jbrenorv · June 27, 2021 18:39
diff --git a/interpolacao_polinomial.ipynb b/interpolacao_polinomial.ipynb
 {
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "interpolacao_polinomial.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyMtsxHIMZmQD8l78GCQVmUu",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/jbrenorv/1482a72757c2f9a6b158e2ae64512871/interpolacao_polinomial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JHnOYqEUaFHq"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 156,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K57R13g2aZ3j"
      },
      "source": [
        "def coefs(x, y, k):\n",
        "  \"\"\"\n",
        "  Parameters:\n",
        "    x: as abscissas\n",
        "    y: as ordenadas\n",
        "    k: quantidade de pontos\n",
        "  \"\"\"\n",
        "\n",
        "  nablas = [y]\n",
        "  output = [y[0]]\n",
        "  c_nb = np.zeros(k)\n",
        "\n",
        "  for ordem in range(1, k):\n",
        "    for i in range(k - ordem):\n",
        "      # Nabla anterior, para calcular o atual\n",
        "      p_nb = nablas[ordem -1]\n",
        "\n",
        "      # Nabla atual\n",
        "      c_nb[i] = (p_nb[i+1] - p_nb[i]) / (x[i + ordem] - x[i])\n",
        "    \n",
        "    output.append( round(c_nb[0], 3) )\n",
        "    nablas.append( c_nb )\n",
        "  \n",
        "  return output\n"
      ],
      "execution_count": 157,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AwcgguP7UVSm"
      },
      "source": [
        "def polinomio_interpolador(x, m):\n",
        "  \"\"\"\n",
        "  Parameters:\n",
        "    x: as abscissas\n",
        "    m: os coeficientes\n",
        "  \"\"\"\n",
        "\n",
        "  output = f'{m[0]}'\n",
        "\n",
        "  for j in range(1, len(x)):\n",
        "    if m[j] == 0:\n",
        "      continue\n",
        "\n",
        "    parcela = f'{abs(m[j])}'\n",
        "    \n",
        "    for i in range(j):\n",
        "      parcela = parcela + f'(x - {x[i]})'\n",
        "    \n",
        "    output = output + f' {\"+\" if m[j] > 0 else \"-\"} {parcela}'\n",
        "  \n",
        "  return output"
      ],
      "execution_count": 158,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m64tGrGrey16"
      },
      "source": [
        "def predict(x, m, _x):\n",
        "  \"\"\"\n",
        "  Parameters:\n",
        "     x: as abscissas\n",
        "     m: os coeficientes\n",
        "    _x: para calcular P(_x)\n",
        "  \"\"\"\n",
        "\n",
        "  output = m[0]\n",
        "\n",
        "  for j in range(1, len(x)):\n",
        "    if m[j] == 0:\n",
        "      continue\n",
        "\n",
        "    parcela = m[j]\n",
        "    \n",
        "    for i in range(j):\n",
        "      parcela = parcela * (_x - x[i])\n",
        "    \n",
        "    output = output + parcela\n",
        "  \n",
        "  return output"
      ],
      "execution_count": 159,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H1AhC4xarxIX"
      },
      "source": [
        "x = [0, 15, 30, 45]\n",
        "y = [184, 96, 119, 196]\n",
        "k = 4\n",
        "\n",
        "m = coefs(x, y, k)"
      ],
      "execution_count": 160,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "3tOGO64NW4n7",
        "outputId": "c9ae01f0-6a64-47ce-8010-baeb3cfbae11"
      },
      "source": [
        "print(polinomio_interpolador(x, m))"
      ],
      "execution_count": 161,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "184 - 5.867(x - 0) + 0.247(x - 0)(x - 15) - 0.003(x - 0)(x - 15)(x - 30)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WUH4SUgGlpEF"
      },
      "source": [
