mirror of
https://github.com/jkriege2/JKQtPlotter.git
synced 2024-12-25 10:01:38 +08:00
added weighted sum of deviations (chi-square) and coefficient of determination (R^2) to statistics library
added log regression model to statistics library added output of R^2 and chi^2 to regression adaptors (output in graph label) bugfixed some documentation typos
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jkriege2
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@ -72,21 +72,21 @@ All statistics functions use all values in the given range and convert each valu
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\defgroup jkqtptools_math_statistics_1dhist 1-dimensional Histograms
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\ingroup jkqtptools_math_statistics
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\defgroup jkqtptools_math_statistics_1dhist_kernels Kernels for 1-dimensional Histograms
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\ingroup jkqtptools_math_statistics_1dhist
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\defgroup jkqtptools_math_statistics_2dhist 2-dimensional Histograms
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\ingroup jkqtptools_math_statistics
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\defgroup jkqtptools_math_statistics_2dhist_kernels Kernels for 2-dimensional Histograms
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\ingroup jkqtptools_math_statistics_2dhist
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\defgroup jkqtptools_math_statistics_1dkde 1-dimensional Kernel Density Estimates
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\ingroup jkqtptools_math_statistics
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\defgroup jkqtptools_math_statistics_1dkde_kernels Kernels for 1-dimensional Histograms
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\ingroup jkqtptools_math_statistics_1dkde
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\defgroup jkqtptools_math_statistics_2dkde 2-dimensional Kernel Density Estimates
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\ingroup jkqtptools_math_statistics
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\defgroup jkqtptools_math_statistics_2dkde_kernels Kernels for 2-dimensional Histograms
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\ingroup jkqtptools_math_statistics_2dkde
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\defgroup jkqtptools_math_statistics_adaptors Statistics To Plot Adaptors
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\ingroup jkqtptools_math_statistics
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@ -189,7 +189,10 @@ Again these two steps can be simplified using an "adaptor":
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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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```
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... or even shorter:
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```.cpp
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jkqtpstatAddLinearWeightedRegression(graphD);
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```
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@ -208,8 +211,9 @@ which performs a simple non-weighted regression. The difference between the two
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# Linearizable Regression Models
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In addition to the simple linear regression model `f(x)=a+b*x`, it is also possible to fit a few non-linear models by transforming the data:
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- power-law function`f(x)=a*x^b`, which is a linear function in a log-log-plot
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- exponential function `f(x)=a*exp(b*x)`, which is a linear function in a semi-log-plot
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- power-law function`f(x)=a*x^b`, which is a linear function in a log(x)-log(y)-plot
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- exponential function `f(x)=a*exp(b*x)`, which is a linear function in a x-log(y)-plot
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- logarithm function `f(x)=a+b*ln(x)`, which is a linear function in a exp(x)-y-plot
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The available models are defined in the enum `JKQTPStatRegressionModelType`. And there exists a function `jkqtpStatGenerateRegressionModel()`, which returns a C++-functor representing the function.
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To demonstrate these fitting options, we first generate data from an exponential and a power-law model. Note that we also add normally distributed errors, but in order to ensure that we do not obtain y-values <0, we use loops that draw normally distributed random numbers, until this condition is met:
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@ -234,11 +238,11 @@ To demonstrate these fitting options, we first generate data from an exponential
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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_powerlaw, b0_powerlaw)+d1(gen);
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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_powerlaw, b0_powerlaw)+d1(gen);
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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, model_exp(x, a0_exp, b0_exp)+d1(gen));
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datastore1->appendToColumn(colNLLinYExp, yexp);
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}
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```
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@ -284,6 +288,7 @@ Of course also "adaptors" exist that allow to perform the steps above in a singl
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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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```
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... or even shorter:
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```.cpp
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jkqtpstatAddRegression(graphD_exp, JKQTPStatRegressionModelType::Exponential);
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jkqtpstatAddRegression(graphD_powerlaw, JKQTPStatRegressionModelType::PowerLaw);
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@ -206,11 +206,15 @@ int main(int argc, char* argv[])
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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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@ -218,11 +222,12 @@ int main(int argc, char* argv[])
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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_powerlaw, b0_powerlaw)+d1(gen);
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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_powerlaw, b0_powerlaw)+d1(gen);
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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, model_exp(x, a0_exp, b0_exp)+d1(gen));
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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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@ -235,6 +240,11 @@ int main(int argc, char* argv[])
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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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@ -253,6 +263,7 @@ int main(int argc, char* argv[])
