3DNonAutNonHomODE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## EDO lineal no autónoma y no homogenea (3D) ##\n",
    "\n",
    "Sea $\\nu\\in\\mathbb{R}$ y la EDO en $\\mathbb{R}^3$ dada por:\n",
    "\\begin{gather*}\n",
    "    \\dfrac{d\\boldsymbol{X}}{dt}=\\boldsymbol{A}(t)\\boldsymbol{X}+\\nu\\boldsymbol{g}(t)\\,, \\quad \\textrm{donde} \\quad \\boldsymbol{A}(t)=\\left[\\begin{array}{ccc}\n",
    "        0 & -2 & 0\\\\\n",
    "        1 & 0 & 0 \\\\\n",
    "        te^{-0.5t} & te^{-0.3t} & 1\n",
    "    \\end{array}\\right]\\,, \\quad \\boldsymbol{g}(t)=\\left[\\begin{array}{c}\n",
    "        e^{0.5t}\\\\\n",
    "        0.2 t \\\\\n",
    "        0.1t\n",
    "    \\end{array}\\right]\\,, \\quad X(0)=p_0\\,.\n",
    "\\end{gather*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Librerías necesarias: \n",
    "from numpy import *  \n",
    "from scipy import *  \n",
    "import scipy.linalg as la\n",
    "from scipy.integrate import odeint \n",
    "import matplotlib.pyplot as plt        \n",
    "from mpl_toolkits.mplot3d import Axes3D  \n",
    "from pylab import * \n",
    "#\n",
    "rcParams['xtick.direction']  = 'out'\n",
    "rcParams['ytick.direction']  = 'out'\n",
    "rcParams['mathtext.fontset'] = 'cm'\n",
    "rcParams['mathtext.rm']      = 'serif'\n",
    "rcParams['text.usetex']      = True\n",
    "rcParams['axes.labelsize']   = 26\n",
    "rcParams['axes.titlesize']   = 22\n",
    "rcParams['xtick.labelsize']  = 16\n",
    "rcParams['ytick.labelsize']  = 16\n",
    "rcParams['legend.fontsize']  = 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Condiciones iniciales y parámetros\n",
    "t0 = 0\n",
    "tf = 50\n",
    "N  = 50\n",
    "#\n",
    "# Define intervalo de integración\n",
    "time = linspace(t0,tf,N*tf)\n",
    "#\n",
    "# Define los campos\n",
    "nu = 0 \n",
    "#\n",
    "def DField(x,t):\n",
    "    x1 = x[0]\n",
    "    x2 = x[1]\n",
    "    x3 = x[2]\n",
    "    F1 = -2*x2 + nu*e**(-0.5*t) \n",
    "    F2 = x1 + 0.2*nu*t\n",
    "    F3 = t*e**(-0.5*t)*x1 + t*e**(-0.3*t)*x2 - x3 + 0.1*nu*t + 0.1*nu*t#x1 + x2 - x3\n",
    "    FG = [F1,F2,F3]\n",
    "    return FG\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "Failed to import any qt binding",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "Input \u001b[0;32mIn [4]\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m rr \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[0;32m----> 4\u001b[0m     \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mqt\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m      6\u001b[0m     get_ipython()\u001b[38;5;241m.\u001b[39mrun_line_magic(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmatplotlib\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124minline\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2204\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2202\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2203\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2204\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2205\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3340\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3336\u001b[0m         \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mWarning: Cannot change to a different GUI toolkit: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m   3337\u001b[0m                 \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m Using \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m instead.