Hermite_and_Newtons_Divided_Difference_Interpolation.ipynb

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        "Make sure you remove `raise NotImplementedError()` and fill in any place that says `# YOUR CODE HERE`, as well as your `NAME`, `ID`, and `SECTION` below:"
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      "source": [
        "---"
      ]
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        "# Part 1: Hermite Interpolation\n",
        "---\n",
        "Hermite Interpolation is an example of a variant of the interpolation problem, where the interpolant matches one or more **derivatives of $f$**  at each of the nodes, in addition to the function values."
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      "source": [
        "## Importing the necessary libraries"
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      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from itertools import combinations\n",
        "from numpy.polynomial import Polynomial"
      ],
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        "## Creating the components for Hermite interpolation\n",
        "\n",
        "For the case of Hermite Interpolation, we look for a polynomial that matches both $f'(x_i)$ and $f(x_i)$ at the nodes $x_i = x_0,\\dots,x_n$. Say you have $n+1$ data points, $(x_0, y_0), (x_1, y_1), x_2, y_2), \\dots, (x_n, y_n)$ and you happen to know the first-order derivative at all of these points, namely, $(x_0, y_0 ^\\prime ), (x_1, y_1 ^\\prime ), x_2, y_2 ^\\prime ), \\dots ,(x_n, y_n ^\\prime )$. According to hermite interpolation, since there are $2n + 2$ conditions; $n+1$ for $f(x_i)$ plus $n+1$ for $f'(x_i)$; you can fit a polynomial of order $2n+1$. \n",
        "\n",
        "General form of a $2n+1$ degree Hermite polynomial:\n",
        "\n",
        "$$p_{2n+1} = \\sum_{k=0}^{n} \\left(f(x_k)h_k(x) + f'(x_k)\\hat{h}_k(x)\\right), \\tag{1}$$\n",
        "\n",
        "where $h_k$ and $\\hat{h}_k$ are defined using Lagrange basis functions by the following equations:\n",
        "\n",
        "$$h_k(x) = (1-2(x-x_k)l^\\prime_k(x_k))l^2_k(x_k), \\tag{2}$$\n",
        "\n",
        "and\n",
        "\n",
        "$$\\hat{h}_k(x) = (x-x_k)l^2_k(x_k), \\tag{3}$$\n",
        "\n",
        "where the Lagrange basis function being:\n",
        "\n",
        "$$l_k(x) = \\prod_{j=0, j\\neq k}^{n} \\frac{x-x_j}{x_k-x_j}. \\tag{4}$$\n",
        "\n",
        "**Note** that, we can rewrite Equation $(2)$ in this way,\n",
        "\n",
        "\\begin{align}\n",
        "h_k(x) &= \\left(1-2(x-x_k)l^\\prime_k(x_k) \\right)l^2_k(x_k) \\\\\n",
        "&= \\left(1 - 2xl^\\prime_k(x_k) + 2x_kl^\\prime_k(x_k) \\right)l^2_k(x_k) \\\\\n",
        "&= \\left(1 + 2x_kl^\\prime_k(x_k) - 2l'_k(x_k)x \\right) l^2_k(x_k) \\tag{5}\n",
        "\\end{align}\n",
        "Replacing $l^\\prime_k(x_k)$ with $m$, we get:\n",
        "$$h_k(x) = (1 - 2xm + 2x_km)l^2_k(x_k). \\tag{6}$$\n",
        "\n",
        "# Tasks:\n",
        "\n",
        "* The functions: `l(k, x)`, `h(k, x)` and `h_hat(k, x)` calculate the corresponding $l_k$, $h_k$, and $\\hat{h}_k$, respectively.\n",
        "\n",
        "* Function `l(k, x)` has already been defined for you. Your task is to complete the `h(k, x)`, `h_hat(k, x)`, and `hermit(x, y, y_prime)` functions.\n",
        "\n",
        "* Later we will draw some plots to check if the code is working.\n",