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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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@ -110,15 +110,17 @@ std::function<double (double, double, double)> jkqtpStatGenerateRegressionModel(
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case JKQTPStatRegressionModelType::Linear: return [](double x, double a, double b)->double { return a+b*x; };
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case JKQTPStatRegressionModelType::PowerLaw: return [](double x, double a, double b)->double { return a*pow(x,b); };
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case JKQTPStatRegressionModelType::Exponential: return [](double x, double a, double b)->double { return a*exp(b*x); };
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case JKQTPStatRegressionModelType::Logarithm: return [](double x, double a, double b)->double { return a+b*log(x); };
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}
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateRegressionModel()");
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}
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QString jkqtpstatRegressionModel2Latex(JKQTPStatRegressionModelType type, double a, double b) {
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switch(type) {
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case JKQTPStatRegressionModelType::Linear: return QString("f(x)=%1+%2{\\cdot}x").arg(jkqtp_floattolatexqstr(a, 3)).arg(jkqtp_floattolatexqstr(b, 3));
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case JKQTPStatRegressionModelType::Linear: return QString("f(x)=%1%2{\\cdot}x").arg(jkqtp_floattolatexqstr(a, 2, true, 1e-16,1e-2, 1e4,false)).arg(jkqtp_floattolatexqstr(b, 2, true, 1e-16,1e-2, 1e4,true));
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case JKQTPStatRegressionModelType::PowerLaw: return QString("f(x)=%1{\\cdot}x^{%2}").arg(jkqtp_floattolatexqstr(a, 3)).arg(jkqtp_floattolatexqstr(b, 3));
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case JKQTPStatRegressionModelType::Exponential: return QString("f(x)=%1{\\cdot}\\exp(%2{\\cdot}x)").arg(jkqtp_floattolatexqstr(a, 3)).arg(jkqtp_floattolatexqstr(b, 3));
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case JKQTPStatRegressionModelType::Logarithm: return QString("f(x)=%1%2{\\cdot}\\ln(x)").arg(jkqtp_floattolatexqstr(a, 2, true, 1e-16,1e-2, 1e4,false)).arg(jkqtp_floattolatexqstr(b, 2, true, 1e-16,1e-2, 1e4,true));
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}
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpstatRegressionModel2Latex()");
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}
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@ -130,11 +132,13 @@ std::function<double (double)> jkqtpStatGenerateRegressionModel(JKQTPStatRegress
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std::pair<std::function<double (double)>, std::function<double (double)> > jkqtpStatGenerateTransformation(JKQTPStatRegressionModelType type) {
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auto logF=[](double x)->double { return log(x); };
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auto expF=[](double x)->double { return exp(x); };
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auto idF=&jkqtp_identity<double>;
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switch(type) {
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case JKQTPStatRegressionModelType::Linear: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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case JKQTPStatRegressionModelType::PowerLaw: return std::pair<std::function<double(double)>,std::function<double(double)> >(logF, logF);
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case JKQTPStatRegressionModelType::Exponential: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, logF);
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case JKQTPStatRegressionModelType::Logarithm: return std::pair<std::function<double(double)>,std::function<double(double)> >(logF, idF);
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}
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateTransformation()");
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}
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@ -147,8 +151,9 @@ std::pair<std::function<double (double)>, std::function<double (double)> > jkqtp
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case JKQTPStatRegressionModelType::Linear: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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case JKQTPStatRegressionModelType::PowerLaw: return std::pair<std::function<double(double)>,std::function<double(double)> >(logF, expF);
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case JKQTPStatRegressionModelType::Exponential: return std::pair<std::function<double(double)>,std::function<double(double)> >(logF, expF);
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case JKQTPStatRegressionModelType::Logarithm: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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}
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateTransformation()");
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateParameterATransformation()");
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}
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std::pair<std::function<double (double)>, std::function<double (double)> > jkqtpStatGenerateParameterBTransformation(JKQTPStatRegressionModelType type) {
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@ -159,6 +164,7 @@ std::pair<std::function<double (double)>, std::function<double (double)> > jkqtp
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case JKQTPStatRegressionModelType::Linear: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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case JKQTPStatRegressionModelType::PowerLaw: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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case JKQTPStatRegressionModelType::Exponential: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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case JKQTPStatRegressionModelType::Logarithm: return std::pair<std::function<double(double)>,std::function<double(double)> >(idF, idF);
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}
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateTransformation()");
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throw std::runtime_error("unknown JKQTPStatRegressionModelType in jkqtpStatGenerateParameterBTransformation()");
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}
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@ -1800,7 +1800,7 @@ inline void jkqtpstatKDE1D(InputIt first, InputIt last, double binXLeft, double
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/*! \brief calculate the linear regression coefficients for a given data range \a firstX / \a firstY ... \a lastX / \a lastY where the model is \f$ f(x)=a+b\cdot x \f$
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i\left(y_i-(a+b\cdot x_i)\right)^2 \f]
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-(a+b\cdot x_i)\right)^2 \f]
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\ingroup jkqtptools_math_statistics_regression
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\tparam InputItX standard iterator type of \a firstX and \a lastX.
