ConjugateGradient.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 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_CONJUGATE_GRADIENT_H
11 #define EIGEN_CONJUGATE_GRADIENT_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
26 template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
27 EIGEN_DONT_INLINE
28 void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
29  const Preconditioner& precond, int& iters,
30  typename Dest::RealScalar& tol_error)
31 {
32  using std::sqrt;
33  using std::abs;
34  typedef typename Dest::RealScalar RealScalar;
35  typedef typename Dest::Scalar Scalar;
36  typedef Matrix<Scalar,Dynamic,1> VectorType;
37 
38  RealScalar tol = tol_error;
39  int maxIters = iters;
40 
41  int n = mat.cols();
42 
43  VectorType residual = rhs - mat * x; //initial residual
44  VectorType p(n);
45 
46  p = precond.solve(residual); //initial search direction
47 
48  VectorType z(n), tmp(n);
49  RealScalar absNew = internal::real(residual.dot(p)); // the square of the absolute value of r scaled by invM
50  RealScalar rhsNorm2 = rhs.squaredNorm();
51  RealScalar residualNorm2 = 0;
52  RealScalar threshold = tol*tol*rhsNorm2;
53  int i = 0;
54  while(i < maxIters)
55  {
56  tmp.noalias() = mat * p; // the bottleneck of the algorithm
57 
58  Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
59  x += alpha * p; // update solution
60  residual -= alpha * tmp; // update residue
61 
62  residualNorm2 = residual.squaredNorm();
63  if(residualNorm2 < threshold)
64  break;
65 
66  z = precond.solve(residual); // approximately solve for "A z = residual"
67 
68  RealScalar absOld = absNew;
69  absNew = internal::real(residual.dot(z)); // update the absolute value of r
70  RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
71  p = z + beta * p; // update search direction
72  i++;
73  }
74  tol_error = sqrt(residualNorm2 / rhsNorm2);
75  iters = i;
76 }
77 
78 }
79 
80 template< typename _MatrixType, int _UpLo=Lower,
81  typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
83 
84 namespace internal {
85 
86 template< typename _MatrixType, int _UpLo, typename _Preconditioner>
87 struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
88 {
89  typedef _MatrixType MatrixType;
90  typedef _Preconditioner Preconditioner;
91 };
92 
93 }
94 
143 template< typename _MatrixType, int _UpLo, typename _Preconditioner>
144 class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
145 {
146  typedef IterativeSolverBase<ConjugateGradient> Base;
147  using Base::mp_matrix;
148  using Base::m_error;
149  using Base::m_iterations;
150  using Base::m_info;
151  using Base::m_isInitialized;
152 public:
153  typedef _MatrixType MatrixType;
154  typedef typename MatrixType::Scalar Scalar;
155  typedef typename MatrixType::Index Index;
156  typedef typename MatrixType::RealScalar RealScalar;
157  typedef _Preconditioner Preconditioner;
158 
159  enum {
160  UpLo = _UpLo
161  };
162 
163 public:
164 
167 
178  ConjugateGradient(const MatrixType& A) : Base(A) {}
179 
180  ~ConjugateGradient() {}
181 
187  template<typename Rhs,typename Guess>
188  inline const internal::solve_retval_with_guess<ConjugateGradient, Rhs, Guess>
189  solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
190  {
191  eigen_assert(m_isInitialized && "ConjugateGradient is not initialized.");
192  eigen_assert(Base::rows()==b.rows()
193  && "ConjugateGradient::solve(): invalid number of rows of the right hand side matrix b");
194  return internal::solve_retval_with_guess
195  <ConjugateGradient, Rhs, Guess>(*this, b.derived(), x0);
196  }
197 
199  template<typename Rhs,typename Dest>
200  void _solveWithGuess(const Rhs& b, Dest& x) const
201  {
202  m_iterations = Base::maxIterations();
203  m_error = Base::m_tolerance;
204 
205  for(int j=0; j<b.cols(); ++j)
206  {
207  m_iterations = Base::maxIterations();
208  m_error = Base::m_tolerance;
209 
210  typename Dest::ColXpr xj(x,j);
211  internal::conjugate_gradient(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj,
212  Base::m_preconditioner, m_iterations, m_error);
213  }
214 
215  m_isInitialized = true;
216  m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
217  }
218 
220  template<typename Rhs,typename Dest>
221  void _solve(const Rhs& b, Dest& x) const
222  {
223  x.setOnes();
224  _solveWithGuess(b,x);
225  }
226 
227 protected:
228 
229 };
230 
231 
232 namespace internal {
233 
234 template<typename _MatrixType, int _UpLo, typename _Preconditioner, typename Rhs>
235 struct solve_retval<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner>, Rhs>
236  : solve_retval_base<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner>, Rhs>
237 {
238  typedef ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> Dec;
239  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
240 
241  template<typename Dest> void evalTo(Dest& dst) const
242  {
243  dec()._solve(rhs(),dst);
244  }
245 };
246 
247 } // end namespace internal
248 
249 } // end namespace Eigen
250 
251 #endif // EIGEN_CONJUGATE_GRADIENT_H