MueLu_AggregateQualityEstimateFactory_def.hpp

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#ifndef MUELU_AGGREGATEQUALITYESTIMATEFACTORY_DEF_HPP
#define MUELU_AGGREGATEQUALITYESTIMATEFACTORY_DEF_HPP
#include <iomanip>
#include "MueLu_AggregateQualityEstimateFactory_decl.hpp"

#include "MueLu_Level.hpp"

#include <Teuchos_SerialDenseVector.hpp>
#include <Teuchos_LAPACK.hpp>

#include "MueLu_Aggregates_decl.hpp"
#include <Xpetra_IO.hpp>
#include "MueLu_MasterList.hpp"
#include "MueLu_Monitor.hpp"
#include "MueLu_Utilities.hpp"

#include <vector>

namespace MueLu {

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::AggregateQualityEstimateFactory() {}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::~AggregateQualityEstimateFactory() {}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level& currentLevel) const {
  Input(currentLevel, "A");
  Input(currentLevel, "Aggregates");
  Input(currentLevel, "CoarseMap");
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
RCP<const ParameterList> AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
  RCP<ParameterList> validParamList = rcp(new ParameterList());

#define SET_VALID_ENTRY(name) validParamList->setEntry(name, MasterList::getEntry(name))
  SET_VALID_ENTRY("aggregate qualities: good aggregate threshold");
  SET_VALID_ENTRY("aggregate qualities: file output");
  SET_VALID_ENTRY("aggregate qualities: file base");
  SET_VALID_ENTRY("aggregate qualities: check symmetry");
  SET_VALID_ENTRY("aggregate qualities: algorithm");
  SET_VALID_ENTRY("aggregate qualities: zero threshold");
  SET_VALID_ENTRY("aggregate qualities: percentiles");
  SET_VALID_ENTRY("aggregate qualities: mode");

#undef SET_VALID_ENTRY

  validParamList->set<RCP<const FactoryBase>>("A", Teuchos::null, "Generating factory of the matrix A");
  validParamList->set<RCP<const FactoryBase>>("Aggregates", Teuchos::null, "Generating factory of the aggregates");
  validParamList->set<RCP<const FactoryBase>>("CoarseMap", Teuchos::null, "Generating factory of the coarse map");

  return validParamList;
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level& currentLevel) const {
  FactoryMonitor m(*this, "Build", currentLevel);

  RCP<Matrix> A              = Get<RCP<Matrix>>(currentLevel, "A");
  RCP<Aggregates> aggregates = Get<RCP<Aggregates>>(currentLevel, "Aggregates");

  RCP<const Map> map = Get<RCP<const Map>>(currentLevel, "CoarseMap");

  assert(!aggregates->AggregatesCrossProcessors());
  ParameterList pL = GetParameterList();
  std::string mode = pL.get<std::string>("aggregate qualities: mode");
  GetOStream(Statistics1) << "AggregateQuality: mode " << mode << std::endl;

  RCP<Xpetra::MultiVector<magnitudeType, LO, GO, NO>> aggregate_qualities;
  if (mode == "eigenvalue" || mode == "both") {
    aggregate_qualities = Xpetra::MultiVectorFactory<magnitudeType, LO, GO, NO>::Build(map, 1);
    ComputeAggregateQualities(A, aggregates, aggregate_qualities);
    OutputAggQualities(currentLevel, aggregate_qualities);
  }
  if (mode == "size" || mode == "both") {
    RCP<LocalOrdinalVector> aggregate_sizes = Xpetra::VectorFactory<LO, LO, GO, NO>::Build(map);
    ComputeAggregateSizes(A, aggregates, aggregate_sizes);
    Set(currentLevel, "AggregateSizes", aggregate_sizes);
    OutputAggSizes(currentLevel, aggregate_sizes);
  }
  Set(currentLevel, "AggregateQualities", aggregate_qualities);
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::ConvertAggregatesData(RCP<const Aggregates> aggs, ArrayRCP<LO>& aggSortedVertices, ArrayRCP<LO>& aggsToIndices, ArrayRCP<LO>& aggSizes) {
  // Reorder local aggregate information into a format amenable to computing
  // per-aggregate quantities. Specifically, we compute a format
  // similar to compressed sparse row format for sparse matrices in which
  // we store all the local vertices in a single array in blocks corresponding
  // to aggregates. (This array is aggSortedVertices.) We then store a second
  // array (aggsToIndices) whose k-th element stores the index of the first
  // vertex in aggregate k in the array aggSortedVertices.

