numerico_nuevo_algoritmo.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "ewwOYmEjOjez"
      },
      "outputs": [],
      "source": [
        "import scipy\n",
        "import numpy\n",
        "import math\n",
        "import itertools\n",
        "import functools\n",
        "import seaborn as sns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "lo-65Hky7YYb"
      },
      "outputs": [],
      "source": [
        "numpy.set_printoptions(suppress=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZdZS9-fWnAu"
      },
      "source": [
        "#Trabajo práctico"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jpSkdN73Ub6r"
      },
      "source": [
        "## Demostración de sparse matrix (para propósitos de referencia)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cOQmU6YbYBpl",
        "outputId": "aa5e12c1-8eae-44c1-f837-77f8a2c5b2fb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ],
      "source": [
        "scipy.sparse.csr_array((1, 13)).toarray()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "FmvvwHjyOk2C"
      },
      "outputs": [],
      "source": [
        "sparse = scipy.sparse.csr_array([1,2,3,0,0,0,4])\n",
        "sparse_2 = scipy.sparse.csr_array([1,2,3,0,0,0,4])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FsVYxWoEOt0R",
        "outputId": "845f4057-dc18-4c41-baf2-3520ccf50f23"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  (0, 0)\t1\n",
            "  (0, 1)\t2\n",
            "  (0, 2)\t3\n",
            "  (0, 6)\t4\n"
          ]
        }
      ],
      "source": [
        "print(sparse)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "MAr9KRxFgPcQ"
      },
      "outputs": [],
      "source": [
        "sparse_3 = scipy.sparse.lil_array((2,4))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4_GeEec0g-6m",
        "outputId": "4b22a8fb-d985-49b6-bcc7-19d34f8a34f8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<2x4 sparse array of type '<class 'numpy.float64'>'\n",
              "\twith 0 stored elements in List of Lists format>"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "sparse_3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "psZrzJjVg6qM"
      },
      "outputs": [],
      "source": [
        "sparse_3[1,1] = 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P6eKe26-Wq_o"
      },
      "source": [
        "# Parte 1: Generar A y b para NxN nodos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sfNyhayKGtdK"
      },
      "source": [
        "A es una matriz N^2 x N^2, correspondiente a la grilla con N^2 nodos.\n",
        "\n",
        "Buscamos resolver Ax = b, donde x es la temperatura de los nodos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z7EsB--6U8gG"
      },
      "source": [
        "## Funciones auxiliares"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0WpyQA0HKtxW"
      },
      "source": [
        "estas funciones definen el layout de los nodos. i representa el eje horizontal de izq a derecha, j el eje vertical de abajo hacia arriba"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "_ZCmQJGPK3ZJ"
      },
      "outputs": [],
      "source": [
        "@functools.lru_cache\n",
        "def all_nodes(N):\n",
        "  ret = list(itertools.product(range(1, N+1), range(1, N+1)))\n",
        "  return ret\n",
        "\n",
        "@functools.lru_cache\n",
        "def coordinate_to_node_number(grid_rowsize,i,j):\n",
        "  \"\"\"\n",
        "  Determines how we number a node in the 2D position (i,j).\n",
        "  i,j from 1 to grid_rowsize.\n",
        "  Result from 1 to grid_rowsize squared.\n",
        "  \"\"\"\n",
        "  return (i-1)*grid_rowsize + (j-1) + 1\n",
        "\n",
        "\n",
        "# Devuelve la temperatura en las posiciones vacías en el extremo norte, sur, este, oeste\n",
        "def edge_temperature(N, i,j, cardinal_temperatures):\n",
        "  if(i == 0): return cardinal_temperatures['WEST']\n",
        "  if(i == N + 1): return cardinal_temperatures['EAST']\n",
        "  if(j == 0): return cardinal_temperatures['SOUTH']\n",
        "  if(j == N + 1): return cardinal_temperatures['NORTH']\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "id": "laXI_D-IdVmH"
      },
      "outputs": [],
      "source": [
        "assert(coordinate_to_node_number(3,i=1,j=1) == 1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "assert(coordinate_to_node_number(3,i=1,j=3) == 3)"
      ],
      "metadata": {
        "id": "DtXkuCF74NXF"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "oOjai3dXw_9C"
      },
      "outputs": [],
      "source": [
        "assert(coordinate_to_node_number(3,i=3,j=3) == 9)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "c0X1tj6Sddum"
      },
      "outputs": [],
      "source": [
        "assert(all_nodes(N=3)[0]== (1,1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GkOL7yqEU_by"
      },
      "source": [
        "coordinate_to_node_number nos numera los nodos dependiendo de su posición en la grilla, del 1 al N^2.\n",
        "\n",
