logic.cc

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/* Copyright (C) 2002-2008 Stefan Buehler  <sbuehler@ltu.se>
 
   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version.
 
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
 
   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */
 
#include <cmath> 
#include <algorithm> 
#include <stdexcept>
#include "logic.h"
#include "sorting.h"
 
 
// For checking, if a Numeric equal zero we have to take into account the
// numerical precicion. If a value is smaller than *precision* it is 
// taken to be 0.
#define precision 0.
 
 
 
bool is_bool( const Index& x )
{
  return ( x==0 || x==1 );
}
 
 
 
 
bool is_multiple( const Index& x, const Index& y )
{
  assert( y != 0 );
  return ( 0 == fmod( Numeric(x), Numeric(y) ) );
}
 
 
 
 
bool is_size( ConstVectorView   x,
              const Index&      n ) 
{
  return( n == x.nelem() );
}
 
 
bool is_size( ConstMatrixView   x,
              const Index&      r,
              const Index&      c ) 
{
  return( r == x.nrows() &&
          c == x.ncols()     );
}
 
 
bool is_size( ConstTensor3View  x,
              const Index&      p,
              const Index&      r,
              const Index&      c ) 
{
  return( p == x.npages()     &&
          r == x.nrows()      &&
          c == x.ncols()     );
}
 
 
bool is_size( ConstTensor4View  x,
              const Index&      b,
              const Index&      p,
              const Index&      r,
              const Index&      c ) 
{
  return( b == x.nbooks()     &&
          p == x.npages()     &&
          r == x.nrows()      &&
          c == x.ncols()     );
}
 
 
bool is_size( ConstTensor5View  x,
              const Index&      s,
              const Index&      b,
              const Index&      p,
              const Index&      r,
              const Index&      c ) 
{
  return( s == x.nshelves()   &&
          b == x.nbooks()     &&
          p == x.npages()     &&
          r == x.nrows()      &&
          c == x.ncols()     );
}
 
 
bool is_size( ConstTensor6View  x,
              const Index&      v,
              const Index&      s,
              const Index&      b,
              const Index&      p,
              const Index&      r,
              const Index&      c ) 
{
  return( v == x.nvitrines()  &&
          s == x.nshelves()   &&
          b == x.nbooks()     &&
          p == x.npages()     &&
          r == x.nrows()      &&
          c == x.ncols()     );
}
 
 
bool is_size( ConstTensor7View  x,
              const Index&      l,
              const Index&      v,
              const Index&      s,
              const Index&      b,
              const Index&      p,
              const Index&      r,
              const Index&      c ) 
{
  return( l == x.nlibraries() &&
          v == x.nvitrines()  &&
          s == x.nshelves()   &&
          b == x.nbooks()     &&
          p == x.npages()     &&
          r == x.nrows()      &&
          c == x.ncols()     );
}
 
 
bool is_sorted( ConstVectorView   x )
{
  if( x.nelem() > 1 )
    {
      for( Index i=1; i<x.nelem(); i++ )
        {
          if( x[i] < x[i-1] )
            return false;
        }
    }
  return true;
}
 
 
bool is_increasing( ConstVectorView   x )
{
  if( x.nelem() > 1 )
    {
      for( Index i=1; i<x.nelem(); i++ )
        {
          if( x[i] <= x[i-1] )
            return false;
        }
    }
  return true;
}
 
 
bool is_increasing( const ArrayOfIndex&   x )
{
  if( x.nelem() > 1 )
    {
      for( Index i=1; i<x.nelem(); i++ )
        {
          if( x[i] <= x[i-1] )
            return false;
        }
    }
  return true;
}
 
 
bool is_decreasing( ConstVectorView   x )
{
  if( x.nelem() > 1 )
    {
      for( Index i=1; i<x.nelem(); i++ )
        {
          if( x[i] >= x[i-1] )
            return false;
        }
    }
  return true;
}
 
 
 
bool is_unique( const ArrayOfIndex&   x )
{
  // We simply compare the second element to the first, 
  // the third to the first and second, and so on.
 
  for (Index i=1; i<x.nelem(); ++i)
    for (Index s=0; s<i; ++s)
      if (x[i]==x[s])
        return false;
  
  return true;
}
 
 
bool is_singular( ConstMatrixView A )
{
  assert( A.nrows() == A.ncols() );
  Numeric temp = 0.;
    
  for( Index i=0; i<A.nrows(); i++)
    {
      Numeric big = 0.;
      for( Index j=0; j<A.nrows(); j++)
        {
          if ((temp = fabs(A(i,j))) > big)
            big = temp;
        }
      // Due to numerical precision the values can deviate from 0.0
      if (big < precision)
        {
        throw runtime_error ("Matrix is singular.");
        return true;
        }
    }
  return false;
}
 
 
 
bool is_diagonal( ConstMatrixView A )
{
 assert( A.nrows() == A.ncols() );
 
 for( Index i=1; i<A.ncols(); i++ )
        {
          for( Index j=0; j<i; j++ )
            {
              if( fabs(A(i,j)) > precision ||  
                  fabs(A(j,i)) > precision )
                return false;
            }
        }
 return true;
}
 
 
bool is_same_within_epsilon( const Numeric& a,
                             const Numeric& b,
                             const Numeric& epsilon )
{
  if ( abs(a-b) <= abs( epsilon * max(a,b) ) )
    return true;
  else
    return false;
}