Fixed_Point_Iteration.ipynb

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      "name": "Fixed_Point_Iteration.ipynb",
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      "source": [
        "Make sure you remove `raise NotImplementedError()` and fill in any place that says `# YOUR CODE HERE`, as well as your `NAME`, `ID`, and `LAB_SECTION` below:"
      ]
    },
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      "source": [
        "NAME = \"Syed Zuhair Hossain\"\n",
        "ID = \"19101573\"\n",
        "LAB_SECTION = \"02\""
      ],
      "execution_count": null,
      "outputs": []
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      "source": [
        "---"
      ]
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      "source": [
        "# Fixed Point Iteration\n",
        "\n",
        "### Fixed point:\n",
        "A number $\\xi$ is called a **fixed point** to function $g(x)$ if $g(\\xi) = \\xi$. Using fixed points are a nice strategy to find roots of an equation. In this method if we are trying to find a root of $f(x) = 0$, we try to write the function in the form, $x = g(x)$. That is,\n",
        "$$\n",
        "f(x) = x - g(x) = 0\n",
        "$$\n",
        "\n",
        "So, if $\\xi$ is a fixed point of $g(x)$ it would also be a root of $f(x)=0$, because,\n",
        "$$\n",
        "f(\\xi) = \\xi - g(\\xi) = \\xi - \\xi = 0\n",
        "$$\n",
        "\n",
        "We can find a suitable $g(x)$ in any number of ways. Not all of them would converge, whereas, Some would converge very fast. For example, consider $Eq. 6.1$.\n",
        "\n",
        "\\begin{align}\n",
        "&         &    f(x) &=x^5 + 2.5x^4 - 2x^3 -6x^2 + x + 2 \\\\\n",
        "&\\implies &x - g(x) &=x^5 + 2.5x^4 - 2x^3 -6x^2 + x + 2 \\\\\n",
        "&\\implies &    g(x) &=-x^5 - 2.5x^4 + 2x^3 + 6x^2 - 2 \\tag{6.2}\\\\\n",
        "\\end{align}\n",
        "\n",
        "again, \n",
        "$$\n",
        "f(x) = x^5 + 2.5x^4 - 2x^3 -6x^2 + x + 2 = 0\\\\\n",
        "$$\n",
        "\\begin{align}\n",
        "&\\implies &6x^2 &= x^5 + 2.5x^4 - 2x^3 + x + 2 \\\\\n",
        "&\\implies &x^2  &= \\frac{1}{6}(x^5 + 2.5x^4 - 2x^3 + x + 2)\\\\\n",
        "&\\implies &x    &= \\sqrt{\\frac{1}{6}(x^5 + 2.5x^4 - 2x^3 + x + 2)}\\\\\n",
        "&\\implies &g(x) &= \\sqrt{\\frac{1}{6}(x^5 + 2.5x^4 - 2x^3 + x + 2)}\\tag{6.3}\\\\\n",
        "\\end{align}\n",
        "\n",
        "Similarly,\n",
        "\\begin{align}\n",
        "&         &2.5x^4 &= -x^5 + 2x^3 + 6x^2 - x - 2 \\\\\n",
        "&\\implies &x^4  &= \\frac{1}{2.5}(-x^5 + 2x^3 + 6x^2 - x - 2)\\\\\n",
        "&\\implies &x    &= \\sqrt[\\leftroot{-1}\\uproot{2}\\scriptstyle 4]{\\frac{1}{2.5}(-x^5 + 2x^3 + 6x^2 - x - 2)}\\\\\n",
        "&\\implies &g(x) &= \\sqrt[\\leftroot{-1}\\uproot{2}\\scriptstyle 4]{\\frac{1}{2.5}(-x^5 + 2x^3 + 6x^2 - x - 2)}\\tag{6.4}\\\\\n",
        "\\end{align}\n",
        "\n",
        "### B. Complete the code below\n",
        "For this example we will use a couple of $g(x)$ function to find out which one converges faster."