  const LO LO_ZERO = Teuchos::OrdinalTraits<LO>::zero();
  const LO LO_ONE  = Teuchos::OrdinalTraits<LO>::one();

  LO numAggs = aggs->GetNumAggregates();
  aggSizes   = aggs->ComputeAggregateSizesArrayRCP();

  aggsToIndices = ArrayRCP<LO>(numAggs + LO_ONE, LO_ZERO);

  for (LO i = 0; i < numAggs; ++i) {
    aggsToIndices[i + LO_ONE] = aggsToIndices[i] + aggSizes[i];
  }

  const RCP<LOMultiVector> vertex2AggId     = aggs->GetVertex2AggId();
  const ArrayRCP<const LO> vertex2AggIdData = vertex2AggId->getData(0);

  LO numNodes       = vertex2AggId->getLocalLength();
  aggSortedVertices = ArrayRCP<LO>(numNodes, -LO_ONE);
  std::vector<LO> vertexInsertionIndexByAgg(numNodes, LO_ZERO);

  for (LO i = 0; i < numNodes; ++i) {
    LO aggId = vertex2AggIdData[i];
    if (aggId < 0 || aggId >= numAggs) continue;

    aggSortedVertices[aggsToIndices[aggId] + vertexInsertionIndexByAgg[aggId]] = i;
    vertexInsertionIndexByAgg[aggId]++;
  }
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::ComputeAggregateQualities(RCP<const Matrix> A, RCP<const Aggregates> aggs, RCP<Xpetra::MultiVector<magnitudeType, LO, GO, Node>> agg_qualities) const {
  const SC SCALAR_ONE = Teuchos::ScalarTraits<SC>::one();
  const SC SCALAR_TWO = SCALAR_ONE + SCALAR_ONE;

  const LO LO_ZERO = Teuchos::OrdinalTraits<LO>::zero();
  const LO LO_ONE  = Teuchos::OrdinalTraits<LO>::one();

  using MT         = magnitudeType;
  const MT MT_ZERO = Teuchos::ScalarTraits<MT>::zero();
  const MT MT_ONE  = Teuchos::ScalarTraits<MT>::one();
  ParameterList pL = GetParameterList();

  RCP<const Matrix> AT = A;

  // Algorithm check
  std::string algostr = pL.get<std::string>("aggregate qualities: algorithm");
  MT zeroThreshold    = Teuchos::as<MT>(pL.get<double>("aggregate qualities: zero threshold"));
  enum AggAlgo { ALG_FORWARD = 0,
                 ALG_REVERSE };
  AggAlgo algo;
  if (algostr == "forward") {
    algo = ALG_FORWARD;
    GetOStream(Statistics1) << "AggregateQuality: Using 'forward' algorithm" << std::endl;
  } else if (algostr == "reverse") {
    algo = ALG_REVERSE;
    GetOStream(Statistics1) << "AggregateQuality: Using 'reverse' algorithm" << std::endl;
  } else {
    TEUCHOS_TEST_FOR_EXCEPTION(1, Exceptions::RuntimeError, "\"algorithm\" must be one of (forward|reverse)");
  }

  bool check_symmetry = pL.get<bool>("aggregate qualities: check symmetry");
  if (check_symmetry) {
    RCP<MultiVector> x = MultiVectorFactory::Build(A->getMap(), 1, false);
    x->Xpetra_randomize();

    RCP<MultiVector> tmp = MultiVectorFactory::Build(A->getMap(), 1, false);

    A->apply(*x, *tmp, Teuchos::NO_TRANS);                        // tmp now stores A*x
    A->apply(*x, *tmp, Teuchos::TRANS, -SCALAR_ONE, SCALAR_ONE);  // tmp now stores A*x - A^T*x

    Array<magnitudeType> tmp_norm(1);
    tmp->norm2(tmp_norm());

    Array<magnitudeType> x_norm(1);
    tmp->norm2(x_norm());

    if (tmp_norm[0] > 1e-10 * x_norm[0]) {
      std::string transpose_string = "transpose";
      RCP<ParameterList> whatever;
      AT = Utilities::Transpose(*rcp_const_cast<Matrix>(A), true, transpose_string, whatever);

      assert(A->getMap()->isSameAs(*(AT->getMap())));
    }
  }

  // Reorder local aggregate information into a format amenable to computing
  // per-aggregate quantities. Specifically, we compute a format
  // similar to compressed sparse row format for sparse matrices in which
  // we store all the local vertices in a single array in blocks corresponding
  // to aggregates. (This array is aggSortedVertices.) We then store a second
  // array (aggsToIndices) whose k-th element stores the index of the first
  // vertex in aggregate k in the array aggSortedVertices.

