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Diffstat (limited to 'Eigen/src/Core/SolveTriangular.h')
| -rwxr-xr-x | Eigen/src/Core/SolveTriangular.h | 254 |
1 files changed, 254 insertions, 0 deletions
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h new file mode 100755 index 000000000..a9867e63c --- /dev/null +++ b/Eigen/src/Core/SolveTriangular.h @@ -0,0 +1,254 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. Eigen itself is part of the KDE project. +// +// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_INVERSEPRODUCT_H +#define EIGEN_INVERSEPRODUCT_H + +template<typename XprType> struct ei_is_part { enum {value=false}; }; +template<typename XprType, unsigned int Mode> struct ei_is_part<Part<XprType,Mode> > { enum {value=true}; }; + +template<typename Lhs, typename Rhs, + int TriangularPart = ei_is_part<Lhs>::value ? -1 // this is to solve ambiguous specializations + : (int(Lhs::Flags) & LowerTriangularBit) + ? Lower + : (int(Lhs::Flags) & UpperTriangularBit) + ? Upper + : -1, + int StorageOrder = int(Lhs::Flags) & RowMajorBit ? RowMajor : ColMajor + > +struct ei_trisolve_selector; + +// transform a Part xpr to a Flagged xpr +template<typename Lhs, unsigned int LhsMode, typename Rhs, int TriangularPart, int StorageOrder> +struct ei_trisolve_selector<Part<Lhs,LhsMode>,Rhs,TriangularPart,StorageOrder> +{ + static void run(const Part<Lhs,LhsMode>& lhs, Rhs& other) + { + ei_trisolve_selector<Flagged<Lhs,LhsMode,0>,Rhs>::run(lhs._expression(), other); + } +}; + +// forward substitution, row-major +template<typename Lhs, typename Rhs> +struct ei_trisolve_selector<Lhs,Rhs,Lower,RowMajor> +{ + typedef typename Rhs::Scalar Scalar; + static void run(const Lhs& lhs, Rhs& other) + { + for(int c=0 ; c<other.cols() ; ++c) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(0,c) = other.coeff(0,c)/lhs.coeff(0, 0); + for(int i=1; i<lhs.rows(); ++i) + { + Scalar tmp = other.coeff(i,c) - ((lhs.row(i).start(i)) * other.col(c).start(i)).coeff(0,0); + if (Lhs::Flags & UnitDiagBit) + other.coeffRef(i,c) = tmp; + else + other.coeffRef(i,c) = tmp/lhs.coeff(i,i); + } + } + } +}; + +// backward substitution, row-major +template<typename Lhs, typename Rhs> +struct ei_trisolve_selector<Lhs,Rhs,Upper,RowMajor> +{ + typedef typename Rhs::Scalar Scalar; + static void run(const Lhs& lhs, Rhs& other) + { + const int size = lhs.cols(); + for(int c=0 ; c<other.cols() ; ++c) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(size-1,c) = other.coeff(size-1, c)/lhs.coeff(size-1, size-1); + for(int i=size-2 ; i>=0 ; --i) + { + Scalar tmp = other.coeff(i,c) + - ((lhs.row(i).end(size-i-1)) * other.col(c).end(size-i-1)).coeff(0,0); + if (Lhs::Flags & UnitDiagBit) + other.coeffRef(i,c) = tmp; + else + other.coeffRef(i,c) = tmp/lhs.coeff(i,i); + } + } + } +}; + +// forward substitution, col-major +// FIXME the Lower and Upper specialization could be merged using a small helper class +// performing reflexions on the coordinates... +template<typename Lhs, typename Rhs> +struct ei_trisolve_selector<Lhs,Rhs,Lower,ColMajor> +{ + typedef typename Rhs::Scalar Scalar; + typedef typename ei_packet_traits<Scalar>::type Packet; + enum {PacketSize = ei_packet_traits<Scalar>::size}; + + static void run(const Lhs& lhs, Rhs& other) + { + const int size = lhs.cols(); + for(int c=0 ; c<other.cols() ; ++c) + { + /* let's perform the inverse product per block of 4 columns such that we perfectly match + * our optimized matrix * vector product. + */ + int blockyEnd = (std::max(size-5,0)/4)*4; + for(int i=0; i<blockyEnd;) + { + /* Let's process the 4x4 sub-matrix as usual. + * btmp stores the diagonal coefficients used to update the remaining part of the result. + */ + int startBlock = i; + int endBlock = startBlock+4; + Matrix<Scalar,4,1> btmp; + for (;i<endBlock;++i) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + int remainingSize = endBlock-i-1; + if (remainingSize>0) + other.col(c).block(i+1,remainingSize) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, i+1, i, remainingSize, 1); + btmp.coeffRef(i-startBlock) = -other.coeffRef(i,c); + } + + /* Now