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Diffstat (limited to 'extern/Eigen2/Eigen/src/Core/SolveTriangular.h')
-rw-r--r-- | extern/Eigen2/Eigen/src/Core/SolveTriangular.h | 297 |
1 files changed, 297 insertions, 0 deletions
diff --git a/extern/Eigen2/Eigen/src/Core/SolveTriangular.h b/extern/Eigen2/Eigen/src/Core/SolveTriangular.h new file mode 100644 index 00000000000..12fb0e1d159 --- /dev/null +++ b/extern/Eigen2/Eigen/src/Core/SolveTriangular.h @@ -0,0 +1,297 @@ +// 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_SOLVETRIANGULAR_H +#define EIGEN_SOLVETRIANGULAR_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 = (int(Lhs::Flags) & LowerTriangularBit) + ? LowerTriangular + : (int(Lhs::Flags) & UpperTriangularBit) + ? UpperTriangular + : -1, + int StorageOrder = ei_is_part<Lhs>::value ? -1 // this is to solve ambiguous specializations + : int(Lhs::Flags) & (RowMajorBit|SparseBit) + > +struct ei_solve_triangular_selector; + +// transform a Part xpr to a Flagged xpr +template<typename Lhs, unsigned int LhsMode, typename Rhs, int UpLo, int StorageOrder> +struct ei_solve_triangular_selector<Part<Lhs,LhsMode>,Rhs,UpLo,StorageOrder> +{ + static void run(const Part<Lhs,LhsMode>& lhs, Rhs& other) + { + ei_solve_triangular_selector<Flagged<Lhs,LhsMode,0>,Rhs>::run(lhs._expression(), other); + } +}; + +// forward substitution, row-major +template<typename Lhs, typename Rhs, int UpLo> +struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,RowMajor|IsDense> +{ + typedef typename Rhs::Scalar Scalar; + static void run(const Lhs& lhs, Rhs& other) + { + const bool IsLowerTriangular = (UpLo==LowerTriangular); + const int size = lhs.cols(); + /* We perform the inverse product per block of 4 rows such that we perfectly match + * our optimized matrix * vector product. blockyStart represents the number of rows + * we have process first using the non-block version. + */ + int blockyStart = (std::max(size-5,0)/4)*4; + if (IsLowerTriangular) + blockyStart = size - blockyStart; + else + blockyStart -= 1; + for(int c=0 ; c<other.cols() ; ++c) + { + // process first rows using the non block version + if(!(Lhs::Flags & UnitDiagBit)) + { + if (IsLowerTriangular) + other.coeffRef(0,c) = other.coeff(0,c)/lhs.coeff(0, 0); + else + other.coeffRef(size-1,c) = other.coeff(size-1, c)/lhs.coeff(size-1, size-1); + } + for(int i=(IsLowerTriangular ? 1 : size-2); IsLowerTriangular ? i<blockyStart : i>blockyStart; i += (IsLowerTriangular ? 1 : -1) ) + { + Scalar tmp = other.coeff(i,c) + - (IsLowerTriangular ? ((lhs.row(i).start(i)) * other.col(c).start(i)).coeff(0,0) + : ((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); + } + + // now let's process the remaining rows 4 at once + for(int i=blockyStart; IsLowerTriangular ? i<size : i>0; ) + { + int startBlock = i; + int endBlock = startBlock + (IsLowerTriangular ? 4 : -4); + + /* Process the i cols times 4 rows block, and keep the result in a temporary vector */ + // FIXME use fixed size block but take care to small fixed size matrices... + Matrix<Scalar,Dynamic,1> btmp(4); + if (IsLowerTriangular) + btmp = lhs.block(startBlock,0,4,i) * other.col(c).start(i); + else + btmp = lhs.block(i-3,i+1,4,size-1-i) * other.col(c).end(size-1-i); + + /* Let's process the 4x4 sub-matrix as usual. + * btmp stores the diagonal coefficients used to update the remaining part of the result. + */ + { + Scalar tmp = other.coeff(startBlock,c)-btmp.coeff(IsLowerTriangular?0:3); + if (Lhs::Flags & UnitDiagBit) + other.coeffRef(i,c) = tmp; + else + other.coeffRef(i,c) = tmp/lhs.coeff(i,i); + } + + i += IsLowerTriangular ? 1 : -1; + for (;IsLowerTriangular ? i<endBlock : i>endBlock; i += IsLowerTriangular ? 1 : -1) + { + int remainingSize = IsLowerTriangular ? i-startBlock : startBlock-i; + Scalar tmp = other.coeff(i,c) + - btmp.coeff(IsLowerTriangular ? remainingSize : 3-remainingSize) + - ( lhs.row(i).segment(IsLowerTriangular ? startBlock : i+1, remainingSize) + * other.col(c).segment(IsLowerTriangular ? startBlock : i+1, remainingSize)).coeff(0,0); + + if (Lhs::Flags & UnitDiagBit) + other.coeffRef(i,c) = tmp; + else + other.coeffRef(i,c) = tmp/lhs.coeff(i,i); + } + } + } + } +}; + +// Implements the following configurations: +// - inv(LowerTriangular, ColMajor) * Column vector +// - inv(LowerTriangular,UnitDiag,ColMajor) * Column vector +// - inv(UpperTriangular, ColMajor) * Column vector +// - inv(UpperTriangular,UnitDiag,ColMajor) * Column vector +template<typename Lhs, typename Rhs, int UpLo> +struct ei_solve_triangular_selector<Lhs,Rhs,UpLo,ColMajor|IsDense> +{ + 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) + { + static const bool IsLowerTriangular = (UpLo==LowerTriangular); + 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. blockyEnd represents the number of rows + * we can process using the block version. + */ + int blockyEnd = (std::max(size-5,0)/4)*4; + if (!IsLowerTriangular) + blockyEnd = size-1 - blockyEnd; + for(int i=IsLowerTriangular ? 