testes_funcoes_at_03.ipynb

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        "<a href=\"https://colab.research.google.com/github/fellypesb/calc-num/blob/main/testes_funcoes_at_03.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# **Comparação entre métodos iterativos aplicados no cálculo de zero de funções**\n",
        "\n",
        "Atividade desenvolvida durante as aulas de Cálculo Numérico ministrada pela prof. Dr. Helaine Furtado na Universidade Federal do Oeste do Pará (UFOPA).\n",
        "\n",
        "- **Equipe:** \n",
        "        Almiriane Goulart  \n",
        "        Davi Lima Rodrigues\n",
        "        Fellype Siqueira Barroso\n",
        "          \n",
        "\n",
        "  \n",
        "        "
      ]
    },
    {
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      "source": [
        "# **Teste de funções**\n",
        "O teste de funções foi realizada a partir da classe `IterativeMethods()`. Nesta classe, encontra-se a implementação de 4 métodos iterativos:\n",
        "\n",
        "- Método da Bissecção;\n",
        "- Método de Newton;\n",
        "- Método da Secante;\n",
        "- Método do Ponto Fixo.\n",
        "\n",
        "O construtor desta classe recebe 4 importantes parâmetros que são acessíveis a todos os métodos e que são definidos pelo estudo comparativo que desejamos realizar. São eles: função `f`, critério de erro `tol`, número máximo de iterações `maxiter`, casas decimais de precisão para os resultados `round_`."
      ]
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      "source": [
        "import numpy as np\n",
        "\n",
        "class IterativeMethods:\n",
        "    '''\n",
        "    Esta classe implementa 4 métodos iterativos que podem ser \n",
        "    utilizados para encontrar zeros de funções. \n",
        "    \n",
        "    Parâmetros\n",
        "    --------------\n",
        "    f: lambda\n",
        "        Função a qual irá ser utilizada em todos os métodos com \n",
        "        objetivo de encontrar suas raízes.\n",
        "\n",
        "    tol: float\n",
        "        Tolerância para critério de parada dos métodos.\n",
        "        \n",
        "    maxiter: int\n",
        "        Número máximo de iterações desejadas.\n",
        "\n",
        "    round_: int\n",
        "         Número de casas decimais de precisão desejada.\n",
        "         \n",
        "    '''\n",
        "    \n",
        "    def __init__(self, f, tol:float, maxiter:int, round_:int):\n",
        "        self.f = f\n",
        "        self.tol = tol\n",
        "        self.maxiter = maxiter\n",
        "        self.round_ = round_\n",
        "        \n",
        "    def bisseccao(self, a, b, verbose=False):\n",
        "        '''\n",
        "            Função que calcula o zero de funções com o método da Bissecção.\n",
        "            \n",
        "            O processo iterativo deste método é realizado da seguinte forma:\n",
        "            \n",
        "            x = (a + b)/2\n",
        "\n",
        "            Parâmetros\n",
        "            --------------\n",
        "            a: float\n",
        "                Extremo esquerdo do intervalo de inspeção [a,b].\n",
        "\n",
        "            b: float\n",
        "                Extremo direito do intervalo de inspeção [a,b].\n",
        "\n",
        "            verbose: bool, default=False\n",
        "                Se True, o progresso das iterações é impresso na tela.\n",
        "\n",
        "            Saída\n",
        "            -----------\n",
        "            dict contendo a quantidade de iterações necessárias para\n",
        "            convergência, valor x^* e f(x^*) tal que f(x^*) é aprox. 0.\n",
        "        '''\n",
        "        \n",
        "        if self.f(a)*self.f(b) > 0:\n",
        "            raise ValueError(\"Não há raiz no intervalo fornecido.\")\n",
        "\n",
        "        iter_ = 0\n",
        "\n",
        "        while(iter_ <= self.maxiter and round(abs(b - a), self.round_) > self.tol):\n",
        "            x = round((a + b)/2, self.round_)      \n",
        "\n",
        "            f_a = round(self.f(a), self.round_)\n",
        "            f_b = round(self.f(b), self.round_)\n",
        "            f_x = round(self.f(x), self.round_)\n",
