Project_4_Case_3_An_Interesting_Case_using_Singular_Values_and_Best_Fit.ipynb

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  "metadata": {
    "colab": {
      "name": "Copy of Project 4:  Case 3 - An Interesting Case using Singular Values and Best Fit.ipynb",
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      "collapsed_sections": [],
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/KapilKhanal/AdvLinearAlgebra/blob/master/Project_4_Case_3_An_Interesting_Case_using_Singular_Values_and_Best_Fit.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hd7VYbrPdIg7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#  Libraries that we'll need:\n",
        "import numpy as np\n",
        "import sympy as sym\n",
        "#from scipy import misc\n",
        "from scipy import linalg\n",
        "#from PIL import Image\n",
        "#import imageio\n",
        "import matplotlib.pyplot as plt\n",
        "# importing \"random\" for random operations \n",
        "import random "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "90XAt6FGd-y7",
        "colab_type": "text"
      },
      "source": [
        "#  Singular Value Decomposition and Best Fit\n",
        "\n",
        "We look at some data generated here from three sources:\n",
        "\n",
        "*   Case 0:  A known polynomial function $f(x) = 4 - 3x^2 + 5x^6$\n",
        "*   Case 1:  A known trigonometric function $f(x) = 4 - 2\\cos(x) + \\cos^2 (x)$\n",
        "*   Case 2:  A matrix of data $M$ (specified below) with unknown source function\n",
        "*   Case 3:  An interesting case."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zrZ6Bf0qeQ9n",
        "colab_type": "text"
      },
      "source": [
        "# Overview for Case 3:  An interesting case:\n",
        "\n",
        "For Case 3, you have the option of completing one of the following tasks:\n",
        "\n",
        "* **Option A:**  Re-do Case 0 or Case 1 by adding noise to the function.\n",
        "\n",
        "Using $f$ + (2*random.random()-1)  will add a random number between -1 and 1 to the value of $f$.  How much noise can your method absorb and still produce accurate results?  (e.g. noise with a range of $-1$ to $1$?  noise from a range of $-5$ to $5$?  noise from $-30$ to $30$?)  Which method (best-fit or SVD) accommodates a larger range of error?\n",
        "\n",
        "* **Option B:**  Best Fit for a plane\n",
        "\n",
        "Instead of matching a function $x \\to f(x)$ using a 8th degree polynomial, make a multivariable function $(x_1,x_2) \\to f(x_1,x_2)$ where $f$ is a 3rd degree polynomial in $x_1$ and $x_2$. Generate data based on at least 16 different input points. Modify the procedure for choosing the $M$ matrix, and use Best Fit to find the best fit line. \n",
        "\n",
        "\n",
        "BONUS for Option B:  Do this for 3 dimensions, with noise, or modify the SVD solution to fit this option\n",
        "\n",
        "* **Option C:**  The space of continuous functions of one variable has two different bases:\n",
        "\n",
        "\n",
        "Given an unknown function, we figured out how to write it using basis of polynomials.  We could also have determined how to write it as a basis of powers of sine and cosine functions. Fit the polynomial $f(x) = 4 - 3x^2 + 5x^6$ to a basis of sine & cosine functions of at most power 4. Plot the original function and the best-fit function.\n",
        "\n",
        "BONUS for Option C:  Include noise via $f(x)$ + (2*random.random()-1), and find a way to measure the error in your approximation to the function f(x).  What is the effect of this noise on your approximation?\n",
        "\n",
        "\n",
        "In each case, it may be helpful to re-use data from the previous cases by copy-and-paste into cells below.  Be sure to specify which option you are addressing."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "12lUaj78dga0",
        "colab_type": "text"
      },
      "source": [
        "##OPtion C with basis as trignometric functions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YswdvIe3eFn5",
        "colab_type": "code",
        "outputId": "9ff7a052-0197-495c-e9e8-90d5b262563e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        }
      },
      "source": [
        "#We'll generate random points of data for our system.\n",
