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Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h')
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diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h b/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h new file mode 100644 index 000000000..0aea0e099 --- /dev/null +++ b/runtimes/nn/depend/external/eigen/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h @@ -0,0 +1,216 @@ +// 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 |