        "is_there_a_node_in nos dice si hay un nodo en la posición i,j, en caso contrario se asume que es un nodo que existe en el extremo norte, sur, este, oeste (pues nunca se usan las posiciones noreste, suroeste, etc)\n",
        "\n",
        "nearby_coordinates nos da 4 puntos que son adyacentes vertical u horizontalmente a un punto i,j, sin tomar en cuenta el tamaño de la grilla."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "xrlACe2hU7tK"
      },
      "outputs": [],
      "source": [
        "\n",
        "\n",
        "def is_there_a_node_in(N,i,j):\n",
        "  return (i in range(1,N+1)) and (j in range(1,N+1))\n",
        "\n",
        "# returns an array with the [up, down, left, right] points of i,j\n",
        "def nearby_coordinates(i, j):\n",
        "  return [[i,j+1], [i, j-1], [i-1, j], [i+1, j]]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YdYs0TDkVbdH"
      },
      "source": [
        "::neighbor_nodes toma coordenadas y nos dice si tiene nodos o no."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "id": "JGOPvGSHGrQi"
      },
      "outputs": [],
      "source": [
        "# returns all neighbor nodes that exist in the range 1 <= i,j <= 3, as a map object\n",
        "# If they don't exist in the range, don't return them!\n",
        "def _neighbor_nodes(N,neighbor_points):\n",
        "  return filter(lambda pair: is_there_a_node_in(N,*pair), neighbor_points)\n",
        "# generate row ij based on the nodes we found\n",
        "# TODO: refactor, skip 0 values\n",
        "def _generate_cell_value(current_column, base_node, neighbors):\n",
        "  # The cell aij of the current node is always 4\n",
        "  if(current_column == base_node):\n",
        "    return 4;\n",
        "  elif(current_column in neighbors):\n",
        "    return -1;\n",
        "  return 0;"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G8lH606qKTap"
      },
      "source": [
        "## El algoritmo principal!\n",
        "\n",
        "Este algoritmo genera la fila de A correspondiente a la ecuación Eij.\n",
        "Llamamos akl, a la entrada de a correspondiente a la fila k y columna l.\n",
        "Generamos la fila sabiendo que la entrada diagonal akk debe ser 4, y las entradas correspondientes a los nodos adyacentes al nodo ij son -1."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "id": "tDlsMq95XYFu"
      },
      "outputs": [],
      "source": [
        "def generate_matrix_row(N, i, j, target_matrix):\n",
        "  \"\"\"\n",
        "  N = 4\n",
        "  M = (N - 1) * (N - 1) = 9 nodos\n",
        "  A es una matrix 9x9\n",
        "\n",
        "\n",
        "  A is a MxM matrix.\n",
        "  We're trying to generate a row corresponding to the the node m = coordinate_to_node_number(i,j),\n",
        "  which corresponds to the equation Eij,\n",
        "  1 <= i,j <= M\n",
        "  1 <= m <= MxM\n",
        "\n",
        "  Where the equation Eij is:\n",
        "  T[i,j] = T[(i+1),j] + T[(i-1),j] + T[i,j+1] + T[j-1]\n",
        "\n",
        "  And edge values (existing in a row or column <1 or >3) are predefined constants.\n",
        "  \"\"\"\n",
        "  M = N*N\n",
        "  current_node = coordinate_to_node_number(N,i,j) # corresponde al numero de fila\n",
        "\n",
        "  # the 4 points surrounding i,j in a grid (up, down, left, right)\n",
        "  nearby = nearby_coordinates(i,j)\n",
        "\n",
        "  #  valid node neighbors\n",
        "  neighbors = _neighbor_nodes(N, nearby)\n",
        "\n",
        "  # number them from 1 to M\n",
        "  neighbors = map(lambda pair: coordinate_to_node_number(N, pair[0], pair[1]), neighbors)\n",
        "  neighbors = list(neighbors)\n",
        "\n",
        "  for cell in range(1, M+1):\n",
        "    target_matrix[current_node-1,cell-1] = _generate_cell_value(cell, current_node, neighbors)\n",
        "\n",
        "  return target_matrix\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SSuAuwzyTWQD"
      },
      "source": [
        "Pudiendo generar las filas de A, podemos generar todo A:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "id": "pY6fy6DfRPwB"
      },
      "outputs": [],
      "source": [
        "# Generate matrix\n",
        "# N es la altura de la grilla, o sea N=3 implica 9 nodos en una grilla y A es dimension 9x9\n",
        "# TODO: hacer mas eficiente, crear A de una vez\n",
        "def generate_matrix(N):\n",
        "  target_matrix = scipy.sparse.lil_array((N**2, N**2))\n",
        "  for (i,j) in all_nodes(N):\n",
        "    target_matrix = generate_matrix_row(N, i, j, target_matrix)\n",
        "  return target_matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MmJPcTfpHlaw"
      },
      "source": [
        "Conociendo las temperatures norte, sur, este, oeste, podemos generar b\n",
        "(sabemos que es la suma de las temperaturas de los extremos a los que el nodo es adyacente)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "id": "4c9zXtTqGkOR"
      },
      "outputs": [],
      "source": [
        "\n",
        "\n",
        "# if the node is adjacent to an edge, get the temperatures at the edge\n",
        "def edge_temperatures(N, i, j, cardinal_temperatures):\n",
