TP2_Portrait_de_phase_I.ipynb

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    "# INFO-F-305 - TP 2\n",
    "# Dessin qualitiatif - Portrait de phase I\n",
    "### Jacopo De Stefani - __[jdestefa@ulb.ac.be](mailto:jdestefa@ulb.ac.be)__"
   ]
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    "# Système linéaire, regulier, à dimensions finies - Th 5.1\n",
    "\n",
    "$\\begin{cases}\n",
    "\\dot{\\mathbf{X}}(t) & = \\mathbf{A}(t)\\mathbf{X}(t) + \\mathbf{B}(t)\\mathbf{U}(t) \\\\\n",
    "\\mathbf{Y}(t) & = \\mathbf{C}(t)\\mathbf{X}(t) \\\\\n",
    "\\end{cases}$\n",
    "\n",
    "où $\\mathbf{A}(\\cdot),\\mathbf{B}(\\cdot),\\mathbf{C}(\\cdot)$ sont des matrices continues en $T$.\n",
    "\n",
    "Si on considère le mouvement libre du système (c-à-d $\\mathbf{U}(t) = 0$ $\\forall t$), et on se concentre sur l'état, avec $\\mathbf{A}(t)$ constante, on obtient:\n",
    "\n",
    "$\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$"
   ]
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    "# Rappels Théoriques - Système du second ordre\n",
    "\n",
    "$\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}a_{11} & a_{12}\\\\\n",
    "a_{21} & a_{22}\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "### Equation caractéristique\n",
    "\n",
    "$\\det(A-\\lambda I) = \\lambda^{2}-\\tau\\lambda+\\Delta=0$\n",
    "\n",
    "$\\lambda_{1,2} = \\frac{\\tau \\pm \\sqrt{\\tau^2 - 4 \\Delta}}{2}$\n",
    "\n",
    "où:\n",
    "- $\\tau=a_{11}+a_{22}=tr(A)$\n",
    "- $\\Delta=a_{11}a_{22}-a_{12}a_{21}=\\det(A)$"
   ]
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    "# Cas 1 - Racines réelles et distinctes - $\\lambda_1,\\lambda_2$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\lambda_1 t} \\mathbf{v_1} $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\lambda_2 t} \\mathbf{v_2} $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}1 & 3\\\\\n",
    "3 & 1\\end{bmatrix}\\mathbf{x}$"
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     "text": [
      "A =\n",
      "\n",
      "   1   3\n",
      "   3   1\n",
      "\n",
      "v =\n",
      "\n",
      "  -0.70711   0.70711\n",
      "   0.70711   0.70711\n",
      "\n",
      "lambda =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "  -2   0\n",
      "   0   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = [1 3; 3 1]\n",
    "[v, lambda] = eig(A)"
   ]
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   "source": [
    "# Cas 2 - Racines réelles et multiples - $\\lambda=\\lambda_1=\\lambda_2$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\lambda t} \\mathbf{v_1} $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\lambda t} (\\mathbf{v_2} + t\\mathbf{v_1}) $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}3 & -4\\\\\n",
    "1 & -1\\end{bmatrix}\\mathbf{x}$"
   ]
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     "text": [
      "A =\n",
      "\n",
      "   3  -4\n",
      "   1  -1\n",
      "\n",
      "v =\n",
      "\n",
      "   0.89443   0.89443\n",
      "   0.44721   0.44721\n",
      "\n",
