Solution_of_Nonlinear_Equations_in_One_Variable_Bisection_Method.ipynb

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        "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
        "\n",
        "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
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        "NAME = \"Ahmad Mongy Saad\"\n",
        "ID   = \"120200033\"\n",
        "Section = \"CSE01\""
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      "source": [
        "---"
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      "source": [
        "# CSE 213 Numerical Analysis\n",
        "# Lab 2 - Solution of Nonlinear Equations in One Variable - Bisection Method"
      ]
    },
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      "source": [
        "It is required to solve the equation:\n",
        "$ x - \\cos(x)-1 = 0$\n",
        ", using the bisection method in Python.\n",
        "\n",
        "Start with the interval $[0, \\pi/2]$ and obtain the solution with an error $\\epsilon$ less than $10^{-5}$, where $\\epsilon = |b_n - a_n|/2$ and $|p_n - p| \\leq \\epsilon$."
      ]
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      "source": [
        "### The Bisection Algorithm\n",
        "\n",
        "Given a function `eq` which we want to solve, the interval `[a,b]` in which the solution exists and a tolerance `tol` which our algorithm should stop when the error is smaller than it, the Bisection Algorithm follows the following pseudocode:\n",
        "``` python\n",
        "fa = eq(a)\n",
        "fb = eq(b)\n",
        "while | a - b | / 2 > tol\n",
        "    solution = (a + b) / 2\n",
        "    f_solution = eq(solution)\n",
        "    if fa * f_solution <= 0\n",
        "        b = solution\n",
        "    else\n",
        "        a = solution\n",
        "```"
      ]
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      "id": "empirical-event",
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      "source": [
        "### Define a function `eq1` for the given equation"
      ]
    },
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      "source": [
        "import numpy as np\n",
        "def eq1(x):\n",
        "    return(x-np.cos(x)-1)\n",
        "    raise NotImplementedError()"
      ]
    },
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      "source": [
        "### BEGIN TEST\n",
        "x = np.array([0, 1, 2])\n",
        "assert np.all(np.isclose(eq1(x), np.array([-2.0, -0.5403023058681398, 1.4161468365471426])))\n",
        "### END TEST"
      ]
    },
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      "source": [
        "### Implement the bisection function to solve the equation `eq1` using the bisection method."
      ]
    },
    {
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      "source": [
        "def bisection(equation, a=0, b=np.pi/2, tolerance=1e-5):\n",
        "    \"\"\"\n",
        "    equation (function): a function that we want to solve\n",
        "    a (float): the starting point of the solution interval\n",
        "    b (float): the end point of the solution interval\n",
        "    tolerance (float): the value after which we stop iterating\n",
        "    \"\"\"\n",
        "    fa=equation(a)\n",
        "    fb=equation(b)\n",
        "    while abs(a-b)/2 > tolerance:\n",
        "      solution = (a+b)/2\n",
        "      f_solution = equation(solution)\n",
        "      if fa*f_solution <=0 :\n",
        "        b =solution\n",
        "      else:\n",
        "        a=solution\n",
        "    return((a+b)/2)\n",
        "    # YOUR CODE HERE\n",
        "    raise NotImplementedError()"
      ]
    },
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      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "### BEGIN TEST\n",
        "from matplotlib import pyplot as plt\n",
        "p = bisection(eq1, 0, np.pi/2, 1e-5)\n",
        "assert p == 1.283432589901804\n",
        "plt.figure(figsize=(8,6))\n",
        "plt.grid()\n",
        "plt.xlabel('X-axis')\n",
        "plt.ylabel('Y-axis')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.axvline(x=p, color='m', linestyle='--')\n",
        "x = np.linspace(0, np.pi/2, 50)\n",
        "y = eq1(x)\n",
        "plt.plot(x, y, 'r')\n",
        "plt.show()\n",
        "### END TEST"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "judicial-piece",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "69d98792dd18d9fb896476adeb9d9c44",
          "grade": false,
          "grade_id": "cell-5200b326a0922436",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "judicial-piece"
      },
      "source": [
        "Modify the `bisection` function to print the results as in the following table.\n",
        "```\n",
        "+-----+--------------------+--------------------+--------------------+------+--------------------+\n",