        "\n",
        "---"
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        "### Part 1: Calculate $l_k$\n",
        "This function uses the following equation to calculate $l_k(x)$ and returns a polynomial:\n",
        "\n",
        "$$l_k(x) = \\prod_{j=0, j\\neq k}^{n} \\frac{x-x_j}{x_k-x_j}.$$"
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        "# Already written for you.\n",
        "\n",
        "def l(k, x):\n",
        "    n = len(x)\n",
        "    assert (k < len(x))\n",
        "    \n",
        "    x_k = x[k]\n",
        "    x_copy = np.delete(x, k)\n",
        "    \n",
        "    denominator = np.prod(x_copy - x_k)\n",
        "    \n",
        "    coeff = []\n",
        "    \n",
        "    for i in range(n):\n",
        "        coeff.append(sum([np.prod(x) for x in combinations(x_copy, i)]) * (-1)**(i) / denominator)\n",
        "    \n",
        "    coeff.reverse()\n",
        "    \n",
        "    return Polynomial(coeff)"
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        "### Part 2: Calculate $h_k$\n",
        "This function calculates $h_k(x)$ using the following equation:\n",
        "$$h_k(x) = \\left(1 + 2x_kl^\\prime_k(x_k) - 2l'_k(x_k)x \\right) l^2_k(x_k).$$\n",
        "\n",
        "This equation is basically a multiplication of two polynomials.\n",
        "\n",
        "First polynomial: $1 + 2x_kl^\\prime_k(x_k) - 2l'_k(x_k)x$.\n",
        "\n",
        "Second polynomial: $l^2_k(x_k)$.\n",
        "\n",
        "The `coeff` variable should contain a python list of coefficient values for the **first** polynomial of the equation. These coefficient values are used to create a polynomial `p`."
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        "def h(k, x):\n",
        "    # initialize with None. Replace with appropriate values/function calls\n",
        "    # initialize with None. Replace with appropriate values/function calls\n",
        "    l_k = l(k, x)\n",
        "    l_k_sqr = l_k * l_k\n",
        "    l_k_prime = l_k.deriv(1)\n",
        "    coeff = [1 + 2 * x[k] * l_k_prime(x[k]), -2 * l_k_prime(x[k])]\n",
        "    p = Polynomial(coeff)\n",
        "\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()\n",
        "    # --------------------------------------------\n",
        "    \n",
        "    return p * l_k_sqr"
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      "source": [
        "# Test case for the h(k, x) function\n",
        "x = [3, 5, 7, 9]\n",
        "k = 2\n",
        "h_test = h(k, [3, 5, 7, 9])\n",
        "h_result = Polynomial([-2.5, 0.5]) * (l(k, x) ** 2)\n",
        "\n",
        "assert Polynomial.has_samecoef(h_result, h_test)\n",
        "assert h_result == h_test"
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      "source": [
        "### Part 3: Calculate $\\hat{h}_k$\n",
        "This function calculates $\\hat{h}_k(x)$ using the following equation:\n",
        "\n",
        "$$\\hat{h}_k(x) = (x-x_k)l^2_k(x_k).$$\n",
        "\n",
        "This equation is also a multiplication of two polynomials.\n",
        "\n",
        "First polynomial: $x-x_k$.\n",
        "\n",
        "Second polynomial:  $l^2_k(x_k)$.\n",
        "\n",
        "The `coeff` variable should contain a python list of coefficient values for the **first** polynomial of the equation. These coefficient values are used to create a polynomial `p`."