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@ -1857,7 +1857,7 @@ inline void jkqtpstatLinearRegression(InputItX firstX, InputItX lastX, InputItY
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/*! \brief calculate the weighted linear regression coefficients for a given for a given data range \a firstX / \a firstY / \a firstW ... \a lastX / \a lastY / \a lastW where the model is \f$ f(x)=a+b\cdot x \f$
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_iw_i^2\cdot\left(y_i-(a+b\cdot x_i)\right)^2 \f]
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_iw_i^2\cdot\left(y_i-(a+b\cdot x_i)\right)^2 \f]
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\ingroup jkqtptools_math_statistics_regression
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\tparam InputItX standard iterator type of \a firstX and \a lastX.
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@ -1937,7 +1937,7 @@ inline void jkqtpstatLinearWeightedRegression(InputItX firstX, InputItX lastX, I
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/*! \brief calculate the (robust) iteratively reweighted least-squares (IRLS) estimate for the parameters of the model \f$ f(x)=a+b\cdot x \f$
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for a given data range \a firstX / \a firstY ... \a lastX / \a lastY
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So this function finds an outlier-robust solution to the optimization problem:
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\f[ (a^\ast,b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p \f]
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\f[ (a^\ast,b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p \f]
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\ingroup jkqtptools_math_statistics_regression
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\ingroup jkqtptools_math_statistics_regression
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@ -1957,16 +1957,16 @@ inline void jkqtpstatLinearWeightedRegression(InputItX firstX, InputItX lastX, I
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This is a simple form of the IRLS algorithm to estimate the parameters a and b in a linear model \f$ f(x)=a+b\cdot x \f$.
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This algorithm solves the optimization problem for a \f$ L_p\f$-norm:
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\f[ (a^\ast,b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p \f]
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\f[ (a^\ast,b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p \f]
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by iteratively optimization weights \f$ \vec{w} \f$ and solving a weighted least squares problem in each iteration:
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\f[ (a_n,b_n)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^{(p-2)}\cdot|a+b\cdot x_i-y_i|^2 \f]
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\f[ (a_n,b_n)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^{(p-2)}\cdot|a+b\cdot x_i-y_i|^2 \f]
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The IRLS-algorithm works as follows:
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- calculate initial \f$ a_0\f$ and \f$ b_0\f$ with unweighted regression from x and y
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- perform a number of iterations (parameter \a iterations ). In each iteration \f$ n\f$:
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- calculate the error vector \f$\vec{e}\f$: \f[ e_i = a+b\cdot x_i -y_i \f]
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- estimate new weights \f$\vec{w}\f$: \[ w_i=|e_i|^{(p-2)/2} \f]
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- estimate new weights \f$\vec{w}\f$: \f[ w_i=|e_i|^{(p-2)/2} \f]
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- calculate new estimates \f$ a_n\f$ and \f$ b_n\f$ with weighted regression from \f$ \vec{x}\f$ and \f$ \vec{y}\f$ and \f$ \vec{w}\f$
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.
