Diagnoal Squares.ipynb

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   ],
   "source": [
    "using LinearAlgebra, Interact, Plots"
   ]
  },
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     "data": {
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       "13×13 Array{Int64,2}:\n",
       " 0  0  0  0  0  0  1  0  0  0  0  0  0\n",
       " 0  0  0  0  0  1  1  1  0  0  0  0  0\n",
       " 0  0  0  0  1  1  1  1  1  0  0  0  0\n",
       " 0  0  0  1  1  1  1  1  1  1  0  0  0\n",
       " 0  0  1  1  1  1  1  1  1  1  1  0  0\n",
       " 0  1  1  1  1  1  1  1  1  1  1  1  0\n",
       " 0  0  1  1  1  1  1  1  1  1  1  0  0\n",
       " 0  0  0  1  1  1  1  1  1  1  0  0  0\n",
       " 0  0  0  0  1  1  1  1  1  0  0  0  0\n",
       " 0  0  0  0  0  1  1  1  0  0  0  0  0\n",
       " 0  0  0  0  0  0  1  0  0  0  0  0  0\n",
       " 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"
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     "execution_count": 6,
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   ],
   "source": [
    "3"
   ]
  },
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   "execution_count": 7,
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       "13×13 Array{Int64,2}:\n",
       "  3  -1   0   0   0   0   0   0   0  -1   3  0  0\n",
       " -1   2  -1   0   0   0   0   0  -1   2  -1  0  0\n",
       "  0  -1   2  -1   0   0   0  -1   2  -1   0  0  0\n",
       "  0   0  -1   2  -1   0  -1   2  -1   0   0  0  0\n",
       "  0   0   0  -1   2  -2   2  -1   0   0   0  0  0\n",
       "  0   0   0   0  -2   4  -2   0   0   0   0  0  0\n",
       "  0   0   0  -1   2  -2   2  -1   0   0   0  0  0\n",
       "  0   0  -1   2  -1   0  -1   2  -1   0   0  0  0\n",
       "  0  -1   2  -1   0   0   0  -1   2  -1   0  0  0\n",
       " -1   2  -1   0   0   0   0   0  -1   2  -1  0  0\n",
       "  3  -1   0   0   0   0   0   0   0  -1   3  0  0\n",
       "  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"
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   "source": [
    "A*A'\n",
    "B=Int.(round.(pinv(A*A')*8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a crisscross. 2 in the center with -1 above and below -1. 3 in the corner. 4 surroundd by -2 in the center due to overlap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using UnicodePlots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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    {
     "data": {
      "text/plain": [
       "\u001b[1m      Sparsity Pattern\u001b[22m\n",
       "\u001b[90m      ┌───────┐\u001b[39m    \n",
       "    \u001b[90m1\u001b[39m\u001b[90m │\u001b[39m\u001b[35m⠰\u001b[39m\u001b[35m⣦\u001b[39m\u001b[34m⡀\u001b[39m\u001b[0m⠀\u001b[35m⣠\u001b[39m\u001b[35m⡶\u001b[39m\u001b[0m⠀\u001b[90m│\u001b[39m \u001b[31m> 0\u001b[39m\n",
       "     \u001b[90m │\u001b[39m\u001b[0m⠀\u001b[34m⠈\u001b[39m\u001b[35m⠻\u001b[39m\u001b[35m⠾\u001b[39m\u001b[35m⠋\u001b[39m\u001b[0m⠀\u001b[0m⠀\u001b[90m│\u001b[39m \u001b[34m< 0\u001b[39m\n",
       "     \u001b[90m │\u001b[39m\u001b[34m⢀\u001b[39m\u001b[35m⣴\u001b[39m\u001b[35m⠟\u001b[39m\u001b[35m⠙\u001b[39m\u001b[35m⢷\u001b[39m\u001b[35m⣄\u001b[39m\u001b[0m⠀\u001b[90m│\u001b[39m    \n",
       "   \u001b[90m13\u001b[39m\u001b[90m │\u001b[39m\u001b[31m⠈\u001b[39m\u001b[34m⠁\u001b[39m\u001b[0m⠀\u001b[0m⠀\u001b[0m⠀\u001b[35m⠉\u001b[39m\u001b[0m⠀\u001b[90m│\u001b[39m    \n",
       "\u001b[90m      └───────┘\u001b[39m    \n",
       "\u001b[90m      1\u001b[39m\u001b[90m   \u001b[39m\u001b[90m   13\u001b[39m\n",
       "\u001b[0m      nz = 57"
      ]
     },
     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "UnicodePlots.spy(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
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   "source": [
    "3+2"
   ]
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   "execution_count": 8,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "Plots.PlotlyBackend()"
      ]
     },
     "execution_count": 8,
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   "source": [
    "plotly()"
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               },
               "type": "node"
              }
             ],
