TP6_Simulation_Ordre_2.ipynb

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   "source": [
    "# INFO-F-305 - TP 6\n",
    "# Simulation à l'aide d'Octave\n",
    "# Système d'ordre 2\n",
    "### Jacopo De Stefani - __[jdestefa@ulb.ac.be](mailto:jdestefa@ulb.ac.be)__\n",
    "### Github: https://github.com/jdestefani/ulb-infof305\n",
    "### Slides: https://jdestefani.github.io/ulb-infof305"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "# Comment installer Octave / Jupyter?\n",
    "\n",
    "- **Octave**: Plus d'informations ici: https://www.gnu.org/software/octave/\n",
    "- **Jupyter Notebook**: https://jupyter.readthedocs.io/en/latest/install.html\n",
    "- **Octave kernel for Jupyter**: https://github.com/Calysto/octave_kernel\n",
    "- **Symbolic package (Octave forge)**: https://octave.sourceforge.io/symbolic/index.html\n",
    "\n",
    "\n",
    "# Comment utiliser les notebooks?\n",
    "\n",
    "1. Installer Octave, Jupyter Notebook et le kernel Octave pour Jupyter.\n",
    "2. Se déplacer dans le dossier où les notebooks sont stockés.\n",
    "3. Démarrer ```jupyter notebook``` \n",
    "4. Selectionner le notebook dans l'interface web. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "# Système du second ordre - Bases\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",
    "1. Dessin d'une trajectoire\n",
    "2. Dessin des droites invariantes\n",
    "3. Dessin des isoclines\n",
    "4. Dessin du portrait de phase\n",
    "5. Dessin du diagramme tr(A) - det(A)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
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       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function [t,x] = system_simulation(A)\n",
    "    ode_sys = @(t,x) [A(1,1)*x(1)+A(1,2)*x(2);A(2,1)*x(1)+A(2,2)*x(2)]; # Définition système\n",
    "    [t,x] = ode23 (ode_sys, [0, 10], [2, 0]); # Résolution système\n",
    "endfunction\n",
    "\n",
    "A = [-5 -3; 1 -1];\n",
    "[t,x] = system_simulation(A);\n",
    "plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "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": [
    "plot(x(:,1),x(:,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CCLPZ7J///Ofl5eXnz59Xvff5lXq3CjpNk4hfLSfwOoM0Go3KIC2XyyRJXpb//PmzKIrFYpGmaY2r6yu/aOCvNIkhqPNedpPJpPwtQ5ZlFxcXIYQ8z8/Pz8/OzoqimE6n5csWi0WNK4WBKJvkywo9tlf7/Fie50mSHB4ebvSuo6Ojh4eHereko5x0+IDDg/htfT6v/w9j0zTdtEbAmszd0WPu1AAdo0n0lSBB92gSvSRI0EmaRP8IUlxcsmZ9mkTPCBJ0mCbRJ4IE3aZJ9IYgQedpEv0gSNAHmkQPCBL0hCbRdYIE/aFJdJogRcRvvqlOk+guQYK+0SQ6SpCghzSJLhIk6CdNonMECXpLk+gWQYI+0yQ6RJBi4Sd27Igm0RWCBP2nSXSCIMEgaBLxEyQYCk0icoIEQBQECQbEIImYCRIMiyYRLUGKgt980yRNIk6CBEOkSURIkGCgNInYCBIMlyYRFUGCQdMk4iFIMHSaRCQECdAkoiBI7fObb2KgSbROkIA/aRLtEiTgfzSJFgkS8P9oEm0RJOAtTaIVggS8Q5NoniAB79MkGiZIwEqaRJMECfiIJtEYQQJ+QZNohiABv6ZJNECQgLVoErsmSMC6NImdEqSWubMq3aJJ7I4gAZvRJHZEkICNaRK7IEjANjSJ2gkSsCVNol6CBGxPk6iRIAGVaBJ1ESSgKk2iFoIE1ECTqE6QgHpoEhUJElAbTaIKQQLqpElsTZCAmmkS26kapNlsdnp6enp6en9//+ap29vb2WxWPv706dN0Op1Opy9LgB7TJLbwW5U353leFMXNzU2e5/P5/MePHy9PTafTLMsuLy9DCMvlcjQaLRaLqhsLdEfZJDezZ32VRkhZlo1GoxBCmqZZlr1+arFYlDUKIRRFcXBw8PXr19ls9vT0VGWNQIcYJ7GRqlN24/G4fFCW6V2Pj49JkpycnOzv70+n01Uv23ul4lYBkdCkgajlBF41SEVRlA/+eg3pxWQy+fLlS5qmFxcXH/xTz69U3CogHpo0BLWcwCsFaTQalUFaLpdJkqx62Xw+z/O8yoqATtMk1lHpRw2TyWQ+n4cQsiy7uLjI8/z8/Pzh4eHNy46Pj6+urk5OTu7u7s7OzqqsEegov3Hgl/aqz4/leZ4kyeHhYZWXHR0d/bVkQ+AjyqA44Idg6/N5DX8Ym6bpL2u0/suAHjN3xwfcqQFolCaxiiABTdMk3iVIQAs0ib8SJKAdmsQbggS0RpN4TZCANmkSLwQJaJkmURIkoH2aRBAkIBKahCABsdCkgRMkICKaNGSCBMRFkwZLkIDoaNIwCRIQI00aIEFqk/83DHxAk4ZGkIB4adKgCBIQNU0aDkECYqdJAyFIQAdo0hAIEtANmtR7gtQmHzDYiI9MvwkS0CWa1GOCBHSMJvWVIAHdo0m9JEhAJ2lS/wgS0FWa1DOCBHSYJvWJIAHdpkm9IUhA52lSPwgS0Aea1AOCBPSEJnWdIAH9oUmdJkhAr2hSdwkS0Dea1FGCBPSQJnWRIAH9pEmdI0hAb2lStwgSAFEQJKDPDJI6RJCAntOkrhAkoP80qRMECRgETYqfIAFDoUmRE6SW+YRAk3ziYiZIwLBoUrQECRgcTYqTIAFDpEkREiRgoDQpNoIEDJcmRUWQAIiCIAGDZpAUD0EChk6TIiFIAJoUBUECCEGTIiBIAH/SpHbVHKTZbHZ6enp6enp/f//mqdvb29lsVu/qAOiNOoOU53lRFDc3N9fX1/P5/PVT0+n06uqqxnUB7IJBUovqDFKWZaPRKISQpmmWZa+fWiwWl5eXNa4LYEc0qS01T9mNx+PyQVkmgC7SpFbUHKSiKMoHf72G9Et7/1XvJgFsQZM2Vf0cXmeQRqNRGaTlcpkkyaZvf/6vGjcJgGZUP4fXGaTJZJJl2Ww2u7q6uri4CCHkeX50dFTjKgAaY5DUsL3aRyR5nidJcnh4uNG7jo6OHh4e6t2Srti7/s/z9z/a3grgfT6hm9r6fF7/H8amabppjQCiZZzUGHdqAPgFTWqGILXPsQ7x8zltgCABEAVBAliLQdKuCRLAujRppwQJYAOatDuCBLAZTdoRQQIgCoIEsDGDpF0QJIBtaFLtBAlgS5pUL0EC2J4m1UiQAIiCIEXBlyzoLp/fuggSQFWaVAtBAqiBJlUnSAD10KSKBAmgNppUhSABEAVBAqiTQdLWBAmgZpq0HUECqJ8mbUGQAHZCkzYlSABEQZBi4csU9I/P9UYECWCHNGl9ggSwW5q0JkEC2DlNWocgARAFQQJogkHSLwkSQEM06WOCBNAcTfqAIAE0SpNWESSApmnSuwQJgCgIEkALDJL+SpAi4gCFQfGRf0OQAFqjSa8JEkCbNOmFIAEQBUECaJlBUkmQANqnSUGQACKhSYIEEIuBN0mQAIiCIMVl4N+PgCGfBAQJIC6DbZIgAURnmE0SJIAYDbBJggQQqaE1SZAAiIIgAcRrUIMkQQKI2nCaJEgAsRtIkwQpOgM58oCNDOHMIEgAROG3iu+fzWZZloUQvn37NhqNVi3/9OlT+ex4PP7y5UvFlQIMUDlIev7+R9sbsiuVgpTneVEUNzc3eZ7P5/MfP368u/z6+no0Gi0Wizo2GGC4+t2kSlN2WZaV4540Tcvx0LvLi6I4ODj4+vXrbDZ7enqquMUAQ9bji0lVryGNx+Pywev5ujfLHx8fkyQ5OTnZ39+fTqer/qm9VypuFUCPRdikWk7gVYNUFEX54P7+ftXyyWTy5cuXNE0vLi4++KeeX6m4VQD9FluTajmBVwrSaDQqw7NcLpMkWbV8Pp/neV5lRQD0XqUfNUwmk/l8HkLIsuzi4iLP8/Pz84eHhzfLkyS5uro6OTm5u7s7OzurZ8MBhq1/P3DYqz4/lud5kiSHh4cfL1/1stLR0dHDw0PFLemTnh1nwI5EeK7Y+nxe9e+QQghpmq6zfNXLANhan8ZJ7tQA0G2x/cBha4IEQBQECaDz+jFIEiSAPuhBkwQJoCe63iRBAuiPTjdJkACIgiBFqtNfc4AWdffsIUgAfdPRJgkSQA91sUmCBNBPnWuSIAH0VreaJEgAREGQAPqsQ4MkQYpXhw4jIGZdOZkIEkD/daJJggQwCPE3SZAAiIIgAQxF5IMkQQIYkJibJEgAwxJtkwQJYHDibJIgRS3OgwZgFwQJYIgi/L4rSAADFVuTBAlguKJqkiABDFo8TRIkgKGLpEmCBEAUBCl2kXxzAfothlONIAEQQgRNEiQA/tRukwQJgP9psUmCBEAUBAmA/6etQZIgAfBWK00SpA5o/acvwAA1f+YRJADe13CTBAmAKAgSACs1OUgSJAA+0liTBAmAX2imSYIEwK810CRB6ga//AZat+sTkSABEAVBAmBdOx0kCRIAG9hdkwQJgM3sqEmCBMDGdtEkQQIgCoLUGX75DUSl9pOSIAGwpXqbJEgAbK/GJgkSAJXU1SRBAqCqWpokSABEoaEgzWaz09PT09PT+/v7ZtYIQJOqD5KaCFKe50VR3NzcXF9fz+fzBtbYV375DcSs4jmqiSBlWTYajUIIaZpmWdbAGgFoxfP3P7Z+b0NTduPxuHxQlulde680s1UA1KKWE3hDQSqKonzwwTWk51ea2aouqvLtA2BHajmBNxGk0WhUBmm5XCZJ0sAaAeic3xpYx2QyKX/LkGXZxcVFA2sEoHOaCFII4ebmJs/zs7Ozw8PDZtYIQLc0FKQQQpqmja0LgM5xpwYAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFAQJgCgIEgBRECQAoiBIAERBkACIgiABEAVBAiAKggRAFASpY/b29trehG6wo9ZnX63Jjtq13yq+fzabZVkWQvj27dtoNFq1/NOnT+Wz4/H4y5cvFVcKQP9UClKe50VR3Nzc5Hk+n89//Pjx7vLr6+vRaLRYLOrYYAD6qdKUXZZl5bgnTdNyPPTu8qIoDg4Ovn79OpvNnp6eKm4xAL1U9RrSeDwuH7yer3uz/PHxMUmSk5OT/f396XRacY0A9NLGU3Z5nmdZliTJ58+fQwhFUaRpGkK4v79//bLXyyeTyWQyCSGkaXp7e7vqXz46Otp0Ywbo999/t6PWYUetz75akx21axsHKU3TsjQhhNFoVHZouVwmSfLymjfL5/P5eDx+ede7Hh4eNt0SAPpk7/n5ucr7T09Pj4+Psyy7uLg4ODg4Pz8v0/J6eZIkV1dXJycnd3d3Jycn5dAKAF6rGqQQQp7nSZIcHh5+vHzVywAg1BIkAKjOnRoAiELVOzVUseouD27rsMqqPUZwOG3r9vb2/v7enlnl3f3joFrl6enp6uqq/HvTs7OzjX8x8NySLMuurq5ePygVRXF+ft7WVsVs1R7j2eG0rfPz899///379+9tb0ik3t0/DqoP/Pvf/y531+Pj49///vdN397alN2quzy4rcMqq/YYweG0rcVicXl52fZWxOvd/eOg+kCSJMfHxyGE/f39Ld7e5jWkd+/y4LYOH1h1XwyCw4mmOKg+UP6h6nK5nE6nW3zXafQa0jp3eVjztg7DtOq+GASHE01xUH1sNpvd3d1dXl5+fDOEdzUapHXu8rDObR2GadUeIzicaJCD6gM/f/4simLr/7dDa7+ym0wm8/k8hFDezSHP8/IuD8fHxy+3dTg7O2tr8yL0Zo+1vTlxcTixaw6qddzd3RVF8TKTuWmZWv7D2DXv8sALe+YDDica46DaBXdqACAK7tQAQBQECYAoCBIAURAkAKIgSABE4f8ANM/hAQMJMVkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Implémentation 2\n",