      "lambda =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   1   0\n",
      "   0   1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = [3 -4; 1 -1]\n",
    "[v, lambda] = eig(A)"
   ]
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   "source": [
    "# Cas 3 - Racines complexes et conjuguées - $\\lambda_{1,2} = \\alpha \\pm i\\beta$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières - $\\mathbf{v_{1,2}} = \\mathbf{u} + i \\mathbf{v}$\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\alpha t} (\\cos(\\beta t)\\mathbf{u} - \\sin(\\beta t)\\mathbf{v} ) $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\alpha t} (\\sin(\\beta t)\\mathbf{u} + \\cos(\\beta t)\\mathbf{v}) $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}0 & 4\\\\\n",
    "-1 & 0\\end{bmatrix}\\mathbf{x}$"
   ]
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     "text": [
      "A =\n",
      "\n",
      "   0   4\n",
      "  -1   0\n",
      "\n",
      "v =\n",
      "\n",
      "   0.89443 + 0.00000i   0.89443 - 0.00000i\n",
      "   0.00000 + 0.44721i   0.00000 - 0.44721i\n",
      "\n",
      "lambda =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   0.0000 + 2.0000i                  0\n",
      "                  0   0.0000 - 2.0000i\n",
      "\n"
     ]
    }
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   "source": [
    "A = [0 4; -1 0]\n",
    "[v, lambda] = eig(A)"
   ]
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   "source": [
    "# Mouvement et trajectoire\n",
    "\n",
    "### Mouvement\n",
    "Ensemble des paires $\\{(t,x(t))\\}$ pour un système $\\mathbf{X}(t)=\\varphi(t,t_0,\\mathbf{X_{t_0}},u(\\cdot))$ \n",
    "\n",
    "### Trajectoire\n",
    "Ensemble des valeurs $\\{x(t)\\}$ pour $t\\geq t_0$ pour un système $\\mathbf{X}(t)=\\varphi(t,t_0,\\mathbf{X_{t_0}},u(\\cdot))$\n",
    "\n",
    "### Calcul d'une trajectoire\n",
    "1. Calcul équation solution générale de $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$\n",
    "2. Détermination $c_1$ et $c_2$ dans la solution générale en fonction de $\\mathbf{X}(0)$\n",
    "3. Calcul de la trajectoire pour différent valeurs de $t$"
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   "source": [
    "# Stabilité\n",
    "\n",
    "### Stabilité asymptotique\n",
    "Si le mouvement libre du système (c-à-d en absence d'entrée $\\mathbf{U}(t)$) tends vers l'origine pour chaque valeur de la condition initiale.\n",
    "\n",
    "### Stabilité simple\n",
    "Si le mouvement libre du système (c-à-d en absence d'entrée $\\mathbf{U}(t)$) est limité pour chaque valeur de la condition initiale.\n",
    "\n",
    "### Instabilité\n",
    "S'il existe au moins une condition initiale telle que le mouvement libre du système (c-à-d en absence d'entrée $\\mathbf{U}(t)$) ne soit pas limité."
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    "# Stabilité et valeurs propres\n",
    "\n",
    "### Stabilité asymptotique - Th 5.3\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est asymptotiquement stable si la partie réelle de tous les valeurs propres de A est negative.\n",