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- return the last estimates \f$ a_n\f$ and \f$ b_n\f$
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@ -2024,6 +2024,7 @@ enum class JKQTPStatRegressionModelType {
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Linear, /*!< \brief linear model \f$ f(x)=a+b\cdot x \f$ */
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PowerLaw, /*!< \brief power law model \f$ f(x)=a\cdot x^b \f$ */
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Exponential, /*!< \brief exponential model \f$ f(x)=a\cdot \exp(b\cdot x) \f$ */
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Logarithm, /*!< \brief exponential model \f$ f(x)=a+b\cdot \ln(x) \f$ */
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};
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@ -2064,7 +2065,7 @@ JKQTP_LIB_EXPORT std::pair<std::function<double(double)>,std::function<double(do
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/*! \brief calculate the linear regression coefficients for a given data range \a firstX / \a firstY ... \a lastX / \a lastY where the model is defined by \a type
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^2 \f]
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So this function solves the least-squares optimization problem: \f[ (a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^2 \f]
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by reducing it to a linear fit by transforming x- and/or y-data
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\ingroup jkqtptools_math_statistics_regression
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@ -2108,7 +2109,7 @@ inline void jkqtpstatRegression(JKQTPStatRegressionModelType type, InputItX firs
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/*! \brief calculate the robust linear regression coefficients for a given data range \a firstX / \a firstY ... \a lastX / \a lastY where the model is defined by \a type
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So this function solves the Lp-norm optimization problem: \f[ (a^\ast, b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^p \f]
|
||||
So this function solves the Lp-norm optimization problem: \f[ (a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^p \f]
|
||||
by reducing it to a linear fit by transforming x- and/or y-data
|
||||
\ingroup jkqtptools_math_statistics_regression
|
||||
|
||||
@ -2155,7 +2156,7 @@ inline void jkqtpstatRobustIRLSRegression(JKQTPStatRegressionModelType type, Inp
|
||||
|
||||
|
||||
/*! \brief calculate the robust linear regression coefficients for a given data range \a firstX / \a firstY ... \a lastX / \a lastY where the model is defined by \a type
|
||||
So this function solves the Lp-norm optimization problem: \f[ (a^\ast, b^\ast)=\mathop{arg\;min}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^p \f]
|
||||
So this function solves the Lp-norm optimization problem: \f[ (a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^p \f]
|
||||
by reducing it to a linear fit by transforming x- and/or y-data
|
||||
\ingroup jkqtptools_math_statistics_regression
|
||||
|
||||
@ -2395,11 +2396,124 @@ QString jkqtpstatPolynomialModel2Latex(PolyItP firstP, PolyItP lastP) {
|
||||
|
||||
|
||||
|
||||
/*! \brief calculates the coefficient of determination \f$ R^2 \f$ for a set of measurements \f$ (x_i,y_i) \f$ with a fit function \f$ f(x) \f$
|
||||
\ingroup jkqtptools_math_statistics_poly
|
||||
|
||||
\tparam InputItX standard iterator type of \a firstX and \a lastX.
|
||||
\tparam InputItY standard iterator type of \a firstY and \a lastY.
|
||||
\param firstX iterator pointing to the first item in the x-dataset to use \f$ x_1 \f$
|
||||
\param lastX iterator pointing behind the last item in the x-dataset to use \f$ x_N \f$
|
||||
\param firstY iterator pointing to the first item in the y-dataset to use \f$ y_1 \f$
|
||||
\param lastY iterator pointing behind the last item in the y-dataset to use \f$ y_N \f$
|
||||
\param f function \f$ f(x) \f$, result of a fit to the data
|
||||
\return coeffcicient of determination \f[ R^2=1-\frac{\sum_i\bigl[y_i-f(x_i)\bigr]^2}{\sum_i\bigl[y_i-\overline{y}\bigr]^2} \f] where \f[ \overline{y}=\frac{1}{N}\cdot\sum_iy_i \f]
|
||||
|
||||
|
||||
|
||||
\see https://en.wikipedia.org/wiki/Coefficient_of_determination
|
||||
*/
|
||||
template <class InputItX, class InputItY>
|
||||
inline double jkqtpstatCoefficientOfDetermination(InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, std::function<double(double)> f) {
|
||||
|
||||
auto itX=firstX;
|
||||
auto itY=firstY;
|
||||
|
||||
const double yMean=jkqtpstatAverage(firstX,lastX);
|
||||
double SSres=0;
|
||||
double SStot=0;
|
||||
for (; itX!=lastX && itY!=lastY; ++itX, ++itY) {
|
||||
const double fit_x=jkqtp_todouble(*itX);
|
||||
const double fit_y=jkqtp_todouble(*itY);
|
||||
if (JKQTPIsOKFloat(fit_x) && JKQTPIsOKFloat(fit_y)) {
|
||||
SStot+=jkqtp_sqr(fit_y-yMean);
|
||||
SSres+=jkqtp_sqr(fit_y-f(fit_x));
|
||||
}
|
||||
}
|
||||
|
||||
return 1.0-SSres/SStot;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
/*! \brief calculates the sum of deviations \f$ \chi^2 \f$ for a set of measurements \f$ (x_i,y_i) \f$ with a fit function \f$ f(x) \f$
|
||||
\ingroup jkqtptools_math_statistics_poly
|
||||
|
||||
\tparam InputItX standard iterator type of \a firstX and \a lastX.
|
||||
\tparam InputItY standard iterator type of \a firstY and \a lastY.