        "#The actual points for the system will be stored in containers actual_data_x and actual_data_y\n",
        "\n",
        "actual_data_x = []\n",
        "actual_data_y = []\n",
        "\n",
        "#We'll use (cough... cough...) fifty    data points:\n",
        "\n",
        "    # pick a random number x for range (1,10)\n",
        "actual_data_x = np.unique(np.random.randint(low=1, high=200, size=80))\n",
        "actual_data_y = 4 - 3*actual_data_x**2 + 5*actual_data_x**6\n",
        "actual_data_y"
      ],
      "execution_count": 161,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([           3622,           20436,          588102,         2656966,\n",
              "               8857446,        24133542,        37647096,       170060152,\n",
              "             235228326,       319998804,      2974114086,     20479995204,\n",
              "           23750516166,     31606809702,     53896070022,     61152945412,\n",
              "           69206428806,     87981431206,    154204887876,    190343452632,\n",
              "          233279989204,    539590801126,    889892561254,    963499625556,\n",
              "         1412147662726,   1634701846182,   1756490136916,   2322020410692,\n",
              "         3449348878776,   4164859996422,   4707400717606,   5307600722406,\n",
              "         5970261450822,   6326595060036,   7092595527576,   9352072723846,\n",
              "        11565303788454,  12825820967782,  14929919956804,  16486519750872,\n",
              "        17314129913062,  20007520659256,  21990232506372,  24134044949304,\n",
              "        25269565669926,  28946682240216,  30267225648454,  40992090794232,\n",
              "        42754932832902,  46470571890054,  48426952348536,  54712632866406,\n",
              "        59269557873606,  83886079923204,  93776847810342,  97282134774996,\n",
              "       116490425526726, 134043766570662, 143614501861254, 153748045027462,\n",
              "       170061119902804, 175809141537126, 187791764445382, 274901856214054,\n",
              "       283469561761236, 310519202875206])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 161
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bc_ML5LvdzQ1",
        "colab_type": "text"
      },
      "source": [
        "# Adding basis functions in matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yvz0I0J5q26F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Create the matrix M from the data in actual_data_x\n",
        "M_entries = []\n",
        "#Basis funcitons\n",
        "for x in actual_data_x:\n",
        "  M_entries.append([np.cos(x), np.sin(x),np.cos(2*x),np.sin(2*x),np.cos(3*x),np.sin(3*x),np.cos(4*x),np.sin(4*x)])\n",
        "\n",
        "M = []\n",
        "M = np.matrix(M_entries)\n",
        "\n",
        "\n",
        "#and create the vector b from the data in actual_data_y:\n",
        "b = []\n",
        "b = (np.matrix(actual_data_y)).transpose()\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lb9sNbVtsuYL",
        "colab_type": "code",
        "outputId": "73058e71-e844-48d4-f7a7-63bcc189222a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "x = sym.symbols('x')\n",
        "\n",
        "xdata = []\n",
        "fdata = []\n",
        "\n",
        "#set up our 100 data points on the interval from (1, 5):\n",
        "xdata = np.random.randint(low=1, high=200, size=80)\n",
        "xdata = np.unique(xdata)\n",
        "# find the ouput for our function on each data point:\n",
        "fdata = 4 - 3*xdata**2 + 5*xdata**6\n",
        "\n",
        "# Create the plot in red, and our datapoints in blue:  \n",
        "plt.plot(xdata,fdata, color='red') + plt.plot(actual_data_x, actual_data_y, 'bo')\n",
        "\n",
        "# Add a title\n",
        "plt.title('Our test data (in blue) compared to the actual data (in red)')\n",
        "\n",
        "# Add X and y Label\n",
        "plt.xlabel('x axis')\n",
        "plt.ylabel('output')\n",
        "\n",
        "# Add a grid\n",
        "plt.grid(alpha=.4,linestyle='--')"
      ],
      "execution_count": 163,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iWbtxq04uTq5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fUuQu-swudqp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M1Ifz--Xuibe",
        "colab_type": "code",