             "instanceArgs": {
              "namespace": "html",
              "tag": "div"
             },
             "nodeType": "DOM",
             "props": {
              "className": "interact-flex-row interact-widget"
             },
             "type": "node"
            }
           }
          },
          "systemjs_options": null
         },
         "nodeType": "Scope",
         "props": {},
         "type": "node"
        }
       ],
       "instanceArgs": {
        "namespace": "html",
        "tag": "div"
       },
       "nodeType": "DOM",
       "props": {},
       "type": "node"
      },
      "text/html": [
       "<div\n",
       "    class=\"webio-mountpoint\"\n",
       "    data-webio-mountpoint=\"11049335783665900241\"\n",
       ">\n",
       "    <script>\n",
       "    if (window.require && require.defined && require.defined(\"nbextensions/webio/main\")) {\n",
       "        console.log(\"Jupyter WebIO extension detected, not mounting.\");\n",
       "    } else if (window.WebIO) {\n",
       "        WebIO.mount(\n",
       "            document.querySelector('[data-webio-mountpoint=\"11049335783665900241\"]'),\n",
       "            {\"props\":{},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"field interact-widget\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{},\"nodeType\":\"Scope\",\"type\":\"node\",\"instanceArgs\":{\"imports\":{\"data\":[{\"name\":\"knockout\",\"type\":\"js\",\"url\":\"\\/assetserver\\/13343124133b197c0e073adb2f41642d90e90c3b-knockout.js\"},{\"name\":\"knockout_punches\",\"type\":\"js\",\"url\":\"\\/assetserver\\/56c6e466c4398af333cf30a2083dbb4a8f193711-knockout_punches.js\"},{\"name\":null,\"type\":\"js\",\"url\":\"\\/assetserver\\/026909c53d9c67b1ec7ad48eecff7976b5afbaec-all.js\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/9802c3a0a490e346147d3fa6034b48fef7565660-style.css\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/4f8d310203e2eb782fa2a8edc8e0af0819838eb9-bulma_confined.min.css\"}],\"type\":\"async_block\"},\"id\":\"knockout-component-55936b86-1a77-43dd-b85a-6fde9c0d46dc\",\"handlers\":{\"changes\":[\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\"],\"index\":[\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\"]},\"systemjs_options\":null,\"mount_callbacks\":[\"function () {\\n    var handler = (function (ko, koPunches) {\\n    ko.punches.enableAll();\\n    ko.bindingHandlers.numericValue = {\\n        init : function(element, valueAccessor, allBindings, data, context) {\\n            var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n            stringified.subscribe(function(value) {\\n                var val = parseFloat(value);\\n                if (!isNaN(val)) {\\n                    valueAccessor()(val);\\n                }\\n            })\\n            valueAccessor().subscribe(function(value) {\\n                var str = JSON.stringify(value);\\n                if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n                     return;\\n                 if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n                     return;\\n                stringified(str);\\n            })\\n            ko.applyBindingsToNode(element, { value: stringified, valueUpdate: allBindings.get('valueUpdate')}, context);\\n        }\\n    };\\n    var json_data = {\\\"formatted_vals\\\":[\\\"1\\\",\\\"2\\\",\\\"3\\\",\\\"4\\\",\\\"5\\\",\\\"6\\\",\\\"7\\\",\\\"8\\\",\\\"9\\\",\\\"10\\\",\\\"11\\\",\\\"12\\\",\\\"13\\\",\\\"14\\\",\\\"15\\\",\\\"16\\\",\\\"17\\\",\\\"18\\\",\\\"19\\\",\\\"20\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"knockout-component-55936b86-1a77-43dd-b85a-6fde9c0d46dc\\\",\\\"id\\\":\\\"ob_02\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"knockout-component-55936b86-1a77-43dd-b85a-6fde9c0d46dc\\\",\\\"id\\\":\\\"ob_01\\\",\\\"type\\\":\\\"observable\\\"})};\\n    var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-1];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"knockout-component-55936b86-1a77-43dd-b85a-6fde9c0d46dc\\\",\\\"id\\\":\\\"ob_02\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? 