0 : size-1; IsLowerTriangular ? i<blockyEnd : 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 + (IsLowerTriangular ? 4 : -4); + Matrix<Scalar,4,1> btmp; + for (;IsLowerTriangular ? i<endBlock : i>endBlock; + i += IsLowerTriangular ? 1 : -1) + { + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + int remainingSize = IsLowerTriangular ? endBlock-i-1 : i-endBlock-1; + if (remainingSize>0) + other.col(c).segment((IsLowerTriangular ? i : endBlock) + 1, remainingSize) -= + other.coeffRef(i,c) + * Block<Lhs,Dynamic,1>(lhs, (IsLowerTriangular ? i : endBlock) + 1, i, remainingSize, 1); + btmp.coeffRef(IsLowerTriangular ? i-startBlock : remainingSize) = -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( + IsLowerTriangular ? size-endBlock : endBlock+1, + &(lhs.const_cast_derived().coeffRef(IsLowerTriangular ? endBlock : 0, IsLowerTriangular ? startBlock : endBlock+1)), + lhs.stride(), + btmp, &(other.coeffRef(IsLowerTriangular ? endBlock : 0, c))); +// if (IsLowerTriangular) +// other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock) +// * other.col(c).block(startBlock,endBlock-startBlock)).lazy(); +// else +// other.col(c).end(size-endBlock) += (lhs.block(endBlock, startBlock, size-endBlock, endBlock-startBlock) +// * other.col(c).block(startBlock,endBlock-startBlock)).lazy(); + } + + /* Now we have to process the remaining part as usual */ + int i; + for(i=blockyEnd; IsLowerTriangular ? i<size-1 : i>0; i += (IsLowerTriangular ? 1 : -1) ) + { + 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 + */ + if(IsLowerTriangular) + other.col(c).end(size-i-1) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, i+1,i, size-i-1,1); + else + other.col(c).start(i) -= other.coeffRef(i,c) * Block<Lhs,Dynamic,1>(lhs, 0,i, i, 1); + } + if(!(Lhs::Flags & UnitDiagBit)) + other.coeffRef(i,c) /= lhs.coeff(i,i); + } + } +}; + +/** "in-place" version of MatrixBase::solveTriangular() where the result is written in \a other + * + * \nonstableyet + * + * The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here. + * This function will const_cast it, so constness isn't honored here. + * + * See MatrixBase:solveTriangular() for the details. + */ +template<typename Derived> +template<typename OtherDerived> +void MatrixBase<Derived>::solveTriangularInPlace(const MatrixBase<OtherDerived>& _other) const +{ + MatrixBase<OtherDerived>& other = _other.const_cast_derived(); + ei_assert(derived().cols() == derived().rows()); + ei_assert(derived().cols() == other.rows()); + ei_assert(!(Flags & ZeroDiagBit)); + ei_assert(Flags & (UpperTriangularBit|LowerTriangularBit)); + + enum { copy = ei_traits<OtherDerived>::Flags & RowMajorBit }; + + typedef typename ei_meta_if<copy, + typename ei_plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::ret OtherCopy; + OtherCopy otherCopy(other.derived()); + + ei_solve_triangular_selector<Derived, typename ei_unref<OtherCopy>::type>::run(derived(), otherCopy); + + if (copy) + other = otherCopy; +} + +/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular. + * + * \nonstableyet + * + * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other. + * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the + * diagonal must be non zero). 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, which + * can be done by marked(), and that is automatically the case with expressions such as those returned + * by extract(). + * + * \addexample SolveTriangular \label How to solve a triangular system (aka. how to multiply the inverse of a triangular matrix by another one) + * + * Example: \include MatrixBase_marked.cpp + * Output: \verbinclude MatrixBase_marked.out + * + * This function is essentially a wrapper to the faster solveTriangularInPlace() function creating + * a temporary copy of \a other, calling solveTriangularInPlace() on the copy and returning it. + * Therefore, if \a other is not needed anymore, it is quite faster to call solveTriangularInPlace() + * instead of solveTriangular(). + * + * For users coming from BLAS, this function (and more specifically solveTriangularInPlace()) offer + * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines. + * + * \b Tips: to perform a \em "right-inverse-multiply" you can simply transpose the operation, e.g.: + * \code + * M * T^1 <=> T.transpose().solveTriangularInPlace(M.transpose()); + * \endcode + * + * \sa solveTriangularInPlace(), marked(), extract() + */ +template<typename Derived> +template<typename OtherDerived> +typename ei_plain_matrix_type_column_major<OtherDerived>::type +MatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const +{ + typename ei_plain_matrix_type_column_major<OtherDerived>::type res(other); + solveTriangularInPlace(res); + return res; +} + +#endif // EIGEN_SOLVETRIANGULAR_H |