    "\n",
    "### Stabilité simple - Th 5.4\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est (simplement) stable si la partie réelle de tous les valeurs propres de A est negative ou nulle et celles ayant partie réelle nulle ont une multiplicité égale à 1. \n",
    "\n",
    "\n",
    "### Instabilité - Th 5.5\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est instable s'il existe soit une valeur propre de A avec partie réelle positive soit une valeur propre ayant partie réelle nulle et une multiplicité supérieure à 1. "
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   "source": [
    "# Points d'équilibre\n",
    "\n",
    "### Definition\n",
    "Un point d’équilibre est un point où la trajectoire coincide avec la condition initiale. \n",
    "\n",
    "- Si $\\det(\\mathbf{A}) \\neq 0$ alors le seul état d’équilibre est (0, 0) sinon il en existe aussi d’autres.\n",
    "\n",
    "### Noeud stable\n",
    "Si les valeurs propres de $\\mathbf{A}$ sont réelles et négatives.\n",
    "\n",
    "### Noeud instable\n",
    "Si les valeurs propres de $\\mathbf{A}$ sont réelles et positives.\n",
    "\n",
    "### Selle\n",
    "Si les valeurs propres de $\\mathbf{A}$ sont réelles et ayant signe discorde.\n"
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   "source": [
    "# Exercice 1 - Noeud stable\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} -2 & 1 \\\\ 1 & -2 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer valeurs propres\n",
    "2. Calculer vecteurs propres\n",
    "3. Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "4. Dessiner les vecteurs vitesse pour les points suivants (en normalisant leurs tailles):\n",
    "    - $(1,1),(-1,-1)$ et $(-1,1),(1,-1)$\n",
    "    - $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$"
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     "text": [
      "A =\n",
      "\n",
      "  -2   1\n",
      "   1  -2\n",
      "\n",
      "V =\n",
      "\n",
      "   0.70711   0.70711\n",
      "  -0.70711   0.70711\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "  -3   0\n",
      "   0  -1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. et 2. - Calcul valeur propres et vecteurs propres\n",
    "A = [-2 1; 1 -2]\n",
    "[V,L] = eig(A)"
   ]
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     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#3. Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "line_range = -1.5:.1:1.5;\n",
    "line_1 = (V(2,1)/V(1,1)) * line_range;\n",
    "line_2 = (V(2,2)/V(1,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,line_1,\"linewidth\",10);\n",
    "plot(line_range,line_2,\"linewidth\",10);\n",
    "quiver([0;0],[0;0],V(1,:),V(2,:),\"linewidth\",10,\"color\",\"k\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "  -1\n",
      "  -1\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   1\n",
      "   1\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   3\n",
      "  -3\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -3\n",
