Merge pull request #19 from AndrewYongZhenNing/develop

Corrected Sinh model's definition, init fit parameter & fold definition.

.github/workflows/build-macos.yml

@@ -1,6 +1,6 @@
 name: Build macOS
 
-on: [push, workflow_dispatch]
+on: [push]
 
 jobs:
   build:

examples/exRand.cpp

@@ -7,7 +7,7 @@
 using namespace std;
 using namespace Latan;
 
-constexpr Index  n             = 8;
+constexpr Index  size          = 8;
 constexpr Index  nDraw         = 20000;
 constexpr Index  nSample       = 2000;
 const     string stateFileName = "exRand.seed";
@@ -40,14 +40,14 @@ int main(void)
     p << PlotFunction(compile("return exp(-x_0^2/2)/sqrt(2*pi);", 1), -5., 5.);
     p.display();
 
-    DMat       var(n, n);
+    DMat       var(size, size);
-    DVec       mean(n);
+    DVec       mean(size);
-    DMatSample sample(nSample, n, 1);
+    DMatSample sample(nSample, size, 1);
 
     cout << "-- generating " << nSample << " Gaussian random vectors..." << endl;
-    var   = DMat::Random(n, n);
+    var   = DMat::Random(size, size);
     var  *= var.adjoint();
-    mean  = DVec::Random(n); 
+    mean  = DVec::Random(size); 
     RandomNormal mgauss(mean, var, rd());
     sample[central] = mgauss();
     FOR_STAT_ARRAY(sample, s)

lib/Core/Math.cpp

@@ -18,7 +18,6 @@
  */
 
 #include <LatAnalyze/Core/Math.hpp>
-#include <LatAnalyze/Numerical/GslFFT.hpp>
 #include <LatAnalyze/includes.hpp>
 #include <gsl/gsl_cdf.h>
 
@@ -49,42 +48,16 @@ DMat MATH_NAMESPACE::corrToVar(const DMat &corr, const DVec &varDiag)
     return res;
 }
 
-double MATH_NAMESPACE::conditionNumber(const DMat &mat)
+double MATH_NAMESPACE::svdDynamicRange(const DMat &mat)
 {
     DVec s = mat.singularValues();
 
     return s.maxCoeff()/s.minCoeff();
 }
 
-double MATH_NAMESPACE::cdr(const DMat &mat)
+double MATH_NAMESPACE::svdDynamicRangeDb(const DMat &mat)
 {
-    return 10.*log10(conditionNumber(mat));
+    return 10.*log10(svdDynamicRange(mat));
-}
-
-template <typename FFT>
-double nsdr(const DMat &m)
-{
-    Index  n = m.rows();
-    FFT    fft(n);
-    CMat   buf(n, 1);
-
-    FOR_VEC(buf, i)
-    {
-        buf(i) = 0.;
-        for (Index j = 0; j < n; ++j)
-        {
-            buf(i) += m(j, (i+j) % n);
-        }
-        buf(i) /= n;
-    }
-    fft(buf, FFT::Forward);
-
-    return 10.*log10(buf.real().maxCoeff()/buf.real().minCoeff());
-}
-
-double MATH_NAMESPACE::nsdr(const DMat &mat)
-{
-    return ::nsdr<GslFFT>(mat);
 }
 
 /******************************************************************************

lib/Core/Math.hpp

@@ -73,9 +73,8 @@ namespace MATH_NAMESPACE
     DMat corrToVar(const DMat &corr, const DVec &varDiag);
 
     // matrix SVD dynamic range
-    double conditionNumber(const DMat &mat);
+    double svdDynamicRange(const DMat &mat);
-    double cdr(const DMat &mat);
+    double svdDynamicRangeDb(const DMat &mat);
-    double nsdr(const DMat &mat);
     
     // Constants
     constexpr double pi  = 3.1415926535897932384626433832795028841970;

lib/Core/Plot.cpp

@@ -515,16 +515,14 @@ void Dash::operator()(PlotOptions &option) const
 }
 
 // LogScale constructor ////////////////////////////////////////////////////////
-LogScale::LogScale(const Axis axis, const double basis)
+LogScale::LogScale(const Axis axis)
 : axis_(axis)
-, basis_(basis)
 {}
 
 // Logscale modifier ///////////////////////////////////////////////////////////
 void LogScale::operator()(PlotOptions &option) const
 {
-    option.scaleMode[static_cast<int>(axis_)]     |= Plot::Scale::log;
+    option.scaleMode[static_cast<int>(axis_)] |= Plot::Scale::log;
-    option.logScaleBasis[static_cast<int>(axis_)]  = basis_;
 }
 