        "outputId": "26f0f497-76ef-479f-94a0-aec3aaa0026f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        }
      },
      "source": [
        "#  (We've already used 'x' as a variable, so we'll call the solution vector c.)\n",
        "from scipy import linalg\n",
        "c = linalg.inv(M.transpose() * M) * M.transpose() * b\n",
        "c"
      ],
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[ 1.58310047e+13],\n",
              "        [-1.21781676e+13],\n",
              "        [-8.88159723e+11],\n",
              "        [ 2.62251954e+13],\n",
              "        [-1.27682859e+13],\n",
              "        [ 7.64752457e+12],\n",
              "        [-1.09397514e+13],\n",
              "        [-1.80336215e+13]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 164
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rW_-GgyupL5b",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c03252e2-e045-4753-e14b-288a016ab340"
      },
      "source": [
        "c[2,0]"
      ],
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-888159722514.416"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 165
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jQfKJP928kAp",
        "colab_type": "code",
        "outputId": "33b0ac68-9cc4-4168-89ff-19dce0ac1bb9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "error = ((b-M*c).transpose() * (b-M*c))[0,0]\n",
        "error**0.5"
      ],
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "650512390408546.2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 166
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zu6dAoyF82XR",
        "colab_type": "code",
        "outputId": "30661057-6073-4d07-f408-21d4311b285a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "#Show a plot of the solutions using the best-fit method, and the SVD method:\n",
        "\n",
        "# We'll specify that x is a variable:\n",
        "x = sym.symbols('x')\n",
        "\n",
        "\n",
        "#set up our 100 data points on the interval from (-2pi, 2pi):\n",
        "\n",
        "best_fit = c[0,0]*np.cos(xdata) +c[1,0]*np.sin(xdata)+ c[2,0]*np.cos(2*xdata)+c[3,0]*np.sin(2*xdata) + c[4,0]*np.cos(3*xdata) + c[5,0]*np.sin(3*xdata) + c[6,0]*np.cos(4*xdata) + c[7,0]*np.sin(4*xdata)\n",
        "# Create the actual plot in red, and our datapoints in blue,\n",
        "# and the best-fit method in green:  \n",
        "plt.plot(xdata,fdata, color='red', linewidth=2 )+plt.plot(xdata,best_fit, color='green')\n",
        "\n",
        "#Restrict the output values to this range:\n",
        "\n",
        "\n",
        "# Add a title\n",
        "plt.title('Our test data (blue) for the original function (red) and our best-fit solution (green)')\n",
        "plt.ylim()\n",
        "# Add X and y Label\n",
        "plt.xlabel('x axis')\n",
        "plt.ylabel('output')\n",
        "\n",
        "# Add a grid\n",
        "plt.grid(alpha=.4,linestyle='--')"
      ],
      "execution_count": 167,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zxw0ngMFF2-X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "U, S, Vh = linalg.svd(M, full_matrices=True)\n",
        "Vh =Vh.T\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mfoCQW1komMH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "94bce486-8d7c-4554-9da8-eaba7a848680"
      },
      "source": [
        "Vh.shape"
      ],
      "execution_count": 169,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(8, 8)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 169
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qFgDPCOEKlud",
        "colab_type": "code",
        "outputId": "bd8d6661-9296-4d23-f99d-34859807db3a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# We can compare the original matrix M to the matrix reconstructed (called a1) from the SVD:\n",
        "# If they are close, then allclose(M, a1) should be True.\n",
        "\n",
        "#First, recast S as a matrix instead of a vector:\n",
        "sigma = np.zeros((U.shape[1], Vh.shape[0]))\n",
        "for i in range(min(sigma.shape)):\n",
        "     sigma[i, i] = S[i]\n",
        "a1 = np.dot(U, np.dot(sigma, Vh.T))\n",
        "#does a1 approximate M?\n",
        "a1.shape\n",
        "np.allclose(M, a1)\n"
      ],
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 170