\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m (gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select))\n\u001b[1;32m   3338\u001b[0m         gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n\u001b[0;32m-> 3340\u001b[0m \u001b[43mpt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mactivate_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbackend\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3341\u001b[0m configure_inline_support(\u001b[38;5;28mself\u001b[39m, backend)\n\u001b[1;32m   3343\u001b[0m \u001b[38;5;66;03m# Now we must activate the gui pylab wants to use, and fix %run to take\u001b[39;00m\n\u001b[1;32m   3344\u001b[0m \u001b[38;5;66;03m# plot updates into account\u001b[39;00m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/IPython/core/pylabtools.py:359\u001b[0m, in \u001b[0;36mactivate_matplotlib\u001b[0;34m(backend)\u001b[0m\n\u001b[1;32m    354\u001b[0m \u001b[38;5;66;03m# Due to circular imports, pyplot may be only partially initialised\u001b[39;00m\n\u001b[1;32m    355\u001b[0m \u001b[38;5;66;03m# when this function runs.\u001b[39;00m\n\u001b[1;32m    356\u001b[0m \u001b[38;5;66;03m# So avoid needing matplotlib attribute-lookup to access pyplot.\u001b[39;00m\n\u001b[1;32m    357\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pyplot \u001b[38;5;28;01mas\u001b[39;00m plt\n\u001b[0;32m--> 359\u001b[0m \u001b[43mplt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mswitch_backend\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbackend\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    361\u001b[0m plt\u001b[38;5;241m.\u001b[39mshow\u001b[38;5;241m.\u001b[39m_needmain \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[1;32m    362\u001b[0m \u001b[38;5;66;03m# We need to detect at runtime whether show() is called by the user.\u001b[39;00m\n\u001b[1;32m    363\u001b[0m \u001b[38;5;66;03m# For this, we wrap it into a decorator which adds a 'called' flag.\u001b[39;00m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/matplotlib/pyplot.py:267\u001b[0m, in \u001b[0;36mswitch_backend\u001b[0;34m(newbackend)\u001b[0m\n\u001b[1;32m    260\u001b[0m \u001b[38;5;66;03m# Backends are implemented as modules, but \"inherit\" default method\u001b[39;00m\n\u001b[1;32m    261\u001b[0m \u001b[38;5;66;03m# implementations from backend_bases._Backend.  This is achieved by\u001b[39;00m\n\u001b[1;32m    262\u001b[0m \u001b[38;5;66;03m# creating a \"class\" that inherits from backend_bases._Backend and whose\u001b[39;00m\n\u001b[1;32m    263\u001b[0m \u001b[38;5;66;03m# body is filled with the module's globals.\u001b[39;00m\n\u001b[1;32m    265\u001b[0m backend_name \u001b[38;5;241m=\u001b[39m cbook\u001b[38;5;241m.\u001b[39m_backend_module_name(newbackend)\n\u001b[0;32m--> 267\u001b[0m \u001b[38;5;28;01mclass\u001b[39;00m \u001b[38;5;21;01mbackend_mod\u001b[39;00m(matplotlib\u001b[38;5;241m.\u001b[39mbackend_bases\u001b[38;5;241m.\u001b[39m_Backend):\n\u001b[1;32m    268\u001b[0m     \u001b[38;5;28mlocals\u001b[39m()\u001b[38;5;241m.\u001b[39mupdate(\u001b[38;5;28mvars\u001b[39m(importlib\u001b[38;5;241m.\u001b[39mimport_module(backend_name)))\n\u001b[1;32m    270\u001b[0m required_framework \u001b[38;5;241m=\u001b[39m _get_required_interactive_framework(backend_mod)\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/matplotlib/pyplot.py:268\u001b[0m, in \u001b[0;36mswitch_backend.<locals>.backend_mod\u001b[0;34m()\u001b[0m\n\u001b[1;32m    267\u001b[0m \u001b[38;5;28;01mclass\u001b[39;00m \u001b[38;5;21;01mbackend_mod\u001b[39;00m(matplotlib\u001b[38;5;241m.\u001b[39mbackend_bases\u001b[38;5;241m.\u001b[39m_Backend):\n\u001b[0;32m--> 268\u001b[0m     \u001b[38;5;28mlocals\u001b[39m()\u001b[38;5;241m.