testInversion.cxx

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// stress inversion of matrices with varios methods 
#include "Math/SMatrix.h"
#include "TMatrixTSym.h"
#include "TDecompChol.h"
#include "TDecompBK.h"

#include "TRandom.h"
#include <vector>
#include <string>
#include <iostream>
#include <cmath>
#include <limits>

#include "TStopwatch.h"

// matrix size
#ifndef N
#define N 5
#endif

bool doSelfTest = true; 

//timer
namespace test { 


#ifdef REPORT_TIME
   void reportTime( std::string s, double time); 
#endif

   void printTime(TStopwatch & time, std::string s) { 
      int pr = std::cout.precision(8);
      std::cout << s << "\t" << " time = " << time.RealTime() << "\t(sec)\t" 
         //    << time.CpuTime() 
                << std::endl;
      std::cout.precision(pr);
   }



   class Timer {

   public: 

      Timer(const std::string & s = "") : fName(s), fTime(0) 
      {
         fWatch.Start();
      }
      Timer(double & t, const std::string & s = "") : fName(s), fTime(&t) 
      {
         fWatch.Start();
      } 
        
      ~Timer() { 
         fWatch.Stop();
         printTime(fWatch,fName);
#ifdef REPORT_TIME
         // report time
         reportTime(fName, fWatch.RealTime() );
#endif
         if (fTime) *fTime += fWatch.RealTime();
      }


   private: 
        
      std::string fName;
      double * fTime; 
      TStopwatch fWatch; 
        
   }; 
}

using namespace ROOT::Math; 



typedef  SMatrix<double,N,N, MatRepSym<double,N> >  SymMatrix; 

// create matrix
template<class M> 
M * createMatrix() { 
   return new M(); 
}
// specialized for TMatrix 
template<>
TMatrixTSym<double> * createMatrix<TMatrixTSym<double> >() { 
   return new TMatrixTSym<double>(N); 
} 

//print matrix
template<class M> 
void printMatrix(const M & m) { 
   std::cout << m << std::endl;
}
template<>
void printMatrix<TMatrixTSym<double> >(const TMatrixTSym<double> & m ) { 
   m.Print(); 
} 

// generate matrices 
template<class M> 
void genMatrix(M  & m ) { 
   TRandom & r = *gRandom; 
   // generate first diagonal elemets
   for (int i = 0; i < N; ++i) {
      double maxVal = i*10000/(N-1) + 1;  // max condition is 10^4 
      m(i,i) = r.Uniform(0, maxVal);  
   }
   for (int i = 0; i < N; ++i) {
      for (int j = 0; j < i; ++j) {         
         double v = 0.3*std::sqrt( m(i,i) * m(j,j) ); // this makes the matrix pos defined 
         m(i,j) = r.Uniform(0, v);
         m(j,i) = m(i,j); // needed for TMatrix
      }
   }   
}

// generate all matrices
template<class M>
void generate(std::vector<M*> & v) { 
   int n = v.size(); 
   gRandom->SetSeed(111);
   for (int i = 0; i < n; ++i) {
      v[i] = createMatrix<M>();
      genMatrix(*v[i] ); 
   }
}


struct Choleski {};
struct BK {};
struct QR {};
struct Cramer {};
struct Default {};

template <class M, class Type>
struct TestInverter { 
   static bool Inv ( const M & , M & ) { return false;} 
   static bool Inv2 ( M & ) { return false;} 
};

template <>
struct TestInverter<SymMatrix, Choleski> { 
   static bool Inv ( const SymMatrix & m, SymMatrix & result ) {
      int ifail = 0; 
      result = m.InverseChol(ifail);
      return  ifail == 0;
   } 
   static bool Inv2 ( SymMatrix & m ) {
      return m.InvertChol(); 
   } 
};

template <>
struct TestInverter<SymMatrix, BK> { 
   static bool Inv ( const SymMatrix & m, SymMatrix & result ) {
      int ifail = 0; 
      result = m.Inverse(ifail);
      return ifail==0;
   } 
   static bool Inv2 ( SymMatrix & m ) {
      return m.Invert(); 
   } 
};

template <>
struct TestInverter<SymMatrix, Cramer> { 
   static bool Inv ( const SymMatrix & m, SymMatrix & result ) {
      int ifail = 0; 
      result = m.InverseFast(ifail);
      return ifail==0;
   } 
   static bool Inv2 ( SymMatrix & m ) {
      return m.InvertFast(); 
   } 
};

#ifdef LATER
template <>
struct TestInverter<SymMatrix, QR> { 
   static bool Inv ( const SymMatrix & m, SymMatrix & result ) {
      ROOT::Math::QRDecomposition<double> d; 
      int ifail = 0; 
      result = m.InverseFast(ifail);
      return ifail==0;
   } 
};
#endif

//TMatrix functions 

template <>
struct TestInverter<TMatrixDSym, Default> { 
   static bool Inv ( const TMatrixDSym & m, TMatrixDSym & result ) {
      result = m; 
      result.Invert(); 
      return true;
   } 
   static bool Inv2 ( TMatrixDSym & m ) { 
      m.Invert(); 
      return true; 
   }
};

template <>
struct TestInverter<TMatrixDSym, Cramer> { 
   static bool Inv ( const TMatrixDSym & m, TMatrixDSym & result ) {
      result = m; 
      result.InvertFast(); 
      return true;
   } 
   static bool Inv2 ( TMatrixDSym & m ) { 
      m.InvertFast(); 
      return true; 
   }
};

template <>
struct TestInverter<TMatrixDSym, Choleski> { 
   static bool Inv ( const TMatrixDSym & m, TMatrixDSym & result ) {
      TDecompChol chol(m); 
      if (!chol.Decompose() ) return false; 
      chol.Invert(result); 
      return true;
   } 
};

