x^{2} - 3 y^{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[    2*x*y + 2],\n",
       "[x**2 - 3*y**2]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le gradient --- Affichage amélioré\n",
    "gradient = sp.Matrix([df_dx,df_dy])\n",
    "gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$\\nabla f = \\left[\\begin{matrix}2 x y + 2\\\\x^{2} - 3 y^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Affichage amelioré ++\n",
    "display(Markdown(r\"$$\\nabla f = \"+sp.latex(gradient)+\"$$\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 x - 2 y$"
      ],
      "text/plain": [
       "4*x - 2*y"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BONUS Équation du plan tangent en (x_0, y_0)\n",
    "\n",
    "# x0, y0 = sp.symbols('x_0 y_0', real=True)\n",
    "x0, y0 = 1, 1\n",
    "\n",
    "plan_tangent = f(x0,y0) + (x-x0)*df_dx.subs({x:x0,y:y0}) + (y-y0)*df_dy.subs({x:x0,y:y0})\n",
    "plan_tangent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-3**(1/4), 3**(3/4)/3), (3**(1/4), -3**(3/4)/3)]"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Points critiques\n",
    "critical_points = sp.solve([df_dx, df_dy], (x, y))\n",
    "critical_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$P_{0} = \\left( - \\sqrt[4]{3}, \\  \\frac{3^{\\frac{3}{4}}}{3}\\right)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "$$P_{1} = \\left( \\sqrt[4]{3}, \\  - \\frac{3^{\\frac{3}{4}}}{3}\\right)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " # Points critiques --- Affichage amélioré\n",
    "for i in range(len(critical_points)):\n",
    "    # display(Math(f'P_{i} = {sp.latex(critical_points[i])}'))\n",
    "    display(Markdown(r\"$$P_{\"+str(i)+\"} = \"+sp.latex(critical_points[i])+\"$$\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 y & 2 x\\\\2 x & - 6 y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[2*y,  2*x],\n",
       "[2*x, -6*y]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La matrice Hessienne\n",
    "d2f_dxx = sp.diff(df_dx,x)\n",
    "d2f_dxy = sp.diff(df_dx,y)\n",
    "d2f_dyx = sp.diff(df_dy,x)\n",
    "d2f_dyy = sp.diff(df_dy,y)\n",
    "hessian = sp.Matrix([[d2f_dxx, d2f_dxy], [d2f_dyx, d2f_dyy]])\n",
    "hessian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 4 x^{2} - 12 y^{2}$"
      ],
      "text/plain": [
       "-4*x**2 - 12*y**2"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le determinant de la matrice Hessienne\n",
    "det_hessian = d2f_dxx*d2f_dyy - d2f_dxy*d2f_dyx\n",
    "det_hessian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x_c,y_c) = (-3**(1/4),3**(3/4)/3)\n",
      "H(x_c,y_c) = Matrix([[2*3**(3/4)/3, -2*3**(1/4)], [-2*3**(1/4), -2*3**(3/4)]])\n",
      "det(H(x_c,y_c)) = -8*sqrt(3)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "Le point critique est un point selle"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x_c,y_c) = (3**(1/4),-3**(3/4)/3)\n",
      "H(x_c,y_c) = Matrix([[-2*3**(3/4)/3, 2*3**(1/4)], [2*3**(1/4), 2*3**(3/4)]])\n",
      "det(H(x_c,y_c)) = -8*sqrt(3)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "Le point critique est un point selle"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Analyse de la nature des points critiques\n",
    "\n",
    "for x_c,y_c in critical_points:\n",
    "    hessian_at_critical = hessian.subs({x:x_c, y:y_c})\n",
    "    det_hessian_at_critical = det_hessian.subs({x:x_c, y:y_c})\n",
    "    print(f\"(x_c,y_c) = ({x_c},{y_c})\")\n",
    "    print(f\"H(x_c,y_c) = {hessian_at_critical}\")\n",
    "    print(f\"det(H(x_c,y_c)) = {det_hessian_at_critical}\\n\")\n",
    "    if det_hessian_at_critical > 0:\n",
    "        if hessian_at_critical[0,0] > 0:\n",