      "   3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 4.a Dessiner les vecteurs vitesse pour les points suivants (en normalisant leurs tailles) $(1,1),(-1,-1)$ et $(-1,1),(1,-1)$\n",
    "point_sequence = [[1,1];[-1,-1];[-1,1];[1,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\")\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "   1\n",
      "  -2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -2\n",
      "   1\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -1\n",
      "   2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   2\n",
      "  -1\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   0.00000\n",
      "   1.50000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 4.b Dessiner les vecteurs vitesse pour les points suivants (en normalisant leurs tailles) $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$\n",
    "point_sequence = [[0,1];[1,0];[0,-1];[-1,0];[-0.5,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAAsTAAALEwEAmpwYAAAAHXRFWHRTb2Z0d2FyZQBHUEwgR2hvc3RzY3JpcHQgOS4xNnO9PXQAABZ0SURBVHic7d09bttY2wZg6sPUyQasdlxIdQC9K5DqAHYbF0nrwm+dIr2A9CrcB3DaeAXSBuLCtbyBZAP6CmI4ehVZlsW/83NdxcBWYg6pQz73cw5lZrDZbAoA6Nv/9b0DAFAUAgmAQAgkAIIgkAAIgkACIAh/1fz5+/v7h4eHm5ub7RffvXs3Go2KohiPxzt/BAB71Qqkq6ur5XL56dOn7Refnp5Go9Ht7W29HQMgL7WW7G5vb3fSqCiK9Xr99u3bz58/z+fz379/19k+APlo/h7Sr1+/hsPhbDZ78+bN1dVV49sHIEl17yH9aTqdTqfToigmk8n9/f3ev3N+ft74/xeAQDw+Pp7wU80H0mKxGI/Hk8nk8F87bXdjNxgMsn1Wk2Pvey/64dj73otOlYd88pSjyUBarVYfPnz4/v379fX1bDb7+fPn5eXl4R/JcMAAUlWznreVB6vVajgcnp2d7f3T8/NzM6TcOPa+96Ifjr3vvejByRW++SW70otLdgCkoanoDeVJDYPBYDAY9L0XrcuzXSo59jw59hw0daRtzZBeK5+RA2CvUGZIAGQuxEDKYe0OgB0hBpLlO4AwtTphCDGQKqZKAEFpdcIQdCCZKgHkI+hAAiAE3axXRRNIlu8A+tLNelU0gWT5DiBt0QRSxVQJIEnxBZKpEkCS4gskANrT4ypUxIFk7Q6gcT2uQkUcSNbuAFIScSABkBKBBEAQBBJApkK7E59aIIX2/gIEK7Q78akFUmjvLwBHSi2QADgs2JUkgQSQl2BXkgQSQBaCnRhVBBJAFoKdGFUEEgBBEEgAyQp/mW5bXoEU19gA1BT+Mt22vAIprrEBOE2kzXdegQSQg0ibb4EEQBAEEkAiIl2pqwik6IcQoBTpSl1FIEU/hABpEEgAEUtpjUcg/SulcQUykdIaj0D6V0rjCqQtyQZaIO2R5EgDKUmygRZIeyQ50gCBE0gAcUh+8UYgvSD5MwCIRfKLNwLpBcmfAQCBEEjHMlUCepFP8RFIxzJVAnqRT/ERSAAhymdiVBFIr5bhWQJ0L5+JUUUgvVqGZwlABwQSQCgyX4ARSLVkfvYAzcp8AUYg1ZL52QM0QmtbEkjNcD4BJ9PalgRSM5xPADUJJIB+WFnZIZCa5yQDjmFlZYdAap6TDOAEAgmgO1ZQDhBILXLmATusoBzQViDd39/P5/OWNh4LZx4lrQnOgWO0EkhXV1fX19dtbDlSzsVsDQaDwWCw2WzKL/reHXqjPT1GK4F0e3v76dOnNrYcKedinsooKke//EImwQHuIQG0Qv/xWr0F0mBLX/vQi9yOl+Kfs73vvaBrWS2NNFLSewukzZa+9qEXuR0vFZlEwhop6ZbseqM8Ja/6LEN1iWpHcuDSPtlfLW335uampS0nQ23KQTnKVYXaDidSZYhPZoYErdtex9A+p8rI1ieQ+uc8zoTGOW3Gtz6B1D/ncW60ILCXQILuWLhLjHFslkAKi/M7eSbEKTGazRJIYXF+50PzES9j1xKBFChnfMK0HbEzgi0RSIFyxqdt5/eTgEIgQb9kUkQMVtsEUgRcBkkyCY6OIWubQIqAyyBVFu5gm0CC/skkKARSXJSt9Jj+QkUgxUTxSpKFuwAZjl4IpCi5WpK0/a9UGOJ+af56IZCi5GpJzM6AmjORJ4EEARFC5EwgRU8Ji9fgH4UHgYNASoDlu3jthJChJHMCKR066xjtnRgZSvIkkNKhv47U3kzyuQYyJJCgf5vNZqefEEVt8w4HSCAlyJUWKXPcLnm3AySQEuRKi5exI2cCCcLy5/IdZEIgQYhkEhkSSBAoH7RrivcwFgIpF67JGFm+a4T3MBYCKReuSSBwAglIk1WB6AgkIE1WBaIjkICkmBjFSyABSTExipdAAiAIAgmInmW6NAgkisL1TOQs06VBIFEUrmcgAAIJgCAIJACCIJCAyLjlmSqBxLNc9oTJLc9UCSSe5bIHuiSQgAiYr+dAIPEytYDema/nQCDxMrWAvmiGsiKQeAXVgY5phrIikHgF1QFoj0ACwmIini2BxIlUDVpiIp4tgcSJVA2gWQKJukyVaIQTCYFEXaZKNMKJhEAC+mRiREUg0ZjBYKC48FomRlT+6nsHSIfKAtRhhgR0zUyavQQSrVBxOMBkmr1qLdnN5/PlclkUxZcvX0ajUfX6u3fvym/H4/HNzU3NXSRGKg5/GgwGTgwOOD2QVqvVer2+u7tbrVaLxeLr16/l609PT6PR6Pb2tqE9JG5qEBVnAoedvmS3XC7LadBkMinnSaX1ev327dvPnz/P5/Pfv383sI/ETA0CjlTrHtJ4PC6/2F6v+/Xr13A4nM1mb968ubq6qrV3QOT8MgDHqxVI6/W6/OLh4aF6cTqd3tzcTCaTjx8/HvjZwZY6+0BEjHWGNpuNWXIOGinppwfSaDQqA+np6Wk4HFavLxaL1Wr14o9vtpy8D8TFWEOqGinpp3+oYTqdLhaLoiiWy2U5GVqtVh8+fPj+/fv19fVsNvv58+fl5eXJ2wfi5cMsnKDuSbNarYbD4dnZ2ZGvl87Pzx8fH+v8f4maagUJO7nC13100GQyedXrUFi7S5dWgzo8qYE++ZhDYqQRdQgk+qR+ARWBBNRimktTBBKhUNciZZpLUwQSoVDX4qKBoHECieCodFHQQNA4gURwVDrIk0ACXsH8lfYIJMLl2bsBMn+lPXWf1ADtUfsgK2ZIwAvMU+mGQCIOamKPTFXphkAiDmpi9zQBdEwgERlVsjOaADomkIiMKgmpEkjA/zAHpS8CiYgpnW0wB6UvAomIKZ2QEoFECkyVIAECiRSYKkECBBLky8ySoAgkkqLCvoqZJUERSCRFhYV4CSQAgiCQAAiCQIIsuLtG+AQS6VOLC3fXiIFAIn1qMURBIEHKzA6JiEAiIxlWZ7NDIiKQyIjqDCETSAAEQSABEASBBInI8A4ZiRFI5C6ZOu4OGbETSOROHYdACCSIWzIzPBBIEDczPJIhkCBKJkakRyDBHuGXexMj0iOQYA/lHronkCAa4c/boA6BBIcElQHmbaRNIMEhIWRAUKEI7fmr7x2AOAwGg77CKYRQjNp2onszQyaQ4CgKWbw2m02VSQemm4a4d5bsIESW6Zp1TNgMtnSwS/xJIMGrdVCwdOuNO/CWbjYbb3gILNnBqylekSoH7s9+onzFsPbODAlO1/hUyWJRB7aDZ/tr63W9E0hwusZ7ak16N6r3uZob/ZlM/exZ3gQS9E/5695OAhXPxJKh6ZJAggbULFsmRr3YTqBqBDf/qP6aZOqMQIIGSJR4PTd2zyVTV/uVI5+yg370+OgHdhweiJ3P5m3PpdresdyYIUHDjmyilbO4mDB1oJVAms/n79+/f//+/cPDQxvbj5czOAeHk8YJELsj7zC52E/QfCCtVqv1en13d/ff//53sVg0vv1IlWdneSo7TTOxd6BNjNJweMK0fbG73o/XfCAtl8vRaFQUxWQyWS6XjW8/XtW5K5MyIXtycHgdzznwKq0s2Y3H4/KLMpnYvn0tivJk3NN2YMKkAT1eK4G0Xq/LLw7cQ8rzwbrlwW7/F0hJmUkZTowaKenNB9JoNCoD6enpaTgcPvfXNlsa34fQVC2ST+lkK4fznG3VxZ7J5/sbKenN/x7SdDotP8uwXC4/fvzY+PbjtX1ebvb9i2E5nLVZyaQSsaO8up97sjgHtPKLsXd3d6vV6vLy8uzsrI3tx2j77NyZ1EumVO0dRymVg+1Fkb73JSZtPalhMpm0tOWo7T07n0smp3KkDkeOYc2EgT6BJzUExCMd03BkJTKysMOz7ILz2gmT6VSkDBnsMEMK16smTNrtfnn/oT6BFLoXH+noV25DUHO6Y+ygEEgROTBh2s4kpS1Glu+gEEjROfyEkuqVfnYuP42/1caOnAmkWO1Npr1f057GZzamSuRMIEVpZ73uuV/AFEst8cZCGwRS3F78XSWlsw0dzGMMHBnye0hRem6lbi/PqomRISNDAil6ByrX9q/WKnA1eQ+hbQIpZQpog3p8M2UhmXAPCQ4J4V6ONCITAgkOCSoMQkhHaI9AgmgElY7QOIEEe5iLQPcEEuwR/lxEZJIegQRRCj8y4bUEEgBBEEgQN2t3JEMgkbvYC7q1O5IhkMhdMgU99mQFgQSJSCZZyZZAAiAIAgkSZPmOGAkkSJDlO2IkkCBlpkpERCBBykyViIhAIn1mCRAFgUT6zBIKqUwMBBJkQSoTPoEEQBAEEgBBEEgkxZ0SiJdAIinulLyK/CYoAgnyJb8JikAiBTp9SIBAIgU6fUiAQCJiJkaQEoFExEyMICUCCYAgCCQiY5kOUiWQiIxlus7IfjomkIiD4tg92U/HBBJxUBwheQIJgCAIJMI1GAys1EE+BBLh2mw2VupCo0WgPQIJeAUtAu0RSARHDw55EkgERw8eBX0DjRNIhEKBi4u+gcYJJEKhwEVKJ0FTBBJQi06Cpggk+qS5BioCiT5prhOjw6COv+r88Hw+Xy6XRVF8+fJlNBpVr7979678djwe39zc1NxFIBY6DOo4PZBWq9V6vb67u1utVovF4uvXr+XrT09Po9Ho9va2oT0kQYPBQOVKmyHmBKcv2S2Xy3IaNJlMynlSab1ev3379vPnz/P5/Pfv3w3sI8lRqpJniDlBrXtI4/G4/GJ7ve7Xr1/D4XA2m7158+bq6qrW3pEWNxiAA45dsvv27duPHz+qb2ezWVEU6/V6MpkURfHw8FD90XQ6nU6nRVFMJpP7+/vnNrhdmzRTmTDQGSqvdEOfvO2S/vfff5+2kWMD6eLi4uLiYvuV+/v7Moeenp6Gw2H1+mKxGI/HZVAd4ASFHLjSM7E90Ofn56dt5PQPNUyn08ViURTFcrn8+PFjURSr1erDhw/fv3+/vr6ezWY/f/68vLw8efukwc1t4Eh1i8VqtRoOh2dnZ0e+Xjo/P398fKzz/wWiozvJxMkVvtbvIRVF8dzS3ItLdqRN6eFPTgkO86QGWqH0cIDPW7KXQAK6pl9hL4FEYwaDgc4XOJlAojGbzUbny2tpYqgIJKBPmhgqAom6dLhAIwQSdelwaYTOBoHEiZQPmqWzQSBxIuWDluh1siWQgLDodbIlkHgFrSvQHoHEK2hd6