Desarrollo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Declaraciones de las funciones y objetos utilizados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols, Matrix, pprint, Eq, init_printing, zeros\n",
    "from numpy import linspace, meshgrid\n",
    "init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los __simbolos__ se declaran con la función `symbol()`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_1, x_2, x_3 = symbols('x_1, x_2, x_3')\n",
    "y_1, y_2, y_3 = symbols('y_1, y_2, y_3')\n",
    "b_1, b_2, b_3 = symbols('b_1, b_2, b_3')\n",
    "c_1, c_2, c_3 = symbols('c_1, c_2, c_3')\n",
    "A, k = symbols('A, k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Declaramos los vectores que contienen las variables anteriores usando `Matrix` y los guardamos en el diccionario del elemento modelo `e_mod`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_mod = {}\n",
    "e_mod['x'] = Matrix([x_1, x_2, x_3])\n",
    "e_mod['y'] = Matrix([y_1, y_2, y_3])\n",
    "e_mod['b'] = Matrix([b_1, b_2, b_3])\n",
    "e_mod['c'] = Matrix([c_1, c_2, c_3])\n",
    "e_mod['A'] = A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Substituyendo los valores de _b<sub>i</sub>_ y _c<sub>i</sub>_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_mod['b'] = e_mod['b'].subs(b_1, e_mod['y'][1]-e_mod['y'][2])\n",
    "e_mod['b'] = e_mod['b'].subs(b_2, e_mod['y'][2]-e_mod['y'][0])\n",
    "e_mod['b'] = e_mod['b'].subs(b_3, e_mod['y'][0]-e_mod['y'][1])\n",
    "e_mod['c'] = e_mod['c'].subs(c_1, e_mod['x'][2]-e_mod['x'][1])\n",
    "e_mod['c'] = e_mod['c'].subs(c_2, e_mod['x'][0]-e_mod['x'][2])\n",
    "e_mod['c'] = e_mod['c'].subs(c_3, e_mod['x'][1]-e_mod['x'][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construimos la matriz `Ke` del elemento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{k \\left(\\left(- x_{2} + x_{3}\\right)^{2} + \\left(y_{2} - y_{3}\\right)^{2}\\right)}{4 A} & \\frac{k \\left(\\left(x_{1} - x_{3}\\right) \\left(- x_{2} + x_{3}\\right) + \\left(- y_{1} + y_{3}\\right) \\left(y_{2} - y_{3}\\right)\\right)}{4 A} & \\frac{k \\left(\\left(- x_{1} + x_{2}\\right) \\left(- x_{2} + x_{3}\\right) + \\left(y_{1} - y_{2}\\right) \\left(y_{2} - y_{3}\\right)\\right)}{4 A}\\\\\\frac{k \\left(\\left(x_{1} - x_{3}\\right) \\left(- x_{2} + x_{3}\\right) + \\left(- y_{1} + y_{3}\\right) \\left(y_{2} - y_{3}\\right)\\right)}{4 A} & \\frac{k \\left(\\left(x_{1} - x_{3}\\right)^{2} + \\left(- y_{1} + y_{3}\\right)^{2}\\right)}{4 A} & \\frac{k \\left(\\left(- x_{1} + x_{2}\\right) \\left(x_{1} - x_{3}\\right) + \\left(- y_{1} + y_{3}\\right) \\left(y_{1} - y_{2}\\right)\\right)}{4 A}\\\\\\frac{k \\left(\\left(- x_{1} + x_{2}\\right) \\left(- x_{2} + x_{3}\\right) + \\left(y_{1} - y_{2}\\right) \\left(y_{2} - y_{3}\\right)\\right)}{4 A} & \\frac{k \\left(\\left(- x_{1} + x_{2}\\right) \\left(x_{1} - x_{3}\\right) + \\left(- y_{1} + y_{3}\\right) \\left(y_{1} - y_{2}\\right)\\right)}{4 A} & \\frac{k \\left(\\left(- x_{1} + x_{2}\\right)^{2} + \\left(y_{1} - y_{2}\\right)^{2}\\right)}{4 A}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           ⎛          2            2⎞                                        \n",