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(WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"knockout-component-616e1977-37c8-44d0-9d32-e9c25938019b\\\",\\\"id\\\":\\\"ob_03\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/13343124133b197c0e073adb2f41642d90e90c3b-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/56c6e466c4398af333cf30a2083dbb4a8f193711-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol,Any}(:className=>\"field interact-widget\"), 1), Node{DOM}(DOM(:html, :div), Any[Scope(\"knockout-component-c89cdec2-77a6-4ae9-81ef-afd7ac0c635c\", Node{DOM}(DOM(:html, :div), Any[Node{DOM}(DOM(:html, :div), Any[Node{DOM}(DOM(:html, :label), Any[\"j\"], Dict{Symbol,Any}(:className=>\"interact \",:style=>Dict{Any,Any}(:padding=>\"5px 10px 0px 10px\")), 1)], Dict{Symbol,Any}(:className=>\"interact-flex-row-left\"), 2), Node{DOM}(DOM(:html, :div), Any[Node{DOM}(DOM(:html, :input), Any[], Dict{Symbol,Any}(:max=>40,:min=>20,:attributes=>Dict{Any,Any}(:type=>\"range\",Symbol(\"data-bind\")=>\"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\"=>\"horizontal\"),:step=>5,:className=>\"slider slider is-fullwidth\",:style=>Dict{Any,Any}()), 0)], Dict{Symbol,Any}(:className=>\"interact-flex-row-center\"), 1), Node{DOM}(DOM(:html, :div), Any[Node{DOM}(DOM(:html, :p), Any[], Dict{Symbol,Any}(:attributes=>Dict(\"data-bind\"=>\"text: formatted_val\")), 0)], Dict{Symbol,Any}(:className=>\"interact-flex-row-right\"), 1)], Dict{Symbol,Any}(:className=>\"interact-flex-row interact-widget\"), 7), Dict{String,Tuple{Observables.AbstractObservable,Union{Nothing, Bool}}}(\"changes\"=>(Observable{Int64} with 1 listeners. 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       "30, nothing)), Set(String[]), nothing, Asset[Asset(\"js\", \"knockout\", \"/Users/daniel/.julia/packages/Knockout/JE2Yq/src/../assets/knockout.js\"), Asset(\"js\", \"knockout_punches\", \"/Users/daniel/.julia/packages/Knockout/JE2Yq/src/../assets/knockout_punches.js\"), Asset(\"js\", nothing, \"/Users/daniel/.julia/packages/InteractBase/R8JgH/src/../assets/all.js\"), Asset(\"css\", nothing, \"/Users/daniel/.julia/packages/InteractBase/R8JgH/src/../assets/style.css\"), Asset(\"css\", nothing, \"/Users/daniel/.julia/packages/Interact/0klKX/src/../assets/bulma_confined.min.css\")], Dict{Any,Any}(\"changes\"=>Any[JSString(\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\")],\"index\"=>Any[JSString(\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\")]), ConnectionPool(Channel{Any}(sz_max:9223372036854775807,sz_curr:0), Set(AbstractConnection[]), Channel{AbstractConnection}(sz_max:32,sz_curr:0)), WebIO.JSString[JSString(\"function () {\\n    var handler = (function (ko, koPunches) {\\n    ko.punches.enableAll();\\n    ko.bindingHandlers.numericValue = {\\n        init : function(element, valueAccessor, allBindings, data, context) {\\n            var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n            stringified.subscribe(function(value) {\\n                var val = parseFloat(value);\\n                if (!isNaN(val)) {\\n                    valueAccessor()(val);\\n                }\\n            })\\n            valueAccessor().subscribe(function(value) {\\n                var str = JSON.stringify(value);\\n                if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n                     return;\\n                 if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n                     return;\\n                stringified(str);\\n            })\\n            ko.applyBindingsToNode(element, { value: stringified, valueUpdate: allBindings.get('valueUpdate')}, context);\\n        }\\n    };\\n    var json_data = {\\\"formatted_vals\\\":[\\\"20\\\",\\\"25\\\",\\\"30\\\",\\\"35\\\",\\\"40\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"knockout-component-c89cdec2-77a6-4ae9-81ef-afd7ac0c635c\\\",\\\"id\\\":\\\"ob_06\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"knockout-component-c89cdec2-77a6-4ae9-81ef-afd7ac0c635c\\\",\\\"id\\\":\\\"ob_05\\\",\\\"type\\\":\\\"observable\\\"})};\\n    var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-1];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"knockout-component-c89cdec2-77a6-4ae9-81ef-afd7ac0c635c\\\",\\\"id\\\":\\\"ob_06\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"knockout-component-c89cdec2-77a6-4ae9-81ef-afd7ac0c635c\\\",\\\"id\\\":\\\"ob_05\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/13343124133b197c0e073adb2f41642d90e90c3b-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/56c6e466c4398af333cf30a2083dbb4a8f193711-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol,Any}(:className=>\"field interact-widget\"), 1), Observable{Any} with 0 listeners. Value:\n",
