From c03db58ad12f8eccf55ad97eaec1ec4cc4f74fb4 Mon Sep 17 00:00:00 2001 From: Tuan Vu Date: Tue, 23 Feb 2016 08:34:33 -0800 Subject: [PATCH 1/4] chapter 1 Learning Numpy + Scipy --- .../Learning NumPy-checkpoint.ipynb | 686 ++++++++++++++++++ .../Learning SciPy-checkpoint.ipynb | 533 ++++++++++++++ ch01/Learning NumPy.ipynb | 686 ++++++++++++++++++ ch01/Learning SciPy.ipynb | 557 ++++++++++++++ ch01/README.md | 4 + ch01/charts/1400_01_01.png | Bin 0 -> 27121 bytes ch01/charts/1400_01_02.png | Bin 0 -> 31411 bytes ch01/charts/1400_01_03.png | Bin 0 -> 33990 bytes ch01/charts/1400_01_04.png | Bin 0 -> 43330 bytes ch01/charts/1400_01_05.png | Bin 0 -> 32270 bytes ch01/charts/1400_01_06.png | Bin 0 -> 40480 bytes ch01/charts/1400_01_07.png | Bin 0 -> 43859 bytes ch01/charts/1400_01_08.png | Bin 0 -> 41857 bytes 13 files changed, 2466 insertions(+) create mode 100644 ch01/.ipynb_checkpoints/Learning NumPy-checkpoint.ipynb create mode 100644 ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb create mode 100644 ch01/Learning NumPy.ipynb create mode 100644 ch01/Learning SciPy.ipynb create mode 100644 ch01/README.md create mode 100644 ch01/charts/1400_01_01.png create mode 100644 ch01/charts/1400_01_02.png create mode 100644 ch01/charts/1400_01_03.png create mode 100644 ch01/charts/1400_01_04.png create mode 100644 ch01/charts/1400_01_05.png create mode 100644 ch01/charts/1400_01_06.png create mode 100644 ch01/charts/1400_01_07.png create mode 100644 ch01/charts/1400_01_08.png diff --git a/ch01/.ipynb_checkpoints/Learning NumPy-checkpoint.ipynb b/ch01/.ipynb_checkpoints/Learning NumPy-checkpoint.ipynb new file mode 100644 index 00000000..c9c3d4d8 --- /dev/null +++ b/ch01/.ipynb_checkpoints/Learning NumPy-checkpoint.ipynb @@ -0,0 +1,686 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Table of Contents\n", + "* [1) Numpy Array](#1%29-Numpy-Array)\n", + "* [2) Reshape](#2%29-Reshape) \n", + "* [3) copy](#3%29-copy)\n", + "* [4) Operation](#4%29-Operation)\n", + "* [5) Indexing](#5%29-Indexing)\n", + "* [6) Handling nonexisting values](#6%29-Handling-nonexisting-values)\n", + "* [7) Comparing runtime](#7%29-Comparing runtime)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.10.1'" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "np.version.full_version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Numpy Array" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 2, 3, 4, 5])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([0,1,2,3,4,5])\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.ndim" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(6L,)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Reshape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**We can now transform this array to a two-dimensional matrix** " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1],\n", + " [2, 3],\n", + " [4, 5]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = a.reshape((3,2))\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b.ndim" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3L, 2L)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1],\n", + " [77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b[1][0] = 77\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 1, 77, 3, 4, 5])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) copy" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1],\n", + " [77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = a.reshape((3,2)).copy()\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-99, 1],\n", + " [ 77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c[0][0] = -99\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 1, 77, 3, 4, 5])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-99, 1],\n", + " [ 77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** c and a are totally independent copies**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) Operation" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2, 4, 6, 8, 10])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d = np.array([1,2,3,4,5])\n", + "d * 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Indexing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**In addition to normal list indexing, it allows you to use arrays themselves as indices\n", + "by performing:**" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([77, 3, 4])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[np.array([2,3,4])]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, False, False, True], dtype=bool)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a > 4" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([77, 5])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>4]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 4, 3, 4, 4])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>4] = 4\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 4, 3, 4, 4])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.clip(0,4)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Handling nonexisting values" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., nan, 3., 4.])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.array([1, 2, np.NAN, 3, 4]) # let's pretend we have read this from a text file\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, False, False], dtype=bool)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isnan(c)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., 3., 4.])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c[~np.isnan(c)]" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.mean(c[~np.isnan(c)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 7) Comparing runtime" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compare the runtime behavior of NumPy compared with normal Python lists." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Normal Python: 0.785233 sec\n", + "Naive NumPy: 1.111960 sec\n", + "Good NumPy: 0.015943 sec\n" + ] + } + ], + "source": [ + "# %load performance_test.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "\n", + "import timeit\n", + "\n", + "normal_py_sec = timeit.timeit('sum(x*x for x in range(1000))',\n", + " number=10000)\n", + "naive_np_sec = timeit.timeit('sum(na*na)',\n", + " setup=\"import numpy as np; na=np.arange(1000)\",\n", + " number=10000)\n", + "good_np_sec = timeit.timeit('na.dot(na)',\n", + " setup=\"import numpy as np; na=np.arange(1000)\",\n", + " number=10000)\n", + "\n", + "print(\"Normal Python: %f sec\" % normal_py_sec)\n", + "print(\"Naive NumPy: %f sec\" % naive_np_sec)\n", + "print(\"Good NumPy: %f sec\" % good_np_sec)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb b/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb new file mode 100644 index 00000000..4c7e972c --- /dev/null +++ b/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb @@ -0,0 +1,533 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On top of the efficient data structures of NumPy, SciPy offers a magnitude of\n", + "algorithms working on those arrays. Whatever numerical heavy algorithm you take\n", + "from current books on numerical recipes, most likely you will find support for them\n", + "in SciPy in one way or the other. Whether it is matrix manipulation, linear algebra,\n", + "optimization, clustering, spatial operations, or even fast Fourier transformation, the\n", + "toolbox is readily filled. Therefore, it is a good habit to always inspect the scipy\n", + "module before you start implementing a numerical algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1.00000000e+00 2.27200000e+03]\n", + " [ 2.00000000e+00 nan]\n", + " [ 3.00000000e+00 1.38600000e+03]\n", + " [ 4.00000000e+00 1.36500000e+03]\n", + " [ 5.00000000e+00 1.48800000e+03]\n", + " [ 6.00000000e+00 1.33700000e+03]\n", + " [ 7.00000000e+00 1.88300000e+03]\n", + " [ 8.00000000e+00 2.28300000e+03]\n", + " [ 9.00000000e+00 1.33500000e+03]\n", + " [ 1.00000000e+01 1.02500000e+03]]\n", + "(743L, 2L)\n" + ] + } + ], + "source": [ + "# %load analyze_webstats.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "%matplotlib inline\n", + "import os\n", + "from utils import DATA_DIR, CHART_DIR\n", + "import scipy as sp\n", + "import matplotlib.pyplot as plt\n", + "\n", + "sp.random.seed(3) # to reproduce the data later on\n", + "\n", + "data = sp.genfromtxt(os.path.join(DATA_DIR, \"web_traffic.tsv\"), delimiter=\"\\t\")\n", + "print(data[:10])\n", + "print(data.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Number of invalid entries:', 8)\n" + ] + } + ], + "source": [ + "# all examples will have three classes in this file\n", + "colors = ['g', 'k', 'b', 'm', 'r']\n", + "linestyles = ['-', '-.', '--', ':', '-']\n", + "\n", + "x = data[:, 0]\n", + "y = data[:, 1]\n", + "print(\"Number of invalid entries:\", sp.sum(sp.isnan(y)))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "x = x[~sp.isnan(y)]\n", + "y = y[~sp.isnan(y)]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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bgP8G8HcA5qWZKUIIIfnHr388yvFO7HHvhcJt6Ow8EytXrhhtkdut8+o558+E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\n0hEkyO6Kz803rw7tyvC6L+6JjNwVzyjeODtva9f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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot input data\n", + "def plot_models(x, y, models, fname, mx=None, ymax=None, xmin=None):\n", + "\n", + " plt.figure(num=None, figsize=(8, 6))\n", + " plt.clf()\n", + " plt.scatter(x, y, s=10)\n", + " plt.title(\"Web traffic over the last month\")\n", + " plt.xlabel(\"Time\")\n", + " plt.ylabel(\"Hits/hour\")\n", + " plt.xticks(\n", + " [w * 7 * 24 for w in range(10)], ['week %i' % w for w in range(10)])\n", + "\n", + " if models:\n", + " if mx is None:\n", + " mx = sp.linspace(0, x[-1], 1000)\n", + " for model, style, color in zip(models, linestyles, colors):\n", + " # print \"Model:\",model\n", + " # print \"Coeffs:\",model.coeffs\n", + " plt.plot(mx, model(mx), linestyle=style, linewidth=2, c=color)\n", + "\n", + " plt.legend([\"d=%i\" % m.order for m in models], loc=\"upper left\")\n", + "\n", + " plt.autoscale(tight=True)\n", + " plt.ylim(ymin=0)\n", + " if ymax:\n", + " plt.ylim(ymax=ymax)\n", + " if xmin:\n", + " plt.xlim(xmin=xmin)\n", + " plt.grid(True, linestyle='-', color='0.75')\n", + " plt.savefig(fname)\n", + "\n", + "# first look at the data\n", + "plot_models(x, y, None, os.path.join(CHART_DIR, \"1400_01_01.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model parameters of fp1: [ 2.59619213 989.02487106]\n", + "('Error of the model of fp1:', array([ 3.17389767e+08]))\n", + "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", + "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "data": { + "image/png": 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p8MxcD+BAIirMuxMEQRCaDfohcUTU6KrX9p9rx8Nrg/DcDqvLd5z0wdcAeJ+I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\nC8ZrE4lGNbvIk8km7e3ttU3DzYXs1hOwcwt77b2ZxyqNFYy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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create and plot models\n", + "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", + "print(\"Model parameters of fp1: %s\" % fp1)\n", + "print(\"Error of the model of fp1:\", res1)\n", + "f1 = sp.poly1d(fp1)\n", + "\n", + "fp2, res2, rank2, sv2, rcond2 = sp.polyfit(x, y, 2, full=True)\n", + "print(\"Model parameters of fp2: %s\" % fp2)\n", + "print(\"Error of the model of fp2:\", res2)\n", + "f2 = sp.poly1d(fp2)\n", + "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", + "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", + "f100 = sp.poly1d(sp.polyfit(x, y, 100))\n", + "\n", + "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tgY/lXQhfXyiyP9Lb5mVQG3PR18cEPgWiBd7rgxdNIboh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\nzVJec2szFjUswo1v3ogTnjwBPSb3wEWvXIT2E/cBP9oCfB8HGgh48xZ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zzoh41stkNXjVyC1V1K5dO7Zt21Zs3aZNm4qa6Js1a1asd3z4Mnfu3HLTLuue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lAXwAHf97sB1NNcdx6Af3zfnxf0/W6jgq+99lr06tVL/X/Lli3RsmXLqBsoFAhoIDRA46qN0feK\nvqhfrT7qV6uPcyqdgxQpBZIkAQT27tobddnxwuPxoHPnjvB4jgEAJKkjdu3apbTJ4NqVK/9Cx46/\nAwBEcQz69HkJqampyM3NTXjbpk6dgrlzPwAAtG49BXv27DFo9z0A7oIojkOrVndiwYKf0aPHc2jd\nujUuvrhBUtplBffc0wp33bUWACBJUth2GL2D3NxcnazXrRuDL76YhLlzfwI5EKIo4J579DJZsWIV\n5s6dCwBo3bo1rrmmmWl9U6ZMxLx5PwFQ6hTFjli7do2vPg+AsepvgpAOQfgAXq8XwFIAwMqVY5Cd\nfbtaZl5e3kmTdXlCNO/dCszGpy3vssWxY8dOW3kvXboUS5cutXaxGfMn6oNQDX4wfL52AK8hNMgu\nBUB9ANsRCLJbBqAFFJN+0oPsvF4vv9v6HTdt2xTVfWWleVjVOpLpYwxXpxWztlEgW1ZW1ikTiGQ1\nzsFvQjeKebDybrT1+N0gRvILTrxk5JbRxhVMnz6jrER1xsE20Z98nEnyxkmMov8KwB4AxQB2AegK\nZZvcAhhvk3sdSvT8FgB3a773b5PLBjAiTH0JFVw0naSss6xZJcKybJdVc7NZMN+0af8zbWt5JP7g\nNiXCzB/pGu1iwSzxklF7ghcE3brFfzSvDXPYQXYnF2eSvE8awZf152QR/MnQlKNBWZBjtORm5LM2\nSwaSiEVKWS0QoqknUgbBaHY/RGpPcFk2wZctziTCKQ84k+QdjuDt42LPACTzyFRAOR60d+8XUVKy\nHiUl68Me+ao9yhOAenTqM890j7tsM5TlEazRyNp/dOxHHw3GK6/0CWmflWOEI9Xn/z24rNatWye1\nT5QXhDvWtizLsGHjpMCM+U/FD84gE315glULRqTrjLJ9xWsdORWsK/Fq6dHWd6ZEdSdiTCZqXJ8J\n8i5POJPkDdtEHxui7STl0U+cSMSyLzz4/nBkps32pa0rnkn2dCD4ZOB0nwATIddEvpvTXd7lDWeS\nvMMRvG2iTyCiNYWfSqa/SGZuv7k5L+8IevR42rAMqybnCRMm6+qyUrYZrNR5MlHe22fDho1TGGbM\nfyp+cJI1+GhwKpn0E61lmlkC/Bp8MjTa8m5diSZYLhHPcSZoOLaJ/szFmSRvhNHg/fvMTwsIgsBE\nPk9ubi7q16+fsPL8KCoqQuXKNVBSsh4A4HA0Rl7ekXKruZVVe3Nzc3HOOeecUrIpC4wePR69e78I\nj4cQBEIURWRkDIvamqFFsvp2eYPfQhZP/0lEGWeKvMsLziR5C4IAkoLRb7aJ3kZElKUZ2TZZ6xHY\nRbACXq8Aj2djzLsJzkQkYgdJsneh2LCRLJyMVLVnPPwk1rt3YwAoMxKLRxPp0eNpPPlkelT3x1pf\nLHWVd4STRSI0RBs2bNgIhq3BnyTEEzgWCxKxFzwaTSbe+k4nrSmcLCLJKWDRuAaiSEjS5bZlw4YN\nG5Zg++DD4HTx45S1zz/W+k4XeWsRThbRyOn48eMAAlp+vO/udJR1eYYt77LFmSRv2wdvw8YpjNGj\nx6NWrbqoVasuJkyYbGvuNmzYsASb4M8AlHXgmh0oF0A4WViRUyJS9dqwYePMhG2iD4PTzcxT1sFc\n0dZ3uslbi1iD7IzM+IcO7Y07RuF0lnV5hC3vssWZJG/bRG8DQNkHrp1OgXLxIpwsIv2m1fIffvgR\n1KpVt0wOzrFhw8apDZvgbdgo5/DvuDh0aC9mzZppm+tt2LBhCfY+eBs2TgHYlhAbNmxEC1uDt2Hj\nFIEdvGjDho1oYGvwNmycQjgds/zZsGEjObAJ3oaNUww2sduwYcMKbBO9DRs2bNiwcRrCJngbNmzY\nsGHjNIRN8DZMUVRUZG/DsmHDho1TFDbB2zBEIk6fs2HDhg0bJw82wdsIgZ3/3IYNGzZOfdgEb8OG\nDRs2bJyGsAneRgjshCo2bNiw8f/t3X/oXXUdx/Hna3NBjsBaP6z8o9G0MixhI+yHoBNkEPSDDFKC\nigz6Y0ZEJlGRFBETUigpioaTJqn1RxG4pKRmNWdpm7Noy0GWllFEwaBfq++7P85Rvn39brvo99xz\n7+f7fPzzPffcs3M/n/fu9/s659x7Pp/5533wWpYDqkjSfDPgdUIGuyTNLy/RS5LUIANekqQGGfCS\nJDXIgJckqUEGvCRJDTLgJUlqkAEvSVKDDHhJkhpkwEuS1CADXpKkBhnwkiQ1yICXJKlBBrwkSQ0y\n4CVJapABL0lSgwx4SZIaZMBLktSguQr4JNuSHE7yUJJrxm6PJEmzam4CPsla4EZgG3AucHmSVwz5\nmvv37x9y91rCek+PtZ4u6z1d1rszNwEPvAY4WlUPV9Vx4FbgzUO+oG+S6bLe02Otp8t6T5f17sxT\nwL8YeGTR40f7dZIkaYl5CvgauwGSJM2LVM1Hbia5ALi2qrb1jz8KLFTVjkXbzEdnJElaIVWV5dbP\nU8CfBhwBLgH+APwUuLyqfjVqwyRJmkGnjd2ASVXVf5JsB+4E1gI7DXdJkpY3N2fwkiRpcvP0JbtR\nJflhks2n2GZjknv7gXhuTbJuWu1rzYT13p7kaJKFJM+ZVttaNGG9b+kHmnowyc7+YzM9BRPWe2eS\ng0keSPKNJOun1b6WTFLrRdt+Psmxods0LQb85IpTf5N/B/C5qjob+Cvw3sFb1a5J6v1juu9k/Hb4\n5jRvknrvrqqXV9V5wDOBK4dvVrMmqfcHq+r8qno18Dtg+/DNatIktSbJFuCMSbadF00GfJKrk1zV\nL9+Q5K5+eWuS3f3ypUn2Jbk/ye2PHx0n2dwf8d2X5LtJzlyy7zVJdiX59JL1AS4Gvtmvuhl4y7A9\nnQ1j1Bugqg5W1aoL9xHrvWfRw58BZw3Vx1kyYr2P9dsEOB1YGLan4xur1ulGSr0O+Aiw7DfS51GT\nAQ/cDVzYL28B1veXEy8E9iZ5LvAx4JKq2gzcD3yo3+YLwNuqagtwE/CZRftdB9wCHKmqTyx5zQ3A\n36rq8V/C37N6BuIZo96r2aj1TvfR0zuBPSfapjGj1TvJTcBjwDn9vlo3Vq23A9+uqj8O0amxtPoZ\n2s+BzUmeBfwTuI/uzfIG4CrgArrx7Pd1B8c8A9gHvAx4JfD9fv1aulvyoDuq+zJwW1V9dmo9mQ/W\ne7rGrvcXgb1V9ZMV7NMsG63eVfWeJGvowusdwK4V7tusmXqtk7wIuAy4qL9a0owmA76qjif5DfBu\nuv/8Q8BWYFNVHU6yCfheVV2x+N8lOQ/4ZVW9brnd9vvamuT6qvrXkuf/ApyRZE1/Fn8W3Vl880aq\n96o1Zr2TfBLYUFXvW7kezbax399VtZDkNuBqGg/4kWp9PrAJONo/Pj3Jr6vqnBXr2EhavUQP8CPg\nw8Defvn9dEeHAPcCr0/yUoAk65OcDRwGnpdu1DySrEty7qJ9fhW4A7i9/8zmCdXdb/gD4O39qncB\n3xqiYzNqqvVeRlNH3hOYer2TXAlcClyx9LlVYIx6b+p/BngTsFrG/Zj23+47quqFVbWxqjYCf28h\n3KH9gD8TuKeq/gT8o19HVf2Z7gjx60keoL/E089SdxmwI8lB4ADw2sU7raob+vVfW+ZyzjV0nwc9\nBDwb2DlQ32bR1Oud5ANJHqH7rsOhJF8ZsH+zZoz395eA5wP3JDmQ5ONDdW4GTbXe/fKuJIfozmJf\nAHxq0B7OjjHe2/+36cp2ZzwOdCNJUoNaPoOXJGnVMuAlSWqQAS9JUoMMeEmSGmTAS5LUIANekqQG\nGfCSniTJhv5e9wNJHkvyaL98LMmNY7dP0ql5H7ykk+qHpz1WVdeP3RZJk/MMXtIkApDkoiTf6Zev\nTXJzkruTPJzkrUmuS3IoyZ50M3ydchpPScMw4CU9HRuBi+nGSt8N3FVVr6IbXvSN6aaWPdk0npIG\n0uRscpKmooA9VfXfJL8A1lbVnf1zDwIvoZvH/ETTeEoakAEv6en4NzwxpenxResX6P6+hBNP4ylp\nQF6il/RUTTJF7xFOPo2npIEY8JImUYt+LrcMT55msyaZxlPSMLxNTpKkBnkGL0lSgwx4SZIaZMBL\nktQgA16SpAYZ8JIkNciAlySpQQa8JEkNMuAlSWrQ/wCEvz0VQks8WwAAAABJRU5ErkJggg==\n", 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"C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" + ] + }, + { + "data": { + "image/png": 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rZKjaKIhbzVvE3t4htvYWsbe3OLG31bC1zAxtrLVobvxUk3IXvSAIgiCkG/p+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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nQRBKEBF4QRAEQShB/h/FgRnAbyi23gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fit and plot a model using the knowledge about inflection point\n", + "inflection = 3.5 * 7 * 24\n", + "xa = x[:inflection]\n", + "ya = y[:inflection]\n", + "xb = x[inflection:]\n", + "yb = y[inflection:]\n", + "\n", + "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", + "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", + "\n", + "plot_models(x, y, [fa, fb], os.path.join(CHART_DIR, \"1400_01_05.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Errors for the complete data set:\n", + "Error d=1: 317389767.339778\n", + "Error d=2: 179983507.878179\n", + "Error d=3: 139350144.031725\n", + "Error d=10: 121942326.363664\n", + "Error d=53: 109452409.941658\n", + "Errors for only the time after inflection point\n", + "Error d=1: 145045835.134473\n", + "Error d=2: 61116348.809620\n", + "Error d=3: 33214248.905598\n", + "Error d=10: 21611594.265136\n", + "Error d=53: 18656112.352438\n", + "Error inflection=132950348.197616\n", + "Trained only on data after inflection point" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:3: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + " app.launch_new_instance()\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Errors for only the time after inflection point\n", + "Error d=1: 22143941.107618\n", + "Error d=2: 19768846.989176\n", + "Error d=3: 19766452.361027\n", + "Error d=10: 18949296.656480\n", + "Error d=53: 18300790.344968\n", + "fbt2(x)= \n", + " 2\n", + "0.086 x - 94.02 x + 2.744e+04" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "fbt2(x)-100,000= \n", + " 2\n", + "0.086 x - 94.02 x - 7.256e+04\n", + "Test errors for only the time after inflection point\n", + "Error d=1: 6397694.386394\n", + "Error d=2: 6010775.401243\n", + "Error d=3: 6047678.658526\n", + "Error d=10: 7037716.777815\n", + "Error d=53: 7052767.755482\n", + " 2\n", + "0.086 x - 94.02 x + 2.744e+04\n", + " 2\n", + "0.086 x - 94.02 x - 7.256e+04\n", + "100,000 hits/hour expected at week 9.616071\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "data": { + "image/png": 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AZ4hoHZQo+ocBzARwFRF9DeAK9X8w8wYAKwFsAPA6gDHqBQDAGABLAGwCsJmZV3uQ96QS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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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ExsaSlpbmcF5paWmcP3+e2bNnExcXV76AvEz//v1JTk42Owxhoo7bOsra+84q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ExmlZn2gdN/7WUyT2Xed1YptM7o02UouPVBqramymaw+szd/P7p1pZ3wxrHkK6diYwJexEm5/Gc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\nIh4H+nOAQ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VHBx8y3XoiIiI6837vr6++Pn55bosWrQo1zIzMjJISkpy+uvbQgjHiF4ZzfFh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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def error(f, x, y):\n", + " return sp.sum((f(x) - y) ** 2)\n", + "\n", + "print(\"Errors for the complete data set:\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))\n", + "\n", + "\n", + "# extrapolating into the future\n", + "plot_models(\n", + " x, y, [f1, f2, f3, f10, f100],\n", + " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "print(\"Trained only on data after inflection point\")\n", + "fb1 = fb\n", + "fb2 = sp.poly1d(sp.polyfit(xb, yb, 2))\n", + "fb3 = sp.poly1d(sp.polyfit(xb, yb, 3))\n", + "fb10 = sp.poly1d(sp.polyfit(xb, yb, 10))\n", + "fb100 = sp.poly1d(sp.polyfit(xb, yb, 100))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [fb1, fb2, fb3, fb10, fb100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "plot_models(\n", + " x, y, [fb1, fb2, fb3, fb10, fb100],\n", + " os.path.join(CHART_DIR, \"1400_01_07.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "# separating training from testing data\n", + "frac = 0.3\n", + "split_idx = int(frac * len(xb))\n", + "shuffled = sp.random.permutation(list(range(len(xb))))\n", + "test = sorted(shuffled[:split_idx])\n", + "train = sorted(shuffled[split_idx:])\n", + "fbt1 = sp.poly1d(sp.polyfit(xb[train], yb[train], 1))\n", + "fbt2 = sp.poly1d(sp.polyfit(xb[train], yb[train], 2))\n", + "print(\"fbt2(x)= \\n%s\"%fbt2)\n", + "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))\n", + "fbt3 = sp.poly1d(sp.polyfit(xb[train], yb[train], 3))\n", + "fbt10 = sp.poly1d(sp.polyfit(xb[train], yb[train], 10))\n", + "fbt100 = sp.poly1d(sp.polyfit(xb[train], yb[train], 100))\n", + "\n", + "print(\"Test errors for only the time after inflection point\")\n", + "for f in [fbt1, fbt2, fbt3, fbt10, fbt100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))\n", + "\n", + "plot_models(\n", + " x, y, [fbt1, fbt2, fbt3, fbt10, fbt100],\n", + " os.path.join(CHART_DIR, \"1400_01_08.