        "\n",
        "            product = round((f_a * f_x), self.round_)\n",
        "            if(product > 0):\n",
        "                a = x\n",
        "            else:\n",
        "                b = x\n",
        "\n",
        "            iter_ += 1\n",
        "            if verbose:\n",
        "                print(f'Iteração: {iter_} \\t f(a): {f_a} \\t f(b): {f_b} \\t f(x): {f_x} \\t Aproximação: {x}')\n",
        "        if iter_ > self.maxiter:\n",
        "            print(\"Número máximo de iterações alcançado!\")\n",
        "        else:\n",
        "            return {'iter':iter_, 'raiz':x, 'f(x)':round(self.f(x), self.round_)}\n",
        "    \n",
        "    def fixedpoint(self, x0, g, verbose=False):\n",
        "        '''\n",
        "            Função que calcula o zero de funções com o método do Ponto Fixo.\n",
        "            O processo iterativo é realizado da seguinte forma:\n",
        "\n",
        "            x = g(x)\n",
        "\n",
        "            Parâmetros\n",
        "            --------------\n",
        "            x0: float\n",
        "                Chute inicial.\n",
        "\n",
        "            g: lambda\n",
        "                Função alcançada apartir de f(x).\n",
        "                Ex: f(x) = xe^x-1\n",
        "                    g(x) = 1/e^x\n",
        "\n",
        "            verbose: bool, default=False\n",
        "                Se True, o progresso das iterações é impresso na tela.\n",
        "\n",
        "            Saída\n",
        "            -----------\n",
        "            dict contendo a quantidade de iterações necessárias para\n",
        "            convergência, valor x^* e f(x^*) tal que f(x^*) é aprox. 0.\n",
        "        '''\n",
        "        \n",
        "        iter_ = 0 \n",
        "        while( iter_ <= self.maxiter and round(abs(self.f(x0)), self.round_) > self.tol):\n",
        "            x0 = round(g(x0), self.round_)\n",
        "            iter_ += 1\n",
        "            if verbose:\n",
        "                print(f'Iterações: {iter_} \\t Aproximação: {x0}') \n",
        "        if iter_ > self.maxiter:\n",
        "            print(\"Número máximo de iterações alcançado!\")\n",
        "        else:\n",
        "            return {'iter':iter_, 'raiz':x0, 'f(x)':round(self.f(x0), self.round_)}\n",
        "        \n",
        "    def newton(self, x0, df, verbose=False):\n",
        "        '''\n",
        "            Função que calcula o zero de funções com o método de Newton.\n",
        "            O processo iterativo é realizado da seguinte forma:\n",
        "\n",
        "            x = x - f(x)/f'(x)\n",
        "\n",
        "            Parâmetros\n",
        "            --------------\n",
        "            x0: float\n",
        "                Chute inicial.\n",
        "\n",
        "            df: lambda\n",
        "                Derivada da função a qual queremos encontrar suas raízes.\n",
        "\n",
        "            verbose: bool, default=False\n",
        "                Se True, o progresso das iterações é impresso na tela.\n",
        "\n",
        "            Saída\n",
        "            -----------\n",
        "            dict contendo a quantidade de iterações necessárias para\n",
        "            convergência, valor x^* e f(x^*) tal que f(x^*) é aprox. 0.\n",
        "        '''\n",
        "        \n",
        "        iter_ = 0 \n",
        "        while( iter_ <= self.maxiter and round(abs(self.f(x0)), self.round_) > self.tol):\n",
        "\n",
        "            x0 = round(x0 - (self.f(x0)/df(x0)), self.round_)\n",
        "            iter_ += 1\n",
        "            if verbose:\n",
        "                 print(f'Iterações: {iter_} \\t Aproximação: {x0}') \n",
        "        if iter_ > self.maxiter:\n",
        "            print(\"Número máximo de iterações alcançado!\")\n",
        "        else:\n",
        "            return {'iter':iter_, 'raiz':x0, 'f(x)':round(self.f(x0), self.round_)}\n",
        "        \n",
        "    def secant(self, x0, x1, verbose=False):\n",
        "        '''\n",
        "            Função que calcula o zero de funções com o método da Secante.\n",
        "            \n",