 // PlotRange constructors //////////////////////////////////////////////////////
@@ -917,11 +915,11 @@ ostream & Latan::operator<<(ostream &out, const Plot &plot)
     out << "unset log" << endl;
     if (plot.options_.scaleMode[x] & Plot::Scale::log)
     {
-        out << "set log x " << plot.options_.logScaleBasis[x] << endl;;
+        out << "set log x" << endl;
     }
     if (plot.options_.scaleMode[y] & Plot::Scale::log)
     {
-        out << "set log y " << plot.options_.logScaleBasis[y] << endl;
+        out << "set log y" << endl;
     }
     if (!plot.options_.label[x].empty())
     {

lib/Core/Plot.hpp

@@ -227,7 +227,6 @@ struct PlotOptions
     std::string              caption;
     std::string              title;
     unsigned int             scaleMode[2];
-    double                   logScaleBasis[2];
     Range                    scale[2];
     std::string              label[2];
     std::string              lineColor;
@@ -315,14 +314,13 @@ class LogScale: public PlotModifier
 {
 public:
     // constructor
-    explicit LogScale(const Axis axis, const double basis = 10);
+    explicit LogScale(const Axis axis);
     // destructor
     virtual ~LogScale(void) = default;
     // modifier
     virtual void operator()(PlotOptions &option) const;
 private:
     const Axis axis_;
-    const double basis_;
 };
 
 class PlotRange: public PlotModifier

lib/Core/Utilities.hpp

@@ -108,6 +108,23 @@ inline std::string strFrom(const T x)
 }
 
 // specialization for vectors
+template<>
+inline std::vector<Index> strTo<std::vector<Index>>(const std::string &str)
+{
+    std::vector<Index>  res;
+    std::vector<double> vbuf;
+    double              buf;
+    std::istringstream  stream(str);
+    
+    while (!stream.eof())
+    {
+        stream >> buf;
+        res.push_back(buf);
+    }
+    
+    return res;
+}
+
 template<>
 inline DVec strTo<DVec>(const std::string &str)
 {

lib/Numerical/DWT.cpp

@@ -135,26 +135,3 @@ DVec DWT::backward(const std::vector<DWTLevel>& dwt) const
 
     return res;
 }
-
-// concatenate levels //////////////////////////////////////////////////////////
-DVec DWT::concat(const std::vector<DWTLevel> &dwt, const int maxLevel, const bool dropLow)
-{
-    unsigned int level = ((maxLevel >= 0) ? (maxLevel + 1) : dwt.size());
-    Index nlast = dwt[level - 1].first.size();
-    Index n = 2*dwt.front().first.size() - ((dropLow) ? nlast : 0);
-    Index pt = n, nl;
-    DVec  res(n);
-
-    for (unsigned int l = 0; l < level; ++l)
-    {
-        nl  = dwt[l].second.size();
-        pt -= nl;
-        res.segment(pt, nl) = dwt[l].second;
-    }
-    if (!dropLow)
-    {
-        res.segment(0, nl) = dwt[level-1].first;
-    }
-
-    return res;
-}

lib/Numerical/DWT.hpp

@@ -46,8 +46,6 @@ public:
     // DWT
     std::vector<DWTLevel> forward(const DVec &data, const unsigned int level) const;
     DVec                  backward(const std::vector<DWTLevel>& dwt) const;
-    // concatenate levels
-    static DVec concat(const std::vector<DWTLevel>& dwt, const int maxLevel = -1, const bool dropLow = false);
 private:
     DWTFilter filter_;
 };

lib/Physics/CorrelatorFitter.cpp

@@ -253,16 +253,39 @@ DMatSample CorrelatorUtils::shift(const DMatSample &c, const Index ts)
     }
 }
 
-DMatSample CorrelatorUtils::fold(const DMatSample &c)
+DMatSample CorrelatorUtils::fold(const DMatSample &c, const CorrelatorModels::ModelPar &par)
 {
     const Index nt  = c[central].rows();
     DMatSample  buf = c;
+    int         sign;
+    bool        fold = false;
     