\u001b[39mupdate(\u001b[38;5;28mvars\u001b[39m(\u001b[43mimportlib\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mimport_module\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbackend_name\u001b[49m\u001b[43m)\u001b[49m))\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/importlib/__init__.py:126\u001b[0m, in \u001b[0;36mimport_module\u001b[0;34m(name, package)\u001b[0m\n\u001b[1;32m    124\u001b[0m             \u001b[38;5;28;01mbreak\u001b[39;00m\n\u001b[1;32m    125\u001b[0m         level \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m--> 126\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_bootstrap\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_gcd_import\u001b[49m\u001b[43m(\u001b[49m\u001b[43mname\u001b[49m\u001b[43m[\u001b[49m\u001b[43mlevel\u001b[49m\u001b[43m:\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpackage\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlevel\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap>:1050\u001b[0m, in \u001b[0;36m_gcd_import\u001b[0;34m(name, package, level)\u001b[0m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap>:1027\u001b[0m, in \u001b[0;36m_find_and_load\u001b[0;34m(name, import_)\u001b[0m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap>:1006\u001b[0m, in \u001b[0;36m_find_and_load_unlocked\u001b[0;34m(name, import_)\u001b[0m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap>:688\u001b[0m, in \u001b[0;36m_load_unlocked\u001b[0;34m(spec)\u001b[0m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap_external>:883\u001b[0m, in \u001b[0;36mexec_module\u001b[0;34m(self, module)\u001b[0m\n",
      "File \u001b[0;32m<frozen importlib._bootstrap>:241\u001b[0m, in \u001b[0;36m_call_with_frames_removed\u001b[0;34m(f, *args, **kwds)\u001b[0m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/matplotlib/backends/backend_qt5agg.py:5\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;124;03mRender to qt from agg\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_qtagg\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m      6\u001b[0m     _BackendQTAgg, FigureCanvasQTAgg, FigureManagerQT, NavigationToolbar2QT,\n\u001b[1;32m      7\u001b[0m     backend_version,  FigureCanvasAgg,  FigureCanvasQT\n\u001b[1;32m      8\u001b[0m )\n\u001b[1;32m     11\u001b[0m \u001b[38;5;129m@_BackendQTAgg\u001b[39m\u001b[38;5;241m.\u001b[39mexport\n\u001b[1;32m     12\u001b[0m \u001b[38;5;28;01mclass\u001b[39;00m \u001b[38;5;21;01m_BackendQT5Agg\u001b[39;00m(_BackendQTAgg):\n\u001b[1;32m     13\u001b[0m     \u001b[38;5;28;01mpass\u001b[39;00m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/matplotlib/backends/backend_qtagg.py:9\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mctypes\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mtransforms\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Bbox\n\u001b[0;32m----> 9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mqt_compat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m QT_API, _enum, _setDevicePixelRatio\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m cbook\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_agg\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m FigureCanvasAgg\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/matplotlib/backends/qt_compat.py:128\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    126\u001b[0m         \u001b[38;5;28;01mbreak\u001b[39;00m\n\u001b[1;32m    127\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 128\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mFailed to import any qt binding\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    129\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# We should not get there.\u001b[39;00m\n\u001b[1;32m    130\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mAssertionError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUnexpected QT_API: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mQT_API\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mImportError\u001b[0m: Failed to import any qt binding"
     ]
    }
   ],
   "source": [
    "rr = 0\n",
    "#\n",
    "if rr == 0:\n",
    "    %matplotlib qt\n",
    "else:\n",
    "    %matplotlib inline\n",
    "#\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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   "source": [
    "# Define condición inicial (Puedes jugar con los valores) \n",
    "x0,y0,z0 = (e**rand(1))*rand(3)\n",
    "#\n",