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "from scipy.optimize import fsolve\n", + "print(fbt2)\n", + "print(fbt2 - 100000)\n", + "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", + "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ch01/Learning NumPy.ipynb b/ch01/Learning NumPy.ipynb new file mode 100644 index 00000000..c9c3d4d8 --- /dev/null +++ b/ch01/Learning NumPy.ipynb @@ -0,0 +1,686 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Table of Contents\n", + "* [1) Numpy Array](#1%29-Numpy-Array)\n", + "* [2) Reshape](#2%29-Reshape) \n", + "* [3) copy](#3%29-copy)\n", + "* [4) Operation](#4%29-Operation)\n", + "* [5) Indexing](#5%29-Indexing)\n", + "* [6) Handling nonexisting values](#6%29-Handling-nonexisting-values)\n", + "* [7) Comparing runtime](#7%29-Comparing runtime)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.10.1'" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "np.version.full_version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Numpy Array" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 2, 3, 4, 5])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([0,1,2,3,4,5])\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.ndim" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(6L,)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Reshape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**We can now transform this array to a two-dimensional matrix** " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1],\n", + " [2, 3],\n", + " [4, 5]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = a.reshape((3,2))\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b.ndim" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3L, 2L)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1],\n", + " [77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b[1][0] = 77\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 1, 77, 3, 4, 5])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) copy" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1],\n", + " [77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = a.reshape((3,2)).copy()\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-99, 1],\n", + " [ 77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c[0][0] = -99\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0, 1, 77, 3, 4, 5])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-99, 1],\n", + " [ 77, 3],\n", + " [ 4, 5]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** c and a are totally independent copies**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) Operation" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2, 4, 6, 8, 10])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d = np.array([1,2,3,4,5])\n", + "d * 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Indexing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**In addition to normal list indexing, it allows you to use arrays themselves as indices\n", + "by performing:**" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([77, 3, 4])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[np.array([2,3,4])]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, False, False, True], dtype=bool)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a > 4" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([77, 5])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>4]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 4, 3, 4, 4])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>4] = 4\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 1, 4, 3, 4, 4])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.clip(0,4)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Handling nonexisting values" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., nan, 3., 4.])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.array([1, 2, np.NAN, 3, 4]) # let's pretend we have read this from a text file\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([False, False, True, False, False], dtype=bool)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isnan(c)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., 3., 4.])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c[~np.isnan(c)]" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.mean(c[~np.isnan(c)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 7) Comparing runtime" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compare the runtime behavior of NumPy compared with normal Python lists." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Normal Python: 0.785233 sec\n", + "Naive NumPy: 1.111960 sec\n", + "Good NumPy: 0.015943 sec\n" + ] + } + ], + "source": [ + "# %load performance_test.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "\n", + "import timeit\n", + "\n", + "normal_py_sec = timeit.timeit('sum(x*x for x in range(1000))',\n", + " number=10000)\n", + "naive_np_sec = timeit.timeit('sum(na*na)',\n", + " setup=\"import numpy as np; na=np.arange(1000)\",\n", + " number=10000)\n", + "good_np_sec = timeit.timeit('na.dot(na)',\n", + " setup=\"import numpy as np; na=np.arange(1000)\",\n", + " number=10000)\n", + "\n", + "print(\"Normal Python: %f sec\" % normal_py_sec)\n", + "print(\"Naive NumPy: %f sec\" % naive_np_sec)\n", + "print(\"Good NumPy: %f sec\" % good_np_sec)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ch01/Learning SciPy.ipynb b/ch01/Learning SciPy.ipynb new file mode 100644 index 00000000..70ac4934 --- /dev/null +++ b/ch01/Learning SciPy.ipynb @@ -0,0 +1,557 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On top of the efficient data structures of NumPy, SciPy offers a magnitude of\n", + "algorithms working on those arrays. Whatever numerical heavy algorithm you take\n", + "from current books on numerical recipes, most likely you will find support for them\n", + "in SciPy in one way or the other. Whether it is matrix manipulation, linear algebra,\n", + "optimization, clustering, spatial operations, or even fast Fourier transformation, the\n", + "toolbox is readily filled. Therefore, it is a good habit to always inspect the scipy\n", + "module before you start implementing a numerical algorithm." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Reading in the data" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1.00000000e+00 2.27200000e+03]\n", + " [ 2.00000000e+00 nan]\n", + " [ 3.00000000e+00 1.38600000e+03]\n", + " [ 4.00000000e+00 1.36500000e+03]\n", + " [ 5.00000000e+00 1.48800000e+03]\n", + " [ 6.00000000e+00 1.33700000e+03]\n", + " [ 7.00000000e+00 1.88300000e+03]\n", + " [ 8.00000000e+00 2.28300000e+03]\n", + " [ 9.00000000e+00 1.33500000e+03]\n", + " [ 1.00000000e+01 1.02500000e+03]]\n", + "(743L, 2L)\n" + ] + } + ], + "source": [ + "# %load analyze_webstats.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "%matplotlib inline\n", + "import os\n", + "from utils import DATA_DIR, CHART_DIR\n", + "import scipy as sp\n", + "import matplotlib.pyplot as plt\n", + "\n", + "sp.random.seed(3) # to reproduce the data later on\n", + "\n", + "data = sp.genfromtxt(os.path.join(DATA_DIR, \"web_traffic.tsv\"), delimiter=\"\\t\")\n", + "print(data[:10])\n", + "print(data.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Preprocessing and cleaning the data" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Number of invalid entries:', 8)\n" + ] + } + ], + "source": [ + "# all examples will have three classes in this file\n", + "colors = ['g', 'k', 'b', 'm', 'r']\n", + "linestyles = ['-', '-.', '--', ':', '-']\n", + "\n", + "x = data[:, 0]\n", + "y = data[:, 1]\n", + "print(\"Number of invalid entries:\", sp.sum(sp.isnan(y)))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Remove the invalid entries\n", + "x = x[~sp.isnan(y)]\n", + "y = y[~sp.isnan(y)]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\matplotlib\\collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", + " if self._edgecolors == str('face'):\n" + ] + }, + { + "data": { + "image/png": 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bgP8G8HcA5qWZKUIIIfnHr388yvFO7HHvhcJt6Ow8EytXrhhtkdut8+o558+E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\n0hEkyO6Kz803rw7tyvC6L+6JjNwVzyjeODtva9f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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot input data\n", + "def plot_models(x, y, models, fname, mx=None, ymax=None, xmin=None):\n", + "\n", + " plt.figure(num=None, figsize=(8, 6))\n", + " plt.clf()\n", + " # plot the (x,y) points with dots of size 10\n", + " plt.scatter(x, y, s=10)\n", + " plt.title(\"Web traffic over the last month\")\n", + " plt.xlabel(\"Time\")\n", + " plt.ylabel(\"Hits/hour\")\n", + " plt.xticks(\n", + " [w * 7 * 24 for w in range(10)], ['week %i' % w for w in range(10)])\n", + "\n", + " if models:\n", + " if mx is None:\n", + " mx = sp.linspace(0, x[-1], 1000)\n", + " for model, style, color in zip(models, linestyles, colors):\n", + " # print \"Model:\",model\n", + " # print \"Coeffs:\",model.coeffs\n", + " plt.plot(mx, model(mx), linestyle=style, linewidth=2, c=color)\n", + "\n", + " plt.legend([\"d=%i\" % m.order for m in models], loc=\"upper left\")\n", + "\n", + " plt.autoscale(tight=True)\n", + " plt.ylim(ymin=0)\n", + " if ymax:\n", + " plt.ylim(ymax=ymax)\n", + " if xmin:\n", + " plt.xlim(xmin=xmin)\n", + " plt.grid(True, linestyle='-', color='0.75')\n", + " plt.savefig(fname)\n", + "\n", + "# first look at the data\n", + "plot_models(x, y, None, os.path.join(CHART_DIR, \"1400_01_01.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model parameters of fp1: [ 2.59619213 989.02487106]\n", + "('Error of the model of fp1:', array([ 3.17389767e+08]))\n", + "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", + "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "data": { + "image/png": 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J6uqWYNiwWwJryYvAC4IgCEIRIgIvCIIgCFmipKQElZWTEI32QDTaA5WVk1BSUhLItZvF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\nC8ZrE4lGNbvIk8km7e3ttU3DzYXs1hOwcwt77b2ZxyqNFYy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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create and plot models\n", + "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", + "print(\"Model parameters of fp1: %s\" % fp1)\n", + "print(\"Error of the model of fp1:\", res1)\n", + "f1 = sp.poly1d(fp1)\n", + "\n", + "fp2, res2, rank2, sv2, rcond2 = sp.polyfit(x, y, 2, full=True)\n", + "print(\"Model parameters of fp2: %s\" % fp2)\n", + "print(\"Error of the model of fp2:\", res2)\n", + "f2 = sp.poly1d(fp2)\n", + "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", + "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", + "f100 = sp.poly1d(sp.polyfit(x, y, 100))\n", + "\n", + "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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tgY/lXQhfXyiyP9Lb5mVQG3PR18cEPgWiBd7rgxdNIboh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\nzVJec2szFjUswo1v3ogTnjwBPSb3wEWvXIT2E/cBP9oCfB8HGgh48xZ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zzoh41stkNXjVyC1V1K5dO7Zt21Zs3aZNm4qa6Js1a1asd3z4Mnfu3HLTLuue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lAXwAHf97sB1NNcdx6Af3zfnxf0/W6jgq+99lr06tVL/X/Lli3RsmXLqBsoFAhoIDRA46qN0feK\nvqhfrT7qV6uPcyqdgxQpBZIkAQT27tobddnxwuPxoHPnjvB4jgEAJKkjdu3apbTJ4NqVK/9Cx46/\nAwBEcQz69HkJqampyM3NTXjbpk6dgrlzPwAAtG49BXv27DFo9z0A7oIojkOrVndiwYKf0aPHc2jd\nujUuvrhBUtplBffc0wp33bUWACBJUth2GL2D3NxcnazXrRuDL76YhLlzfwI5EKIo4J579DJZsWIV\n5s6dCwBo3bo1rrmmmWl9U6ZMxLx5PwFQ6hTFjli7do2vPg+AsepvgpAOQfgAXq8XwFIAwMqVY5Cd\nfbtaZl5e3kmTdXlCNO/dCszGpy3vssWxY8dOW3kvXboUS5cutXaxGfMn6oNQDX4wfL52AK8hNMgu\nBUB9ANsRCLJbBqAFFJN+0oPsvF4vv9v6HTdt2xTVfWWleVjVOpLpYwxXpxWztlEgW1ZW1ikTiGQ1\nzsFvQjeKebDybrT1+N0gRvILTrxk5JbRxhVMnz6jrER1xsE20Z98nEnyxkmMov8KwB4AxQB2AegK\nZZvcAhhvk3sdSvT8FgB3a773b5PLBjAiTH0JFVw0naSss6xZJcKybJdVc7NZMN+0af8zbWt5JP7g\nNiXCzB/pGu1iwSzxklF7ghcE3brFfzSvDXPYQXYnF2eSvE8awZf152QR/MnQlKNBWZBjtORm5LM2\nSwaSiEVKWS0QoqknUgbBaHY/RGpPcFk2wZctziTCKQ84k+QdjuDt42LPACTzyFRAOR60d+8XUVKy\nHiUl68Me+ao9yhOAenTqM890j7tsM5TlEazRyNp/dOxHHw3GK6/0CWmflWOEI9Xn/z24rNatWye1\nT5QXhDvWtizLsGHjpMCM+U/FD84gE315glULRqTrjLJ9xWsdORWsK/Fq6dHWd6ZEdSdiTCZqXJ8J\n8i5POJPkDdtEHxui7STl0U+cSMSyLzz4/nBkps32pa0rnkn2dCD4ZOB0nwATIddEvpvTXd7lDWeS\nvMMRvG2iTyCiNYWfSqa/SGZuv7k5L+8IevR42rAMqybnCRMm6+qyUrYZrNR5MlHe22fDho1TGGbM\nfyp+cJI1+GhwKpn0E61lmlkC/Bp8MjTa8m5diSZYLhHPcSZoOLaJ/szFmSRvhNHg/fvMTwsIgsBE\nPk9ubi7q16+fsPL8KCoqQuXKNVBSsh4A4HA0Rl7ekXKruZVVe3Nzc3HOOeecUrIpC4wePR69e78I\nj4cQBEIURWRkDIvamqFFsvp2eYPfQhZP/0lEGWeKvMsLziR5C4IAkoLRb7aJ3kZElKUZ2TZZ6xHY\nRbACXq8Aj2djzLsJzkQkYgdJsneh2LCRLJyMVLVnPPwk1rt3YwAoMxKLRxPp0eNpPPlkelT3x1pf\nLHWVd4STRSI0RBs2bNgIhq3BnyTEEzgWCxKxFzwaTSbe+k4nrSmcLCLJKWDRuAaiSEjS5bZlw4YN\nG5Zg++DD4HTx45S1zz/W+k4XeWsRThbRyOn48eMAAlp+vO/udJR1eYYt77LFmSRv2wdvw8YpjNGj\nx6NWrbqoVasuJkyYbGvuNmzYsASb4M8AlHXgmh0oF0A4WViRUyJS9dqwYePMhG2iD4PTzcxT1sFc\n0dZ3uslbi1iD7IzM+IcO7Y07RuF0lnV5hC3vssWZJG/bRG8DQNkHrp1OgXLxIpwsIv2m1fIffvgR\n1KpVt0wOzrFhw8apDZvgbdgo5/DvuDh0aC9mzZppm+tt2LBhCfY+eBs2TgHYlhAbNmxEC1uDt2Hj\nFIEdvGjDho1oYGvwNmycQjgds/zZsGEjObAJ3oaNUww2sduwYcMKbBO9DRs2bNiwcRrCJngbNmzY\nsGHjNIRN8DZMUVRUZG/DsmHDho1TFDbB2zBEIk6fs2HDhg0bJw82wdsIgZ3/3IYNGzZOfdgEb8OG\nDRs2bJyGsAneRgjshCo2bNiw8f/t3X/oXXUdx/Hna3NBjsBaP6z8o9G0MixhI+yHoBNkEPSDDFKC\nigz6Y0ZEJlGRFBETUigpioaTJqn1RxG4pKRmNWdpm7Noy0GWllFEwaBfq++7P85Rvn39brvo99xz\n7+f7fPzzPffcs3M/n/fu9/s659x7Pp/5533wWpYDqkjSfDPgdUIGuyTNLy/RS5LUIANekqQGGfCS\nJDXIgJckqUEGvCRJDTLgJUlqkAEvSVKDDHhJkhpkwEuS1CADXpKkBhnwkiQ1yICXJKlBBrwkSQ0y\n4CVJapABL0lSgwx4SZIaZMBLktSguQr4JNuSHE7yUJJrxm6PJEmzam4CPsla4EZgG3AucHmSVwz5\nmvv37x9y91rCek+PtZ4u6z1d1rszNwEPvAY4WlUPV9Vx4FbgzUO+oG+S6bLe02Otp8t6T5f17sxT\nwL8YeGTR40f7dZIkaYl5CvgauwGSJM2LVM1Hbia5ALi2qrb1jz8KLFTVjkXbzEdnJElaIVWV5dbP\nU8CfBhwBLgH+APwUuLyqfjVqwyRJmkGnjd2ASVXVf5JsB+4E1gI7DXdJkpY3N2fwkiRpcvP0JbtR\nJflhks2n2GZjknv7gXhuTbJuWu1rzYT13p7kaJKFJM+ZVttaNGG9b+kHmnowyc7+YzM9BRPWe2eS\ng0keSPKNJOun1b6WTFLrRdt+Psmxods0LQb85IpTf5N/B/C5qjob+Cvw3sFb1a5J6v1juu9k/Hb4\n5jRvknrvrqqXV9V5wDOBK4dvVrMmqfcHq+r8qno18Dtg+/DNatIktSbJFuCMSbadF00GfJKrk1zV\nL9+Q5K5+eWuS3f3ypUn2Jbk/ye2PHx0n2dwf8d2X5LtJzlyy7zVJdiX59JL1AS4Gvtmvuhl4y7A9\nnQ1j1Bugqg5W1aoL9xHrvWfRw58BZw3Vx1kyYr2P9dsEOB1YGLan4xur1ulGSr0O+Aiw7DfS51GT\nAQ/cDVzYL28B1veXEy8E9iZ5LvAx4JKq2gzcD3yo3+YLwNuqagtwE/CZRftdB9wCHKmqTyx5zQ3A\n36rq8V/C37N6BuIZo96r2aj1TvfR0zuBPSfapjGj1TvJTcBjwDn9vlo3Vq23A9+uqj8O0amxtPoZ\n2s+BzUmeBfwTuI/uzfIG4CrgArrx7Pd1B8c8A9gHvAx4JfD9fv1aulvyoDuq+zJwW1V9dmo9mQ/W\ne7rGrvcXgb1V9ZMV7NMsG63eVfWeJGvowusdwK4V7tusmXqtk7wIuAy4qL9a0owmA76qjif5DfBu\nuv/8Q8BWYFNVHU6yCfheVV2x+N8lOQ/4ZVW9brnd9vvamuT6qvrXkuf/ApyRZE1/Fn8W3Vl880aq\n96o1Zr2TfBLYUFXvW7kezbax399VtZDkNuBqGg/4kWp9PrAJONo/Pj3Jr6vqnBXr2EhavUQP8CPg\nw8Defvn9dEeHAPcCr0/yUoAk65OcDRwGnpdu1DySrEty7qJ9fhW4A7i9/8zmCdXdb/gD4O39qncB\n3xqiYzNqqvVeRlNH3hOYer2TXAlcClyx9LlVYIx6b+p/BngTsFrG/Zj23+47quqFVbWxqjYCf28h\n3KH9gD8TuKeq/gT8o19HVf2Z7gjx60keoL/E089SdxmwI8lB4ADw2sU7raob+vVfW+ZyzjV0nwc9\nBDwb2DlQ32bR1Oud5ANJHqH7rsOhJF8ZsH+zZoz395eA5wP3JDmQ5ONDdW4GTbXe/fKuJIfozmJf\nAHxq0B7OjjHe2/+36cp2ZzwOdCNJUoNaPoOXJGnVMuAlSWqQAS9JUoMMeEmSGmTAS5LUIANekqQG\nGfCSniTJhv5e9wNJHkvyaL98LMmNY7dP0ql5H7ykk+qHpz1WVdeP3RZJk/MMXtIkApDkoiTf6Zev\nTXJzkruTPJzkrUmuS3IoyZ50M3ydchpPScMw4CU9HRuBi+nGSt8N3FVVr6IbXvSN6aaWPdk0npIG\n0uRscpKmooA9VfXfJL8A1lbVnf1zDwIvoZvH/ETTeEoakAEv6en4NzwxpenxResX6P6+hBNP4ylp\nQF6il/RUTTJF7xFOPo2npIEY8JImUYt+LrcMT55msyaZxlPSMLxNTpKkBnkGL0lSgwx4SZIaZMBL\nktQgA16SpAYZ8JIkNciAlySpQQa8JEkNMuAlSWrQ/wCEvz0VQks8WwAAAABJRU5ErkJggg==\n", 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"C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" + ] + }, + { + "data": { + "image/png": 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rZKjaKIhbzVvE3t4htvYWsbe3OLG31bC1zAxtrLVobvxUk3IXvSAIgiCkG/p+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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nQRBKEBF4QRAEQShB/h/FgRnAbyi23gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fit and plot a model using the knowledge about inflection point\n", + "inflection = 3.5 * 7 * 24\n", + "xa = x[:inflection]\n", + "ya = y[:inflection]\n", + "xb = x[inflection:]\n", + "yb = y[inflection:]\n", + "\n", + "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", + "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", + "\n", + "plot_models(x, y, [fa, fb], os.path.join(CHART_DIR, \"1400_01_05.png\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Errors for the complete data set:\n", + "Error d=1: 317389767.339778\n", + "Error d=2: 179983507.878179\n", + "Error d=3: 139350144.031725\n", + "Error d=10: 121942326.363664\n", + "Error d=53: 109452409.941658\n", + "Errors for only the time after inflection point\n", + "Error d=1: 145045835.134473\n", + "Error d=2: 61116348.809620\n", + "Error d=3: 33214248.905598\n", + "Error d=10: 21611594.265136\n", + "Error d=53: 18656112.352438\n", + "Error inflection=132950348.197616\n", + "Trained only on data after inflection point" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:3: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + " app.launch_new_instance()\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Errors for only the time after inflection point\n", + "Error d=1: 22143941.107618\n", + "Error d=2: 19768846.989176\n", + "Error d=3: 19766452.361027\n", + "Error d=10: 18949296.656480\n", + "Error d=53: 18300790.344968\n", + "fbt2(x)= \n", + " 2\n", + "0.086 x - 94.02 x + 2.744e+04" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "fbt2(x)-100,000= \n", + " 2\n", + "0.086 x - 94.02 x - 7.256e+04\n", + "Test errors for only the time after inflection point\n", + "Error d=1: 6397694.386394\n", + "Error d=2: 6010775.401243\n", + "Error d=3: 6047678.658526\n", + "Error d=10: 7037716.777815\n", + "Error d=53: 7052767.755482\n", + " 2\n", + "0.086 x - 94.02 x + 2.744e+04\n", + " 2\n", + "0.086 x - 94.02 x - 7.256e+04\n", + "100,000 hits/hour expected at week 9.616071\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + }, + { + "data": { + "image/png": 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AZ4hoHZQo+ocBzARwFRF9DeAK9X8w8wYAKwFsAPA6gDHqBQDAGABLAGwCsJmZV3uQ96QS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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg\nW1++lX/88PmMW4kx5izGxOaM/42v21bzh5tzl6Iu3HnaaUxDfUwD/Xz5Iz/ne9+6l319g4zuxYwf\nPsmBU5vypr2b+OiJow3yazdexJnAm8+gaCxIDhtW5mmt1sqL5MTbY7WvZkcipfugsQCQypq7hgi8\nCHxMEp0P3mo+Z7MXp2FNRxGsaO3JbvZBN9u/oauxyDIvGom0GZrZ29z1PY0BfSR2w6hqa9didLe5\n1bnt2tpsLIOGYtBw9rB47qldjILk9zdtMLvZ0WNH+fuj3/NX33/FH27/kP/61V956adL+ZEPH+FJ\nb0ziEX8dwdevuJ4vXXopn/3Y2dxuVjv2TfXFFw0+pQUjn7j3wt484OkB/PtVv+c//f1PTJcHGBcG\nGec1YfphE/54+8f87eFv+Xj1cct7WFXlrLeJti7ero8aVmPH6++lPr+xBN5tYUymwOvzmy6CbkQE\nXgQ+JokKvJWrOLrrq16worUnOxGseEXD7Dg7bdGJCny0j7D51JWx+1Lb/WBFu/ZYbZfz55tP3mIu\nBg2DzJzazurjWh2u5u+OfMdf7v2S39/2Pr+04SUeUjiU6bIA4yof4wYfDysczhh5AePOLoxJSn/p\neMT6pBkn8RklZ3CXaaczfu9j/IaYBvj517Ou58f+8xj7ezRhnP4M4wcvMFoEGP6vTJ9XrdnCbHx1\nDTOB0jdv2e2Xb9fOVvY1emiivRPaviNGjLLdfOIWyXDRZwoi8CLwMUn0IYkVlGb8eFhHYzcUsljt\ngPrzGGuUTtrGo9WCYl13PC56q65X+rHLIws99mcZs8qX3Sh4+6LxgKl4G9MwBpmZnbfyaCXvrtzN\n679bz/8s/ye/+OWLvGjNIv71rOvZNyDA9Fs/d5/egy/6fxfxGSVncKuZreLqtoUHwK1ntuaz5p7F\nfZf05V89+yse9vIwvusfd/H096fz4jWLedWGVfzetvf4y71f8p7KPXyi5kQDGxgLQFbNIla/jTYx\npqMfIU6bIMUsjViFuXgLoZHHWgcMGo/ZtGmTjfTcD06L5/212re2tpZPnDhhui3dEIFXFm0q1qyA\niNjN6ykvL0fXrl0TSiMUCgFQ5hbX/7azPwAsWLAYBQXjwcwoLJyN/PyxdfvqtzEzwuEvAQDBYA9U\nVh6oO2deXhtUV68HsALAVASDQRQXF2HMmNEJXVs0tOvQiHbNGhs3bsSPf9xbzWsIwPlQJhWMzDcA\n3HlnAWpra+D3+zF3bontazHaN9I+iu327duNdu06RlkXQiDQG0eOHDRJ5x4A0wGcwJw5szFhQkH9\nuWtC2H98P3Yd2oX9x/ejoroC+4/vx75j+7D/2H7sO74Pn278DF9t2wBuxmjaJgdVXGXruiJgAMeB\n9nntccYpZ6Bdbju0atIKTy9+FrVHJgDHWmP4lZvw1KpnEK58FTjWCoGay3Gk4mCD+2TnmY2F8R0I\nhUIRtqy/z5HPrv54/T0iOg9+P6GmpkY9Tp9GCH5/L/h8voj7Z0xTe3cAoLi4CCNHDrN1nfV5WQPg\nQigTXJqfQ4/Vt8Ts+YuWTir54IMPMGLECMyePRu7du2NsF8yvyXx4Ma3O1MgIjAzmW60Uv5MXJBm\nNXg9bnd10dbHGjBHO3eswK5k4NQdeOutoyLa1YmaWrq8jYNsxItVDcrodm3gTQkEeGrRQ7x291p+\na8tb/Nz653jgIzcxLvcxBgxj/PY6pqE+7rWwF3cp6sItpreIywXun+rnk2edzOfOO5cvWXIJX/fM\ndTz8peHsuzrAuGQyo+c09p3bhN/d/C6v37WeAy2bKbOBmbQH669pxYrnY9YcE+lCF6tpQd8c5WwI\nWLM4Bm3dA6wNpqOv3Vu1y9ttjzfaROktEDDNt9W1R5sKub43SJAHDRoa9fyp5u233+Znn302qV4H\nN5AavLjoY+JmP3i3XwjjR8mqzVg7TzIGzIiGkzZvbV9lQo5prPStVXoNGKPQrfrbxusurK2t5Ufn\nzeVA26Yc6NyU/1SUz7eqA6LQFQH+6fR+PPjFwfyLJ3/Bpz50KmM8GPfENyBK4MEAt5/dns+bfx73\ne6If//b53/Lov43mKW9N4Tn/nsND5wxXRy/L4fvnPsQHjh3gcG2Ymc3vd6xpRc2aFoqL5/Hhw4d5\n06ZNrrRTG7Erlmaue6uBhPT7W8Ux9Ox5UQPBjdZcEE/cg7GgYRy6NlqTnNm3JLLg3XBq6FgxH2b5\nS7bQankSgU8fRODjJF0F3io9/QueaIBNokS7Zqs2b0XgG9bojGMJGNOtC2ILNuOZRYW8cc9G/mTn\nJ7x602p+et3TXFJawve9cx//8e9/5JteuImvWH4Fn//4+dxpTiduOq1pfJHg9zZh3EXcfX53/vmy\nn/MF03ux79cBxpUBposD7L+gCY959E7+6NuPeMuBLXzo+KGoo5dFs5dVQOX/b+/c46Sorjz+O909\nDCNiwPcTZAMxmiiJsDjsLvG1Kj42Gx+74iMZRVBjQDDgc30AYsARmJHwiGzwkRhQYsyaqBBADRIV\nlJfiKjCAKL4yIeosCDMOzNk/umumurpu1a3qqq7q7vP9fPjQ01Nz69apqvu795xz79XJE1DlahhJ\nX07eIWvHyus2rW5/Yz63l6WF7Tosfhc38i/wuUl+WR4eS+Kn3TLM6ePtZ1TYdeCcKMS77XeaaRSI\nwIvAu+LnIXHLvA3ihdAZHTuJhZfOhd9RgZ2b26luM2c+xEOHDjON0DYzKtdx6pDOvHzrcn7mf5/h\nuavmct1rdTy49lxOfD/FdGmSe0/sw/gxMcYcyrgz6Xv1sqOmHsUnzTqJT517KtN/JhnnXck4fQQn\nBlbwI6sf4UUNi/iNj97gCdPv41SXKk5VVCmvyUnYnATVnFRoXh/Bi8Azc3vYJvdvjbUDtnBNzeuu\nyYle1zXIPlduoqHqb/yMCM3X6La4kcqGTp1hN5vYuf6dOhlqgc+dUeFWlp0Nwx5RO3Vu4ogIvAi8\nK14fEreGIl8XmtsI3Xyclxc+6E6JdYS1e89u/mz3Z9zw9wZetmUZJ4+vZPStZQy8nRNnpXjo74fy\nRU9exHc9fRefMOME7jr+AMZd/hZEwR1VjNFHMq4nPvPRM3nIU0N4xHMjePDkczkxsIKTfTvxiLpR\nvPrj1Xzv9Emc2i8t1qqMbJ37qGtvt3uWHrF1rHBo9sroemRU32XHjSdyTc0wpRCa664rvuZ66u4W\np5ox4SYediNJc3a9m5vfeC6t16k7u0T1vjitWaFy0dvVx6vA6+y94Jc9e/bw8OHDee3ataF3IoJE\nBF4E3hXrvGwrdnHksF4Atxi79bPuspFOIxK769nXto93fLmDN+7YyK988Ar/YcMf+OE1D3PtX2r5\n1iW38lVPX8V0WZJxdX/GT3ozbk4nivmZurX/z/bnY+uP5X4P9eNzfn0OX/67y/nG52/k8X8ezzNf\nn8lPrH+Cl25Zyrc/eCcnu3dmpFK29rdrALOFa5zt773EPv2sD2CdB97hsk3HYu0S/ax1Mn/nvohS\nx7WmwyHZ9fAbo7YKlZ+9083TPJ06WNl/lx3O0Q0jWO0apHdN9Rw4JdmpOj86Lnq30EC+TJs2jQHw\nySefzDNm/CLWbnkzIvAi8K6Y52VbG1ndudN+0e08WBssnTnFBl/u/pJTX6tiHLyY0eNJTn6rE89e\nOZsnL5/MP134U6YLk4wh/8oYejJjBPFB9x/kf/Wy28AYRdxz4rF87uPn8mW/vYxHPjuS7112L89+\nYzYveHsBL3ljCa/6YBV/9H8fcXOrt8Si5uZmnjq13lagnFcUNLYu9XfvnEaF1nqqBM1u9G1NLnSr\nk9NMCTtRNATeqIfTimxevEXpMrKXEJ46td7VHsY9cfMYOAm8zn2zC6cE3TG3E22/4T6d1RbN9tBd\nE0L3/IceeigD4Geffbb9uziP3A1E4EXgXWloaLBtlFWNYVAjAS8Lr7Q36okNjC4vMw5JMXrOZxw/\ni5P/2IknvDSBx/xpDNf8voYvmHcBV/+ymvtM78PdJ3f3vXpZt8nduPf03nzKf5/C5//mfP7R73/E\no54bxeNfHM8PrXqIh0+7jpNfr+Tk4ZV8d+14TlW67/1txOC92E4nE9tphJMtis6b06g8OF5F2E1M\njQ6bl2mNTvFcla2y8x3UYmn952YDa5lEnZSj6iA8Bl6TvcIQeB3RC1NwwkywW7VqFY8ZM0Zre9s4\nIQIvAu9KtsCbG0D1yCHfHm5zc3NaEPd/jXHo85z8eiXPWzePh0y5ghOnVXDi3BQPmFTNg389mGl4\ngnHjMenRsZ9R9T3gTnd2YowkpmEJPvFnJ3H1pIGcOCfFie9V8OVTfsgL3lrASxuW8juN7/Bfd/2V\nW/e15tTZroHRWavbfM0VFftluY29jcTU98Ps6kwkKnPis01NTe0jf7vNacxuUiNjO5+wjNFhUI26\ndMTairW8ZLKzraian82Ghoac0bLZq1BfP8N3mMdLcp7d+6IjWNbQhI5r3jg+SBe97t+GLTh+2p1i\nGY37QQReBN4Vp6VT7Vysdi/MF7u+4C1/28LrPlnHL2x9gZ98+0me9fosnvDnCTxq4Si+4ndX8ODH\nB3P/Of25V30v7vqzrv7E+m4wbgbjJ4cwhiYYQ4gH3HcK37L4Fq79Sy3PXTOXn9nwDL+4+UVOHdaZ\nsd8bDNrU7hrNdeX6c3lmu7/VtrIrQyXwqtizm8C7uS+d3Ou5rv3s+fn5Tj1UxVjtRph2e6wbxxpi\nlUhUMVFlTnkqVPvBO3kQnNzF1nuU71xpN8+B9fqd7K/r6fEjkLrXGOSU2yBEuZBTZqNABF4E3pWG\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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ExsaSlpbmcF5paWmcP3+e2bNnExcXV76AvEz//v1JTk42Owxhoo7bOsra+84q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ExmlZn2gdN/7WUyT2Xed1YptM7o02UouPVBqramymaw+szd/P7p1pZ3wxrHkK6diYwJexEm5/Gc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\nIh4H+nOAQ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VHBx8y3XoiIiI6837vr6++Pn55bosWrQo1zIzMjJISkpy+uvbQgjHiF4ZzfFh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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def