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LanuGPVTKr0z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#  and  discard U_d, Sigma_d, Vh_d\n",
        "useSigs = 5\n",
        "\n",
        "#Use these parts of U, S, and Vh\n",
        "(Vrows, Vcols) = Vh.shape\n",
        "(Urows, Ucols) = U.shape\n",
        "U_use = U[:Urows, :useSigs]\n",
        "Vh_use = Vh[:Vrows, :useSigs]\n",
        "sigma_use = sigma[:useSigs, :useSigs]\n",
        "\n",
        "#discard these parts of U, S, and Vh:\n",
        "U_d = U[:Urows, useSigs:]\n",
        "Vh_d = Vh[:Vrows, useSigs:]\n",
        "sigma_d = sigma[useSigs:, useSigs:]\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tf3uOasRKv-F",
        "colab_type": "code",
        "outputId": "b85d2f3e-5812-4dac-e8ec-24946b3e730e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        }
      },
      "source": [
        "svdsol = (Vh_use @ linalg.inv(sigma_use) @ U_use.transpose()) @ b\n",
        "svdsol"
      ],
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[ 1.30910085e+13],\n",
              "        [ 4.00066189e+12],\n",
              "        [-1.13139851e+13],\n",
              "        [ 1.68148155e+13],\n",
              "        [ 1.43014641e+12],\n",
              "        [-4.08933715e+12],\n",
              "        [-6.21232145e+12],\n",
              "        [-1.68272427e+12]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 172
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FXzq4amMK1Ur",
        "colab_type": "code",
        "outputId": "6e7a6d02-c9dc-4163-c25d-286011d2a558",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "error = ((b-M*svdsol).transpose() * (b-M*svdsol))[0,0]\n",
        "error**0.5"
      ],
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "667167175754737.2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 173
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DR650Y16K7pD",
        "colab_type": "code",
        "outputId": "281761f4-0eb8-44c2-f15f-484eecea51d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "#Show a plot of the solutions using the best-fit method, and the SVD method:\n",
        "\n",
        "# We'll specify that x is a variable:\n",
        "x = sym.symbols('x')\n",
        "\n",
        "\n",
        "# find the ouput for our function on each data point:\n",
        "fdata = 4 - 3*xdata**2 + 5*xdata**6\n",
        "svd_best_fit = svdsol[0,0]*np.cos(xdata) +svdsol[1,0]*np.sin(xdata)+ svdsol[2,0]*np.cos(2*xdata)+svdsol[3,0]*np.sin(2*xdata) + svdsol[4,0]*np.cos(3*xdata) + svdsol[5,0]*np.sin(3*xdata) + svdsol[6,0]*np.cos(4*xdata) + svdsol[7,0]*np.sin(4*xdata)\n",
        "# Create the actual plot in red, and our datapoints in blue,\n",
        "# and the best-fit method in green:  \n",
        "plt.plot(xdata,fdata, color='red', linewidth=2 ) + plt.plot(actual_data_x, actual_data_y, 'bo', alpha=0.3)+plt.plot(xdata,svd_best_fit, color='purple') + plt.plot(xdata,best_fit, color='green')\n",
        "\n",
        "#Restrict the output values to this range:\n",
        "\n",
        "\n",
        "# Add a title\n",
        "plt.title('Our test data (blue) for the original function (red) and our best-fit solution (green)')\n",
        "plt.ylim()\n",
        "# Add X and y Label\n",
        "plt.xlabel('x axis')\n",
        "plt.ylabel('output')\n",
        "\n",
        "# Add a grid\n",
        "plt.grid(alpha=.4,linestyle='--')"
      ],
      "execution_count": 174,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XrPEtUAUdAlp",
        "colab_type": "text"
      },
      "source": [
        "#Refelection\n",
        "The matrix M is set up as\n",
        "\\begin{matrix}\n",
        "1 & sin(xdata_i) & cos(xdata_i) & sin(2*xdata_i) & cos(2*xdata_i)...&..sin(4*xdata_i) & cos(4*xdata_i) \\\\\n",
        ".. & .. & .. \\\\\n",
        "1 & sin(xdata_n) & cos(xdata_n) & sin(2*xdata_n) & cos(2*xdata_n)...&..sin(4*xdata_n) & cos(4*xdata_n) \n",
        "\\end{matrix}\n",
        "\n",
        "\n",
        "\n",
        "I learned a lot from this project about fitting data with lines. Especially trying out the svd for the cases where matrix in not ivertible. That I think makes it powerful compare to the best fit method by least squares method. The estimate are a little off when trying the trignometric basis.. \n",
        "\n",
        "It seems to model some part of it good but not quite perfect"
      ]
    }
  ]
}