|
||||
\param firstX iterator pointing to the first item in the x-dataset to use \f$ x_1 \f$
|
||||
\param lastX iterator pointing behind the last item in the x-dataset to use \f$ x_N \f$
|
||||
\param firstY iterator pointing to the first item in the y-dataset to use \f$ y_1 \f$
|
||||
\param lastY iterator pointing behind the last item in the y-dataset to use \f$ y_N \f$
|
||||
\param f function \f$ f(x) \f$, result of a fit to the data
|
||||
\return sum of deviations \f[ \chi^2=\sum_i\bigl[y_i-f(x_i)\bigr]^2 \f]
|
||||
|
||||
|
||||
|
||||
\see https://en.wikipedia.org/wiki/Coefficient_of_determination
|
||||
*/
|
||||
template <class InputItX, class InputItY>
|
||||
inline double jkqtpstatSumOfDeviations(InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, std::function<double(double)> f) {
|
||||
|
||||
auto itX=firstX;
|
||||
auto itY=firstY;
|
||||
|
||||
double SSres=0;
|
||||
for (; itX!=lastX && itY!=lastY; ++itX, ++itY) {
|
||||
const double fit_x=jkqtp_todouble(*itX);
|
||||
const double fit_y=jkqtp_todouble(*itY);
|
||||
if (JKQTPIsOKFloat(fit_x) && JKQTPIsOKFloat(fit_y)) {
|
||||
SSres+=jkqtp_sqr(fit_y-f(fit_x));
|
||||
}
|
||||
}
|
||||
|
||||
return SSres;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
/*! \brief calculates the weighted sum of deviations \f$ \chi^2 \f$ for a set of measurements \f$ (x_i,y_i,w_i) \f$ with a fit function \f$ f(x) \f$
|
||||
\ingroup jkqtptools_math_statistics_poly
|
||||
|
||||
\tparam InputItX standard iterator type of \a firstX and \a lastX.
|
||||
\tparam InputItY standard iterator type of \a firstY and \a lastY.
|
||||
\tparam InputItW standard iterator type of \a firstW and \a lastW.
|
||||
\param firstX iterator pointing to the first item in the x-dataset to use \f$ x_1 \f$
|
||||
\param lastX iterator pointing behind the last item in the x-dataset to use \f$ x_N \f$
|
||||
\param firstY iterator pointing to the first item in the y-dataset to use \f$ y_1 \f$
|
||||
\param lastY iterator pointing behind the last item in the y-dataset to use \f$ y_N \f$
|
||||
\param firstW iterator pointing to the first item in the weight-dataset to use \f$ w_1 \f$
|
||||
\param lastW iterator pointing behind the last item in the weight-dataset to use \f$ w_N \f$
|
||||
\param f function \f$ f(x) \f$, result of a fit to the data
|
||||
\param fWeightDataToWi an optional function, which is applied to the data from \a firstW ... \a lastW to convert them to weight, i.e. \c wi=fWeightDataToWi(*itW)
|
||||
e.g. if you use data used to draw error bars, you can use jkqtp_inversePropSaveDefault(). The default is jkqtp_identity(), which just returns the values.
|
||||
In the case of jkqtp_inversePropSaveDefault(), a datapoint x,y, has a large weight, if it's error is small and in the case if jkqtp_identity() it's weight
|
||||
is directly proportional to the given value.
|
||||
\return weighted sum of deviations \f[ \chi^2=\sum_iw_i^2\cdot\bigl[y_i-f(x_i)\bigr]^2 \f]
|
||||
|
||||
|
||||
\see https://en.wikipedia.org/wiki/Reduced_chi-squared_statistic
|
||||
*/
|
||||
template <class InputItX, class InputItY, class InputItW>
|
||||
inline double jkqtpstatWeightedSumOfDeviations(InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, InputItW firstW, InputItW lastW, std::function<double(double)> f, std::function<double(double)> fWeightDataToWi=&jkqtp_identity<double>) {
|
||||
|
||||
auto itX=firstX;
|
||||
auto itY=firstY;
|
||||
auto itW=firstW;
|
||||
|
||||
double SSres=0;
|
||||
for (; itX!=lastX && itY!=lastY && itW!=lastW; ++itX, ++itY, ++itW) {
|
||||
const double fit_x=jkqtp_todouble(*itX);
|
||||
const double fit_y=jkqtp_todouble(*itY);
|
||||
const double fit_w2=jkqtp_sqr(fWeightDataToWi(jkqtp_todouble(*itW)));
|
||||
if (JKQTPIsOKFloat(fit_x) && JKQTPIsOKFloat(fit_y) && JKQTPIsOKFloat(fit_w2)) {
|
||||
SSres+=fit_w2*jkqtp_sqr(fit_y-f(fit_x));
|
||||
}
|
||||
}
|
||||
|
||||
