{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Monomial interpolation"
      ]
    },
    {
      "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": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "x = np.linspace(0, 1, 200)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now plot the monomial basis on the interval [0,1] up to $x^9$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.collections.LineCollection at 0x7f6d60f82c88>"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wcEkX7vdzXbiQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f6d60f82fd0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n = 10\n",
        "\n",
        "for i in range(n):\n",
        "    pt.plot(x, x**i)\n",
        "    \n",
        "pt.vlines(np.linspace(0, 1, n), 0, 1, alpha=0.5, linestyle=\"--\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* How do the entries of the Vandermonde matrix relate to this plot?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "------------------\n",
        "* Guess the condition number of the Vandermonde matrix for $n=5,10,20$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "686.43494181859546"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "n = 5\n",
        "\n",
        "V = np.array([np.linspace(0, 1, n)**i for i in range(n)]).T\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
}