TARGETS += switchchain_canonical_creationfreqs

#include "exports.hpp"

#include "graph.hpp"

#include "graph_powerlaw.hpp"

#include "graph_spectrum.hpp"

#include "switchchain.hpp"

#include <algorithm>

#include <fstream>

#include <iostream>

#include <numeric>

#include <random>

#include <vector>

int main(int argc, char* argv[]) {

    // Simulation parameters

    const int numVerticesMin = 10000;

    const int numVerticesMax = 10000;

    const int numVerticesStep = 1000;

    float tauValues[] = {2.1f, 2.5f, 2.9f};

    auto getMixingTime = [](int n, float tau) {

        return int(100.0f * (50.0f - 5.0f * (tau - 2.0f)) * n);

    };

    auto getMeasurements = [](int n, float tau) {

        (void)n;

        (void)tau;

        return 5000000;

    };

    // Output file

    std::ofstream outfile;

    if (argc >= 2)

        outfile.open(argv[1]);

    else

        outfile.open("graphdata_canonical_creationfreqs.m");

    if (!outfile.is_open()) {

        std::cout << "ERROR: Could not open output file.\n";

        return 1;

    }

    // Output Mathematica-style comment to indicate file contents

    outfile << "(*\n";

    outfile << "n from " << numVerticesMin << " to " << numVerticesMax

            << " step " << numVerticesStep << std::endl;

    outfile << "tauValues: " << tauValues << std::endl;

    outfile << "Canonical degree sequence.\n";

    outfile << "mixingTime: 100 * (50 - 5 (tau - 2)) n\n";

    outfile << "measurements: 5000000\n";

    outfile << "measureSkip: 0\n";

    outfile << "histogram is conditioned on successful switches\n";

    outfile << "data:\n";

    outfile << "1: {n,tau}\n";

    outfile << "2: { {delta1, freq1} , {delta2, freq2} , ... }\n";

    outfile << "3: {successful switches, total attempted switches}\n";

    outfile << "*)" << std::endl;

    // Mathematica does not accept normal scientific notation

    outfile << std::fixed;

    outfile << '{' << '\n';

    bool outputComma = false;

    Graph g;

    for (int numVertices = numVerticesMin; numVertices <= numVerticesMax;

         numVertices += numVerticesStep) {

        for (float tau : tauValues) {

            DegreeSequence ds;

            generateCanonicalPowerlawGraph(numVertices, tau, g, ds);

            SwitchChain chain;

            if (!chain.initialize(g)) {

                std::cerr << "Could not initialize Markov chain.\n";

                return 1;

            }

            std::cout << "Running (n,tau) = (" << numVertices << ',' << tau

                      << "). " << std::flush;

            // Mix

            int mixingTime = getMixingTime(numVertices, tau);

            for (int i = 0; i < mixingTime; ++i) {

                chain.doMove();

            }

            std::cout << "Mixing done. " << std::flush;

            int range = 500;

            // Keep track of [-range, range]

            std::vector<int> frequencies(2*range+1, 0);

            // frequencies[x+range] corresponds to frequency of x

            // clip anything outside of range to range!

            int prevTriangles = chain.g.countTriangles();

            chain.g.getTrackedTriangles() = prevTriangles;

            int movesDone = 0;

            int measurements = getMeasurements(numVertices, tau);

            for (int i = 0; i < measurements; ++i) {

                if (chain.doMove(true)) {

                    ++movesDone;

                    int newTriangles = chain.g.getTrackedTriangles();

                    int diff = newTriangles - prevTriangles;

                    prevTriangles = newTriangles;

                    // Add 'diff' to histogram

                    if (diff < -range)

                        diff = -range;

                    else if (diff > range)

                        diff = range;

                    frequencies[diff+range]++;

                }

            }

            std::cout << "Measuring done. " << std::flush;

            std::vector<std::pair<int, int>> histogram;

            for (int i = -range; i <= range; ++i) {

                histogram.push_back(std::make_pair(i, frequencies[i + range]));

            }

            if (outputComma)

                outfile << ',' << '\n';

            outputComma = true;

            outfile << '{' << '{' << numVertices << ',' << tau << '}';

            outfile << ',' << histogram;

            outfile << ',' << '{' << movesDone << ',' << measurements << '}';

            outfile << '}' << std::flush;

            std::cout << "Output done." << std::endl;

        }

    }

    outfile << '\n' << '}';

    return 0;