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        "def h_hat(k, x):\n",
        "    # Initialize with none\n",
        "    l_k = l(k, x)\n",
        "    l_k_sqr = l_k * l_k\n",
        "    coeff = [-x[k], 1]\n",
        "    p = Polynomial(coeff)\n",
        "    \n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()\n",
        "    # --------------------------------------------\n",
        "    \n",
        "    return p * l_k_sqr"
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        "# Test case for the h(k, x) function\n",
        "x = [3, 5, 7, 9]\n",
        "k = 2\n",
        "h_test = h_hat(k, [3, 5, 7, 9])\n",
        "h_result = Polynomial([-7, 1]) * (l(k, x) ** 2)\n",
        "\n",
        "assert Polynomial.has_samecoef(h_result, h_test)\n",
        "assert h_result == h_test"
      ],
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        "### Part 4: The Hermite Polynomial\n",
        "This function uses the following equation:\n",
        "\n",
        "$$p_{2n+1} = \\sum_{k=0}^{n} \\left(f(x_k)h_k(x) + f'(x_k)\\hat{h}_k(x)\\right).$$\n",
        "\n",
        "The polynomial denoted by the equation is calculated by the variable `f`."
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      "source": [
        "def hermit(x, y, y_prime):\n",
        "    assert len(x) == len(y)\n",
        "    assert len(y) == len(y_prime)\n",
        "    \n",
        "    f = Polynomial([0.0])\n",
        "    # --------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    for i in range(len(x)):\n",
        "        f += y[i] * h(i, x) + y_prime[i] * h_hat(i, x)\n",
        "    #raise NotImplementedError()\n",
        "    # --------------------------------------------\n",
        "    return f"
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      "source": [
        "## Testing our methods by plotting graphs.\n",
        "\n",
        "**Note:** \n",
        "\n",
        "* For each of the 5 plots, there will be 2 curves plotted: one being the original function, and the other being the interpolated curve. \n",
        "\n",
        "* The original functions are displayed in orange color, while the hermite interpolated curves are in blue.\n",
        "\n",
        "* `x`, `y`, and `y_prime` contain $x_i$, $f(x_i)$, and $f'(x_i)$ of the given nodes of the original function $f$.\n",
        "\n",
        "Upon calling the `hermit()` function, it returns a polynomial `f`. For example, for plot 1, it is called `f3`.\n",
        "\n",
        "In general, a polynomial may look like the following: $f = 1 + 2x + 3x^2$. Next, we pass in a number of $x$ values to the polynomial by calling the `.linspace()` function on the polynomial object using `f.linspace()`. This function outputs a tuple, which is stored in a variable called `data`. First element of `data` contains a 1D numpy array of $x_i$ values generated by `linspace()`, and the second element of `data` contains a 1D numpy array of the corresponding $y_i$ values outputted by our example polynomial:\n",
        "$f = 1 + 2x + 3x^2$. \n",
        "\n",
        "Using `test_x`, we generate a range of $x_i$ values to plot the original function, and `test_y` contains the corresponding $y_i$ values of the original function. For the first plot, our original function is the *sine curve*.\n",
        "\n",
        "For all the plots:\n",
        "\n",
        "`plt.plot(test_x, test_y)` plots the original function.\n",
        "\n",
        "`plt.plot(data[0], data[1])` plots the interpolated polynomial."
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      "source": [
        "pi      = np.pi\n",
        "x       = np.array([0.0, pi/2.0,  pi, 3.0*pi/2.0])\n",
        "y       = np.array([0.0,    1.0, 0.0,       -1.0])\n",
        "y_prime = np.array([1.0,    0.0, 1.0,        0.0])"
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      "source": [
        "**Plot 1:** trying to interpolate a sine curve (`np.sin()`) using first 2 nodes in `x` and `y`, and their corresponding derivative in `y_prime`."