error(f, x, y):\n", + " return sp.sum((f(x) - y) ** 2)\n", + "\n", + "print(\"Errors for the complete data set:\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))\n", + "\n", + "\n", + "# extrapolating into the future\n", + "plot_models(\n", + " x, y, [f1, f2, f3, f10, f100],\n", + " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "print(\"Trained only on data after inflection point\")\n", + "fb1 = fb\n", + "fb2 = sp.poly1d(sp.polyfit(xb, yb, 2))\n", + "fb3 = sp.poly1d(sp.polyfit(xb, yb, 3))\n", + "fb10 = sp.poly1d(sp.polyfit(xb, yb, 10))\n", + "fb100 = sp.poly1d(sp.polyfit(xb, yb, 100))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [fb1, fb2, fb3, fb10, fb100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "plot_models(\n", + " x, y, [fb1, fb2, fb3, fb10, fb100],\n", + " os.path.join(CHART_DIR, \"1400_01_07.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "# separating training from testing data\n", + "frac = 0.3\n", + "split_idx = int(frac * len(xb))\n", + "shuffled = sp.random.permutation(list(range(len(xb))))\n", + "test = sorted(shuffled[:split_idx])\n", + "train = sorted(shuffled[split_idx:])\n", + "fbt1 = sp.poly1d(sp.polyfit(xb[train], yb[train], 1))\n", + "fbt2 = sp.poly1d(sp.polyfit(xb[train], yb[train], 2))\n", + "print(\"fbt2(x)= \\n%s\"%fbt2)\n", + "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))\n", + "fbt3 = sp.poly1d(sp.polyfit(xb[train], yb[train], 3))\n", + "fbt10 = sp.poly1d(sp.polyfit(xb[train], yb[train], 10))\n", + "fbt100 = sp.poly1d(sp.polyfit(xb[train], yb[train], 100))\n", + "\n", + "print(\"Test errors for only the time after inflection point\")\n", + "for f in [fbt1, fbt2, fbt3, fbt10, fbt100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))\n", + "\n", + "plot_models(\n", + " x, y, [fbt1, fbt2, fbt3, fbt10, fbt100],\n", + " os.path.join(CHART_DIR, \"1400_01_08.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)\n", + "\n", + "from scipy.optimize import fsolve\n", + "print(fbt2)\n", + "print(fbt2 - 100000)\n", + "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", + "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ch01/README.md b/ch01/README.md new file mode 100644 index 00000000..b1b8f19c --- /dev/null +++ b/ch01/README.md @@ -0,0 +1,4 @@ +Chapter 1 +--- + +1. 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8zr6%J)c7d;61lfBn4f z?k-Fu5&_~#nf;yy_GClw#%i4}c9kuJM;#5r0OnK#7U}b_<$uy*|JY(e+W{MP7H}d6 NVx)HlSE1v4^Izm<(Eb1b literal 0 HcmV?d00001 From 1d8e4e5acc086b17ab06ab7c1cfc280980323538 Mon Sep 17 00:00:00 2001 From: Tuan Vu Date: Tue, 23 Feb 2016 09:33:32 -0800 Subject: [PATCH 2/4] SciPy --- .../Learning SciPy-checkpoint.ipynb | 580 +++++++++++++----- ch01/Learning SciPy.ipynb | 574 +++++++++++------ ch01/charts/1400_01_08.png | Bin 41857 -> 40955 bytes 3 files changed, 813 insertions(+), 341 deletions(-) diff --git a/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb b/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb index 4c7e972c..3bbdb3df 100644 --- a/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb +++ b/ch01/.ipynb_checkpoints/Learning SciPy-checkpoint.ipynb @@ -1,5 +1,19 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Table of Contents\n", + "* [1) Reading in the data](#1%29-Reading-in-the-data)\n", + "* [2) Preprocessing and cleaning the data](#2%29-Preprocessing-and-cleaning-the-data) \n", + "* [3) fit a simple straight line](#3%29-fit-a simple-straight-line)\n", + "* [4) fit polynomial function](#4%29-fit-polynomial-function)\n", + "* [5) Stepping back to go forward – another look at our data](#5%29-Stepping-back-to-go-forward-–-another-look-at-our-data)\n", + "* [6) Training and testing](#6%29-Training-and-testing)\n", + "* [7) Answering our initial question](#7%29-Answering-our-initial-question)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -13,9 +27,16 @@ "module before you start implementing a numerical algorithm." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Reading in the data" + ] + }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 31, "metadata": { "collapsed": false }, @@ -60,9 +81,16 @@ "print(data.shape)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Preprocessing and cleaning the data" + ] + }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -87,19 +115,20 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ + "# Remove the invalid entries\n", "x = x[~sp.isnan(y)]\n", "y = y[~sp.isnan(y)]" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -108,7 +137,7 @@ "data": { "image/png": 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bgP8G8HcA5qWZKUIIIfnHr388yvFO7HHvhcJt6Ow8EytXrhhtkdut8+o558+E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\n0hEkyO6Kz803rw7tyvC6L+6JjNwVzyjeODtva9f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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -151,9 +180,27 @@ "plot_models(x, y, None, os.path.join(CHART_DIR, \"1400_01_01.png\"))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) fit a simple straight line" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's assume for a second that the underlying model is a straight line. Then the\n", + "challenge is how to best put that line into the chart so that it results in the smallest\n", + "approximation error. SciPy's polyfit() function does exactly that. Given data x and\n", + "y and the desired order of the polynomial (a straight line has order 1), it finds the\n", + "model function that minimizes the error function defined earlier:" + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -163,24 +210,41 @@ "output_type": "stream", "text": [ "Model parameters of fp1: [ 2.59619213 989.02487106]\n", - "('Error of the model of fp1:', array([ 3.17389767e+08]))\n", - "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", - "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" + "('Error of the model of fp1:', array([ 3.17389767e+08]))\n" ] - }, + } + ], + "source": [ + "# create and plot models\n", + "\n", + "# Simple straight line\n", + "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", + "print(\"Model parameters of fp1: %s\" % fp1)\n", + "print(\"Error of the model of fp1:\", res1)\n", + "f1 = sp.poly1d(fp1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means the best straight line fit is the following function\n", + "\n", + "$f(x) = 2.59619213 * x + 989.02487106$" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ { "data": { "image/png": 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p8MxcD+BAIirMuxMEQRCaDfohcUTU6KrX9p9rx8Nrg/DcDqvLd5z0wdcAeJ+I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\nC8ZrE4lGNbvIk8km7e3ttU3DzYXs1hOwcwt77b2ZxyqNFYy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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -188,26 +252,50 @@ } ], "source": [ - "# create and plot models\n", - "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", - "print(\"Model parameters of fp1: %s\" % fp1)\n", - "print(\"Error of the model of fp1:\", res1)\n", - "f1 = sp.poly1d(fp1)\n", - "\n", + "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) fit polynomial function" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", + "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" + ] + } + ], + "source": [ + "# Let's now fit a more complex model, a polynomial of degree 2\n", "fp2, res2, rank2, sv2, rcond2 = sp.polyfit(x, y, 2, full=True)\n", "print(\"Model parameters of fp2: %s\" % fp2)\n", "print(\"Error of the model of fp2:\", res2)\n", - "f2 = sp.poly1d(fp2)\n", - "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", - "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", - "f100 = sp.poly1d(sp.polyfit(x, y, 100))\n", - "\n", - "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + "f2 = sp.poly1d(fp2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**$f(x) = 0.0105322215 * x**2 - 5.26545650 * x + 1974.76082$**" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -216,7 +304,7 @@ "data": { "image/png": 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tgY/lXQhfXyiyP9Lb5mVQG3PR18cEPgWiBd7rgxdNIboh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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -229,7 +317,32 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + } + ], + "source": [ + "# Let's try it for degrees 3, 10, and 100\n", + "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", + "\n", + "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", + "\n", + "f100 = sp.poly1d(sp.polyfit(x, y, 100))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, "metadata": { "collapsed": false }, @@ -238,7 +351,7 @@ "data": { "image/png": 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zzoh41stkNXjVyC1V1K5dO7Zt21Zs3aZNm4qa6Js1a1asd3z4Mnfu3HLTLuue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lAXwAHf97sB1NNcdx6Af3zfnxf0/W6jgq+99lr06tVL/X/Lli3RsmXLqBsoFAhoIDRA46qN0feK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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -250,13 +363,36 @@ " x, y, [f1, f2, f3, f10, f100], os.path.join(CHART_DIR, \"1400_01_04.png\"))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Stepping back to go forward – another look at our data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, we step back and take another look at the data. It seems that there is an inflection\n", + "point between weeks 3 and 4. So let's separate the data and train two lines using\n", + "week 3.5 as a separation point:" + ] + }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error inflection=132950348.197616\n" + ] + }, { "name": "stderr", "output_type": "stream", @@ -267,12 +403,36 @@ "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" ] - }, + } + ], + "source": [ + "# fit and plot a model using the knowledge about inflection point\n", + "inflection = 3.5 * 7 * 24 # calculate the inflection point in hours\n", + "xa = x[:inflection] # data before the inflection point\n", + "ya = y[:inflection]\n", + "xb = x[inflection:] # data after\n", + "yb = y[inflection:]\n", + "\n", + "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", + "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", + "\n", + "fa_error = error(fa, xa, ya)\n", + "fb_error = error(fb, xb, yb)\n", + "print(\"Error inflection=%f\" % (fa_error + fb_error))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ { "data": { "image/png": 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rZKjaKIhbzVvE3t4htvYWsbe3OLG31bC1zAxtrLVobvxUk3IXvSAIgiCkG/p+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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -280,22 +440,14 @@ } ], "source": [ - "# fit and plot a model using the knowledge about inflection point\n", - "inflection = 3.5 * 7 * 24\n", - "xa = x[:inflection]\n", - "ya = y[:inflection]\n", - "xb = x[inflection:]\n", - "yb = y[inflection:]\n", - "\n", - "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", - "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", - "\n", + "# From the first line, we train with the data up to week 3, and in the second line we\n", + "# train with the remaining data.\n", "plot_models(x, y, [fa, fb], os.path.join(CHART_DIR, \"1400_01_05.png\"))" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -316,37 +468,81 @@ "Error d=3: 33214248.905598\n", "Error d=10: 21611594.265136\n", "Error d=53: 18656112.352438\n", - "Error inflection=132950348.197616\n", - "Trained only on data after inflection point" + "Error inflection=132950348.197616\n" ] - }, + } + ], + "source": [ + "def error(f, x, y):\n", + " return sp.sum((f(x) - y) ** 2)\n", + "\n", + "print(\"Errors for the complete data set:\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The models of degree 10 and 53 don't seem to expect a bright future of our\n", + "start-up. They tried so hard to model the given data correctly that they are clearly\n", + "useless to extrapolate beyond. This is called overfitting. On the other hand, the\n", + "lower degree models seem not to be capable of capturing the data good enough.\n", + "This is called underfitting." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:3: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - " app.launch_new_instance()\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" - ] - }, + "data": { + "image/png": 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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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4QQrwohlgghfhFC3CSEmCSE+EkI8ZnQdxaLuqWohIRExUCSvoSERKLRGnrZ0Z4A3gCwiOS5AE4A\n+LPQtxGOtKWohIREBeGU2mVPQkKiwkEAn5H0CiHWA1BJfu7/bh2AVgDaIfyWohISEhUISfoSEhKJ\nRjEQ2B63xPK5D/qcIxB+S1EJCYkKhDTvS0hIJBKxbJW8GZG3FJWQkKggSNKXkJAoK2j56/QeQe8B\ngCRLAPQGMFEIsRb6lsKXVmRHJSQkdMiUPQkJCQkJiVMEUtOXkJCQkJA4RSBJX0JCQkJC4hSBJH0J\nCQkJCYlTBJL0JSQkJCQkThFI0peQkJCQkDhFIElfQkJCQkLiFIEkfQkJCQkJiVMEkvQlJCQkJCRO\nEfw/4o+ncwCrqEoAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# extrapolating into the future\n", + "plot_models(\n", + " x, y, [f1, f2, f3, f10, f100],\n", + " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\n", + "Trained only on data after inflection point\n", "Errors for only the time after inflection point\n", "Error d=1: 22143941.107618\n", "Error d=2: 19768846.989176\n", "Error d=3: 19766452.361027\n", "Error d=10: 18949296.656480\n", - "Error d=53: 18300790.344968\n", - "fbt2(x)= \n", - " 2\n", - "0.086 x - 94.02 x + 2.744e+04" + "Error d=53: 18300790.344968\n" ] }, { @@ -359,70 +555,11 @@ " warnings.warn(msg, RankWarning)\n" ] }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "fbt2(x)-100,000= \n", - " 2\n", - "0.086 x - 94.02 x - 7.256e+04\n", - "Test errors for only the time after inflection point\n", - "Error d=1: 6397694.386394\n", - "Error d=2: 6010775.401243\n", - "Error d=3: 6047678.658526\n", - "Error d=10: 7037716.777815\n", - "Error d=53: 7052767.755482\n", - " 2\n", - "0.086 x - 94.02 x + 2.744e+04\n", - " 2\n", - "0.086 x - 94.02 x - 7.256e+04\n", - "100,000 hits/hour expected at week 9.616071\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" - ] - }, - { - "data": { - "image/png": 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AZ4hoHZQo+ocBzARwFRF9DeAK9X8w8wYAKwFsAPA6gDHqBQDAGABLAGwCsJmZV3uQ96QS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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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ExsaSlpbmcF5paWmcP3+e2bNnExcXV76AvEz//v1JTk42Owxhoo7bOsra+84q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VHBx8y3XoiIiI6837vr6++Pn55bosWrQo1zIzMjJISkpy+uvbQgjHiF4ZzfFh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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -430,27 +567,6 @@ } ], "source": [ - "def error(f, x, y):\n", - " return sp.sum((f(x) - y) ** 2)\n", - "\n", - "print(\"Errors for the complete data set:\")\n", - "for f in [f1, f2, f3, f10, f100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", - "\n", - "print(\"Errors for only the time after inflection point\")\n", - "for f in [f1, f2, f3, f10, f100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", - "\n", - "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))\n", - "\n", - "\n", - "# extrapolating into the future\n", - "plot_models(\n", - " x, y, [f1, f2, f3, f10, f100],\n", - " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", - " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", - "\n", "print(\"Trained only on data after inflection point\")\n", "fb1 = fb\n", "fb2 = sp.poly1d(sp.polyfit(xb, yb, 2))\n", @@ -466,47 +582,179 @@ " x, y, [fb1, fb2, fb3, fb10, fb100],\n", " os.path.join(CHART_DIR, \"1400_01_07.png\"),\n", " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", - "\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Training and testing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we only had some data from the future that we could use to measure our models\n", + "against, then we should be able to judge our model choice only on the resulting\n", + "approximation error." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ "# separating training from testing data\n", "frac = 0.3\n", "split_idx = int(frac * len(xb))\n", "shuffled = sp.random.permutation(list(range(len(xb))))\n", "test = sorted(shuffled[:split_idx])\n", - "train = sorted(shuffled[split_idx:])\n", + "train = sorted(shuffled[split_idx:])" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fbt2(x)= \n", + " 2\n", + "0.1031 x - 117.5 x + 3.544e+04\n", + "fbt2(x)-100,000= \n", + " 2\n", + "0.1031 x - 117.5 x - 6.456e+04\n" + ] + } + ], + "source": [ "fbt1 = sp.poly1d(sp.polyfit(xb[train], yb[train], 1))\n", "fbt2 = sp.poly1d(sp.polyfit(xb[train], yb[train], 2))\n", "print(\"fbt2(x)= \\n%s\"%fbt2)\n", - "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))\n", + "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test errors for only the time after inflection point\n", + "Error d=1: 5884534.411054\n", + "Error d=2: 6524875.605450\n", + "Error d=3: 6538982.705184\n", + "Error d=10: 7323509.948000\n", + "Error d=53: 12778972.159027\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + } + ], + "source": [ "fbt3 = sp.poly1d(sp.polyfit(xb[train], yb[train], 3))\n", "fbt10 = sp.poly1d(sp.polyfit(xb[train], yb[train], 10))\n", "fbt100 = sp.poly1d(sp.polyfit(xb[train], yb[train], 100))\n", "\n", "print(\"Test errors for only the time after inflection point\")\n", "for f in [fbt1, fbt2, fbt3, fbt10, fbt100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))\n", - "\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Uvv76a2mWdqKMjAyzQxAVYcFM39V++QVSUsBDT+FfNHnVZM5kneGWprdwS7Nb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "plot_models(\n", " x, y, [fbt1, fbt2, fbt3, fbt10, fbt100],\n", " os.path.join(CHART_DIR, \"1400_01_08.png\"),\n", " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 7) Answering our initial question" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally we have arrived at a model which we think represents the underlying process best; it is now a simple task of finding out when our infrastructure will reach 100,000 requests per hour. We have to calculate when our model function reaches the value 100,000.\n", "\n", - "from scipy.optimize import fsolve\n", - "print(fbt2)\n", - "print(fbt2 - 100000)\n", - "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", - "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + "Having a polynomial of degree 2, we could simply compute the inverse of the function and calculate its value at 100,000. Of course, we would like to have an approach that is applicable to any model function easily.