        "            O método iterativo é realizado da Seguinte forma:\n",
        "\n",
        "            x1 = (x0*f(x1) - x1*f(x0)) / (f(x1) - f(x0))  \n",
        "\n",
        "            Parametros\n",
        "            --------------\n",
        "            x0: float\n",
        "                Primeiro chute inicial.\n",
        "\n",
        "            x1: float\n",
        "                Segundo chute inicial.\n",
        "\n",
        "            verbose: bool, default=False\n",
        "                Se True, o progresso das iterações é impresso na tela.\n",
        "\n",
        "            Saída\n",
        "            -----------\n",
        "            dict contendo a quantidade de iterações necessárias para convergência\n",
        "            e valor x, tal que f(x) é aprox. 0.\n",
        "        '''\n",
        "        iter_ = 0\n",
        "\n",
        "        while( iter_ <= self.maxiter and round(abs(self.f(x1)), self.round_) > self.tol):\n",
        "            c = x1\n",
        "            x1 = round((x0*self.f(x1) - x1*self.f(x0)) / (self.f(x1) - self.f(x0)), self.round_)\n",
        "            x0 = c\n",
        "            iter_ += 1\n",
        "            if verbose:\n",
        "                print(f'Iterações: {iter_} \\t Aproximação: {x1}')\n",
        "\n",
        "        if iter_ > self.maxiter:\n",
        "            print(\"Número máximo de iterações alcançado!\")\n",
        "        else:\n",
        "            return {'iter':iter_, 'raiz': x1, 'f(x)':round(self.f(x1), self.round_)}\n"
      ],
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      "source": [
        "Definiu-se que para todos os testes que serão realizados a seguir  o número de casas decimais `round_ = 14` e o número máximo de iterações `maxiter = 40`. \n",
        "\n",
        "# **Função de teste 1**\n",
        "\n",
        "$f(x) = e^{-x^2} - \\cos x$\n",
        "\n",
        "$\\varepsilon = 10^{-7}$\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
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      "source": [
        "# Plot do gráfico da função de estudo 1.\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "function  = lambda x: np.exp(-x**2) - np.cos(x)\n",
        "\n",
        "x = np.linspace(-4,4)\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.plot(x, function(x))\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 2,
      "outputs": [
        {
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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "11KWGIplAQCD"
      },
      "source": [
        "Ao analisar o gráfico é possível observar várias raízes da função. Uma dessas raízes se encontra no intervalo entre $[1, 2]$ ou mais precisamente entre o intervalo $[1; 1,5]$, utilizaremos essa informação para ser explorada pelos métodos iterativos abaixo, na tentativa de aproximação do valor $x^*$, isto é, o zero da função. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RAkrGjYlXwch"
      },
      "source": [
        "# Teste da função 1 pelos métodos iterativos.\n",
        "\n",
        "f = lambda x:np.exp(-x**2)-np.cos(x)\n",
        "df = lambda x: -2*x*np.exp(-x**2)+np.sin(x)\n",
        "g1 = lambda x: np.cos(x) + x - np.exp(-x**2) # Converge lentamente - 13 iterações\n",
        "g2 = lambda x: x + 1/0.6*(-np.exp(-x**2)+np.cos(x)) # Converge rapidamente - 5 iterações \n",
        "\n",
        "metodo = IterativeMethods(f=f, tol=1e-7, round_=14, maxiter=40)\n",
        "\n",
        "bisseccao = metodo.bisseccao(a=1, b=1.5)\n",
        "newton = metodo.newton(x0=1.5, df=df)\n",
        "secante = metodo.secant(x0=1, x1=1.5)\n",
        "pontoFixo = metodo.fixedpoint(x0=1.5, g=g2)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "dVErkm7AXks0",
        "outputId": "78a86975-4341-4235-d85a-b9a2748d45a1"
      },
      "source": [
        "# Visualização em formato tabular dos resultados obtidos para a função 1.\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "pd.options.display.precision = 14\n",
        "results = pd.DataFrame({'Bissecção':bisseccao, 'Newton':newton, 'Secante':secante, 'Ponto Fixo': pontoFixo})\n",
        "\n",
        "results.rename(index={'iter':'Iterações', 'raiz':'Aproximação'}).T"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iterações</th>\n",
              "      <th>Aproximação</th>\n",