return SSres;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@ -212,38 +212,46 @@ std::string jkqtp_tolower(const std::string& s){
|
||||
return res;
|
||||
}
|
||||
|
||||
std::string jkqtp_floattolatexstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent){
|
||||
if ((belowIsZero>0) && (fabs(data)<belowIsZero)) return "\\rm{0}";
|
||||
if (data==0) return "\\rm{0}";
|
||||
std::string jkqtp_floattolatexstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent, bool ensurePlusMinus){
|
||||
if ((belowIsZero>0) && (fabs(data)<belowIsZero)) {
|
||||
if (ensurePlusMinus) return "+\\rm{0}";
|
||||
else return "\\rm{0}";
|
||||
}
|
||||
if (fabs(data)<5*std::numeric_limits<double>::epsilon()) {
|
||||
if (ensurePlusMinus) return "+\\rm{0}";
|
||||
else return "\\rm{0}";
|
||||
}
|
||||
|
||||
double adata=fabs(data);
|
||||
std::string res=jkqtp_floattostr(data, past_comma, remove_trail0);
|
||||
/*std::string form="%."+inttostr(past_comma)+"lf";
|
||||
std::string res=jkqtp_format(form,data);
|
||||
std::string s="";
|
||||
if (data<0) s="-";*/
|
||||
|
||||
long exp=(long)floor(log(adata)/log(10.0));
|
||||
//std::cout<<"data="<<data<<" res="<<res<<" exp="<<exp<<" past_comma="<<past_comma<<std::endl;
|
||||
//if (exp==0 || exp==-1 || exp==1) return res;
|
||||
if ((minNoExponent<=fabs(data)) && (fabs(data)<=maxNoExponent)) return res;
|
||||
//if ((-past_comma<exp) && (exp<past_comma)) return res;
|
||||
|
||||
//std::cout<<"adata="<<adata<<" log(adata)/log(10)="<<log(adata)/log(10.0)<<" exp="<<exp<<" adata/pow(10, exp)="<<adata/pow(10.0, (double)exp)<<"\n";
|
||||
std::string v=jkqtp_floattostr(data/pow(10.0, static_cast<double>(exp)), past_comma, remove_trail0);
|
||||
//std::cout<<"floattolatexstr: v="<<v<<" exp="<<exp<<std::endl;
|
||||
if (v!="1" && v!="10") return v+std::string("{\\times}10^{")+jkqtp_inttostr(exp)+"}";
|
||||
if (v=="10") exp=exp+1;
|
||||
return std::string("10^{")+jkqtp_inttostr(exp)+"}";
|
||||
long exp=static_cast<long>(floor(log(adata)/log(10.0)));
|
||||
if ((minNoExponent>fabs(data)) || (fabs(data)>maxNoExponent)) {
|
||||
std::string v=jkqtp_floattostr(data/pow(10.0, static_cast<double>(exp)), past_comma, remove_trail0);
|
||||
if (v!="1" && v!="10") {
|
||||
res=v+std::string("{\\times}10^{")+jkqtp_inttostr(exp)+"}";
|
||||
} else {
|
||||
if (v=="10") exp=exp+1;
|
||||
res=std::string("10^{")+jkqtp_inttostr(exp)+"}";
|
||||
}
|
||||
}
|
||||
if (ensurePlusMinus && res.size()>0) {
|
||||
if (res[0]!='-' && res[0]!='+') {
|
||||
if (data<0) res="-"+res;
|
||||
else res="+"+res;
|
||||
}
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
std::string jkqtp_floattohtmlstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent){
|
||||
std::string result;
|
||||
if ((belowIsZero>0) && (fabs(data)<belowIsZero)) return "0";
|
||||
if (data==0) return "0";
|
||||
if (fabs(data)<5*std::numeric_limits<double>::epsilon()) return "0";
|
||||
double adata=fabs(data);
|
||||
std::string res=jkqtp_floattostr(data, past_comma, remove_trail0);
|
||||
|
||||
long exp=(long)floor(log(adata)/log(10.0));
|
||||
long exp=static_cast<long>(floor(log(adata)/log(10.0)));
|
||||
if ((minNoExponent<=fabs(data)) && (fabs(data)<maxNoExponent)) return res;
|
||||
//if ((-past_comma<exp) && (exp<past_comma)) result= res;
|
||||
else {
|
||||
@ -568,9 +576,9 @@ QString jkqtp_floattounitqstr(double data, int past_comma, bool remove_trail0)
|
||||
return QString::fromStdString(jkqtp_floattounitstr(data, past_comma, remove_trail0));
|
||||
}
|
||||
|
||||
QString jkqtp_floattolatexqstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent)
|
||||
QString jkqtp_floattolatexqstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent, bool ensurePlusMinus)
|
||||
{
|
||||
return QString::fromStdString(jkqtp_floattolatexstr(data, past_comma, remove_trail0, belowIsZero, minNoExponent, maxNoExponent));
|
||||