    "            display(Markdown(\"Le point critique est un minimum local\"))\n",
    "        elif hessian_at_critical[0,0] < 0:\n",
    "            display(Markdown(\"Le point critique est un maximum local\"))\n",
    "    elif det_hessian_at_critical < 0:\n",
    "        display(Markdown(\"Le point critique est un point selle\"))\n",
    "    else:\n",
    "        display(Markdown(\"Le test ne permet pas de conclure\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (x_c,y_c) = (- \\sqrt[4]{3},\\frac{3^{\\frac{3}{4}}}{3})$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle H(x_c,y_c) = \\left[\\begin{matrix}\\frac{2 \\cdot 3^{\\frac{3}{4}}}{3} & - 2 \\sqrt[4]{3}\\\\- 2 \\sqrt[4]{3} & - 2 \\cdot 3^{\\frac{3}{4}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\det(H(x_c,y_c)) = - 8 \\sqrt{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "Le point critique est un point selle"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "---"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (x_c,y_c) = (\\sqrt[4]{3},- \\frac{3^{\\frac{3}{4}}}{3})$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle H(x_c,y_c) = \\left[\\begin{matrix}- \\frac{2 \\cdot 3^{\\frac{3}{4}}}{3} & 2 \\sqrt[4]{3}\\\\2 \\sqrt[4]{3} & 2 \\cdot 3^{\\frac{3}{4}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\det(H(x_c,y_c)) = - 8 \\sqrt{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "Le point critique est un point selle"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "---"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Analyse de la nature des points critiques --- Affichage amélioré\n",
    "\n",
    "for x_c,y_c in critical_points:\n",
    "    hessian_at_critical = hessian.subs({x:x_c, y:y_c})\n",
    "    det_hessian_at_critical = det_hessian.subs({x:x_c, y:y_c})\n",
    "    display(Math(f\"(x_c,y_c) = ({sp.latex(x_c)},{sp.latex(y_c)})\"))\n",
    "    display(Math(f\"H(x_c,y_c) = {sp.latex(hessian_at_critical)}\"))\n",
    "    display(Math(f\"\\\\det(H(x_c,y_c)) = {sp.latex(det_hessian_at_critical)}\"))\n",
    "    if det_hessian_at_critical > 0:\n",
    "        if hessian_at_critical[0,0] > 0:\n",
    "            display(Markdown(\"Le point critique est un minimum local\"))\n",
    "        elif hessian_at_critical[0,0] < 0:\n",
    "            display(Markdown(\"Le point critique est un maximum local\"))\n",
    "    elif det_hessian_at_critical < 0:\n",
    "        display(Markdown(\"Le point critique est un point selle\"))\n",
    "    else:\n",
    "        display(Markdown(\"Le test ne permet pas de conclure\"))\n",
    "    display(Markdown(\"---\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Affichage des courbes de niveau et des points critiques\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = sp.lambdify((x,y), f(x,y), 'numpy')\n",
    "\n",
    "x = np.linspace(-2,2,100)\n",
    "y = np.linspace(-2,2,100)\n",
    "X,Y = np.meshgrid(x,y)\n",
    "Z = g(X,Y)\n",
    "\n",
    "plt.contour(X,Y,Z, levels=30)\n",
    "\n",
    "xx_c = [ float(P[0]) for P in critical_points ]\n",
    "yy_c = [ float(P[1]) for P in critical_points ]\n",
    "plt.scatter( xx_c, yy_c, color='red')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Contour plot')\n",
    "plt.grid(True)\n",
    "# plt.savefig('contour_plot.png')\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapitre 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation directe (base canonique)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit les points\n",
    "\\begin{array}{|l|ccc|}\n",
    "\\hline\n",
    "x & 0 & 2 & 4 \\\\\n",
