Eigen  3.3.90 (mercurial changeset b6e6d0cf6a77)
LeastSquareConjugateGradient.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2015 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_LEAST_SQUARE_CONJUGATE_GRADIENT_H
11 #define EIGEN_LEAST_SQUARE_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 least_square_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
29  const Preconditioner& precond, Index& 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  Index maxIters = iters;
40 
41  Index m = mat.rows(), n = mat.cols();
42 
43  VectorType residual = rhs - mat * x;
44  VectorType normal_residual = mat.adjoint() * residual;
45 
46  RealScalar rhsNorm2 = (mat.adjoint()*rhs).squaredNorm();
47  if(rhsNorm2 == 0)
48  {
49  x.setZero();
50  iters = 0;
51  tol_error = 0;
52  return;
53  }
54  RealScalar threshold = tol*tol*rhsNorm2;
55  RealScalar residualNorm2 = normal_residual.squaredNorm();
56  if (residualNorm2 < threshold)
57  {
58  iters = 0;
59  tol_error = sqrt(residualNorm2 / rhsNorm2);
60  return;
61  }
62 
63  VectorType p(n);
64  p = precond.solve(normal_residual); // initial search direction
65 
66  VectorType z(n), tmp(m);
67  RealScalar absNew = numext::real(normal_residual.dot(p)); // the square of the absolute value of r scaled by invM
68  Index i = 0;
69  while(i < maxIters)
70  {
71  tmp.noalias() = mat * p;
72 
73  Scalar alpha = absNew / tmp.squaredNorm(); // the amount we travel on dir
74  x += alpha * p; // update solution
75  residual -= alpha * tmp; // update residual
76  normal_residual = mat.adjoint() * residual; // update residual of the normal equation
77 
78  residualNorm2 = normal_residual.squaredNorm();
79  if(residualNorm2 < threshold)
80  break;
81 
82  z = precond.solve(normal_residual); // approximately solve for "A'A z = normal_residual"
83 
84  RealScalar absOld = absNew;
85  absNew = numext::real(normal_residual.dot(z)); // update the absolute value of r
86  RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
87  p = z + beta * p; // update search direction
88  i++;
89  }
90  tol_error = sqrt(residualNorm2 / rhsNorm2);
91  iters = i;
92 }
93 
94 }
95 
96 template< typename _MatrixType,
97  typename _Preconditioner = LeastSquareDiagonalPreconditioner<typename _MatrixType::Scalar> >
99 
100 namespace internal {
101 
102 template< typename _MatrixType, typename _Preconditioner>
103 struct traits<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >
104 {
105  typedef _MatrixType MatrixType;
106  typedef _Preconditioner Preconditioner;
107 };
108 
109 }
110 
148 template< typename _MatrixType, typename _Preconditioner>
149 class LeastSquaresConjugateGradient : public IterativeSolverBase<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> >
150 {
152  using Base::matrix;
153  using Base::m_error;
154  using Base::m_iterations;
155  using Base::m_info;
156  using Base::m_isInitialized;
157 public:
158  typedef _MatrixType MatrixType;
159  typedef typename MatrixType::Scalar Scalar;
160  typedef typename MatrixType::RealScalar RealScalar;
161  typedef _Preconditioner Preconditioner;
162 
163 public:
164 
167 
178  template<typename MatrixDerived>
179  explicit LeastSquaresConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
180 
182 
184  template<typename Rhs,typename Dest>
185  void _solve_with_guess_impl(const Rhs& b, Dest& x) const
186  {
187  m_iterations = Base::maxIterations();
188  m_error = Base::m_tolerance;
189 
190  for(Index j=0; j<b.cols(); ++j)
191  {
192  m_iterations = Base::maxIterations();
193  m_error = Base::m_tolerance;
194 
195  typename Dest::ColXpr xj(x,j);
196  internal::least_square_conjugate_gradient(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
197  }
198 
199  m_isInitialized = true;
200  m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
201  }
202 
204  using Base::_solve_impl;
205  template<typename Rhs,typename Dest>
206  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const
207  {
208  x.setZero();
209  _solve_with_guess_impl(b.derived(),x);
210  }
211 
212 };
213 
214 } // end namespace Eigen
215 
216 #endif // EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:324
A conjugate gradient solver for sparse (or dense) least-square problems.
Definition: LeastSquareConjugateGradient.h:98
Derived & derived()
Definition: EigenBase.h:45
Definition: EigenBase.h:29
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Definition: Constants.h:436
Definition: Eigen_Colamd.h:50
LeastSquaresConjugateGradient()
Definition: LeastSquareConjugateGradient.h:166
LeastSquaresConjugateGradient(const EigenBase< MatrixDerived > &A)
Definition: LeastSquareConjugateGradient.h:179
Base class for linear iterative solvers.
Definition: IterativeSolverBase.h:143
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Definition: Constants.h:440