{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sympy import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_printing()\n",
    "u = Function('u')\n",
    "t, eps= symbols('t epsilon')\n",
    "omega = symbols('omega', positive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Note:** This notebook requires SymPy 1.5 to work.\n",
    "</div>\n",
    "\n",
    "Consider the following system\n",
    "\n",
    "$$\\ddot{u} + 4 u + \\varepsilon u^2 \\ddot{u} = 0 \\enspace .$$\n",
    "\n",
    "This system can be rewritten as\n",
    "$$(1 + \\varepsilon u^2)\\ddot u + 4u = 0 \\enspace ,$$\n",
    "or\n",
    "$$\\ddot u + \\frac{4u}{1 + \\varepsilon u^2} = 0 \\enspace .$$\n",
    "As a first order system it reads\n",
    "$$\\begin{pmatrix}\n",
    "\\dot u \\\\ \n",
    "\\dot v\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "v \\\\ \n",
    "-\\frac{4u}{1 + \\varepsilon u^2}\n",
    "\\end{pmatrix} \\enspace ,$$\n",
    "with Jacobian matrix\n",
    "$$J(u,v) = \\begin{bmatrix}\n",
    "0 & 1 \\\\ \n",
    "-\\frac{4(1 - \\varepsilon u^2)}{(1+ \\varepsilon u^2)^2} & 0\n",
    "\\end{bmatrix} \\enspace .$$\n",
    "This system has a fixed point in $(0,0)$, with eigenvalues\n",
    "$$\\lambda_1 = -2i,\\quad \\lambda_2 = 2i \\enspace ,$$\n",
    "and we can conclude that this fixed point is a center."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\omega^{2} u{\\left(t \\right)} + \\left(\\epsilon u^{2}{\\left(t \\right)} + 1\\right) \\frac{d^{2}}{d t^{2}} u{\\left(t \\right)}$"
      ],
      "text/plain": [
       "                          2      \n",
       " 2        ⎛   2       ⎞  d       \n",
       "ω ⋅u(t) + ⎝ε⋅u (t) + 1⎠⋅───(u(t))\n",
       "                          2      \n",
       "                        dt       "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = (1 + eps*u(t)**2)*diff(u(t), t, 2) + omega**2*u(t)\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOCAYAAAD9lDaoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVQoFW2QPRLBYBRFv2ABWAKtKitIwQ7UOmMHlEmt1BkdJaWOIo2SHbAGO4hzMCbInbl5f/e97+VFRVGELMs6IYQZFPpiRv6iU4dNuCAxSpJkDzd5nvfIrbEn4luNYAXH8AManHqHW5OK+vBs8IMjcZOGWNENdgh8thKRi1eBpit5f6LlpD8gcAUFc/x7pYjiEu4QPM/y9xwFBQE70YqvSRSmJssC44YfQWGI6ZYF+O71mkQQ4w/KAovAxhClaar6AHcm3vBmbRjT2PU5T6/wuQ+2DA8dHnsYSSe7W0SjAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ode_order(eq, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Straightforward expansion\n",
    "\n",
    "Let's take $u = u_0 +\\varepsilon u_1 + \\cdots$. Replacing this in the equation we obtain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "u0 = Function('u0')\n",
    "u1 = Function('u1')\n",
    "subs = [(u(t), u0(t) + eps*u1(t))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\epsilon^{4} \\operatorname{u_{1}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + 2 \\epsilon^{3} \\operatorname{u_{0}}{\\left(t \\right)} \\operatorname{u_{1}}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + \\epsilon^{3} \\operatorname{u_{1}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)} + \\epsilon^{2} \\operatorname{u_{0}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + 2 \\epsilon^{2} \\operatorname{u_{0}}{\\left(t \\right)} \\operatorname{u_{1}}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)} + \\epsilon \\omega^{2} \\operatorname{u_{1}}{\\left(t \\right)} + \\epsilon \\operatorname{u_{0}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)} + \\epsilon \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + \\omega^{2} \\operatorname{u_{0}}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "            2                             2                      2            \n",