        "| It# |         a          |         b          |         p          | f(a) |        f(b)        |\n",
        "+-----+--------------------+--------------------+--------------------+------+--------------------+\n",
        "|  1  |         0          |        1.25        |       0.625        | 3.0  | 1.6824939607034732 |\n",
        "|  2  |       0.625        |        1.25        |       0.9375       | 3.0  | 1.6824939607034732 |\n",
        "|  3  |       0.625        |       0.9375       |      0.78125       | 3.0  | 1.6824939607034732 |\n",
        "|  4  |      0.78125       |       0.9375       |      0.859375      | 3.0  | 1.6824939607034732 |\n",
        "|  5  |      0.859375      |       0.9375       |     0.8984375      | 3.0  | 1.6824939607034732 |\n",
        "|  6  |      0.859375      |     0.8984375      |     0.87890625     | 3.0  | 1.6824939607034732 |\n",
        "|  7  |     0.87890625     |     0.8984375      |    0.888671875     | 3.0  | 1.6824939607034732 |\n",
        "|  8  |     0.87890625     |    0.888671875     |    0.8837890625    | 3.0  | 1.6824939607034732 |\n",
        "|  9  |    0.8837890625    |    0.888671875     |   0.88623046875    | 3.0  | 1.6824939607034732 |\n",
        "|  10 |    0.8837890625    |   0.88623046875    |   0.885009765625   | 3.0  | 1.6824939607034732 |\n",
        "|  11 |    0.8837890625    |   0.885009765625   |  0.8843994140625   | 3.0  | 1.6824939607034732 |\n",
        "|  12 |    0.8837890625    |  0.8843994140625   |  0.88409423828125  | 3.0  | 1.6824939607034732 |\n",
        "|  13 |  0.88409423828125  |  0.8843994140625   | 0.884246826171875  | 3.0  | 1.6824939607034732 |\n",
        "|  14 |  0.88409423828125  | 0.884246826171875  | 0.8841705322265625 | 3.0  | 1.6824939607034732 |\n",
        "|  15 | 0.8841705322265625 | 0.884246826171875  | 0.8842086791992188 | 3.0  | 1.6824939607034732 |\n",
        "|  16 | 0.8842086791992188 | 0.884246826171875  | 0.8842277526855469 | 3.0  | 1.6824939607034732 |\n",
        "|  17 | 0.8842086791992188 | 0.8842277526855469 | 0.8842182159423828 | 3.0  | 1.6824939607034732 |\n",
        "+-----+--------------------+--------------------+--------------------+------+--------------------+\n",
        "```\n",
        "However, add another column `abs(pn - pn_1)/pn` which shows the value $abs(p_n - p_{n-1})/p_n)$."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "complicated-cookie",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "35edced7ed1b8bb9fea5adbea687f735",
          "grade": false,
          "grade_id": "cell-b113edf31551a1ae",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "complicated-cookie"
      },
      "source": [
        "`prettytable` is a small library that let you print tables in nice formatting easily.\n",
        "\n",
        "You should\n",
        "First install prettytable by running the following cell:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "cooperative-miniature",
      "metadata": {
        "id": "cooperative-miniature",
        "outputId": "01305078-599e-486f-c8b2-ab83ca029b49",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: prettytable in /usr/local/lib/python3.7/dist-packages (3.2.0)\n",
            "Requirement already satisfied: importlib-metadata in /usr/local/lib/python3.7/dist-packages (from prettytable) (4.11.3)\n",
            "Requirement already satisfied: wcwidth in /usr/local/lib/python3.7/dist-packages (from prettytable) (0.2.5)\n",
            "Requirement already satisfied: zipp>=0.5 in /usr/local/lib/python3.7/dist-packages (from importlib-metadata->prettytable) (3.7.0)\n",
            "Requirement already satisfied: typing-extensions>=3.6.4 in /usr/local/lib/python3.7/dist-packages (from importlib-metadata->prettytable) (3.10.0.2)\n"
          ]
        }
      ],
      "source": [
        "!pip install prettytable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "american-supervisor",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "0a338055e220930153104158dce6c157",
          "grade": false,
          "grade_id": "cell-86511fbff729055c",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "american-supervisor"
      },
      "outputs": [],
      "source": [
        "from prettytable import PrettyTable\n",
        "table = PrettyTable()\n",
        "table.field_names = ['It#', 'a', 'b', 'p', 'f(a)', 'f(b)', 'abs(pn-pn_1)/pn']\n",
        "# Add rows to the table using table.add_row([<values>]). Replace values with the columns at the added row.\n",
        "def bisection(equation, a=0, b=np.pi/2, tolerance=1e-5):\n",
        "    \"\"\"\n",
        "    equation (function): a function that we want to solve\n",
        "    a (float): the starting point of the solution interval\n",
        "    b (float): the end point of the solution interval\n",