        "Guardar em x_axis, todos os números da forma k*0.1, com k natural, entre 0 e 45.1. Ou seja, a sequência (0, 0.1, 0.2, ..., 45, 45.1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eAURKBnYcc4L"
      },
      "source": [
        "i = 0.1\n",
        "a = x[0]\n",
        "b = x[-1] + i\n",
        "x_axis = np.arange(a, b, i)"
      ],
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lgt8YYKzmvFK"
      },
      "source": [
        "E depois obter a imagem desses números no polinômio interpolador e armazenar em y_axis. E nesse processo, encontrar uma aproximação para o ponto de mínimo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oiqYQq3Elk0B"
      },
      "source": [
        "y_axis = []\n",
        "x_min = 0.\n",
        "y_min = 100000. # um numero bem grande\n",
        "\n",
        "# Para cada z em x_axis...\n",
        "for z in x_axis:\n",
        "\n",
        "  # seja t = P(z)\n",
        "  t = predict(x, m, z)\n",
        "\n",
        "  # adiciona t em y_axis\n",
        "  y_axis.append(t)\n",
        "\n",
        "  # Testando se t é menor que o mínimo atual\n",
        "  if (t < y_min):\n",
        "\n",
        "    # se for, atualiza o mínimo\n",
        "    y_min = t\n",
        "    x_min = z\n"
      ],
      "execution_count": 163,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "5fR-30J_dTOj",
        "outputId": "96d9c7db-b03b-4a07-952d-11b6eca36afa"
      },
      "source": [
        "plt.plot(x_axis, y_axis)\n",
        "plt.show()"
      ],
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WzmDDE_Po4CL"
      },
      "source": [
        "Mostrar o ponto crítico encontrado"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "vaAiZO4bipMR",
        "outputId": "ee8d65df-7a95-41a6-9219-90d0d964f6a9"
      },
      "source": [
        "print(f'min= ({x_min}, {y_min})')"
      ],
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "min= (18.2, 93.667576)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "nDO9LHcsTO27",
        "outputId": "ef0c87d3-7e07-4007-8c50-17c0985d6fc7"
      },
      "source": [
        "predict(x, m, 18.2)"
      ],
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "93.667576"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 166
        }
      ]
    }
  ]
 }
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "interpolacao_polinomial.ipynb",
	"provenance": [],
	"collapsed_sections": [],
	"toc_visible": true,
	"authorship_tag": "ABX9TyMtsxHIMZmQD8l78GCQVmUu",
	"include_colab_link": true
	},
	"kernelspec": {
	"name": "python3",
	"display_name": "Python 3"
	},
	"language_info": {
	"name": "python"
	}
	},
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/jbrenorv/1482a72757c2f9a6b158e2ae64512871/interpolacao_polinomial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "JHnOYqEUaFHq"
	},
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt"
	],
	"execution_count": 156,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "K57R13g2aZ3j"
	},
	"source": [
	"def coefs(x, y, k):\n",
	" \"\"\"\n",
	" Parameters:\n",
	" x: as abscissas\n",
	" y: as ordenadas\n",
	" k: quantidade de pontos\n",
	" \"\"\"\n",
	"\n",
	" nablas = [y]\n",
	" output = [y[0]]\n",
	" c_nb = np.zeros(k)\n",
	"\n",
	" for ordem in range(1, k):\n",
	" for i in range(k - ordem):\n",
	" # Nabla anterior, para calcular o atual\n",
	" p_nb = nablas[ordem -1]\n",
	"\n",
	" # Nabla atual\n",
	" c_nb[i] = (p_nb[i+1] - p_nb[i]) / (x[i + ordem] - x[i])\n",
	" \n",
	" output.append( round(c_nb[0], 3) )\n",
	" nablas.append( c_nb )\n",
	" \n",
	" return output\n"
	],
	"execution_count": 157,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "AwcgguP7UVSm"
	},
	"source": [
	"def polinomio_interpolador(x, m):\n",
	" \"\"\"\n",
	" Parameters:\n",
	" x: as abscissas\n",
