approximation.cpp File Reference

#include <cstdlib>
#include <cmath>
#include <iostream>
#include <iomanip>
#include "DGtal/arithmetic/LighterSternBrocot.h"
#include "DGtal/base/StdRebinders.h"

Include dependency graph for approximation.cpp:

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Functions
void	usage (int, char **argv)
int	main (int argc, char **argv)

Detailed Description

Author

Jacques-Olivier Lachaud (jacqu.nosp@m.es-o.nosp@m.livie.nosp@m.r.la.nosp@m.chaud.nosp@m.@uni.nosp@m.v-sav.nosp@m.oie..nosp@m.fr ) Laboratory of Mathematics (CNRS, UMR 5127), University of Savoie, France

Date

2012/02/06

An example file named approximation.

This file is part of the DGtal library.

Definition in file approximation.cpp.

Function Documentation

main()

int main	(	int	argc,
		char **	argv
	)

Main.

[approximation-types]

[approximation-types]

[approximation-process]

[approximation-process]

Definition at line 73 of file approximation.cpp.

{
  if ( argc < 2 )
    {
      usage( argc, argv );
      return 1;
    }
 
  typedef DGtal::int64_t Integer;
  typedef DGtal::int64_t Quotient;
  typedef LighterSternBrocot<Integer, Quotient, StdMapRebinder> SB; // the type of the Stern-Brocot tree
  typedef SB::Fraction Fraction; // the type for fractions
  typedef std::back_insert_iterator< Fraction > OutputIterator;
 
  long double epsilon = 1e-14;
  long double number0 = strtold( argv[ 1 ], 0 );
  long double number = number0;
  ASSERT( number >= 0.0 );
  Fraction f;
  OutputIterator itback = std::back_inserter( f );
  Quotient i = 0;
  while ( true )
    {
      long double int_part = floorl( number );
      Quotient u = NumberTraits<long double>::castToInt64_t( int_part );
      *itback++ = std::make_pair( u, i++ );
      long double approx =
        ( (long double) NumberTraits<Integer>::castToDouble( f.p() ) )
        / ( (long double) NumberTraits<Integer>::castToDouble( f.q() ) );
      std::cout << "z = " << f.p() << " / " << f.q()
                << " =~ " << std::setprecision( 16 ) << approx << std::endl;
      number -= int_part;
      if ( ( (number0 - epsilon ) < approx )
           && ( approx < (number0 + epsilon ) ) ) break;
      number = 1.0 / number;
    }
  std::cout << "z = " << f.p() << " / " << f.q() << std::endl;
  return 0;
}

References DGtal::NumberTraitsImpl< std::decay< T >::type >::castToInt64_t(), and usage().

usage()

void usage	(	int	,
		char **	argv
	)

Examples

arithmetic/approximation.cpp, arithmetic/convergents-biginteger.cpp, arithmetic/convergents.cpp, arithmetic/extended-euclid.cpp, arithmetic/fraction.cpp, arithmetic/lower-integer-convex-hull.cpp, arithmetic/pattern.cpp, geometry/meshes/curvature-comparator-ii-cnc-3d.cpp, geometry/meshes/curvature-measures-icnc-3d.cpp, geometry/meshes/curvature-measures-icnc-XY-3d.cpp, geometry/meshes/curvature-measures-nc-3d.cpp, geometry/meshes/curvature-measures-nc-XY-3d.cpp, geometry/meshes/digpoly-curvature-measures-cnc-3d.cpp, geometry/meshes/digpoly-curvature-measures-cnc-XY-3d.cpp, geometry/meshes/obj-curvature-measures-icnc-3d.cpp, geometry/meshes/obj-curvature-measures-icnc-XY-3d.cpp, geometry/meshes/vol-curvature-measures-icnc-3d.cpp, geometry/meshes/vol-curvature-measures-icnc-XY-3d.cpp, graph/volDistanceTraversal.cpp, math/polynomial-derivative.cpp, math/polynomial2-derivative.cpp, shapes/viewMarchingCubes.cpp, shapes/viewPolygonalMarchingCubes.cpp, topology/trackImplicitPolynomialSurfaceToOFF.cpp, topology/volBreadthFirstTraversal.cpp, topology/volMarchingCubes.cpp, topology/volScanBoundary.cpp, topology/volToOFF.cpp, and topology/volTrackBoundary.cpp.

Definition at line 64 of file approximation.cpp.

{
  std::cerr << "Usage: " << argv[ 0 ] << " <floating point number>" << std::endl;
  std::cerr << "\t - computes the successive rational approximation of this number, up to a precision of 1e-14." << std::endl;
}

Referenced by main().