solving_fxeq0.ipynb

solving_fxeq0.ipynb

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        "<a href=\"https://colab.research.google.com/gist/aleksejalex/0e27790a7c2c89115725c3df39c2c367/solving_fxeq0.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# 1) numericke reseni pomoci existujiciho solveru z knihovny SciPy\n",
        "funkce [`fsolve`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html)"
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          "text": [
            "The root of the equation is: [1.].\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import fsolve\n",
        "\n",
        "def f(x):\n",
        "    \"\"\"\n",
        "    toto bude vase funkce\n",
        "    mocnina se napise **, exp() ... np.exp(), odmocnina ... np.sqrt(), abs.hodnota ... np.abs()\n",
        "    \"\"\"\n",
        "    return (x-2)**2 - 1  # tohle analyticky ma dva koreny, x=1 a x=3\n",
        "\n",
        "\n",
        "# Initial guess for the root\n",
        "x0 = 0\n",
        "# pozor, lze si vsimnout:\n",
        "# 1) zalezi na init. guess: zaporny guess vrati mensi koren (1), kladny guess vrati vetsi koren (3)\n",
        "# 2) pokud init. guess je hooodne daleko od pravdy, vysledek je velmi nepresny\n",
        "\n",
        "# Solve the equation f(x) = 0\n",
        "root = fsolve(f, x0)\n",
        "\n",
        "print(f\"The root of the equation is: {root}.\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# kontrola jak jsme daleko (tj. jestli |f(x)-0| je minimalni):\n",
        "np.isclose(f(root), [0.0])"
      ],
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True])"
            ]
          },
          "metadata": {},
          "execution_count": 2
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    },
    {
      "cell_type": "code",
      "source": [
        "# koren rce\n",
        "root"
      ],
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      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# hodnota f v bode nalezeho jako koren (ma byt malinke cislo):\n",
        "f(root)"
      ],
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          "data": {
            "text/plain": [
              "array([4.4408921e-16])"
            ]
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          "metadata": {},
          "execution_count": 4
        }
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      "execution_count": 4,
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    {
      "cell_type": "markdown",
      "source": [
        "# 2) pomoci symbolickych vypoctu (knihovna SymPy)\n",
        "solver [sympy.solve](https://docs.sympy.org/latest/guides/solving/solve-equation-algebraically.html)\n",
        "\n",
        "Vyhoda je, ze vraci vsechny koreny (protoze pocita analyticky). Nevyhoda je, ze u slozitejsich veci selze."
      ],
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      "source": [
        "import sympy as sp\n",
        "\n",
        "# Define the symbol\n",
        "x = sp.Symbol('x')\n",
        "\n",
        "# Define the function g(x)\n",
        "g = (x-2)**2 - 1  # stejna fce jako f, ktera byla vyse, ale jiny pythonovsky objekt, proto ji radsi nazvu g\n",
        "# pozor, fce jako exp, log, sin musi byt z balicku SymPy, tj. napr. g = (sp.sin(x)-2)**2 - 1\n",
        "\n",
        "# Find the symbolic solutions\n",
        "solutions = sp.solve(g, x)\n",
        "\n",
        "print(\"Symbolic solutions of the equation g(x) = 0:\")\n",
        "for solution in solutions:\n",
        "    print(solution)\n"
      ],
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          "text": [
            "Symbolic solutions of the equation g(x) = 0:\n",
            "1\n",
            "3\n"
          ]
        }
      ]
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