       " 4   2     d              3              d            3   2     d            2\n",
       "ε ⋅u₁ (t)⋅───(u₁(t)) + 2⋅ε ⋅u₀(t)⋅u₁(t)⋅───(u₁(t)) + ε ⋅u₁ (t)⋅───(u₀(t)) + ε \n",
       "            2                             2                      2            \n",
       "          dt                            dt                     dt             \n",
       "\n",
       "          2                             2                                  2  \n",
       "   2     d              2              d              2             2     d   \n",
       "⋅u₀ (t)⋅───(u₁(t)) + 2⋅ε ⋅u₀(t)⋅u₁(t)⋅───(u₀(t)) + ε⋅ω ⋅u₁(t) + ε⋅u₀ (t)⋅───(u\n",
       "          2                             2                                  2  \n",
       "        dt                            dt                                 dt   \n",
       "\n",
       "            2                       2       \n",
       "           d            2          d        \n",
       "₀(t)) + ε⋅───(u₁(t)) + ω ⋅u₀(t) + ───(u₀(t))\n",
       "            2                       2       \n",
       "          dt                      dt        "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aux = eq.subs(subs)\n",
    "aux.doit().expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = Poly(aux.doit(), eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\operatorname{u_{1}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)}, \\  2 \\operatorname{u_{0}}{\\left(t \\right)} \\operatorname{u_{1}}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + \\operatorname{u_{1}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)}, \\  \\operatorname{u_{0}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)} + 2 \\operatorname{u_{0}}{\\left(t \\right)} \\operatorname{u_{1}}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)}, \\  \\omega^{2} \\operatorname{u_{1}}{\\left(t \\right)} + \\operatorname{u_{0}}^{2}{\\left(t \\right)} \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)}, \\  \\omega^{2} \\operatorname{u_{0}}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} \\operatorname{u_{0}}{\\left(t \\right)}\\right]$"
      ],
      "text/plain": [
       "⎡         2                         2                   2                  2  \n",
       "⎢  2     d                         d             2     d            2     d   \n",
       "⎢u₁ (t)⋅───(u₁(t)), 2⋅u₀(t)⋅u₁(t)⋅───(u₁(t)) + u₁ (t)⋅───(u₀(t)), u₀ (t)⋅───(u\n",
       "⎢         2                         2                   2                  2  \n",
       "⎣       dt                        dt                  dt                 dt   \n",
       "\n",
       "                        2                             2            2          \n",
       "                       d           2           2     d            d           \n",
       "₁(t)) + 2⋅u₀(t)⋅u₁(t)⋅───(u₀(t)), ω ⋅u₁(t) + u₀ (t)⋅───(u₀(t)) + ───(u₁(t)), ω\n",
       "                        2                             2            2          \n",
       "                      dt                            dt           dt           \n",
       "\n",