template <>
struct TestInverter<TMatrixDSym, BK> { 
   static bool Inv ( const TMatrixDSym & m, TMatrixDSym & result ) {
      TDecompBK d(m); 
      if (!d.Decompose() ) return false; 
      d.Invert(result); 
      return true;
   } 
};


template<class M, class T>
double invert( const std::vector<M* >  & matlist, double & time,std::string s) { 
   M result = *(matlist.front());
   test::Timer t(time,s);
   int nloop = matlist.size(); 
   double sum = 0;
   for (int l = 0; l < nloop; l++)      
   {
      const M & m = *(matlist[l]); 
      bool ok = TestInverter<M,T>::Inv(m,result);
      if (!ok) {
         std::cout << "inv failed for matrix " << l << std::endl;
         printMatrix<M>( m);
         return -1; 
      }
      sum += result(0,1);
   }
   return sum; 
}

// invert without copying the matrices (une INv2) 

template<class M, class T>
double invert2( const std::vector<M* >  & matlist, double & time,std::string s) { 

   // copy vector of matrices 
   int nloop = matlist.size(); 
   std::vector<M *> vmat(nloop); 
   for (int l = 0; l < nloop; l++)      
   {
      vmat[l] = new M( *matlist[l] );
   }

   test::Timer t(time,s);
   double sum = 0;
   for (int l = 0; l < nloop; l++)      
   {
      M & m = *(vmat[l]); 
      bool ok = TestInverter<M,T>::Inv2(m);
      if (!ok) {
         std::cout << "inv failed for matrix " << l << std::endl;
         printMatrix<M>( m);
         return -1; 
      }
      sum += m(0,1);
   }
   return sum; 
}

bool equal(double d1, double d2, double stol = 10000) { 
   std::cout.precision(12);  // tolerance is 1E-12
   double eps = stol * std::numeric_limits<double>::epsilon(); 
   if ( std::abs(d1) > 0 && std::abs(d2) > 0 )
      return  ( std::abs( d1-d2) < eps * std::max(std::abs(d1), std::abs(d2) ) ); 
   else if ( d1 == 0 )  
      return std::abs(d2) < eps; 
   else // d2 = 0
      return std::abs(d1) < eps; 
}

// test matrices symmetric and positive defines 
bool stressSymPosInversion(int n, bool selftest ) { 

   // test smatrix 

   std::vector<SymMatrix *> v1(n); 
   generate(v1);
   std::vector<TMatrixDSym *> v2(n); 
   generate(v2);


   bool iret = true; 
   double time = 0;
   double s1 = invert<SymMatrix, Choleski> (v1, time,"SMatrix Chol");
   double s2 = invert<SymMatrix, BK> (v1, time,"SMatrix   BK");
   double s3 = invert<SymMatrix, Cramer> (v1, time,"SMatrix Cram");
   bool ok = ( equal(s1,s2) && equal(s1,s3) );  
   if (!ok) { 
      std::cout << "result SMatrix choleski  " << s1 << " BK   " << s2 << " cramer " << s3 << std::endl;
      std::cerr <<"Error:  inversion test for SMatrix FAILED ! " << std::endl;
   }
   iret  &= ok; 
   std::cout << std::endl;    
   
   double m1 = invert<TMatrixDSym, Choleski> (v2, time,"TMatrix Chol");
   double m2 = invert<TMatrixDSym, BK> (v2, time,"TMatrix   BK");
   double m3 = invert<TMatrixDSym, Cramer> (v2, time,"TMatrix Cram");
   double m4 = invert<TMatrixDSym, Default> (v2, time,"TMatrix  Def");

   ok =  ( equal(m1,m2) && equal(m1,m3) && equal(m1,m4) );
   if (!ok) {
      std::cout << "result TMatrix choleski  " << m1 << " BK   " << m2 
                << " cramer " << m3 << " default " << m4 << std::endl;
      std::cerr <<"Error:  inversion test for TMatrix FAILED ! " << std::endl;
   }
   iret  &= ok; 
   std::cout << std::endl; 
   
   
      // test using self inversion 
   if (selftest) { 
      std::cout << "\n - self inversion test \n"; 
      double s11 = invert2<SymMatrix, Choleski> (v1, time,"SMatrix Chol");
      double s12 = invert2<SymMatrix, BK> (v1, time,"SMatrix   BK");
      double s13 = invert2<SymMatrix, Cramer> (v1, time,"SMatrix Cram");
      ok =  ( equal(s11,s12) && equal(s11,s13) ); 
      if (!ok) {
         std::cout << "result SMatrix choleski  " << s11 << " BK   " << s12 << " cramer " << s13 << std::endl;
         std::cerr <<"Error:  self inversion test for SMatrix FAILED ! " << std::endl;
      }
      iret  &= ok; 
      std::cout << std::endl; 
      
      double m13 = invert2<TMatrixDSym, Cramer> (v2, time,"TMatrix Cram");
      double m14 = invert2<TMatrixDSym, Default> (v2, time,"TMatrix  Def");
      ok =  ( equal(m13,m14)  ); 
      if (!ok) { 
         std::cout << "result TMatrix  cramer " << m13 << " default " << m14 << std::endl;      
         std::cerr <<"Error:  self inversion test for TMatrix FAILED ! " << std::endl;
      }
      iret  &= ok; 
      std::cout << std::endl; 
   }

   return iret; 
}

int testInversion(int n = 100000) { 
   bool ok = stressSymPosInversion(n, doSelfTest); 
   std::cerr << "Test inversion of positive defined matrix ....... "; 
   if (ok) std::cerr << "OK \n"; 
   else std::cerr << "FAILED \n"; 
   return (ok) ? 0 : -1; 
}

int main() { 
   return testInversion(); 
}

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