              "      <th>f(x)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Bissecção</th>\n",
              "      <td>23.0</td>\n",
              "      <td>1.44741421937942</td>\n",
              "      <td>-0.00000003302604</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Newton</th>\n",
              "      <td>3.0</td>\n",
              "      <td>1.44741427129931</td>\n",
              "      <td>0.00000000000196</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Secante</th>\n",
              "      <td>4.0</td>\n",
              "      <td>1.44741424993837</td>\n",
              "      <td>-0.00000001358646</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ponto Fixo</th>\n",
              "      <td>5.0</td>\n",
              "      <td>1.44741420734217</td>\n",
              "      <td>-0.00000004068334</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Iterações       Aproximação              f(x)\n",
              "Bissecção        23.0  1.44741421937942 -0.00000003302604\n",
              "Newton            3.0  1.44741427129931  0.00000000000196\n",
              "Secante           4.0  1.44741424993837 -0.00000001358646\n",
              "Ponto Fixo        5.0  1.44741420734217 -0.00000004068334"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BknMpRCnBfh6"
      },
      "source": [
        "Ao analisar os resultados obtidos podemos perceber que o método da bisseccão foi o mais lento e menos preciso. Enquanto que, os demais métodos atingiram a convergência em menos de 10 iterações. O método de Newton, foi o método mais rápido e preciso, pois necessitou da menor quantidade de iterações e o valor de $f(x^*)$ mais próximo de zero. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "pP-qqm8lUqxS",
        "outputId": "0be15dfa-c674-4145-c4a0-582fcfd15020"
      },
      "source": [
        "# Plot da função de estudo 1 com a aproximação encontrada pelos métodos.\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "function  = lambda x: np.exp(-x**2) - np.cos(x)\n",
        "\n",
        "x = np.linspace(-6,6)\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.plot(x, function(x))\n",
        "plt.scatter(1.44741427129931,0, label='Aproximação encontrada', c='r')\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QHAnmvPpif_n"
      },
      "source": [
        "# **Função de teste 2**\n",
        "\n",
        "$f(x) = x^3 - x - 1$\n",
        "\n",
        "$\\varepsilon = 10^{-5}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "yJVOH3DtVOyM",
        "outputId": "892558de-2be1-4948-cc5f-2123c0c8e6f4"
      },
      "source": [
        "# Plot do gráfico da função de estudo 2\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "function  = lambda x: x**3 - x - 1\n",
        "\n",
        "x = np.linspace(-2,2)\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.plot(x, function(x))\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mymUvkz1DSo9"
      },
      "source": [
        "Ao analisar o gráfico acima podemos observar a existência de uma raíz localizada no intervalo $[0; 1,5]$ para esta função. Essa informação será utilizada pelos métodos a seguir."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WVidFllfkUoi"
      },
      "source": [
        "# Teste da função 2 pelos métodos iterativos\n",
        "\n",
        "f = lambda x: x**3 - x - 1\n",
        "df = lambda x: 3*x**2 - 1\n",
        "\n",
        "g1 = lambda x: x**3 - 1 # Overflow erro no arredondamento\n",
        "g2 = lambda x: (x + 1)**1/3 # não converge\n",
        "g3 = lambda x: 1/x**2 - 1  # divisão por zero\n",
        "g4 = lambda x: ((1/x)+1)**0.5 # converge em 9 iterações\n",
        "\n",
        "\n",
        "metodo = IterativeMethods(f=f, tol=1e-5, round_=14, maxiter=40)\n",
        "\n",
        "bisseccao = metodo.bisseccao(a=0, b=1.5)\n",
        "newton = metodo.newton(x0=0, df=df)\n",
        "secante = metodo.secant(x0=0, x1=0.5)\n",
        "pontoFixo = metodo.fixedpoint(x0=0.5, g=g4)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "nJWKGCT6wLmO",
        "outputId": "d95b1eff-ce74-4abe-b72e-81670f1a19af"
      },
      "source": [
        "# Visualização em formato tabular dos resultados para função de estudo 2.\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "pd.options.display.precision = 14\n",