    "\n",
    "sys_str = sprintf('[%f*x(1)+%f*x(2);%f*x(1)+%f*x(2)]',A(1,1),A(1,2),A(2,1),A(2,2)); # Définition système (1)\n",
    "sys_ode = inline(sys_str,'t','x'); # Définition système (2)\n",
    "[ts,ys] = ode45(sys_ode,[0,20],[2,0]); # Résolution système\n",
    "plot(ys(:,1),ys(:,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# 2. Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "function [eigenline_1,eigenline_2,V] = compute_eigenlines(A,line_range)\n",
    "    [V,L] = eig(A);\n",
    "    eigenline_1 = (V(2,1)/V(1,1)) * line_range;\n",
    "    eigenline_2 = (V(2,2)/V(1,2)) * line_range;\n",
    "endfunction\n",
    "\n",
    "function [line_range,eigenline_1,eigenline_2] = plot_eigenlines(A)\n",
    "    line_range = -1.5:.1:1.5;\n",
    "    [eigenline_1,eigenline_2,V] = compute_eigenlines(A,line_range);\n",
    "    hold on;\n",
    "    plot(line_range,eigenline_1,\"linewidth\",10);\n",
    "    plot(line_range,eigenline_2,\"linewidth\",10);\n",
    "    quiver([0;0],[0;0],V(1,:),V(2,:),1.5,\"linewidth\",10,\"color\",\"k\");\n",
    "    legend(\"v_1\",\"v_2\",\"location\",\"south\");\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "[line_range,eigenline_1,eigenline_2] = plot_eigenlines(A);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# 3. Calculer les isoclines\n",
    "function [isocline_1,isocline_2] = compute_isoclines(A,line_range)\n",
    "    isocline_1 = -(A(1,1)/A(1,2)) * line_range;\n",
    "    isocline_2 = -(A(2,1)/A(2,2)) * line_range;\n",
    "endfunction\n",
    "\n",
    "function [line_range,isocline_1,isocline_2] = plot_isoclines(A)\n",
    "    line_range = -1.5:.1:1.5;\n",
    "    [isocline_1,isocline_2] = compute_isoclines(A,line_range);\n",
    "    hold on;\n",
    "    plot(line_range,isocline_1,\"linewidth\",5);\n",
    "    plot(line_range,isocline_2,\"linewidth\",5);\n",
    "    legend(\"isocline_1\",\"isocline_2\",\"location\",\"south\");\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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": [
    "[line_range,isocline_1,isocline_2] = plot_isoclines(A);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# 4. Portrait de phase\n",
    "function [x1,x2,x1p,x2p] = plot_portrait_phase(A)\n",
    "    #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",
    "    norms=sqrt(x1p.^2+x2p.^2);\n",
    "    # Vector field plot\n",
    "    hold on;\n",
    "    quiver(x1,x2,x1p./norms,x2p./norms,0.5);\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "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": [
    "[x1,x2,x1p,x2p] = plot_portrait_phase(A);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# 4. Portrait de phase complet\n",
    "function [x1,x2,x1p,x2p] = plot_portrait_phase_complete(A)\n",
    "    #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",
    "    norms=sqrt(x1p.^2+x2p.^2);\n",
    "    \n",
    "    [eigenline_1,eigenline_2,V] = compute_eigenlines(A,x1range);\n",