       "            2       ⎤\n",
       "2          d        ⎥\n",
       " ⋅u₀(t) + ───(u₀(t))⎥\n",
       "            2       ⎥\n",
       "          dt        ⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs = poly.coeffs()\n",
    "coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle C_{1} \\sin{\\left(\\omega t \\right)} + C_{2} \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "C₁⋅sin(ω⋅t) + C₂⋅cos(ω⋅t)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol0 = dsolve(coefs[-1], u0(t)).rhs\n",
    "sol0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\omega^{2} \\left(C_{1} \\sin{\\left(\\omega t \\right)} + C_{2} \\cos{\\left(\\omega t \\right)}\\right)^{3}$"
      ],
      "text/plain": [
       "  2                            3\n",
       "-ω ⋅(C₁⋅sin(ω⋅t) + C₂⋅cos(ω⋅t)) "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aux = (u0(t)**2*u0(t).diff(t, 2)).subs(u0(t), sol0).doit()\n",
    "aux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\operatorname{u_{1}}{\\left(t \\right)} = \\frac{C_{1} \\left(- C_{1}^{2} + 3 C_{2}^{2}\\right) \\sin^{3}{\\left(\\omega t \\right)}}{8} + \\frac{3 C_{2} \\left(- C_{1}^{2} + 3 C_{2}^{2}\\right) \\cos^{3}{\\left(\\omega t \\right)}}{8} + \\frac{C_{2} \\left(3 C_{1}^{2} - 5 C_{2}^{2}\\right) \\cos^{5}{\\left(\\omega t \\right)}}{8} + \\left(\\frac{3 C_{1}^{3}}{8} + \\frac{3 C_{1}^{2} C_{2} \\omega t}{8} + \\frac{3 C_{1} C_{2}^{2}}{8} + \\frac{3 C_{2}^{3} \\omega t}{8} + C_{3}\\right) \\sin{\\left(\\omega t \\right)} + \\left(- \\frac{3 C_{1}^{3} \\omega t}{8} - \\frac{3 C_{1} C_{2}^{2} \\omega t}{8} - \\frac{C_{2}^{3}}{2} + \\frac{C_{2} \\left(- 3 C_{1}^{2} + 5 C_{2}^{2}\\right) \\sin^{4}{\\left(\\omega t \\right)}}{8} + C_{4}\\right) \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "           ⎛    2       2⎞    3             ⎛    2       2⎞    3           ⎛  \n",
       "        C₁⋅⎝- C₁  + 3⋅C₂ ⎠⋅sin (ω⋅t)   3⋅C₂⋅⎝- C₁  + 3⋅C₂ ⎠⋅cos (ω⋅t)   C₂⋅⎝3⋅\n",
       "u₁(t) = ──────────────────────────── + ────────────────────────────── + ──────\n",
       "                     8                               8                        \n",
       "\n",
       "  2       2⎞    5        ⎛    3       2                 2       3         ⎞   \n",
       "C₁  - 5⋅C₂ ⎠⋅cos (ω⋅t)   ⎜3⋅C₁    3⋅C₁ ⋅C₂⋅ω⋅t   3⋅C₁⋅C₂    3⋅C₂ ⋅ω⋅t     ⎟   \n",
       "────────────────────── + ⎜───── + ──────────── + ──────── + ───────── + C₃⎟⋅si\n",
       "       8                 ⎝  8          8            8           8         ⎠   \n",
       "\n",
       "         ⎛      3              2         3      ⎛      2       2⎞    4        \n",
       "         ⎜  3⋅C₁ ⋅ω⋅t   3⋅C₁⋅C₂ ⋅ω⋅t   C₂    C₂⋅⎝- 3⋅C₁  + 5⋅C₂ ⎠⋅sin (ω⋅t)   \n",
       "n(ω⋅t) + ⎜- ───────── - ──────────── - ─── + ────────────────────────────── + \n",
       "         ⎝      8            8          2                  8                  \n",
       "\n",
       "  ⎞         \n",
       "  ⎟         \n",
       "C₄⎟⋅cos(ω⋅t)\n",