    "y & 7 & 11 & 55\\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "Écrire dans la base canonique de $\\R_2[x]$ le polynôme $p$ qui interpole ces points.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} + a_{1} x + a_{2} x^{2}$"
      ],
      "text/plain": [
       "a0 + a1*x + a2*x**2"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Points d'interpolation\n",
    "x_vals = [0, 2, 4,]\n",
    "y_vals = [7, 11, 55]\n",
    "\n",
    "n = len(x_vals)-1  # Degré du polynôme\n",
    "coeffs = sp.symbols(f'a0:{n+1}')\n",
    "poly = sum(coeffs[i] * x**i for i in range(n+1))\n",
    "poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} = 7$"
      ],
      "text/plain": [
       "Eq(a0, 7)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} + 2 a_{1} + 4 a_{2} = 11$"
      ],
      "text/plain": [
       "Eq(a0 + 2*a1 + 4*a2, 11)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} + 4 a_{1} + 16 a_{2} = 55$"
      ],
      "text/plain": [
       "Eq(a0 + 4*a1 + 16*a2, 55)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Le système à résoudre\n",
    "eqs = [ sp.Eq(  poly.subs(x, x_vals[i]) , y_vals[i] )  for i in range(n+1) ]\n",
    "\n",
    "for eq in eqs :\n",
    "\tdisplay(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 5 x^{2} - 8 x + 7$"
      ],
      "text/plain": [
       "5*x**2 - 8*x + 7"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le polyôme interpolant\n",
    "solution = sp.solve(eqs, coeffs)\n",
    "p1 = poly.subs(solution)\n",
    "p1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation polynomiale composite : spline linéaire\n",
    "\n",
    "Soit les points\n",
    "\\begin{array}{|l|ccc|}\n",
    "\\hline\n",
    "x & 0 & 2 & 4 \\\\\n",
    "y & 7 & 11 & 55\\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "Écrire la spline linéaire qui interpole ces même points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Points à interpoler\n",
    "x_vals = [0, 2, 4]\n",
    "y_vals = [7, 11, 55]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{cases} a_{0} x + b_{0} & \\text{for}\\: x < 2 \\\\a_{1} x + b_{1} & \\text{for}\\: x < 4 \\end{cases}$"
      ],
      "text/plain": [
       "Piecewise((a0*x + b0, x < 2), (a1*x + b1, x < 4))"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Construction des fonctions linéaires par morceaux\n",
    "splines = []\n",
    "for i in range(len(x_vals) - 1):\n",
    "    a, b = sp.symbols(f'a{i} b{i}')\n",
    "    spline = a * x + b\n",
    "    splines.append(spline)\n",
    "\n",
    "spline = sp.Piecewise(*[(s, x < x_vals[i+1]) for i, s in enumerate(splines)])\n",
    "spline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b_{0} = 7$"
      ],
      "text/plain": [
       "Eq(b0, 7)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 a_{0} + b_{0} = 11$"
      ],
      "text/plain": [
       "Eq(2*a0 + b0, 11)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 a_{1} + b_{1} = 11$"
      ],
      "text/plain": [
       "Eq(2*a1 + b1, 11)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 a_{1} + b_{1} = 55$"
      ],
      "text/plain": [
       "Eq(4*a1 + b1, 55)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Les equations\n",
    "equations = []\n",
    "for i in range(len(x_vals) - 1):\n",
    "    equations.append(sp.Eq(splines[i].subs(x, x_vals[i]), y_vals[i]))\n",
    "    equations.append(sp.Eq(splines[i].subs(x, x_vals[i+1]), y_vals[i+1]))\n",
    "\n",
    "for eq in equations:\n",
    "    display(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{a0: 2, b0: 7, a1: 22, b1: -33}"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Résolution du système\n",
    "params = [sp.symbols(f'a{i} b{i}') for i in range(len(x_vals) - 1)]\n",