    "    [isocline_1,isocline_2] = compute_isoclines(A,x1range);\n",
    "    \n",
    "    # Vector field plot\n",
    "    hold on;\n",
    "    quiver(x1,x2,x1p./norms,x2p./norms,0.5);\n",
    "    # Isoclines\n",
    "    plot(x1range,isocline_1,\"linewidth\",5);\n",
    "    plot(x1range,isocline_2,\"linewidth\",5);\n",
    "    # Vecteurs propres\n",
    "    plot(x1range,eigenline_1,\"linewidth\",5);\n",
    "    plot(x1range,eigenline_2,\"linewidth\",5);\n",
    "    legend(\"field\",\"v_1\",\"v_2\",\"isocline_1\",\"isocline_2\",\"location\",\"south\",\"orientation\", \"horizontal\");\n",
    "    \n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "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": [
    "[x1,x2,x1p,x2p] = plot_portrait_phase_complete(A);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symbolic pkg v2.7.1: Python communication link active, SymPy v1.3.\n",
      "ode_sys = (sym 2×1 matrix)\n",
      "\n",
      "  ⎡d                             ⎤\n",
      "  ⎢──(x₁(t)) = -5⋅x₁(t) - 3⋅x₂(t)⎥\n",
      "  ⎢dt                            ⎥\n",
      "  ⎢                              ⎥\n",
      "  ⎢  d                           ⎥\n",
      "  ⎢  ──(x₂(t)) = x₁(t) - x₂(t)   ⎥\n",
      "  ⎣  dt                          ⎦\n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "                  -2⋅t         -4⋅t\n",
      "  x₁(t) = - 3⋅C₁⋅ℯ     - 3⋅C₂⋅ℯ    \n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "                -2⋅t       -4⋅t\n",
      "  x₂(t) = 3⋅C₁⋅ℯ     + C₂⋅ℯ    \n",
      "\n"
     ]
    }
   ],
   "source": [
    "pkg load symbolic\n",
    "syms x1(t) x2(t);\n",
    "ode_sys = [diff(x1(t),t) == A(1,1)*x1(t) + A(1,2)*x2(t);  diff(x2(t),t) == A(2,1)*x1(t) + A(2,2)*x2(t)]\n",
    "solutions = dsolve(ode_sys);\n",
    "solutions{1}\n",
    "solutions{2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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": [
    "# Plan Tr(A)-det(A)\n",
    "\n",
    "x = -10:0.1:10;\n",
    "plot (x, 1/4*x.^2);\n",
    "hold on;\n",
    "A_vec = [[-2 1; 1 -2];[2 1; 2 3];[5 9; 6 2];[0 1; 0 1];[0 -1; 1 0];[1/3 -2; 3 -1]]; #cbind like\n",
    "i = 0;\n",
    "while i<(rows(A_vec)/2)# Column-wise iteration\n",
    "    A = A_vec(2*i+1:2*(i+1),1:2); # Get the proper submatrix\n",
    "    plot(trace(A),det(A),sprintf(\";[%d %d];o\",trace(A),det(A)))\n",
    "    i++;\n",
    "endwhile\n",
    "set(gca, \"xaxislocation\", \"origin\");\n",
    "set(gca, \"yaxislocation\", \"origin\");\n",
    "h = legend; legend(h,\"location\",\"southwest\");\n",
    "xlabel(\"tr(A)\");\n",
    "ylabel(\"det(A)\");\n",
    "box off;\n",
    "hold off;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Fuction to avoid repetition of phase portrait code\n",
    "function portrait_phase_single_x_0(A,t_range,x_0)\n",
    "    # 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);\n",
    "    # Vector field plot\n",
    "    hold on;\n",
    "    quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "    # Trajectory computation\n",
    "    sys_str = sprintf('[%d*x(1)+%d*x(2);%d*x(1)+%d*x(2)]',A(1,1),A(1,2),A(2,1),A(2,2));\n",
    "    sys_ode = inline(sys_str,'t','x');\n",
    "    # Trajectory plot\n",
    "    [t,x] = ode45(sys_ode,t_range,x_0);\n",
    "    plot(x(:,1),x(:,2))\n",
    "    grid on;\n",