-    FOR_STAT_ARRAY(buf, s)
+    switch (par.type)
     {
-        for (Index t = 0; t < nt; ++t)
+        case CorrelatorType::cosh:
+        case CorrelatorType::cst:
+            sign = 1;
+            fold = true;
+            break;
+        case CorrelatorType::sinh:
+            sign = -1;
+            fold = true;
+            break;
+        case CorrelatorType::linear:
+            cout << "Linear model is asymmetric: will not fold." << endl;
+            break;
+        default:
+            break;
+    }
+
+    if (fold)
+    {
+        FOR_STAT_ARRAY(buf, s)
         {
-            buf[s](t) = 0.5*(c[s](t) + c[s]((nt - t) % nt));
+            for (Index t = 0; t < nt; ++t)
+            {
+                buf[s](t) = 0.5*(c[s](t) + sign*c[s]((nt - t) % nt));
+            }
         }
     }
 

lib/Physics/CorrelatorFitter.hpp

@@ -56,7 +56,7 @@ namespace CorrelatorModels
 namespace CorrelatorUtils
 {
     DMatSample shift(const DMatSample &c, const Index ts);
-    DMatSample fold(const DMatSample &c);
+    DMatSample fold(const DMatSample &c, const CorrelatorModels::ModelPar &par);
     DMatSample fourierTransform(const DMatSample &c, FFT &fft, 
                                 const unsigned int dir = FFT::Forward);
 };

lib/Statistics/Histogram.cpp

@@ -146,6 +146,16 @@ double Histogram::getX(const Index i) const
     return x_(i);
 }
 
+double Histogram::getXMin(void) const
+{
+    return xMin_;
+}
+
+double Histogram::getXMax(void) const
+{
+    return xMax_;
+}
+
 double Histogram::operator[](const Index i) const
 {
     return bin_(i)*(isNormalized() ? norm_ : 1.);

lib/Statistics/Histogram.hpp

@@ -52,6 +52,8 @@ public:
     const StatArray<double> & getData(void) const;
     const StatArray<double> & getWeight(void) const;
     double                    getX(const Index i) const;
+    double                    getXMin(void) const;
+    double                    getXMax(void) const;
     double                    operator[](const Index i) const;
     double                    operator()(const double x) const;
     // percentiles & confidence interval

lib/Statistics/XYSampleData.cpp

@@ -300,6 +300,67 @@ const XYStatData & XYSampleData::getData(void)
 }
 
 // fit /////////////////////////////////////////////////////////////////////////
+
+void XYSampleData::fitSample(std::vector<Minimizer *> &minimizer,
+                             const std::vector<const DoubleModel *> &v,
+                             SampleFitResult &result,
+                             DVec &init,
+                             Index s)
+{
+    result.resize(nSample_);
+    result.chi2_.resize(nSample_);
+    result.model_.resize(v.size());
+    FitResult sampleResult;
+    setDataToSample(s);
+    if (s == central)
+    {
+        sampleResult        = data_.fit(minimizer, init, v);
+        init                = sampleResult.segment(0, init.size());
+        result.nPar_        = sampleResult.getNPar();
+        result.nDof_        = sampleResult.nDof_;
+        result.parName_     = sampleResult.parName_;
+        result.corrRangeDb_ = Math::svdDynamicRangeDb(getFitCorrMat());
+    }
+    else
+    {
+        sampleResult = data_.fit(*(minimizer.back()), init, v);
+    }
+    result[s]       = sampleResult;
+    result.chi2_[s] = sampleResult.getChi2();
+    for (unsigned int j = 0; j < v.size(); ++j)
+    {
+        result.model_[j].resize(nSample_);
+        result.model_[j][s] = sampleResult.getModel(j);
+    }
+
+    
+}
+
+SampleFitResult XYSampleData::fit(std::vector<Minimizer *> &minimizer,
+                                  const DVec &init,
+                                  const std::vector<const DoubleModel *> &v,
+                                  Index s)
+{
+    computeVarMat();
+    
+    SampleFitResult result;
+    DVec      initCopy = init;
+
+    fitSample(minimizer, v, result, initCopy, s);
+    
+    return result;
+}
+
+SampleFitResult XYSampleData::fit(Minimizer &minimizer,
+                                  const DVec &init,
+                                  const std::vector<const DoubleModel *> &v,
+                                  Index s)
+{
+    vector<Minimizer *> mv{&minimizer};
+    
+    return fit(mv, init, v, s);
+}
+
 SampleFitResult XYSampleData::fit(std::vector<Minimizer *> &minimizer,
                                   const DVec &init,
                                   const std::vector<const DoubleModel *> &v)
@@ -307,43 +368,14 @@ SampleFitResult XYSampleData::fit(std::vector<Minimizer *> &minimizer,
     computeVarMat();
     
     SampleFitResult      result;
-    FitResult            sampleResult;
     DVec                 initCopy = init;
     Minimizer::Verbosity verbCopy = minimizer.back()->getVerbosity();
     
-    result.resize(nSample_);
-    result.chi2_.resize(nSample_);
-    result.model_.resize(v.size());
     FOR_STAT_ARRAY(result, s)
     {
-        setDataToSample(s);
+        fitSample(minimizer, v, result, initCopy, s);
-        if (s == central)
-        {
-            sampleResult = data_.fit(minimizer, initCopy, v);
-            initCopy     = sampleResult.segment(0, initCopy.size());
-            if (verbCopy != Minimizer::Verbosity::Debug)
-            {
-                minimizer.back()->setVerbosity(Minimizer::Verbosity::Silent);
-            }
-        }
-        else
-        {
-            
-            sampleResult = data_.fit(*(minimizer.back()), initCopy, v);
-        }
-        result[s]       = sampleResult;
-        result.chi2_[s] = sampleResult.getChi2();
-        for (unsigned int j = 0; j < v.size(); ++j)
-        {
-            result.model_[j].resize(nSample_);
-            result.model_[j][s] = sampleResult.getModel(j);
-        }
     }
     minimizer.back()->setVerbosity(verbCopy);
-    result.nPar_       = sampleResult.getNPar();
-    result.nDof_       = sampleResult.nDof_;
-    result.parName_    = sampleResult.parName_;
-    result.corrRangeDb_ = Math::cdr(getFitCorrMat());
     
     return result;
 }

lib/Statistics/XYSampleData.hpp

@@ -103,6 +103,13 @@ public:
     // get internal XYStatData
     const XYStatData & getData(void);
     // fit
+    void            fitSample(std::vector<Minimizer *> &minimizer, 
+                              const std::vector<const DoubleModel *> &v, 
+                              SampleFitResult &sampleResult, DVec &init, Index s);
+    SampleFitResult fit(std::vector<Minimizer *> &minimizer, const DVec &init, 
+                        const std::vector<const DoubleModel *> &v, Index s);
+    SampleFitResult fit(Minimizer &minimizer, const DVec &init, 
+                        const std::vector<const DoubleModel *> &v, Index s);
     SampleFitResult fit(std::vector<Minimizer *> &minimizer, const DVec &init, 
                         const std::vector<const DoubleModel *> &v);
     SampleFitResult fit(Minimizer &minimizer, const DVec &init, 

lib/Statistics/XYStatData.cpp

@@ -358,7 +358,7 @@ FitResult XYStatData::fit(vector<Minimizer *> &minimizer, const DVec &init,
         result    = (*m)(chi2);
         totalInit = result;
     }
-    result.corrRangeDb_ = Math::cdr(getFitCorrMat());
+    result.corrRangeDb_ = Math::svdDynamicRangeDb(getFitCorrMat());
     result.chi2_       = chi2(result);
     result.nPar_       = nPar;
     result.nDof_       = layout.totalYSize - nPar;

physics/2pt-fit.cpp

@@ -24,7 +24,7 @@ int main(int argc, char *argv[])
 {
     // parse arguments /////////////////////////////////////////////////////////
     OptParser            opt;
-    bool                 parsed, doLaplace, doPlot, doHeatmap, doCorr, fold, doScan, noGuess;
+    bool                 parsed, doLaplace, doPlot, doHeatmap, doCorr, fold, doScan;
     string               corrFileName, model, outFileName, outFmt, savePlot;
     Index                ti, tf, shift, nPar, thinning;
     double               svdTol;
@@ -59,8 +59,6 @@ int main(int argc, char *argv[])
                   "show the fit plot");
     opt.addOption("h", "heatmap"  , OptParser::OptType::trigger, true,
                   "show the fit correlation heatmap");
-    opt.addOption("", "no-guess"  , OptParser::OptType::trigger, true,
-                  "do not try to guess fit parameters");
     opt.addOption("", "save-plot", OptParser::OptType::value, true,
                     "saves the source and .pdf", "");
     opt.addOption("", "scan", OptParser::OptType::trigger, true,
@@ -89,7 +87,6 @@ int main(int argc, char *argv[])
     fold         = opt.gotOption("fold");
     doPlot       = opt.gotOption("p");
     doHeatmap    = opt.gotOption("h");
-    noGuess      = opt.gotOption("no-guess");
     savePlot     = opt.optionValue("save-plot");
     doScan       = opt.gotOption("scan");
     switch (opt.optionValue<unsigned int>("v"))
@@ -117,6 +114,7 @@ int main(int argc, char *argv[])
     nt      = corr[central].rows();
     corr    = corr.block(0, 0, nt, 1);
     corr    = CorrelatorUtils::shift(corr, shift);
+
     if (doLaplace)
     {
         vector<double> filter = {1., -2., 1.};
@@ -158,6 +156,11 @@ int main(int argc, char *argv[])
         }
     }
     
