{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/javascript": [ "if(window['d3'] === undefined ||\n", " window['Nyaplot'] === undefined){\n", " var path = {\"d3\":\"https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min\",\"downloadable\":\"http://cdn.rawgit.com/domitry/d3-downloadable/master/d3-downloadable\"};\n", "\n", "\n", "\n", " var shim = {\"d3\":{\"exports\":\"d3\"},\"downloadable\":{\"exports\":\"downloadable\"}};\n", "\n", " require.config({paths: path, shim:shim});\n", "\n", "\n", "require(['d3'], function(d3){window['d3']=d3;console.log('finished loading d3');require(['downloadable'], function(downloadable){window['downloadable']=downloadable;console.log('finished loading downloadable');\n", "\n", "\tvar script = d3.select(\"head\")\n", "\t .append(\"script\")\n", "\t .attr(\"src\", \"http://cdn.rawgit.com/domitry/Nyaplotjs/master/release/nyaplot.js\")\n", "\t .attr(\"async\", true);\n", "\n", "\tscript[0][0].onload = script[0][0].onreadystatechange = function(){\n", "\n", "\n", "\t var event = document.createEvent(\"HTMLEvents\");\n", "\t event.initEvent(\"load_nyaplot\",false,false);\n", "\t window.dispatchEvent(event);\n", "\t console.log('Finished loading Nyaplotjs');\n", "\n", "\t};\n", "\n", "\n", "});});\n", "}\n" ], "text/plain": [ "\"if(window['d3'] === undefined ||\\n window['Nyaplot'] === undefined){\\n var path = {\\\"d3\\\":\\\"https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min\\\",\\\"downloadable\\\":\\\"http://cdn.rawgit.com/domitry/d3-downloadable/master/d3-downloadable\\\"};\\n\\n\\n\\n var shim = {\\\"d3\\\":{\\\"exports\\\":\\\"d3\\\"},\\\"downloadable\\\":{\\\"exports\\\":\\\"downloadable\\\"}};\\n\\n require.config({paths: path, shim:shim});\\n\\n\\nrequire(['d3'], function(d3){window['d3']=d3;console.log('finished loading d3');require(['downloadable'], function(downloadable){window['downloadable']=downloadable;console.log('finished loading downloadable');\\n\\n\\tvar script = d3.select(\\\"head\\\")\\n\\t .append(\\\"script\\\")\\n\\t .attr(\\\"src\\\", \\\"http://cdn.rawgit.com/domitry/Nyaplotjs/master/release/nyaplot.js\\\")\\n\\t .attr(\\\"async\\\", true);\\n\\n\\tscript[0][0].onload = script[0][0].onreadystatechange = function(){\\n\\n\\n\\t var event = document.createEvent(\\\"HTMLEvents\\\");\\n\\t event.initEvent(\\\"load_nyaplot\\\",false,false);\\n\\t window.dispatchEvent(event);\\n\\t console.log('Finished loading Nyaplotjs');\\n\\n\\t};\\n\\n\\n});});\\n}\\n\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "true" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "require 'nyaplot'" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "require 'daru'" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ ":resolve" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N = 10\n", "M = [0, 1, 3, 9]\n", "\n", "def normal_rand(mu = 0, sigma = 1.0)\n", " random = Random.new\n", " (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu\n", "end\n", "\n", "\n", "def create_dataset(num)\n", " dataset = Daru::DataFrame.new({'x': [], 'y': []}) \n", "\n", " num.times do |i|\n", " x = i.to_f / (num - 1).to_f\n", " y = Math.sin(2 * Math::PI * x) + normal_rand(0, 0.3)\n", " dataset.add_row(Daru::Vector.new([x, y], index: [:x, :y]))\n", " end\n", " \n", " return dataset\n", "end\n", "\n", "def rms_error(dataset, f)\n", " err = 0.0\n", " dataset.each_row do |line|\n", " err += 0.5 * (line.y - f.call(line.x))**2\n", " end\n", "\n", " Math.sqrt(2 * err / dataset.size)\n", "end\n", "\n", "def resolve(dataset, m)\n", " t = dataset.y\n", "\n", " columns = {}\n", " (m+1).times do |i|\n", " columns[\"x**#{i}\"] = dataset.x ** i\n", " end\n", " phi = Daru::DataFrame.new(columns)\n", "\n", " tmp = (phi.transpose.to_matrix * phi.to_matrix).inv\n", " ws = (tmp * phi.transpose.to_matrix) * Vector.elements(t.to_a)\n", "\n", " f = lambda {|x|\n", " y = 0\n", " ws.each_with_index do |w, i|\n", " y += w * (x ** i)\n", " end\n", "\n", " y\n", " }\n", "\n", " return f, ws\n", "end\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Table ot the coefficients\n", "#\n", " M=0 M=1 M=3 M=9\n", " 0 -0.0651390 0.71921545 0.27349850 0.49988837\n", " 1 nil -1.5687089 8.12152893 114.506346\n", " 2 nil nil -28.212160 -2833.6958\n", " 3 nil nil 19.8975562 26750.7509\n", " 4 nil nil nil -128370.52\n", " 5 nil nil nil 351243.492\n", " 6 nil nil nil -572297.82\n", " 7 nil nil nil 549787.641\n", " 8 nil nil nil -287517.24\n", " 9 nil nil nil 63122.5835\n" ] }, { "data": { "text/html": [ "