    "flattened_params = sum(params, ()) # aplatissement de la liste\n",
    "solution = sp.solve(equations, flattened_params)\n",
    "solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{cases} 2 x + 7 & \\text{for}\\: x < 2 \\\\22 x - 33 & \\text{for}\\: x < 4 \\end{cases}$"
      ],
      "text/plain": [
       "Piecewise((2*x + 7, x < 2), (22*x - 33, x < 4))"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "splines_solved = [spline.subs(solution) for spline in splines]\n",
    "spline_solved = sp.Piecewise(*[(s, x < x_vals[i+1]) for i, s in enumerate(splines_solved)])\n",
    "spline_solved"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation de Lagrange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit les points\n",
    "\\begin{array}{|l|ccc|}\n",
    "\\hline\n",
    "x & 0&2&3\\\\\n",
    "y & 7&11&28\\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "Écrire dans la base de Lagrange de $\\R_2[x]$ le polynôme $p$ qui interpole ces points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{y_{0} \\left(x - x_{1}\\right) \\left(x - x_{2}\\right)}{\\left(x_{0} - x_{1}\\right) \\left(x_{0} - x_{2}\\right)} + \\frac{y_{1} \\left(x - x_{0}\\right) \\left(x - x_{2}\\right)}{\\left(- x_{0} + x_{1}\\right) \\left(x_{1} - x_{2}\\right)} + \\frac{y_{2} \\left(x - x_{0}\\right) \\left(x - x_{1}\\right)}{\\left(- x_{0} + x_{2}\\right) \\left(- x_{1} + x_{2}\\right)}$"
      ],
      "text/plain": [
       "y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((-x0 + x1)*(x1 - x2)) + y2*(x - x0)*(x - x1)/((-x0 + x2)*(-x1 + x2))"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le polyôme interpolant des points quelconques \n",
    "n = 2\n",
    "p1 = sp.polys.specialpolys.interpolating_poly(n+1, x, X='x', Y='y') \n",
    "p1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{11 x \\left(x - 3\\right)}{2} + \\frac{28 x \\left(x - 2\\right)}{3} + \\frac{7 \\left(x - 3\\right) \\left(x - 2\\right)}{6}$"
      ],
      "text/plain": [
       "-11*x*(x - 3)/2 + 28*x*(x - 2)/3 + 7*(x - 3)*(x - 2)/6"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Le polyôme interpolant des points donnés\n",
    "x_vals = [0, 2, 3]\n",
    "y_vals = [7, 11, 28]\n",
    "p2 = sp.polys.specialpolys.interpolating_poly(n+1, x, X=x_vals, Y=y_vals)\n",
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 5 x^{2} - 8 x + 7$"
      ],
      "text/plain": [
       "5*x**2 - 8*x + 7"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p3 = sp.simplify(p2)\n",
    "p3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation dans la base de Newton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit les points\n",
    "\n",
    "\\begin{array}{|l|rccccc|}\n",
    "\\hline\n",
    "x & -2&1&4&-1&3&-4\\\\\n",
    "\\hline\n",
    "y & -1&2&59&4&24&-53\\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "\n",
    "- Écrire la base de Newton de $\\R_5[x]$ associée à ces points.\n",
    "- Écrire le tableau des différences divisées.\n",
    "- En déduire les coordonnées du polynôme qui interpole  ces points dans la base de Newton."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tableau des différences divisées\n",
    "def ddt(xx,yy):\n",
    "    n = len(yy)\n",
    "    t = [[0]*n for _ in range(n)]\n",
    "    for i in range(n): \n",
    "        t[i][0] = yy[i]\n",
    "    for j in range(1,n):\n",
    "        for i in range(j,n):\n",
    "            t[i][j] = (t[i][j-1]-t[i-1][j-1])/sp.S(xx[i]-xx[i-j])\n",
    "    return t\n",
    "\n",
    "# base de Newton\n",
    "def nb(x,xx):\n",
    "    b = [1]\n",
    "    for j in range(len(xx)-1):\n",
    "        b.append(b[-1]*sp.S(x-xx[j]))\n",
