Assn_1911007.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOrEq8NZLdlEjEDmUhonQEB",
      "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/github/abhich2507/Numerical_Python/blob/main/Assn_1911007.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bOJkdQJTxrYK",
        "outputId": "365ed0e6-71c8-4f82-8e6c-85987cd2d4ca"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A= [[ 6.00000000e+00  3.31152776e-15 -5.24604773e-14  3.44156801e-09]\n",
            " [ 3.28225807e-15  4.00000000e+00  1.21079839e-11 -1.90734863e-06]\n",
            " [-5.30689896e-14  1.21084736e-11  8.00000000e+00  3.27398426e-11]\n",
            " [ 3.44156639e-09 -1.90734863e-06  3.27418150e-11  2.00000000e+00]]\n",
            "Q= [[ 1.00000000e+00 -1.64109789e-15  6.63363074e-15 -1.72078319e-09]\n",
            " [ 3.28216462e-15  1.00000000e+00 -1.51356311e-12  9.53674316e-07]\n",
            " [-6.63365891e-15  1.51357872e-12  1.00000000e+00 -1.63709061e-11]\n",
            " [ 1.72078319e-09 -9.53674316e-07  1.63709075e-11  1.00000000e+00]]\n",
            "eigenvalues= [6. 4. 8. 2.]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-2-8d2af50ea353>:15: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  R[j,j] = mag(Ap[:,j])\n",
            "<ipython-input-2-8d2af50ea353>:16: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  Q[:,j] = Ap[:,j]/R[j,j]\n",
            "<ipython-input-2-8d2af50ea353>:13: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  R[i,j] = Q[:,i]@A[:,j]\n"
          ]
        }
      ],
      "source": [
        "#1\n",
        "\n",
        "import numpy as np\n",
        "def mag(xs):\n",
        "    return np.sqrt(np.sum(xs*xs))\n",
        "def qrdec(A):\n",
        "    n = A.shape[0]\n",
        "    Ap = np.copy(A)\n",
        "    Q = np.zeros((n,n))\n",
        "    R = np.zeros((n,n))\n",
        "    for j in range(n):\n",
        "        for i in range(j):\n",
        "            R[i,j] = Q[:,i]@A[:,j]\n",
        "            Ap[:,j] -= R[i,j]*Q[:,i]\n",
        "        R[j,j] = mag(Ap[:,j])\n",
        "        Q[:,j] = Ap[:,j]/R[j,j]\n",
        "    return Q, R\n",
        "A=np.array([[4.0,2.0/3.0,-4.0/3.0,4.0/3.0],[2.0/3.0,4.0,0,0],[-4.0/3.0,0,6,2],[4.0/3.0,0.0,2.0,6.0]],dtype=complex)\n",
        "'''\n",
        "Q,R=qrdec(A)\n",
        "print('Q=',Q)\n",
        "print('R=',R)\n",
        "'''\n",
        "for k in range(1,20):\n",
        "    Q,R=qrdec(A)\n",
        "    A=R@Q\n",
        "    m=[]\n",
        "    for i in range(1,np.shape(A)[0]):\n",
        "        for j in range(i+1):\n",
        "            m.append(abs(A[i][j]))\n",
        "    f=sum(m)\n",
        "    if f<=0.00001:\n",
        "        break\n",
        "eigenvalues=np.diagonal(A)\n",
        "print('A=',A)\n",
        "print('Q=',Q)\n",
        "print('eigenvalues=',eigenvalues)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1b"
      ],
      "metadata": {
        "id": "QHheiWWbyGxr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Define the matrix\n",
        "A = np.array([[4.0, 2.0/3.0, -4.0/3.0, 4.0/3.0],\n",
        "              [2.0/3.0, 4.0, 0, 0],\n",
        "              [-4.0/3.0, 0, 6, 2],\n",
        "              [4.0/3.0, 0.0, 2.0, 6.0]], dtype=complex)\n",
        "\n",
        "# Choose an initial guess for the eigenvector\n",
        "v_initial = np.array([1, 1, 1, 1])\n",
        "\n",
        "# Define a function to calculate the relative error\n",
        "def relative_error(new_val, old_val):\n",
        "    return abs((new_val - old_val) / new_val) * 100\n",
        "\n",
        "# Initialize variables\n",
        "old_eigenvalue = 0.0\n",
        "tolerance = 0.0001\n",
        "\n",
        "# Iterative method to find the largest eigenvalue and its corresponding eigenvector\n",
        "while True:\n",