        "  # toma los 4 vecinos, y toma los que NO son nodos (o sea estan en la esquina)\n",
        "  edges = filter(lambda pair: not is_there_a_node_in(N, *pair), nearby_coordinates(i,j))\n",
        "  # ve si sus temperaturas son NW, NS, etc.\n",
        "  return map(lambda pair: edge_temperature(N, *pair, cardinal_temperatures), edges)\n",
        "\n",
        "def generate_b_entry(N, i, j, cardinal_temperatures):\n",
        "  # this is the b value corresponding to the (i,j)th equation\n",
        "  return sum(edge_temperatures(N, i,j, cardinal_temperatures))\n",
        "\n",
        "def generate_b(N, cardinal_temperatures):\n",
        "  return [generate_b_entry(N, i, j, cardinal_temperatures) for (i,j) in all_nodes(N)]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A69IiuwXIbb2"
      },
      "source": [
        "## Ejemplos\n",
        "N = 4, M = 9, A is a 9x9 matrix\n",
        "it has exactly 2 valid node neighbors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "id": "wzNAla_HoOOW"
      },
      "outputs": [],
      "source": [
        "test_matrix = generate_matrix(3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iHOZ-cj2Zrbx",
        "outputId": "979e1cb2-12eb-4814-b348-d5c076ba16c2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 4. -1.  0. -1.  0.  0.  0.  0.  0.]\n",
            " [-1.  4. -1.  0. -1.  0.  0.  0.  0.]\n",
            " [ 0. -1.  4.  0.  0. -1.  0.  0.  0.]\n",
            " [-1.  0.  0.  4. -1.  0. -1.  0.  0.]\n",
            " [ 0. -1.  0. -1.  4. -1.  0. -1.  0.]\n",
            " [ 0.  0. -1.  0. -1.  4.  0.  0. -1.]\n",
            " [ 0.  0.  0. -1.  0.  0.  4. -1.  0.]\n",
            " [ 0.  0.  0.  0. -1.  0. -1.  4. -1.]\n",
            " [ 0.  0.  0.  0.  0. -1.  0. -1.  4.]]\n"
          ]
        }
      ],
      "source": [
        "print(test_matrix.toarray())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YfRvpYVaZytH",
        "outputId": "4d17e08f-6b5f-4c38-9be9-62e743666466"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 0.0, 0.0, 0.0, 0, 0.0, 0.0, 0.0, 0.0]"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "CARDINAL_TEMPS = {'NORTH': 0.,'SOUTH': 0., 'EAST': 0., 'WEST': 0.}\n",
        "generate_b(3, CARDINAL_TEMPS)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mUDUxYyoWdI5"
      },
      "source": [
        "# PARTE 2: Algoritmo SOR"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rI3eCw3mk06m"
      },
      "source": [
        "Implementa la fórmula derivada del sistema matricial A = D + L + U (Wikipedia en inglés) con la tecnica de reemplazo progresivo de Gauss-Sordel (?).\n",
        "\n",
        "Para usar, debo reemplazar la funcion A[i,j] con algo que devuelva valores aii de una matriz cuadrada a, y la función b(index) con algo que me devuelva valores de un vector b, para solucionar Ax=b.\n",
        "\n",
        "_x_iterations es una lista de k elementos, cada elemento representa una iteración x(k) que es un vector de n entradas, y la voy rellenando en secuencia, reutilizando valores."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HKLssx57gi9F"
      },
      "source": [
        "## Datos de entrada de solve for x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yK4JKI78udPA"
      },
      "source": [
        "El algoritmo para generar las entradas de x(k) fue derivado de la formulación matricial, y se ve así:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o7v9pr5Ee-XY"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "id": "jvrtF7D_g91e"
      },
      "outputs": [],
      "source": [
        "from numpy.lib.index_tricks import IndexExpression\n",
        "\n",
        "def a_times_x_j_k(A, i,j,x):\n",
        "    return A[i,j] * x[0, j]\n",
        "\n",
        "def x_i(b,A, index, previous_iteration, curr_iteration, omega, n):\n",
        "  # sumando 1\n",
        "  sum1 = (1 - omega)* previous_iteration[0, index]\n",
        "\n",
        "  # sumando 2\n",
        "    # factor\n",
        "  factor = omega / A[index,index]\n",
        "\n",
        "  # sumatorias\n",
        "  current_iteration_sum = 0\n",
        "  elems =  A[[index], :].nonzero()\n",
        "  for j in [j for j in elems[1] if j < index]:\n",
        "    current_iteration_sum += a_times_x_j_k(A, index, j, curr_iteration)\n",
        "\n",
        "  # sumatorias\n",
        "  old_iteration_sum = 0\n",
        "  for j in [j for j in elems[1] if j > index]:\n",
        "    old_iteration_sum += a_times_x_j_k(A, index, j, previous_iteration)\n",
        "\n",
        "    # bi\n",
        "  bi = b[index]\n",
        "\n",
        "    # factor (bi - sumatorias)\n",
        "  sum2 = factor * (bi - current_iteration_sum - old_iteration_sum)\n",
        "\n",
        "  return sum1 + sum2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4AID71joa_rN"
      },
      "source": [
        "Calcula un vector x dados los calculos anteriores. En el calculo de xi, utiliza las entradas xj, j < i ya calculadas."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "id": "v0mCEzy2g89J"
      },
      "outputs": [],
      "source": [