    "    return b\n",
    "\n",
    "# polynome d'interpolation dans la base de Newton\n",
    "def ni(x,xx,yy):\n",
    "    t = ddt(xx,yy)\n",
    "    base = nb(x,xx)\n",
    "    p = sum( t[i][i]*base[i] for i in range(len(xx)) )\n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-1 & 0 & 0 & 0 & 0 & 0\\\\2 & 1 & 0 & 0 & 0 & 0\\\\59 & 19 & 3 & 0 & 0 & 0\\\\4 & 11 & 4 & 1 & 0 & 0\\\\24 & 5 & 6 & 1 & 0 & 0\\\\-53 & 11 & -2 & 1 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ -1,  0,  0, 0, 0, 0],\n",
       "[  2,  1,  0, 0, 0, 0],\n",
       "[ 59, 19,  3, 0, 0, 0],\n",
       "[  4, 11,  4, 1, 0, 0],\n",
       "[ 24,  5,  6, 1, 0, 0],\n",
       "[-53, 11, -2, 1, 0, 0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x + \\left(x - 4\\right) \\left(x - 1\\right) \\left(x + 2\\right) + 3 \\left(x - 1\\right) \\left(x + 2\\right) + 1$"
      ],
      "text/plain": [
       "x + (x - 4)*(x - 1)*(x + 2) + 3*(x - 1)*(x + 2) + 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3} - 2 x + 3$"
      ],
      "text/plain": [
       "x**3 - 2*x + 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_data=[-2,1,4,-1,3,-4]\n",
    "y_data=[-1,2,59,4,24,-53]\n",
    "\n",
    "# lista = sorted([(xi,yi) for (xi,yi) in zip(x_data,y_data)])\n",
    "# x_data = [xi for (xi,yi) in lista]\n",
    "# y_data = [yi for (xi,yi) in lista]\n",
    "\n",
    "t = ddt(x_data,y_data)\n",
    "display(sp.Matrix(t))\n",
    "p = ni(x,x_data,y_data)\n",
    "display(p)\n",
    "display(p.simplify())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation non polynomiale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit les points\n",
    "\\begin{array}{|c|ccc|}\n",
    "\\hline\n",
    "x & 0 & \\frac{\\pi}{6} & \\frac{\\pi}{3}\\\\\n",
    "\\hline\n",
    "y & 5 & 1+\\sqrt{3} & -1\\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "Soit $V[x]$ l'espace vectoriel engendré par $\\Set{\\cos(x),\\cos(2x),\\cos(3x)}$. \n",
    "\n",
    "Écrire la fonction $v$ qui interpole ces points dans la base donnée. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')\n",
    "coeffs = sp.symbols(f'a,b,c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a \\cos{\\left(x \\right)} + b \\cos{\\left(2 x \\right)} + c \\cos{\\left(3 x \\right)}$"
      ],
      "text/plain": [
       "a*cos(x) + b*cos(2*x) + c*cos(3*x)"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_vals = [0, sp.pi/6, sp.pi/3]\n",
    "y_vals = [5, 1+sp.sqrt(3), -1]\n",
    "n = len(x_vals)-1\n",
    "\n",
    "# Base non polynomiale : { cos(x), cos(2x), cos(3x) }\n",
    "v = sum(coeffs[i] * sp.cos((i+1)*x) for i in range(n+1))\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b + c = 5$"
      ],
      "text/plain": [
       "Eq(a + b + c, 5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{3} a}{2} + \\frac{b}{2} = 1 + \\sqrt{3}$"
      ],
      "text/plain": [
       "Eq(sqrt(3)*a/2 + b/2, 1 + sqrt(3))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a}{2} - \\frac{b}{2} - c = -1$"
      ],
      "text/plain": [
       "Eq(a/2 - b/2 - c, -1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eqs = [ sp.Eq( v.subs(x, x_vals[i]) , y_vals[i] ) for i in range(n+1) ]\n",
    "for eq in eqs:\n",
    "\tdisplay(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\cos{\\left(x \\right)} + 2 \\cos{\\left(2 x \\right)} + \\cos{\\left(3 x \\right)}$"
      ],
      "text/plain": [
       "2*cos(x) + 2*cos(2*x) + cos(3*x)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution = sp.solve(eqs, coeffs)\n",
    "v1 = v.subs(solution)\n",
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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