    "    axis tight;\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "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": [
    "portrait_phase_single_x_0(A,[0,10],[0.5;0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "function portrait_phase_20_rand_x_0(A,t_range,x_range,y_range)\n",
    "    # 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",
    "    norms=sqrt(x1p.^2+x2p.^2);\n",
    "    # Vector field plot\n",
    "    hold on;\n",
    "    quiver(x1,x2,x1p./norms,x2p./norms,0.5);\n",
    "    \n",
    "    sys_str = sprintf('[%d*x(1)+%d*x(2);%d*x(1)+%d*x(2)]',A(1,1),A(1,2),A(2,1),A(2,2));\n",
    "    sys_ode = inline(sys_str,'t','x');\n",
    "    [x_grid,y_grid] = meshgrid(x_range, y_range);\n",
    "    for i=0:1:20\n",
    "        # Trajectory calculation\n",
    "        x_0 = [x_grid(1,randi(size(x_grid,2),1));y_grid(randi(size(y_grid,2),1),1)];\n",
    "        [t,x] = ode45(sys_ode,t_range,x_0);\n",
    "        # Trajectory plot\n",
    "        plot(x(:,1),x(:,2),sprintf(\";[%d %d];o-\",x_0))\n",
    "    end\n",
    "    grid on;\n",
    "    axis tight;\n",
    "    h = legend; legend(h,\"location\",\"southeastoutside\");\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "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": [
    "portrait_phase_20_rand_x_0(A,[0,10],-1.5:.1:1.5,-1.5:.1:1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 1 - Selle\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}1 & 3\\\\\n",
    "3 & 1\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: $\\mathbf{x}(0)=[0.5,0]$\n",
    "- Temps de simulation: $[0,1]$ \n",
    "- Fonction(s) d'entrée: $\\emptyset$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "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": [
    "portrait_phase_single_x_0([1 3;3 1],[0,1],[0.5;0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 2 - Selle\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}1 & 3\\\\\n",
    "3 & 1\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: $\\mathbf{x}(0)=[-0.5,0]$\n",
    "- Temps de simulation: $[0,1]$ \n",
    "- Fonction(s) d'entrée: $\\emptyset$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "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": [
    "portrait_phase_single_x_0([1 3;3 1],[0,1],[-0.5;0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 3 - Selle\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}1 & 3\\\\\n",
    "3 & 1\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Temps de simulation: $[0,1]$ \n",
    "- Fonction(s) d'entrée: $\\emptyset$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "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": [
    "portrait_phase_20_rand_x_0([1 3;3 1],[0,1],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 4: noeud stable\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-4 & -2\\\\\n",
    "3 & -11\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: $\\mathbf{x}(0)=[1.5,0]$ \n",
    "- Intervalle de temps de simulation $[0,1]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "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": [
    "portrait_phase_single_x_0([-4 -2;3 -11],[0,1],[1.5;0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 5: noeud stable\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-4 & -2\\\\\n",
    "3 & -11\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: $\\mathbf{x}(0)=[-1.5,-1.5]$ \n",
