wrong commited file

Code/precision.cpp

+#include <boost/numeric/interval.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+#include <eigen3/Eigen/Dense>
+#include <random>
+#include <algorithm>
+#include <iostream>
+
+//types
+using interval = boost::numeric::interval<double> ;
+using rational = boost::multiprecision::cpp_rational ;
+using MatDX = Eigen::MatrixXd ;
+using VecDX = Eigen::VectorXd ;
+using MatIX = Eigen::Matrix<interval, Eigen::Dynamic, Eigen::Dynamic> ;
+using VecIX = Eigen::Matrix<interval, Eigen::Dynamic, 1> ;
+using MatRX = Eigen::Matrix<rational, Eigen::Dynamic, Eigen::Dynamic> ;
+using VecRX = Eigen::Matrix<rational, Eigen::Dynamic, 1> ;
+  
+namespace Eigen {
+  namespace internal {
+    template<typename X, typename S, typename P>
+    struct is_convertible<X,boost::numeric::interval<S,P> > {
+      enum { value = is_convertible<X,S>::value };
+    };
+
+    template<typename S, typename P1, typename P2>
+    struct is_convertible<boost::numeric::interval<S,P1>,boost::numeric::interval<S,P2> > {
+      enum { value = true };
+    };
+  }
+}
+
+//command line
+char* get_cmd_option( char ** begin, char ** end, 
+                      const std::string & option
+                    ) {
+    char ** itr = std::find(begin, end, "--" + option);
+    if (itr != end && ++itr != end)
+    {
+        return *itr;
+    }
+    return 0;
+}
+
+bool cmd_option_exists( char** begin, char** end, 
+                        const std::string& option
+                      ) {
+    return std::find(begin, end, "--" + option) != end;
+}
+
+template<typename T>
+bool get_cmd_value(
+    char ** begin, 
+    char** end, 
+    const std::string& option,
+    T* output
+    ) {
+  if(cmd_option_exists(begin, end, option)) {
+    std::stringstream ss ;
+    ss << get_cmd_option(begin, end, option) ;
+    T t ;
+    ss >> t ;
+    if(!ss.fail()) {
+      *output = t ;
+      return true ;
+    }
+  }
+  return false ;
+}
+
+int main(int argc, char** argv) {
+  //test variables
+  unsigned int dim = 10 ;
+  get_cmd_value(argv, argv + argc, "dim", &dim) ;
+
+  //alea
+  std::random_device seed ;
+  std::mt19937_64 mt(seed()) ;
+  std::uniform_real_distribution<double> random_double(-1, 1) ;
+
+  //initialization
+  MatDX matd(dim, dim) ;
+  VecDX vecd(dim) ;
+  MatIX mati(dim, dim) ;
+  VecIX veci(dim) ;
+  MatRX matr(dim, dim) ;
+  VecRX vecr(dim) ;
+
+  for(unsigned int i = 0; i < dim; ++i) {
+    for(unsigned int j = 0; j < dim; ++j) {
+      double d = random_double(mt) ;
+      matd(i, j) = d ;
+      mati(i, j) = d ;
+      matr(i, j) = d ;
+    }
+    double d = random_double(mt) ;
+    vecd(i) = d ;
+    veci(i) = d ;
+    vecr(i) = d ;
+  }
+
+  rational detr = matr.fullPivLu().determinant() ;
+
+  std::cout << "==========" << std::endl ;
+  {
+    std::cout << "solve fullPivLu" << std::endl ;
+    double detd = matd.fullPivLu().determinant() ;
+    try {
+      interval deti = mati.fullPivLu().determinant() ;
+      std::cout << detd 
+        << " in [" << deti.lower() << " -- " << deti.upper() 
+        << "] error " << detd - (double) detr 
+        << " wrt. " << deti.upper() - deti.lower() << std::endl ;
+    } catch(std::exception& e) {
+      std::cout << "interval computation failed" << std::endl ;
+      std::cout << detd << " error " << detd - (double) detr << std::endl ;
+    }
+    std::cout << "==========" << std::endl ;
+  }
+  {
+    std::cout << "solve partialPivLu" << std::endl ;
+    double detd = matd.partialPivLu().determinant() ;
+    try {
+      interval deti = mati.partialPivLu().determinant() ;
+      std::cout << detd 
+        << " in [" << deti.lower() << " -- " << deti.upper() 
+        << "] error " << detd - (double) detr 
+        << " wrt. " << deti.upper() - deti.lower() << std::endl ;
+    } catch(std::exception& e) {
+      std::cout << "interval computation failed" << std::endl ;
+      std::cout << detd << " error " << detd - (double) detr << std::endl ;
+    }
+    std::cout << "==========" << std::endl ;
+  }
+
+  return 0 ;
+}