        "    v_updated = np.dot(A, v_initial)\n",
        "    eigenvalue = np.linalg.norm(v_updated)\n",
        "    error = relative_error(eigenvalue, old_eigenvalue)\n",
        "    v_updated = v_updated / eigenvalue\n",
        "\n",
        "    # Check if the error is within tolerance\n",
        "    if error < tolerance:\n",
        "        break\n",
        "\n",
        "    old_eigenvalue = eigenvalue\n",
        "    v_initial = v_updated\n",
        "\n",
        "# Print the results\n",
        "print('Largest eigenvalue =', eigenvalue)\n",
        "print('Eigenvector =', v_updated)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qDFFXw2dyUw3",
        "outputId": "e0e3f9b4-ff9a-4e93-b1a4-212cec5ca40a"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Largest eigenvalue = 7.999992178241464\n",
            "Eigenvector = [1.12119132e-03+0.j 3.74030152e-04+0.j 7.06358506e-01+0.j\n",
            " 7.07853278e-01+0.j]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2A"
      ],
      "metadata": {
        "id": "BVHjEZjmyaOb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "x=np.arange(0.00,1.05,0.05)\n",
        "y=np.array([0.486,0.866,0.944,1.144,1.103,1.202,1.166,1.191,1.124,1.095,1.122,1.102,1.099,1.017,1.111,1.117,1.152,1.265,1.380,1.575,1.857])\n",
        "x2=x**2\n",
        "x3=x**3\n",
        "x4=x**4\n",
        "x5=x**5\n",
        "x6=x**6\n",
        "xy=x*y\n",
        "x2y=x2*y\n",
        "x3y=x3*y\n",
        "sumx=np.sum(x)\n",
        "sumy=np.sum(y)\n",
        "sumx2=np.sum(x2)\n",
        "sumx3=np.sum(x3)\n",
        "sumx4=np.sum(x4)\n",
        "sumx5=np.sum(x5)\n",
        "sumx6=np.sum(x6)\n",
        "sumxy=np.sum(xy)\n",
        "sumx2y=np.sum(x2y)\n",
        "sumx3y=np.sum(x3y)\n",
        "A=np.array([[len(x),sumx,sumx2,sumx3],[sumx,sumx2,sumx3,sumx4],[sumx2,sumx3,sumx4,sumx5],[sumx3,sumx4,sumx5,sumx6]])\n",
        "B=np.array([sumy,sumxy,sumx2y,sumx3y])\n",
        "X=np.linalg.solve(A, B)\n",
        "def f(x,a,b,c,d):\n",
        "    return a + b*x + c*x*2 + d*x*3\n",
        "plt.scatter(x,y,color='r')\n",
        "plt.title(\"Data fitting\")\n",
        "plt.plot(x,f(x,X[0],X[1],X[2],X[3]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "tcI1LoLVyZgk",
        "outputId": "35c3f3bc-c256-4ee7-8b00-ddd923b1e005"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7e0e8d6703d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2B"
      ],
      "metadata": {
        "id": "MD1tOXUNy-7U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "x=np.arange(0.00,1.05,0.05)\n",
        "y=np.array([0.486,0.866,0.944,1.144,1.103,1.202,1.166,1.191,1.124,1.095,1.122,1.102,1.099,1.017,1.111,1.117,1.152,1.265,1.380,1.575,1.857])\n",
        "x2=x**2\n",
        "x3=x**3\n",
        "x4=x**4\n",
        "x5=x**5\n",
        "x6=x**6\n",
        "xy=x*y\n",
        "x2y=x2*y\n",
        "x3y=x3*y\n",
        "sumx=np.sum(x)\n",
        "sumy=np.sum(y)\n",
        "sumx2=np.sum(x2)\n",
        "sumx3=np.sum(x3)\n",
        "sumx4=np.sum(x4)\n",
        "sumx5=np.sum(x5)\n",
        "sumx6=np.sum(x6)\n",
        "sumxy=np.sum(xy)\n",
        "sumx2y=np.sum(x2y)\n",
        "sumx3y=np.sum(x3y)\n",
        "A=np.array([[len(x),sumx,sumx2,sumx3],[sumx,sumx2,sumx3,sumx4],[sumx2,sumx3,sumx4,sumx5],[sumx3,sumx4,sumx5,sumx6]])\n",
        "B=np.array([sumy,sumxy,sumx2y,sumx3y])\n",
        "X=np.linalg.solve(A, B)\n",
        "def f(x,a,b,c,d):\n",
        "    return a + b*x + c*x*2 + d*x*3\n",
        "plt.scatter(x,y,color=\"r\")\n",
        "plt.title(\"Data fitting\")\n",
        "plt.plot(x,f(x,X[0],X[1],X[2],X[3]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "o9cbyOngy-Mt",
        "outputId": "17c0fd36-999f-4b88-e65e-e93b2f527de1"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7e0e8d9a16f0>]"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}