        "    tolerance (float): the value after which we stop iterating\n",
        "    \"\"\"\n",
        "    table = PrettyTable()\n",
        "    table.field_names = ['It#', 'a', 'b', 'p', 'f(a)', 'f(b)', 'abs(pn-pn_1)/pn']\n",
        "    fa=equation(a)\n",
        "    fb=equation(b)\n",
        "    it = 0\n",
        "    while abs(a-b)/2 > tolerance:\n",
        "      it+=1\n",
        "      solution = (a+b)/2\n",
        "      f_solution = equation(solution)\n",
        "      table.add_row([it,a,b,(a+b)/2, fa,fb,2*abs(a+b/2 -solution)/(a+b)])\n",
        "      if fa*f_solution <=0 :\n",
        "        b =solution\n",
        "      else:\n",
        "        a=solution\n",
        "    print(table)\n",
        "    return((a+b)/2)\n",
        "    # YOUR CODE HERE\n",
        "    raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "clean-leather",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "086613758269ad438989edaaa948ea6d",
          "grade": true,
          "grade_id": "cell-08c9e2a6ccfffee2",
          "locked": true,
          "points": 3,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "clean-leather",
        "outputId": "c216b074-ec1d-4c8d-a6b8-25cc3bd5601c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "+-----+-------------------+--------------------+--------------------+------+--------------------+---------------------+\n",
            "| It# |         a         |         b          |         p          | f(a) |        f(b)        |   abs(pn-pn_1)/pn   |\n",
            "+-----+-------------------+--------------------+--------------------+------+--------------------+---------------------+\n",
            "|  1  |         0         |        2.5         |        1.25        | -2.0 | 2.3011436155469336 |         0.0         |\n",
            "|  2  |        1.25       |        2.5         |       1.875        | -2.0 | 2.3011436155469336 |  0.3333333333333333 |\n",
            "|  3  |        1.25       |       1.875        |       1.5625       | -2.0 | 2.3011436155469336 |         0.4         |\n",
            "|  4  |        1.25       |       1.5625       |      1.40625       | -2.0 | 2.3011436155469336 |  0.4444444444444444 |\n",
            "|  5  |        1.25       |      1.40625       |      1.328125      | -2.0 | 2.3011436155469336 | 0.47058823529411764 |\n",
            "|  6  |        1.25       |      1.328125      |     1.2890625      | -2.0 | 2.3011436155469336 | 0.48484848484848486 |\n",
            "|  7  |        1.25       |     1.2890625      |     1.26953125     | -2.0 | 2.3011436155469336 | 0.49230769230769234 |\n",
            "|  8  |     1.26953125    |     1.2890625      |    1.279296875     | -2.0 | 2.3011436155469336 |  0.4961832061068702 |\n",
            "|  9  |    1.279296875    |     1.2890625      |    1.2841796875    | -2.0 | 2.3011436155469336 | 0.49809885931558934 |\n",
            "|  10 |    1.279296875    |    1.2841796875    |   1.28173828125    | -2.0 | 2.3011436155469336 |  0.4990476190476191 |\n",
            "|  11 |   1.28173828125   |    1.2841796875    |   1.282958984375   | -2.0 | 2.3011436155469336 |  0.4995242626070409 |\n",
            "|  12 |   1.282958984375  |    1.2841796875    |  1.2835693359375   | -2.0 | 2.3011436155469336 |  0.4997622444127437 |\n",
            "|  13 |   1.282958984375  |  1.2835693359375   |  1.28326416015625  | -2.0 | 2.3011436155469336 |  0.4998810939357907 |\n",
            "|  14 |  1.28326416015625 |  1.2835693359375   | 1.283416748046875  | -2.0 | 2.3011436155469336 | 0.49994055403638094 |\n",
            "|  15 | 1.283416748046875 |  1.2835693359375   | 1.2834930419921875 | -2.0 | 2.3011436155469336 |  0.4999702787849967 |\n",
            "|  16 | 1.283416748046875 | 1.2834930419921875 | 1.2834548950195312 | -2.0 | 2.3011436155469336 |  0.4999851389508099 |\n",
            "|  17 | 1.283416748046875 | 1.2834548950195312 | 1.2834358215332031 | -2.0 | 2.3011436155469336 | 0.49999256936497793 |\n",
            "+-----+-------------------+--------------------+--------------------+------+--------------------+---------------------+\n"
          ]
        }
      ],
      "source": [
        "### BEGIN TEST\n",
        "p = bisection(eq1, 0, 2.5, 1e-5)\n",
        "### END TEST"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "vertical-conditions",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "55fdde2b61f66e0f8dae02c1623a778e",
          "grade": false,
          "grade_id": "cell-93c4d105a09e3c0d",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "vertical-conditions"
      },
      "source": [
        "Define a function `eq2` to ﬁnd the positive solutions of the equation $f(x) = e^x - 5x + 2$ in the interval \n",
        "$[0.1, 1]$ by the bisection method.\n",
        "\n",