\n", + "\n", + "This can be done by subtracting 100,000 from the polynomial, which results in another polynomial, and finding its root. SciPy's optimize module has the function fsolve that achieves this, when providing an initial starting position with parameter\n", + "x0. As every entry in our input data file corresponds to one hour, and we have 743 of them, we set the starting position to some value after that. Let fbt2 be the winning polynomial of degree 2." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 53, "metadata": { - "collapsed": true + "collapsed": false }, - "outputs": [], - "source": [] + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 2\n", + "0.1031 x - 117.5 x + 3.544e+04\n", + " 2\n", + "0.1031 x - 117.5 x - 6.456e+04\n", + "100,000 hits/hour expected at week 9.195553\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve\n", + "print(fbt2)\n", + "print(fbt2 - 100000)\n", + "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", + "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + ] } ], "metadata": { diff --git a/ch01/Learning SciPy.ipynb b/ch01/Learning SciPy.ipynb index 70ac4934..3bbdb3df 100644 --- a/ch01/Learning SciPy.ipynb +++ b/ch01/Learning SciPy.ipynb @@ -1,5 +1,19 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Table of Contents\n", + "* [1) Reading in the data](#1%29-Reading-in-the-data)\n", + "* [2) Preprocessing and cleaning the data](#2%29-Preprocessing-and-cleaning-the-data) \n", + "* [3) fit a simple straight line](#3%29-fit-a simple-straight-line)\n", + "* [4) fit polynomial function](#4%29-fit-polynomial-function)\n", + "* [5) Stepping back to go forward – another look at our data](#5%29-Stepping-back-to-go-forward-–-another-look-at-our-data)\n", + "* [6) Training and testing](#6%29-Training-and-testing)\n", + "* [7) Answering our initial question](#7%29-Answering-our-initial-question)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -22,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 31, "metadata": { "collapsed": false }, @@ -76,7 +90,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -101,7 +115,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 33, "metadata": { "collapsed": true }, @@ -114,24 +128,16 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\matplotlib\\collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", - " if self._edgecolors == str('face'):\n" - ] - }, { "data": { "image/png": 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s+uDF9f+HAWywvm8A8FHr+0cAbFTVIVV9HsBuAO8VkYkAulX1cWu/exzHEEIIIcRFVi34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\n0hEkyO6Kz803rw7tyvC6L+6JjNwVzyjeODtva9f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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -144,7 +150,6 @@ "\n", " plt.figure(num=None, figsize=(8, 6))\n", " plt.clf()\n", - " # plot the (x,y) points with dots of size 10\n", " plt.scatter(x, y, s=10)\n", " plt.title(\"Web traffic over the last month\")\n", " plt.xlabel(\"Time\")\n", @@ -175,9 +180,27 @@ "plot_models(x, y, None, os.path.join(CHART_DIR, \"1400_01_01.png\"))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) fit a simple straight line" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's assume for a second that the underlying model is a straight line. Then the\n", + "challenge is how to best put that line into the chart so that it results in the smallest\n", + "approximation error. SciPy's polyfit() function does exactly that. Given data x and\n", + "y and the desired order of the polynomial (a straight line has order 1), it finds the\n", + "model function that minimizes the error function defined earlier:" + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -187,24 +210,41 @@ "output_type": "stream", "text": [ "Model parameters of fp1: [ 2.59619213 989.02487106]\n", - "('Error of the model of fp1:', array([ 3.17389767e+08]))\n", - "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", - "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" + "('Error of the model of fp1:', array([ 3.17389767e+08]))\n" ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" - ] - }, + } + ], + "source": [ + "# create and plot models\n", + "\n", + "# Simple straight line\n", + "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", + "print(\"Model parameters of fp1: %s\" % fp1)\n", + "print(\"Error of the model of fp1:\", res1)\n", + "f1 = sp.poly1d(fp1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means the best straight line fit is the following function\n", + "\n", + "$f(x) = 2.59619213 * x + 989.02487106$" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ { "data": { "image/png": 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p8MxcD+BAIirMuxMEQRCaDfohcUTU6KrX9p9rx8Nrg/DcDqvLd5z0wdcAeJ+I\n/kpEtymfW7OdMUEQBEFwytSpj6Fjx85IJBih0NRGQR8y5GZHMy4++ujjBTXPvBOcCPxKAK8qx+4F\noEz5CIIgCELO0bbIGxq+AEDYsmVDo6Ab9bnr551XZ68rlHnmnWAr8Mx8p/IZo3zuZOYxQWROEARB\nENxClBoUZ9Tfro2Yv/HGwWlpFIO73lbgiehtg8/8IDInCIIgCHboW+TnnXde4z6r/nb1XP35l19+\nBTp27Fzw7nonLvoRms9fkZzWZ1E2MyUIgiAITonH4xg0qLxxJbh58+ZZirNRf7vaot+yZQNeeGF2\nY4Vg6NBh2LlzZ5C34xtOXPQLNZ/3mfkWAGdnP2uCIAhCcyATd7jW/f7II49j+PCRjcPkhg27BQBs\n+9t37tyJeDxuMCRuFurr6x1NkpOPOHHRd9B8OhLRhQDaBJA3QRAEochxOh7dCL37ffjwEYbHWfW3\nJxKc4o5X3fWRyFFILjKzrGAD75y46D9F0iW/CMCHAG4DMCibmRIEQRCKH7P+cTfna1HHvYfD0xCJ\nHIXx48c1tsjV1rm2vz0SOQpEnHb9iorrsXXrRkSjUV/vN2icuOi7MnM35XMoM5/HzO8HkTlBEAQh\n9+RjRLl23Hs4fGTKuPfzzz8PRIQRI0YaegXUFv3WrRsRChnLYJs2bUyXli0UnLjoWxDRUCKaTUTP\nE9EfiaiwqzWCIAiCIzJxodthtT67Ffpx70RN497j8Tjmzp1n6xUoKSmxFXFnS8vmL7aLzRDRdCQX\nw50BgAAMAFDPzOkDB3OMLDZT2Ii9g0NsHSyFau94PI6ysg6mi7X4eR3A+YIuVvlKutj/gH/8Y7Tj\nPOf7gjJWeF5sRqEnM5cz83xmfouZrwVwkq85FARBEJotbhd0MWr5A01Cff7557nyChTygjJWOBH4\neiI6RP2HiA4GUJ+9LAmCIAj5gFcXehBo3ecAUFbWAaWl7dG6dTvMnTsP48ePK1jXul84cdGfC+AJ\nJBedAYCuAK5j5rybzU5c9IWN2Ds4xNbBUuj2zmcXdpO7fiGAEwEsQXn5Djz99BlZ6U7IN6xc9BG7\nk5n5LSL6BYDDADCAr5k5v8IpBUEQhKxR7CJZrDhx0QPA8QCOAnAcgL5EdE32siQIgiAIzmjqRjgR\noVByyFw4PM22OyEfh/75jZNhcv8CMAHAaUj6P3oqH0EQ8pjm8AITBKCpP/7HH7fjhx92YPToPzUO\nmTN6BrJIsNlDAAAgAElEQVQ59C+fcNKCPwHAacxcwcx/VD/ZzpggCN5pLi8wQVDRzlQXDodNn4FM\nZ88rJJwI/BcAOmc7I4Ig+ENzeoEJghGJREKeAVgIPBG9TEQvA+gIYCkRzVW3EdFLdgkTUUsi+oiI\nPieiL4joTmV7ByKaR0TfKGm205wzmoiWE9EyIjpfs/0EIlqi7KvK6I4FQRCKEOmScUY+D/3zG6sW\n/ATlcyeAywDcB2Ci5mMJM8cAnMPMxwI4FsCFRHQygFEA5jHzLwC8pfwPIuoOoC+A7gAuBDCViNTQ\n/2kABjHzoQAOVVa0EwTBgOb0AhOSNNcuGbNKTTgcLuopaJ1iOg6eiN4AMAfA68y8LKOLEJUCeA/A\nTQBmAjiLmTcRUScA7zDz4UQ0GkADMz+gnDMHycrFGgDzmfkIZXs/AGcz840G15Fx8AWM2NtfrMYu\ni62DJZv29jqdbD6PbQfs8zd16mON672PHz8ON944uPFY1d5qBaBYZ6oDvE9Vey2AHQDuJKLPiOgR\nIrqUiFq7uHCIiD4HsAnAXGb+GMC+zLxJOWQTgH2V7/sB+E5z+ncA9jfYvk7ZLgiCBcX8UhMyI5st\nfj+6CqzyF4/HsXPnTk0f++0YNuwWw2OnT5+RstZ7s4OZbT8AwgBOBXA3gA+QdK2PdHKucn5bAPOR\nHEu/Xbdvm/L3YQBXa7Y/DuAKJKP452m2nwHgZZPrsJ+sWrXK1/QEa8TewSG2DpZs23vKlEc5Gi3l\naLSUp0x51PLYWCzG0WgpAysZWMnRaCnHYrHA8+Elf2r6kUgrDodbMrCUgdRja2trefny5Vm9z3xC\n0T1D7bWdyU5RzQSA/ymfvxLRzwCcb31Wyvm1RPQ2gAsAbCKiTsy8kYg6A9isHLYOQBfNaQcg2XJf\np3zXbl9ndJ2ePXti6NChjf/36tULvXr1cprNNHbs2IGamhr7AwVfEHsHh9g6WLJt74suOg/nn78Y\nQLL/2epaiUQCAwb0RyKxQzm+P9auXYtwOJxRHhKJBBYt+gT9+78HAFi0aBpWrOjtOt2PPvoE/fv3\nQ9KB3JS/ZJpN6RNNA9GDaGhoOpaoP2655TYcfXQP7Ltvp6zcZ66prq5GdXW1s4PNlJ+bWsXjkWyB\nR5FsuW8BMMDBeR0BtFO+twLwLoBfARgH4E/K9lEA7le+dwfwOYAWALoBWImmGIGPAJyM5HK1rwG4\n0OSavtaMpJUTLGLv4BBbB0u+2duPlrYeP1rMTWnco7TMo1xVNdk0/draWq6qmqxr1a/k8vJFHI2W\nNu7z8z7zDVi04J2Mgz+fmWsBXAxgNYCDAYxwcF5nAPOJaDGAj5Hsg38NwP0AziOibwD0Vv4HMy8F\n8ByApQBeB1ChZB4AKpB02S8HsIKZ5zi4viAIgmBANqLI/R29cRWAhYhEIrjhhsGm6bdp0wZDhtyM\nXbu2YevWjQiF0iWNmxqAzQ4nq8l9ycxHEtF0AM8z8+tEtJiZjwkmi86RKPrCRuwdHGLrYHFi73yP\naneK1/tQz5s+fUZjdHxl5aS0CohV+mpk/YAB/XH00cdixIiRKaMLtmzZkLPg0027N+Ht1W+jW7tu\nOPmAk31L12sUvcrLRLQMyWC3t4hoHwAx33InCILQzCmmcexeBFR7/wAsvQtW6aueidGj/4Qbbxyc\nsi+R4EAj6rfv2Y4Xl72IIa8PwVFTj0KniZ1w1eyr8PdP/571a6s4acG3BNAaQC0z1yvD5MqYeWMQ\nGXSDtOALG7F3cIitg8XK3l7HsRcLO3fuRMeOnRvvPxI5Clu3bkSbNm08p6naW23Rq276ROJLANmx\n8e6fduO9Ne9hfs18zF89H59t+AyMJj0qjZbi9J+fjiu7X4nBxw+2SMkdGa0HD+B/zHy8+g8z/0BE\n7yG5hKwgCIIgeGLq1McwdOgw1NfXK1tmob6+Hh07djZ0z2sxctXrx99XVFyPQYPKEY/H0bFjZyQS\n/uU9Vh/Dh2s/bBT0j9d9jPqG+sb9LcItcMoBp6B3t97o3a03Ttr/JLQIt/AvAw4wFXhlCNt+AEqJ\n6HgkI9gZQBsApcFkTxAEobhRg8eGDesBAM1mamF1UaT6+i8AzAJwGJIyswx1dcCwYT0waFB5oy20\ngq6dxU6tCGi3PfXUzEaPierSnzBhHIYP927jukQdFq5f2CjoH3z7AeKJpgpFiEI4ef+TGwX91C6n\nojSaW6m0mqr2WgDlSK4Bv1CzaxeAJ5n5haznziXioi9sxN7BIbYOluYUZOcUfddEOHwkQqGQYVeF\nflpao+A5rZt/4MCxmDp1cqMtta76CRPGY+jQm23z18ANWLxxcaOgv7vmXez+aXfKMcfse0yjoJ/x\n8zPQtmVbf4zjAk8uemZ+EsCTRHQFM8/OVuYEQRCE5iPsKumei+RCoVpPBoCUaWkBYPjwo9C0Dpk9\n2uWTAWDEiB4p89arMDOWbVnWKOjvrH4H2/ZsSznmsL0PaxT0s7uejY6lHT3ceXBYuegHMPM/AXQl\nolu1u5AcWP9g1nMnCIJQRDS3Vrodah850GQT9f/p02egrKxD2jh2IsL999+HUaOaKgJt2rRJqSxc\neOFMWxszM2p21CQFvWY+3l79NjbuTo0dP7DtgTi327no3a03zul2DvYr28+fGw8IKxf9Dcz8qLKO\nu/YgVeDHBJA/V4iLvrAReweH2DpYampq8Prr81y7iZsrevc90ZGIRJKjui+//Aq88MJsQzuqFaj1\n69enlO9GF31ZA67+81UIHQzMr5mPNbVrUq7baa9OyRZ612QrvVv7/H9GrFz0tsPkCgkR+CSF2koo\nVHsXImLrYFmxYgW6dz8GdXW3A7gPQB2qqiZhyBD3Il+oz7cbUgV+FoAxiEQiuP/++zB69J9thxSq\n5XvLj1vwzup3ML9mPt5a9Ra+2fZNynHtW7bHOd3OaRT0wzse7sr9nw946oMnooc1/zKSLffG/5l5\niE/5E3zEKLpUEITck2x83AdA7UvugRtuSO8LtqK5PN9q//zQoUcpQ+iWob4eGDVK2/8eT5uCdmd8\nJ95d8y7WfbsO096YhsWbFqfs36vFXjjzwDMbBf2YTscgRE7meytM7KLoVWEfA+BvaBJ5ZuYZQWTQ\nDc29BV/oE2YUmr0LGbF1sNTU1OCll15TxHkZAPfPZ6E/314wmgTngQfGYsSI0WhoqEeoJIQb7hmM\nvY4uxbvfvouF6xciwQmUH1iOGWtmoCRcgtN+flqjoJ+434mIhqM5vit/ySSKXk1gaD4KuiAIQqEw\ndOjNIEJGY7GbG9rguUSC0UANGDl5JPisBuDA49FwwCJM+2EK8GHy+EgogtMOOA1nHXgWrj37WvQ6\noBdaRlrm9iZyiKP14IXCoLlOmCEIhcKQITenrI7mhub4fCcaEuh56XH482EjMWbGXeAuJUCLPcre\nj5M+5vVHATWnIPztTGz8ZB32Lts76aHqKh4qR0F2RPQZMx8XQH4yorm76FX8DsIJKqinUO1diBSL\nrQsl4MypvZ3cj9UUrfrzCsU+Kg3cgC83f9k4Fn3B6gWojdemHrT5EKCmBqE1YTSsagBiXwNI7bIo\nlvLtBE+ryRHRbiLaRUS7APRQvyufnVnLrZAxfi6HWEyrXMXj8bS5qoXCpZjKJuD8fvTPt9l5hWAf\nZsbyrcvx6MJH0ff5vug0oROOfuRoDHtjGF76+iXUxmtxcPuD8fvjf49T1p0OTIgAU9egb5v++PHT\nnah6oNKn9eeLExkmZ0FzqgUaEXRQTzbt3Vyij51S6GW70ALO7Ozt9X7MzgOQt/b5tvbbxoll5tfM\nx3c7v0vZv3/Z/o2zxZ3T9Rwc2O7AtPvUrjhn5KUo9PLthkxXkxOEgkY/VaV+EQtBENzhxvW/afcm\nzF0+F++seQcLvl2AldtXpuzvWNoR53Q9p1HUD+1waNpY9FTPm/MV55o7IvCCKc0xqEcoDIqtbHq9\nH6vzvNrHTrztvGHb92zHgjULGqeA/fL7L1P2tylpg7O7nt04dO3IfY60HIuuXi+RYIRC3dHQ0ACz\nFeeEVMRFb4Hfbp5CC3hRKYYgO3HRp1IsLsxCeab8DLJzc57b9OyeE6MugQ1bv8Unmz5pFPRPN3wK\n1s5uXgdgzRnJSPe1VahdthWtW7W2vQ81ZkY7Dt5qxTktxVK+neApyE7wl0IIeDHDz6C9XFFRcT12\n7dqGXbu2NXtxLyaKoWxq8Xo/Zue5SU/blVVXtwTDht1iGJTKYQa6VgPnTEL9NTF0quyEi566COP/\nNx6LNixCCCHQmhBC70bxx72GITKxFfCvJ4EPbkBoQxiRkLHjWPuO7NfvGpSVdcDee3dSWuxJQqEQ\nJkwYZxhYJ0G06UgL3gK/aoGFFhCUK4KudRdK6y8bNKcWTj5QCPY2e0+FIiEsXL+wcejaezXvoQ51\njeeFKIQT9zsRvbv2xukHnI7Ljr8S9Xu+aExjwoRxGD58pOUiO6nXjgM4BuqMf6HQUQiHkw1U1aug\nf3b1noeLLjov7+3tFxJkJwg6xGUvNDfsKrTTp89AIsEAHYbQfiFcPOwSXD77cry75l3s/ml3yrFH\n73M0zj7wbPzy4F/izAPPRNuWbRuvQfWpWqNO7DN8+EiMGDES0WjUxfMWRygEbNmyIcUboZ8DQB9E\ne/75iw1Ta3aoa+0Wwyd5O/6xatUq39KaMuVRjkZLORot5SlTHvUt3WLCT3tbEYvFOBotZWAlAys5\nGi3lWCwWyLXzhaBs3ZyJxWKN5SrX9rZ6/zQ0NPDn333OoV5Rxm8vYIxsy7gTKZ/DHj6Mb3rlJv73\nl//mzbs3u7qW0+dNe17fvgM4FGrFQJTD4ZaW70yj9JcvX+7NUAWIonuGmigueguyEWQXj8eLrt/Q\nL4JyY0qXSWG4jAuZfHIZG5X3/1u7CB+s+wDzVycD4zbu3ph6Ui3hmtMH4LxDzsM5Xc/B/m32d31N\noClYzmysvnqM/jzA3Tj+fLJ30EiQXZ4wffoMdOzYOaNAu1wHkmT7+kHcnzq0SGbA8odcl8l8wyhY\nLZFI+H4NNzbnvRqAHv8FLhmBupv34IhHjsDglwfj6SVPY+Pujdi39b44saQnwq+2QGRKS0w+eBpm\nXD4Dvzv6d67FHUCaO13/vE2fPgNlZR2w117tUVU1xfA8N0gQrQlmTftC/CCPXfR+uIVz7ebP9vWf\ne+75QO9P60L147hCwq+ynesymY9k22XsxObf//A9//vLf/NNr9zEhz18WJrLvXRMKf/mmd/wwx89\nzF9u/pIbGhoa825W1jN9DtTzm+xzDwOlDES5qmqy6X1GIq24sjJ9vxW57hIJEli46HMuyn5+ilng\nc91vnO3rx2IxHjhwcN71i1dVTS5KAbMq29oXsdVvEESZyIcy4AW9CLt5l9iJrJHNa2O1/PLXL/Mt\nc27hY6Ydkyboe927F9PvQoxTRjM6vcSRFq0c27a2tpYnTqz07TmIxWIcibRSxN267Hh9/kTgReBt\n8buQZNLaEYEPnsrKyQxE8ypPfmFWttUyGgq14nC4pWVZzWaZKAbPgJcgO7v7brR59AvGQTM5dF6E\nT3rsJA6PCacIesndJdx7Rm++Z8E9fFvlSEa4xFNZ7tt3AAMRT+daVVScPFuZlC8ReBF4W7JRSDJp\nleT6pVdsLnor3LQyChGjst30Ql3q+L6zUSZyXZnNBk7eJVb3Ha+P83tr3uMx74zhQ+/9BeMvqS30\nyF0RPuiegzn0ywiHDynhysmTG9NsKsfWLnE9tbW1ighblwejd5qTcqFtnVdWThaB94gIvEfysZDk\n2m2ZzeuvWrUq5/en4rSfsFDxS+DV8/z25jQngU/vm17JoG84/PMSvvede/mCf17ApfeWpgg63Ul8\n3LTjePgbw/m1b17j72u/N7RZekV1KUciztzzTQK/UnkOommCbSTkdr+ftrzEYjFLN7zXCmQ+vruz\nhQi8R5pTIckH/LK3X4KTSZCPF4Ks3Pjhos8mufZW+Y2dvSPRVnx71d+4z/jfMvUPM0YhrR+9+5Tu\n/IdX/8AvLH2B129fnyaaelGtra3lWCzGU6Y86nhMuZ6kiz7KQJT79Olve820iopO4L2MkffyXDSn\nd7cIvEeaUyHJB+zs7eRB91sYghLdoAXNjyC7bJOL62fjmrFYLC2KvqGhgb9Y/wWHTooy+vyKMaJD\nmqAfXHUw//6l3/OsJbN4w64NjeealRX9RDF6IVUF3y21tbVcW1treF9Ohdzs+Nra2pRtkUgrw2vp\nr2t3H83p3S0C7xFtIcn1y645YPVQOhHAQnXt5iLfuX4B5uPzlI1KlprmwIGD+Z6HxvKTnz3J1/zn\nGj7gwQPSBB23Eff/d39+4rMnePX21YbpWbXU1f160fTaxeK1Qm1WQTQr5268Rk5/o1yX7yARgfeA\nttZdbO7CfMXsoXQqgIUa9d7cBD4fnye/fgOtqK3ZuobDR7dgXNyPy6cOTRP0juM68nFjT+DQyVGO\n7NuSJ09+xHU+Q6FWrvvAtTjxBtj9Rtp7tjvPyEXvtFLi5r5E4EXgTdHWuisrJxdkq9COXLWgrK6b\nicAXelBcPrnos0m+eln8yNf4hx/k8JEtOPTrCO93934pYl7+RDljFPiimRfx+PfG8+KNi/nHPT+a\ndoVYPSfa2JBwuKVpv7tXj5dXW9h5F7TH1dbWpkXRi8B7QwTeBdpCVF6+iCORVp4f/Hx0QzLnrgVl\nd91MXPSpD7/zSOF8Ih+C7LJNvgo8s/vnYld8F7++/HUeMXcEH//I8Yw7Ulvore5pxUfc251DZ0b5\nuqGD+Mq+V5v2kbvJhyqQ+lavvjVvV56yLfBG3gX1/pKR/aneNieT2oiLPh0ReBfoBd5pwdOTj25I\n5ty9YJ1cN9MgO6c2z9eKV7Ywul9x0RtjVTb21O3ht2ve5r/O/yufNv00jtwVSXW7/xWMa09inDWU\nwweVcO3u2sY0v/rqq5QKqFlXkt1zoredVWveSRk3e7d5/Y3s8tN0f8ZDMZ08mxJkl4oIvEu0Lnp9\n4IgT8rmVkq8Cr415yPQ6Vi+KfBaXbGB2v7l+ARZCJasuUccfrv2Q7333Xj53xrnc8p6WKYIeGhPi\nk/5+Eo+aN4r/MGkoU0lLNhuKtnz58owF3qrFbdWHre7X29tuGKjX38gqP6n3YDy23g9yXb6DRATe\nA5kITiYiGsSLL99c9EYVqmxcJ9cVr6BFzep+c/ECzMe4Dy2JhgR/tuEznvi/ifzrp37NZfeVpQXG\nHT3taB72+jB+adlLvGPPjsb07bqHVq1alTaMLRJpxZFIK8cuerete3Wb0Rh4p/3lmaDNT2XlZMP4\nAKMZ7PxABF4E3pZMConTIBe7BzRbuA3sydZ1jbpE7PoNvfQrWu0rtEqV0/xajSoI+gWYb5VK5uRY\n9KWbl/Lkjybz5c9ezh0eSB+L/ouHf8E3vnwjP/fFc7x592bDa7jpflJ/Oyf97E49UNpj9d/Nplt2\n2l+e6bMRiyVnqtNXMrL9zInAi8DbkmkhsSrEXmZ0yia5egG7EXg/xsKb9WFmct+ZVDrc4ibOIHlN\n41EFZlPVZqPM5VO30Fcbv+LHFz3O/Wf3504TOqUJ+s8n/Zyve/E6nvn5TF5bu9bxtdwEkGZqD+3v\nZNaHrrrJrdZTsOsv9+vZyMWaDiLwIvC2eC0kXl74bien8BO3Lxy/hcCJi95NHp22jvwQniAn4HGT\njp3bWF+2sxmgmKuyHYvFONK+JaPHg4xLrmQMozRB33f8vnzV81fx3xf9nVduW9m4LrrX65ndl58C\nr2LmodF3BVhNU2vWX+72N1Oj+rXPlvoRgc8uIvAe8VJIMnnh50MrOlPxzCQPVjEP2aiE2LnzMzlf\nj1+tITc2sLqmW8FRXa1u70HNg9u57b1WIrf8sIWf//J5rnilgg+ffHiaoLe7vx3/5pnf8MMfPcxf\nbv4yI0F3gnofXitUVukaCWeqMC9tnPrVrn9dH3Dnpqw1zVffgolKUn7rpgpGC9NKRjYQgReBt8Vt\nIYnFYimurlCoxHReZatAmiBd83b50ZJtV6udvbNRuTALTHLnBg/O8+G2pa220Mz6hJ3ch9m4ZTvR\n0KfrZJ5xN/fIzFwbq+VXvn6Fb51zKx/7yLFpgt763tZ8wcwLeOyCsbxo/SKuT9TbXt8tTvrLn3vu\necfnObmWWReMXdeMFfoKnJPfIX1JWe3wN+1ogaUcDrd09Pv7gQi8CLwtbguJk+UVtfgRwOKnwAbZ\nl2yE0zWz/a4AadP0s5WcLexsoHfRGuXPaYuyyR6p45bNgrL0+XRbXuzO+eGnH3jeynk8+s3RfPLf\nT+bwmHCKoJfcXcLnPHkO373gbv7g2w/4p/qfLK+XKU4j3gcOHOx75c5smJuXKZuthrXZuebNBf5O\n15VCvxCBF4G3xUsLPumOSm/t+F2o8zEqOVPy4aH0Kkq58LoYoe97dxNFb3Qfqend0+hmdTqpitvy\nktbqL2nFby1/i8e8M4bPeuIsbnF3ixRBD48J86nTT+W/vPUXnr9qPu+p2+PJZtr8O/097bp4/BB4\n1QPjRoDtyrD+HDMPjdP8GrnoQ6ESZVuTJ6FPn/6BvbPy4V0SFDkTeABdALwN4EsAXwAYomzvAGAe\ngG8AzAXQTnPOaADLASwDcL5m+wkAlij7qkyu56vhvPbBJ19+2RP4bLeknVw/G65oLxWqbNz3xImV\nOak8+UEmAm+GVqT79Onvuny7+Z3qE/U8snI0h86IMg0IcYs7UwWd7iQ+/tHjefgbw/m1b17jnbGd\nju/DKB+ZjKpw0rVh5aI3y5P2fDVALhQqcTVTnd2cE8Z97c4mntF7vLSVEO3/2nKo9skH5a4XgQ9G\n4DsBOFb5vheArwEcAWAcgJHK9j8BuF/53h3A5wCiALoCWAGAlH0fAzhJ+f4agAsNruer4TKJovcS\nkORHy8Ev3IqnenwmLXyvouOnCDe1RiLcp09/39J1SyaVFy8ueif5qa2tVQSntNFLlan9GxoaeMmm\nJVxVXcWXzrqU245tm9aP3n1Kd/7Dq3/gF5a+wFt/3OrpOmbjx/UxAm6fK6cjNlatWmXYctaLrVY4\n9UF0TrpFtNc08kzo++cnTpzkOE4iFoulVH6t5tPX26ZpMZl7GsuO04A7L8+CCHwOXPQAXgTwS6V1\nvi83VQKWcVPr/U+a4+cA6AWgM4CvNNv7AXjEIH1fDZdJIVFfiE4LplvByqar3GtevM6HreLU3tmq\n4KTGUKxkIBpYUJAWv8fmG70g3ZRtbass1T4R3rzZePIXMxoaGnj51uX86MJHue+/+/LPxv0sTdAP\nqjqIB/93MD/9f0/zhl0bXKVvln8z93amAq+mb3fcc889n/Kbpotti5RRBkYCr+/DduKR0B5nlqYq\n2mZT1qrpEmk9N6kBdGaLO2nzmIwNiFjek9F1vTwLIvABC7zSIl8DoAzAds12Uv8H8DCAqzX7Hgdw\nheKen6fZfgaAlw2u4avhvBaSTPsdnQa4ZMNF7VY8nbqEnVCsAu/mdwqq+0Vva7M86lth2gpcONzS\nUd6+3fEtP/nZk1z+n3Lu8mCXNEHfb+J+/LsXfsf/+PQfXLO9Ju38TMu5lU29uOi9eLcGDhycJmpN\nYmu88MqUKY8yoIpqsg/bLN+p97mUgaUcjaYvlKUPwFO9AkQtTYcxNlUMtJUD9Vk3j9Y38iC48Upk\n8iyIwCc/EQQAEe0FYDaAocy8i4ga9zEzExH7cZ2ePXti6NChjf/36tULvXr18pzejh07UFNT4+qc\nRCKBRYs+Qf/+7wEAFi2ahhUreiMcDlueM2BAfyQSOwAA4XB/vPjifzF37jwAwIUXXogTTzze8vzk\neebXcJN/fV7Wrl1rmrb+eKJyhEJjlXzPxPr16x1f287e2vt86qmZmDPH/XWMbKXdNn78A/jii3sB\nAEcd9QC2bt2KrVu3Or4HPQsXfoo5c+Yo+bT+HdW8uLG/0T04QWtrszzqy/L//d80PPXUDMydq9r9\nX4Z2/6HuB6zevho1O2pQs6MG2/Zsa9zXu31vlO5Tiq7tuqJbu27o1q4b9i7du3E/b2fUbG8qA27t\nZ4ZZebnoovNw/vmLATTZTvu/vjxa5cfsN0gkEjj66B4oL2/6TTdv3ox//vNJzJnzBoDdAPoDaNpf\nU1OD3r3PxMCBv0MicT2SYUzvoaLiDzjvvPMM3zEAcPXV/cH8IACA6CosXvx5ynGjR/8JnTr9C3Pn\njkWyTdQfDQ03AHgMwE0p6an38dFHn+Dqq/sBCCPZthoLoAFHHHEfvvrqKwDJ9BcvnoYVK1YgHA4b\n2mnhwk/xu99dDeYGAPeCiEDUHw0NFYbX9fosAN7e3YVCdXU1qqurnR1spvx+fZDsT38DwDDNtmUA\nOinfO6PJRT8KwCjNcXMAnIykG1/ror8KeeqidxvBqqKtaTf1V+Vm4plMuwvM7tGu5eN2PXi3LSmn\nY97VgCEzsh0rEUR3jWpru1XInHiWtu/Zzi9+9SIPeW0IHzX1qLQWepuxbfj/Pf3/eNKHk/iTbz/h\nH/f8aGgrvW389mYE6QnQo3fRq6jPvX5ymNQuL+0QtKWmXQmxWPo8HFa/bdNvb+xBSL3npr7zUKjE\ncDIctf/eyE5GQXebN2+2zF8mMT3Sgg/ARY+k+30mgEm67eOg9LUroq4PsmsBoBuAlWgKsvtIEXtC\nngfZ2UWwmm13O4tUNt25XtyQVsc7eVDN7O3Hfdq/dPwJqtKSyRSt2a5EqKub2Q2PMrrf3fHdPGf5\nHB45dySf+NiJHBoTShH0Vve04vNmnsdj3xvLH333Edcl6kzTstqu7/4x6+fNJvpYBjNhtasIGQXZ\n6a+RKrpNLuzkb9RCEeFkZcAoiNcoH3bBvqrttRUM7Qpv+t9AH/1udr7TZ81JpdtLxUwEPhiBPx1A\ngyLanymfC5EcJvcmjIfJ3Y5k9PwyABdotqvD5FYAeMjker4aLtMgO33L3enLoba2lvv06c9q31vf\nvsv35ooAACAASURBVANMr5EtgfcTp/nMd4F3kw/1JWXVt+kHXm2Tuj659fCo2t21PPebufy3+X/j\n0/9xOkfuiqQIevSuKJ/xjzP4jrfv4AWrF3Csznll1C7/2qFibqc5tRIGJ6JhJDRehTWT+JLNmzen\nxT5UVU02XG7WradLrVSoxxjdn12l1ug5cpOOk0qUW0TgAxD4oD/ZFHi7F4KT/U5ecE01dnV2qKWO\nhCRbAuIHXgVea1M/7tOpiz7T+0h1a5YyEOGJEyd5yrMTvNgmVeBTh0fVJer4w7Uf8pj5Y/icJ87h\nlve0TBuLjt8T45chDh0a5QcnP2R7PTfuXCcV40xs4jSQTv9cqucYrWFuPCSsKc9fffWVY6HSi6OR\n7exs5sVGVra2qyTYeTCc5k0E3j0i8B5RC4ndC8HpC9aJiz61z83/iUSygZfWkBHah9JLS8SpS9vt\nS8ftfcRiwa+g5fa+VBd9NFrKkWgrHlX1F574v4n866d+zWX3laX1ox897Wge+vpQfn7J8xxu3dLT\nvRm5c+0i17288O2Eyl0lzf2QMCM3+8CBgx1VwPTddfrtZhUI/z1a7rpE/Bza6UdaIvAi8Lao/WZ+\ntDC0NVqz/akPmLNZpTLBj4qB2xaw1fXUh9LtSz1oL4YTMfUyH7ifWNmkoaGBP/7iY57y8RT+zazf\ncIf7O6QJOv5IjF/3Z3R/mCNtW6UIZCaVFzMRsSobenELQuC1122qeNsv4KKvxKjnlpcvsr2emZdD\nu98vj5ZVn7jTLhH9b5bJ+8SPfnctIvAi8Lb4JfBuHka3LzOv+FXj9sOdpuJF4P3OgxlOBcgoQjqo\nioeKkU2WbVzG0z+dzlfPvpo7T+jM5U+Upwh6lwe78LUvXsszP5/JKzavsLSpmQg48bCkd184W+0s\nFnM3O2SmLnrtdWtra3nixEm2FTYjgVYjxcvLP7btbks9P3uLVZl5UozuwSy/flaqs/EMi8CLwNvi\nh4veSeG1qglnw/1u11Lwmo5fAs+cvSVbveD191XFIejuk1gsxpH2rRg9JjEu+S1jKKW10CuequB+\nz/fjxxY+xl9u+JL37EldpMXO/uq9qffnRlCdiKXR9dy6j/3o0klvxTsXePWYvn0HcHn5QLYKmNVe\nz8vSvE5x4iVw8r7y85kTgc8MEXiP+BFkZ1d4vbQ0MhV9ty0FK/ysyTudXc1pHvyoHHn14ATdbbBu\n+zqe9fksrnilgg+ffHiaoLe7vx1f9sxl/FD1Q/zFpi8cVV7t7OdE/PTCTNTS08plXlv+Ruk4LRP6\n39bJXPD6PnQ1DScuehWjPvwgW8tOKndWldpMvAp+PS8i8CLwtvhVSIz6l6yWgGQ2b7H49SCYtRS8\nPJx+eRwyWdxH38Jx4s51klcvL8QgvAq1sVp+5etX+NY5t/IB93Rh3JEq6K3vbc0XzLyAxy4YywvX\nLeT6RH3K+U66n6zQl0+zctR03J3cNO2qt4plpnENbp8dI/s4aUkbTVrlRuC1ec10fQertDN5NtR7\n1AYDZvpu8tNbKQIvAm+Ln4VELbza/kuzJSBVwdK3WPQrP2X6sGcyEYsRmT7gXpfn1V/TiRB4iYuw\nWoxDX8nxW+B//OlHfnPlm3z7m7dzr8d7cXhMOLWV/pcWjPJeHDo7ym+veJt/qv/JMj1/Bd66ldk0\np0Pq6BCjriE7t7rXlqOXe43FrPv9ja5pdJ2qqsmOo+j1afn9jFrl3Snq86Cd48GPyH4/EYEXgbfF\n70ISi2kjkJNj3PUvRq3wNL0YnY1/9YITd5zeJW3UivFD1NxMBqJ+jFpYdlHeXvLqNmAu06jgeH2c\n31/zPt/1zl189pNnc4u7U9dFD48J8ymPn8J/mvsnDh9Swoh8aXsv2jw4jS9xc4+1tbW8efPmNFun\n/h7mLXcneTE6xmmL1M1vbhfsavb7mpVJN+PgndyzU8wqIW4qcsbPTnplTQQ+N4jAe8SPQqIVxKaX\nnfrCS0ayavdrH5LUhybpps9GZLbZA69/sVgNoTHKu9vAPSf2tqoAqS9TvedD21frpVXktfVnFoCm\nFQM1nfpEPX+y7hMe9/44vvBfF3Lre1unTS5z3CPH8W1v3MavfvMq74ztNLSJU2F0E19id596z5Q+\nsj7194jwAw+MNxQdpyvVefWW+BW4aee90F5HnVd+4MDBGT2vXn4jr5Uhq/PNBF71VPj9bvKKCLwI\nvC2ZFhKjl57efax9kZm599R1mNU09C+4bNSUjQTbrmVsNfzGCXb2Nu73TRdyM5e60YvXSR4zbf0Z\niQGFWnKoUwsOnRLlo+87htvd3y4tMO6IyUfwza/ezLOXzuYtP2yxzaMb1/by5ct9KzvprXTjcdVA\niWm5cLNUbybdIU7u2Z3AG8cf6CuS5eWLAm3VmnkSnNrKygZWz3m23kduEYEXgbcl07nojV56Vg+Z\nkwqB0YPmVKTcPHheBJ45s359I3ubv8z/orFL+rApc9eit6FHTm2tv/8mL8wKRofXGSeEGX0uYgxH\nmqAfVHUQn3r/6Rw+pgVH2rfyrRWkF6RIpBU/88yzvrW2nJX1z03LsZpGsuw3ebaceJXMtjnNt9fW\nvjbIzMkIAjuB91sYsynw2vzmi6DrEYEXgbclGwJv5LJVj9e/hK36k90IltcXoBsXvfa+MxV4rdvX\n6GWuejTcDJly+sLSn2N3jJa0kQlt3ufw8S34pPtOZtySPhYdt+3D+M1lHD6hBS/buCwj29mhD+68\n7rpBppWjTNPXeprsWroqsVjMdAEVFbtRJ/ryn4mAW52v9RBNmDDJ0jWtHmvlovd7iJhVupm66AsF\nEXgReFuy4aJXcdrCTG5LFzK7fkCrdN225PX5tGv5en0xpMyPbtIySq84ORcos3y5eRGavfRjsRhH\n2rZiHPkQ4+ITGH9Mb6Hv/cDefNx9x3Po5CjTz0o4FC6xqOR5dzebVVa0YpuceCWzMeVG19WXDatu\nEaOKnNnsjWmVJ12l1qgyalYGM3kmUs9tChi0mnUyFovx8uXLHaTnf3Cak4qr2/MLARF4EXhb/A6y\ns8NKaIyGaNmJoXp9vcvYy6x1bvHyYvjqq69MW3zpq495Eyd3FStjz4v6W2zfs51f/OpFHvLaED5q\nylFpgl5yZwlf/PTF/OD/HuTPN3zOiYZESh6MbOS0cuSmsmJ0n9deO8iyRe0n+m4WvS3dzRCXFNVI\npBX36dPfMA0nq61lLvDuFoTK5lLIuSKfxV8EXgTelmwMk7N7INzWuNUKhNVLItPgt0xw+hKYMuVR\nvu66wSmio3olzFYfsxqX7iZ/TgS+traWI6WtGAeXM34ZYfyeksumatdFvzPKGECM04cz9p/NkRbe\nXN92NjMTBTux0Ir/rFnPOhIWLy9xd/m3dt0b3W/6bHipq72pZcWswmvU4ndzn2pXgpsKktW7pG/f\nAUpa9lPZ5gv57r4XgReBt8XPQpKNB0L7UrJLP1sTZljhdlhScravphZaZeVkw3zb9dX6kc+qqskc\nadmKwweX8EXjfs2nPn4q4686t/tfwac9fhrf8fYdvGD1Aq7dnbmN7Spz6UKeuiKbnbCpH213iNnv\n46XMOu3bdtK9ZJSu2ZLKoVCrlNEmRqMkzETdS7+01oOg72Yx+v3M3iVN5Ts5L0YhtOALwesgAi8C\nb4tfhSQbD4RZoJ7eFWnmqs/2Q2l3PaO8qdN5ErVM6ZPVdzGYtV4zuZ9YLMa7f9zN1Wur+ZLxlzFd\nE2L8GWlj0fF7YvzyBsbBT3KkND1yP5OxwFZC4zTg0Uk8gbZP2MxuXsqLm3OM8mTXlZXurWrqAzeb\nE8Gu/LvJs5m3R1/JNvIsGb1LzOIKtHl2M9IjCJe5E49hPiACLwJvS74KvJP0/BxO5HcezfI2cOBg\nwz5Zo7m9rfY7tW2iIcGfb/icH/zfg3zx0xdz2X1l6ZHuNxH/4ZU/8H+X/Ze379luKuBOAsW82stp\nN4K+tW50rtpatpt4RX+ek9gNt+e48UBp0ds6k9kLMxX4dDsbx4YYLaRkVFHRPg9