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151 lines
7.4 KiB
Markdown
151 lines
7.4 KiB
Markdown
# Example (JKQTPlotter): Plotting a Statistical Distribution of Data {#JKQTPlotterDistributionPlot}
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This project (see [`test_distributionplot`](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/test_distributionplot) demonstrates how to combine several different graphs and geometric elements to show a set of random values and their statistics.
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[JKQTPlotterBasicJKQTPDatastore]: @ref JKQTPlotterBasicJKQTPDatastore "Basic Usage of JKQTPDatastore"
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[JKQTPlotterBasicJKQTPDatastoreIterators]: @ref JKQTPlotterBasicJKQTPDatastoreIterators "Iterator-Based usage of JKQTPDatastore"
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[JKQTPlotterBasicJKQTPDatastoreStatistics]: @ref JKQTPlotterBasicJKQTPDatastoreStatistics "Advanced 1-Dimensional Statistics with JKQTPDatastore"
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[JKQTPlotterBasicJKQTPDatastoreRegression]: @ref JKQTPlotterBasicJKQTPDatastoreRegression "Regression Analysis (with the Statistics Library)"
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[JKQTPlotterBasicJKQTPDatastoreStatistics2D]: @ref JKQTPlotterBasicJKQTPDatastoreStatistics2D "Advanced 2-Dimensional Statistics with JKQTPDatastore"
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[statisticslibrary]: @ref jkqtptools_math_statistics "JKQTPlotter Statistics Library"
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[JKQTPlotterBoxplotStyling]: @ref JKQTPlotterBoxplotStyling "Styling different aspects of boxplots"
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[JKQTPlotterBoxplotsGraphs]: @ref JKQTPlotterBoxplotsGraphs "Boxplots"
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***Note*** that this example explains how to generate the statistics plots by hand, i.e. by calculating all the statistical properties for the boxplots and then adding the necessary graphs. The internal [statisticslibrary] offers methods to perform these calculations, which are explained in the tutorial [JKQTPlotterBasicJKQTPDatastoreStatistics] in detail. Several examples give more details on boxplots: [JKQTPlotterBoxplotsGraphs], [JKQTPlotterBoxplotStyling].
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The source code of the main application is (see [`test_distributionplot.cpp`](test_distributionplot.cpp).
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After adding all necessary data to the JKQTDatastore:
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```.cpp
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// 1. create a plotter window and get a pointer to the internal datastore (for convenience)
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JKQTPlotter plot;
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plot.getPlotter()->setUseAntiAliasingForGraphs(true); // nicer (but slower) plotting
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plot.getPlotter()->setUseAntiAliasingForSystem(true); // nicer (but slower) plotting
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plot.getPlotter()->setUseAntiAliasingForText(true); // nicer (but slower) text rendering
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JKQTPDatastore* ds=plot.getDatastore();
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// 2. now we create random values drawn from a gaussian distribution
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QVector<double> RANDVAL; // will store the values themselves
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std::map<int, double> hist; // is used to calculate the histogram of the data
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for (int i=-5; i<=15; i++) hist[i]=0;
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std::random_device rd; // random number generators:
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std::mt19937 gen{rd()};
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// draw 301 random values from a gaussian distribution around 5 with width 3
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const double th_mean=5;
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const double th_std=3;
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std::normal_distribution<> d{th_mean,th_std};
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size_t NDATA=301;
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double sum=0;
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double square_sum=0;
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for (size_t i=0; i<NDATA; i++) {
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const double v=d(gen);
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RANDVAL<<v; // store data
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++hist[std::round(v)]; // calculate histogram
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// accumulate data for statistics:
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sum+=v;
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square_sum+=(v*v);
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}
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// normalize histogram
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for (auto& hi: hist) {
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hi.second=hi.second/static_cast<double>(NDATA);
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}
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// sort random data in order to calculate the statistical properties:
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qSort(RANDVAL);
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const double rndMean=sum/static_cast<double>(NDATA);
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const double rndMin=RANDVAL.first();
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const double rndMax=RANDVAL.last();
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const double rndMedian=RANDVAL[RANDVAL.size()/2];
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const double rndQ25=RANDVAL[RANDVAL.size()/4];
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const double rndQ75=RANDVAL[RANDVAL.size()*3/4];
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const double rndMedianConfidence=2.0*1.57*fabs(rndQ75-rndQ25)/sqrt(static_cast<double>(NDATA));
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// 3. make data available to JKQTPlotter by adding it to the internal datastore.