}

(*

n from 10000 to 10000 step 1000

tauValues: {2.1,2.5,2.9}

Canonical degree sequence.

mixingTime: 100 * (50 - 5 (tau - 2)) n

measurements: 5000000

measureSkip: 0

histogram is conditioned on successful switches

data:

1: {n,tau}

2: { {delta1, freq1} , {delta2, freq2} , ... }

3: {successful switches, total attempted switches}

*)

{

{{10000,2.100000},{{-500,115},{-499,1},{-498,2},{-497,0},{-496,1},{-495,0},{-494,2},{-493,2},{-492,2},{-491,0},{-490,0},{-489,1},{-488,0},{-487,0},{-486,0},{-485,0},{-484,0},{-483,0},{-482,0},{-481,0},{-480,0},{-479,2},{-478,0},{-477,0},{-476,0},{-475,1},{-474,0},{-473,0},{-472,2},{-471,0},{-470,1},{-469,0},{-468,0},{-467,2},{-466,0},{-465,2},{-464,0},{-463,0},{-462,0},{-461,0},{-460,1},{-459,0},{-458,1},{-457,1},{-456,0},{-455,1},{-454,3},{-453,0},{-452,0},{-451,1},{-450,0},{-449,2},{-448,0},{-447,0},{-446,0},{-445,0},{-444,3},{-443,0},{-442,2},{-441,0},{-440,1},{-439,1},{-438,1},{-437,2},{-436,1},{-435,2},{-434,0},{-433,0},{-432,1},{-431,0},{-430,3},{-429,1},{-428,1},{-427,2},{-426,1},{-425,2},{-424,0},{-423,1},{-422,0},{-421,0},{-420,3},{-419,2},{-418,2},{-417,2},{-416,0},{-415,1},{-414,1},{-413,1},{-412,3},{-411,2},{-410,3},{-409,1},{-408,0},{-407,1},{-406,0},{-405,2},{-404,2},{-403,1},{-402,1},{-401,2},{-400,1},{-399,1},{-398,3},{-397,2},{-396,3},{-395,4},{-394,1},{-393,2},{-392,0},{-391,4},{-390,3},{-389,2},{-388,0},{-387,2},{-386,0},{-385,1},{-384,4},{-383,2},{-382,4},{-381,3},{-380,2},{-379,0},{-378,1},{-377,2},{-376,2},{-375,3},{-374,2},{-373,2},{-372,1},{-371,4},{-370,0},{-369,0},{-368,3},{-367,1},{-366,2},{-365,4},{-364,0},{-363,1},{-362,3},{-361,2},{-360,2},{-359,5},{-358,4},{-357,1},{-356,2},{-355,1},{-354,3},{-353,3},{-352,2},{-351,2},{-350,3},{-349,2},{-348,4},{-347,2},{-346,1},{-345,1},{-344,4},{-343,2},{-342,2},{-341,1},{-340,2},{-339,1},{-338,4},{-337,3},{-336,2},{-335,4},{-334,2},{-333,4},{-332,6},{-331,5},{-330,7},{-329,2},{-328,1},{-327,3},{-326,2},{-325,5},{-324,3},{-323,1},{-322,2},{-321,3},{-320,2},{-319,3},{-318,3},{-317,3},{-316,2},{-315,2},{-314,6},{-313,2},{-312,4},{-311,5},{-310,5},{-309,2},{-308,2},{-307,8},{-306,4},{-305,3},{-304,4},{-303,7},{-302,2},{-301,2},{-300,5},{-299,4},{-298,4},{-297,1},{-296,6},{-295,1},{-294,3},{-293,5},{-292,6},{-291,5},{-290,3},{-289,6},{-288,4},{-287,6},{-286,3},{-285,6},{-284,3},{-283,6},{-282,4},{-281,5},{-280,6},{-279,4},{-278,5},{-277,4},{-276,5},{-275,3},{-274,5},{-273,7},{-272,4},{-271,8},{-270,6},{-269,7},{-268,4},{-267,6},{-266,6},{-265,5},{-264,6},{-263,6},{-262,11},{-261,5},{-260,6},{-259,5},{-258,2},{-257,5},{-256,5},{-255,4},{-254,8},{-253,7},{-252,7},{-251,16},{-250,8},{-249,11},{-248,11},{-247,9},{-246,10},{-245,10},{-244,5},{-243,10},{-242,9},{-241,8},{-240,11},{-239,7},{-238,6},{-237,8},{-236,7},{-235,11},{-234,13},{-233,22},{-232,6},{-231,14},{-230,8},{-229,15},{-228,10},{-227,3},{-226,10},{-225,10},{-224,7},{-223,12},{-222,7},{-221,14},{-220,8},{-219,15},{-218,7},{-217,9},{-216,18},{-215,8},{-214,7},{-213,11},{-212,12},{-211