        "Convince yourself that the solutions seems accurate from the plot of $f(x) = e^x - 5x + 2$  in the range $[0.0, 2.5]$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "impressed-artist",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "e6f8d5d148b04a39ec73dd97611aaa8a",
          "grade": false,
          "grade_id": "cell-304ff57b80148bdc",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "impressed-artist"
      },
      "outputs": [],
      "source": [
        "def eq2(x):\n",
        "    # YOUR CODE HERE\n",
        "    return((np.e)**x - 5*x +2)\n",
        "    raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "numerous-allocation",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "24fbf7915a0df4c4ec70dc30a6b2cc24",
          "grade": true,
          "grade_id": "cell-d02fc2578605fe09",
          "locked": true,
          "points": 1,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "numerous-allocation",
        "outputId": "3cd03076-849a-4192-cdc2-01c40934db26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 753
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "+-----+--------------------+-------------------+--------------------+------+--------------------+---------------------+\n",
            "| It# |         a          |         b         |         p          | f(a) |        f(b)        |   abs(pn-pn_1)/pn   |\n",
            "+-----+--------------------+-------------------+--------------------+------+--------------------+---------------------+\n",
            "|  1  |         0          |        2.5        |        1.25        | 3.0  | 1.6824939607034715 |         0.0         |\n",
            "|  2  |         0          |        1.25       |       0.625        | 3.0  | 1.6824939607034715 |         0.0         |\n",
            "|  3  |       0.625        |        1.25       |       0.9375       | 3.0  | 1.6824939607034715 |  0.3333333333333333 |\n",
            "|  4  |       0.625        |       0.9375      |      0.78125       | 3.0  | 1.6824939607034715 |         0.4         |\n",
            "|  5  |      0.78125       |       0.9375      |      0.859375      | 3.0  | 1.6824939607034715 | 0.45454545454545453 |\n",
            "|  6  |      0.859375      |       0.9375      |     0.8984375      | 3.0  | 1.6824939607034715 |  0.4782608695652174 |\n",
            "|  7  |      0.859375      |     0.8984375     |     0.87890625     | 3.0  | 1.6824939607034715 |  0.4888888888888889 |\n",
            "|  8  |     0.87890625     |     0.8984375     |    0.888671875     | 3.0  | 1.6824939607034715 |  0.4945054945054945 |\n",
            "|  9  |     0.87890625     |    0.888671875    |    0.8837890625    | 3.0  | 1.6824939607034715 |  0.4972375690607735 |\n",
            "|  10 |    0.8837890625    |    0.888671875    |   0.88623046875    | 3.0  | 1.6824939607034715 |  0.4986225895316804 |\n",
            "|  11 |    0.8837890625    |   0.88623046875   |   0.885009765625   | 3.0  | 1.6824939607034715 |  0.4993103448275862 |\n",
            "|  12 |    0.8837890625    |   0.885009765625  |  0.8843994140625   | 3.0  | 1.6824939607034715 |  0.4996549344375431 |\n",
            "|  13 |    0.8837890625    |  0.8843994140625  |  0.88409423828125  | 3.0  | 1.6824939607034715 | 0.49982740766309974 |\n",
            "|  14 |  0.88409423828125  |  0.8843994140625  | 0.884246826171875  | 3.0  | 1.6824939607034715 |  0.4999137187230371 |\n",
            "|  15 |  0.88409423828125  | 0.884246826171875 | 0.8841705322265625 | 3.0  | 1.6824939607034715 | 0.49995685563896797 |\n",
            "|  16 | 0.8841705322265625 | 0.884246826171875 | 0.8842086791992188 | 3.0  | 1.6824939607034715 |  0.4999784287501618 |\n",
            "|  17 | 0.8842086791992188 | 0.884246826171875 | 0.8842277526855469 | 3.0  | 1.6824939607034715 | 0.49998921460773527 |\n",
            "+-----+--------------------+-------------------+--------------------+------+--------------------+---------------------+\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "### BEGIN TEST\n",
        "p = bisection(eq2, 0, 2.5, 1e-5)\n",
        "assert p == 0.8842182159423828\n",
        "plt.figure(figsize=(8,6))\n",
        "plt.grid()\n",
        "plt.xlabel('X-axis')\n",
        "plt.ylabel('Y-axis')\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.axvline(x=p, color='m', linestyle='--')\n",
        "x = np.linspace(0, 2.5, 50)\n",
        "y = eq2(x)\n",
        "plt.plot(x, y, 'r')\n",
        "plt.show()\n",
        "### END TEST"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "quick-punishment",
      "metadata": {
        "id": "quick-punishment"
      },
      "source": [
        "**THANK YOU**"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.1"
    },
    "colab": {
      "name": "Lab 2 - Solution of Nonlinear Equations in One Variable - Bisection Method -Ahmad Mongy Saad -120200033.ipynb",
      "provenance": [],
      "collapsed_sections": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}