mirror of
https://github.com/jkriege2/JKQtPlotter.git
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343 lines
19 KiB
C++
343 lines
19 KiB
C++
/** \example datastore_regression.cpp
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* Explains how to use the internal statistics library (see \ref jkqtptools_statistics ) together with JKQTPDatastore to perform different types of regression and polynomial fitting.
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*
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* \ref JKQTPlotterBasicJKQTPDatastoreRegression
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*/
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#include "jkqtpexampleapplication.h"
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#include <QApplication>
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#include "jkqtplotter/jkqtplotter.h"
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#include "jkqtplotter/graphs/jkqtppeakstream.h"
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#include "jkqtplotter/graphs/jkqtpboxplot.h"
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#include "jkqtplotter/graphs/jkqtpstatisticsadaptors.h"
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#include "jkqtplotter/graphs/jkqtpevaluatedfunction.h"
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#include "jkqtcommon_statistics_and_math/jkqtpstatisticstools.h"
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#include "jkqtcommon/jkqtpstringtools.h"
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#include <random>
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#include <cmath>
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int main(int argc, char* argv[])
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{
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JKQTPAppSettingController highDPIController(argc, argv);
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JKQTPExampleApplication app(argc, argv);
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// 1. create a window with several plotters and get a pointer to the internal datastores (for convenience)
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QWidget mainWidget;
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QGridLayout* lay;
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mainWidget.setLayout(lay=new QGridLayout);
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JKQTPlotter* plot1=new JKQTPlotter(&mainWidget);
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plot1->getPlotter()->setPlotLabel("Simple Linear Regression");
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JKQTPDatastore* datastore1=plot1->getDatastore();
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lay->addWidget(plot1,0,0);
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JKQTPlotter *plot2=new JKQTPlotter(datastore1, &mainWidget);
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plot2->getPlotter()->setPlotLabel("Weighted Linear Regression");
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lay->addWidget(plot2,1,0);
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JKQTPlotter* plot3=new JKQTPlotter(datastore1, &mainWidget);
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plot3->getPlotter()->setPlotLabel("Robust Linear Regression");
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lay->addWidget(plot3,0,1);
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JKQTPlotter *plot6=new JKQTPlotter(datastore1, &mainWidget);
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plot6->getPlotter()->setPlotLabel("Polynomial Fitting");
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lay->addWidget(plot6,1,1);
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JKQTPlotter* plot4=new JKQTPlotter(datastore1, &mainWidget);
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plot4->getPlotter()->setPlotLabel("Exponential Regression");
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lay->addWidget(plot4,0,2);
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JKQTPlotter* plot5=new JKQTPlotter(datastore1, &mainWidget);
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plot5->getPlotter()->setPlotLabel("Power-Law Regression");
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lay->addWidget(plot5,1,2);
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// 2.1. To demonstrate linear regression, we create a dataset with a linear dependence between two
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// columns and added gaussian noise
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std::random_device rd; // random number generators:
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std::mt19937 gen{rd()};
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std::normal_distribution<> d1{0,1};
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double a0=-5;
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double b0=2;
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size_t colLinX=datastore1->addColumn("lin data, x");
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size_t colLinY=datastore1->addColumn("lin data, y");
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for (double x=-5; x<=10; x++) {
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datastore1->appendToColumn(colLinX, x);
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datastore1->appendToColumn(colLinY, a0+b0*x+d1(gen));
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}
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// we visualize this data with a simple scatter graph:
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JKQTPXYLineGraph* graphD;
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plot1->addGraph(graphD=new JKQTPXYLineGraph(plot1));
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graphD->setXYColumns(colLinX, colLinY);
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graphD->setDrawLine(false);
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graphD->setTitle(QString("data $f(x)=%1+%2\\cdot x+\\mathcal{N}(0,1)$").arg(jkqtp_floattolatexqstr(a0,1)).arg(jkqtp_floattolatexqstr(b0,1)));
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// 2.2. Now we calculate the regression line and add a plot to the graph:
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/*double coeffA=0, coeffB=0;
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jkqtpstatLinearRegression(datastore1->begin(colLinX), datastore1->end(colLinX), datastore1->begin(colLinY), datastore1->end(colLinY), coeffA, coeffB);