  ArrayRCP<LO> aggSortedVertices, aggsToIndices, aggSizes;
  ConvertAggregatesData(aggs, aggSortedVertices, aggsToIndices, aggSizes);

  LO numAggs = aggs->GetNumAggregates();

  // Compute the per-aggregate quality estimate

  typedef Teuchos::SerialDenseMatrix<LO, MT> DenseMatrix;
  typedef Teuchos::SerialDenseVector<LO, MT> DenseVector;

  ArrayView<const LO> rowIndices;
  ArrayView<const SC> rowValues;
  ArrayView<const SC> colValues;
  Teuchos::LAPACK<LO, MT> myLapack;

  // Iterate over each aggregate to compute the quality estimate
  for (LO aggId = LO_ZERO; aggId < numAggs; ++aggId) {
    LO aggSize = aggSizes[aggId];
    DenseMatrix A_aggPart(aggSize, aggSize, true);
    DenseVector offDiagonalAbsoluteSums(aggSize, true);

    // Iterate over each node in the aggregate
    for (LO idx = LO_ZERO; idx < aggSize; ++idx) {
      LO nodeId = aggSortedVertices[idx + aggsToIndices[aggId]];
      A->getLocalRowView(nodeId, rowIndices, rowValues);
      AT->getLocalRowView(nodeId, rowIndices, colValues);

      // Iterate over each element in the row corresponding to the current node
      for (LO elem = LO_ZERO; elem < rowIndices.size(); ++elem) {
        LO nodeId2 = rowIndices[elem];
        SC val     = (rowValues[elem] + colValues[elem]) / SCALAR_TWO;

        LO idxInAgg = -LO_ONE;  // -1 if element is not in aggregate

        // Check whether the element belongs in the aggregate. If it does
        // find, its index. Otherwise, add it's value to the off diagonal
        // sums
        for (LO idx2 = LO_ZERO; idx2 < aggSize; ++idx2) {
          if (aggSortedVertices[idx2 + aggsToIndices[aggId]] == nodeId2) {
            // Element does belong to aggregate
            idxInAgg = idx2;
            break;
          }
        }

        if (idxInAgg == -LO_ONE) {  // Element does not belong to aggregate

          offDiagonalAbsoluteSums[idx] += Teuchos::ScalarTraits<SC>::magnitude(val);

        } else {  // Element does belong to aggregate

          A_aggPart(idx, idxInAgg) = Teuchos::ScalarTraits<SC>::real(val);
        }
      }
    }

    // Construct a diagonal matrix consisting of the diagonal
    // of A_aggPart
    DenseMatrix A_aggPartDiagonal(aggSize, aggSize, true);
    MT diag_sum = MT_ZERO;
    for (int i = 0; i < aggSize; ++i) {
      A_aggPartDiagonal(i, i) = Teuchos::ScalarTraits<SC>::real(A_aggPart(i, i));
      diag_sum += Teuchos::ScalarTraits<SC>::real(A_aggPart(i, i));
    }

    DenseMatrix ones(aggSize, aggSize, false);
    ones.putScalar(MT_ONE);

    // Compute matrix on top of generalized Rayleigh quotient
    // topMatrix = A_aggPartDiagonal - A_aggPartDiagonal*ones*A_aggPartDiagonal/diag_sum;
    DenseMatrix tmp(aggSize, aggSize, false);
    DenseMatrix topMatrix(A_aggPartDiagonal);

    tmp.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, MT_ONE, ones, A_aggPartDiagonal, MT_ZERO);
    topMatrix.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, -MT_ONE / diag_sum, A_aggPartDiagonal, tmp, MT_ONE);

    // Compute matrix on bottom of generalized Rayleigh quotient
    DenseMatrix bottomMatrix(A_aggPart);
    MT matrixNorm = A_aggPart.normInf();

    // Forward mode: Include a small perturbation to the bottom matrix to make it nonsingular
    const MT boost = (algo == ALG_FORWARD) ? (-1e4 * Teuchos::ScalarTraits<MT>::eps() * matrixNorm) : MT_ZERO;

    for (int i = 0; i < aggSize; ++i) {
      bottomMatrix(i, i) -= offDiagonalAbsoluteSums(i) + boost;
    }