+    if (fold)
+    {
+        corr = CorrelatorUtils::fold(corr,modelPar);
+    }
+
     // fit /////////////////////////////////////////////////////////////////////
     DVec                init(nPar);
     NloptMinimizer      globMin(NloptMinimizer::Algorithm::GN_CRS2_LM);
@@ -170,14 +173,13 @@ int main(int argc, char *argv[])
     fitter.setThinning(thinning);
 
     // set initial values ******************************************************
-    if ((modelPar.type != CorrelatorType::undefined) and !noGuess)
+    if (modelPar.type != CorrelatorType::undefined)
     {
         init = CorrelatorModels::parameterGuess(corr, modelPar);
     }
     else
     {
-        init.fill(1.);
+        init.fill(0.1);
-        init(0) = 0.2;
     }
 
     // set limits for minimisers ***********************************************

utils/sample-dwt.cpp

@@ -17,7 +17,6 @@
  * along with LatAnalyze 3.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-#include <LatAnalyze/Core/Math.hpp>
 #include <LatAnalyze/Core/OptParser.hpp>
 #include <LatAnalyze/Core/Plot.hpp>
 #include <LatAnalyze/Io/Io.hpp>
@@ -54,12 +53,6 @@ int main(int argc, char *argv[])
         cerr << "usage: " << argv[0];
         cerr << " <options> <input file>" << endl;
         cerr << endl << "Possible options:" << endl << opt << endl;
-        cerr << "Available DWT filters:" << endl;
-        for (auto &fv: DWTFilters::fromName)
-        {
-            cerr << fv.first << " ";
-        }
-        cerr << endl << endl;
         
         return EXIT_FAILURE;
     }
@@ -75,45 +68,22 @@ int main(int argc, char *argv[])
     DMatSample            in = Io::load<DMatSample>(inFilename), res;
     Index                 nSample = in.size(), n = in[central].rows();
     vector<DMatSample>    out(ss ? 1 : level, DMatSample(nSample)), 
-                          outh(ss ? 0 : level, DMatSample(nSample)),
+                          outh(ss ? 0 : level, DMatSample(nSample));
-                          concath(ss ? 0 : level, DMatSample(nSample));
-    DMatSample            concat(nSample, n, 1);
     DWT                   dwt(*DWTFilters::fromName.at(filterName));
     vector<DWT::DWTLevel> dataDWT(level);
 
-    FOR_STAT_ARRAY(in, s)
-    {
-        in[s].conservativeResize(n, 1);
-    }
     if (!ss)
     {
-        DMatSample buf(nSample);
-
         cout << "-- compute discrete wavelet transform" << endl;
         cout << "filter '" << filterName << "' / " << level << " level(s)" << endl;
         FOR_STAT_ARRAY(in, s)
         {
-            dataDWT = dwt.forward(in[s], level);
+            dataDWT = dwt.forward(in[s].col(0), level);
             for (unsigned int l = 0; l < level; ++l)
             {
-                out[l][s]     = dataDWT[l].first;
+                out[l][s]  = dataDWT[l].first;
-                outh[l][s]    = dataDWT[l].second;
+                outh[l][s] = dataDWT[l].second;
-                concath[l][s] = DWT::concat(dataDWT, l, true);
             }
-            concat[s] = DWT::concat(dataDWT);
-        }
-        cout << "Data CDR " << Math::cdr(in.correlationMatrix()) << " dB" << endl;
-        cout << "DWT CDR " << Math::cdr(concat.correlationMatrix()) << " dB" << endl;
-        for (unsigned int l = 0; l < level; ++l)
-        {
-            cout << "DWT level " << l << " CDR: L= ";
-            cout << Math::cdr(out[l].correlationMatrix()) << " dB / H= ";
-            cout << Math::cdr(outh[l].correlationMatrix()) << " dB" << endl;
-        }
-        for (unsigned int l = 0; l < level; ++l)
-        {
-            cout << "DWT detail level " << l << " CDR: ";
-            cout << Math::cdr(concath[l].correlationMatrix()) << " dB" << endl;
         }
     }
     else
@@ -132,7 +102,7 @@ int main(int argc, char *argv[])
         }
         FOR_STAT_ARRAY(in, s)
         {
-            dataDWT.back().first = in[s];
+            dataDWT.back().first = in[s].col(0);
             out[0][s] = dwt.backward(dataDWT);
         }
     }
@@ -145,9 +115,7 @@ int main(int argc, char *argv[])
             {
                 Io::save<DMatSample>(out[l], outFilename + "/L" + strFrom(l) + ".h5");
                 Io::save<DMatSample>(outh[l], outFilename + "/H" + strFrom(l) + ".h5");
-                Io::save<DMatSample>(concath[l], outFilename + "/concatH" + strFrom(l) + ".h5");
             }
-            Io::save<DMatSample>(concat, outFilename + "/concat.h5");
         }
         else
         {