       "Node{DOM}(DOM(:html, :div), Any[[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0]], Dict{Symbol,Any}(:className=>\"interact-flex-row interact-widget\"), 1)], Dict{Symbol,Any}(), 4)"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "application/vnd.webio.node+json": {
       "kernelId": "55de57ea-e07f-486e-a6cc-05127324d517"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@manipulate for n = 1:1:20, i = 20:5:40, j = 20:5:40\n",
    "    A = fill(0,100,100);\n",
    "    for a=0:n\n",
    "        A[i.+((a-n):(n-a)),j.+((-a):(a))].=1  #this line that needs to change.\n",
    "    end\n",
    "    svdvals(A)[1:10]\n",
    "    A\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "281\n",
      "282\n",
      "283\n",
      "284\n",
      "285\n",
      "286\n",
      "287\n",
      "288\n",
      "289\n",
      "290\n",
      "291\n",
      "292\n",
      "293\n",
      "294\n",
      "295\n",
      "296\n",
      "297\n",
      "298\n",
      "299\n",
      "300\n",
      "all done\n"
     ]
    }
   ],
   "source": [
    "x=[]\n",
    "y1=[]\n",
    "y2=[]\n",
    "y3=[]\n",
    "y4=[]\n",
    "y5=[]\n",
    "\n",
    "for n = 1:1:300\n",
    "    A = fill(0,1000,1000); #creates a really big matrix.\n",
    "    i, j = 500, 500 #start at center to prevent us going off the edge\n",
    "    for a = 0:n\n",
    "        A[i.+((a-n):(n-a)),j.+((-a):(a))].=1  #makes the diamond\n",
    "    end\n",
    "    push!(y1,svdvals(A)[1]) #list of first singular value\n",
    "    push!(y2,svdvals(A)[2]) #list of second singular value\n",
    "    push!(y3,svdvals(A)[3]) #list of third singular value\n",
    "    push!(y4,svdvals(A)[4]) #list of fourth singular value\n",
    "    push!(y5,svdvals(A)[5]) #list of fifth singular value\n",
    "    println(n)\n",
    "\n",
    "\n",
    "end\n",
    "println(\"all done\")\n",
    "#scatter([y1,y2,y3,y4,y5],legend=:left, labels=[\"sigma1\",\"sigma2\",\"sigma3\",\"sigma4\",\"sigma5\"])\n",
    "#scatter!(y2,legend=false)\n",
    "#scatter!(y3,legend=false)\n",
    "#scatter!(y4,legend=false)\n",
    "#scatter!(1:1:40,y5,legend=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.PyPlotBackend()"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyplot()\n",
    "#scatter(x,y1,legend=:left, labels=\"sigma1\", xlabel=\"half of the diagnol length\", title=\"singular values\")\n",
    "#scatter(x,y2, labels=\"sigma2\")\n",
    "#scatter!(x,y3,labels=\"sigma3\")\n",
    "#scatter!(x,y4,labels=\"sigma4\")\n",
    "#scatter!(x,y5,labels=\"sigma5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 600x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(1:30,y1[1:30],legend=:left, labels=\"sigma1\", xlabel=\"half of the diagonal length\", title=\"Singular Values\", ms=6)\n",
    "scatter!(1:30,y2[1:30], labels=\"sigma2\", ms=6)\n",
    "scatter!(1:30,y3[1:30],labels=\"sigma3\", ms=6)\n",
    "savefig(\"diagnolsquare1.png\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 600x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(1:300,y1,legend=:left, labels=\"sigma1\", xlabel=\"half of the diagonal length\", title=\"Singular Values\", ms=6)\n",
    "scatter!(1:300,y2, labels=\"sigma2\",ms=6)\n",
    "scatter!(1:300,y3,labels=\"sigma3\",ms=6)\n",
    "scatter!(1:300,y4,labels=\"sigma4\",ms=6)\n",
    "scatter!(1:300,y5,labels=\"sigma5\",ms=6)\n",
    "savefig(\"diagnolsquare2.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.6677801739674971\n",
       " 1.2723113839530213"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:40\n",
    "m=[ones(40) x]\n",
    "m\\float.(y1[1:40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.6440176675395933\n",
       " 1.2732069181299916"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:300\n",
    "m=[ones(300) x]\n",
    "m\\float.(y1[1:300])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.6875530887855904  \n",