O12V3az+vWAVM\n5hsi8CLwtngpJGa1aD8fQCetYycv/0zux8l5RmJolbfly5ebCpeZGKQKvvUCJnv27OHF6xbzlI+n\n8BXPXsF7P7B3mqAfXHkwhy6JJKPhW39k+MI38pS4EQmzFrPZTG7+CXzTWPTy8o9tRx94id1Qz9HO\nU25XkfDSIlQXa1K/W4mrPm9WlTOvQhqLmQ+LZbYT+NTKkF1aRjbMdovaznuRb4jAi8Db4raQ2L0o\n/HAjO2nxuH3g/a6UWLVmrfLmZn50regn0zOOaq7ZXsPTP53OJ9zXk3GbwVj0W4jpN2HuObgXRzq0\n9NQ6cWpvu9/MaqIXpx4Zs23JtCOszh9QXj7YUAj1ZcGL+Dpd791NJL2ZHdXfSq2E2AVeasuNvlxm\n6gq3mpTKzEXvpbLg5rp+EUQlwk9E4EXgbdFPvKLHyhXq9wNg1+eu/+60L9jpsCqn92PlCrWrnHid\nHz2lL3OvDxk9JjFdFuauk7qmC/rwvZmuDHPle5Uc2aclAys4uZSpef+t0zzYVe6sWkCpFZWlhnYz\nsol2m5X3o2l78l61y5eajSU3y7fVsxCLxTQTETmPjNcH2lk9c03nGQ+l9PJbZVr5VjF77qyGyZlV\nfpy46Jvs4e+cBkbke+S8FhF4EXhbjCKN1QfSaLufAu+m8mDWN2bXF2yVrp8Cb+aq16enzo/uhnXb\n1/Ezi5/hG1+6kfe9q1OaoLcb246pX4hxUpTxs9cZWNEoak2C6ry1ZHbPRq1CK7sYRY7rPR9uAvas\nAraMRFEVeDUfVq1oN9H2EyaorXftMseVtvawq2gYn2c/xM7Jdf1eJMWoHHjt7nMSeKi1hx+zEtrl\nKZ9b7ioi8CLwtixfvtzwpWz2MvSrhuum8pDaanP3wrNrbWfqolen8nRSUVCD7OyutTO2k1/95lW+\n7Y3buMs9XRh3pAp663tb8/kzz+dx74/jhesW8g8//mDawkkVRevV58zs6HWIldXERG7HWaf+jsZx\nCPpKYHpAo/1UsvYt6pVpaRK1MG1Ve/UYZBLsZZRfPyvmZmRTcAqpZR0UIvAi8LakCnzqZBpWQ1sy\nbbkbvXDM+lZThSDd1WwlCkbpmnksnORbe5yTxTj096x1G6vH/PjTj/zmyjf59jdv516P9+LwmHBq\nK/0vLRjlJzOdFeFwtxKOlLRKEzbtHOz6/lltd4bR6nNG86tn4uVQKwz2nhPnM6UZiZaRqGrzbhTQ\naORVsPv9rVrEToLz9Om77RJgTg24c4J5kKb/cxeoZFtwvLx3CqU17gUReBF4W6zmRnf6MnT7ENm5\nzY3F5R7WBlCp625PnDjJ8BpmIu7VLW/ncbCbyCRF4EPLONythP/21t/47CfP5hZ3t0gR9PCYMPd6\nvBePfGMkhw8tYUS+NK1wOXFfmrnXY7H0QCft+PxMu2W05UpbqTBqjTsJHDOrpJhhFtCotYXedW1W\nlo0qn5mMlbYK0jS7b7vWq/7ZMRq/7qUF7PRcP4fc+iHKxd7qF4EXgbfFbnUz7cPmNKLZCU6jyLUv\n0NTpOe80dNManWfcesysT9NsqlejtOoT9bxw3UK+bPzlfO2D1zJuT59c5thpx/Kw14bxq9+8yrWx\nppaancvb7n7s+npTBd7YO5JJwJaTMfVGs6Wp16itrU1Jw+xYI6wCGo36851U0ry0xM2wE2+rmAM9\nTlz6XlvATu/RD8HxS5Qz/W0KARF4EXhbjIK+zFrpTkTO7QvOi3vd7qVn5c61itw1u2+7hVn0L6OG\nhgb+YtMX/FD1Q3zZM5dxu/vbNYp5+RPljDvBR0w+gm9+9WaevXQ2P/DwREfCYna9TEYJNNkjonzs\nPStOX8J217ezbeqwN/fxF86mTvUezObUFmbl3FlFNL0bw2jJWK0Xx8/hZJkIvJ+evWzmu1ARgReB\nt0QN+nLiHjVrsfrxEOldyHrXrv5F4eS6ahraPtLUvshUd7add8KqVbRnzx5evnU5P7bwMe73fD/e\nZ/w+aZHu3Sq78aD/DuKXql/i9TvXp5zvxoZWYqHf7vT3icVivHnzZuVYbWT4JEcVPatKmp2Xw+yY\nJs+CdxF2NnVqUxeBm3Hq+vs0O9asm8Ls3o09TU1BhUblMBaLmQYS+rGyohcXvZeWuN+iLC764kEE\n3iXqw1RePoO1/dlGrkwrkXPzEBm9CPVC3PSidTdjlxOBs5rj3UnlRQ10isVivLZ2Lc/4fAaX/6ec\nuzzYJU3QO0/ozFfPvpqnfzqdV21rehDtZvuyEmE3LzurIDCztLRiZOU2d/MSdlJJMvotU7sOrAXO\nDKdTp6qVSL8Foel65mXZ6pr6fnqrOQC0EwgBLU1/ey/3oP1Yoe3u8yrU2fgNiq3lriICLwJvivoS\nTc72pb6AWqS8EJy0wNS07B4i6yldta20z9nKVWx0XTcuavt8JCdg0c9UFmnbiq8dPzA5xesf02eL\n63B/B77i2St4ysdT+Kvvv+KGhgZDO7iZ7cvJfiPb62f90ndRWF3Lym3uNL9GaTZ5CJwNUdN3pWgD\n0Zy+tPXdT1Z2MctHJqRXVMy7Kay8IMateqMV9prK79q1a00rA27F1m1QY6Yt8WIWZT8RgReBt6Sy\ncjKXl19n4ApNvvzMXhJermMdAa5eu6ml4218tPE4d/2yq0YvEO161X369OfIXq0Y/7+9cw+Sqrrz\n+PfXj3lAKBEnUdStcoyJxgTXCCbjJtb6WNkhuq4PLBXXYh0MpRON+F50NRrjGokGNIpAOQZ8RGTR\nbEpLUWFXkmjQgPIQBQeZRFR0VBRnF2cY6N/+0d3M7dv32X3v7e7b30/V1HTfvn3Oub97+3zP+Z3f\nOefQ8xTtKcXFKBJ0TIf+4KEf6Jm/OEtTBzRpKu1tW1e/q305VZZ2wW92ouLHW2AlJF7Ka4WfYDFz\nHqWuBZ4ffipurDoPQQTN0LNfvFWqU8PUyeXvtsPe2Wefb2lvP4vdePE+mDHOWvCziUylqPWGBAWe\nAu/Kb37zqKECMrovGxRIq0ij5w017MTCqReTr5jMS3+ap2s55evUS3dz6eZFJDWsWfHV+dltUn8o\nihsLBb3plqbs9qrfv0pxwOOaamguWoDHywpbfn+UTg0Y5+PFFbOfnlVQlbSdW9xvNH4peZqXqjXe\nK6/PVxAMbfOa1rPPPr+gjOZnx4uHxe6+54eQ7IYh/DTWvXgfzGzevNlT47AaiMP4PAWeAu/K5s2b\nC8ZrE4lGNbvIk8km7e3ttU3DzYXs1hOwcwt77b2ZxyqNFYy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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -212,26 +252,50 @@ } ], "source": [ - "# create and plot models\n", - "fp1, res1, rank1, sv1, rcond1 = sp.polyfit(x, y, 1, full=True)\n", - "print(\"Model parameters of fp1: %s\" % fp1)\n", - "print(\"Error of the model of fp1:\", res1)\n", - "f1 = sp.poly1d(fp1)\n", - "\n", + "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) fit polynomial function" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model parameters of fp2: [ 1.05322215e-02 -5.26545650e+00 1.97476082e+03]\n", + "('Error of the model of fp2:', array([ 1.79983508e+08]))\n" + ] + } + ], + "source": [ + "# Let's now fit a more complex model, a polynomial of degree 2\n", "fp2, res2, rank2, sv2, rcond2 = sp.polyfit(x, y, 2, full=True)\n", "print(\"Model parameters of fp2: %s\" % fp2)\n", "print(\"Error of the model of fp2:\", res2)\n", - "f2 = sp.poly1d(fp2)\n", - "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", - "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", - "f100 = sp.poly1d(sp.polyfit(x, y, 100))\n", - "\n", - "plot_models(x, y, [f1], os.path.join(CHART_DIR, \"1400_01_02.png\"))" + "f2 = sp.poly1d(fp2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**$f(x) = 0.0105322215 * x**2 - 5.26545650 * x + 1974.76082$**" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -240,7 +304,7 @@ "data": { "image/png": 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tgY/lXQhfXyiyP9Lb5mVQG3PR18cEPgWiBd7rgxdNIboh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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -253,7 +317,32 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + } + ], + "source": [ + "# Let's try it for degrees 3, 10, and 100\n", + "f3 = sp.poly1d(sp.polyfit(x, y, 3))\n", + "\n", + "f10 = sp.poly1d(sp.polyfit(x, y, 10))\n", + "\n", + "f100 = sp.poly1d(sp.polyfit(x, y, 100))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, "metadata": { "collapsed": false }, @@ -262,7 +351,7 @@ "data": { "image/png": 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zzoh41stkNXjVyC1V1K5dO7Zt21Zs3aZNm4qa6Js1a1asd3z4Mnfu3HLTLuue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lAXwAHf97sB1NNcdx6Af3zfnxf0/W6jgq+99lr06tVL/X/Lli3RsmXLqBsoFAhoIDRA46qN0feK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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -274,13 +363,36 @@ " x, y, [f1, f2, f3, f10, f100], os.path.join(CHART_DIR, \"1400_01_04.png\"))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Stepping back to go forward – another look at our data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, we step back and take another look at the data. It seems that there is an inflection\n", + "point between weeks 3 and 4. So let's separate the data and train two lines using\n", + "week 3.5 as a separation point:" + ] + }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error inflection=132950348.197616\n" + ] + }, { "name": "stderr", "output_type": "stream", @@ -291,12 +403,36 @@ "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" ] - }, + } + ], + "source": [ + "# fit and plot a model using the knowledge about inflection point\n", + "inflection = 3.5 * 7 * 24 # calculate the inflection point in hours\n", + "xa = x[:inflection] # data before the inflection point\n", + "ya = y[:inflection]\n", + "xb = x[inflection:] # data after\n", + "yb = y[inflection:]\n", + "\n", + "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", + "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", + "\n", + "fa_error = error(fa, xa, ya)\n", + "fb_error = error(fb, xb, yb)\n", + "print(\"Error inflection=%f\" % (fa_error + fb_error))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ { "data": { "image/png": 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rZKjaKIhbzVvE3t4htvYWsbe3OLG31bC1zAxtrLVobvxUk3IXvSAIgiCkG/p+\n8EuXLq8T7FAohBMnTtTt17Jly7pafiDQHbNnz0oLcY+FCLwgCILQaNBGo7MapMZq8JsxY0ajsHAW\niAh33z0pI9rhReAFQRCERoFevBcuXBKxrbY2jN27d1uOTBcKhTBx4qS0HbXOjKgCT0QBInrGq8wI\ngiAIQjIw1tjvvnsSCgtn1bndmzfPQc+ePeuGps0Gogo8M9cA6EJE6d/YIAiCIAgOuP32UaisPICp\nU+9FRUUFzjzzTBQXF9dF1BcXF9W1tRuj7fXb0hU7Y9GXA/iQiP4G4Ji6jpn50eRlSxAEQRDcQxPo\ngoIeABAh0N27d8fZZ5+Nhx9+GP3798eoUcPrjtEzZsxojBw5zHRbOmJH4Leoiw9ACyjDxWZP3zpB\nEAShUWAl0Ndddx2uvfbaukliool3Jgi7RkyBZ+YHPMiHIAgZiBZklEkfPaFxY/WsBgKKHGbTMx0z\nip6I3jVZ3vEic4IgpC9W3YkEIVOx80xrXewyATvd5O7WLfdBmfGtLJmZEgQhvbHqQywImcJ3332H\nnTt31v1v55nOtEJtTIFn5jW65UNmHg/gZ8nPmiAIgiAkh3//+9/48Y9/jKefftp0OzNH9IGvqKjI\nuEKtHRd9G93SjogGAGjpQd4EQUhTMrHLkCBohEIhXHvttfjiiy/Qr18/AJHPtM/XHcyMdu06YvDg\nW5CX1wZt23ZAbW1m9ZG346L/FIpLvgzAfwDcBWBkMjMlCEL6M2bMaFRWHkBl5QGMGTM61dkRBFvo\n3ewvv/wqTjvttLptY8aMxr59u+H3E8LhL1FdvQbPP/8cqqvXo6amDLW1yKhCrZ0o+tM9yIcgCBlI\nun/ghMaNMSJe384OAAUFPTBy5DAbz/EKANPBHMbMmTMwduwfM+LZt+Oib0JE+US0ioheJKI7iSjo\nReYEQRAEIR6sAuKiTSm+YMFitGvXEeEww+8/Dz5fbyhDv0wFsB7ARkye/D/Jzrpr2HHRPw6gF4D5\n6u/e6l9BEARBSDvC4bBpQNy6devQpk0e/P5zG7jZ9bX72tovAAB+P0HpOGZnTLj0w06u+zDzj3X/\nv01EnycrQ4IgCILgJlpE/L333ou9e/di4sSJmDZtWlQ3OxGpv3IA/A+AcxAMBjOi7V3DjsDXENGZ\nzLwZAIjoDAA1yc2WIAiCIMRPYeEsTJzYA+Ewg5nRtm17BIM+tGzZElOmTEFOTk5EG33DseqLAaDu\n/9mzi3DyLdFxAAAgAElEQVTHHaMyRtwBewJ/N4B3iKhc/f90ALcmLUeCIAiCECcLFixGWdkneOqp\nZzFjxsOYMuV/UF39hbq1O15+eSXatFHa5QsKxgNQJp4ZM2a06Vj1mTS5jBGKFnBQtxNRUwBnQ5lk\n5r/MnJa9+4mI7VyPXcrLy9G1a1fX0hOiI/b2DrG1t4i9vSEUCiEvrw2GDPkAy5e3QiDQHURUFzUf\nDPZAZeUBAEBeXpsG6zNSxInAzGS2zU6QHaAE2XUHcAGAQUR0i1uZEwRBEAQ3MI4sR0QoLJxlu+96\nJo0zbwc73eSeBlAI4FIAFwLooy6CIAiCkBbou7j5fAvqBH3cuLGorDyAfft2R7jbjSMxLl26PKPG\nmbdDTBc9EX0FoJurvu8kIS76zEbs7R1ia28ReycXzTWvudxvvXUGiovnoEWLFrjqqqtw8skdsGrV\nyyCiuvZ27TgNo8t+377ddcF36UyiLvovAHR0N0uCIAiCkFx8Ph8efPBBrFz5PGpq1kb0iY8273s4\nrIxDn+m1eUuBJ6JXiehVAO0AbCCiN7R1RPQ377IoCIIgCNYYJ4oBFIFesGAxLrzwQgQCOQDqB2Bd\ntGhJhDtef7wSmMd1g+Tk5xegoqIiZdeWCJYueiK6XP+vYTMz83tJy1WciIs+sxF7e4fY2lvE3tGJ\nVpt2cnwoFEK7dh3roui16PilS5fXdYmbPXsW7r57kqk7Xp+Gsn0FgKl1A9yk46RK8bro74ESPf8d\nM//TsKSduAuCIAiZh9WY8fEc/8QTT5nuo5/58I47RkVs07vjly5djpYtW6K4uAiBQHcoY9BvzJj5\n341Eq8F3BDAAQH8ofeA/AvA6gLeY+ahnOXSA1OAzG7G3d4itvUXsbY4xOM5pf/SKigpdbVs5vrBw\nFj777FM8+eQzmDNnDvLzxzY4ThvkhlkZ5S4c/rLB+c3STse+8nHV4Jl5NzM/wcyDoXSPe1L9+wYR\nvU1Ek5KTXUEQBCGdSMf+4QsWLEbbth1QXV0dsf6mm26E3+9DOBzCxIkTTb0CWo1+//498PnMZVCr\nyWfS/O9GbA10w8xhZv43M9/HzJcCGAxgZ3KzJgiCIKSaRF3o0TDrj25HRLWZ32pqvgBwP5SJYJTj\ni4qKVNG/GDU1X1q61nNycmKKuN61n47t77Gw0w9+NoBpAI4BWA3gfADjmdm8sSOFiIs+sxF7e4fY\n2lsy1d6JutCdnAewH2RnzFcg0B379+9By5YtUVZWhnnz5mPZsl8CuMBWnhMN8kslifaDv5qZDwP4\nFYBtAM6AMgGNIAiCICSM0wFljDX/kpJi5OTkYO7c+bj44n4A/PD7/2DbK5AJA9rEgx2B12ac+xWA\nF1WxT/tR7QRBEITEiNeF7gV69zkAtGjRGvn541FdvR7MfwQRYd++3RnpWncLO9PFvkpEGwFUAfgj\nEf1A/S0IgiBkOWZTqKYL2pzuSnt8GZQ4cAUiSrv8eo0dgX8AwGwAh5m5hoiOArg+qbkSBEEQ0oZ0\nF0rmWgAfA5gC4Bz4/cNszRwHpP+1JYIdF/2/mXk/M9cAgNoH/rXkZksQhERJx65NguA2OTk5yM8f\nB+BW+HwPori4CFOm/Dmqaz6ZPQPSiWhj0Xckot4AcomoFxH1Vv/+DECuZzkUBMExjeUDJggAUFj4\nCI4cqcSePTuRnz8Wfr8fgHkhV3Ppa2PNZ+IIdXaJVoPvD2Ue+E4A5qi/5wCYAGUYW0EQ0pDG9AET\nBI3mzZvj5JNPrvtfCrnRR7Jbxsw/BzCcmX+uW65j5pdiJUxETYnoIyL6jIi+IKIH1PVtiOhNIvpa\nnaGule6YKUS0iYg2EtHVuvW9iWi9uq0ksUsWBEHIPqRJpp5wOGxZyE3nngFuE81FP1T9eToRTdAt\ndxHRhFgJM3MVgJ8zc08APQEMIKKLAEwG8CYz/wjA2+r/IKJuAAYB6AZlDPwFRKR13n8cwEhmPgvA\nWUQ0IK6rFYRGQGP6gAkK2VhbjVVgYWZ8++23cRVqMn2EOrtEc9Fr7ex5FktMmPmY+rMJlMl4GcB1\nAJar65cDuEH9fT2AFcxczczbAGwGcJE66U0eM3+s7vek7hhBEExoLB8wIf4mmXSu8UcrsGj5zs+f\ngM6dOyM3Nw8lJfMjrsXv90fM7z579qwGhdxsHdwmAm02nWQsUAoQnwGoBDBDXXdQt520/wE8BuD3\num1LANwIoDeUGr+2/jIAr1qcj91k69atrqYnREfs7R1ia29Jpr2rqqo4GMxlYAsDWzgYzOWqqqqo\nx8yfv4iDwVwOBnN5/vxFrucn1vljHW91PVq+/f6mDBADYOAqBoJ111JVVcWbNm1iZuaSknlJu850\nQdU9Uw2O5qJ/TLfMNf5vs/BQy4qL/lQotfHuhu3qDRIEQRDiwWmTTDKDMN1oKli4cEmDGeKAyHyH\nw2+ra9sC+BDanO133lmAvLw2mDHjEZSUzMfEiZMadbBptIFuyqCIL0GZ9f5/1d+AQ1Fm5sNE9C6U\nyPzviKgDM+9R3e971d12AuisO+xUAN+q6081rDedya5Pnz7Iz8+v+79v377o27evk6xGcOjQIZSX\nl8d9vOAMsbd3iK29Jdn2vuaaq3D11esAKO7paOcKh8MYOnQIwuFD6v5DsGPHjrquZfESDodRVvYJ\nhgz5AABQVvY4Nm++wlG64XAYn3/+GYYNWwJgBoBaXHPNE9i1a5ch301BNAJEQG0tAzgEIAzgZgBj\n0aNHFdateyIp15lqSktLUVpaam9nq6o9R7q+19rZz3BMOwCt1N/NALwP4FoAswD8WV0/GcBM9Xc3\nKO78JgC6AtiC+tnuPgJwEZQCxmsABlic01XXh7gxvUXs7R1ia29JN3snw0UfT1NB9DQ2cCDQLCIN\nY76rqqrq3PCBQDPVdb+Fhw0r42AwlwcOHMJAkIEgDxo01JXrTDcQxUWfTIHvAeBTAOsArAdwr7q+\nDYC3AHwN4A2tEKBuuwdKcN1GAP1163uraWwGMDfKOV01XLq9lNmO2Ns7xNbeYsfeibZdOyUZ50uk\n4KDlJ1YaZvk2HjtixCguLp6nFhY2MLCBg8FcPnz4sKc29oKUCHwqFhH4zEbs7R1ia2+JZe9kBr15\nTTwFB7OauVkax44ds3X+TZs2NfAo+HzNssbGeqIJvOYCbwARHUF9W3szAMcjPfvcMqb/32OIiK2u\nJx7Ky8vRtWtX19IToiP29g6xtbdEs3coFEJeXhtUV68HAASDPVBZeSD7u3CpVFRUoF27jnXXHwh0\nx/79e9CyZaTEMDN69eqFXr16oaSkBC1atLBMU7P3ggWLUVAwvk7wwuEvAWSXjYkIzExm26KNZNeC\nmfPUJaD7nZeO4i4IgiBkFgsWLEbbth10UfMrUFNTg3btOjaIwicivPPOO+jRowdyc3Mtx5nXr9PG\ng9i/fw98Pjtzq2UXje+KBUEQ0ojGOvJg/TzuXwC4H8DZUDpsbTTt1hYKhZCbm4uCggIsXLikQXc8\nfRe9NWs+rTsuJycHLVu2RGHhrEZnYxF4QRCEFCMjD94Mvz+AYDBoulUv3iUl8xv046+oqIhYt3r1\n6ojCwYIFizFx4iQwM2bPntVobCwCLwiC4BHRhodtFEOn6jB6LubOLWngyQDQQLwnTrzb0Xn0A+TU\n1HyBu++e1GgGvBGBFwRB8IBsnBAmUYyeC/3/AJCX1watW7dFTc0JACcAALW1QDjMAM6B338eiouL\n0LJly4jCwYABAxpVYckKyyj6TESi6BX00yJmEplq70xEbO0tmzdvRrdu56uR4iEEAr1x5MjBuN7R\nTH2/nVDfs+BtAP0AVAPww+cLgIjUaPiGdtRss2vXrojnW4umB4Di4qKsctHHFUUvZCZSSxCEdGYF\ngAtRU1ODRYuWOD668b3fS6CI+9UA1oOIdNHwOaifUVxdY9HM0VhjHETgs4hkTiIhCEL8+P1+zJ49\nC0qU+HoAGzFxorO24Mb0fmvt837/M1BkajyAHPh8vrpoeKtpYKOlmc1eDzNE4AVBEDzgjjtGWUaJ\nCw0ZM2Y0jh49hJKSuQgGb0Qw2AOzZ8/C7bePQmHhLBAR7r57UoO54IV6ROCziMban1YQMoFE38/G\n+H7n5ORg3LixqKw8gMLCWbj77klo0aI1JkyYqHoy7kFBwfhG1GThDAmyi0KmBiK5HYTjVVBPpto7\nE8kWW2dKwJne3tHybOd6zPaxOi5T7BOL+qC7NVCi6ftAmcfsQihNHpHDz2bL820HCbJrZLjZ1pRN\nQT3R+iALmUemPptW76fd6zEeb3Vcptpn7dq1mDFjBo4ePRqxXukadyGASwD4EAj0hhKAJ1hiNQtN\nJi6Q2eRcxY35nZ2QTHtn02xdbpDpz7bXz2aixLJ3vNdjdVym2UfPli1beNCgQXzffffVrauqqqqb\n6x2YxkCQA4FmPHDgENP3OtOfbycgymxygRSXLwQh6eijjwGgoKAHRo4clvFuS0FIFU5d/072/+EP\nf4jnnntOq7TVHe/z+RAOhwBMB7ARNTXAK6/0wL59uxtlhLwdxEUvWNIYg3qEzCDbns14r8fquETs\nE6spy6nrP96mAq2P+4IFi9GuXUeEwwyf7wIY3fIi7lGwqtpn4oI0d9FrrrNMw6t8i4veO7LFhZkp\n75Rde8d7PVbHOU0v1nti1/WvnddpU4E+v1VVVXz48OGI4wOBZjxnTnHMdzlbnm87IIqLXmrwHpGp\nAS9AdpSQG+tIVtlONjybeuK9HqvjnKTn1kA6+m/dwoX2RutjZkyYoHSBy8trg8GDb0FeXhu0bdsB\ntbW1dfsREcaOvcP0XZYgWhOslD8TF6RpDT6TA168xOtSd6bU/pJBY6rhpAPpYO9Yz3tx8TwGgjG/\nU9Fq+WbfupKSeRwM5nIg0IyLi+eZnnvFihUMgIFfM7BBl48NTNQ0Zo3dmKd0sLdXIEoNPuWi7OYi\nAp/ZePlSNnaXfWP6AKYKvaCm2t72Xe/TGMhlIMglJeZirO1v5Zo3+9ZpIm92/pqaGj7nnHNUgX9Q\nJ/D1eZkzp8jym2l2zk2bNjm0UOYiAh8nbr6U2gsWrRTb2PHqIygFrtQLTraTTjVKO8975D4bOBBo\nFvc7Ybz2aF35qqqquKKigm+//Xb+wQ/acyDQjIPBXB44cIgtb4LV9YnAi8DHxO2XMlop1i6pdisn\n8/xbt2715PpE4N19tlP9TKYbXgiOE5vbFW83vVrGYDk7bnu96Dt9R9OpQOU1IvBx4vZHMFFRSbVb\nOdnnX7nyRc+uz8m1ZKOAufVsp/qZTEeSLfDx2Hz+/EXs8zVjIMh+f1PL46I964m8B/o8FxfPs9Uc\n4NTrmU5NIl4iAh8n6STwqa51Jvv8VVVVPGLEKE+vz84Hyw2vSzoS7dk21qSi7ZfsZyJTC1aJ1Chj\niWw8Njd2N3Nyrw4fPmyra1os9M9UINBMFffo+Yn3/ROBVxbpJucR2TYwRzYQqwtRScl85Oc3jvm3\nNbQuTrm5rdG8eauUdevM5G6lQPzdMhO9brOuYgsWLEarVu1RXe183PbBg2/BSSe1xV133e34PTDm\nRXvfcnJyUFg4G8qkMUoXOGZukGYoFMLEiZMa1fvnOlbKn4kL0rgGr+GWm0tc9MnFSS0jEzF7tutr\nhxtsX3cynolUe6uSgZ1vid3rtrK52frI59hehLzG4cOH1UC36M+D2TctVle6qqoqPueccxkgJmrK\nfn/TBvsm8hxIDV5c9DFJx4ck1W7LbAiys4PTbkOZhlsCrx3ntmu+MQl8PIFlhw8f5sOHD0ekYTxW\n2yeyoGo/Qr5e4OsneLFbqLC6Dv3+8+Yt5FdeeUXNn/k1x1uATMdvd7IQgY+TxvSQpANujjvghiB4\n3bXRy8KNla21a/b5mpnWqrwi1d4qN6mqqrIMsjNep53rtiOqPl+zun0GDRpqK8DOjEGDhqoiH+SB\nA4c0qLlbdX+zu95ObEA870Vj+naLwMdJY3pI0gE7U2rGetHdFgavRNdrQXMjyC4R7KSdCm+O2+fU\n7uuIEaNsjfoWy+52aseBQDPd1KqRtXmzdK3Op603eguc5MVOzd4YYe/Gc9GYvt0i8HFgLHWni+s4\nm4n2UtoRwEx17aYi36n8AKZr7TwZhUPtvg4bVmbadu30vlvVgrXjNEG2m66T9ny7x0crIM6btzBi\nf/1+diLm7eZLBF4E3hJjqTtdP0iZSLSCktVLafdDaHcs7XSjMQl8uhbC3MqX/vm2I/BWohbtPdF/\njwYNGmoqmIkUiJ3aQp/XWOcdO3YsDx8+nDdu3Bhx7fV94+2Othc9XyLwIvCmGF9KbejEeF78dK71\npyJvsV7+RAQ+04Pi0slFn0yyWeDN7qGxsmAmwEa3tF1xNtbU9e3u+nM5veZ4bRHLu7B582YOBAJM\nROz350QUxu18Z0XgzRGBd4BbAp/Otf5U5M3Oy5mIiz4y/eiRwula8EpWvszSFRd9QxLJV7TnW2vu\ni9ZGblbrjxV0Znzm4/FeWXkQ4rGFMe/GAsfMmTMZABP52aynhrjo40ME3iGJuujTtZbCnLq8xTqv\nMebBKo1oebUTrJOu4pIsrK431R/AbCtkxWoe2rRpky0xjvWeWEXdxyo0mAXYxeolEo8tYuXn9ddf\n50BAW9+w652dc9rZJ9XPt5eIwMeBUXCcPOyJiGiyP3ypLHzECugxizQ2YsftGK1dM5UFL69FLdr1\npuIDmCpR9+6dsm4eihR4pXYbCCiL8Zm3ek+iudSt2t3nzzcfgz6WOz1RexibDwKBZrx3796YzRNu\nIQIvAh+TRB4Su+1oTtve3CDaByTZH2DjOYxNItFEN9FI+lgfyGTi5r21m99otUqvP4Cp8px4cV47\nzUNbt26NGhxnlqadNmhj9zf989xwkBvrdnajOz1aPuyiH1OBKCeikJHsd04EXgQ+Jok+JNEeYuOH\nx+vaZaoKF2b5sCPwdu0Tr4szkeu241Vw697azW+sWqXVSHbJigFIx2YhN7EbQGpWu3WSL2Mhwax2\nrneT+3w5pgJv3M/Mne7k3dAXLPTXEq2QkUxE4EXgYxLvQ2I1MISGVUk8Ve5jpx9Ct4XAjoveSR7t\nBOSZ1WKMtX071+hl/3wn6cSqVRqfbScFB6d5T9WznepCs36d3t6J5ita7TzS1huYqGnUUeysChxO\n+9IHAs0ixpTXXO9vvvkmE/kYMI8PSBYi8CLwMYnnIYk2tKOG1QueDrXoRMUzkTzECrKLp0YRa59E\n7oPXdnMq8FosglkQlVPB0afn5Br0blonQ9+6VYj0ykVvllf9uVeufNGVfOkLp9EFvt5zM2dOUcz2\ndWPAnROPmVKAaMZm49bfeOPNTBRgwG9ZyEgGIvAi8DFx+pDYmZxBI5Xt4GZ4WRO1wu6MW8nwHsTT\nVJIKz4ed+6TfZ+DAIab7OxF4rYZmbM+PJRrGdAOBZlE9W06u0QnJfKfsBsSNGDHKsnYf77msAuji\nHfDJWICzcx8azjin7/6m7y2wgf3+pnWBdslGBF4EPibxC7y92bgS/fC4/eHysi3ZjFQOvqJ3zTu5\nxlR4XaLdJ6Nr3m6QXWyhinymrYKyrPMS/1CsyRaEeN+jWE08sQTeyXmsXObaNn3asWxodr3R0o/1\nTahvv5/GQED3zD0Q8fzZeWbcQgTeA4EH0BnAuwC+BPAFgHHq+jYA3gTwNYA3ALTSHTMFwCYAGwFc\nrVvfG8B6dVuJxflcNVz8LvoAJ3vI1HSOSo73g+nU3smqmc2ZU+zItqnyupgRr8Brx5rVMuvTm1ZX\nW7Tqc20k3ceQMMuf3ftpx/Nh5aLXpxHtXPpmFrs2t7ou/Xp9s42VhyZaIdLqOouL53FJyTxdelpT\nQUCXf6U2b8ebEy8i8N4IfAcAPdXfLQD8F8C5AGYBmKSu/zOAmervbgA+AxAEcDqAzQBI3fYxgJ+o\nv18DMMDkfK4aLpEgO6ciwezehyXZWAlBonEETuydrAJOfQxFgAcOHOJauk5JpNBgpztWvLYeOHCI\n+qG2X4BN1BXtFsZ8mL1HTuMM7AZ0bt261VIYrQaaMbra7daA9TVv8+uNbJ83FuCiXYvxu2Z2rurq\nai4sLNTN876hLv5COYezqWvjeRdE4FPgogfwVwC/UGvn7bm+ELCR62vvf9btvxpAXwAdAXylWz8Y\nwEKT9F01XCIPiZnrLBpOA8iSLfBOXqpY3W3sYtfeybr+yBiKLQwEk1rLsMLtrntm99LJs609y4cP\nH1bbfHPrPtLJ8iC57RWxqqkbYwTiea7s5HXlyhcbCKOZ2OrvmVUQXbT7Gs0jYZam8Zqt4iTmz1/E\nRJEFO63AYSygLF26lAHwD394RkRelAJLIOo12blvdkiVwB+vPs7fHv6W1+1Zx29vfZtXfrGSF3y8\ngB967yHOfz2f//DSH3jxmsWunjMtBF6tkW8HkAfgoG49af8DeAzA73XblgC4UXXPv6lbfxmAV03O\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -304,22 +440,14 @@ } ], "source": [ - "# fit and plot a model using the knowledge about inflection point\n", - "inflection = 3.5 * 7 * 24\n", - "xa = x[:inflection]\n", - "ya = y[:inflection]\n", - "xb = x[inflection:]\n", - "yb = y[inflection:]\n", - "\n", - "fa = sp.poly1d(sp.polyfit(xa, ya, 1))\n", - "fb = sp.poly1d(sp.polyfit(xb, yb, 1))\n", - "\n", + "# From the first line, we train with the data up to week 3, and in the second line we\n", + "# train with the remaining data.\n", "plot_models(x, y, [fa, fb], os.path.join(CHART_DIR, \"1400_01_05.png\"))" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -340,37 +468,81 @@ "Error d=3: 33214248.905598\n", "Error d=10: 21611594.265136\n", "Error d=53: 18656112.352438\n", - "Error inflection=132950348.197616\n", - "Trained only on data after inflection point" + "Error inflection=132950348.197616\n" ] - }, + } + ], + "source": [ + "def error(f, x, y):\n", + " return sp.sum((f(x) - y) ** 2)\n", + "\n", + "print(\"Errors for the complete data set:\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", + "\n", + "print(\"Errors for only the time after inflection point\")\n", + "for f in [f1, f2, f3, f10, f100]:\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", + "\n", + "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The models of degree 10 and 53 don't seem to expect a bright future of our\n", + "start-up. They tried so hard to model the given data correctly that they are clearly\n", + "useless to extrapolate beyond. This is called overfitting. On the other hand, the\n", + "lower degree models seem not to be capable of capturing the data good enough.\n", + "This is called underfitting." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:3: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - " app.launch_new_instance()\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:6: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" - ] - }, + "data": { + "image/png": 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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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4QQrwohlgghfhFC3CSEmCSE+EkI8ZnQdxaLuqWohIRExUCSvoSERKLRGnrZ0Z4A3gCwiOS5AE4A\n+LPQtxGOtKWohIREBeGU2mVPQkKiwkEAn5H0CiHWA1BJfu7/bh2AVgDaIfyWohISEhUISfoSEhKJ\nRjEQ2B63xPK5D/qcIxB+S1EJCYkKhDTvS0hIJBKxbJW8GZG3FJWQkKggSNKXkJAoK2j56/QeQe8B\ngCRLAPQGMFEIsRb6lsKXVmRHJSQkdMiUPQkJCQkJiVMEUtOXkJCQkJA4RSBJX0JCQkJC4hSBJH0J\nCQkJCYlTBJL0JSQkJCQkThFI0peQkJCQkDhFIElfQkJCQkLiFIEkfQkJCQkJiVMEkvQlJCQkJCRO\nEfw/4o+ncwCrqEoAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# extrapolating into the future\n", + "plot_models(\n", + " x, y, [f1, f2, f3, f10, f100],\n", + " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", + " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\n", + "Trained only on data after inflection point\n", "Errors for only the time after inflection point\n", "Error d=1: 22143941.107618\n", "Error d=2: 19768846.989176\n", "Error d=3: 19766452.361027\n", "Error d=10: 18949296.656480\n", - "Error d=53: 18300790.344968\n", - "fbt2(x)= \n", - " 2\n", - "0.086 x - 94.02 x + 2.744e+04" + "Error d=53: 18300790.344968\n" ] }, { @@ -383,70 +555,11 @@ " warnings.warn(msg, RankWarning)\n" ] }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "fbt2(x)-100,000= \n", - " 2\n", - "0.086 x - 94.02 x - 7.256e+04\n", - "Test errors for only the time after inflection point\n", - "Error d=1: 6397694.386394\n", - "Error d=2: 6010775.401243\n", - "Error d=3: 6047678.658526\n", - "Error d=10: 7037716.777815\n", - "Error d=53: 7052767.755482\n", - " 2\n", - "0.086 x - 94.02 x + 2.744e+04\n", - " 2\n", - "0.086 x - 94.02 x - 7.256e+04\n", - "100,000 hits/hour expected at week 9.616071\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", - " warnings.warn(msg, RankWarning)\n" - ] - }, - { - "data": { - "image/png": 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AZ4hoHZQo+ocBzARwFRF9DeAK9X8w8wYAKwFsAPA6gDHqBQDAGABLAGwCsJmZV3uQ96QS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\n4arh4n1I3HJLRvtwJNNFH39hI77xsDW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DtWHedXAXl20rY3+XJowfNWH0fIRxyWT2XRXg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\nhoasRqZuxs85dWBnTh3dmUfWjeZfrfkV179Sz+NeGsen3n8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SEePxWIne7a6fI/BlZ2dz3nnnsWHDBqdDqZQmfaWUUhETG2s1799xB6SkOB1N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ExsaSlpbmcF5paWmcP3+e2bNnExcXV76AvEz//v1JTk42Owxhoo7bOsra+84q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VHBx8y3XoiIiI6837vr6++Pn55bosWrQo1zIzMjJISkpy+uvbQgjHiF4ZzfFh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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -454,27 +567,6 @@ } ], "source": [ - "def error(f, x, y):\n", - " return sp.sum((f(x) - y) ** 2)\n", - "\n", - "print(\"Errors for the complete data set:\")\n", - "for f in [f1, f2, f3, f10, f100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, x, y)))\n", - "\n", - "print(\"Errors for only the time after inflection point\")\n", - "for f in [f1, f2, f3, f10, f100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, xb, yb)))\n", - "\n", - "print(\"Error inflection=%f\" % (error(fa, xa, ya) + error(fb, xb, yb)))\n", - "\n", - "\n", - "# extrapolating into the future\n", - "plot_models(\n", - " x, y, [f1, f2, f3, f10, f100],\n", - " os.path.join(CHART_DIR, \"1400_01_06.png\"),\n", - " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", - "\n", "print(\"Trained only on data after inflection point\")\n", "fb1 = fb\n", "fb2 = sp.poly1d(sp.polyfit(xb, yb, 2))\n", @@ -490,47 +582,179 @@ " x, y, [fb1, fb2, fb3, fb10, fb100],\n", " os.path.join(CHART_DIR, \"1400_01_07.png\"),\n", " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", - "\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Training and testing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we only had some data from the future that we could use to measure our models\n", + "against, then we should be able to judge our model choice only on the resulting\n", + "approximation error." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ "# separating training from testing data\n", "frac = 0.3\n", "split_idx = int(frac * len(xb))\n", "shuffled = sp.random.permutation(list(range(len(xb))))\n", "test = sorted(shuffled[:split_idx])\n", - "train = sorted(shuffled[split_idx:])\n", + "train = sorted(shuffled[split_idx:])" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fbt2(x)= \n", + " 2\n", + "0.1031 x - 117.5 x + 3.544e+04\n", + "fbt2(x)-100,000= \n", + " 2\n", + "0.1031 x - 117.5 x - 6.456e+04\n" + ] + } + ], + "source": [ "fbt1 = sp.poly1d(sp.polyfit(xb[train], yb[train], 1))\n", "fbt2 = sp.poly1d(sp.polyfit(xb[train], yb[train], 2))\n", "print(\"fbt2(x)= \\n%s\"%fbt2)\n", - "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))\n", + "print(\"fbt2(x)-100,000= \\n%s\"%(fbt2-100000))" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test errors for only the time after inflection point\n", + "Error d=1: 5884534.411054\n", + "Error d=2: 6524875.605450\n", + "Error d=3: 6538982.705184\n", + "Error d=10: 7323509.948000\n", + "Error d=53: 12778972.159027\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n", + "C:\\Anaconda2\\lib\\site-packages\\numpy\\lib\\polynomial.py:594: RankWarning: Polyfit may be poorly conditioned\n", + " warnings.warn(msg, RankWarning)\n" + ] + } + ], + "source": [ "fbt3 = sp.poly1d(sp.polyfit(xb[train], yb[train], 3))\n", "fbt10 = sp.poly1d(sp.polyfit(xb[train], yb[train], 10))\n", "fbt100 = sp.poly1d(sp.polyfit(xb[train], yb[train], 100))\n", "\n", "print(\"Test errors for only the time after inflection point\")\n", "for f in [fbt1, fbt2, fbt3, fbt10, fbt100]:\n", - " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))\n", - "\n", + " print(\"Error d=%i: %f\" % (f.order, error(f, xb[test], yb[test])))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Uvv76a2mWdqKMjAyzQxAVYcFM39V++QVSUsBDT+FfNHnVZM5kneGWprdwS7Nb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "plot_models(\n", " x, y, [fbt1, fbt2, fbt3, fbt10, fbt100],\n", " os.path.join(CHART_DIR, \"1400_01_08.png\"),\n", " mx=sp.linspace(0 * 7 * 24, 6 * 7 * 24, 100),\n", - " ymax=10000, xmin=0 * 7 * 24)\n", + " ymax=10000, xmin=0 * 7 * 24)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 7) Answering our initial question" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally we have arrived at a model which we think represents the underlying process best; it is now a simple task of finding out when our infrastructure will reach 100,000 requests per hour. We have to calculate when our model function reaches the value 100,000.\n", "\n", - "from scipy.optimize import fsolve\n", - "print(fbt2)\n", - "print(fbt2 - 100000)\n", - "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", - "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + "Having a polynomial of degree 2, we could simply compute the inverse of the function and calculate its value at 100,000. Of course, we would like to have an approach that is applicable to any model function easily.\n", + "\n", + "This can be done by subtracting 100,000 from the polynomial, which results in another polynomial, and finding its root. SciPy's optimize module has the function fsolve that achieves this, when providing an initial starting position with parameter\n", + "x0. As every entry in our input data file corresponds to one hour, and we have 743 of them, we set the starting position to some value after that. Let fbt2 be the winning polynomial of degree 2." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 53, "metadata": { - "collapsed": true + "collapsed": false }, - "outputs": [], - "source": [] + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 2\n", + "0.1031 x - 117.5 x + 3.544e+04\n", + " 2\n", + "0.1031 x - 117.5 x - 6.456e+04\n", + "100,000 hits/hour expected at week 9.195553\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve\n", + "print(fbt2)\n", + "print(fbt2 - 100000)\n", + "reached_max = fsolve(fbt2 - 100000, x0=800) / (7 * 24)\n", + "print(\"100,000 hits/hour expected at week %f\" % reached_max[0])" + ] } ], "metadata": { diff --git a/ch01/charts/1400_01_08.png b/ch01/charts/1400_01_08.png index 6ea93e465b8d3dd59379c946071e47ae072855b6..7d96b9de460f270eb369d18230bb5167e9ebb502 100644 GIT binary patch literal 40955 zcmd43WmHvt_b$9P-Q69E2qK`Aw19wgHv)o+Gz!usjie|lDj*=zB_$nF3X%fSEz;fb 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8zr6%J)c7d;61lfBn4f z?k-Fu5&_~#nf;yy_GClw#%i4}c9kuJM;#5r0OnK#7U}b_<$uy*|JY(e+W{MP7H}d6 NVx)HlSE1v4^Izm<(Eb1b From 474d5b569fc5056ca8542cb6bc8e349da05a927e Mon Sep 17 00:00:00 2001 From: Tuan Vu Date: Tue, 23 Feb 2016 09:33:47 -0800 Subject: [PATCH 3/4] Classyfying --- ... with Real-world Examples-checkpoint.ipynb | 369 ++++++++++++++++++ ...Classifying with Real-world Examples.ipynb | 369 ++++++++++++++++++ 2 files changed, 738 insertions(+) create mode 100644 ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb create mode 100644 ch02/Classifying with Real-world Examples.ipynb diff --git a/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb b/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb new file mode 100644 index 00000000..4f5870c1 --- /dev/null +++ b/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb @@ -0,0 +1,369 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**In this chapter, we will be using the Iris dataset**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Visualization is a good first step" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 5.1, 3.5, 1.4, 0.2],\n", + " [ 4.9, 3. , 1.4, 0.2]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# %load chapter.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "%matplotlib inline\n", + "from matplotlib import pyplot as plt\n", + "import numpy as np\n", + "\n", + "# We load the data with load_iris from sklearn\n", + "from sklearn.datasets import load_iris\n", + "data = load_iris()\n", + "\n", + "# load_iris returns an object with several fields\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "features[0:2]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['sepal length (cm)',\n", + " 'sepal width (cm)',\n", + " 'petal length (cm)',\n", + " 'petal width (cm)']" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "feature_names" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "target" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['setosa', 'versicolor', 'virginica'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "target_names" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for t in range(3):\n", + " if t == 0:\n", + " c = 'r'\n", + " marker = '>'\n", + " elif t == 1:\n", + " c = 'g'\n", + " marker = 'o'\n", + " elif t == 2:\n", + " c = 'b'\n", + " marker = 'x'\n", + " plt.scatter(features[target == t, 0],\n", + " features[target == t, 1],\n", + " marker=marker,\n", + " c=c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Building our first classification model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum of setosa: 1.9.\n", + "Minimum of others: 3.0.\n" + ] + } + ], + "source": [ + "# We use NumPy fancy indexing to get an array of strings:\n", + "labels = target_names[target]\n", + "\n", + "# The petal length is the feature at position 2\n", + "plength = features[:, 2]\n", + "\n", + "# Build an array of booleans:\n", + "is_setosa = (labels == 'setosa')\n", + "\n", + "# This is the important step:\n", + "max_setosa =plength[is_setosa].max()\n", + "min_non_setosa = plength[~is_setosa].min()\n", + "print('Maximum of setosa: {0}.'.format(max_setosa))\n", + "\n", + "print('Minimum of others: {0}.'.format(min_non_setosa))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# ~ is the boolean negation operator\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "# Build a new target variable, is_virigina\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Initialize best_acc to impossibly low value\n", + "best_acc = -1.0\n", + "for fi in range(features.shape[1]):\n", + " # We are going to test all possible thresholds\n", + " thresh = features[:,fi]\n", + " for t in thresh:\n", + "\n", + " # Get the vector for feature `fi`\n", + " feature_i = features[:, fi]\n", + " # apply threshold `t`\n", + " pred = (feature_i > t)\n", + " acc = (pred == is_virginica).mean()\n", + " rev_acc = (pred == ~is_virginica).mean()\n", + " if rev_acc > acc:\n", + " reverse = True\n", + " acc = rev_acc\n", + " else:\n", + " reverse = False\n", + "\n", + " if acc > best_acc:\n", + " best_acc = acc\n", + " best_fi = fi\n", + " best_t = t\n", + " best_reverse = reverse\n", + "\n", + "print(best_fi, best_t, best_reverse, best_acc)\n", + "\n", + "def is_virginica_test(fi, t, reverse, example):\n", + " 'Apply threshold model to a new example'\n", + " test = example[fi] > t\n", + " if reverse:\n", + " test = not test\n", + " return test\n", + "from threshold import fit_model, predict\n", + "\n", + "# ning accuracy was 96.0%.\n", + "# ing accuracy was 90.0% (N = 50).\n", + "correct = 0.0\n", + "\n", + "for ei in range(len(features)):\n", + " # select all but the one at position `ei`:\n", + " training = np.ones(len(features), bool)\n", + " training[ei] = False\n", + " testing = ~training\n", + " model = fit_model(features[training], is_virginica[training])\n", + " predict(model, features[testing])\n", + " predictions = predict(model, features[testing])\n", + " correct += np.sum(predictions == is_virginica[testing])\n", + "acc = correct/float(len(features))\n", + "print('Accuracy: {0:.1%}'.format(acc))\n", + "\n", + "\n", + "###########################################\n", + "############## SEEDS DATASET ##############\n", + "###########################################\n", + "\n", + "from load import load_dataset\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", + "features, labels = load_dataset('seeds')\n", + "\n", + "\n", + "\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "classifier = KNeighborsClassifier(n_neighbors=1)\n", + "from sklearn.cross_validation import KFold\n", + "\n", + "kf = KFold(len(features), n_folds=5, shuffle=True)\n", + "means = []\n", + "for training,testing in kf:\n", + " # We learn a model for this fold with `fit` and then apply it to the\n", + " # testing data with `predict`:\n", + " classifier.fit(features[training], labels[training])\n", + " prediction = classifier.predict(features[testing])\n", + "\n", + " # np.mean on an array of booleans returns fraction\n", + " # of correct decisions for this fold:\n", + " curmean = np.mean(prediction == labels[testing])\n", + " means.append(curmean)\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))\n", + "\n", + "\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import StandardScaler\n", + "\n", + "classifier = KNeighborsClassifier(n_neighbors=1)\n", + "classifier = Pipeline([('norm', StandardScaler()), ('knn', classifier)])\n", + "\n", + "means = []\n", + "for training,testing in kf:\n", + " # We learn a model for this fold with `fit` and then apply it to the\n", + " # testing data with `predict`:\n", + " classifier.fit(features[training], labels[training])\n", + " prediction = classifier.predict(features[testing])\n", + "\n", + " # np.mean on an array of booleans returns fraction\n", + " # of correct decisions for this fold:\n", + " curmean = np.mean(prediction == labels[testing])\n", + " means.append(curmean)\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ch02/Classifying with Real-world Examples.ipynb b/ch02/Classifying with Real-world Examples.ipynb new file mode 100644 index 00000000..4f5870c1 --- /dev/null +++ b/ch02/Classifying with Real-world Examples.ipynb @@ -0,0 +1,369 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**In this chapter, we will be using the Iris dataset**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Visualization is a good first step" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 5.1, 3.5, 1.4, 0.2],\n", + " [ 4.9, 3. , 1.4, 0.2]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# %load chapter.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "%matplotlib inline\n", + "from matplotlib import pyplot as plt\n", + "import numpy as np\n", + "\n", + "# We load the data with load_iris from sklearn\n", + "from sklearn.datasets import load_iris\n", + "data = load_iris()\n", + "\n", + "# load_iris returns an object with several fields\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "features[0:2]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['sepal length (cm)',\n", + " 'sepal width (cm)',\n", + " 'petal length (cm)',\n", + " 'petal width (cm)']" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "feature_names" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", + " 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", + " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "target" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['setosa', 'versicolor', 'virginica'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "target_names" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for t in range(3):\n", + " if t == 0:\n", + " c = 'r'\n", + " marker = '>'\n", + " elif t == 1:\n", + " c = 'g'\n", + " marker = 'o'\n", + " elif t == 2:\n", + " c = 'b'\n", + " marker = 'x'\n", + " plt.scatter(features[target == t, 0],\n", + " features[target == t, 1],\n", + " marker=marker,\n", + " c=c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) Building our first classification model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum of setosa: 1.9.\n", + "Minimum of others: 3.0.\n" + ] + } + ], + "source": [ + "# We use NumPy fancy indexing to get an array of strings:\n", + "labels = target_names[target]\n", + "\n", + "# The petal length is the feature at position 2\n", + "plength = features[:, 2]\n", + "\n", + "# Build an array of booleans:\n", + "is_setosa = (labels == 'setosa')\n", + "\n", + "# This is the important step:\n", + "max_setosa =plength[is_setosa].max()\n", + "min_non_setosa = plength[~is_setosa].min()\n", + "print('Maximum of setosa: {0}.'.format(max_setosa))\n", + "\n", + "print('Minimum of others: {0}.'.format(min_non_setosa))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# ~ is the boolean negation operator\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "# Build a new target variable, is_virigina\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Initialize best_acc to impossibly low value\n", + "best_acc = -1.0\n", + "for fi in range(features.shape[1]):\n", + " # We are going to test all possible thresholds\n", + " thresh = features[:,fi]\n", + " for t in thresh:\n", + "\n", + " # Get the vector for feature `fi`\n", + " feature_i = features[:, fi]\n", + " # apply threshold `t`\n", + " pred = (feature_i > t)\n", + " acc = (pred == is_virginica).mean()\n", + " rev_acc = (pred == ~is_virginica).mean()\n", + " if rev_acc > acc:\n", + " reverse = True\n", + " acc = rev_acc\n", + " else:\n", + " reverse = False\n", + "\n", + " if acc > best_acc:\n", + " best_acc = acc\n", + " best_fi = fi\n", + " best_t = t\n", + " best_reverse = reverse\n", + "\n", + "print(best_fi, best_t, best_reverse, best_acc)\n", + "\n", + "def is_virginica_test(fi, t, reverse, example):\n", + " 'Apply threshold model to a new example'\n", + " test = example[fi] > t\n", + " if reverse:\n", + " test = not test\n", + " return test\n", + "from threshold import fit_model, predict\n", + "\n", + "# ning accuracy was 96.0%.\n", + "# ing accuracy was 90.0% (N = 50).\n", + "correct = 0.0\n", + "\n", + "for ei in range(len(features)):\n", + " # select all but the one at position `ei`:\n", + " training = np.ones(len(features), bool)\n", + " training[ei] = False\n", + " testing = ~training\n", + " model = fit_model(features[training], is_virginica[training])\n", + " predict(model, features[testing])\n", + " predictions = predict(model, features[testing])\n", + " correct += np.sum(predictions == is_virginica[testing])\n", + "acc = correct/float(len(features))\n", + "print('Accuracy: {0:.1%}'.format(acc))\n", + "\n", + "\n", + "###########################################\n", + "############## SEEDS DATASET ##############\n", + "###########################################\n", + "\n", + "from load import load_dataset\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", + "features, labels = load_dataset('seeds')\n", + "\n", + "\n", + "\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "classifier = KNeighborsClassifier(n_neighbors=1)\n", + "from sklearn.cross_validation import KFold\n", + "\n", + "kf = KFold(len(features), n_folds=5, shuffle=True)\n", + "means = []\n", + "for training,testing in kf:\n", + " # We learn a model for this fold with `fit` and then apply it to the\n", + " # testing data with `predict`:\n", + " classifier.fit(features[training], labels[training])\n", + " prediction = classifier.predict(features[testing])\n", + "\n", + " # np.mean on an array of booleans returns fraction\n", + " # of correct decisions for this fold:\n", + " curmean = np.mean(prediction == labels[testing])\n", + " means.append(curmean)\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))\n", + "\n", + "\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import StandardScaler\n", + "\n", + "classifier = KNeighborsClassifier(n_neighbors=1)\n", + "classifier = Pipeline([('norm', StandardScaler()), ('knn', classifier)])\n", + "\n", + "means = []\n", + "for training,testing in kf:\n", + " # We learn a model for this fold with `fit` and then apply it to the\n", + " # testing data with `predict`:\n", + " classifier.fit(features[training], labels[training])\n", + " prediction = classifier.predict(features[testing])\n", + "\n", + " # np.mean on an array of booleans returns fraction\n", + " # of correct decisions for this fold:\n", + " curmean = np.mean(prediction == labels[testing])\n", + " means.append(curmean)\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From a52b474ca5e617c87568825fc0cdd8dc317b8369 Mon Sep 17 00:00:00 2001 From: Tuan Vu Date: Thu, 25 Feb 2016 09:12:40 -0800 Subject: [PATCH 4/4] chapter 2 --- ... with Real-world Examples-checkpoint.ipynb | 776 +++++++++++++++++- ...Classifying with Real-world Examples.ipynb | 776 +++++++++++++++++- ch02/figure1.png | Bin 0 -> 31997 bytes ch02/figure2.png | Bin 0 -> 12329 bytes ch02/figure4sklearn.png | Bin 0 -> 19327 bytes ch02/figure5sklearn.png | Bin 0 -> 16820 bytes ch02/figure5sklearn_with_11_neighbors.png | Bin 0 -> 17674 bytes 7 files changed, 1468 insertions(+), 84 deletions(-) create mode 100644 ch02/figure1.png create mode 100644 ch02/figure2.png create mode 100644 ch02/figure4sklearn.png create mode 100644 ch02/figure5sklearn.png create mode 100644 ch02/figure5sklearn_with_11_neighbors.png diff --git a/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb b/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb index 4f5870c1..7de7c824 100644 --- a/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb +++ b/ch02/.ipynb_checkpoints/Classifying with Real-world Examples-checkpoint.ipynb @@ -1,14 +1,5 @@ { "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - }, { "cell_type": "markdown", "metadata": {}, @@ -25,7 +16,71 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6zDV5JZTMeBGgXGCqo8G5CcjxUC5kZaLZB+oky/Hh51On+sr37NxZrgf5B8i5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\nOByB5f8DbE5K4VyaEEUAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure1.