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        "n      = 1\n",
        "f3     = hermit(x[:(n+1)], y[:(n+1)], y_prime[:(n+1)])\n",
        "data   = f3.linspace(n=50, domain=[-3, 3])\n",
        "test_x = np.linspace(-3, 3, 50, endpoint=True)\n",
        "test_y = np.sin(test_x)\n",
        "\n",
        "plt.plot(data[0], data[1])\n",
        "plt.plot(test_x, test_y)\n",
        "plt.show()"
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "d8f7bf96ae4f35419f880d25e72cff09",
          "grade": false,
          "grade_id": "plot02",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "W7v9mEcLPlvh"
      },
      "source": [
        "**Plot 2:** trying to interpolate a sine curve (`np.sin()`) using first 3 nodes in `x` and `y` and their corresponding derivative in `y_prime`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "25f490548e99af7d5fccb9fd5c653e80",
          "grade": true,
          "grade_id": "plot02_ans",
          "locked": true,
          "points": 1,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "qnNNOyC5Plvh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "681518a8-80fd-490e-ddc1-57b838a19e91"
      },
      "source": [
        "n      = 2\n",
        "f5     = hermit(x[:(n+1)], y[:(n+1)], y_prime[:(n+1)])\n",
        "data   = f5.linspace(n=50, domain=[-0.7, 3])\n",
        "test_x = np.linspace(-2*pi, 2*pi, 50, endpoint=True)\n",
        "test_y = np.sin(test_x)\n",
        "\n",
        "plt.plot(test_x, test_y) # 25-\n",
        "plt.plot(data[0], data[1]) # 10-33\n",
        "plt.show()\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "aae683a514e99dfecaa8672e1d6a4cb3",
          "grade": false,
          "grade_id": "plot03",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "InK1vx-bPlvi"
      },
      "source": [
        "**Plot 3:** trying to interpolate a sine curve (`np.sin()`) using first 4 nodes in `x` and `y` and their corresponding derivative in `y_prime`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "29fc16454184db75748c0381eff20504",
          "grade": true,
          "grade_id": "plot03_ans",
          "locked": true,
          "points": 1,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "eondZ70xPlvi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "2c2affb1-1d31-4cd9-f4d0-e9bb0e509650"
      },
      "source": [
        "n      = 3\n",
        "f7     = hermit(x[:(n+1)], y[:(n+1)], y_prime[:(n+1)])\n",
        "data   = f7.linspace(n=50, domain=[-0.3, 3])\n",
        "test_x = np.linspace(-2*pi, 2*pi, 50, endpoint=True)\n",
        "test_y = np.sin(test_x)\n",
        "\n",
        "plt.plot(data[0], data[1])\n",
        "plt.plot(test_x, test_y)\n",
        "plt.show()\n"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "d8edc2554aa6f2946081a47711e0f556",
          "grade": false,
          "grade_id": "plot04",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "qR1mUG58Plvi"
      },
      "source": [
        "**Plot 4:** trying to interpolate an exponential curve (`np.exp()`) using all nodes in `x` and `y` and their corresponding derivatives in `y_prime`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "4978eef584205c7563997760c20241c6",
          "grade": true,
          "grade_id": "plot04_test",
          "locked": true,
          "points": 1,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "tMgsKsC9Plvi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "371201a2-5cc5-48e9-942a-fd846a48facd"
      },
      "source": [
        "#defining new set of given node information: x, y and y'\n",
        "x       = np.array([0.0, 1.0,          2.0       ])\n",
        "y       = np.array([1.0, 2.71828183,  54.59815003])\n",
        "y_prime = np.array([0.0, 5.43656366, 218.39260013])\n",
        "\n",
        "\n",
        "f7      = hermit( x, y, y_prime)\n",
        "data    = f7.linspace(n=50, domain=[-0.5, 2.2])\n",
        "test_x  = np.linspace(-0.5, 2.2, 50, endpoint=True)\n",
        "test_y  = np.exp(test_x**2)\n",
        "\n",
        "plt.plot(data[0], data[1])\n",
        "plt.plot(test_x, test_y)\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "5419db887410ebe73b42fa5f21ffc50e",
          "grade": false,
          "grade_id": "plot05",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "DYVL-_XcPlvi"