return QString::fromStdString(jkqtp_floattolatexstr(data, past_comma, remove_trail0, belowIsZero, minNoExponent, maxNoExponent, ensurePlusMinus));
|
||||
}
|
||||
|
||||
QString jkqtp_floattohtmlqstr(double data, int past_comma, bool remove_trail0, double belowIsZero, double minNoExponent, double maxNoExponent)
|
||||
|
||||
@ -163,7 +163,7 @@ JKQTP_LIB_EXPORT std::string jkqtp_floattounitstr(double data, int past_comma=5,
|
||||
/** \brief convert a double to a string, encoding powers of ten as exponent in LaTeX notation (e.g. <code>-1.23\\cdot 10^{-5}</code>)
|
||||
* \ingroup jkqtptools_string
|
||||
*/
|
||||
JKQTP_LIB_EXPORT std::string jkqtp_floattolatexstr(double data, int past_comma=5, bool remove_trail0=false, double belowIsZero=1e-16, double minNoExponent=1e-3, double maxNoExponent=1e4);
|
||||
JKQTP_LIB_EXPORT std::string jkqtp_floattolatexstr(double data, int past_comma=5, bool remove_trail0=false, double belowIsZero=1e-16, double minNoExponent=1e-3, double maxNoExponent=1e4, bool ensurePlusMinus=false);
|
||||
/** \brief convert a double to a string, encoding powers of ten as exponent with HTML tags
|
||||
* \ingroup jkqtptools_string
|
||||
*/
|
||||
@ -176,7 +176,7 @@ JKQTP_LIB_EXPORT QString jkqtp_floattounitqstr(double data, int past_comma=5, bo
|
||||
/** \brief convert a double to a string, encoding powers of ten as exponent in LaTeX notation (e.g. <code>-1.23\\cdot 10^{-5}</code>)
|
||||
* \ingroup jkqtptools_string
|
||||
*/
|
||||
JKQTP_LIB_EXPORT QString jkqtp_floattolatexqstr(double data, int past_comma=5, bool remove_trail0=false, double belowIsZero=1e-16, double minNoExponent=1e-3, double maxNoExponent=1e4);
|
||||
JKQTP_LIB_EXPORT QString jkqtp_floattolatexqstr(double data, int past_comma=5, bool remove_trail0=false, double belowIsZero=1e-16, double minNoExponent=1e-3, double maxNoExponent=1e4, bool ensurePlusMinus=false);
|
||||
/** \brief convert a double to a string, encoding powers of ten as exponent with HTML tags
|
||||
* \ingroup jkqtptools_string
|
||||
*/
|
||||
|
||||
@ -689,7 +689,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddLinearRegression(JKQTBasePlotter* pl
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
|
||||
g->setParamsV(cA, cB);
|
||||
g->setTitle(QString("regression: $f(x) = %1 + %2 \\cdot x$").arg(jkqtp_floattolatexqstr(cA)).arg(jkqtp_floattolatexqstr(cB)));
|
||||
g->setTitle(QString("regression: $f(x) = %1%2{\\cdot}x, \\chi^2=%4, R^2=%3$").arg(jkqtp_floattolatexqstr(cA, 2, true, 1e-16,1e-2, 1e4,false)).arg(jkqtp_floattolatexqstr(cB, 2, true, 1e-16,1e-2, 1e4,true)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB)),3)));
|
||||
plotter->addGraph(g);
|
||||
if (coeffA) *coeffA=cA;
|
||||
if (coeffB) *coeffB=cB;
|
||||
@ -765,7 +765,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddRobustIRLSLinearRegression(JKQTBaseP
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
|
||||
g->setParamsV(cA, cB);
|
||||
g->setTitle(QString("robust regression: $f(x) = %1 + %2 \\cdot x$").arg(jkqtp_floattolatexqstr(cA)).arg(jkqtp_floattolatexqstr(cB)));
|
||||
g->setTitle(QString("robust regression: $f(x) = %1%2{\\cdot}x, \\chi^2=%4, R^2=%3$").arg(jkqtp_floattolatexqstr(cA, 2, true, 1e-16,1e-2, 1e4,false)).arg(jkqtp_floattolatexqstr(cB, 2, true, 1e-16,1e-2, 1e4,true)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB)),3)));
|
||||
plotter->addGraph(g);
|
||||
if (coeffA) *coeffA=cA;
|
||||
if (coeffB) *coeffB=cB;
|
||||
@ -853,7 +853,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddLinearWeightedRegression(JKQTBasePlo
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setSpecialFunction(JKQTPXFunctionLineGraph::SpecialFunction::Line);
|
||||
g->setParamsV(cA, cB);
|
||||
g->setTitle(QString("weighted regression: $f(x) = %1 + %2 \\cdot x$").arg(jkqtp_floattolatexqstr(cA)).arg(jkqtp_floattolatexqstr(cB)));
|
||||
