334template<
typename Scalar,
int StorageOrder,
typename PivIndex,
int SizeAtCompileTime=Dynamic>
335struct partial_lu_impl
337 static const int UnBlockedBound = 16;
338 static const bool UnBlockedAtCompileTime = SizeAtCompileTime!=
Dynamic && SizeAtCompileTime<=UnBlockedBound;
339 static const int ActualSizeAtCompileTime = UnBlockedAtCompileTime ? SizeAtCompileTime :
Dynamic;
341 static const int RRows = SizeAtCompileTime==2 ? 1 :
Dynamic;
342 static const int RCols = SizeAtCompileTime==2 ? 1 :
Dynamic;
346 typedef typename MatrixType::RealScalar RealScalar;
358 static Index unblocked_lu(MatrixTypeRef& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)
360 typedef scalar_score_coeff_op<Scalar> Scoring;
361 typedef typename Scoring::result_type Score;
362 const Index rows = lu.rows();
363 const Index cols = lu.cols();
364 const Index size = (std::min)(rows,cols);
367 const Index endk = UnBlockedAtCompileTime ? size-1 : size;
368 nb_transpositions = 0;
369 Index first_zero_pivot = -1;
370 for(
Index k = 0; k < endk; ++k)
372 int rrows = internal::convert_index<int>(rows-k-1);
373 int rcols = internal::convert_index<int>(cols-k-1);
375 Index row_of_biggest_in_col;
376 Score biggest_in_corner
377 = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);
378 row_of_biggest_in_col += k;
380 row_transpositions[k] = PivIndex(row_of_biggest_in_col);
382 if(biggest_in_corner != Score(0))
384 if(k != row_of_biggest_in_col)
386 lu.row(k).swap(lu.row(row_of_biggest_in_col));
390 lu.col(k).tail(fix<RRows>(rrows)) /= lu.coeff(k,k);
392 else if(first_zero_pivot==-1)
396 first_zero_pivot = k;
400 lu.bottomRightCorner(fix<RRows>(rrows),fix<RCols>(rcols)).noalias() -= lu.col(k).tail(fix<RRows>(rrows)) * lu.row(k).tail(fix<RCols>(rcols));
404 if(UnBlockedAtCompileTime)
407 row_transpositions[k] = PivIndex(k);
408 if (Scoring()(lu(k, k)) == Score(0) && first_zero_pivot == -1)
409 first_zero_pivot = k;
412 return first_zero_pivot;
430 static Index blocked_lu(
Index rows,
Index cols, Scalar* lu_data,
Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions,
Index maxBlockSize=256)
434 const Index size = (std::min)(rows,cols);
437 if(UnBlockedAtCompileTime || size<=UnBlockedBound)
439 return unblocked_lu(lu, row_transpositions, nb_transpositions);
447 blockSize = (blockSize/16)*16;
448 blockSize = (std::min)((std::max)(blockSize,
Index(8)), maxBlockSize);
451 nb_transpositions = 0;
452 Index first_zero_pivot = -1;
453 for(
Index k = 0; k < size; k+=blockSize)
455 Index bs = (std::min)(size-k,blockSize);
456 Index trows = rows - k - bs;
457 Index tsize = size - k - bs;
463 BlockType A_0 = lu.block(0,0,rows,k);
464 BlockType A_2 = lu.block(0,k+bs,rows,tsize);
465 BlockType A11 = lu.block(k,k,bs,bs);
466 BlockType A12 = lu.block(k,k+bs,bs,tsize);
467 BlockType A21 = lu.block(k+bs,k,trows,bs);
468 BlockType A22 = lu.block(k+bs,k+bs,trows,tsize);
470 PivIndex nb_transpositions_in_panel;
473 Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,
474 row_transpositions+k, nb_transpositions_in_panel, 16);
475 if(ret>=0 && first_zero_pivot==-1)
476 first_zero_pivot = k+ret;
478 nb_transpositions += nb_transpositions_in_panel;
480 for(
Index i=k; i<k+bs; ++i)
482 Index piv = (row_transpositions[i] += internal::convert_index<PivIndex>(k));
483 A_0.row(i).swap(A_0.row(piv));
489 for(
Index i=k;i<k+bs; ++i)
490 A_2.row(i).swap(A_2.row(row_transpositions[i]));
493 A11.template triangularView<UnitLower>().solveInPlace(A12);
495 A22.noalias() -= A21 * A12;
498 return first_zero_pivot;
504template<
typename MatrixType,
typename TranspositionType>
505void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions,
typename TranspositionType::StorageIndex& nb_transpositions)
508 if (lu.rows() == 0 || lu.cols() == 0) {
509 nb_transpositions = 0;
512 eigen_assert(lu.cols() == row_transpositions.size());
513 eigen_assert(row_transpositions.size() < 2 || (&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1);
517 typename TranspositionType::StorageIndex,
518 EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime)>
519 ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions);
524template<
typename MatrixType>
525void PartialPivLU<MatrixType>::compute()
527 check_template_parameters();
530 eigen_assert(m_lu.rows()<NumTraits<int>::highest());
533 m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
535 m_l1_norm = RealScalar(0);
537 eigen_assert(m_lu.rows() == m_lu.cols() &&
"PartialPivLU is only for square (and moreover invertible) matrices");
538 const Index size = m_lu.rows();
540 m_rowsTranspositions.resize(size);
542 typename TranspositionType::StorageIndex nb_transpositions;
543 internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);
544 m_det_p = (nb_transpositions%2) ? -1 : 1;
546 m_p = m_rowsTranspositions;
548 m_isInitialized =
true;
551template<
typename MatrixType>
554 eigen_assert(m_isInitialized &&
"PartialPivLU is not initialized.");
555 return Scalar(m_det_p) * m_lu.diagonal().prod();
561template<
typename MatrixType>
564 eigen_assert(m_isInitialized &&
"LU is not initialized.");
566 MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()
567 * m_lu.template triangularView<Upper>();
570 res = m_p.inverse() * res;
580template<
typename DstXprType,
typename MatrixType>
581struct Assignment<DstXprType,
Inverse<
PartialPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename PartialPivLU<MatrixType>::Scalar>, Dense2Dense>
585 static void run(DstXprType &dst,
const SrcXprType &src,
const internal::assign_op<typename DstXprType::Scalar,typename LuType::Scalar> &)
587 dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
600template<
typename Derived>
601inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
615template<
typename Derived>