cds-numerical-methods/Week 1/02 Polynomial Interpolation.ipynb

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    "# CDS: Numerical Methods Assignments\n",
    "\n",
    "- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
    "\n",
    "- Solutions must be submitted via the Jupyter Hub.\n",
    "\n",
    "- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
    "\n",
    "## Submission\n",
    "\n",
    "1. Name all team members in the the cell below\n",
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    "5. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
    "6. submit your solutions  **in time (before the deadline)**"
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    "## Polynomial Interpolation\n",
    "\n",
    "In the following you will construct the interpolating polynomial for the pairs $x_k = [2,3,4,5,6]$ and $y_k = [2,5,5,5,6]$ using the \"inversion method\" via the Vandermonde matrix, as discussed in the lecture."
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    "# Import packages here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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   "source": [
    "### Task 1\n",
    "\n",
    "Set up the Vandermonde matrix and calculate its determinant using $\\text{numpy.linalg.det()}$."
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    "def GetVDMMatrix(xk):\n",
    "    \"\"\"Don't forget to write a docstring ...\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
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    "# print the Vandermonde matrix here in an appropriate format and calculate the determinant\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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    "\"\"\"Check that GetVDMMatrix returns the correct output\"\"\"\n",
    "assert np.allclose( GetVDMMatrix([2.0, 4.0]), [[1.0, 2.0], [1.0, 4.0]] )"
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    "### Task 2\n",
    "\n",
    "Write a function that constructs the interpolating polynomial for $\\text{x}$ (a user-defined array of $x$ values) using the Vandermonde matrix from the previous task and $\\text{numpy.linalg.inv()}$."
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    "def interpVDM(xk, yk, x):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
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    "\"\"\"Check that interpVDM returns the correct output\"\"\"\n",
    "assert np.allclose( interpVDM([1.0, 3.0], [4.0, 6.0], [2.5]), [5.5] )\n",
    "assert np.allclose( interpVDM([5.0, 14.0], [12.0, -3.0], [6.5]), [9.5] )"
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   "source": [
    "### Task 3\n",
    "\n",
    "Plot the interpolating polynomial from $x=2$ to $x=6$ using $x$-step-sizes of $0.01$."
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    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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