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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, 0 insertions, 297 deletions
diff --git a/extern/Eigen2/Eigen/src/Core/SolveTriangular.h b/extern/Eigen2/Eigen/src/Core/SolveTriangular.h deleted file mode 100644 index 12fb0e1d159..00000000000 --- a/extern/Eigen2/Eigen/src/Core/SolveTriangular.h +++ /dev/null @@ -1,297 +0,0 @@ -// 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 |