        "def x(b, A, previous_iteration, curr_iteration, omega, n):\n",
        "  # we need to initialize this in order to use our results\n",
        "  # from this same iteration\n",
        "  for index in range(0,n):\n",
        "    curr_iteration[0,index] = x_i(b, A, index, previous_iteration, curr_iteration, omega, n)\n",
        "\n",
        "  return curr_iteration"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tRY7avoua0nc"
      },
      "source": [
        "Corre las iteraciones del vector x, guardándolas en un a lista de _x_iterations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "id": "IiceM2Jz80em"
      },
      "outputs": [],
      "source": [
        "\n",
        "# PRINCIPAL\n",
        "def solve_for_x_until(b, A,  seed, until=1, omega=1.5):\n",
        "  assert(until > 0)\n",
        "  n = len(b)\n",
        "  assert(len(seed) == n)\n",
        "\n",
        "  # crea matriz de 2 filas\n",
        "  previous_iteration = numpy.array(seed, ndmin=2)\n",
        "  curr_iteration = numpy.empty((1, n))\n",
        "\n",
        "  error = math.inf\n",
        "  iterations=[]\n",
        "  error_log = []\n",
        "  while error > until:\n",
        "    curr_iteration = x(b, A, previous_iteration, curr_iteration, omega, n)\n",
        "    # intercambiar columnas\n",
        "    iterations.append((curr_iteration - previous_iteration))\n",
        "    # error\n",
        "    ssq_difference = numpy.sum(((curr_iteration - previous_iteration)[0]**2))\n",
        "    ssq_current_iteration = numpy.sum((curr_iteration)[0]**2)\n",
        "    error = ssq_difference / ssq_current_iteration\n",
        "    error_log.append(error)\n",
        "\n",
        "    previous_iteration = numpy.copy(curr_iteration)\n",
        "\n",
        "  return (curr_iteration, iterations, error_log)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cKTml084Ei6o"
      },
      "source": [
        "\n",
        "# Tests"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "id": "FatLCEpe89MT"
      },
      "outputs": [],
      "source": [
        "CARDINAL_TEMPS_2 = {'NORTH': 100.,'SOUTH': -100., 'EAST': 100., 'WEST': -100.}\n",
        "GRID = 31\n",
        "_b = generate_b(N=GRID, cardinal_temperatures=CARDINAL_TEMPS_2)\n",
        "_A = generate_matrix(N=GRID) # must be an array of arrays nxn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "id": "HjELVxCx-CgT"
      },
      "outputs": [],
      "source": [
        "(_x, iterations, errors) = solve_for_x_until(_b, _A, seed = [1]* (GRID**2), until=0.01, omega=1.5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7nR2mtsDAGD0",
        "outputId": "eb3d9547-fdcc-47fb-d81e-3372f24fb806"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1.0181963426940048,\n",
              " 0.12530477210243185,\n",
              " 0.04315955585956537,\n",
              " 0.019470405591805802,\n",
              " 0.010532988460412595,\n",
              " 0.006454791885305585]"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ],
      "source": [
        "errors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "vD25ObQx43Am",
        "outputId": "902c6b3e-9f1c-4d6d-8e66-d26512ed673f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 73
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "reshaped = numpy.reshape(_x, (GRID, GRID))\n",
        "sns.heatmap(reshaped)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "id": "HpHpk5oI8I7S"
      },
      "outputs": [],
      "source": [
        "import json"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "id": "-bn4pvqqmaTz"
      },
      "outputs": [],
      "source": [
        "import seaborn as sns"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D26Ie-F6Dayw"
      },
      "source": [
        "# N = 4"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "id": "C_BUQ9eUDcFT"
      },
      "outputs": [],
      "source": [
        "CARDINAL_TEMPS_2 = {'NORTH': 1.,'SOUTH': 1., 'EAST': 1., 'WEST': 1.}\n",
        "GRID = 3\n",
        "_b = generate_b(N=GRID, cardinal_temperatures=CARDINAL_TEMPS_2)\n",
        "_A = generate_matrix(N=GRID) # must be an array of arrays nxn\n",
        "\n",
        "iterations_needed = []\n",
        "for _omega in numpy.arange(1,2,0.05):\n",
        " (_x, iterations, errors) = solve_for_x_until(_b, _A, seed = [0]* (GRID**2), until=0.01, omega=_omega)\n",
        " iterations_needed.append({\"OMEGA\": _omega, \"ITERATIONS\":len(iterations), \"ERRORS\": errors})"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "iterations_needed"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OnzER2HM4xgD",
        "outputId": "dd742d5a-5996-4a70-e6a2-ea1e3014fc5b"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[{'OMEGA': 1.0,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.11858558320025171,\n",
              "   0.028525084367650867,\n",
              "   0.007640723573057503]},\n",
              " {'OMEGA': 1.05,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.11303272420495704,\n",
              "   0.025337031053655194,\n",
              "   0.006053007653359389]},\n",
