{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Chebyshev polynomials"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part I: Plotting the Chebyshev polynomials"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "image/png": 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EhIr7KjDqj6OgTFBi0yZmF+j1wu13le3CNRkerNLlJddkXINdZbvYi54e9sVY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I99rOhir/cIs7PP0+3rLCu+vvxy3qp5NL/H1VhbtkilvndA9OytWTM/DaaCZCbJhcAFtjcXK+ul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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7faf089e20b8>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.linspace(-1, 1, 100)\n",
        "\n",
        "pt.xlim([-1.2, 1.2])\n",
        "pt.ylim([-1.2, 1.2])\n",
        "\n",
        "for k in range(10): # crank up\n",
        "    pt.plot(x, np.cos(k*np.arccos(x)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part II: Understanding the Nodes\n",
        "\n",
        "What if we interpolate random data?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n = 50 # crank up\n",
        "\n",
        "i = np.arange(n, dtype=np.float64)\n",
        "\n",
        "# Chebyshev nodes:\n",
        "#nodes = np.cos((2*(i+1)-1)/(2*n)*np.pi)\n",
        "\n",
        "# Equispace nodes:\n",
        "nodes = np.linspace(-1, 1, n)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7faf089ab160>]"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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4HNgGvB/4+iQ1DwBnJDkNeBK4FNjQG/sa8HbgO0neCBxTVT+Z7I2qKh17lSTNUHp/K5/b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\nL6Xzq0MJAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7faf089a5c50>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.plot(nodes, 0*nodes, \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part III: Chebyshev Interpolation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "V = np.cos(i*np.arccos(nodes.reshape(-1, 1)))\n",
        "data = np.random.randn(n)\n",
        "coeffs = la.solve(V, data)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7faf08b9f4a8>]"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7faf08b9f898>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.linspace(-1, 1, 1000)\n",
        "Vfull = np.cos(i*np.arccos(x.reshape(-1, 1)))\n",
        "pt.plot(x, np.dot(Vfull, coeffs))\n",
        "pt.plot(nodes, data, \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part IV: Conditioning"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n = 10 # crank up\n",
        "\n",
        "i = np.arange(n, dtype=np.float64)\n",
        "nodes = np.cos((2*(i+1)-1)/(2*n)*np.pi)\n",
        "V = np.cos(i*np.arccos(nodes.reshape(-1, 1)))\n",
        "\n",
        "la.cond(V)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "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": "3.5.1+"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}