      },
      "source": [
        "**Plot 5:** trying to interpolate $y = (x-3)^2 + 1$ using all nodes in `x` and `y` and their corresponding derivatives in `y_prime`.\n",
        "\n",
        "For this plot you might be able to see only one curve due to the two curves overlapping. This means that our polynomial is accurately interpolating the original function.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "92cc6293f29ebf42544cedf49e4c1fc5",
          "grade": true,
          "grade_id": "plot05_test",
          "locked": true,
          "points": 3,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "tuHX_czoPlvj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "16281964-5182-4a59-ed35-a13ff6e4a0a6"
      },
      "source": [
        "#defining new set of given node information: x, y and y'\n",
        "x       = np.array([1.0, 3.0, 5.0])\n",
        "y       = np.array([5.0, 1.0, 5.0])\n",
        "y_prime = np.array([-4.0, 0.0, 4.0])\n",
        "\n",
        "f7      = hermit( x, y, y_prime)\n",
        "data    = f7.linspace(n=50, domain=[-10, 10])\n",
        "test_x  = np.linspace(-10, 10, 50, endpoint=True)\n",
        "test_y  = (test_x-3)**2 + 1\n",
        "\n",
        "plt.plot(data[0], data[1])\n",
        "plt.plot(test_x, test_y)\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
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      "source": [
        "## Part 2: Polynomial Interpolation Using Newton's Divided Difference Form\n",
        "---\n"
      ]
    },
    {
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      "source": [
        "### Newton's Divided Difference Form\n",
        "\n",
        "Newton form of a $n$ degree polynomial:\n",
        "\n",
        "$$p_n(x) = \\sum_{k=0}^{n} a_kn_k(x),$$\n",
        "where the basis is:\n",
        "$$n_k(x) = \\prod_{j=0}^{k-1}(x-x_j),$$\n",
        "$$ n_0(x)=1,$$\n",
        "\n",
        "and the coefficients are: $$a_k = f[x_0, x_1, ..., x_k],$$\n",
        "\n",
        "where the notation $f[x_0, x_1,\\dots,x_k]$ denotes the divided difference.\n",
        "\n",
        "By expanding the Newton form, we get:\n",
        "\n",
        "$$p(x) = f [x_0] + (x-x_0) f[x_0,x_1] + (x-x_0) (x-x_1) f[x_0,x_1,x_2] + \\dots + (x-x_0) (x-x_1) \\dots (x-x_{k-1}) f[x_0, x_1, \\dots, x_k]$$\n",
        "\n",
        "### Tasks: \n",
        "1. Complete the `calc_div_diff(x,y)` function which takes input `x` and `y`, and calculates all the divided differences. You may use the lambda function `difference()` inside the `calc_div_diff(x,y)` function to calculate the divided differences.\n",
        "\n",
        "2. Complete the `__call__()` function which takes an input `x`, and calculates `y` using all the difference coefficients. `x` can be a single value or a numpy. In this case, it is a numpy array.\n",
        "\n",
        "`res` variable must contain all results (corresponding y for x)."
      ]
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      "source": [
        "class Newtons_Divided_Differences:\n",
        "  \n",
        "    def __init__(self, differences):\n",
        "        self.differences = differences\n",
        "\n",
        "    def __call__(self, x):\n",
        "        '''\n",
        "        this function is for calculating y from given x using all the difference coefficients\n",
        "        x can be a single value or a numpy\n",
        "        the formula being used:\n",
        "        f(x) = f [x0] + (x-x0) f[x0,x1] + (x-x0) (x-x1) f[x0,x1,x2] + . . . + (x-x0) (x-x1) . . . (x-xk-1) f[x0, x1, . . ., xk]\n",
        "\n",
        "        work on this after implementing 'calc_div_diff'. Then you should have\n",
        "        f[x0], f[x0,x1]. . . . . ., f[x0, x1, . . ., xk] stored in self.differences\n",
        "\n",
        "        'res' variable must return all the results (corresponding y for x)\n",
        "        '''\n",
        "\n",
        "        res = np.zeros(len(x)) #Initialization to avoid runtime error. You can change this line if you wish\n",
        "\n",
        "        #----------------------------------------------\n",
        "        # YOUR CODE HERE\n",
        "        for i in range(len(x)):\n",
        "            for j in range(len(differences)):\n",
