diff options
Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h | 216 |
1 files changed, 0 insertions, 216 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h b/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h deleted file mode 100644 index 0aea0e099..000000000 --- a/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h +++ /dev/null @@ -1,216 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -#ifndef EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H -#define EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H - -namespace Eigen { - -namespace internal { - -/** \internal Low-level conjugate gradient algorithm for least-square problems - * \param mat The matrix A - * \param rhs The right hand side vector b - * \param x On input and initial solution, on output the computed solution. - * \param precond A preconditioner being able to efficiently solve for an - * approximation of A'Ax=b (regardless of b) - * \param iters On input the max number of iteration, on output the number of performed iterations. - * \param tol_error On input the tolerance error, on output an estimation of the relative error. - */ -template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner> -EIGEN_DONT_INLINE -void least_square_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x, - const Preconditioner& precond, Index& iters, - typename Dest::RealScalar& tol_error) -{ - using std::sqrt; - using std::abs; - typedef typename Dest::RealScalar RealScalar; - typedef typename Dest::Scalar Scalar; - typedef Matrix<Scalar,Dynamic,1> VectorType; - - RealScalar tol = tol_error; - Index maxIters = iters; - - Index m = mat.rows(), n = mat.cols(); - - VectorType residual = rhs - mat * x; - VectorType normal_residual = mat.adjoint() * residual; - - RealScalar rhsNorm2 = (mat.adjoint()*rhs).squaredNorm(); - if(rhsNorm2 == 0) - { - x.setZero(); - iters = 0; - tol_error = 0; - return; - } - RealScalar threshold = tol*tol*rhsNorm2; - RealScalar residualNorm2 = normal_residual.squaredNorm(); - if (residualNorm2 < threshold) - { - iters = 0; - tol_error = sqrt(residualNorm2 / rhsNorm2); - return; - } - - VectorType p(n); - p = precond.solve(normal_residual); // initial search direction - - VectorType z(n), tmp(m); - RealScalar absNew = numext::real(normal_residual.dot(p)); // the square of the absolute value of r scaled by invM - Index i = 0; - while(i < maxIters) - { - tmp.noalias() = mat * p; - - Scalar alpha = absNew / tmp.squaredNorm(); // the amount we travel on dir - x += alpha * p; // update solution - residual -= alpha * tmp; // update residual - normal_residual = mat.adjoint() * residual; // update residual of the normal equation - - residualNorm2 = normal_residual.squaredNorm(); - if(residualNorm2 < threshold) - break; - - z = precond.solve(normal_residual); // approximately solve for "A'A z = normal_residual" - - RealScalar absOld = absNew; - absNew = numext::real(normal_residual.dot(z)); // update the absolute value of r - RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction - p = z + beta * p; // update search direction - i++; - } - tol_error = sqrt(residualNorm2 / rhsNorm2); - iters = i; -} - -} - -template< typename _MatrixType, - typename _Preconditioner = LeastSquareDiagonalPreconditioner<typename _MatrixType::Scalar> > -class LeastSquaresConjugateGradient; - -namespace internal { - -template< typename _MatrixType, typename _Preconditioner> -struct traits<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> > -{ - typedef _MatrixType MatrixType; - typedef _Preconditioner Preconditioner; -}; - -} - -/** \ingroup IterativeLinearSolvers_Module - * \brief A conjugate gradient solver for sparse (or dense) least-square problems - * - * This class allows to solve for A x = b linear problems using an iterative conjugate gradient algorithm. - * The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability. - * Otherwise, the SparseLU or SparseQR classes might be preferable. - * The matrix A and the vectors x and b can be either dense or sparse. - * - * \tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix. - * \tparam _Preconditioner the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner - * - * \implsparsesolverconcept - * - * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() - * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations - * and NumTraits<Scalar>::epsilon() for the tolerance. - * - * This class can be used as the direct solver classes. Here is a typical usage example: - \code - int m=1000000, n = 10000; - VectorXd x(n), b(m); - SparseMatrix<double> A(m,n); - // fill A and b - LeastSquaresConjugateGradient<SparseMatrix<double> > lscg; - lscg.compute(A); - x = lscg.solve(b); - std::cout << "#iterations: " << lscg.iterations() << std::endl; - std::cout << "estimated error: " << lscg.error() << std::endl; - // update b, and solve again - x = lscg.solve(b); - \endcode - * - * By default the iterations start with x=0 as an initial guess of the solution. - * One can control the start using the solveWithGuess() method. - * - * \sa class ConjugateGradient, SparseLU, SparseQR - */ -template< typename _MatrixType, typename _Preconditioner> -class LeastSquaresConjugateGradient : public IterativeSolverBase<LeastSquaresConjugateGradient<_MatrixType,_Preconditioner> > -{ - typedef IterativeSolverBase<LeastSquaresConjugateGradient> Base; - using Base::matrix; - using Base::m_error; - using Base::m_iterations; - using Base::m_info; - using Base::m_isInitialized; -public: - typedef _MatrixType MatrixType; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef _Preconditioner Preconditioner; - -public: - - /** Default constructor. */ - LeastSquaresConjugateGradient() : Base() {} - - /** Initialize the solver with matrix \a A for further \c Ax=b solving. - * - * This constructor is a shortcut for the default constructor followed - * by a call to compute(). - * - * \warning this class stores a reference to the matrix A as well as some - * precomputed values that depend on it. Therefore, if \a A is changed - * this class becomes invalid. Call compute() to update it with the new - * matrix A, or modify a copy of A. - */ - template<typename MatrixDerived> - explicit LeastSquaresConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {} - - ~LeastSquaresConjugateGradient() {} - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve_with_guess_impl(const Rhs& b, Dest& x) const - { - m_iterations = Base::maxIterations(); - m_error = Base::m_tolerance; - - for(Index j=0; j<b.cols(); ++j) - { - m_iterations = Base::maxIterations(); - m_error = Base::m_tolerance; - - typename Dest::ColXpr xj(x,j); - internal::least_square_conjugate_gradient(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error); - } - - m_isInitialized = true; - m_info = m_error <= Base::m_tolerance ? Success : NoConvergence; - } - - /** \internal */ - using Base::_solve_impl; - template<typename Rhs,typename Dest> - void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const - { - x.setZero(); - _solve_with_guess_impl(b.derived(),x); - } - -}; - -} // end namespace Eigen - -#endif // EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H |