       "  ⎠         "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(u1(t).diff(t, 2) + omega**2*u1(t) + aux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle - C_{1}^{2} \\omega^{2} \\left(C_{1} \\sin{\\left(\\omega t \\right)} + C_{2} \\cos{\\left(\\omega t \\right)}\\right) \\sin^{2}{\\left(\\omega t \\right)} - 2 C_{1} C_{2} \\omega^{2} \\left(C_{1} \\sin{\\left(\\omega t \\right)} + C_{2} \\cos{\\left(\\omega t \\right)}\\right) \\sin{\\left(\\omega t \\right)} \\cos{\\left(\\omega t \\right)} - C_{2}^{2} \\omega^{2} \\left(C_{1} \\sin{\\left(\\omega t \\right)} + C_{2} \\cos{\\left(\\omega t \\right)}\\right) \\cos^{2}{\\left(\\omega t \\right)} + \\omega^{2} \\operatorname{u_{1}}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} \\operatorname{u_{1}}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "    2  2                                2                 2                   \n",
       "- C₁ ⋅ω ⋅(C₁⋅sin(ω⋅t) + C₂⋅cos(ω⋅t))⋅sin (ω⋅t) - 2⋅C₁⋅C₂⋅ω ⋅(C₁⋅sin(ω⋅t) + C₂⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                2  2                                2         \n",
       "cos(ω⋅t))⋅sin(ω⋅t)⋅cos(ω⋅t) - C₂ ⋅ω ⋅(C₁⋅sin(ω⋅t) + C₂⋅cos(ω⋅t))⋅cos (ω⋅t) + ω\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "            2       \n",
       "2          d        \n",
       " ⋅u₁(t) + ───(u₁(t))\n",
       "            2       \n",
       "          dt        "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_aux = expand(coefs[-2].subs(u0(t), sol0))\n",
    "eq_aux.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{C_{1} \\left(- C_{1}^{2} + 3 C_{2}^{2}\\right) \\sin^{3}{\\left(\\omega t \\right)}}{8} + \\frac{3 C_{2} \\left(- C_{1}^{2} + 3 C_{2}^{2}\\right) \\cos^{3}{\\left(\\omega t \\right)}}{8} + \\frac{C_{2} \\left(3 C_{1}^{2} - 5 C_{2}^{2}\\right) \\cos^{5}{\\left(\\omega t \\right)}}{8} + \\left(\\frac{3 C_{1}^{3}}{8} + \\frac{3 C_{1}^{2} C_{2} \\omega t}{8} + \\frac{3 C_{1} C_{2}^{2}}{8} + \\frac{3 C_{2}^{3} \\omega t}{8} + C_{3}\\right) \\sin{\\left(\\omega t \\right)} + \\left(- \\frac{3 C_{1}^{3} \\omega t}{8} - \\frac{3 C_{1} C_{2}^{2} \\omega t}{8} - \\frac{C_{2}^{3}}{2} + \\frac{C_{2} \\left(- 3 C_{1}^{2} + 5 C_{2}^{2}\\right) \\sin^{4}{\\left(\\omega t \\right)}}{8} + C_{4}\\right) \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "   ⎛    2       2⎞    3             ⎛    2       2⎞    3           ⎛    2     \n",
       "C₁⋅⎝- C₁  + 3⋅C₂ ⎠⋅sin (ω⋅t)   3⋅C₂⋅⎝- C₁  + 3⋅C₂ ⎠⋅cos (ω⋅t)   C₂⋅⎝3⋅C₁  - 5⋅\n",
       "──────────────────────────── + ────────────────────────────── + ──────────────\n",
       "             8                               8                               8\n",
       "\n",
       "  2⎞    5        ⎛    3       2                 2       3         ⎞           \n",
       "C₂ ⎠⋅cos (ω⋅t)   ⎜3⋅C₁    3⋅C₁ ⋅C₂⋅ω⋅t   3⋅C₁⋅C₂    3⋅C₂ ⋅ω⋅t     ⎟           \n",
       "────────────── + ⎜───── + ──────────── + ──────── + ───────── + C₃⎟⋅sin(ω⋅t) +\n",
       "                 ⎝  8          8            8           8         ⎠           \n",
       "\n",
       " ⎛      3              2         3      ⎛      2       2⎞    4          ⎞     \n",
       " ⎜  3⋅C₁ ⋅ω⋅t   3⋅C₁⋅C₂ ⋅ω⋅t   C₂    C₂⋅⎝- 3⋅C₁  + 5⋅C₂ ⎠⋅sin (ω⋅t)     ⎟     \n",
       " ⎜- ───────── - ──────────── - ─── + ────────────────────────────── + C₄⎟⋅cos(\n",
       " ⎝      8            8          2                  8                    ⎠     \n",
       "\n",
       "    \n",
       "    \n",
       "ω⋅t)\n",
       "    "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1 = dsolve(eq_aux, u1(t)).rhs\n",
    "sol1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "C1, C2, C3, C4 = symbols(\"C1 C2 C3 C4\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3*omega*t*sin(omega*t)/8 + (5*sin(omega*t)**4/8 - 3/4)*cos(omega*t) - 5*cos(omega*t)**5/8 + 9*cos(omega*t)**3/8\n"