    // Compute generalized eigenvalues
    LO sdim, info;
    DenseVector alpha_real(aggSize, false);
    DenseVector alpha_imag(aggSize, false);
    DenseVector beta(aggSize, false);

    DenseVector workArray(14 * (aggSize + 1), false);

    LO(*ptr2func)
    (MT*, MT*, MT*);
    ptr2func  = NULL;
    LO* bwork = NULL;
    MT* vl    = NULL;
    MT* vr    = NULL;

    const char compute_flag = 'N';
    if (algo == ALG_FORWARD) {
      // Forward: Solve the generalized eigenvalue problem as is
      myLapack.GGES(compute_flag, compute_flag, compute_flag, ptr2func, aggSize,
                    topMatrix.values(), aggSize, bottomMatrix.values(), aggSize, &sdim,
                    alpha_real.values(), alpha_imag.values(), beta.values(), vl, aggSize,
                    vr, aggSize, workArray.values(), workArray.length(), bwork,
                    &info);
      TEUCHOS_ASSERT(info == LO_ZERO);

      MT maxEigenVal = MT_ZERO;
      for (int i = LO_ZERO; i < aggSize; ++i) {
        // NOTE: In theory, the eigenvalues should be nearly real
        // TEUCHOS_ASSERT(fabs(alpha_imag[i]) <= 1e-8*fabs(alpha_real[i])); // Eigenvalues should be nearly real
        maxEigenVal = std::max(maxEigenVal, alpha_real[i] / beta[i]);
      }

      (agg_qualities->getDataNonConst(0))[aggId] = (MT_ONE + MT_ONE) * maxEigenVal;
    } else {
      // Reverse: Swap the top and bottom matrices for the generalized eigenvalue problem
      // This is trickier, since we need to grab the smallest non-zero eigenvalue and invert it.
      myLapack.GGES(compute_flag, compute_flag, compute_flag, ptr2func, aggSize,
                    bottomMatrix.values(), aggSize, topMatrix.values(), aggSize, &sdim,
                    alpha_real.values(), alpha_imag.values(), beta.values(), vl, aggSize,
                    vr, aggSize, workArray.values(), workArray.length(), bwork,
                    &info);

      TEUCHOS_ASSERT(info == LO_ZERO);

      MT minEigenVal = MT_ZERO;

      for (int i = LO_ZERO; i < aggSize; ++i) {
        MT ev = alpha_real[i] / beta[i];
        if (ev > zeroThreshold) {
          if (minEigenVal == MT_ZERO)
            minEigenVal = ev;
          else
            minEigenVal = std::min(minEigenVal, ev);
        }
      }
      if (minEigenVal == MT_ZERO)
        (agg_qualities->getDataNonConst(0))[aggId] = Teuchos::ScalarTraits<MT>::rmax();
      else
        (agg_qualities->getDataNonConst(0))[aggId] = (MT_ONE + MT_ONE) / minEigenVal;
    }
  }  // end aggId loop
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::OutputAggQualities(const Level& level, RCP<const Xpetra::MultiVector<magnitudeType, LO, GO, Node>> agg_qualities) const {
  ParameterList pL = GetParameterList();

  magnitudeType good_agg_thresh = Teuchos::as<magnitudeType>(pL.get<double>("aggregate qualities: good aggregate threshold"));
  using MT                      = magnitudeType;

  ArrayRCP<const MT> data = agg_qualities->getData(0);

  LO num_bad_aggs = 0;
  MT worst_agg    = 0.0;

  MT mean_bad_agg  = 0.0;
  MT mean_good_agg = 0.0;

  for (size_t i = 0; i < agg_qualities->getLocalLength(); ++i) {
    if (data[i] > good_agg_thresh) {
      num_bad_aggs++;
      mean_bad_agg += data[i];
    } else {
      mean_good_agg += data[i];
    }
    worst_agg = std::max(worst_agg, data[i]);
  }

  if (num_bad_aggs > 0) mean_bad_agg /= num_bad_aggs;
  mean_good_agg /= agg_qualities->getLocalLength() - num_bad_aggs;