              " {'OMEGA': 1.1,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.10784264459784157,\n",
              "   0.022368733016265272,\n",
              "   0.004652347424897425]},\n",
              " {'OMEGA': 1.1500000000000001,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.10315528664547169,\n",
              "   0.019715426100256873,\n",
              "   0.003473094868046225]},\n",
              " {'OMEGA': 1.2000000000000002,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.09915244667294705,\n",
              "   0.01750077576183169,\n",
              "   0.0025637918824527686]},\n",
              " {'OMEGA': 1.2500000000000002,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.09606740914798859,\n",
              "   0.01588631952404651,\n",
              "   0.0019981168097932818]},\n",
              " {'OMEGA': 1.3000000000000003,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.09419653580458699,\n",
              "   0.01508492948131394,\n",
              "   0.0018922297912206765]},\n",
              " {'OMEGA': 1.3500000000000003,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.09391307398005444,\n",
              "   0.015379741436643534,\n",
              "   0.0024320093122334016]},\n",
              " {'OMEGA': 1.4000000000000004,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.09568337383362896,\n",
              "   0.01715040273494665,\n",
              "   0.003915732951853292]},\n",
              " {'OMEGA': 1.4500000000000004,\n",
              "  'ITERATIONS': 4,\n",
              "  'ERRORS': [1.0,\n",
              "   0.10008553136584415,\n",
              "   0.020908929091680305,\n",
              "   0.006821070898854517]},\n",
              " {'OMEGA': 1.5000000000000004,\n",
              "  'ITERATIONS': 5,\n",
              "  'ERRORS': [1.0,\n",
              "   0.10783014041970196,\n",
              "   0.02734784057063088,\n",
              "   0.011910597540750105,\n",
              "   0.005755646606870399]},\n",
              " {'OMEGA': 1.5500000000000005,\n",
              "  'ITERATIONS': 6,\n",
              "  'ERRORS': [1.0,\n",
              "   0.11978225178578138,\n",
              "   0.03740335505037514,\n",
              "   0.020398559327878363,\n",
              "   0.01016136106409608,\n",
              "   0.004425533310134844]},\n",
              " {'OMEGA': 1.6000000000000005,\n",
              "  'ITERATIONS': 6,\n",
              "  'ERRORS': [1.0,\n",
              "   0.13698268006295636,\n",
              "   0.052335806314548795,\n",
              "   0.03421498888212512,\n",
              "   0.017738600914367467,\n",
              "   0.009036677751163699]},\n",
              " {'OMEGA': 1.6500000000000006,\n",
              "  'ITERATIONS': 8,\n",
              "  'ERRORS': [1.0,\n",
              "   0.1606653243532902,\n",
              "   0.07382725553263288,\n",
              "   0.05642305077487252,\n",
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              "   0.017759758557035907,\n",
              "   0.010735102072228246,\n",
              "   0.00746979983789199]},\n",
              " {'OMEGA': 1.7000000000000006,\n",
              "  'ITERATIONS': 9,\n",
              "  'ERRORS': [1.0,\n",
              "   0.19226504061042513,\n",
              "   0.10409092679358045,\n",
              "   0.09187109370203039,\n",
              "   0.05266163873963281,\n",
              "   0.03338438410231939,\n",
              "   0.020669255885197132,\n",
              "   0.02112307030318691,\n",
              "   0.004145134728090181]},\n",
              " {'OMEGA': 1.7500000000000007,\n",
              "  'ITERATIONS': 10,\n",
              "  'ERRORS': [1.0,\n",
              "   0.23340777322911774,\n",
              "   0.1459761189542484,\n",
              "   0.14818117335964184,\n",
              "   0.0889121621096572,\n",
              "   0.05982680981416853,\n",
              "   0.03837622261884396,\n",
              "   0.05745715298772524,\n",
              "   0.014323798588705475,\n",
              "   0.0034004420510008303]},\n",
              " {'OMEGA': 1.8000000000000007,\n",
              "  'ITERATIONS': 11,\n",
              "  'ERRORS': [1.0,\n",
              "   0.28587132252489694,\n",
              "   0.20303225901088168,\n",
              "   0.2371443001784727,\n",
              "   0.1468157031127534,\n",
              "   0.10194786601349905,\n",
              "   0.06894061334803127,\n",
              "   0.1564487110632378,\n",
              "   0.04362336176894396,\n",
              "   0.012183998718884162,\n",
              "   0.007378111571424289]},\n",
              " {'OMEGA': 1.8500000000000008,\n",
              "  'ITERATIONS': 17,\n",
              "  'ERRORS': [1.0,\n",
              "   0.35150201328961694,\n",
              "   0.27946389618018097,\n",
              "   0.37636241106755075,\n",
              "   0.23515974469559411,\n",
              "   0.16474482385900358,\n",
              "   0.11981969646170437,\n",
              "   0.4506203706164433,\n",
              "   0.11703125219331229,\n",