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JKQTPXFunctionLineGraph *graphRegLine=new JKQTPXFunctionLineGraph(plot1);
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graphRegLine->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
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graphRegLine->setParamsV(coeffA, coeffB);
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graphRegLine->setTitle(QString("regression: $f(x) = %1 + %2 \\cdot x$").arg(jkqtp_floattolatexqstr(coeffA)).arg(jkqtp_floattolatexqstr(coeffB)));
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plot1->addGraph(graphRegLine);*/
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// this code can also be written with one function call, using the "adaptor" jkqtpstatAddLinearRegression():
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//jkqtpstatAddLinearRegression(plot1->getPlotter(), datastore1->begin(colLinX), datastore1->end(colLinX), datastore1->begin(colLinY), datastore1->end(colLinY));
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// or even shorter:
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jkqtpstatAddLinearRegression(graphD);
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// 3.1. We extend the example above by
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//std::random_device rd; // random number generators:
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//std::mt19937 gen{rd()};
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std::uniform_real_distribution<> de{0.5,1.5};
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std::uniform_int_distribution<> ddecide{0,4};
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//double a0=-5;
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//double b0=2;
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size_t colWLinX=datastore1->addColumn("wlin data, x");
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size_t colWLinY=datastore1->addColumn("wlin data, y");
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size_t colWLinE=datastore1->addColumn("wlin data, errors");
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for (double x=-5; x<=10; x++) {
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double factor=1;
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if (ddecide(gen)==4) {
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factor=4;
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}
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const double err=de(gen)*factor;
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datastore1->appendToColumn(colWLinX, x);
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datastore1->appendToColumn(colWLinY, a0+b0*x+err);
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datastore1->appendToColumn(colWLinE, err);
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}
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// we visualize this data with a simple scatter graph:
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JKQTPXYLineErrorGraph* graphE;
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plot2->addGraph(graphE=new JKQTPXYLineErrorGraph(plot2));
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graphE->setXYColumns(colWLinX, colWLinY);
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graphE->setYErrorColumn(static_cast<int>(colWLinE));
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graphE->setDrawLine(false);
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graphE->setTitle(QString("data $f(x)=%1+%2\\cdot x+\\mbox{Noise}$").arg(jkqtp_floattolatexqstr(a0,1)).arg(jkqtp_floattolatexqstr(b0,1)));
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// 2.2. Now we calculate the regression line and add a plot to the graph:
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/*double coeffA=0, coeffB=0;
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jkqtpstatLinearWeightedRegression(datastore1->begin(colWLinX), datastore1->end(colWLinX),
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datastore1->begin(colWLinY), datastore1->end(colWLinY),
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datastore1->begin(colWLinE), datastore1->end(colWLinE),
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coeffA, coeffB, false, false,
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&jkqtp_inversePropSaveDefault<double>);
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// note that in addition to the three data-columns we also provided a C++ functor
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// jkqtp_inversePropSaveDefault(), which calculates 1/error. This is done, because the function
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// jkqtpstatLinearWeightedRegression() uses the data from the range datastore1->begin(colWLinE) ... datastore1->end(colWLinE)
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// directly as weights, but we calculated errors, which are inversely proportional to the
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// weight of each data point when solving the least squares problem, as data points with
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// larger errors should be weighted less than thos with smaller errors
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//
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// Now we can plot the resulting linear function:
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JKQTPXFunctionLineGraph *graphRegLine=new JKQTPXFunctionLineGraph(plot2);
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graphRegLine->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
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graphRegLine->setParamsV(coeffA, coeffB);
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graphRegLine->setTitle(QString("weighted regression: $f(x) = %1 + %2 \\cdot x$").arg(jkqtp_floattolatexqstr(coeffA)).arg(jkqtp_floattolatexqstr(coeffB)));
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plot2->addGraph(graphRegLine);*/
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// this code can also be written with one function call, using the "adaptor" jkqtpstatAddLinearRegression():
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//jkqtpstatAddLinearWeightedRegression(plot2->getPlotter(),
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// datastore1->begin(colLinX), datastore1->end(colLinX),
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// datastore1->begin(colLinY), datastore1->end(colLinY),
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// datastore1->begin(colWLinE), datastore1->end(colWLinE),