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "from matplotlib import pyplot as plt\n", + "\n", + "# We load the data with load_iris from sklearn\n", + "from sklearn.datasets import load_iris\n", + "\n", + "# load_iris returns an object with several fields\n", + "data = load_iris()\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "fig,axes = plt.subplots(2, 3)\n", + "pairs = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]\n", + "\n", + "# Set up 3 different pairs of (color, marker)\n", + "color_markers = [\n", + " ('r', '>'),\n", + " ('g', 'o'),\n", + " ('b', 'x'),\n", + " ]\n", + "for i, (p0, p1) in enumerate(pairs):\n", + " ax = axes.flat[i]\n", + "\n", + " for t in range(3):\n", + " # Use a different color/marker for each class `t`\n", + " c,marker = color_markers[t]\n", + " ax.scatter(features[target == t, p0], features[\n", + " target == t, p1], marker=marker, c=c)\n", + " ax.set_xlabel(feature_names[p0])\n", + " ax.set_ylabel(feature_names[p1])\n", + " ax.set_xticks([])\n", + " ax.set_yticks([])\n", + "fig.tight_layout()\n", + "fig.savefig('figure1.png')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 46, "metadata": { "collapsed": false }, @@ -37,7 +92,7 @@ " [ 4.9, 3. , 1.4, 0.2]])" ] }, - "execution_count": 6, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -70,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -84,7 +139,7 @@ " 'petal width (cm)']" ] }, - "execution_count": 7, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -95,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 48, "metadata": { "collapsed": false }, @@ -112,7 +167,7 @@ " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])" ] }, - "execution_count": 8, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -123,7 +178,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 49, "metadata": { "collapsed": false }, @@ -135,7 +190,7 @@ " dtype='|S10')" ] }, - "execution_count": 9, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -146,7 +201,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 50, "metadata": { "collapsed": false }, @@ -155,7 +210,7 @@ "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -186,32 +241,85 @@ "# 2) Building our first classification model" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the goal is to separate the three types of flowers, we can immediately make a few\n", + "suggestions just by looking at the data. For example, petal length seems to be able\n", + "to separate Iris Setosa from the other two flower species on its own." + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Maximum of setosa: 1.9.\n", - "Minimum of others: 3.0.\n" - ] + "data": { + "text/plain": [ + "array(['setosa', 'setosa', 'setosa', 'setosa', 'setosa', 'setosa',\n", + " 'setosa', 'setosa', 'setosa', 'setosa'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "# We use NumPy fancy indexing to get an array of strings:\n", "labels = target_names[target]\n", - "\n", + "labels[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, True, True, True, True, True, True, True, True], dtype=bool)" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ "# The petal length is the feature at position 2\n", "plength = features[:, 2]\n", "\n", "# Build an array of booleans:\n", "is_setosa = (labels == 'setosa')\n", - "\n", + "is_setosa[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum of setosa: 1.9.\n", + "Minimum of others: 3.0.\n" + ] + } + ], + "source": [ "# This is the important step:\n", "max_setosa =plength[is_setosa].max()\n", "min_non_setosa = plength[~is_setosa].min()\n", @@ -220,9 +328,29 @@ "print('Minimum of others: {0}.'.format(min_non_setosa))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Therefore, we can build a simple model: if the petal length is smaller than 2, then\n", + "this is an Iris Setosa flower; otherwise it is either Iris Virginica or Iris Versicolor." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem of recognizing Iris Setosa apart from the other two species was\n", + "very easy. However, we cannot immediately see what the best threshold is for\n", + "distinguishing Iris Virginica from Iris Versicolor. We can even see that we will never\n", + "achieve perfect separation with these features. We could, however, look for the best\n", + "possible separation, the separation that makes the fewest mistakes. For this, we will\n", + "perform a little computation." + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 54, "metadata": { "collapsed": true }, @@ -230,10 +358,79 @@ "source": [ "# ~ is the boolean negation operator\n", "features = features[~is_setosa]\n", - "labels = labels[~is_setosa]\n", + "labels = labels[~is_setosa]" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['versicolor', 'virginica'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.unique(labels)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ "# Build a new target variable, is_virigina\n", - "is_virginica = (labels == 'virginica')\n", - "\n", + "is_virginica = (labels == 'virginica')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The is_setosa array is a\n", + "Boolean array and we use it to select a subset of the other two arrays, features and\n", + "labels. Finally, we build a new boolean array, virginica, by using an equality\n", + "comparison on labels." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we run a loop over all possible features and thresholds to see which one\n", + "results in better accuracy. Accuracy is simply the fraction of examples that the\n", + "model classifies correctly." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3, 1.6000000000000001, False, 0.93999999999999995)\n" + ] + } + ], + "source": [ "# Initialize best_acc to impossibly low value\n", "best_acc = -1.0\n", "for fi in range(features.shape[1]):\n", @@ -259,14 +456,206 @@ " best_t = t\n", " best_reverse = reverse\n", "\n", - "print(best_fi, best_t, best_reverse, best_acc)\n", - "\n", + "print(best_fi, best_t, best_reverse, best_acc)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ "def is_virginica_test(fi, t, reverse, example):\n", " 'Apply threshold model to a new example'\n", " test = example[fi] > t\n", " if reverse:\n", " test = not test\n", - " return test\n", + " return test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does this model look like? If we run the code on the whole data, the model that\n", + "is identified as the best makes decisions by splitting on the petal width. One way\n", + "to gain intuition about how this works is to visualize the decision boundary. That\n", + "is, we can see which feature values will result in one decision versus the other and\n", + "exactly where the boundary is." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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FTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure2.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from sklearn.datasets import load_iris\n", + "data = load_iris()\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "# We use NumPy fancy indexing to get an array of strings:\n", + "labels = target_names[target]\n", + "\n", + "is_setosa = (labels == 'setosa')\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Hand fixed thresholds:\n", + "t = 1.65\n", + "t2 = 1.75\n", + "\n", + "# Features to use: 3 & 2\n", + "f0, f1 = 3, 2\n", + "\n", + "if COLOUR_FIGURE:\n", + " area1c = (1., .8, .8)\n", + " area2c = (.8, .8, 1.)\n", + "else:\n", + " area1c = (1., 1, 1)\n", + " area2c = (.7, .7, .7)\n", + "\n", + "# Plot from 90% of smallest value to 110% of largest value\n", + "# (all feature values are positive, otherwise this would not work very well)\n", + "\n", + "x0 = features[:, f0].min() * .9\n", + "x1 = features[:, f0].max() * 1.1\n", + "\n", + "y0 = features[:, f1].min() * .9\n", + "y1 = features[:, f1].max() * 1.1\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.fill_between([t, x1], [y0, y0], [y1, y1], color=area2c)\n", + "ax.fill_between([x0, t], [y0, y0], [y1, y1], color=area1c)\n", + "ax.plot([t, t], [y0, y1], 'k--', lw=2)\n", + "ax.plot([t2, t2], [y0, y1], 'k:', lw=2)\n", + "ax.scatter(features[is_virginica, f0],\n", + " features[is_virginica, f1], c='b', marker='o', s=40)\n", + "ax.scatter(features[~is_virginica, f0],\n", + " features[~is_virginica, f1], c='r', marker='x', s=40)\n", + "ax.set_ylim(y0, y1)\n", + "ax.set_xlim(x0, x1)\n", + "ax.set_xlabel(feature_names[f0])\n", + "ax.set_ylabel(feature_names[f1])\n", + "fig.tight_layout()\n", + "fig.savefig('figure2.png')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) Evaluation – holding out data and cross-validation" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training accuracy was 96.0%.\n", + "Testing accuracy was 90.0% (N = 50).\n", + "\n" + ] + } + ], + "source": [ + "# %load heldout.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "# This script demonstrates the difference between the training accuracy and\n", + "# testing (held-out) accuracy.\n", + "\n", + "import numpy as np\n", + "from sklearn.datasets import load_iris\n", + "from threshold import fit_model, accuracy\n", + "\n", + "data = load_iris()\n", + "features = data['data']\n", + "labels = data['target_names'][data['target']]\n", + "\n", + "# We are going to remove the setosa examples as they are too easy:\n", + "is_setosa = (labels == 'setosa')\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "\n", + "# Now we classify virginica vs non-virginica\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Split the data in two: testing and training\n", + "testing = np.tile([True, False], 50) # testing = [True,False,True,False,True,False...]\n", + "\n", + "# Training is the negation of testing: i.e., datapoints not used for testing,\n", + "# will be used for training\n", + "training = ~testing\n", + "\n", + "model = fit_model(features[training], is_virginica[training])\n", + "train_accuracy = accuracy(features[training], is_virginica[training], model)\n", + "test_accuracy = accuracy(features[testing], is_virginica[testing], model)\n", + "\n", + "print('''\\\n", + "Training accuracy was {0:.1%}.\n", + "Testing accuracy was {1:.1%} (N = {2}).\n", + "'''.format(train_accuracy, test_accuracy, testing.sum()))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy: 87.0%\n" + ] + } + ], + "source": [ "from threshold import fit_model, predict\n", "\n", "# ning accuracy was 96.0%.\n", @@ -283,9 +672,33 @@ " predictions = predict(model, features[testing])\n", " correct += np.sum(predictions == is_virginica[testing])\n", "acc = correct/float(len(features))\n", - "print('Accuracy: {0:.1%}'.format(acc))\n", - "\n", - "\n", + "print('Accuracy: {0:.1%}'.format(acc))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) More complex model" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 15.26 14.84 0.871 5.763 3.312 2.221 5.22 ]\n", + "['Canadian' 'Kama' 'Rosa']\n" + ] + } + ], + "source": [ "###########################################\n", "############## SEEDS DATASET ##############\n", "###########################################\n", @@ -302,14 +715,39 @@ " 'length of kernel groove',\n", "]\n", "features, labels = load_dataset('seeds')\n", - "\n", - "\n", - "\n", + "print features[0]\n", + "print np.unique(labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Classifying with scikit-learn" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean accuracy: 89.0%\n" + ] + } + ], + "source": [ "from sklearn.neighbors import KNeighborsClassifier\n", "classifier = KNeighborsClassifier(n_neighbors=1)\n", "from sklearn.cross_validation import KFold\n", "\n", "kf = KFold(len(features), n_folds=5, shuffle=True)\n", + "# `means` will be a list of mean accuracies (one entry per fold)\n", "means = []\n", "for training,testing in kf:\n", " # We learn a model for this fold with `fit` and then apply it to the\n", @@ -321,9 +759,136 @@ " # of correct decisions for this fold:\n", " curmean = np.mean(prediction == labels[testing])\n", " means.append(curmean)\n", - "print('Mean accuracy: {:.1%}'.format(np.mean(means)))\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Looking at the decision boundaries" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "ValueError", + "evalue": "too many values to unpack", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 72\u001b[0m \u001b[0mlabels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnames\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mell\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mell\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlabels\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 73\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 74\u001b[1;33m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplot_decision\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabels\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 75\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msavefig\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'figure4.png'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 76\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32m\u001b[0m in \u001b[0;36mplot_decision\u001b[1;34m(features, labels)\u001b[0m\n\u001b[0;32m 47\u001b[0m \u001b[0mmodel\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfit_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlabels\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 48\u001b[0m C = predict(\n\u001b[1;32m---> 49\u001b[1;33m np.vstack([X.ravel(), Y.ravel()]).T, model).reshape(X.shape)\n\u001b[0m\u001b[0;32m 50\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mCOLOUR_FIGURE\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 51\u001b[0m \u001b[0mcmap\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mListedColormap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\Users\\tvu\\Documents\\GitHub\\BuildingMachineLearningSystemsWithPython\\ch02\\knn.py\u001b[0m in \u001b[0;36mpredict\u001b[1;34m(model, features)\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 30\u001b[0m \u001b[1;34m'''Apply k-nn model'''\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 31\u001b[1;33m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_feats\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 32\u001b[0m \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 33\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mf\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: too many values to unpack" + ] + } + ], + "source": [ + "# %load figure4_5_no_sklearn.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from matplotlib.colors import ListedColormap\n", + "from load import load_dataset\n", + "import numpy as np\n", + "from knn import fit_model, predict\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", "\n", "\n", + "def plot_decision(features, labels):\n", + " '''Plots decision boundary for KNN\n", + "\n", + " Parameters\n", + " ----------\n", + " features : ndarray\n", + " labels : sequence\n", + "\n", + " Returns\n", + " -------\n", + " fig : Matplotlib Figure\n", + " ax : Matplotlib Axes\n", + " '''\n", + " y0, y1 = features[:, 2].min() * .9, features[:, 2].max() * 1.1\n", + " x0, x1 = features[:, 0].min() * .9, features[:, 0].max() * 1.1\n", + " X = np.linspace(x0, x1, 100)\n", + " Y = np.linspace(y0, y1, 100)\n", + " X, Y = np.meshgrid(X, Y)\n", + "\n", + " model = fit_model(1, features[:, (0, 2)], np.array(labels))\n", + " C = predict(\n", + " np.vstack([X.ravel(), Y.ravel()]).T, model).reshape(X.shape)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .6, .6), (.6, 1., .6), (.6, .6, 1.)])\n", + " else:\n", + " cmap = ListedColormap([(1., 1., 1.), (.2, .2, .2), (.6, .6, .6)])\n", + " fig,ax = plt.subplots()\n", + " ax.set_xlim(x0, x1)\n", + " ax.set_ylim(y0, y1)\n", + " ax.set_xlabel(feature_names[0])\n", + " ax.set_ylabel(feature_names[2])\n", + " ax.pcolormesh(X, Y, C, cmap=cmap)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .0, .0), (.0, 1., .0), (.0, .0, 1.)])\n", + " ax.scatter(features[:, 0], features[:, 2], c=labels, cmap=cmap)\n", + " else:\n", + " for lab, ma in zip(range(3), \"Do^\"):\n", + " ax.plot(features[labels == lab, 0], features[\n", + " labels == lab, 2], ma, c=(1., 1., 1.))\n", + " return fig,ax\n", + "\n", + "\n", + "features, labels = load_dataset('seeds')\n", + "names = sorted(set(labels))\n", + "labels = np.array([names.index(ell) for ell in labels])\n", + "\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.savefig('figure4.png')\n", + "\n", + "features -= features.mean(0)\n", + "features /= features.std(0)\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.savefig('figure5.png')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean accuracy: 91.0%\n" + ] + } + ], + "source": [ "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import StandardScaler\n", "\n", @@ -343,6 +908,133 @@ " means.append(curmean)\n", "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ffDPTpk0LOWfq1KlkZ2dTWloaEqAg+nYhVpKHM9kBvG3fEQ/nGqdI3xNPdpgx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\nlX95ye77qTGmyhiz3RiTaYz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0FU87nB6IRqv2oNZDYTpV6EwQR4wgwq6TM0bceLV0imId3Gksb7zxRl64+vfv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\n7s29/ioRnRX1GL1S6lyIaDIR7cndh5e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ZQ2stdndD9zpqNUvaIgUAkTop5dNsd2uWVDaLFOCdUI0aNQozZ87EiBEjMDg4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\nIsUwDMNIC4sUwzAMIy3/H2I7PX2zN3xaAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure4_5_sklearn.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from matplotlib.colors import ListedColormap\n", + "from load import load_dataset\n", + "import numpy as np\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", + "\n", + "\n", + "def plot_decision(features, labels, num_neighbors=1):\n", + " '''Plots decision boundary for KNN\n", + "\n", + " Parameters\n", + " ----------\n", + " features : ndarray\n", + " labels : sequence\n", + "\n", + " Returns\n", + " -------\n", + " fig : Matplotlib Figure\n", + " ax : Matplotlib Axes\n", + " '''\n", + " y0, y1 = features[:, 2].min() * .9, features[:, 2].max() * 1.1\n", + " x0, x1 = features[:, 0].min() * .9, features[:, 0].max() * 1.1\n", + " X = np.linspace(x0, x1, 1000)\n", + " Y = np.linspace(y0, y1, 1000)\n", + " X, Y = np.meshgrid(X, Y)\n", + "\n", + " model = KNeighborsClassifier(num_neighbors)\n", + " model.fit(features[:, (0,2)], labels)\n", + " C = model.predict(np.vstack([X.ravel(), Y.ravel()]).T).reshape(X.shape)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .7, .7), (.7, 1., .7), (.7, .7, 1.)])\n", + " else:\n", + " cmap = ListedColormap([(1., 1., 1.), (.2, .2, .2), (.6, .6, .6)])\n", + " fig,ax = plt.subplots()\n", + " ax.set_xlim(x0, x1)\n", + " ax.set_ylim(y0, y1)\n", + " ax.set_xlabel(feature_names[0])\n", + " ax.set_ylabel(feature_names[2])\n", + " ax.pcolormesh(X, Y, C, cmap=cmap)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .0, .0), (.1, .6, .1), (.0, .0, 1.)])\n", + " ax.scatter(features[:, 0], features[:, 2], c=labels, cmap=cmap)\n", + " else:\n", + " for lab, ma in zip(range(3), \"Do^\"):\n", + " ax.plot(features[labels == lab, 0], features[\n", + " labels == lab, 2], ma, c=(1., 1., 1.), ms=6)\n", + " return fig,ax\n", + "\n", + "\n", + "features, labels = load_dataset('seeds')\n", + "names = sorted(set(labels))\n", + "labels = np.array([names.index(ell) for ell in labels])\n", + "\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.tight_layout()\n", + "fig.savefig('figure4sklearn.png')\n", + "\n", + "features -= features.mean(0)\n", + "features /= features.std(0)\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.tight_layout()\n", + "fig.savefig('figure5sklearn.png')\n", + "\n", + "fig,ax = plot_decision(features, labels, 11)\n", + "fig.tight_layout()\n", + "fig.savefig('figure5sklearn_with_11_neighbors.png')\n" + ] } ], "metadata": { diff --git a/ch02/Classifying with Real-world Examples.ipynb b/ch02/Classifying with Real-world Examples.ipynb index 4f5870c1..7de7c824 100644 --- a/ch02/Classifying with Real-world Examples.ipynb +++ b/ch02/Classifying with Real-world Examples.ipynb @@ -1,14 +1,5 @@ { "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - }, { "cell_type": "markdown", "metadata": {}, @@ -25,7 +16,71 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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6zDV5JZTMeBGgXGCqo8G5CcjxUC5kZaLZB+oky/Hh51On+sr37NxZrgf5B8i5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\nOByB5f8DbE5K4VyaEEUAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure1.