we can efficiently update the remaining part of the result as a matrix * vector product. + * NOTE in order to reduce both compilation time and binary size, let's directly call + * the fast product implementation. It is equivalent to the following code: + * other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock) + * * other.col(c).block(startBlock,endBlock-startBlock)).lazy(); + */ + // FIXME this is cool but what about conjugate/adjoint expressions ? do we want to evaluate them ? + // this is a more general problem though. + ei_cache_friendly_product_colmajor_times_vector( + size-endBlock, &(lhs.const_cast_derived().coeffRef(endBlock,startBlock)), lhs.stride(), + btmp, &(other.coeffRef(endBlock,c))); + } + + /* Now we have to process the remaining part as usual */ + int i; + for(i=blockyEnd; i<size-1; ++i) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + + /* NOTE we cannot use lhs.col(i).end(size-i-1) because Part::coeffRef gets called by .col() to + * get the address of the start of the row + */ + other.col(c).end(size-i-1) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, i+1,i, size-i-1,1); + } + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + } + } +}; + +// backward substitution, col-major +// see the previous specialization for details on the algorithm +template<typename Lhs, typename Rhs> +struct ei_trisolve_selector<Lhs,Rhs,Upper,ColMajor> +{ + typedef typename Rhs::Scalar Scalar; + static void run(const Lhs& lhs, Rhs& other) + { + const int size = lhs.cols(); + for(int c=0 ; c<other.cols() ; ++c) + { + int blockyEnd = size-1 - (std::max(size-5,0)/4)*4; + for(int i=size-1; i>blockyEnd;) + { + int startBlock = i; + int endBlock = startBlock-4; + Matrix<Scalar,4,1> btmp; + /* Let's process the 4x4 sub-matrix as usual. + * btmp stores the diagonal coefficients used to update the remaining part of the result. + */ + for (; i>endBlock; --i) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + int remainingSize = i-endBlock-1; + if (remainingSize>0) + other.col(c).block(endBlock+1,remainingSize) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, endBlock+1, i, remainingSize, 1); + btmp.coeffRef(remainingSize) = -other.coeffRef(i,c); + } + + ei_cache_friendly_product_colmajor_times_vector( + endBlock+1, &(lhs.const_cast_derived().coeffRef(0,endBlock+1)), lhs.stride(), + btmp, &(other.coeffRef(0,c))); + } + + for(int i=blockyEnd; i>0; --i) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + other.col(c).start(i) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, 0,i, i, 1); + } + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(0,c) /= lhs.coeff(0,0); + } + } +}; + +/** "in-place" version of MatrixBase::solveTriangular() where the result is written in \a other + * + * \sa solveTriangular() + */ +template<typename Derived> +template<typename OtherDerived> +void MatrixBase<Derived>::solveTriangularInPlace(MatrixBase<OtherDerived>& other) const +{ + ei_assert(derived().cols() == derived().rows()); + ei_assert(derived().cols() == other.rows()); + ei_assert(!(Flags & ZeroDiagBit)); + ei_assert(Flags & (UpperTriangularBit|LowerTriangularBit)); + + ei_trisolve_selector<Derived, OtherDerived>::run(derived(), other.derived()); +} + +/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular. + * + * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other + * It works as a forward (resp. backward) substitution if \c *this is an upper (resp. lower) + * triangular matrix. + * + * It is required that \c *this be marked as either an upper or a lower triangular matrix, as + * can be done by marked(), and as is automatically the case with expressions such as those returned + * by extract(). + * Example: \include MatrixBase_marked.cpp + * Output: \verbinclude MatrixBase_marked.out + * + * \sa marked(), extract() + */ +template<typename Derived> +template<typename OtherDerived> +typename OtherDerived::Eval MatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const +{ + typename OtherDerived::Eval res(other); + solveTriangularInPlace(res); + return res; +} + +#endif // EIGEN_INVERSEPRODUCT_H |