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4c92150676
part of a matrix. Triangular also provide an optimised method for forward and backward substitution. Further optimizations regarding assignments and products might come later. Updated determinant() to take into account triangular matrices. Started the QR module with a QR decompostion algorithm. Help needed to build a QR algorithm (eigen solver) based on it.
368 lines
13 KiB
C++
368 lines
13 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_PRODUCT_H
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#define EIGEN_PRODUCT_H
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template<int Index, int Size, typename Lhs, typename Rhs>
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struct ei_product_unroller
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{
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static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
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typename Lhs::Scalar &res)
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{
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ei_product_unroller<Index-1, Size, Lhs, Rhs>::run(row, col, lhs, rhs, res);
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res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
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}
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};
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template<int Size, typename Lhs, typename Rhs>
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struct ei_product_unroller<0, Size, Lhs, Rhs>
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{
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static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
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typename Lhs::Scalar &res)
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{
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res = lhs.coeff(row, 0) * rhs.coeff(0, col);
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}
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};
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template<int Index, typename Lhs, typename Rhs>
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struct ei_product_unroller<Index, Dynamic, Lhs, Rhs>
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{
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static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
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};
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// prevent buggy user code from causing an infinite recursion
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template<int Index, typename Lhs, typename Rhs>
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struct ei_product_unroller<Index, 0, Lhs, Rhs>
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{
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static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
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};
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template<bool RowMajor, int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller
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{
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static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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ei_packet_product_unroller<RowMajor, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
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if (RowMajor)
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res = ei_padd(res, ei_pmul(ei_pset1(lhs.coeff(row, Index)), rhs.packetCoeff(Index, col)));
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else
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res = ei_padd(res, ei_pmul(lhs.packetCoeff(row, Index), ei_pset1(rhs.coeff(Index, col))));
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}
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};
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template<bool RowMajor, int Size, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<RowMajor, 0, Size, Lhs, Rhs, PacketScalar>
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{
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static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
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{
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if (RowMajor)
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res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.packetCoeff(0, col));
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else
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res = ei_pmul(lhs.packetCoeff(row, 0), ei_pset1(rhs.coeff(0, col)));
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}
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};
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template<bool RowMajor, int Index, typename Lhs, typename Rhs, typename PacketScalar>
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struct ei_packet_product_unroller<RowMajor, Index, Dynamic, Lhs, Rhs, PacketScalar>
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{
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static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
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};
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/** \class Product
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*
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* \brief Expression of the product of two matrices
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*
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* \param Lhs the type of the left-hand side
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* \param Rhs the type of the right-hand side
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* \param EvalMode internal use only
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*
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* This class represents an expression of the product of two matrices.
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* It is the return type of the operator* between matrices, and most of the time
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* this is the only way it is used.
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*
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* \sa class Sum, class Difference
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*/
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template<typename Lhs, typename Rhs> struct ei_product_eval_mode
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{
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enum{ value = Lhs::MaxRowsAtCompileTime >= 16 && Rhs::MaxColsAtCompileTime >= 16
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? CacheOptimalProduct : NormalProduct };
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};
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template<typename Lhs, typename Rhs, int EvalMode>
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struct ei_traits<Product<Lhs, Rhs, EvalMode> >
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{
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typedef typename Lhs::Scalar Scalar;
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typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
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typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
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typedef typename ei_unref<LhsNested>::type _LhsNested;
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typedef typename ei_unref<RhsNested>::type _RhsNested;
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enum {
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LhsCoeffReadCost = _LhsNested::CoeffReadCost,
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RhsCoeffReadCost = _RhsNested::CoeffReadCost,
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LhsFlags = _LhsNested::Flags,
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RhsFlags = _RhsNested::Flags,
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RowsAtCompileTime = Lhs::RowsAtCompileTime,
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ColsAtCompileTime = Rhs::ColsAtCompileTime,
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MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
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Flags = (( (RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
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? (unsigned int)(LhsFlags | RhsFlags)