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// &coeffA, &coeffB, false, false,
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// &jkqtp_inversePropSaveDefault<double>);
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// or even shorter:
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jkqtpstatAddLinearWeightedRegression(graphE);
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// to demonstrate the effect of the weighting, we also add a simple linear regression that
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// does not take into account the errors:
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jkqtpstatAddLinearRegression(graphE);
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// 4.1. To demonstrate IRLS linear regression, we create a dataset with a linear dependence between two
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// columns and added gaussian noise and some outliers
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//std::random_device rd; // random number generators:
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//std::mt19937 gen{rd()};
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//std::normal_distribution<> d1{0,1};
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//double a0=-5;
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//double b0=2;
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size_t colRLinX=datastore1->addColumn("lin data, x");
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size_t colRLinY=datastore1->addColumn("lin data, y");
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for (double x=-5; x<=10; x++) {
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datastore1->appendToColumn(colRLinX, x);
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if (jkqtp_approximatelyEqual(x, -5)||jkqtp_approximatelyEqual(x, -3)) datastore1->appendToColumn(colRLinY, a0+b0*x+d1(gen)+12);
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else datastore1->appendToColumn(colRLinY, a0+b0*x+d1(gen));
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}
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// we visualize this data with a simple scatter graph:
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//JKQTPXYLineGraph* graphD;
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plot3->addGraph(graphD=new JKQTPXYLineGraph(plot3));
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graphD->setXYColumns(colRLinX, colRLinY);
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graphD->setDrawLine(false);
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graphD->setTitle(QString("data $f(x)=%1+%2\\cdot x+\\mathcal{N}(0,1)$").arg(jkqtp_floattolatexqstr(a0,1)).arg(jkqtp_floattolatexqstr(b0,1)));
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// 4.2. Now we calculate the regression line and add a plot to the graph:
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double coeffA=0, coeffB=0;
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jkqtpstatRobustIRLSLinearRegression(datastore1->begin(colRLinX), datastore1->end(colRLinX), datastore1->begin(colRLinY), datastore1->end(colRLinY), coeffA, coeffB);
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JKQTPXFunctionLineGraph *graphRegLine=new JKQTPXFunctionLineGraph(plot3);
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graphRegLine->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
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graphRegLine->setParamsV(coeffA, coeffB);
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graphRegLine->setTitle(QString("robust regression: $f(x) = %1 + %2 \\cdot x$, $p=1.1$").arg(jkqtp_floattolatexqstr(coeffA)).arg(jkqtp_floattolatexqstr(coeffB)));
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plot3->addGraph(graphRegLine);
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// this code can also be written with one function call, using the "adaptor" jkqtpstatAddLinearRegression():
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//jkqtpstatAddRobustIRLSLinearRegression(plot3->getPlotter(), datastore1->begin(colRLinX), datastore1->end(colRLinX), datastore1->begin(colRLinY), datastore1->end(colRLinY));
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// or even shorter:
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//jkqtpstatAddRobustIRLSLinearRegression(graphD);
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// as a comparison, we also add the result of the normal/non-robust linear regression:
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jkqtpstatAddLinearRegression(graphD);
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// the following code demonstrates the influence of the rgularization parameter p:
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// - the closer it is to 1, the more robust the fit is (it is closer to the L1-norm)
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// - the closer it is to 2, the closer the fit is to the least squares solution (i.e. the normal regression)
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double p;
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p=1.1;
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auto g=jkqtpstatAddRobustIRLSLinearRegression(graphD, nullptr, nullptr, false, false, p);
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g->setTitle(g->getTitle()+", $p="+jkqtp_floattolatexqstr(p)+"$");
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p=1.5;
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g=jkqtpstatAddRobustIRLSLinearRegression(graphD, nullptr, nullptr, false, false, p);
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g->setTitle(g->getTitle()+", $p="+jkqtp_floattolatexqstr(p)+"$");
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p=1.7;
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g=jkqtpstatAddRobustIRLSLinearRegression(graphD, nullptr, nullptr, false, false, p);
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g->setTitle(g->getTitle()+", $p="+jkqtp_floattolatexqstr(p)+"$");
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p=2;
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g=jkqtpstatAddRobustIRLSLinearRegression(graphD, nullptr, nullptr, false, false, p);
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g->setTitle(g->getTitle()+", $p="+jkqtp_floattolatexqstr(p)+"$");
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// 5.1. The functions for linear regression can also be used to calculate some non-linear models by transforming the input data.