     ]
    }
   ],
   "source": [
    "print(sol1.subs({C1: 0, C2: 1, C3: 0, C4: -S(1)/4}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_app = sol0 + eps*sol1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ C_{2} - 1, \\  - \\frac{C_{2}^{3}}{2} + \\frac{3 C_{2} \\left(- C_{1}^{2} + 3 C_{2}^{2}\\right)}{8} + \\frac{C_{2} \\left(3 C_{1}^{2} - 5 C_{2}^{2}\\right)}{8} + C_{4}, \\  C_{1} \\omega, \\  - \\frac{3 C_{1}^{3} \\omega}{8} - \\frac{3 C_{1} C_{2}^{2} \\omega}{8} + \\omega \\left(\\frac{3 C_{1}^{3}}{8} + \\frac{3 C_{1} C_{2}^{2}}{8} + C_{3}\\right)\\right]$"
      ],
      "text/plain": [
       "⎡            3        ⎛    2       2⎞      ⎛    2       2⎞                   3\n",
       "⎢          C₂    3⋅C₂⋅⎝- C₁  + 3⋅C₂ ⎠   C₂⋅⎝3⋅C₁  - 5⋅C₂ ⎠               3⋅C₁ \n",
       "⎢C₂ - 1, - ─── + ──────────────────── + ────────────────── + C₄, C₁⋅ω, - ─────\n",
       "⎣           2             8                     8                           8 \n",
       "\n",
       "            2       ⎛    3          2     ⎞⎤\n",
       "⋅ω   3⋅C₁⋅C₂ ⋅ω     ⎜3⋅C₁    3⋅C₁⋅C₂      ⎟⎥\n",
       "── - ────────── + ω⋅⎜───── + ──────── + C₃⎟⎥\n",
       "         8          ⎝  8        8         ⎠⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aux_eqs = [\n",
    "        sol0.subs(t, 0)-1,\n",
    "        sol1.subs(t, 0),\n",
    "        diff(sol0, t).subs(t, 0),\n",
    "        diff(sol1, t).subs(t, 0)]\n",
    "aux_eqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{C_{1}, C_{2}, C_{3}, C_{4}\\right\\}$"
      ],
      "text/plain": [
       "{C₁, C₂, C₃, C₄}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef = u_app.free_symbols - eq.free_symbols\n",
    "coef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ C_{1} : 0, \\  C_{2} : 1, \\  C_{3} : 0, \\  C_{4} : 0\\right\\}$"
      ],
      "text/plain": [
       "{C₁: 0, C₂: 1, C₃: 0, C₄: 0}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs_sol = solve(aux_eqs, coef)\n",
    "subs_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\epsilon \\left(\\frac{3 \\omega t \\sin{\\left(\\omega t \\right)}}{8} + \\frac{\\left(5 \\sin^{4}{\\left(\\omega t \\right)} - 4\\right) \\cos{\\left(\\omega t \\right)}}{8} - \\frac{5 \\cos^{5}{\\left(\\omega t \\right)}}{8} + \\frac{9 \\cos^{3}{\\left(\\omega t \\right)}}{8}\\right) + \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "  ⎛                 ⎛     4         ⎞                 5             3     ⎞   \n",
       "  ⎜3⋅ω⋅t⋅sin(ω⋅t)   ⎝5⋅sin (ω⋅t) - 4⎠⋅cos(ω⋅t)   5⋅cos (ω⋅t)   9⋅cos (ω⋅t)⎟   \n",
       "ε⋅⎜────────────── + ────────────────────────── - ─────────── + ───────────⎟ + \n",
       "  ⎝      8                      8                     8             8     ⎠   \n",
       "\n",
       "        \n",
       "        \n",
       "cos(ω⋅t)\n",
       "        "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_app2 = u_app.subs(subs_sol)\n",
    "trigsimp(u_app2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epsilon*(3*omega*t*sin(omega*t)/8 + (5*sin(omega*t)**4/8 - 1/2)*cos(omega*t) - 5*cos(omega*t)**5/8 + 9*cos(omega*t)**3/8) + cos(omega*t)\n"
     ]
    }
   ],
   "source": [