g->setTitle(QString("weighted regression: $f(x) = %1%2{\\cdot}x, \\chi^2=%4, R^2=%3$").arg(jkqtp_floattolatexqstr(cA, 2, true, 1e-16,1e-2, 1e4,false)).arg(jkqtp_floattolatexqstr(cB, 2, true, 1e-16,1e-2, 1e4,true)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatWeightedSumOfDeviations(firstX,lastX,firstY,lastY,firstW,lastW,jkqtpStatGenerateRegressionModel(JKQTPStatRegressionModelType::Linear, cA, cB),fWeightDataToWi),3)));
|
||||
plotter->addGraph(g);
|
||||
if (coeffA) *coeffA=cA;
|
||||
if (coeffB) *coeffB=cB;
|
||||
@ -938,7 +938,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddRegression(JKQTBasePlotter* plotter,
|
||||
jkqtpstatRegression(type, firstX, lastX, firstY, lastY, cA, cB, fixA, fixB);
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setPlotFunctionFunctor(jkqtpStatGenerateRegressionModel(type, cA, cB));
|
||||
g->setTitle(QString("regression: $%1$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)));
|
||||
g->setTitle(QString("regression: $%1, \\chi^2=%3, R^2=%2$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)));
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plotter->addGraph(g);
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if (coeffA) *coeffA=cA;
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if (coeffB) *coeffB=cB;
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@ -1014,7 +1014,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddRobustIRLSRegression(JKQTBasePlotter
|
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jkqtpstatRobustIRLSRegression(type, firstX, lastX, firstY, lastY, cA, cB, fixA, fixB, p, iterations);
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setPlotFunctionFunctor(jkqtpStatGenerateRegressionModel(type, cA, cB));
|
||||
g->setTitle(QString("robust regression: $%1$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)));
|
||||
g->setTitle(QString("robust regression: $%1, \\chi^2=%3, R^2=%2$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)));
|
||||
plotter->addGraph(g);
|
||||
if (coeffA) *coeffA=cA;
|
||||
if (coeffB) *coeffB=cB;
|
||||
@ -1104,7 +1104,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddWeightedRegression(JKQTBasePlotter*
|
||||
jkqtpstatWeightedRegression(type, firstX, lastX, firstY, lastY, firstW, lastW, cA, cB, fixA, fixB, fWeightDataToWi);
|
||||
JKQTPXFunctionLineGraph* g=new JKQTPXFunctionLineGraph(plotter);
|
||||
g->setPlotFunctionFunctor(jkqtpStatGenerateRegressionModel(type, cA, cB));
|
||||
g->setTitle(QString("weighted regression: $%1$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)));
|
||||
g->setTitle(QString("weighted regression: $%1, \\chi^2=%3, R^2=%2$").arg(jkqtpstatRegressionModel2Latex(type, cA, cB)).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpStatGenerateRegressionModel(type, cA, cB)),3)));
|
||||
plotter->addGraph(g);
|
||||
if (coeffA) *coeffA=cA;
|
||||
if (coeffB) *coeffB=cB;
|
||||
@ -1176,7 +1176,7 @@ inline JKQTPXFunctionLineGraph* jkqtpstatAddPolyFit(JKQTBasePlotter* plotter, In
|
||||
JKQTPXFunctionLineGraph* gPoly=new JKQTPXFunctionLineGraph(plotter);
|
||||
jkqtpstatPolyFit(firstX,lastX,firstY,lastY,P,std::back_inserter(pFit));
|
||||
gPoly->setPlotFunctionFunctor(jkqtpstatGeneratePolynomialModel(pFit.begin(), pFit.end()));
|
||||
gPoly->setTitle(QString("regression: $%1$").arg(jkqtpstatPolynomialModel2Latex(pFit.begin(), pFit.end())));
|
||||
gPoly->setTitle(QString("regression: $%1, \\chi^2=%3, R^2=%2$").arg(jkqtpstatPolynomialModel2Latex(pFit.begin(), pFit.end())).arg(jkqtp_floattolatexqstr(jkqtpstatCoefficientOfDetermination(firstX,lastX,firstY,lastY,jkqtpstatGeneratePolynomialModel(pFit.begin(), pFit.end())),3)).arg(jkqtp_floattolatexqstr(jkqtpstatSumOfDeviations(firstX,lastX,firstY,lastY,jkqtpstatGeneratePolynomialModel(pFit.begin(), pFit.end())),3)));
|
||||
std::copy(pFit.begin(), pFit.end(), firstRes);
|
||||
plotter->addGraph(gPoly);
|
||||
return gPoly;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user