        "results = pd.DataFrame({'Bissecção':bisseccao, 'Newton':newton, 'Secante':secante, 'Ponto Fixo': pontoFixo})\n",
        "\n",
        "results.rename(index={'iter':'Iterações', 'raiz':'Aproximação'}).T"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iterações</th>\n",
              "      <th>Aproximação</th>\n",
              "      <th>f(x)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Bissecção</th>\n",
              "      <td>18.0</td>\n",
              "      <td>1.32471656799317</td>\n",
              "      <td>-0.00000592464044</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Newton</th>\n",
              "      <td>20.0</td>\n",
              "      <td>1.32471878861526</td>\n",
              "      <td>0.00000354549288</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Secante</th>\n",
              "      <td>26.0</td>\n",
              "      <td>1.32471794706667</td>\n",
              "      <td>-0.00000004340576</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ponto Fixo</th>\n",
              "      <td>9.0</td>\n",
              "      <td>1.32471948003467</td>\n",
              "      <td>0.00000649414938</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Iterações       Aproximação              f(x)\n",
              "Bissecção        18.0  1.32471656799317 -0.00000592464044\n",
              "Newton           20.0  1.32471878861526  0.00000354549288\n",
              "Secante          26.0  1.32471794706667 -0.00000004340576\n",
              "Ponto Fixo        9.0  1.32471948003467  0.00000649414938"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nhty7NfzEOm0"
      },
      "source": [
        "Para esta função o método da Secante foi o mais lento necessitando de 26 iterações para atingir a convergência. O método do Ponto Fixo foi o mais rápido de todos e necessitou de apenas 9 iterações. Apesar do método da Secante ter sido o método mais lento o valor da sua $f(x^*)$ foi o mais próxima de zero tendo encontrado, portanto, a aproximação mais precisa."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "4DfPZlfXV0CQ",
        "outputId": "16104b33-e566-415c-ce2a-d6ee59ea5865"
      },
      "source": [
        "# Plot do gráfico da função de estudo 2 e a aproximação encontrada pelos métodos.\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "function  = lambda x: x**3 - x - 1\n",
        "\n",
        "x = np.linspace(-2,2)\n",
        "plt.figure(figsize=(13,5))\n",
        "plt.plot(x, function(x))\n",
        "plt.scatter(1.32471794706667, 0, label='Aproximação encontrada', c='r')\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TJf8T3J6_t4v"
      },
      "source": [
        "# **Função de teste 3**\n",
        "\n",
        "$f(x) = x^3-9x+2$  \n",
        "\n",
        "$\\varepsilon = 10^{-10}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "jNfQtREYWOuB",
        "outputId": "6a2d5b94-f00d-4c20-b8c5-a140432838b4"
      },
      "source": [
        "# Plot do gráfico da função de estudo 3\n",
        "\n",
        "function = lambda x: x**3 - 9*x + 2\n",
        "\n",
        "x = np.linspace(-4,4)\n",
        "\n",
        "plt.figure(figsize=(13, 5))\n",
        "plt.plot(x, function(x))\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d6lstsPUGbHX"
      },
      "source": [
        "Ao analisar o gráfico da função de estudo 3 (três) podemos visualizar a presença de 3 (três) raízes, isto é corente, pois trata-se de uma raíz cúbica. Uma dessas raízes está localizada no intervalo entre $[0, 1]$. Sabendo disso, buscou-se encontrar o valor $x^*$ por meio dessa informação e utilizando os métodos iterativos a seguir."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b4M6IkXSBiu6"
      },
      "source": [
        "# Teste da função de estudo 3 pelos métodos iterativos\n",
        "\n",
        "f = lambda x: x**3 - 9*x + 2\n",
        "df = lambda x: 3*x**2 - 9\n",
        "\n",
        "g1 = lambda x: (x**3 + 2)/9 # converge em 6 iterações\n",
        "g2 = lambda x: - 2/(x**2 - 9) # converge em 6 iterações com maior precisão\n",
        "g3 = lambda x: (9*x - 2)**1/3 # não converge\n",
        "g4 = lambda x: (9-2/x)**1/2 # ocorre divisão por zero\n",
        "\n",
        "metodo = IterativeMethods(f=f, tol=1e-10, maxiter=40, round_=14)\n",
        "\n",
        "bisseccao = metodo.bisseccao(a=0, b=1)\n",
        "newton = metodo.newton(x0=0, df=df)\n",