       "⎢         k⋅⎝(-x₂ + x₃)  + (y₂ - y₃) ⎠            k⋅((x₁ - x₃)⋅(-x₂ + x₃) + (-\n",
       "⎢         ────────────────────────────            ────────────────────────────\n",
       "⎢                     4⋅A                                               4⋅A   \n",
       "⎢                                                                             \n",
       "⎢                                                            ⎛         2      \n",
       "⎢k⋅((x₁ - x₃)⋅(-x₂ + x₃) + (-y₁ + y₃)⋅(y₂ - y₃))           k⋅⎝(x₁ - x₃)  + (-y\n",
       "⎢───────────────────────────────────────────────           ───────────────────\n",
       "⎢                      4⋅A                                             4⋅A    \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢k⋅((-x₁ + x₂)⋅(-x₂ + x₃) + (y₁ - y₂)⋅(y₂ - y₃))  k⋅((-x₁ + x₂)⋅(x₁ - x₃) + (-\n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎣                      4⋅A                                              4⋅A   \n",
       "\n",
       "                                                                    ⎤\n",
       "y₁ + y₃)⋅(y₂ - y₃))  k⋅((-x₁ + x₂)⋅(-x₂ + x₃) + (y₁ - y₂)⋅(y₂ - y₃))⎥\n",
       "───────────────────  ───────────────────────────────────────────────⎥\n",
       "                                           4⋅A                      ⎥\n",
       "                                                                    ⎥\n",
       "       2⎞                                                           ⎥\n",
       "₁ + y₃) ⎠            k⋅((-x₁ + x₂)⋅(x₁ - x₃) + (-y₁ + y₃)⋅(y₁ - y₂))⎥\n",
       "─────────            ───────────────────────────────────────────────⎥\n",
       "                                           4⋅A                      ⎥\n",
       "                                                                    ⎥\n",
       "                                ⎛          2            2⎞          ⎥\n",
       "y₁ + y₃)⋅(y₁ - y₂))           k⋅⎝(-x₁ + x₂)  + (y₁ - y₂) ⎠          ⎥\n",
       "───────────────────           ────────────────────────────          ⎥\n",
       "                                          4⋅A                       ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_e = zeros(3,3)\n",
    "for i in range(0,3):\n",
    "    for j in range(0,3):\n",
    "        K_e[i,j] = e_mod['b'][i]*e_mod['b'][j]+e_mod['c'][i]*e_mod['c'][j]\n",
    "e_mod['K'] = k / 4 / e_mod['A'] * K_e\n",
    "e_mod['F'] = Matrix([0,0,0])\n",
    "e_mod['K']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación creamos las coordenadas para una malla regular. `div` es el número de nodos en __x__ y en __y__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "div = 3\n",
    "\n",