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// This is also supported by the statistics library. the supported models are defined in JKQTPStatRegressionModelType
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//std::random_device rd; // random number generators:
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//std::mt19937 gen{rd()};
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//std::normal_distribution<> d1{0,1};
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double a0_powerlaw=20;
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double b0_powerlaw=0.25;
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double a0_exp=5;
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double b0_exp=0.5;
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double a0_log=0;
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double b0_log=1;
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size_t colNLLinX=datastore1->addColumn("non-lin data, x");
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size_t colNLLinYExp=datastore1->addColumn("non-lin data, y, exponential model");
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size_t colNLLinYPow=datastore1->addColumn("non-lin data, y, power-law model");
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size_t colNLLinYLog=datastore1->addColumn("non-lin data, y, log-law model");
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auto model_powerlaw=jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::PowerLaw);
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auto model_exp=jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Exponential);
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auto model_log=jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Logarithm);
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for (double x=0.1; x<=10; x+=0.5) {
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datastore1->appendToColumn(colNLLinX, x);
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double ypow=model_powerlaw(x, a0_powerlaw, b0_powerlaw)+d1(gen);
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while (ypow<0) {
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ypow=model_powerlaw(x, a0_powerlaw, b0_powerlaw)+d1(gen);
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}
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datastore1->appendToColumn(colNLLinYPow, ypow);
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double yexp=model_exp(x, a0_exp, b0_exp)+d1(gen);
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while (yexp<0) {
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yexp=model_exp(x, a0_exp, b0_exp)+d1(gen);
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}
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datastore1->appendToColumn(colNLLinYExp, yexp);
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datastore1->appendToColumn(colNLLinYLog, model_log(x, a0_log, b0_log));
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}
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// we visualize this data with a simple scatter graphs:
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JKQTPXYLineGraph* graphD_powerlaw;
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plot5->addGraph(graphD_powerlaw=new JKQTPXYLineGraph(plot5));
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graphD_powerlaw->setXYColumns(colNLLinX, colNLLinYPow);
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graphD_powerlaw->setDrawLine(false);
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graphD_powerlaw->setTitle(QString("data $%1+\\mathcal{N}(0,1)$").arg(jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType::PowerLaw, a0_powerlaw, b0_powerlaw)));
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JKQTPXYLineGraph* graphD_exp;
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plot4->addGraph(graphD_exp=new JKQTPXYLineGraph(plot4));
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graphD_exp->setXYColumns(colNLLinX, colNLLinYExp);
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graphD_exp->setDrawLine(false);
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graphD_exp->setTitle(QString("data $%1+\\mathcal{N}(0,1)$").arg(jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType::Exponential, a0_exp, b0_exp)));
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JKQTPXYLineGraph* graphD_log;
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plot5->addGraph(graphD_log=new JKQTPXYLineGraph(plot5));
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graphD_log->setXYColumns(colNLLinX, colNLLinYLog);
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graphD_log->setDrawLine(false);
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graphD_log->setTitle(QString("data $%1+\\mathcal{N}(0,1)$").arg(jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType::Logarithm, a0_log, b0_log)));
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// 5.2. Now we calculate the regression models and add a plot to the graph:
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double cA=0, cB=0;
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JKQTPXFunctionLineGraph* gFunc;
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jkqtpstatRegression(JKQTPStatRegressionModelType::Exponential, datastore1->begin(colNLLinX), datastore1->end(colNLLinX), datastore1->begin(colNLLinYExp), datastore1->end(colNLLinYExp), cA, cB);
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plot4->addGraph(gFunc=new JKQTPXFunctionLineGraph(plot4));
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gFunc->setPlotFunctionFunctor(jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Exponential, cA, cB));
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gFunc->setTitle(QString("regression: $%1$").arg(jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType::Exponential, cA, cB)));
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cA=0; cB=0;
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jkqtpstatRegression(JKQTPStatRegressionModelType::PowerLaw, datastore1->begin(colNLLinX), datastore1->end(colNLLinX), datastore1->begin(colNLLinYPow), datastore1->end(colNLLinYPow), cA, cB);
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plot5->addGraph(gFunc=new JKQTPXFunctionLineGraph(plot5));
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gFunc->setPlotFunctionFunctor(jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::PowerLaw, cA, cB));
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gFunc->setTitle(QString("regression: $%1$").arg(jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType::PowerLaw, cA, cB)));
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// Note: Here we used the normal linear regression functions, but variants for IRLS and weighted regression are also available!