       " 1.269486681836151   \n",
       " 6.889517358220293e-5"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:40\n",
    "m=[ones(40) x x.^2]\n",
    "m\\float.(y1[1:40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.6501751663218943  \n",
       " 1.2730845837170985  \n",
       " 4.064266209056828e-7"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:300\n",
    "m=[ones(300) x x.^2]\n",
    "m\\float.(y1[1:300])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the first sigma value we have about 0.668 + 1.27 * n = sigma value. We also see that x^2 coeeficent for a polynominal formula is very small. Taking a larger sample size cause the polynominal to get even smaller now lets look look at the loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00014306595628136657"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:40\n",
    "\n",
    "m=[ones(40) x]\n",
    "\n",
    "f1=m\\float.(y1[1:40])\n",
    "\n",
    "sum((m*f1-y1[1:40]).^2)/40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.104098112513614e-5"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=1:300\n",
    "m=[ones(300) x]\n",
    "f1=m\\float.(y1[1:300])\n",
    "sum((m*f1-y1).^2)/300"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average loss is small and our equation is a very good fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "ename": "DimensionMismatch",
     "evalue": "DimensionMismatch(\"left hand side has 39 rows, but right hand side has 299 rows\")",
     "output_type": "error",
     "traceback": [
      "DimensionMismatch(\"left hand side has 39 rows, but right hand side has 299 rows\")",
      "",
      "Stacktrace:",
      " [1] \\(::QRPivoted{Float64,Array{Float64,2}}, ::Array{Float64,1}) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/qr.jl:857",
      " [2] \\(::Array{Float64,2}, ::Array{Float64,1}) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/generic.jl:907",
      " [3] top-level scope at In[18]:3"
     ]
    }
   ],
   "source": [
    "x=2:40\n",
    "m=[ones(39) x]\n",
    "m\\float.(y2[2:end])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.33502211773404045   \n",
       " 0.4160628670845756    \n",
       " 0.00014740405776619267"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=2:40\n",
    "m=[ones(39) x x.^2]\n",
    "m\\float.(y2[2:40])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still linear but a lot less linear (we drop the 0 value cause it is an outlier)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.27654245874423466\n",
       " 0.4226928369143208 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.30622412717010106   \n",
       " 0.24320321212347806   \n",
       " 0.00019562140368996673"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=3:40\n",
    "m=[ones(38) x]\n",
    "display(m\\float.(y2[3:40]))\n",
    "\n",
    "x=3:40\n",
    "m=[ones(38) x x.^2]\n",
    "display(m\\float.(y3[3:1:40]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks really similar to the second sigma value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "No current plot/subplot",
     "output_type": "error",
     "traceback": [
      "No current plot/subplot",
      "",
      "Stacktrace:",
      " [1] error(::String) at ./error.jl:33",
      " [2] current at /Users/daniel/.julia/packages/Plots/47Tik/src/plot.jl:15 [inlined]",
      " [3] savefig(::String) at /Users/daniel/.julia/packages/Plots/47Tik/src/output.jl:123",
      " [4] top-level scope at In[21]:1"
     ]
    }
   ],
   "source": [
    "\n",
    "savefig(\"diagnolsquare2.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.999897500496883"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " 1.2732069181299916 * π"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.02324117312442"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.6440176675395933 * π"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "syntax: extra token \"a\" after end of expression",
     "output_type": "error",
     "traceback": [
      "syntax: extra token \"a\" after end of expression",
      ""
     ]
    }
   ],
   "source": [
    "For a diamond. (4n+2)/pi"
   ]
  }
 ],
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