    "xx = linspace(0,0.1,div)\n",
    "yy = linspace(0,0.1,div)\n",
    "\n",
    "dx = xx[1] - xx[0]\n",
    "dy = yy[1] - yy[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El elemento modelo es copiado en con el siguiente ciclo `for`, ya con las coordenadas de cada elemento substituidas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "elementos = []\n",
    "\n",
    "for j, y in enumerate(yy[:-1]):\n",
    "    for i, x in enumerate(xx[:-1]):\n",
    "        var = {'x_1': x, 'x_2': x, 'x_3': x+dx,\n",
    "               'y_1': y, 'y_2': y+dy, 'y_3': y,\n",
    "               'A': dx*dy/2, 'k': 50.0}\n",
    "        e1 = {'n':[i+j*div,i+(j+1)*div,i+1+j*div]}\n",
    "        for ee in e_mod:\n",
    "            e1[ee] = e_mod[ee].subs(var)\n",
    "        elementos.append(e1)\n",
    "        \n",
    "        var = {'x_1': x, 'x_2': x+dx, 'x_3': x+dx,\n",
    "               'y_1': y+dx, 'y_2': y+dy, 'y_3': y,\n",
    "               'A': dx*dy/2, 'k': 50.0}\n",
    "        e2 = {'n':[i+(j+1)*div,i+1+(j+1)*div,i+1+j*div]}\n",
    "        for ee in e_mod:\n",
    "            e2[ee] = e_mod[ee].subs(var)    \n",
    "        elementos.append(e2)\n",
    "\n",
    "n = i+1+(j+1)*div"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modificamos ahora los elemntos con generación (en este ejemplo ningúno)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = 0\n",
    "for e in elementos:\n",
    "    F = Q * e['A']/3 * Matrix([1,1,1])\n",
    "    e.update({'F':F})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vector fuerza, aplicado en los nodos de los elementos con flujo de calor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "F1 = 10000 * dy / 2 * Matrix([1,1,0])\n",
    "for e in elementos:\n",
    "    if e['x'][1] == 0:\n",
    "        e['F'] = e['F'] + F1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensamblamos la matriz __K__  y el vector __F__ del sistema utilizando la información de los nodos. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}50.0 & -25.0 & 0 & -25.0 & 0 & 0 & 0 & 0 & 0\\\\-25.0 & 100.0 & -25.0 & 0 & -50.0 & 0 & 0 & 0 & 0\\\\0 & -25.0 & 50.0 & 0 & 0 & -25.0 & 0 & 0 & 0\\\\-25.0 & 0 & 0 & 100.0 & -50.0 & 0 & -25.0 & 0 & 0\\\\0 & -50.0 & 0 & -50.0 & 200.0 & -50.0 & 0 & -50.0 & 0\\\\0 & 0 & -25.0 & 0 & -50.0 & 100.0 & 0 & 0 & -25.0\\\\0 & 0 & 0 & -25.0 & 0 & 0 & 50.0 & -25.0 & 0\\\\0 & 0 & 0 & 0 & -50.0 & 0 & -25.0 & 100.0 & -25.0\\\\0 & 0 & 0 & 0 & 0 & -25.0 & 0 & -25.0 & 50.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡50.0   -25.0    0    -25.0    0      0      0      0      0  ⎤\n",
       "⎢                                                             ⎥\n",
       "⎢-25.0  100.0  -25.0    0    -50.0    0      0      0      0  ⎥\n",
       "⎢                                                             ⎥\n",
       "⎢  0    -25.0  50.0     0      0    -25.0    0      0      0  ⎥\n",
       "⎢                                                             ⎥\n",