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// 5.3. Of course also adaptors exist:
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//jkqtpstatAddRegression(plot4->getPlotter(), JKQTPStatRegressionModelType::Exponential, datastore1->begin(colNLLinX), datastore1->end(colNLLinX), datastore1->begin(colNLLinYExp), datastore1->end(colNLLinYExp));
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//jkqtpstatAddRegression(plot5->getPlotter(), JKQTPStatRegressionModelType::PowerLaw, datastore1->begin(colNLLinX), datastore1->end(colNLLinX), datastore1->begin(colNLLinYPow), datastore1->end(colNLLinYPow));
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//jkqtpstatAddRegression(graphD_exp, JKQTPStatRegressionModelType::Exponential);
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//jkqtpstatAddRegression(graphD_powerlaw, JKQTPStatRegressionModelType::PowerLaw);
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jkqtpstatAddRegression(graphD_log, JKQTPStatRegressionModelType::Logarithm);
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// 6.1. To demonstrate polynomial fitting, we generate data for a polynomial model
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std::vector<double> pPoly {1,2,-2,0.5};
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size_t colPolyX=datastore1->addColumn("polynomial data, x");
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size_t colPolyY=datastore1->addColumn("polynomial data, y");
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for (double x=-10; x<=10; x++) {
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datastore1->appendToColumn(colPolyX, x);
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datastore1->appendToColumn(colPolyY, jkqtp_polyEval(x, pPoly.begin(), pPoly.end())+d1(gen)*50.0);
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}
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// we visualize this data with a simple scatter graph:
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JKQTPXYLineGraph* graphP;
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plot6->addGraph(graphP=new JKQTPXYLineGraph(plot6));
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graphP->setXYColumns(colPolyX, colPolyY);
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graphP->setDrawLine(false);
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graphP->setTitle(QString("data $%1+\\mathcal{N}(0,50)$").arg(jkqtp_polynomialModel2Latex(pPoly.begin(), pPoly.end())));
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// 6.2. now we can fit polynomials with different number of coefficients:
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for (size_t p=0; p<=5; p++) {
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std::vector<double> pFit;
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JKQTPXFunctionLineGraph* gPoly;
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jkqtpstatPolyFit(datastore1->begin(colPolyX), datastore1->end(colPolyX), datastore1->begin(colPolyY), datastore1->end(colPolyY), p, std::back_inserter(pFit));
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plot6->addGraph(gPoly=new JKQTPXFunctionLineGraph(plot6));
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gPoly->setPlotFunctionFunctor(jkqtp_generatePolynomialModel(pFit.begin(), pFit.end()));
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gPoly->setTitle(QString("regression: $%1$").arg(jkqtp_polynomialModel2Latex(pFit.begin(), pFit.end())));
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}
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// 6.3. of course also the "adaptor" shortcuts are available:
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//for (size_t p=0; p<=5; p++) {
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// jkqtpstatAddPolyFit(plot6->getPlotter(), datastore1->begin(colPolyX), datastore1->end(colPolyX), datastore1->begin(colPolyY), datastore1->end(colPolyY), p);
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// jkqtpstatAddPolyFit(graphP, p);
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//}
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// autoscale the plot so the graph is contained
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plot1->zoomToFit();
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plot1->getXAxis()->setShowZeroAxis(false);
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plot1->getYAxis()->setShowZeroAxis(false);
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plot1->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideTopLeft);
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plot2->zoomToFit();
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plot2->getXAxis()->setShowZeroAxis(false);
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plot2->getYAxis()->setShowZeroAxis(false);
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plot2->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideTopLeft);
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plot3->zoomToFit();
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plot3->getXAxis()->setShowZeroAxis(false);
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plot3->getYAxis()->setShowZeroAxis(false);
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plot3->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideTopLeft);
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plot4->zoomToFit();
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plot4->getXAxis()->setShowZeroAxis(false);
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plot4->getYAxis()->setShowZeroAxis(false);
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plot4->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideTopLeft);
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plot4->setAbsoluteX(0.05, plot4->getXMax());
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plot4->zoomToFit();
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plot5->getXAxis()->setShowZeroAxis(false);
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plot5->getYAxis()->setShowZeroAxis(false);
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plot5->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideTopLeft);
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plot5->setAbsoluteX(0.05, plot5->getXMax());
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plot5->zoomToFit();
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plot6->getXAxis()->setShowZeroAxis(false);
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plot6->getYAxis()->setShowZeroAxis(false);
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plot6->getPlotter()->setKeyPosition(JKQTPKeyPosition::JKQTPKeyInsideBottomRight);
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plot6->zoomToFit();
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// show plotter and make it a decent size
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mainWidget.show();
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mainWidget.resize(1600,800);
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return app.exec();
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}
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