	" m: os coeficientes\n",
	" \"\"\"\n",
	"\n",
	" output = f'{m[0]}'\n",
	"\n",
	" for j in range(1, len(x)):\n",
	" if m[j] == 0:\n",
	" continue\n",
	"\n",
	" parcela = f'{abs(m[j])}'\n",
	" \n",
	" for i in range(j):\n",
	" parcela = parcela + f'(x - {x[i]})'\n",
	" \n",
	" output = output + f' {\"+\" if m[j] > 0 else \"-\"} {parcela}'\n",
	" \n",
	" return output"
	],
	"execution_count": 158,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "m64tGrGrey16"
	},
	"source": [
	"def predict(x, m, _x):\n",
	" \"\"\"\n",
	" Parameters:\n",
	" x: as abscissas\n",
	" m: os coeficientes\n",
	" _x: para calcular P(_x)\n",
	" \"\"\"\n",
	"\n",
	" output = m[0]\n",
	"\n",
	" for j in range(1, len(x)):\n",
	" if m[j] == 0:\n",
	" continue\n",
	"\n",
	" parcela = m[j]\n",
	" \n",
	" for i in range(j):\n",
	" parcela = parcela * (_x - x[i])\n",
	" \n",
	" output = output + parcela\n",
	" \n",
	" return output"
	],
	"execution_count": 159,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "H1AhC4xarxIX"
	},
	"source": [
	"x = [0, 15, 30, 45]\n",
	"y = [184, 96, 119, 196]\n",
	"k = 4\n",
	"\n",
	"m = coefs(x, y, k)"
	],
	"execution_count": 160,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 0
	},
	"id": "3tOGO64NW4n7",
	"outputId": "c9ae01f0-6a64-47ce-8010-baeb3cfbae11"
	},
	"source": [
	"print(polinomio_interpolador(x, m))"
	],
	"execution_count": 161,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	"184 - 5.867(x - 0) + 0.247(x - 0)(x - 15) - 0.003(x - 0)(x - 15)(x - 30)\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "WUH4SUgGlpEF"
	},
	"source": [
	"Guardar em x_axis, todos os números da forma k*0.1, com k natural, entre 0 e 45.1. Ou seja, a sequência (0, 0.1, 0.2, ..., 45, 45.1)"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "eAURKBnYcc4L"
	},
	"source": [
	"i = 0.1\n",
	"a = x[0]\n",
	"b = x[-1] + i\n",
	"x_axis = np.arange(a, b, i)"
	],
	"execution_count": 162,
	"outputs": []
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "lgt8YYKzmvFK"
	},
	"source": [
	"E depois obter a imagem desses números no polinômio interpolador e armazenar em y_axis. E nesse processo, encontrar uma aproximação para o ponto de mínimo."
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "oiqYQq3Elk0B"
	},
	"source": [
	"y_axis = []\n",
	"x_min = 0.\n",
	"y_min = 100000. # um numero bem grande\n",
	"\n",
	"# Para cada z em x_axis...\n",
	"for z in x_axis:\n",
	"\n",
	" # seja t = P(z)\n",
	" t = predict(x, m, z)\n",
	"\n",
	" # adiciona t em y_axis\n",
	" y_axis.append(t)\n",
	"\n",
	" # Testando se t é menor que o mínimo atual\n",
	" if (t < y_min):\n",
	"\n",
	" # se for, atualiza o mínimo\n",
	" y_min = t\n",
	" x_min = z\n"
	],
	"execution_count": 163,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 265
	},
	"id": "5fR-30J_dTOj",
	"outputId": "96d9c7db-b03b-4a07-952d-11b6eca36afa"
	},
	"source": [
	"plt.plot(x_axis, y_axis)\n",
	"plt.show()"
	],
	"execution_count": 164,
	"outputs": [
	{
	"output_type": "display_data",
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "WzmDDE_Po4CL"
	},
	"source": [
	"Mostrar o ponto crítico encontrado"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 0
	},
	"id": "vaAiZO4bipMR",
	"outputId": "ee8d65df-7a95-41a6-9219-90d0d964f6a9"
	},
	"source": [
	"print(f'min= ({x_min}, {y_min})')"
	],
	"execution_count": 165,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	"min= (18.2, 93.667576)\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 0
	},
	"id": "nDO9LHcsTO27",
	"outputId": "ef0c87d3-7e07-4007-8c50-17c0985d6fc7"
	},
	"source": [
	"predict(x, m, 18.2)"
	],
	"execution_count": 166,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"93.667576"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 166
	}
	]
	}
	]
	}