       "⎢-25.0    0      0    100.0  -50.0    0    -25.0    0      0  ⎥\n",
       "⎢                                                             ⎥\n",
       "⎢  0    -50.0    0    -50.0  200.0  -50.0    0    -50.0    0  ⎥\n",
       "⎢                                                             ⎥\n",
       "⎢  0      0    -25.0    0    -50.0  100.0    0      0    -25.0⎥\n",
       "⎢                                                             ⎥\n",
       "⎢  0      0      0    -25.0    0      0    50.0   -25.0    0  ⎥\n",
       "⎢                                                             ⎥\n",
       "⎢  0      0      0      0    -50.0    0    -25.0  100.0  -25.0⎥\n",
       "⎢                                                             ⎥\n",
       "⎣  0      0      0      0      0    -25.0    0    -25.0  50.0 ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = zeros(n+1,n+1)\n",
    "F = zeros(n+1,1)\n",
    "for e in elementos:\n",
    "    for i, j in enumerate(e['n']):\n",
    "        for k, m in enumerate(e['n']):\n",
    "            #print(j,m)\n",
    "            K[j,m] = K[j,m] + e['K'][i,k]\n",
    "        F[j] = F[j] + e['F'][i]\n",
    "        \n",
    "K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente construimos un vector con las temperaturas conocidas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}250.0\\\\0\\\\0\\\\500.0\\\\0\\\\0\\\\250.0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡250.0⎤\n",
       "⎢     ⎥\n",
       "⎢  0  ⎥\n",
       "⎢     ⎥\n",
       "⎢  0  ⎥\n",
       "⎢     ⎥\n",
       "⎢500.0⎥\n",
       "⎢     ⎥\n",
       "⎢  0  ⎥\n",
       "⎢     ⎥\n",
       "⎢  0  ⎥\n",
       "⎢     ⎥\n",
       "⎢250.0⎥\n",
       "⎢     ⎥\n",
       "⎢  0  ⎥\n",
       "⎢     ⎥\n",
       "⎣  0  ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construimos un vector con la temperatura conocida para los nodos que tienen dicha condición. Las temperaturas incógnita se colocan como `None`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}100\\\\100\\\\100\\\\\\text{None}\\\\\\text{None}\\\\100\\\\100\\\\100\\\\100\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡100 ⎤\n",
       "⎢    ⎥\n",
       "⎢100 ⎥\n",
       "⎢    ⎥\n",
       "⎢100 ⎥\n",
       "⎢    ⎥\n",
       "⎢None⎥\n",
       "⎢    ⎥\n",
       "⎢None⎥\n",
       "⎢    ⎥\n",
       "⎢100 ⎥\n",
       "⎢    ⎥\n",
       "⎢100 ⎥\n",
       "⎢    ⎥\n",
       "⎢100 ⎥\n",
       "⎢    ⎥\n",
       "⎣100 ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Tf = Matrix([None] * int(n+1))\n",
    "for i, e in enumerate(elementos):\n",
    "    for x, y, nn in zip(e['x'],e['y'],e['n']):\n",
    "        if x > 0.09999:\n",
    "            Tf[nn]= 100\n",
    "        if y > 0.09999:\n",
    "            Tf[nn]= 100\n",
    "        if y < 0.00001:\n",
    "            Tf[nn]= 100\n",