              "   0.04091344626315357,\n",
              "   0.02505127726918139,\n",
              "   0.027834329521225578,\n",
              "   0.01753181842236467,\n",
              "   0.016208519663936327,\n",
              "   0.010503903881180825,\n",
              "   0.016863752671028666,\n",
              "   0.009209572113973531]},\n",
              " {'OMEGA': 1.9000000000000008,\n",
              "  'ITERATIONS': 23,\n",
              "  'ERRORS': [1.0,\n",
              "   0.43207123169842143,\n",
              "   0.3798668861636498,\n",
              "   0.5901762091131393,\n",
              "   0.36210250001654093,\n",
              "   0.25175970752094257,\n",
              "   0.20088653000513862,\n",
              "   1.518804482426721,\n",
              "   0.27383808058089393,\n",
              "   0.12749365619025207,\n",
              "   0.07853189824667792,\n",
              "   0.11382593236974024,\n",
              "   0.07243406161149066,\n",
              "   0.06263056413816966,\n",
              "   0.048314391239456696,\n",
              "   0.10923064203599668,\n",
              "   0.05652653329742514,\n",
              "   0.028428112298289742,\n",
              "   0.019148350798883305,\n",
              "   0.025965163816550972,\n",
              "   0.013887938541035736,\n",
              "   0.01347080012889526,\n",
              "   0.009913389050662509]},\n",
              " {'OMEGA': 1.9500000000000008,\n",
              "  'ITERATIONS': 46,\n",
              "  'ERRORS': [1.0,\n",
              "   0.5290590592901508,\n",
              "   0.5086021705275152,\n",
              "   0.9069184494230362,\n",
              "   0.5312887925646871,\n",
              "   0.36304184383186894,\n",
              "   0.32314576789702315,\n",
              "   7.743385280820632,\n",
              "   0.5507203696628178,\n",
              "   0.36018430663695455,\n",
              "   0.22191982891338827,\n",
              "   0.47448951128739997,\n",
              "   0.2715541742059256,\n",
              "   0.19888804964756274,\n",
              "   0.1957746790082591,\n",
              "   0.9281511579083465,\n",
              "   0.26561860391985986,\n",
              "   0.1980143717214085,\n",
              "   0.11625042506995481,\n",
              "   0.2778084653227227,\n",
              "   0.13093827913325806,\n",
              "   0.10224684291082653,\n",
              "   0.10928721413511142,\n",
              "   0.19144111297581007,\n",
              "   0.11061428872987435,\n",
              "   0.08751215689250073,\n",
              "   0.06382804794032967,\n",
              "   0.16018639408171356,\n",
              "   0.06707536926457375,\n",
              "   0.04715184301424213,\n",
              "   0.05262565683196294,\n",
              "   0.05187195801606174,\n",
              "   0.041046627542284254,\n",
              "   0.03396622220662371,\n",
              "   0.03255454120936665,\n",
              "   0.08325300112960586,\n",
              "   0.03682795213460902,\n",
              "   0.020039103479643227,\n",
              "   0.021639691138007146,\n",
              "   0.017429107466126376,\n",
              "   0.015016507605490196,\n",
              "   0.013324584125320628,\n",
              "   0.014872825946622415,\n",
              "   0.03795217239172023,\n",
              "   0.020112576107926435,\n",
              "   0.008650230801489819]}]"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bvahIwQ9DZyG"
      },
      "source": [
        "# N = 32"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "id": "MKpNAi4V8sjp"
      },
      "outputs": [],
      "source": [
        "CARDINAL_TEMPS_2 = {'NORTH': 1.,'SOUTH': 1., 'EAST': 1., 'WEST': 1.}\n",
        "GRID = 31\n",
        "_b = generate_b(N=GRID, cardinal_temperatures=CARDINAL_TEMPS_2)\n",
        "_A = generate_matrix(N=GRID) # must be an array of arrays nxn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "id": "4u1qLpz5zSP4"
      },
      "outputs": [],
      "source": [
        "iterations_needed = []\n",
        "for _omega in numpy.arange(1,2,0.05):\n",
        " (_x, iterations, errors) = solve_for_x_until(_b, _A, seed = [0]* (GRID**2), until=0.0001, omega=_omega)\n",
        " iterations_needed.append({\"OMEGA\": _omega, \"ITERATIONS\":len(iterations), \"ERRORS\": errors})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "id": "mR37kiVgCp6S",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed66bbcc-c103-42cd-f26f-63357e92a1e7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[{'OMEGA': 1.0,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.12978828165378178,\n",
              "   0.04292655675037578,\n",
              "   0.020494628669286016,\n",
              "   0.011809696286917125,\n",
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              "   0.0010979655590469782,\n",
              "   0.0009428800563671195,\n",
              "   0.0008181723295879876,\n",
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              "   0.00010064561847913979,\n",