ZgeKCsCiZcpCvRFD5QVgcTLFAV6pyvKgUACIqAryoFA4ll6UqBLAoln6UkJkIfKJ6zuvxgL0CV9UsLMkPgfek+gLwKJ/6H9BPoikCgKEyMgAAKJojAxInI6qjQIJCB6Oqo0CKSs6SuBcAikrOkrSY82K14CiY4oE3RDmxUvgQSkSQ8UHYFEF8rSoEDQJVOl6AikXAgDIHACKReBdIvx5qJnesbLwMVCING6lMpBSseSj0C6MV4kkOhapDW9KmqR7j+ETyDRrrJ8l9U8mUbV8h20QSAlSK3shvcZmiWQEhTOROTPkl3uWzKlPJkDyZCxC5BAonXhBGQbLN9FKu3TMlICKR2xlMV4J0kHSliMhwOhEUjpCK3j2/44Q2Kqg9psNj59B00RSLTlcBSlEVQ7oSuToA6BRIueS50E0mjnEBL7XDv0QiDBiXZuhkkjqEkgRcnSUF/2po7hgEYIpChpxnu0/eYbiFRpMnohkGLiIglQvJ9i5wCtRi8EUkxcJCGTSVCTQIK6NArQCIEUAa13+CzcQX0CKQIa8IjIpIQZ3LYJJGiGviF5hrhtAilQerF4GTs4jUAKlF4sRh5qlwnj2xKBFBYneux0Ejkwyi0RSGFxoidDb5EDo9wsgQQNs3CXDx1kswRS/5St9KhTcAKB1D/FK2G6jXwY6/raCqT7+/v5fN7SxiF8232GUpUDnWV9rQTS1dXV9fV1G1tOST5FajAYlAdbfZGJ6nlCm80mt2PPmYE+WSuBdHt7++nTpza2nJJM+qmyHFf/wndZmvveqY5UR1q9Cfkce84yubTb4B5S15SkrKhNcLy/6m/i27dvP378qL6dzWYXFxcv/tR2Xc7qos3qYCmKwsQoW+XMuO+96Mj2Sf7333+ftpEGAuni4uKYBNqRzzhRynnEcz72nGU17tsHe35+ftpGGggkXpRVo7Sjmh9sf9H3TnUk52OHE7QVSDc3Ny1tOUaZl6HtD5v1vS9dy/nY2eYcOIYPNbTInYNtOV+NOR87JefAMQRSi5yCwA596gECCaA7+tQDBFLzdEAAJxBIzdMBAcfQvO4QSAD90LzuEEjN0OkA1CSQmqHTAU6moy0JpFqcRkB9OtqSQKrFaQQ0KPMeVyABhCLzHlcgvVrmLQxASwTSq2XewgDdyLD3FUgAIcqw9xVIx8qwWwFCkE/xEUjHyrBbAUKQT/ERSC/IpzcB6JdAekE+vQkQuOT7Y4EEEIfk+2OBtEfybQhAgATSHsm3IUDskuybBdK/khxgIElJ9s0C6V9JDjCQtpQ6aYEEELGUOmmBlFR/ARAvgZRUfwHkLPb2WiABJCL29jrTQIq9jwBIT6aBFHsfAXBApD13XoEU6SABvEqkPXdegRTpIAGcJq4uPK9AAshKXF24QAIgCAIJIAvhL98JJIAshL98J5AA8hLsVEkgAeQl2KlSaoEUbPIDcFhqgRRs8gOEJrQOPrVAAuBIoXXwAgmAIAgkAIIQcSCFtvoJQB0RB1Joq58ACeix1484kABoXI+9fnyBZKUOIEnxBZKVOoAkRRNIJkYAaYsmkEyMANIWTSABkLagA8kyHUA+gg4ky3QAQWl1nhBiIJkYAYSp1XlCiIFkYgSQoRADCYAMBRRIVuoAchZQIOWwUpdz6Dr2PDn2HDR1pH/V/Pn7+/uHh4ebm5vtF9+9ezcajYqiGI/HO38EQGKamk7UCqSrq6vlcvnp06ftF5+enkaj0e3t7TFbGAwGOUyMAHhRrSW729vbnTQqimK9Xr99+/bz58/z+fz379+HtyCNAJJRc+2u+XtIv379Gg6Hs9nszZs3V1dXjW8fgDDVnGMcu2L27du3Hz9+VN/OZrOLi4uiKObzeVEUz90oev/+/d3d3Z+vn5+fn7KzAMTg8fHxhJ869h7SxcVFmUAvWiwW4/F4Mpkc+Dun7SsACav7Kbttq9Xqw4cP379/v76+ns1mP3/+vLy8bHD7ACSsrQ+5rVar4XB4dnbWxsYBSI9PXQMQhICe1ABAzpq8h3QMT3Yo7X0fUjWfz5fLZVEUX758KQe6lMm4P3f4STpwsJkMdyWra7xoqLZ3Gkj1n+yQhr3vQ6pWq9V6vb67u1utVovF4uvXr+XrmYz7c4efpAMHm8lwV7K6xovmanunS3b1n+yQhr3vQ6qWy2XZIk0mk7J3LmUy7s8dfpIOHGwmw13J6hovmqvt/d9D8mSH5I3H4/KL7TWcfMZ97+Gn6rmDzWe4qZww6G0t2T33ZIc/TafT6XRaFMVkMrm/v29pf/py/PuQhj+PtyiK9Xpd/qL0w8ND9Udpj/u2vYefqucONp/hpnLCoLcVSM0+2SFex78PafjzeMtbnUVRPD09DYfD6vW0x70yGo32Hn6SDhxsJsPNthMGvetP2W3zZIccTKfTxWJRFMVyufz48WM56I+Pj//5z39yGPedw+97d9r158HmNtyUTq7tofxirCc7pO258c1k3DM5zNKBg83qfaD0qkEPJZAAyFz/n7IDgEIgARAIgQRAEAQSAEEQSAAE4f8B4WdtjbXtwFwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "hold on;\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-1.5:.1:1.5;\n",
    "x2range=-1.5:.1:1.5;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Line plot\n",
    "plot(line_range,line_1,\"linewidth\",10,\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linewidth\",10,\"color\",\"k\");\n",
    "grid on;\n",
    "axis tight;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercice 2 - Noeud instable\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} 2 & 1 \\\\ 2 & 3 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer valeurs propres\n",
