Least_Squares_Approximation.ipynb

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        "---"
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      "source": [
        "# Numerical Analysis\n",
        "# Least Squares Approximation"
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        "## Remember\n",
        "\n",
        "Given the dataset $(x, f)$ where $x = \\{x_0, x_1, \\dots, x_n\\}^T$ and $f = \\{f_0, f_1, \\dots, f_n\\}^T$, we can quickly find the best polynomial fit for any specified polynomial degree!\n",
        "\n",
        "Let $x^{(j)}$ be the vector ${x_0^{(j)}, x_1^{(j)}, \\dots, x_n^{(j)}}$, to compute the best fitting polynomial of degree 3 (for example) $p_3 (x) = a_0 + a_1x + a_2 x^2 + a_3 x^3$, we define:\n",
        "\n",
        "$$\n",
        "A = \n",
        "\\begin{bmatrix}\n",
        "    \\textbf{1} & \\textbf{x} & \\textbf{x}^2 & \\textbf{x}^3\n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "where each element is a column vector.\n",
        "\n",
        "Then, to solve $Aa = f$, we left-multiply both sides by $A^T$ and we compute $a = (A^TA)^{-1}(A^Tf)$."
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        "It is required to construct best ﬁt by polynomials of degree n-1 (i.e. having n coefficients) for n = 1, 2, 3, 4, 5 of the function $cos(2\\pi x)$ at 21 equidistant points on the interval $[0,1]$.\n",
        "\n",
        "Least-Squares Approximation Algorithm\n",
        "\n",
        "```\n",
        "Input:\n",
        "    x: vector of x values\n",
        "    y: vector of y values\n",
        "    n: the desired best fit polynomial degree\n",
        "Output:\n",
        "    a: vector of polynomial coefficients a\n",
        "\n",
        "Algorithm:\n",
        "    1. Construct polynomial matrix A such that\n",
        "        A = [[1, x_0, x_0**2, ..., x_0**n],\n",
        "             [1, x_1, x_1**2, ..., x_1**n].\n",
        "             .\n",
        "             .\n",
        "             .,\n",
        "             [1, x_m, x_m**2, ..., x_m**n]]\n",
        "     2. Calculate the vector 'a' using the given formula.\n",
        "\n",
        "```"
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        "#### TO-DO (1)\n",
        "\n",
        "Deﬁne a function `make_poly_matrix` that takes in vector `x` of length of $m$, and the polynomial degree `n` and returns the matrix $A$ with shape $m\\times n$."
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        "import numpy as np\n",
        "\n",
        "# 1. create an empty matrix A with shape m by n.\n",
        "# 2. Loop over the columns of matrix A and make each \n",
        "#    column equals x**i, where `i` is the index of the\n",
        "#    column starting from 1 to n+1.\n",
        "# 3. return A\n",
        "def make_poly_matrix(x, n):\n",
        "    # YOUR CODE HERE\n",
        "    A = np.zeros([len(x),n])\n",
        "    for i in range(len(x)):\n",
        "      for j in range(n):\n",
        "        A[i][j] = x[i]**j\n",
        "    return A\n",
        "    raise NotImplementedError()"
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        "assert np.all(np.equal(make_poly_matrix(np.array([1,2,3]), 4),\n",
        "                                       np.array([[ 1.,  1.,  1.,  1.],\n",
        "                                                 [ 1.,  2.,  4.,  8.],\n",
        "                                                 [ 1.,  3.,  9., 27.]])))"
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        "#### TO-DO (2)\n",
        "\n",
        "Defien a function `LeastSqFit(x, y, n)` that takes in vector `x` and vector `y` and the polynomial degree `n` and return the polynomial coefficients `a`."
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        "from numpy.linalg import pinv, inv\n",
        "\n",
        "def leastSqFit(x, y, n):\n",
        "    # YOUR CODE HERE\n",
        "    A = make_poly_matrix(x, n)\n",
        "    A_T = A.transpose()\n",
        "    a = np.dot((inv(np.dot(A_T,A))),(np.dot(A_T,y)))\n",
        "    return a\n",
        "    raise NotImplementedError()"
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        "assert(np.all(np.isclose(make_poly_matrix(np.linspace(0, 1, 21), 5)@leastSqFit(\n",
        "            np.linspace(0, 1, 21),\n",
        "            np.cos(np.pi * 2 * np.linspace(0, 1, 21)), 5),\n",
        "            np.array([0.97241529,  0.98036196,  0.83726923,  0.59320472,  0.29234577, -0.02702061, \n",
        "                    -0.3324977,  -0.59757911, -0.80164875, -0.92998084, -0.97373993, -0.92998084,\n",
        "                    -0.80164875, -0.59757911, -0.3324977,  -0.02702061,  0.29234577,  0.59320472,\n",
        "                    0.83726923,  0.98036196,  0.97241529]))))"
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        "#### TO-DO (3)\n",
        "\n",
        "Define a function `plotApprox` that does not take any parameters, but should create 21 x values between 0 and 1, calculate $y = cos(2\\pi x)$ and plot these points. Then, iterate over n = 1 to 5, calculating the best fit polynomial of degree n and plotting that polynomial given the same 21 points.\n",
        "\n",
        "![download.png](attachment:download.png)"
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        "import matplotlib.pyplot as plt\n",
        "def col():\n",
        "  return tuple(np.random.random() for i in range(3))\n",
        "def plotApprox():\n",
        "    # YOUR CODE HERE\n",
        "    x = np.linspace(0,1,21)\n",
        "    y = np.cos(2*np.pi*x)\n",
        "    plt.figure(figsize=(6.4*3,4.8*3),facecolor=[0.91,0.91,0.91])\n",
        "    plt.plot(x,y,color=\"blue\")\n",
        "    for  n in range(1,6):\n",
        "      a = leastSqFit(x, y, n)\n",
        "      A = make_poly_matrix(x, n)\n",
        "      y_approx = np.dot(A,a)\n",
        "      plt.plot(x,y_approx, color= col())\n",
        "      print(a)\n",
        "    return plt.show()\n",
        "    raise NotImplementedError()"
      ]
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            "[0.04761905]\n",
            "[ 4.76190476e-02 -5.55111512e-17]\n",
            "[ 1.38010893 -8.41572555  8.41572555]\n",
            "[ 1.38010893e+00 -8.41572555e+00  8.41572555e+00 -3.97903932e-13]\n",
            "[  0.97241529   2.03256349 -41.30130085  78.53747471 -39.26873735]\n"
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            "text/plain": [
              "<Figure size 1382.4x1036.8 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plotApprox()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "HDxU-77cfTWL",
      "metadata": {
        "id": "HDxU-77cfTWL"
      },
      "source": [
        "**\\[THE END\\]**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "O1b9zIJEfTWL",
      "metadata": {
        "id": "O1b9zIJEfTWL"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Ahmad Mongy - 120200033 - Lab8-Least_Squares_Approximation.ipynb",
      "provenance": []
    },
    "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": "3.7.6"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}