,6},{-210,15},{-209,13},{-208,15},{-207,16},{-206,16},{-205,22},{-204,14},{-203,15},{-202,19},{-201,16},{-200,17},{-199,20},{-198,11},{-197,31},{-196,14},{-195,16},{-194,17},{-193,17},{-192,19},{-191,13},{-190,23},{-189,16},{-188,22},{-187,18},{-186,19},{-185,21},{-184,19},{-183,19},{-182,22},{-181,21},{-180,20},{-179,14},{-178,28},{-177,26},{-176,24},{-175,24},{-174,25},{-173,23},{-172,30},{-171,33},{-170,29},{-169,26},{-168,24},{-167,24},{-166,28},{-165,30},{-164,31},{-163,42},{-162,33},{-161,37},{-160,34},{-159,27},{-158,40},{-157,36},{-156,33},{-155,28},{-154,40},{-153,42},{-152,50},{-151,43},{-150,42},{-149,53},{-148,35},{-147,35},{-146,42},{-145,41},{-144,30},{-143,47},{-142,59},{-141,49},{-140,47},{-139,40},{-138,50},{-137,51},{-136,38},{-135,59},{-134,60},{-133,62},{-132,65},{-131,53},{-130,61},{-129,63},{-128,66},{-127,65},{-126,81},{-125,69},{-124,85},{-123,75},{-122,81},{-121,82},{-120,94},{-119,79},{-118,74},{-117,78},{-116,78},{-115,96},{-114,90},{-113,89},{-112,110},{-111,100},{-110,110},{-109,108},{-108,99},{-107,106},{-106,118},{-105,130},{-104,127},{-103,134},{-102,124},{-101,159},{-100,153},{-99,144},{-98,159},{-97,167},{-96,169},{-95,172},{-94,150},{-93,151},{-92,178},{-91,195},{-90,192},{-89,206},{-88,208},{-87,213},{-86,224},{-85,231},{-84,264},{-83,235},{-82,251},{-81,271},{-80,277},{-79,281},{-78,311},{-77,329},{-76,358},{-75,348},{-74,337},{-73,365},{-72,402},{-71,402},{-70,385},{-69,400},{-68,432},{-67,450},{-66,468},{-65,480},{-64,526},{-63,570},{-62,550},{-61,590},{-60,603},{-59,667},{-58,660},{-57,742},{-56,738},{-55,752},{-54,820},{-53,852},{-52,894},{-51,976},{-50,963},{-49,1036},{-48,1141},{-47,1192},{-46,1163},{-45,1274},{-44,1406},{-43,1475},{-42,1566},{-41,1702},{-40,1759},{-39,1893},{-38,1955},{-37,2171},{-36,2250},{-35,2449},{-34,2547},{-33,2685},{-32,3030},{-31,3243},{-30,3419},{-29,3707},{-28,4063},{-27,4291},{-26,4633},{-25,4969},{-24,5404},{-23,5951},{-22,6528},{-21,7074},{-20,7714},{-19,8371},{-18,9340},{-17,10210},{-16,11333},{-15,12550},{-14,14006},{-13,15673},{-12,17716},{-11,20266},{-10,23271},{-9,26698},{-8,31441},{-7,37175},{-6,45065},{-5,55801},{-4,72065},{-3,97457},{-2,143839},{-1,252159},{0,431740},{1,250027},{2,144589},{3,97760},{4,72135},{5,56019},{6,44885},{7,36983},{8,31141},{9,26759},{10,22998},{11,20236},{12,17946},{13,16032},{14,14064},{15,12767},{16,113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}

(* ::Section:: *)

(*Canonical dataset*)

(* Taken from stackoverflow *)

ClearAll[chartColors];

chartColors::usage="plotColors[plotType,plotTheme] gives a list of the colors used in a plot when several curves are drawn. Here plotType is, for example, Plot or ListLogPlot while plotTheme may be \"Scientific\", \"Classic\" etc.";

chartColors[chartType_,plotTheme_]:=("ChartDefaultStyle"/.(Method/.Charting`ResolvePlotTheme[plotTheme,chartType]))/.Directive[x_,__]:>x

cl1=chartColors[Histogram,$PlotTheme]

gsraw=Import[NotebookDirectory[]<>"data/graphdata_canonical_creationfreqs.m"];