              "   9.610177959319869e-05]},\n",
              " {'OMEGA': 1.05,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.12621465645670207,\n",
              "   0.04172149353921875,\n",
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              "   0.00010569120576062036,\n",
              "   0.00010084066812710882,\n",
              "   9.632531845255192e-05]},\n",
              " {'OMEGA': 1.1,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.12321086334376286,\n",
              "   0.04067063314732577,\n",
              "   0.019528894400550192,\n",
              "   0.011307091778805178,\n",
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              "   0.00020922403473875884,\n",
              "   0.00019556334593484834,\n",
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              "   0.00017208171901936448,\n",
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              "   0.00010599905660469497,\n",
              "   0.00010115208600346464,\n",
              "   9.663157473128393e-05]},\n",
              " {'OMEGA': 1.1500000000000001,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.12083958931274834,\n",
              "   0.03978755838332783,\n",
              "   0.019136575290133656,\n",
              "   0.011097916467152793,\n",
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              "   0.00024063350486346923,\n",
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              "   0.0001832227562246621,\n",
              "   0.00017218125015104214,\n",
              "   0.0001621391592524189,\n",
              "   0.00015297555114574608,\n",
              "   0.00014458690632374933,\n",
              "   0.00013688427126725634,\n",
              "   0.0001297909349125816,\n",
              "   0.0001232405207040093,\n",
              "   0.00011717541107084912,\n",
              "   0.00011154543964353976,\n",
              "   0.00010630680050638809,\n",
              "   0.00010142113445170525,\n",
              "   9.685476040031539e-05]},\n",
              " {'OMEGA': 1.2000000000000002,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.11916155501487886,\n",
              "   0.03909984980285181,\n",
              "   0.018808857434292954,\n",
              "   0.010917069215428885,\n",
              "   0.0070831226260742305,\n",
              "   0.004947537856353366,\n",
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              "   0.002200090083234447,\n",
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              "   0.00012586690710578985,\n",
              "   0.00011002001210354704,\n",
              "   9.62425363931385e-05]},\n",
              " {'OMEGA': 1.8000000000000007,\n",
              "  'ITERATIONS': 28,\n",
              "  'ERRORS': [1.0,\n",
              "   0.14454267995131556,\n",
              "   0.0780313105612896,\n",
              "   0.045146306990981586,\n",
              "   0.027440462356055687,\n",
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              "   0.00011638727321992242,\n",
              "   9.869766791897773e-05]},\n",
              " {'OMEGA': 1.8500000000000008,\n",
              "  'ITERATIONS': 30,\n",
              "  'ERRORS': [1.0,\n",
              "   0.14117468675554656,\n",
              "   0.08564380400544191,\n",
              "   0.054628624864393155,\n",
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              "   0.0001059131858167844,\n",
              "   8.834197145968365e-05]},\n",
              " {'OMEGA': 1.9000000000000008,\n",
              "  'ITERATIONS': 44,\n",
              "  'ERRORS': [1.0,\n",
              "   0.13177391104723665,\n",
              "   0.09096422153461473,\n",
              "   0.06495213691829282,\n",
              "   0.04749324892839255,\n",
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              "   0.0012494399634221075,\n",
              "   0.0010763825887410835,\n",
              "   0.0009318486862262629,\n",
              "   0.0008103787670383204,\n",
              "   0.0007076787483566645,\n",
              "   0.0006203436230911205,\n",
              "   0.0005456587668303954,\n",
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              "   0.0004259662758220033,\n",
              "   0.00037778812678607545,\n",
              "   0.00034113883124048356,\n",
              "   0.00030467128830268626,\n",
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              "   0.0002426503588938194,\n",
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              "   0.00012074846829236425,\n",
              "   0.000108847362449929,\n",
              "   9.800347309806813e-05]},\n",
              " {'OMEGA': 1.9500000000000008,\n",
              "  'ITERATIONS': 68,\n",
              "  'ERRORS': [1.0,\n",
              "   0.11550505039907169,\n",
              "   0.09324782854322601,\n",
              "   0.07672079762781511,\n",
              "   0.06401635606396203,\n",
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              "   0.022978826164301917,\n",