    "2. Calculer vecteurs propres\n",
    "3. Dessiner les droites correspondants aux vecteurs propres et les sense des trajectoires associés\n",
    "4. Dessiner les vecteurs vitesse pour les points suivants (en normalisant leurs tailles):\n",
    "    - $(0.5,1),(-0.5,-1)$ et $(-1,1),(1,-1)$\n",
    "    - $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   2   1\n",
      "   2   3\n",
      "\n",
      "V =\n",
      "\n",
      "  -0.70711  -0.44721\n",
      "   0.70711  -0.89443\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   1   0\n",
      "   0   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. et 2. - Calcul valeur propres et vecteurs propres\n",
    "A = [2 1; 2 3]\n",
    "[V,L] = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#3. Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "line_range = -1.5:.1:1.5;\n",
    "line_1 = (V(2,1)/V(1,1)) * line_range;\n",
    "line_2 = (V(2,2)/V(1,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,line_1,\"linewidth\",10);\n",
    "plot(line_range,line_2,\"linewidth\",10);\n",
    "quiver([0;0],[0;0],V(1,:),V(2,:),\"linewidth\",10,\"color\",\"k\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "   2\n",
      "   4\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -2\n",
      "  -4\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -1\n",
      "   1\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   1\n",
      "  -1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#4.a Dessinez les vecteurs vitesse pour les points suivants (en normalisant leurs tailles) $(0.5,1),(-0.5,-1)$ et $(-1,1),(1,-1)$\n",
    "point_sequence = [[0.5,1];[-0.5,-1];[-1,1];[1,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "   1\n",
      "   3\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   2\n",
      "   2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -1\n",
      "  -3\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -2\n",
      "  -2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -2\n",
      "  -4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 4.b Dessiner les vecteurs vitesse pour les points suivants (en normalisant leurs tailles) $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$\n",
    "point_sequence = [[0,1];[1,0];[0,-1];[-1,0];[-0.5,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\");\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-3:.1:3;\n",
    "x2range=-3:.1:3;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Line plot\n",
    "plot(line_range,line_1,\"linewidth\",10,\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linewidth\",10,\"color\",\"k\");\n",
    "grid on;\n",
    "axis tight;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercice 3 - Selle\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} 5 & 9 \\\\ 6 & 2 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer valeurs propres\n",
    "2. Calculer vecteurs propres\n",
    "3. Dessiner les droites correspondants aux vecteurs propres et les sense des trajectoires associés\n",
