Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex > Struct Template Reference

#include <src/eigen/Eigen/src/LU/PartialPivLU.h>

Public Types
typedef Map< Matrix< Scalar, Dynamic, Dynamic, StorageOrder > >	MapLU
typedef Block< MapLU, Dynamic, Dynamic >	MatrixType
typedef Block< MatrixType, Dynamic, Dynamic >	BlockType
typedef MatrixType::RealScalar	RealScalar

Static Public Member Functions
static Index	unblocked_lu (MatrixType &lu, PivIndex *row_transpositions, PivIndex &nb_transpositions)
static Index	blocked_lu (Index rows, Index cols, Scalar *lu_data, Index luStride, PivIndex *row_transpositions, PivIndex &nb_transpositions, Index maxBlockSize=256)

Detailed Description

template<typename Scalar, int StorageOrder, typename PivIndex>
struct Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >

Member Typedef Documentation

BlockType

template<typename Scalar , int StorageOrder, typename PivIndex >

typedef Block<MatrixType,Dynamic,Dynamic> Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::BlockType

MapLU

template<typename Scalar , int StorageOrder, typename PivIndex >

typedef Map<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::MapLU

MatrixType

template<typename Scalar , int StorageOrder, typename PivIndex >

typedef Block<MapLU, Dynamic, Dynamic> Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::MatrixType

RealScalar

template<typename Scalar , int StorageOrder, typename PivIndex >

typedef MatrixType::RealScalar Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::RealScalar

Member Function Documentation

blocked_lu()

template<typename Scalar , int StorageOrder, typename PivIndex >

static Index Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::blocked_lu ( Index  rows, Index  cols, Scalar *  lu_data, Index  luStride, PivIndex *  row_transpositions, PivIndex &  nb_transpositions, Index  maxBlockSize = 256  )

inlinestatic

  {
    MapLU lu1(lu_data,StorageOrder==RowMajor?rows:luStride,StorageOrder==RowMajor?luStride:cols);
    MatrixType lu(lu1,0,0,rows,cols);
 
    const Index size = (std::min)(rows,cols);
 
    // if the matrix is too small, no blocking:
    if(size<=16)
    {
      return unblocked_lu(lu, row_transpositions, nb_transpositions);
    }
 
    // automatically adjust the number of subdivisions to the size
    // of the matrix so that there is enough sub blocks:
    Index blockSize;
    {
      blockSize = size/8;
      blockSize = (blockSize/16)*16;
      blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize);
    }
 
    nb_transpositions = 0;
    Index first_zero_pivot = -1;
    for(Index k = 0; k < size; k+=blockSize)
    {
      Index bs = (std::min)(size-k,blockSize); // actual size of the block
      Index trows = rows - k - bs; // trailing rows
      Index tsize = size - k - bs; // trailing size
 
      // partition the matrix:
      //                          A00 | A01 | A02
      // lu  = A_0 | A_1 | A_2 =  A10 | A11 | A12
      //                          A20 | A21 | A22
      BlockType A_0(lu,0,0,rows,k);
      BlockType A_2(lu,0,k+bs,rows,tsize);
      BlockType A11(lu,k,k,bs,bs);
      BlockType A12(lu,k,k+bs,bs,tsize);
      BlockType A21(lu,k+bs,k,trows,bs);
      BlockType A22(lu,k+bs,k+bs,trows,tsize);
 
      PivIndex nb_transpositions_in_panel;
      // recursively call the blocked LU algorithm on [A11^T A21^T]^T
      // with a very small blocking size:
      Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,
                   row_transpositions+k, nb_transpositions_in_panel, 16);
      if(ret>=0 && first_zero_pivot==-1)
        first_zero_pivot = k+ret;
 
      nb_transpositions += nb_transpositions_in_panel;
      // update permutations and apply them to A_0
      for(Index i=k; i<k+bs; ++i)
      {
        Index piv = (row_transpositions[i] += internal::convert_index<PivIndex>(k));
        A_0.row(i).swap(A_0.row(piv));
      }
 
      if(trows)
      {
        // apply permutations to A_2
        for(Index i=k;i<k+bs; ++i)
          A_2.row(i).swap(A_2.row(row_transpositions[i]));
 
        // A12 = A11^-1 A12
        A11.template triangularView<UnitLower>().solveInPlace(A12);
 
        A22.noalias() -= A21 * A12;
      }
    }
    return first_zero_pivot;
  }

References Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::blocked_lu(), Eigen::RowMajor, and Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::unblocked_lu().

Referenced by Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::blocked_lu().

Here is the call graph for this function:

Here is the caller graph for this function:

unblocked_lu()

template<typename Scalar , int StorageOrder, typename PivIndex >

static Index Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::unblocked_lu ( MatrixType &  lu, PivIndex *  row_transpositions, PivIndex &  nb_transpositions  )

inlinestatic

  {
    typedef scalar_score_coeff_op<Scalar> Scoring;
    typedef typename Scoring::result_type Score;
    const Index rows = lu.rows();
    const Index cols = lu.cols();
    const Index size = (std::min)(rows,cols);
    nb_transpositions = 0;
    Index first_zero_pivot = -1;
    for(Index k = 0; k < size; ++k)
    {
      Index rrows = rows-k-1;
      Index rcols = cols-k-1;
 
      Index row_of_biggest_in_col;
      Score biggest_in_corner
        = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);
      row_of_biggest_in_col += k;
 
      row_transpositions[k] = PivIndex(row_of_biggest_in_col);
 
      if(biggest_in_corner != Score(0))
      {
        if(k != row_of_biggest_in_col)
        {
          lu.row(k).swap(lu.row(row_of_biggest_in_col));
          ++nb_transpositions;
        }
 
        // FIXME shall we introduce a safe quotient expression in cas 1/lu.coeff(k,k)
        // overflow but not the actual quotient?
        lu.col(k).tail(rrows) /= lu.coeff(k,k);
      }
      else if(first_zero_pivot==-1)
      {
        // the pivot is exactly zero, we record the index of the first pivot which is exactly 0,
        // and continue the factorization such we still have A = PLU
        first_zero_pivot = k;
      }
 
      if(k<rows-1)
        lu.bottomRightCorner(rrows,rcols).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rcols);
    }
    return first_zero_pivot;
  }

Referenced by Eigen::internal::partial_lu_impl< Scalar, StorageOrder, PivIndex >::blocked_lu().

Here is the caller graph for this function:

---

The documentation for this struct was generated from the following file:

• src/eigen/Eigen/src/LU/PartialPivLU.h