tutorial/WeightedFigureOfMerit.cc

This example shows how to instantiate a weighted figure of merit and perform a search for the best Korobov lattice.

// This file is part of LatNet Builder.
//
// Copyright (C) 2012-2018  Pierre L'Ecuyer and Universite de Montreal
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "latbuilder/WeightedFigureOfMerit.h"
#include "latticetester/ProductWeights.h"
#include "latticetester/CoordinateSets.h"

#include "latbuilder/ProjDepMerit/Spectral.h"
#include "latticetester/NormaBestLat.h"
#include "latbuilder/ProjDepMerit/CoordUniform.h" 
#include "latbuilder/Kernel/PAlphaPLR.h"

#include "latbuilder/Accumulator.h"
#include "latbuilder/Storage.h"
#include "latbuilder/Functor/binary.h"

#include "latbuilder/LatSeq/Korobov.h"
#include "latbuilder/GenSeq/GeneratingValues.h"

#include "latbuilder/TextStream.h"

#include "Path.h"

#include <iostream>
#include <limits>

using namespace LatBuilder;
using TextStream::operator<<;

template <typename T, typename... ARGS>
std::unique_ptr<T> unique(ARGS&&... args)
{ return std::unique_ptr<T>(new T(std::forward<ARGS>(args)...)); }

template<LatticeType LA>
class Observer {
public:
   typedef LatBuilder::LatDef<LA, EmbeddingType::UNILEVEL> LatDef;

   Observer() { reset(); }

   // initializes the best observed merit value to infinity
   void reset() { m_bestMerit = std::numeric_limits<Real>::infinity(); }

   // returns the best observed lattice
   const LatDef& bestLat() { return m_bestLat; }

   // returns the best observed merit value
   const Real bestMerit() { return m_bestMerit; }

   // notifies the observer that the merit value of a new candidate lattice has
   // been observed; updates the best observed candidate lattice if necessary
   void observe(const LatDef& lat, Real merit)
   {
      std::cout << lat;
      std::cout << "Merit: " << merit;
      if (merit < m_bestMerit) {
         std::cout << " <-- best";
         m_bestMerit = merit;
         m_bestLat = lat;
      }
      std::cout << std::endl;
   }

private:
   LatDef m_bestLat;
   Real m_bestMerit;
};


template <LatticeType LA, EmbeddingType L, Compress C>
void test(const Storage<LA, L, C>& storage, Dimension dimension)
{
   auto weights = unique<LatticeTester::ProductWeights>();
   weights->setDefaultWeight(0.7);

   typedef ProjDepMerit::Spectral<LatticeTester::NormaBestLat<Real>> ProjDep;
   WeightedFigureOfMerit<ProjDep, Functor::Max> figure(2, std::move(weights));
   std::cout << "figure of merit: " << figure << std::endl;

   /*
   // The P_{\alpha,PLR} figure of merit for polynomial lattices
   auto weights = unique<LatticeTester::ProductWeights>();
   weights->setDefaultWeight(0.7);

   typedef ProjDepMerit::CoordUniform<Kernel::PAlphaPLR> ProjDep;
   WeightedFigureOfMerit<ProjDep, Functor::Sum> figure(2, std::move(weights), ProjDep(2));
   std::cout << "figure of merit: " << figure << std::endl;
   */
   // sequence of lattice definitions
   typedef GenSeq::GeneratingValues<LA, decltype(figure)::suggestedCompression()> Coprime;
   auto latSeq = LatSeq::korobov(
         storage.sizeParam(),
         Coprime(storage.sizeParam().modulus()),
         dimension
         );

   LatticeTester::CoordinateSets::FromRanges allProjections(
         1, latSeq.latDimension(),     // range for dimension
         0, latSeq.latDimension() - 1  // range for coordinate index
         );
   std::cout << "projections: " << allProjections << std::endl;

   auto initialMerit = storage.createMeritValue(0.0);

   auto eval = figure.evaluator(storage);
   Observer<LA> obs;
   for (const auto& lat : latSeq) {
      // compute merit value of lattice for all projections
      auto merit = eval(lat, allProjections, initialMerit);
      // notify the observer
      obs.observe(lat, merit);
   }
   std::cout << "BEST LATTICE: " << std::endl << obs.bestLat() << "Merit value: " << obs.bestMerit() << std::endl;
}

int main()
{
   SET_PATH_TO_LATNETBUILDER_FOR_EXAMPLES();
   Dimension dim = 3;
   
   test(Storage<LatticeType::ORDINARY, EmbeddingType::UNILEVEL, Compress::SYMMETRIC>(19), dim);
   /*
   test(Storage<LatticeType::POLYNOMIAL, EmbeddingType::UNILEVEL, Compress::NONE>(PolynomialFromInt(13)), dim);
   */
   

   return 0;
}