1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_SOLVETRIANGULAR_H
11#define EIGEN_SOLVETRIANGULAR_H
12
13namespace Eigen {
14
15namespace internal {
16
17// Forward declarations:
18// The following two routines are implemented in the products/TriangularSolver*.h files
19template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
20struct triangular_solve_vector;
21
22template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
23struct triangular_solve_matrix;
24
25// small helper struct extracting some traits on the underlying solver operation
26template<typename Lhs, typename Rhs, int Side>
27class trsolve_traits
28{
29  private:
30    enum {
31      RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
32    };
33  public:
34    enum {
35      Unrolling   = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
36                  ? CompleteUnrolling : NoUnrolling,
37      RhsVectors  = RhsIsVectorAtCompileTime ? 1 : Dynamic
38    };
39};
40
41template<typename Lhs, typename Rhs,
42  int Side, // can be OnTheLeft/OnTheRight
43  int Mode, // can be Upper/Lower | UnitDiag
44  int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
45  int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
46  >
47struct triangular_solver_selector;
48
49template<typename Lhs, typename Rhs, int Side, int Mode>
50struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
51{
52  typedef typename Lhs::Scalar LhsScalar;
53  typedef typename Rhs::Scalar RhsScalar;
54  typedef blas_traits<Lhs> LhsProductTraits;
55  typedef typename LhsProductTraits::ExtractType ActualLhsType;
56  typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
57  static void run(const Lhs& lhs, Rhs& rhs)
58  {
59    ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
60
61    // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
62
63    bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
64
65    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
66                                                  (useRhsDirectly ? rhs.data() : 0));
67
68    if(!useRhsDirectly)
69      MappedRhs(actualRhs,rhs.size()) = rhs;
70
71    triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
72                            (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
73      ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
74
75    if(!useRhsDirectly)
76      rhs = MappedRhs(actualRhs, rhs.size());
77  }
78};
79
80// the rhs is a matrix
81template<typename Lhs, typename Rhs, int Side, int Mode>
82struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
83{
84  typedef typename Rhs::Scalar Scalar;
85  typedef blas_traits<Lhs> LhsProductTraits;
86  typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
87
88  static void run(const Lhs& lhs, Rhs& rhs)
89  {
90    typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
91
92    const Index size = lhs.rows();
93    const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
94
95    typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
96              Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
97
98    BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);
99
100    triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
101                               (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
102      ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
103  }
104};
105
106/***************************************************************************
107* meta-unrolling implementation
108***************************************************************************/
109
110template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size,
111         bool Stop = LoopIndex==Size>
112struct triangular_solver_unroller;
113
114template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
115struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,false> {
116  enum {
117    IsLower = ((Mode&Lower)==Lower),
118    DiagIndex  = IsLower ? LoopIndex : Size - LoopIndex - 1,
119    StartIndex = IsLower ? 0         : DiagIndex+1
120  };
121  static void run(const Lhs& lhs, Rhs& rhs)
122  {
123    if (LoopIndex>0)
124      rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()
125                                .cwiseProduct(rhs.template segment<LoopIndex>(StartIndex)).sum();
126
127    if(!(Mode & UnitDiag))
128      rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex,DiagIndex);
129
130    triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex+1,Size>::run(lhs,rhs);
131  }
132};
133
134template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
135struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {
136  static void run(const Lhs&, Rhs&) {}
137};
138
139template<typename Lhs, typename Rhs, int Mode>
140struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
141  static void run(const Lhs& lhs, Rhs& rhs)
142  { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
143};
144
145template<typename Lhs, typename Rhs, int Mode>
146struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
147  static void run(const Lhs& lhs, Rhs& rhs)
148  {
149    Transpose<const Lhs> trLhs(lhs);
150    Transpose<Rhs> trRhs(rhs);
151
152    triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
153                              ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
154                              0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
155  }
156};
157
158} // end namespace internal
159
160/***************************************************************************
161* TriangularView methods
162***************************************************************************/
163
164#ifndef EIGEN_PARSED_BY_DOXYGEN
165template<typename MatrixType, unsigned int Mode>
166template<int Side, typename OtherDerived>
167void TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
168{
169  OtherDerived& other = _other.const_cast_derived();
170  eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );
171  eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
172
173  enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit)  && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};
174  typedef typename internal::conditional<copy,
175    typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
176  OtherCopy otherCopy(other);
177
178  internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
179    Side, Mode>::run(derived().nestedExpression(), otherCopy);
180
181  if (copy)
182    other = otherCopy;
183}
184
185template<typename Derived, unsigned int Mode>
186template<int Side, typename Other>
187const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
188TriangularViewImpl<Derived,Mode,Dense>::solve(const MatrixBase<Other>& other) const
189{
190  return internal::triangular_solve_retval<Side,TriangularViewType,Other>(derived(), other.derived());
191}
192#endif
193
194namespace internal {
195
196
197template<int Side, typename TriangularType, typename Rhs>
198struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
199{
200  typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
201};
202
203template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
204 : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
205{
206  typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
207  typedef ReturnByValue<triangular_solve_retval> Base;
208
209  triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
210    : m_triangularMatrix(tri), m_rhs(rhs)
211  {}
212
213  inline Index rows() const { return m_rhs.rows(); }
214  inline Index cols() const { return m_rhs.cols(); }
215
216  template<typename Dest> inline void evalTo(Dest& dst) const
217  {
218    if(!is_same_dense(dst,m_rhs))
219      dst = m_rhs;
220    m_triangularMatrix.template solveInPlace<Side>(dst);
221  }
222
223  protected:
224    const TriangularType& m_triangularMatrix;
225    typename Rhs::Nested m_rhs;
226};
227
228} // namespace internal
229
230} // end namespace Eigen
231
232#endif // EIGEN_SOLVETRIANGULAR_H
233