02-square_error.ipynb

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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "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",
      "#<Daru::DataFrame(10x4)>\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": [
       "<div id='vis-8d4ef26c-ed6e-46fc-9ed7-a6f990e43b80'></div>\n",
       "<script>\n",
       "(function(){\n",
       "    var render = function(){\n",
       "        var model = 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       "        var id_name = '#vis-8d4ef26c-ed6e-46fc-9ed7-a6f990e43b80';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
      ],
      "text/plain": [
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       "<div id='vis-91c03db4-1f2a-40f6-9da2-3984bb798639'></div>\n",
       "<script>\n",
       "(function(){\n",
       "    var render = function(){\n",
       "        var model = {\"panes\":[{\"diagrams\":[{\"type\":\"line\",\"options\":{\"x\":\"m\",\"y\":\"Training set\",\"title\":\"Training set\",\"color\":\"blue\"},\"data\":\"c4713cff-c1d4-4612-b491-01323b4c6f4d\"},{\"type\":\"line\",\"options\":{\"x\":\"m\",\"y\":\"Test set\",\"title\":\"Test set\",\"color\":\"green\"},\"data\":\"c4713cff-c1d4-4612-b491-01323b4c6f4d\"}],\"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\":[{\"Test set\":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\":[]}\n",
       "        var id_name = '#vis-91c03db4-1f2a-40f6-9da2-3984bb798639';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
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       "\treturn;\n",
       "    } else {\n",
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      "text/plain": [
       "#<Nyaplot::Frame:0x007fce16abf478 @properties={:panes=>[#<Nyaplot::Plot:0x007fce16af6c48 @properties={:diagrams=>[#<Nyaplot::Diagram:0x007fce16ac44a0 @properties={:type=>: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]>, #<Nyaplot::Diagram:0x007fce16abfd88 @properties={:type=>: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\"=>#<Nyaplot::DataFrame:0x007fce16ac4c98 @name=\"c4713cff-c1d4-4612-b491-01323b4c6f4d\", @rows=[{:\"Test set\"=>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=>[]}>"
      ]
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "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": []
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