utils/sample-fake.cpp

@@ -18,30 +18,42 @@
  */
 
 #include <LatAnalyze/Io/Io.hpp>
+#include <LatAnalyze/Core/OptParser.hpp>
+
 
 using namespace std;
 using namespace Latan;
 
 int main(int argc, char *argv[])
 {
+    OptParser            opt;
     Index  nSample;
     double val, err;
     string outFileName;
 
-    if (argc != 5)
+    opt.addOption("r", "seed"      , OptParser::OptType::value,   true,
+                    "random generator seed (default: random)"); 
+    opt.addOption("", "help"      , OptParser::OptType::trigger, true,
+                  "show this help message and exit");
+
+    bool parsed = opt.parse(argc, argv);
+    if (!parsed or (opt.getArgs().size() != 4) or opt.gotOption("help"))
     {
         cerr << "usage: " << argv[0];
         cerr << " <central value> <error> <nSample> <output file>" << endl;
+        cerr << endl << "Possible options:" << endl << opt << endl;
 
         return EXIT_FAILURE;
     }
+
     val         = strTo<double>(argv[1]);
     err         = strTo<double>(argv[2]);
     nSample     = strTo<Index>(argv[3]);
     outFileName = argv[4];
 
     random_device         rd;
-    mt19937               gen(rd());
+    SeedType              seed = (opt.gotOption("r")) ? opt.optionValue<SeedType>("r") : rd();
+    mt19937               gen(seed);
     normal_distribution<> dis(val, err);
     DSample               res(nSample);
 

utils/sample-plot-corr.cpp

@@ -68,7 +68,7 @@ int main(int argc, char *argv[])
     var    = sample.varianceMatrix();
     corr   = sample.correlationMatrix();
 
-    cout << "dynamic range " << Math::cdr(corr) << " dB" << endl;
+    cout << "dynamic range " << Math::svdDynamicRangeDb(corr) << " dB" << endl;
     p << PlotCorrMatrix(corr);
     p.display();
     if (!outVarName.empty())

utils/sample-read.cpp

@@ -38,9 +38,23 @@ int main(int argc, char *argv[])
     {
         DMatSample s    = Io::load<DMatSample>(fileName);
         string     name = Io::getFirstName(fileName);
+        Index nRows     = s[central].rows();
+        Index nCols     = s[central].cols();
         cout << scientific;
-        cout << "central value:\n"      << s[central]               << endl;
+        cout << "central value +/-  standard deviation\n" << endl;
-        cout << "standard deviation:\n" << s.variance().cwiseSqrt() << endl;
+        cout << "Re:" << endl;
+        for(Index i = 0; i < nRows; i++)
+        {
+            cout << s[central](i,0) << " +/- " << s.variance().cwiseSqrt()(i,0) << endl;
+        }
+        if(nCols == 2)
+        {
+            cout << "\nIm:" << endl;
+            for(Index i = 0; i < nRows; i++)
+            {
+                cout << s[central](i,1) << " +/- " << s.variance().cwiseSqrt()(i,1) << endl;
+            }   
+        }
         if (!copy.empty())
         {
             Io::save(s, copy, File::Mode::write, name);
@@ -51,8 +65,8 @@ int main(int argc, char *argv[])
         DSample s    = Io::load<DSample>(fileName);
         string  name = Io::getFirstName(fileName);
         cout << scientific;
-        cout << "central value:\n"      << s[central]         << endl;
+        cout << "central value +/-  standard deviation\n" << endl;
-        cout << "standard deviation:\n" << sqrt(s.variance()) << endl;
+        cout << s[central] << " +/- " << sqrt(s.variance()) << endl;
         if (!copy.empty())
         {
             Io::save(s, copy, File::Mode::write, name);