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: (unsigned int)(LhsFlags | RhsFlags) & ~LargeBit )
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| EvalBeforeAssigningBit
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| (ei_product_eval_mode<Lhs, Rhs>::value == (int)CacheOptimalProduct ? EvalBeforeNestingBit : 0))
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& (
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DefaultLostFlagMask & (~RowMajorBit)
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| (
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(
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(!(Lhs::Flags & RowMajorBit)) && (Lhs::Flags & VectorizableBit)
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&& (Lhs::RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0)
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)
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? VectorizableBit
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: (
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(
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(Rhs::Flags & RowMajorBit) && (Rhs::Flags & VectorizableBit)
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&& (Lhs::ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0)
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)
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? RowMajorBit | VectorizableBit
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: 0
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)
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)
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),
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CoeffReadCost
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= Lhs::ColsAtCompileTime == Dynamic
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? Dynamic
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: Lhs::ColsAtCompileTime
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* (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
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+ (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
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};
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};
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template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
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public MatrixBase<Product<Lhs, Rhs, EvalMode> >
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{
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public:
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EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
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typedef typename ei_traits<Product>::LhsNested LhsNested;
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typedef typename ei_traits<Product>::RhsNested RhsNested;
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typedef typename ei_traits<Product>::_LhsNested _LhsNested;
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typedef typename ei_traits<Product>::_RhsNested _RhsNested;
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Product(const Lhs& lhs, const Rhs& rhs)
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: m_lhs(lhs), m_rhs(rhs)
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{
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ei_assert(lhs.cols() == rhs.rows());
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}
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/** \internal */
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template<typename DestDerived>
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void _cacheOptimalEval(DestDerived& res, ei_meta_false) const;
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#ifdef EIGEN_VECTORIZE
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template<typename DestDerived>
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void _cacheOptimalEval(DestDerived& res, ei_meta_true) const;
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#endif
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private:
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int _rows() const { return m_lhs.rows(); }
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int _cols() const { return m_rhs.cols(); }
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const Scalar _coeff(int row, int col) const
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{
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Scalar res;
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const bool unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT;
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if(unroll)
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{
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ei_product_unroller<Lhs::ColsAtCompileTime-1,
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unroll ? Lhs::ColsAtCompileTime : Dynamic,
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_LhsNested, _RhsNested>
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::run(row, col, m_lhs, m_rhs, res);
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}
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else
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{
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res = m_lhs.coeff(row, 0) * m_rhs.coeff(0, col);
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for(int i = 1; i < m_lhs.cols(); i++)
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res += m_lhs.coeff(row, i) * m_rhs.coeff(i, col);
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}
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return res;
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}
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PacketScalar _packetCoeff(int row, int col) const EIGEN_ALWAYS_INLINE
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{
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PacketScalar res;
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if(Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT)
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{
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ei_packet_product_unroller<Flags&RowMajorBit, Lhs::ColsAtCompileTime-1,
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Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
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? Lhs::ColsAtCompileTime : Dynamic,
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_LhsNested, _RhsNested, PacketScalar>
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::run(row, col, m_lhs, m_rhs, res);
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}
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else
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{
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if (Flags&RowMajorBit)
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{
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res = ei_pmul(ei_pset1(m_lhs.coeff(row, 0)),m_rhs.packetCoeff(0, col));
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for(int i = 1; i < m_lhs.cols(); i++)
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res = ei_padd(res, ei_pmul(ei_pset1(m_lhs.coeff(row, i)), m_rhs.packetCoeff(i, col)));
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}
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else
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{
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res = ei_pmul(m_lhs.packetCoeff(row, 0), ei_pset1(m_rhs.coeff(0, col)));
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for(int i = 1; i < m_lhs.cols(); i++)
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res = ei_padd(res, ei_pmul(m_lhs.packetCoeff(row, i), ei_pset1(m_rhs.coeff(i, col))));
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}
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}
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return res;
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}
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protected:
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const LhsNested m_lhs;
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const RhsNested m_rhs;
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};
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/** \returns the matrix product of \c *this and \a other.
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*
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* \note This function causes an immediate evaluation. If you want to perform a matrix product
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* without immediate evaluation, call .lazy() on one of the matrices before taking the product.