      ]
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from numpy.polynomial import Polynomial\n",
        "from ipykernel import kernelapp as app\n",
        "\n",
        "f = Polynomial([2.0, 1.0, -6.0, -2.0, 2.5, 1.0])\n",
        "g1 = Polynomial([-2.0, 0.0, 6.0, 2.0, -2.5, -1.0])\n",
        "\n",
        "def g2(x):\n",
        "    p = Polynomial([2.0, 1.0, 0.0, -2.0, 2.5, 1.0])\n",
        "    return np.sqrt(p(x)/6)\n",
        "\n",
        "def g3(x):\n",
        "    p = Polynomial([-2.0, -1.0, 6.0, 2.0, 0.0, -1.0])\n",
        "    return np.power(p(x)/2.5, 1.0/4.0)\n",
        "\n",
        "a1 = 0.8\n",
        "g1_a = []\n",
        "\n",
        "a2 = 0.8\n",
        "g2_a = []\n",
        "\n",
        "a3 = 0.8\n",
        "g3_a = []\n",
        "\n",
        "# YOUR CODE HERE\n",
        "for i in range(21):\n",
        "  p = g1(a1)\n",
        "  g1_a.append(p)\n",
        "  a1= p\n",
        "  q = g2(a2)\n",
        "  g2_a.append(q)\n",
        "  a2= q\n",
        "  r = g3(a3)\n",
        "  g3_a.append(r)\n",
        "  a3= r \n",
        "\n",
        "# append all the initial guesses to the lists\n",
        "# run a for loop for the iteration method\n",
        "# find the updated values and add the updated values to the lists\n",
        "\n",
        "# raise NotImplementedError()"
      ],
      "execution_count": null,
      "outputs": []
    },
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          "points": 10,
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        },
        "outputId": "05e0a5f1-8b30-421f-ec9c-575dd92b0592"
      },
      "source": [
        "xs = np.linspace(-2.5, 1.6, 100)\n",
        "ys = f(xs)\n",
        "dictionary = {\n",
        "    'x': xs,\n",
        "    'y': ys\n",
        "}\n",
        "plt.axhline(y=0, color='k')\n",
        "plt.plot(xs, f(xs), label='f(x)')\n",
        "plt.plot(xs, g1(xs), label='g1(x)')\n",
        "plt.plot(xs, g2(xs), label='g2(x)')\n",
        "plt.plot(xs, g3(xs), label='g3(x)')\n",
        "plt.legend()\n",
        "\n",
        "if len(g1_a) > 0:\n",
        "    root = np.array([g1_a[len(g1_a)-1], g2_a[len(g2_a)-1], g3_a[len(g3_a)-1]])\n",
        "    plt.plot(root, f(root), 'ro')\n",
        "\n",
        "print(pd.DataFrame({'g1(x)':g1_a, 'g2(x)':g2_a, 'g3(x))':g3_a,}))\n",
        "\n",
        "# Test case:\n",
        "np.testing.assert_array_almost_equal(root, [-2., 0.67242436, 1.33033625])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:16: RuntimeWarning: invalid value encountered in power\n",
            "  app.launch_new_instance()\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "       g1(x)     g2(x)    g3(x))\n",
            "0   1.512320  0.721997  0.912898\n",
            "1  -2.347605  0.688573  1.044444\n",
            "2   0.562201  0.677301  1.160638\n",
            "3  -0.054108  0.673860  1.241682\n",
            "4  -1.982772  0.672844  1.288278\n",
            "5  -1.995936  0.672547  1.311548\n",
            "6  -1.999770  0.672460  1.322205\n",
            "7  -1.999999  0.672435  1.326870\n",
            "8  -2.000000  0.672427  1.328868\n",
            "9  -2.000000  0.672425  1.329716\n",
            "10 -2.000000  0.672425  1.330075\n",
            "11 -2.000000  0.672424  1.330226\n",
            "12 -2.000000  0.672424  1.330290\n",
            "13 -2.000000  0.672424  1.330317\n",
            "14 -2.000000  0.672424  1.330328\n",
            "15 -2.000000  0.672424  1.330333\n",
            "16 -2.000000  0.672424  1.330335\n",
            "17 -2.000000  0.672424  1.330336\n",
            "18 -2.000000  0.672424  1.330336\n",
            "19 -2.000000  0.672424  1.330336\n",
            "20 -2.000000  0.672424  1.330336\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KZdEg2f1xyjN"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}