              "   0.020279556608256744,\n",
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              "   0.014242157571763845,\n",
              "   0.012743980348689225,\n",
              "   0.011439699336116355,\n",
              "   0.010300724870616904,\n",
              "   0.009304128258426712,\n",
              "   0.00843030784808428,\n",
              "   0.007662845995271425,\n",
              "   0.006988244025487581,\n",
              "   0.006394902113137571,\n",
              "   0.005872810515380078,\n",
              "   0.005413380957965871,\n",
              "   0.00500902484280795,\n",
              "   0.004652884955611398,\n",
              "   0.0043387545916893444,\n",
              "   0.004060955649044972,\n",
              "   0.0038142542034109443,\n",
              "   0.0038838637777936394,\n",
              "   0.0036956346992723416,\n",
              "   0.0035100425188132702,\n",
              "   0.00331125516451055,\n",
              "   0.003180471717265038,\n",
              "   0.003050305962510704,\n",
              "   0.0029309179887790646,\n",
              "   0.0028209168653729045,\n",
              "   0.0027113290214859126,\n",
              "   0.0026008115937873966,\n",
              "   0.002495060707274054,\n",
              "   0.0023890947029874673,\n",
              "   0.0022828481846392233,\n",
              "   0.0021801120004592924,\n",
              "   0.002079626915647383,\n",
              "   0.0019810239498380447,\n",
              "   0.0018858609987421808,\n",
              "   0.0017939049834586607,\n",
              "   0.0017044897804668771,\n",
              "   0.001618087209016323,\n",
              "   0.001535683867863527,\n",
              "   0.0014564616652318616,\n",
              "   0.0013802335153076332,\n",
              "   0.001307360517074992,\n",
              "   0.0012378668589334886,\n",
              "   0.0011710958902946755,\n",
              "   0.0011069084056341302,\n",
              "   0.0010452601527497463,\n",
              "   0.000986057311459958,\n",
              "   0.0009289921193568277,\n",
              "   0.0008739171581103319,\n",
              "   0.0008208160474475028,\n",
              "   0.006670119292813043,\n",
              "   0.0010862413895565155,\n",
              "   0.00018681240556106424,\n",
              "   0.00010500762738689968,\n",
              "   7.851045643238735e-05]}]"
            ]
          },
          "metadata": {},
          "execution_count": 80
        }
      ],
      "source": [
        "iterations_needed"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "id": "JxKI7Wji4QRe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "e3414fac-54de-482f-e3eb-820b216131f5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 81
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "reshaped = numpy.reshape(_x, (GRID, GRID))\n",
        "sns.heatmap(reshaped)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E4TqOrSp9Teo"
      },
      "source": [
        "# Parte II"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "id": "DkWLzwrV8BSB"
      },
      "outputs": [],
      "source": [
        "CARDINAL_TEMPS_2 = {'NORTH': 40.,'SOUTH': 20., 'EAST': 90., 'WEST': 20.}\n",
        "GRID = 7\n",
        "_b = generate_b(N=GRID, cardinal_temperatures=CARDINAL_TEMPS_2)\n",
        "_A = generate_matrix(N=GRID) # must be an array of arrays nxn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "id": "05Yy0USZ9Ssg"
      },
      "outputs": [],
      "source": [
        "(_x, iterations, errors) = solve_for_x_until(_b, _A, seed = [0]* (GRID**2), until=0.001, omega=_omega)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "id": "KJcY-eXAD22q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "c9a1c806-cfc0-48ec-823c-f9783dc94257"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 84
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "reshaped = numpy.reshape(_x, (GRID, GRID))\n",
        "sns.heatmap(numpy.flip(reshaped.transpose(), axis=0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8G10hfunSZPx"
      },
      "source": [
        "# Repetir parte 1 con N=4, N=32 y menor tolerancia"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {
        "id": "ic-pSTrTSdPc"
      },
      "outputs": [],
      "source": [
        "CARDINAL_TEMPS_2 = {'NORTH': 1.,'SOUTH': 1., 'EAST': 1., 'WEST': 1.}\n",
        "GRID = 31\n",
        "_b = generate_b(N=GRID, cardinal_temperatures=CARDINAL_TEMPS_2)\n",
        "_A = generate_matrix(N=GRID) # must be an array of arrays nxn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "id": "3Ja-fAlqSdPd"
      },
      "outputs": [],
      "source": [
        "iterations_needed = []\n",
        "for _omega in numpy.arange(1,2,0.05):\n",
        " (_x, iterations, errors) = solve_for_x_until(_b, _A, seed = [0]* (GRID**2), until=0.000000001, omega=_omega)\n",
        " iterations_needed.append({\"OMEGA\": _omega, \"ITERATIONS\":len(iterations), \"ERRORS\": errors})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "id": "BYBsczkVSfiJ"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}