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*
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* \sa lazy(), operator*=(const MatrixBase&)
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*/
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template<typename Derived>
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template<typename OtherDerived>
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const Product<Derived,OtherDerived>
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MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
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{
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return Product<Derived,OtherDerived>(derived(), other.derived());
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}
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/** replaces \c *this by \c *this * \a other.
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*
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* \returns a reference to \c *this
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*/
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template<typename Derived>
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template<typename OtherDerived>
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Derived &
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MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
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{
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return *this = *this * other;
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}
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template<typename Derived>
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template<typename Lhs, typename Rhs>
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Derived& MatrixBase<Derived>::lazyAssign(const Product<Lhs,Rhs,CacheOptimalProduct>& product)
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{
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product._cacheOptimalEval(*this,
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#ifdef EIGEN_VECTORIZE
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typename ei_meta_if<(Flags & VectorizableBit)
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&& (!(Lhs::Flags & RowMajorBit)
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&& (Lhs::RowsAtCompileTime!=Dynamic)
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&& (Lhs::RowsAtCompileTime%ei_packet_traits<Scalar>::size==0) ),
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ei_meta_true,ei_meta_false>::ret()
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#else
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ei_meta_false()
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#endif
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);
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return derived();
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}
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template<typename Lhs, typename Rhs, int EvalMode>
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template<typename DestDerived>
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void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_false) const
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{
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res.setZero();
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const int cols4 = m_lhs.cols() & 0xfffffffC;
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{
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for(int k=0; k<this->cols(); ++k)
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{
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int j=0;
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for(; j<cols4; j+=4)
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{
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const Scalar tmp0 = m_rhs.coeff(j ,k);
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const Scalar tmp1 = m_rhs.coeff(j+1,k);
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const Scalar tmp2 = m_rhs.coeff(j+2,k);
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const Scalar tmp3 = m_rhs.coeff(j+3,k);
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for (int i=0; i<this->rows(); ++i)
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res.coeffRef(i,k) += tmp0 * m_lhs.coeff(i,j) + tmp1 * m_lhs.coeff(i,j+1)
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+ tmp2 * m_lhs.coeff(i,j+2) + tmp3 * m_lhs.coeff(i,j+3);
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}
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for(; j<m_lhs.cols(); ++j)
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{
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const Scalar tmp = m_rhs.coeff(j,k);
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for (int i=0; i<this->rows(); ++i)
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res.coeffRef(i,k) += tmp * m_lhs.coeff(i,j);
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}
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}
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}
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}
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#ifdef EIGEN_VECTORIZE
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template<typename Lhs, typename Rhs, int EvalMode>
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template<typename DestDerived>
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void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res, ei_meta_true) const
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{
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res.setZero();
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const int cols4 = m_lhs.cols() & 0xfffffffC;
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for(int k=0; k<this->cols(); k++)
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{
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int j=0;
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for(; j<cols4; j+=4)
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{
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const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_rhs.coeff(j+0,k));
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const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_rhs.coeff(j+1,k));
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const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_rhs.coeff(j+2,k));
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const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_rhs.coeff(j+3,k));
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for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size)
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{
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res.writePacketCoeff(i,k,\
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ei_padd(
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res.packetCoeff(i,k),
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ei_padd(
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ei_padd(
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ei_pmul(tmp0, m_lhs.packetCoeff(i,j)),
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ei_pmul(tmp1, m_lhs.packetCoeff(i,j+1))),
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ei_padd(
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ei_pmul(tmp2, m_lhs.packetCoeff(i,j+2)),
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ei_pmul(tmp3, m_lhs.packetCoeff(i,j+3))
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)
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)
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)
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);
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}
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}
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for(; j<m_lhs.cols(); ++j)
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{
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const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_rhs.coeff(j,k));
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for (int i=0; i<this->rows(); ++i)
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res.writePacketCoeff(i,k,ei_pmul(tmp, m_lhs.packetCoeff(i,j)));
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}
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}
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}
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#endif // EIGEN_VECTORIZE
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#endif // EIGEN_PRODUCT_H
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