        "              n = 1.0\n",
        "              for k in range(j):\n",
        "                n = (x[i] - data_x[k]) * n\n",
        "              res[i] = res[i] + differences[j] * n\n",
        "        #raise NotImplementedError()\n",
        "        #----------------------------------------------\n",
        "        \n",
        "        return res\n"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "abd6bbf6334a986a608c38206f702989",
          "grade": false,
          "grade_id": "cell-fbe4c16afb6b3b32",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "HZhqt-6JPlvj"
      },
      "source": [
        "# basic rule for calculating the difference, implanted in the lambda function. \n",
        "# You may use it if you wish\n",
        "difference = lambda y2, y1, x2, x1: (y2-y1)/(x2-x1)\n",
        "\n",
        "def calc_div_diff(x,y):\n",
        "    assert(len(x)==len(y))\n",
        "    #write this function to calculate all the divided differences in the list 'b'\n",
        "    b = [y[0]]   #initializing\n",
        "    #----------------------------------------------\n",
        "    # YOUR CODE HERE\n",
        "    for col in range (1, len(x)):\n",
        "      for row in range (len(x) - col):\n",
        "        y[row] = difference(y[row + 1], y[row], x[col + row], x[row])\n",
        "      b.append(y[0])\n",
        "    #raise NotImplementedError()\n",
        "    #----------------------------------------------\n",
        "    return b"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a23dd58fcab86885a166b1e138b9ea08",
          "grade": true,
          "grade_id": "cell-72b9329c6c32517e",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "FancUC_xPlvk"
      },
      "source": [
        "# Test case for the calc_div_diff(x,y) function.\n",
        "\n",
        "data_x = [-3.,-2.,-1.,0.,1.,3.,4.]\n",
        "data_y = [-60.,-80.,6.,1.,45.,30.,16.]\n",
        "\n",
        "test = calc_div_diff(data_x, data_y)\n",
        "\n",
        "assert len(test) == len(data_x)\n"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "e2b6e9e71eaf31b857393044c2768ac0",
          "grade": false,
          "grade_id": "cell-f6a9f264b02b2642",
          "locked": true,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "affgKuuNPlvk"
      },
      "source": [
        "### Plotting the polynomial\n",
        "* `data_x` and `data_y` are the coordinates of the given nodes.\n",
        "\n",
        "* `differences` is a list which contains the divided differences as each of its elements: $f[x_0], f[x_0,x_1], f[x_0,x_1,x_2], \\dots$\n",
        "\n",
        "* `obj` is an object of type `Newtons_Divided_Differences`. Creating the object runs the constructor of the class where the `difference` are stored in `self.differences`.\n",
        "\n",
        "* `X` contains $x_i$ values through which we want to plot our polynomial.\n",
        "\n",
        "* Calling the object using `obj(X)` executes the `__call__()` function of the class, which returns a numpy array containing the corresponding $y_i$ values, and storing them in variable `F`.\n",
        "\n",
        "* Using `plt.plot(X,F)`, we plot the $(x_i, y_i)$ pairs of the polynomial."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "3f9ba22ae7061e1d74101e40a2d5a7a4",
          "grade": true,
          "grade_id": "cell-a16b9abefbcdc519",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "akcjxODFPlvk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "85efeb40-1a60-4329-fe46-938a0a6837f9"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "data_x = np.array([-3.,-2.,-1.,0.,1.,3.,4.])\n",
        "data_y = np.array([-30., -50., 36., 31., 75., 60., 46.])\n",
        "differences = calc_div_diff(list(data_x), list(data_y))\n",
        "p = Newtons_Divided_Differences(list(differences))\n",
        "test_x = np.linspace(-3, 4, 50, endpoint=True)\n",
        "test_y = p(test_x)\n",
        "\n",
        "#generating 50 points from -3 to 4 in order to create a smooth line\n",
        "plt.plot(test_x, test_y)\n",
        "plt.plot(data_x, data_y, 'ro')\n",
        "plt.show()\n"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pM4ydWq_Plvk"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}