    "- Intervalle de temps de simulation $[0,1]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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": [
    "portrait_phase_single_x_0([-4 -2;3 -11],[0,1],[-1.5;-1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 6: noeud stable\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-4 & -2\\\\\n",
    "3 & -11\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,1]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "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": [
    "portrait_phase_20_rand_x_0([-4 -2;3 -11],[0,1],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 7: noeud instable \n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}4 & 2\\\\\n",
    "-3 & 11\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,1]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "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": [
    "portrait_phase_20_rand_x_0([4 2;-3 11],[0,1],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 8: une valeur propre nulle\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-1 & -3\\\\\n",
    "-1 & -3\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,1]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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": [
    "portrait_phase_20_rand_x_0([-1 -3;-1 -3],[0,1],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 9: centre elliptique\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}0 & 4\\\\\n",
    "-1 & 0\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,10]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "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": [
    "portrait_phase_20_rand_x_0([0 4;-1 0],[0,10],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 10: foyer stable\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-4 & 5\\\\\n",
    "-5 & 2\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,10]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "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": [
    "portrait_phase_20_rand_x_0([-4 -5;-5 2],[0,10],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 11: Noeud impropre (stable dégénéré)\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-2 & 1\\\\\n",
    "-1 & 0\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,10]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "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": [
    "portrait_phase_20_rand_x_0([-2 1;-1 0],[0,10],-2:.1:2,-2:.1:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas d'étude 12: étoile\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}-1 & 0\\\\\n",
    "0 & -1\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "\n",
    "- Conditions initiales: 20 vecteurs choisis de manière aléatoire uniforme\n",
    "dans la région $[-2,2]\\times[-2,2]$\n",
    "- Intervalle de temps de simulation $[0,10]$. \n",
    "- Fonction(s) d'entrée: $\\emptyset$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "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": [
    "portrait_phase_20_rand_x_0([-1 0;0 -1],[0,10],-2:.1:2,-2:.1:2)"
   ]
  }
 ],
 "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"
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   "window_display": false
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}