    "Tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y modificamos la matriz K, para quitar dichas incognitas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\-25.0 & 0 & 0 & 100.0 & -50.0 & 0 & -25.0 & 0 & 0\\\\0 & -50.0 & 0 & -50.0 & 200.0 & -50.0 & 0 & -50.0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  1      0    0    0      0      0      0      0    0⎤\n",
       "⎢                                                     ⎥\n",
       "⎢  0      1    0    0      0      0      0      0    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢  0      0    1    0      0      0      0      0    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢-25.0    0    0  100.0  -50.0    0    -25.0    0    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢  0    -50.0  0  -50.0  200.0  -50.0    0    -50.0  0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢  0      0    0    0      0      1      0      0    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢  0      0    0    0      0      0      1      0    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎢  0      0    0    0      0      0      0      1    0⎥\n",
       "⎢                                                     ⎥\n",
       "⎣  0      0    0    0      0      0      0      0    1⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i, t in enumerate(Tf):\n",
    "    if t is not None:\n",
    "        for j in range(n+1):\n",
    "            K[i,j] = 0\n",
    "            if i == j:\n",
    "                K[i,j] = 1\n",
    "            F[i] = t\n",
    "K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El sistema se resuelve utilizando el método `LUsolve()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GbNb17U0R28uF4+mi4fKkH5BIZdTj3YAXkxydJMCAYdTJC4k72+ENMLd1dGqx7an1coK9o6G1wFdXrcJTgD/4BXJQMWfu56g7eL0FoDkTse+PcfDC4Kz130R6RN8G1KWXov5iRZzy/KV38a4AHdT7NeRqy563yg/HmtrN5qK2z7U76W5pexGdliSemm1tlv6r2IuZmQn0ZzOrcbBIMjk6ccABEy7J1jh54QXM547aUpH6I8sN16t5UZL4Qapi53kakrSbmYywXg+vRoZZt/43VYZ/ARZ1zXZ2gnrdDzvRz8HHkKSdt7vBr2shJ0cnb+5M3cM48Fvq8Ga1k5chA/rU7s5T+p4siHRrWoCa37p5+y86O4EslwpydAIQgEU3Y+IinevohLiXJiGboPjL91Jge1vMxL3zlHdLra7I4/tXzmp54FPsjZut8/JwGjr4JM1jEDA4nyGDS4XBTIt8kpsz9yAfeSQ218Z0C8CD74xrg+TdjPLBJtcFVZ0rg5GNqX2Wv+KfpQFtNrWb/Zhp+yy7qb+V7dQ1FbicmBvsyhvVAyh8cIk4T/F1q/oAwiHnKV4P4wNdJCbyeGER0HNwdMKuDmxgRiAM6sywm6pDjk4gZ35C+u6gHa53uXykjlLoZn0U3JYKs7yBDVnZZDI8E6PDvH2zw7ytMCx2nsLKEX1ppuDsWJohqaYjJ06cbQlC7uyEBCaQ3XoYZx96nWhnV0cn7FQED995yPOOt8pu6ovaDrm5Dl6onssIEvh3Jkphrt1FHcgkEPxkyzVjP7AlYeUJgVNBAOTncpCfwS+XLCdOxQ71Qwh0CIjEIsLZIyASn/0QygCRWBw4ewRE4rMfQhkgEosDZ48ASczXanKecvZDee8M4DtoOU+5d8N+twzm941ui4OWE3drYO+lNSLxvRz2u2V0eO/E3TJ7e2vS3gb+CIB7B6oOZKJy2/f4fFsQiReMXfpu/xOqDv7bk6lCOfeifIvv+t2WUaS5OekFzvxZU78/JSpnenUuIyASl3EZ5SYikrgk4RUOEnMUIMftidyb3O95Rpz7lZnmrrruF9hRuVEDyhghoDXxCJJyBomI4wkOvtahr4Za4N5av4ne5Lgd8TpdDMyLyll9nSsIiMQVYFZk237rXAXXxgxWbuc3uW//5nJvSxQrIiASF2FZlulm2amfInmPRJNyy3px/2qJxG3H/GFSZ7Op1+4JG5Xz9RWvICASV4BZmV186Es6vQOZqNzK7tzt6iJx2/H1s22u2WZfvjuOyuU6lC4gQBI/SPl2LogpK4IA32AkOSOsr2az7p9ROV9Z8RECvfMUkvifVGznkbQyZiHA12tGWF/RiG2v36JyXofibxHonadoOfEWlFYxftD4qKAsdyATlSuoUpZHQCT2aMTjpZm2q42lQsiBTFQu3qX7K6nPzjPGHu+BmzqQQdP8BP0Ueq9SNz7G+RMQ/CaldQogcAmZaxxynhIASyKngwAufDlPOZ3hUE/WIqA18VoEVX93BETi3YdAHViLgEi8FkHV3x0BkXj3IVAH1iIgEq9FUPV3R4Aktj0Tdt69U+qAEAggoL0TAZAkctoIaO/EaY+PejcHAa2J56Al2ZNEQHsnNhoWfBalnzA5T9kIX69WJPZoBOPpu72cpwTx2lpMJA4iDOJy+6WcpwTxOqaY1sRBtPmTIhxynhLE65hiInF7tB9VVN6mfCu3cy6ey+XlSmcIiMQZIGuSaclBFa8m9Mh5ygQ4S4pE4iWo1evYj0FtNvWSnthROV9f8QoCInEFmJXZfAisBTlPqSGzMJ8k1j+eWQheoZqfbfNim33lPCVHZln6BtX0j2eWYVevxTcYqdQI64VtdpbzFI/K8vg1quofzyzHb7Jm1ClKVG6yMRVeXGhN3J4FUacoUbn2PbxjGkXiZQNqS4NRbSwp5DxlhMq2GfrsPANfvAeW85QZeB1LVM5TjoW02mmKQNqE9TPufJdaTjSFVsr2QEAk3gN1tdkUAZG4KZxStgcCIvEeqKvNpgiIxE3hlLI9EBCJ90BdbTZFgCR+kDTauWkDUiYENkJAzlM2AlZqj4eAnKccD2u1tDUCWhNvjbD0b46A9k5sBDE+i8p5ykbY5mpF4hyRQDp9t5fzlABWxxARiYMog7jcfinnKUG8jimmNXEQbf70CIecpwTxOqaYSNwe7UcVlfb7Oyu3cy6ey+XlSmcIiMQZIGuSaclBFVO/epbzlDUgF+qKxAVQVmTZr5xtNvWqPLGjcr6+4hUEROIKMCuz+RBYC3KeUkNmYT5JLOcpC8ErVPOzbV5ss6+cp+TILEvfoNrAecpXyDCQl6lUrQu+wUgwlLC02VnOU9pw5RpqyNve78RVG73SAgSiTlGicgK1jkDHW62J6wAtLYk6RYnKLe3HvaknEi8balsajGpjSSHnKSNUts3QZ+cZ+OI9sJynzMDrWKJynnIspNVOUwTSJiw5T2mKqpTthoDWxLtBr4ZbISASt0JSenZDQCTeDXo13AoBkbgVktKzGwIi8W7Qq+FWCIjErZCUnt0QEIl3g14Nt0JAJG6FpPTshoBIvBv0argVAto70QrJTA8+i8p5SobJVkmReAGy6bu9nKcswG6LKiJxEFUQl9sv5TwliNcxxbQmDqIt5ylBoHYQE4nbg/6ootJ+f2flds7Fc7m8XOkMAZE4A2RNMi05qGLqV89ynrIG5EJdkbgAyoos+5WzzaZelSd2VM7XV7yCgEhcAWZlNh8Ca0HOU2rILMwXiRcCV6nmZ9tcxGZfOU/JkVmZFolXAuiry3mKR+N4cZG4PdZRpyhRufY9vGMaReL2Axp1ihKVa9/DO6ZRJF42oNUHNzlPWQbomlr67DwDPbwHlvOUGXgdS1TOU46FtNppikDahCXnKU1RlbLdENCaeDfo1XArBETiVkhKz24IiMS7Qa+GWyEgErdCUnp2Q8CT+CWe+F5nB1/IKwiBXREAJ0fcRId6bvI9sf33pFJH+R9qFITA3gjwR7fVD0z/BycLw5A/QY4yAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}100\\\\100\\\\100\\\\105.714285714286\\\\101.428571428571\\\\100\\\\100\\\\100\\\\100\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡      100       ⎤\n",
       "⎢                ⎥\n",
       "⎢      100       ⎥\n",
       "⎢                ⎥\n",
       "⎢      100       ⎥\n",
       "⎢                ⎥\n",
       "⎢105.714285714286⎥\n",
       "⎢                ⎥\n",
       "⎢101.428571428571⎥\n",
       "⎢                ⎥\n",
       "⎢      100       ⎥\n",
       "⎢                ⎥\n",
       "⎢      100       ⎥\n",
       "⎢                ⎥\n",
       "⎢      100       ⎥\n",
       "⎢                ⎥\n",
       "⎣      100       ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = K.LUsolve(F)\n",
    "T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para graficar el sistema utilizamos la librería __matplotlib__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "xc, yc = meshgrid(xx,yy)\n",
    "\n",
    "plt.figure(figsize=(6,5))\n",
    "\n",
    "cs = plt.contourf(xc,yc,T.reshape(xc.shape[0], xc.shape[1]))\n",
    "plt.axis('equal')\n",
    "\n",
    "plt.colorbar(cs)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}