        "secante = metodo.secant(x0=-0.5, x1=0)\n",
        "pontoFixo = metodo.fixedpoint(x0=0, g=g2)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "NqoBDCY3EEEg",
        "outputId": "18e3b339-3098-4b9e-b733-b0b69fbd0a83"
      },
      "source": [
        "# Visualização em formato tabular dos resultados para a função de estudo 3\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "pd.options.display.precision = 14\n",
        "results = pd.DataFrame({'Bissecção':bisseccao, 'Newton':newton, 'Secante':secante, 'Ponto Fixo': pontoFixo})\n",
        "\n",
        "results.rename(index={'iter':'Iterações', 'raiz':'Aproximação'}).T"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iterações</th>\n",
              "      <th>Aproximação</th>\n",
              "      <th>f(x)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Bissecção</th>\n",
              "      <td>34.0</td>\n",
              "      <td>0.22346206387737</td>\n",
              "      <td>0.00000006895952</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Newton</th>\n",
              "      <td>3.0</td>\n",
              "      <td>0.22346207166923</td>\n",
              "      <td>0.00000000000005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Secante</th>\n",
              "      <td>4.0</td>\n",
              "      <td>0.22346207166933</td>\n",
              "      <td>-0.00000000000084</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Ponto Fixo</th>\n",
              "      <td>6.0</td>\n",
              "      <td>0.22346207166902</td>\n",
              "      <td>0.00000000000191</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            Iterações       Aproximação              f(x)\n",
              "Bissecção        34.0  0.22346206387737  0.00000006895952\n",
              "Newton            3.0  0.22346207166923  0.00000000000005\n",
              "Secante           4.0  0.22346207166933 -0.00000000000084\n",
              "Ponto Fixo        6.0  0.22346207166902  0.00000000000191"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ma9vru9gIVnx"
      },
      "source": [
        "Dentre os 4 (quatro) métodos o mais lento e menos preciso foi o da bissecção, como pode ser observado acima. Esse método necessitou de um grande número de iterações para atingir a convergência 34 (trinta e quatro), enquanto que os demais necessitaram de menos de 10 iterações para convergir. O método de Newton assim como para a primeira função foi o método mais rápido e preciso obtendo $f(x^*)$ mais próximo de zero."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "W4MbDaf9W_ix",
        "outputId": "77584c0d-1c55-4ff6-ab50-862d8bfcaf83"
      },
      "source": [
        "# Plot do gráfico da função de estudo 3 e a aproximação encontrada pelos métodos\n",
        "\n",
        "function = lambda x: x**3 - 9*x + 2\n",
        "\n",
        "x = np.linspace(-4,4)\n",
        "\n",
        "plt.figure(figsize=(13, 5))\n",
        "plt.plot(x, function(x))\n",
        "plt.scatter(0.22346207166923, 0, label='Aproximação encontrada', c='r')\n",
        "plt.xlabel('x', weight='bold')\n",
        "plt.ylabel('f(x)', weight='bold')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 936x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sVKUM_FRJx0K"
      },
      "source": [
        "# **Considerações finais**\n",
        "\n",
        "Podemos observar que em dois dos testes realizados o método da bissecção foi o mais lento com necessidade de um grande número de iterações para alcançar a convergência. Em dois teste (função 1 e função 3) o método de Newton foi o mais rápido e preciso de todos necessitando de apenas 3 iterações para convergência. Em apenas um teste (função 2) o método da Secante não foi eficiente, nos demais sempre esteve entre os métodos maís rápidos, porém, sendo inferior ao método de Newton. O método do ponto fixo demonstrou bom desempenho com poucas iterações e assim como o método de Newton em nenhum dos testes resultou no pior desempenho.\n",
        "\n",
        "Vale ressaltar que os resultados obtidos são estritamente condicionados aos valores de entrada fornecidos para cada um dos métodos não sendo possível, dessa forma, realizar qualquer tipo de afirmação categórica ou conclusão definitiva acerca da eficiência dos métodos iterativos abordados. "
      ]
    }
  ]
}