    "colour = ['C3','C5','C0','C7','C9']\n",
    "# Espacio fase\n",
    "fig0 = plt.figure(0,figsize=(12,10))\n",
    "ax0  = fig0.add_subplot(111, projection='3d')\n",
    "#\n",
    "# Series de tiempo por componente\n",
    "#fig1, ax1 = plt.subplots(3, sharex=True,figsize=(12,10))\n",
    "# Axes\n",
    "L   = 15\n",
    "tau = linspace(-L,L,20)\n",
    "m   = size(tau)\n",
    "e1  = [tau,zeros(m),zeros(m)]\n",
    "e2  = [zeros(m),tau,zeros(m)]\n",
    "e3  = [zeros(m),zeros(m),tau]\n",
    "#\n",
    "ax0.plot(e1[0],e1[1],e1[2],'-.k',lw=1,alpha=0.5)\n",
    "ax0.plot(e2[0],e2[1],e2[2],'-.k',lw=1,alpha=0.5)\n",
    "ax0.plot(e3[0],e3[1],e3[2],'-.k',lw=1,alpha=0.5)\n",
    "ax0.plot([0],[0],[0],'o',color='k',ms=8)\n",
    "ax0.plot([0],[0],[0],'o',color='w',ms=6)\n",
    "ax0.text(L+0.6,0,0,'$x_1$',fontsize=30)\n",
    "ax0.text(0,L+0.6,0,'$x_2$',fontsize=30)\n",
    "ax0.text(0,0,L+0.6,'$x_3$',fontsize=30)\n",
    "#\n",
    "for kk in range(5):\n",
    "    #\n",
    "    if kk == 2:\n",
    "        liwe = 3\n",
    "        alp  = 1\n",
    "        m    = 'k'\n",
    "        #\n",
    "        XYZ0 = [x0,y0,z0]\n",
    "    else:\n",
    "        liwe = 1\n",
    "        alp  = 0.5\n",
    "        m    = colour[kk]\n",
    "        #\n",
    "        xi,yi,zi = rand(3)\n",
    "        s1,s2,s3 = (-1)**randint(2)*ones(3)\n",
    "        XYZ0     = [x0+s1*xi,y0+s2*yi,z0+s3*zi]\n",
    "    #\n",
    "    X0 = XYZ0\n",
    "    # Resuelve el sistema\n",
    "    z = odeint(DField, X0,time)\n",
    "    #\n",
    "    xx = z[:,0]\n",
    "    yy = z[:,1]\n",
    "    zz = z[:,2]\n",
    "    #\n",
    "    ax0.plot(xx, yy, zz, lw=liwe,color=colour[kk],alpha=alp)\n",
    "    ax0.plot([X0[0]],[X0[1]],[X0[2]],'o',color=m,ms=8)\n",
    "    ax0.plot([xx[-1]],[yy[-1]],[zz[-1]],'s',color=m,ms=8)\n",
    "    #\n",
    "    #ax1[0].plot(time,xx, lw=liwe,color=colour[kk],alpha=alp)\n",
    "    #ax1[1].plot(time,yy, lw=liwe,color=colour[kk],alpha=alp)\n",
    "    #ax1[2].plot(time,zz, lw=liwe,color=colour[kk],alpha=alp)\n",
    "    #ax1[0].plot([time[0]],[X0[0]],'o',color=m,ms=8)\n",
    "    #ax1[1].plot([time[0]],[X0[1]],'o',color=m,ms=8)\n",
    "    #ax1[2].plot([time[0]],[X0[2]],'o',color=m,ms=8)\n",
    "    #ax1[0].plot([time[-1]],[xx[-1]],'s',color=m,ms=8)\n",
    "    #ax1[1].plot([time[-1]],[yy[-1]],'s',color=m,ms=8)\n",
    "    #ax1[2].plot([time[-1]],[zz[-1]],'s',color=m,ms=8)\n",
    "    #\n",
    "    if kk == 2:\n",
    "        ax0.text(X0[0],X0[1]+0.2,X0[2]+1.5,r'$p_0$',color=colour[kk],fontsize=24)\n",
    "        ax0.text(xx[-1],yy[-1]+0.2,zz[-1]+1.5,r'$X(t)$',color=colour[kk],fontsize=24)\n",
    "    else:\n",
    "        continue\n",
    "    #\n",
    "#\n",
    "#ax1[0].set_ylabel(r'$X_1$')\n",
    "#ax1[1].set_ylabel(r'$X_2$')\n",
    "#ax1[2].set_ylabel(r'$X_3$')\n",
    "#ax1[2].set_xlabel(r'$t$')\n",
    "# Borrar planos\n",
    "ax0.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))\n",
    "ax0.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))\n",
    "ax0.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))\n",
    "#\n",
    "ax0.w_xaxis.line.set_color((1.0, 1.0, 1.0, 0.0)) \n",
    "ax0.w_yaxis.line.set_color((1.0, 1.0, 1.0, 0.0)) \n",
    "ax0.w_zaxis.line.set_color((1.0, 1.0, 1.0, 0.0))\n",
    "#\n",
    "ax0.set_xticks([])\n",
    "ax0.set_yticks([])\n",
    "ax0.set_zticks([])\n",
    "#\n",
    "plt.tight_layout()\n",
    "#\n",
    "if rr == 0:\n",
    "    for angle in range(45,405):\n",
    "        ax0.view_init(30, angle)\n",
    "        plt.draw()\n",
    "        plt.pause(0.0001)\n",
    "    #\n",
    "    #close()\n",
    "    #\n",
    "    savefig('3DplotIn.png')\n",
    "else:\n",
    "    ax0.view_init(30,40)\n",
    "    savefig('3DplotOut.png')\n",
    "#\n",
    "show()\n",
    "#close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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