    "4. Dessiner les vecteurs vitesses pour les points suivants (en normalisant leurs tailles):\n",
    "    - $(1,\\frac{2}{3}),(-1,-\\frac{2}{3})$ et $(-1,1),(1,-1)$\n",
    "    - $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   5   9\n",
      "   6   2\n",
      "\n",
      "V =\n",
      "\n",
      "   0.83205  -0.70711\n",
      "   0.55470   0.70711\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   11    0\n",
      "    0   -4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. et 2. - Calcul valeur propres et vecteurs propres\n",
    "A = [5 9; 6 2]\n",
    "[V,L] = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#3. Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "line_range = -1.5:.1:1.5;\n",
    "line_1 = (V(2,1)/V(1,1)) * line_range;\n",
    "line_2 = (V(2,2)/V(1,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,line_1,\"linewidth\",10);\n",
    "plot(line_range,line_2,\"linewidth\",10);\n",
    "quiver([0;0],[0;0],V(1,:),V(2,:),\"linewidth\",10,\"color\",\"k\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "   11.0000\n",
      "    7.3333\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -11.0000\n",
      "   -7.3333\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   4\n",
      "  -4\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -4\n",
      "   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 4.a Dessinez les vecteurs vitesses pour les points suivants (en normalisant leurs tailles) $(1,2/3),(-1,-2/3)$ et $(-1,1),(1,-1)$\n",
    "point_sequence = [[1,2/3];[-1,-2/3];[-1,1];[1,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity_vec =\n",
      "\n",
      "   9\n",
      "   2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "   5\n",
      "   6\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -9\n",
      "  -2\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -5\n",
      "  -6\n",
      "\n",
      "velocity_vec =\n",
      "\n",
      "  -11.5000\n",
      "   -5.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 4.b Dessiner les vecteurs vitesses pour les points suivants (en normalisant leurs tailles) $(0,1),(1,0),(0,-1),(-1,0),(-0.5,-1)$\n",
    "point_sequence = [[0,1];[1,0];[0,-1];[-1,0];[-0.5,-1]]'; #cbind like\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec\n",
    "    velocity_norm = velocity_vec/norm(velocity_vec);\n",
    "    velocity_sequence = [velocity_sequence,velocity_norm];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "hold on;\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,line_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linestyle\",\":\",\"color\",\"k\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-1.5:.1:1.5;\n",
    "x2range=-1.5:.1:1.5;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Line plot\n",
    "plot(line_range,line_1,\"linewidth\",10,\"color\",\"k\");\n",
    "plot(line_range,line_2,\"linewidth\",10,\"color\",\"k\");\n",
    "grid on;\n",
    "axis tight;"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "4.4.1"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}