(* gsraw=SortBy[gsraw,{#[[1,1]]&,#[[1,2]]&}]; (* Sort by n and then by tau. The {} forces a *stable* sort because otherwise Mathematica sorts also on triangle count and other things. *) *)

gdata=gsraw;

(* Data format: *)

(* gdata[[ tau index , datatype index ]] *)

(* datatype index:

1: {n,tau}

2: {{delta1, freq1}, {delta2, freq2}, ... }

3: {successful moves, move attemps}

*)

ticks={{1,1}}~Join~Map[{10^-#,Superscript[10,-#]}&,Range[1,9]];

histogramData=Map[WeightedData[#[[All,1]],#[[All,2]]]&,gdata[[All,2]]];

largeHistogram=Histogram[histogramData,{-100-0.5,100+0.5,1},{"Log","Probability"},

PlotRange->{Automatic,Automatic},

ChartLegends->Placed[{"\[Tau] = 2.1","\[Tau] = 2.5","\[Tau] = 2.9"},Scaled[{0.8,0.75}]],

ChartStyle->cl1,

FrameTicks->{{ticks,None},{Automatic,None}},

PlotLabel->"n = 10000",

FrameLabel->{"net triangles created by a switch","Probability"},

Frame->True,ImageSize->265,AspectRatio->1]

Export[NotebookDirectory[]<>"plots/triangle_creation_frequencies_large.pdf",largeHistogram]

createCalloutPlotNew[freqs_,bottomTicks_,epilog_,color_]:=Module[{total,plotrange,ticks,h,probs,cpos,callouts,llp,range=501},

total=Total[freqs[[All,2]]];

plotrange={{-7,7},{freqs[[Floor[Length[freqs]/2]-3,2]]/total,0.3+Max[freqs[[All,2]]]/total}};

ticks={{1,1}}~Join~Map[{10^-#,Superscript[10,-#]}&,Range[1,4]];

h=Histogram[WeightedData[freqs[[All,1]],freqs[[All,2]]],{-range-0.5,range+0.5,1},{"Log","Probability"},

PlotRange->plotrange,

PlotRangeClipping->True,

ChartStyle->color,

ImagePadding->{{1,30},{If[bottomTicks==True,15,0.5],0.5}},

Epilog->epilog,

FrameTicks->{{None,ticks},{bottomTicks,None}},

Frame->True,ImageSize->145];

probs=Select[freqs,Abs[#[[1]]]<=2&];

cpos[i_]:=\!\(\*

TagBox[GridBox[{

{"\[Piecewise]", GridBox[{

{"Before", 

RowBox[{"i", "<", "0"}]},

{"After", 

RowBox[{"i", ">", "0"}]},

{"Automatic", "True"}

},

AllowedDimensions->{2, Automatic},

Editable->True,

GridBoxAlignment->{"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},

GridBoxItemSize->{"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},

GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},

Selectable->True]}

},

GridBoxAlignment->{"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},

GridBoxItemSize->{"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},

GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}],

"Piecewise",

DeleteWithContents->True,

Editable->False,

SelectWithContents->True,

Selectable->False]\);

callouts=Map[Callout[{#[[1]],#[[2]]/total},NumberForm[N[#[[2]]/total],{2,3}],cpos[#[[1]]]]&,probs];

llp=ListLogPlot[callouts,PlotStyle->None,PlotRange->plotrange];

histograms3={

createCalloutPlotNew[gdata[[1,2]],None,Text["\[Tau] = 2.1",Scaled[{0.85,0.9}]],cl1[[1]]],

createCalloutPlotNew[gdata[[2,2]],None,Text["\[Tau] = 2.5",Scaled[{0.85,0.9}]],cl1[[2]]],

createCalloutPlotNew[gdata[[3,2]],True,Text["\[Tau] = 2.9",Scaled[{0.85,0.9}]],cl1[[3]]]

};

plotcol=Column[histograms3,Spacings->0]

combiplot=Row[{largeHistogram,plotcol}]

Export[NotebookDirectory[]<>"plots/triangle_creation_frequencies_combiplot.pdf",combiplot]