  if (num_bad_aggs == 0) {
    GetOStream(Statistics1) << "All aggregates passed the quality measure. Worst aggregate had quality " << worst_agg << ". Mean aggregate quality " << mean_good_agg << "." << std::endl;
  } else {
    GetOStream(Statistics1) << num_bad_aggs << " out of " << agg_qualities->getLocalLength() << " did not pass the quality measure. Worst aggregate had quality " << worst_agg << ". "
                            << "Mean bad aggregate quality " << mean_bad_agg << ". Mean good aggregate quality " << mean_good_agg << "." << std::endl;
  }

  if (pL.get<bool>("aggregate qualities: file output")) {
    std::string filename = pL.get<std::string>("aggregate qualities: file base") + "." + std::to_string(level.GetLevelID());
    Xpetra::IO<magnitudeType, LO, GO, Node>::Write(filename, *agg_qualities);
  }

  {
    const auto n = size_t(agg_qualities->getLocalLength());

    std::vector<MT> tmp;
    tmp.reserve(n);

    for (size_t i = 0; i < n; ++i) {
      tmp.push_back(data[i]);
    }

    std::sort(tmp.begin(), tmp.end());

    Teuchos::ArrayView<const double> percents = pL.get<Teuchos::Array<double>>("aggregate qualities: percentiles")();

    GetOStream(Statistics1) << "AGG QUALITY HEADER     : | LEVEL |  TOTAL  |";
    for (auto percent : percents) {
      GetOStream(Statistics1) << std::fixed << std::setprecision(4) << 100.0 * percent << "% |";
    }
    GetOStream(Statistics1) << std::endl;

    GetOStream(Statistics1) << "AGG QUALITY PERCENTILES: | " << level.GetLevelID() << " | " << n << "|";
    for (auto percent : percents) {
      size_t i = size_t(n * percent);
      i        = i < n ? i : n - 1u;
      i        = i > 0u ? i : 0u;
      GetOStream(Statistics1) << std::fixed << std::setprecision(4) << tmp[i] << " |";
    }
    GetOStream(Statistics1) << std::endl;
  }
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::ComputeAggregateSizes(RCP<const Matrix> A, RCP<const Aggregates> aggs, RCP<LocalOrdinalVector> agg_sizes) const {
  ArrayRCP<LO> aggSortedVertices, aggsToIndices, aggSizes;
  ConvertAggregatesData(aggs, aggSortedVertices, aggsToIndices, aggSizes);

  // Iterate over each node in the aggregate
  auto data = agg_sizes->getDataNonConst(0);
  for (LO i = 0; i < (LO)aggSizes.size(); i++)
    data[i] = aggSizes[i];
}

template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void AggregateQualityEstimateFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::OutputAggSizes(const Level& level, RCP<const LocalOrdinalVector> agg_sizes) const {
  ParameterList pL = GetParameterList();
  using MT         = magnitudeType;

  ArrayRCP<const LO> data = agg_sizes->getData(0);

  if (pL.get<bool>("aggregate qualities: file output")) {
    std::string filename = pL.get<std::string>("aggregate qualities: file base") + ".sizes." + std::to_string(level.GetLevelID());
    Xpetra::IO<LO, LO, GO, Node>::Write(filename, *agg_sizes);
  }

  {
    size_t n = (size_t)agg_sizes->getLocalLength();

    std::vector<MT> tmp;
    tmp.reserve(n);

    for (size_t i = 0; i < n; ++i) {
      tmp.push_back(Teuchos::as<MT>(data[i]));
    }

    std::sort(tmp.begin(), tmp.end());

    Teuchos::ArrayView<const double> percents = pL.get<Teuchos::Array<double>>("aggregate qualities: percentiles")();

    GetOStream(Statistics1) << "AGG SIZE    HEADER     : | LEVEL |  TOTAL  |";
    for (auto percent : percents) {
      GetOStream(Statistics1) << std::fixed << std::setprecision(4) << 100.0 * percent << "% |";
    }
    GetOStream(Statistics1) << std::endl;

    GetOStream(Statistics1) << "AGG SIZE    PERCENTILES: | " << level.GetLevelID() << " | " << n << "|";
    for (auto percent : percents) {
      size_t i = size_t(n * percent);
      i        = i < n ? i : n - 1u;
      i        = i > 0u ? i : 0u;
      GetOStream(Statistics1) << std::fixed << std::setprecision(4) << tmp[i] << " |";
    }
    GetOStream(Statistics1) << std::endl;
  }
}

}  // namespace MueLu

#endif  // MUELU_AGGREGATEQUALITYESTIMATE_DEF_HPP