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size_t columnRANDVAL=ds->addCopiedColumn(RANDVAL, "RANDVAL"); // copy random values
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std::pair<size_t,size_t> columnHIST = ds->addCopiedMap(hist, "HIST_X", "HIST_Y"); // copy histogram
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// 4. create a graph of horizontal boxplots:
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JKQTPSingleColumnSymbolsGraph* graphRANDVALS=new JKQTPSingleColumnSymbolsGraph(&plot);
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graphRANDVALS->setDataColumn(columnRANDVAL);
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// draw data as symbols at (x,y)=(data,-0.07):
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graphRANDVALS->setDataDirection(JKQTPSingleColumnSymbolsGraph::DataDirection::X);
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graphRANDVALS->setPosition(-0.07);
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// data should scatter around position=-0.07 with a width=0.08 (i.e. from position-width/2 ... position+width/2)
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//graphRANDVALS->setWidth(0.08);
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//graphRANDVALS->setPositionScatterStyle(JKQTPSingleColumnSymbolsGraph::RandomScatter);
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// data should scatter around position=-0.07 in a BeeSwarmScatter-Plot
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graphRANDVALS->setPositionScatterStyle(JKQTPSingleColumnSymbolsGraph::BeeSwarmScatter);
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// choose small filled circles as symbols, JKQTPGraphSymbols::set their color:
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graphRANDVALS->setSymbolType(JKQTPFilledCircle);
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graphRANDVALS->setSymbolSize(5);
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graphRANDVALS->setColor(QColor("red"));
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graphRANDVALS->setFillColor(graphRANDVALS->getColor().lighter(180));
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// set title:
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graphRANDVALS->setTitle("Random Data");
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// 5. draw the histogram as barchart:
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JKQTPBarVerticalGraph* graphHIST=new JKQTPBarVerticalGraph(&plot);
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graphHIST->setXColumn(columnHIST.first);
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graphHIST->setYColumn(columnHIST.second);
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// set title:
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graphHIST->setTitle("Histogram");
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// 6. draw the theoretical distribution as function graph:
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JKQTPXFunctionLineGraph* graphTheoDist=new JKQTPXFunctionLineGraph(&plot);
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// define the gaussian function used for the random number generator
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graphTheoDist->setPlotFunctionFunctor([&th_mean,&th_std](double x) -> double {
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return 1.0/(th_std*sqrt(2.0*M_PI))*exp(-0.5*(x-th_mean)*(x-th_mean)/th_std/th_std);
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});
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// set title:
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graphTheoDist->setTitle(QString("Theoretical Distribution $\\mu=%1, \\sigma=%2$").arg(th_mean,0, 'f', 1).arg(th_std,0, 'f', 1));
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// 7. create a graph of horizontal boxplots:
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JKQTPBoxplotHorizontalElement* graphBoxPlot=new JKQTPBoxplotHorizontalElement(&plot);
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graphBoxPlot->setPos(0.15);
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graphBoxPlot->setMin(rndMin);
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graphBoxPlot->setPercentile25(rndQ25);
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graphBoxPlot->setMean(rndMean);
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graphBoxPlot->setMedian(rndMedian);
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graphBoxPlot->setMedianConfidenceIntervalWidth(rndMedianConfidence);
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graphBoxPlot->setPercentile75(rndQ75);
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graphBoxPlot->setMax(rndMax);
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graphBoxPlot->setBoxWidthAbsolute(24);
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graphBoxPlot->setMeanSize(16);
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graphBoxPlot->setLineWidth(2);
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graphBoxPlot->setTitle("Statistical Properties");
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graphBoxPlot->setBoxplotColor(QColor("blue"), plot.getPlotter());
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// make fill collor a lighter shade of the outline color
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graphBoxPlot->setFillColor(graphBoxPlot->getLineColor().lighter(180));
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// make whiskers dashed
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graphBoxPlot->setWhiskerLineStyle(Qt::DashLine);
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// 8. add the graphs to the plot, so it is actually displayed
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plot.addGraph(graphRANDVALS);
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plot.addGraph(graphHIST);
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plot.addGraph(graphTheoDist);
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plot.addGraph(graphBoxPlot);
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// 9. autoscale the plot so the graph is contained
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plot.zoomToFit();
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// 10. Move key to top-left
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plot.getPlotter()->setKeyPosition(JKQTPKeyInsideTopLeft);
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// 11. show plotter and make it a decent size
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plot.show();
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plot.resize(800,800);
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```
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The result looks like this:
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