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "from matplotlib import pyplot as plt\n", + "\n", + "# We load the data with load_iris from sklearn\n", + "from sklearn.datasets import load_iris\n", + "\n", + "# load_iris returns an object with several fields\n", + "data = load_iris()\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "fig,axes = plt.subplots(2, 3)\n", + "pairs = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]\n", + "\n", + "# Set up 3 different pairs of (color, marker)\n", + "color_markers = [\n", + " ('r', '>'),\n", + " ('g', 'o'),\n", + " ('b', 'x'),\n", + " ]\n", + "for i, (p0, p1) in enumerate(pairs):\n", + " ax = axes.flat[i]\n", + "\n", + " for t in range(3):\n", + " # Use a different color/marker for each class `t`\n", + " c,marker = color_markers[t]\n", + " ax.scatter(features[target == t, p0], features[\n", + " target == t, p1], marker=marker, c=c)\n", + " ax.set_xlabel(feature_names[p0])\n", + " ax.set_ylabel(feature_names[p1])\n", + " ax.set_xticks([])\n", + " ax.set_yticks([])\n", + "fig.tight_layout()\n", + "fig.savefig('figure1.png')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 46, "metadata": { "collapsed": false }, @@ -37,7 +92,7 @@ " [ 4.9, 3. , 1.4, 0.2]])" ] }, - "execution_count": 6, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -70,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -84,7 +139,7 @@ " 'petal width (cm)']" ] }, - "execution_count": 7, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -95,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 48, "metadata": { "collapsed": false }, @@ -112,7 +167,7 @@ " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])" ] }, - "execution_count": 8, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -123,7 +178,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 49, "metadata": { "collapsed": false }, @@ -135,7 +190,7 @@ " dtype='|S10')" ] }, - "execution_count": 9, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -146,7 +201,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 50, "metadata": { "collapsed": false }, @@ -155,7 +210,7 @@ "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -186,32 +241,85 @@ "# 2) Building our first classification model" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the goal is to separate the three types of flowers, we can immediately make a few\n", + "suggestions just by looking at the data. For example, petal length seems to be able\n", + "to separate Iris Setosa from the other two flower species on its own." + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Maximum of setosa: 1.9.\n", - "Minimum of others: 3.0.\n" - ] + "data": { + "text/plain": [ + "array(['setosa', 'setosa', 'setosa', 'setosa', 'setosa', 'setosa',\n", + " 'setosa', 'setosa', 'setosa', 'setosa'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ "# We use NumPy fancy indexing to get an array of strings:\n", "labels = target_names[target]\n", - "\n", + "labels[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, True, True, True, True, True, True, True, True, True], dtype=bool)" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ "# The petal length is the feature at position 2\n", "plength = features[:, 2]\n", "\n", "# Build an array of booleans:\n", "is_setosa = (labels == 'setosa')\n", - "\n", + "is_setosa[0:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum of setosa: 1.9.\n", + "Minimum of others: 3.0.\n" + ] + } + ], + "source": [ "# This is the important step:\n", "max_setosa =plength[is_setosa].max()\n", "min_non_setosa = plength[~is_setosa].min()\n", @@ -220,9 +328,29 @@ "print('Minimum of others: {0}.'.format(min_non_setosa))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Therefore, we can build a simple model: if the petal length is smaller than 2, then\n", + "this is an Iris Setosa flower; otherwise it is either Iris Virginica or Iris Versicolor." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The problem of recognizing Iris Setosa apart from the other two species was\n", + "very easy. However, we cannot immediately see what the best threshold is for\n", + "distinguishing Iris Virginica from Iris Versicolor. We can even see that we will never\n", + "achieve perfect separation with these features. We could, however, look for the best\n", + "possible separation, the separation that makes the fewest mistakes. For this, we will\n", + "perform a little computation." + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 54, "metadata": { "collapsed": true }, @@ -230,10 +358,79 @@ "source": [ "# ~ is the boolean negation operator\n", "features = features[~is_setosa]\n", - "labels = labels[~is_setosa]\n", + "labels = labels[~is_setosa]" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(['versicolor', 'virginica'], \n", + " dtype='|S10')" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.unique(labels)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ "# Build a new target variable, is_virigina\n", - "is_virginica = (labels == 'virginica')\n", - "\n", + "is_virginica = (labels == 'virginica')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The is_setosa array is a\n", + "Boolean array and we use it to select a subset of the other two arrays, features and\n", + "labels. Finally, we build a new boolean array, virginica, by using an equality\n", + "comparison on labels." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we run a loop over all possible features and thresholds to see which one\n", + "results in better accuracy. Accuracy is simply the fraction of examples that the\n", + "model classifies correctly." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3, 1.6000000000000001, False, 0.93999999999999995)\n" + ] + } + ], + "source": [ "# Initialize best_acc to impossibly low value\n", "best_acc = -1.0\n", "for fi in range(features.shape[1]):\n", @@ -259,14 +456,206 @@ " best_t = t\n", " best_reverse = reverse\n", "\n", - "print(best_fi, best_t, best_reverse, best_acc)\n", - "\n", + "print(best_fi, best_t, best_reverse, best_acc)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ "def is_virginica_test(fi, t, reverse, example):\n", " 'Apply threshold model to a new example'\n", " test = example[fi] > t\n", " if reverse:\n", " test = not test\n", - " return test\n", + " return test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does this model look like? If we run the code on the whole data, the model that\n", + "is identified as the best makes decisions by splitting on the petal width. One way\n", + "to gain intuition about how this works is to visualize the decision boundary. That\n", + "is, we can see which feature values will result in one decision versus the other and\n", + "exactly where the boundary is." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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FTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure2.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from sklearn.datasets import load_iris\n", + "data = load_iris()\n", + "features = data.data\n", + "feature_names = data.feature_names\n", + "target = data.target\n", + "target_names = data.target_names\n", + "\n", + "# We use NumPy fancy indexing to get an array of strings:\n", + "labels = target_names[target]\n", + "\n", + "is_setosa = (labels == 'setosa')\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Hand fixed thresholds:\n", + "t = 1.65\n", + "t2 = 1.75\n", + "\n", + "# Features to use: 3 & 2\n", + "f0, f1 = 3, 2\n", + "\n", + "if COLOUR_FIGURE:\n", + " area1c = (1., .8, .8)\n", + " area2c = (.8, .8, 1.)\n", + "else:\n", + " area1c = (1., 1, 1)\n", + " area2c = (.7, .7, .7)\n", + "\n", + "# Plot from 90% of smallest value to 110% of largest value\n", + "# (all feature values are positive, otherwise this would not work very well)\n", + "\n", + "x0 = features[:, f0].min() * .9\n", + "x1 = features[:, f0].max() * 1.1\n", + "\n", + "y0 = features[:, f1].min() * .9\n", + "y1 = features[:, f1].max() * 1.1\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.fill_between([t, x1], [y0, y0], [y1, y1], color=area2c)\n", + "ax.fill_between([x0, t], [y0, y0], [y1, y1], color=area1c)\n", + "ax.plot([t, t], [y0, y1], 'k--', lw=2)\n", + "ax.plot([t2, t2], [y0, y1], 'k:', lw=2)\n", + "ax.scatter(features[is_virginica, f0],\n", + " features[is_virginica, f1], c='b', marker='o', s=40)\n", + "ax.scatter(features[~is_virginica, f0],\n", + " features[~is_virginica, f1], c='r', marker='x', s=40)\n", + "ax.set_ylim(y0, y1)\n", + "ax.set_xlim(x0, x1)\n", + "ax.set_xlabel(feature_names[f0])\n", + "ax.set_ylabel(feature_names[f1])\n", + "fig.tight_layout()\n", + "fig.savefig('figure2.png')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) Evaluation – holding out data and cross-validation" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training accuracy was 96.0%.\n", + "Testing accuracy was 90.0% (N = 50).\n", + "\n" + ] + } + ], + "source": [ + "# %load heldout.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "# This script demonstrates the difference between the training accuracy and\n", + "# testing (held-out) accuracy.\n", + "\n", + "import numpy as np\n", + "from sklearn.datasets import load_iris\n", + "from threshold import fit_model, accuracy\n", + "\n", + "data = load_iris()\n", + "features = data['data']\n", + "labels = data['target_names'][data['target']]\n", + "\n", + "# We are going to remove the setosa examples as they are too easy:\n", + "is_setosa = (labels == 'setosa')\n", + "features = features[~is_setosa]\n", + "labels = labels[~is_setosa]\n", + "\n", + "# Now we classify virginica vs non-virginica\n", + "is_virginica = (labels == 'virginica')\n", + "\n", + "# Split the data in two: testing and training\n", + "testing = np.tile([True, False], 50) # testing = [True,False,True,False,True,False...]\n", + "\n", + "# Training is the negation of testing: i.e., datapoints not used for testing,\n", + "# will be used for training\n", + "training = ~testing\n", + "\n", + "model = fit_model(features[training], is_virginica[training])\n", + "train_accuracy = accuracy(features[training], is_virginica[training], model)\n", + "test_accuracy = accuracy(features[testing], is_virginica[testing], model)\n", + "\n", + "print('''\\\n", + "Training accuracy was {0:.1%}.\n", + "Testing accuracy was {1:.1%} (N = {2}).\n", + "'''.format(train_accuracy, test_accuracy, testing.sum()))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy: 87.0%\n" + ] + } + ], + "source": [ "from threshold import fit_model, predict\n", "\n", "# ning accuracy was 96.0%.\n", @@ -283,9 +672,33 @@ " predictions = predict(model, features[testing])\n", " correct += np.sum(predictions == is_virginica[testing])\n", "acc = correct/float(len(features))\n", - "print('Accuracy: {0:.1%}'.format(acc))\n", - "\n", - "\n", + "print('Accuracy: {0:.1%}'.format(acc))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4) More complex model" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 15.26 14.84 0.871 5.763 3.312 2.221 5.22 ]\n", + "['Canadian' 'Kama' 'Rosa']\n" + ] + } + ], + "source": [ "###########################################\n", "############## SEEDS DATASET ##############\n", "###########################################\n", @@ -302,14 +715,39 @@ " 'length of kernel groove',\n", "]\n", "features, labels = load_dataset('seeds')\n", - "\n", - "\n", - "\n", + "print features[0]\n", + "print np.unique(labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 5) Classifying with scikit-learn" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean accuracy: 89.0%\n" + ] + } + ], + "source": [ "from sklearn.neighbors import KNeighborsClassifier\n", "classifier = KNeighborsClassifier(n_neighbors=1)\n", "from sklearn.cross_validation import KFold\n", "\n", "kf = KFold(len(features), n_folds=5, shuffle=True)\n", + "# `means` will be a list of mean accuracies (one entry per fold)\n", "means = []\n", "for training,testing in kf:\n", " # We learn a model for this fold with `fit` and then apply it to the\n", @@ -321,9 +759,136 @@ " # of correct decisions for this fold:\n", " curmean = np.mean(prediction == labels[testing])\n", " means.append(curmean)\n", - "print('Mean accuracy: {:.1%}'.format(np.mean(means)))\n", + "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6) Looking at the decision boundaries" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "ValueError", + "evalue": "too many values to unpack", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 72\u001b[0m \u001b[0mlabels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnames\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mell\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mell\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlabels\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 73\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 74\u001b[1;33m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0max\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplot_decision\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabels\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 75\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msavefig\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'figure4.png'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 76\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32m\u001b[0m in \u001b[0;36mplot_decision\u001b[1;34m(features, labels)\u001b[0m\n\u001b[0;32m 47\u001b[0m \u001b[0mmodel\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfit_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlabels\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 48\u001b[0m C = predict(\n\u001b[1;32m---> 49\u001b[1;33m np.vstack([X.ravel(), Y.ravel()]).T, model).reshape(X.shape)\n\u001b[0m\u001b[0;32m 50\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mCOLOUR_FIGURE\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 51\u001b[0m \u001b[0mcmap\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mListedColormap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m.6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1.\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\Users\\tvu\\Documents\\GitHub\\BuildingMachineLearningSystemsWithPython\\ch02\\knn.py\u001b[0m in \u001b[0;36mpredict\u001b[1;34m(model, features)\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 30\u001b[0m \u001b[1;34m'''Apply k-nn model'''\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 31\u001b[1;33m \u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_feats\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 32\u001b[0m \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 33\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mf\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mfeatures\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: too many values to unpack" + ] + } + ], + "source": [ + "# %load figure4_5_no_sklearn.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from matplotlib.colors import ListedColormap\n", + "from load import load_dataset\n", + "import numpy as np\n", + "from knn import fit_model, predict\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", "\n", "\n", + "def plot_decision(features, labels):\n", + " '''Plots decision boundary for KNN\n", + "\n", + " Parameters\n", + " ----------\n", + " features : ndarray\n", + " labels : sequence\n", + "\n", + " Returns\n", + " -------\n", + " fig : Matplotlib Figure\n", + " ax : Matplotlib Axes\n", + " '''\n", + " y0, y1 = features[:, 2].min() * .9, features[:, 2].max() * 1.1\n", + " x0, x1 = features[:, 0].min() * .9, features[:, 0].max() * 1.1\n", + " X = np.linspace(x0, x1, 100)\n", + " Y = np.linspace(y0, y1, 100)\n", + " X, Y = np.meshgrid(X, Y)\n", + "\n", + " model = fit_model(1, features[:, (0, 2)], np.array(labels))\n", + " C = predict(\n", + " np.vstack([X.ravel(), Y.ravel()]).T, model).reshape(X.shape)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .6, .6), (.6, 1., .6), (.6, .6, 1.)])\n", + " else:\n", + " cmap = ListedColormap([(1., 1., 1.), (.2, .2, .2), (.6, .6, .6)])\n", + " fig,ax = plt.subplots()\n", + " ax.set_xlim(x0, x1)\n", + " ax.set_ylim(y0, y1)\n", + " ax.set_xlabel(feature_names[0])\n", + " ax.set_ylabel(feature_names[2])\n", + " ax.pcolormesh(X, Y, C, cmap=cmap)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .0, .0), (.0, 1., .0), (.0, .0, 1.)])\n", + " ax.scatter(features[:, 0], features[:, 2], c=labels, cmap=cmap)\n", + " else:\n", + " for lab, ma in zip(range(3), \"Do^\"):\n", + " ax.plot(features[labels == lab, 0], features[\n", + " labels == lab, 2], ma, c=(1., 1., 1.))\n", + " return fig,ax\n", + "\n", + "\n", + "features, labels = load_dataset('seeds')\n", + "names = sorted(set(labels))\n", + "labels = np.array([names.index(ell) for ell in labels])\n", + "\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.savefig('figure4.png')\n", + "\n", + "features -= features.mean(0)\n", + "features /= features.std(0)\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.savefig('figure5.png')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean accuracy: 91.0%\n" + ] + } + ], + "source": [ "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import StandardScaler\n", "\n", @@ -343,6 +908,133 @@ " means.append(curmean)\n", "print('Mean accuracy: {:.1%}'.format(np.mean(means)))" ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ffDPTpk0LOWfq1KlkZ2dTWloaEqAg+nYhVpKHM9kBvG3fEQ/nGqdI3xNPdpgx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\nlX95ye77qTGmyhiz3RiTaYz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0FU87nB6IRqv2oNZDYTpV6EwQR4wgwq6TM0bceLV0imId3Gksb7zxRl64+vfv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\n7s29/ioRnRX1GL1S6lyIaDIR7cndh5e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ZQ2stdndD9zpqNUvaIgUAkTop5dNsd2uWVDaLFOCdUI0aNQozZ87EiBEjMDg4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\nTnzyySeu9PgLh8MYP348Cgo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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# %load figure4_5_sklearn.py\n", + "# This code is supporting material for the book\n", + "# Building Machine Learning Systems with Python\n", + "# by Willi Richert and Luis Pedro Coelho\n", + "# published by PACKT Publishing\n", + "#\n", + "# It is made available under the MIT License\n", + "\n", + "COLOUR_FIGURE = False\n", + "\n", + "from matplotlib import pyplot as plt\n", + "from matplotlib.colors import ListedColormap\n", + "from load import load_dataset\n", + "import numpy as np\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "\n", + "feature_names = [\n", + " 'area',\n", + " 'perimeter',\n", + " 'compactness',\n", + " 'length of kernel',\n", + " 'width of kernel',\n", + " 'asymmetry coefficien',\n", + " 'length of kernel groove',\n", + "]\n", + "\n", + "\n", + "def plot_decision(features, labels, num_neighbors=1):\n", + " '''Plots decision boundary for KNN\n", + "\n", + " Parameters\n", + " ----------\n", + " features : ndarray\n", + " labels : sequence\n", + "\n", + " Returns\n", + " -------\n", + " fig : Matplotlib Figure\n", + " ax : Matplotlib Axes\n", + " '''\n", + " y0, y1 = features[:, 2].min() * .9, features[:, 2].max() * 1.1\n", + " x0, x1 = features[:, 0].min() * .9, features[:, 0].max() * 1.1\n", + " X = np.linspace(x0, x1, 1000)\n", + " Y = np.linspace(y0, y1, 1000)\n", + " X, Y = np.meshgrid(X, Y)\n", + "\n", + " model = KNeighborsClassifier(num_neighbors)\n", + " model.fit(features[:, (0,2)], labels)\n", + " C = model.predict(np.vstack([X.ravel(), Y.ravel()]).T).reshape(X.shape)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .7, .7), (.7, 1., .7), (.7, .7, 1.)])\n", + " else:\n", + " cmap = ListedColormap([(1., 1., 1.), (.2, .2, .2), (.6, .6, .6)])\n", + " fig,ax = plt.subplots()\n", + " ax.set_xlim(x0, x1)\n", + " ax.set_ylim(y0, y1)\n", + " ax.set_xlabel(feature_names[0])\n", + " ax.set_ylabel(feature_names[2])\n", + " ax.pcolormesh(X, Y, C, cmap=cmap)\n", + " if COLOUR_FIGURE:\n", + " cmap = ListedColormap([(1., .0, .0), (.1, .6, .1), (.0, .0, 1.)])\n", + " ax.scatter(features[:, 0], features[:, 2], c=labels, cmap=cmap)\n", + " else:\n", + " for lab, ma in zip(range(3), \"Do^\"):\n", + " ax.plot(features[labels == lab, 0], features[\n", + " labels == lab, 2], ma, c=(1., 1., 1.), ms=6)\n", + " return fig,ax\n", + "\n", + "\n", + "features, labels = load_dataset('seeds')\n", + "names = sorted(set(labels))\n", + "labels = np.array([names.index(ell) for ell in labels])\n", + "\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.tight_layout()\n", + "fig.savefig('figure4sklearn.png')\n", + "\n", + "features -= features.mean(0)\n", + "features /= features.std(0)\n", + "fig,ax = plot_decision(features, labels)\n", + "fig.tight_layout()\n", + "fig.savefig('figure5sklearn.png')\n", + "\n", + "fig,ax = plot_decision(features, labels, 11)\n", + "fig.tight_layout()\n", + "fig.savefig('figure5sklearn_with_11_neighbors.png')\n" + ] } ], "metadata": { diff --git a/ch02/figure1.png b/ch02/figure1.png new file mode 100644 index 0000000000000000000000000000000000000000..cce3cfc57f75998b2ca4c34e4505c75c65f99d10 GIT binary patch literal 31997 zcmb@ubx>B}-zR+2-AH!{NOyyDDy1ML-Hk|>(v5@&(v5U?cSv`qba(E>Z}*vbc6Q!B z-q~daygA(7=bS6P@re_n{7wc9nFtvIfuPCBN~%I2P-Wno0ude@nWCq&0RO-`iOZ=Y zf-g@*<6!VRlD+IFCkO-u`{f&Ie98L(0-=D&NxoHg{e6()qVqxK?pgGwUUo3ttG7jx zaB-RDu#}7mr36q4*bzh#be|+9%`1{LzcGh|^dwZ=D~wG}%^LB%T|)eZ7C&YF#Ym=1 zIv^N6`s(2+(c?(CcEzdw)xSsgrJw(X7&rx@%uG{nhd4Q?sO+J zBD7uGe-1^Tz=wCP+4G?z{a+lY)1=1vrDz&q&G)fme5|*wnM1VI*$$EQ$-IBRG98}6kv|0f5c_`18r^it1+Sfg?r z_^!~wUHz8%-62jPOxo9P(0cJDp{JZY{LnaYoX}wtJ$&lhts|LmB$;q%Q)i{v82}j4ZM{ z44;~YrfXA(Z<|__{N_kdf0*d2hz${&DJmwuS?aZRmIygqa(}DDus%bx3DN!C&nQnLVleW$UUK=GbAnCLC?#IfrvIGy3W7?|1MQM zHBAVq%C7V_y!@J*pbxR-W*sFoG&HlSic72E3xn6)ZeG>bL#=_nzVw|Pb0Sf1A>DdM 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