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\n", "\n" ], "text/plain": [ "#[#[#:line, :options=>{:x=>:m, :y=>:\"Training set\", :title=>\"Training set\", :color=>\"blue\"}, :data=>\"c4713cff-c1d4-4612-b491-01323b4c6f4d\"}, @xrange=[0, 9], @yrange=[0.00011288602808587366, 0.7477820680605471]>, #:line, :options=>{:x=>:m, :y=>:\"Test set\", :title=>\"Test set\", :color=>\"green\"}, :data=>\"c4713cff-c1d4-4612-b491-01323b4c6f4d\"}, @xrange=[0, 9], @yrange=[0.410798637308882, 0.7901802535073036]>], :options=>{:x_label=>\"M\", :y_label=>\"RMS Error\", :yrange=>[0, 0.9], :legend=>true, :zoom=>true, :width=>800, :xrange=>[0, 9]}}>], :data=>{\"c4713cff-c1d4-4612-b491-01323b4c6f4d\"=>#0.7901802535073036, :\"Training set\"=>0.7477820680605471, :m=>0}, {:\"Test set\"=>0.6200049263932269, :\"Training set\"=>0.5554602636648857, :m=>1}, {:\"Test set\"=>0.6619201379663371, :\"Training set\"=>0.5357657333954127, :m=>2}, {:\"Test set\"=>0.4212656591284058, :\"Training set\"=>0.23861181391981123, :m=>3}, {:\"Test set\"=>0.4312430650725292, :\"Training set\"=>0.217134263059091, :m=>4}, {:\"Test set\"=>0.410798637308882, :\"Training set\"=>0.2035366396183082, :m=>5}, {:\"Test set\"=>0.4856996161055811, :\"Training set\"=>0.11275704213088493, :m=>6}, {:\"Test set\"=>0.49628366279645847, :\"Training set\"=>0.09302530588062327, :m=>7}, {:\"Test set\"=>0.5172729982325514, :\"Training set\"=>0.08474052811982946, :m=>8}, {:\"Test set\"=>0.5351527358812507, :\"Training set\"=>0.00011288602808587366, :m=>9}]>}, :extension=>[]}>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train_set = create_dataset(N)\n", "test_set = create_dataset(N)\n", "df_ws = {}\n", "\n", "fig = Nyaplot::Frame.new\n", "\n", "M.each_with_index do |m, c|\n", " f, ws = resolve(train_set, m)\n", " df_ws[\"M=#{m}\"] = Daru::Vector.new(ws, name: \"M=#{m}\")\n", " \n", " plot = Nyaplot::Plot.new\n", " sc = plot.add_with_df(train_set.to_nyaplotdf, :scatter, :x, :y)\n", " sc.title(\"train_set\")\n", " sc.color('blue')\n", " \n", " linex = (0..1).step(1.0 / (101 - 1)).to_a\n", " liney = linex.map do |x|\n", " Math.sin(2 * Math::PI * x)\n", " end\n", " line_answer = plot.add(:line, linex, liney)\n", " line_answer.title('answer')\n", " line_answer.color('green')\n", " \n", " liney = linex.map do |x|\n", " f.call(x)\n", " end\n", " line_erms = plot.add(:line, linex, liney)\n", " line_erms.title(\"E(RMS#{sprintf(\"%.2f\", rms_error(train_set, f))})\")\n", " line_erms.color('red')\n", "\n", " plot.configure do\n", " x_label(\"M=#{m}\")\n", " y_label('')\n", " xrange([-0.05, 1.05])\n", " yrange([-1.5, 1.5])\n", " legend(true)\n", " height(300)\n", " width(490)\n", " end\n", " \n", " fig.add(plot)\n", "end\n", "\n", "puts 'Table ot the coefficients'\n", "puts Daru::DataFrame.new(df_ws).inspect\n", "\n", "fig.show\n", "\n", "df = Daru::DataFrame.new({m: [], 'Training set': [], 'Test set': []}) \n", "10.times do |m|\n", " f, ws = resolve(train_set, m)\n", " train_error = rms_error(train_set, f)\n", " test_error = rms_error(test_set, f)\n", " df.add_row(Daru::Vector.new([m, train_error, test_error], index: [:m, 'Training set'.to_sym, 'Test set'.to_sym]))\n", "end\n", "\n", "df.plot(type: [:line, :line], x: [:m, :m], y: ['Training set'.to_sym, 'Test set'.to_sym]) do |plot, diagrams|\n", " train_set_diagram = diagrams[0]\n", " test_set_diagram = diagrams[1]\n", " \n", " train_set_diagram.title('Training set')\n", " train_set_diagram.color('blue')\n", " test_set_diagram.title('Test set')\n", " test_set_diagram.color('green')\n", " \n", " plot.x_label('M')\n", " plot.y_label('RMS Error')\n", " plot.yrange([0, 0.9])\n", " plot.legend(true)\n", "end" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Ruby 2.3.1", "language": "ruby", "name": "ruby" }, "language_info": { "file_extension": ".rb", "mimetype": "application/x-ruby", "name": "ruby", "version": "2.3.1" } }, "nbformat": 4, "nbformat_minor": 0 }