    "print(u_app2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 \\epsilon t \\sin{\\left(2 t \\right)}}{4} + \\frac{5 \\epsilon \\sin^{4}{\\left(2 t \\right)} \\cos{\\left(2 t \\right)}}{8} - \\frac{5 \\epsilon \\cos^{5}{\\left(2 t \\right)}}{8} + \\frac{9 \\epsilon \\cos^{3}{\\left(2 t \\right)}}{8} - \\frac{\\epsilon \\cos{\\left(2 t \\right)}}{2} + \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "                        4                        5               3            \n",
       "3⋅ε⋅t⋅sin(2⋅t)   5⋅ε⋅sin (2⋅t)⋅cos(2⋅t)   5⋅ε⋅cos (2⋅t)   9⋅ε⋅cos (2⋅t)   ε⋅co\n",
       "────────────── + ────────────────────── - ───────────── + ───────────── - ────\n",
       "      4                    8                    8               8             \n",
       "\n",
       "                 \n",
       "s(2⋅t)           \n",
       "────── + cos(2⋅t)\n",
       "2                "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_sol = trigsimp(u_app2).subs(omega, 2).expand()\n",
    "final_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TyU1BVITf6eIFqIO/7izEt6AFSsBPIN7LLf59hMLZ/Od0mW32G34LlICxVJLAahRMiXnCNOC8l3Mr106R1YS0knCPJZ8gPzjAoTCOwHK08uDZSqq3eTYNv81D3LuCqzGRtdTM7PItwlnZI06Quc/CpHxr4GJvhtWLKZdUMMvzG37Lw+SsHK12BaPBBnsvJ4yCXZ7vVJkJ5azNaXjhwhVMebGSt/cxfTKB2OzHLlW3TZHhtyk4B1dmtQpmcM0tA5OAScAkYBKYVAL/A08zKttOJtwWAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 \\epsilon t \\sin{\\left(2 t \\right)}}{4} - \\frac{\\epsilon \\cos^{3}{\\left(2 t \\right)}}{8} + \\frac{\\epsilon \\cos{\\left(2 t \\right)}}{8} + \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "                      3                             \n",
       "3⋅ε⋅t⋅sin(2⋅t)   ε⋅cos (2⋅t)   ε⋅cos(2⋅t)           \n",
       "────────────── - ─────────── + ────────── + cos(2⋅t)\n",
       "      4               8            8                "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trigsimp(final_sol).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\epsilon \\left(24 t \\sin{\\left(2 t \\right)} + 6 \\cos{\\left(2 t \\right)} - \\cos{\\left(6 t \\right)}\\right)}{32} + \\left(1 - \\frac{5 \\epsilon}{32}\\right) \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "ε⋅(24⋅t⋅sin(2⋅t) + 6⋅cos(2⋅t) - cos(6⋅t))   ⎛    5⋅ε⎞         \n",
       "───────────────────────────────────────── + ⎜1 - ───⎟⋅cos(2⋅t)\n",
       "                    32                      ⎝     32⎠         "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = (1 - 5*eps/32)*cos(2*t) + eps/32*(6*cos(2*t) - cos(6*t) + 24*t*sin(2*t))\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='9a45dd0d-4c2b-4bf1-a6a6-5fd9002ceaa2'></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f85a59ae4c0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot((sol - final_sol).subs(eps, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint\n",
    "def fun(x, t=0, eps=0.1):\n",
    "    x0, x1 = x\n",
    "    return [x1, -4*x0/(1 + eps*x0**2)]\n",
    "\n",
    "t_vec = np.linspace(0, 100,  1000)\n",
    "x = odeint(fun, [1, 0], t_vec, args=(0.1,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "lam_sol = lambdify((t, eps), final_sol, \"numpy\")\n",
    "uu = lam_sol(t_vec, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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width=\"852.75\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(t_vec, x[:,0])\n",
    "plt.plot(t_vec, uu, '--r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1"
  },
  "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": 1
}