newtonraphson.hh

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// SPDX-FileCopyrightText: 2021-2025 The Ikarus Developers ikarus@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <ikarus/solver/linearsolver/linearsolver.hh>
#include <ikarus/solver/nonlinearsolver/nonlinearsolverbase.hh>
#include <ikarus/solver/nonlinearsolver/nonlinearsolverstate.hh>
#include <ikarus/solver/nonlinearsolver/solverinfos.hh>
#include <ikarus/utils/broadcaster/broadcaster.hh>
#include <ikarus/utils/broadcaster/broadcastermessages.hh>
#include <ikarus/utils/concepts.hh>
#include <ikarus/utils/defaultfunctions.hh>
#include <ikarus/utils/linearalgebrahelper.hh>
 
namespace Ikarus {
 
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
class NewtonRaphson;
 
struct NRSettings
{
  double tol{1e-8};
  int maxIter{20};
  int minIter{0};
};
 
template <typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
struct NewtonRaphsonConfig
{
  using LinearSolver   = LS;
  using UpdateFunction = UF;
  NRSettings parameters{};
  LS linearSolver{};
  UF updateFunction{};
 
  template <typename UF2>
  auto rebindUpdateFunction(UF2&& updateFunction) const {
    NewtonRaphsonConfig<LS, UF2> settings{
        .parameters = parameters, .linearSolver = linearSolver, .updateFunction = std::forward<UF2>(updateFunction)};
    return settings;
  }
 
  template <typename F>
  using Solver = NewtonRaphson<F, LS, UF>;
};
 
// THE CTAD is broken for designated initializers in clang 16, when we drop support this can be simplified
#ifndef DOXYGEN
NewtonRaphsonConfig() -> NewtonRaphsonConfig<utils::SolverDefault, utils::UpdateDefault>;
NewtonRaphsonConfig(NRSettings) -> NewtonRaphsonConfig<utils::SolverDefault, utils::UpdateDefault>;
 
template <typename LS>
NewtonRaphsonConfig(NRSettings, LS) -> NewtonRaphsonConfig<LS, utils::UpdateDefault>;
 
template <typename LS, typename UF>
NewtonRaphsonConfig(NRSettings, LS, UF) -> NewtonRaphsonConfig<LS, UF>;
 
template <typename UF>
NewtonRaphsonConfig(NRSettings, utils::SolverDefault, UF) -> NewtonRaphsonConfig<utils::SolverDefault, UF>;
#endif
 
template <typename F, typename NRConfig>
requires traits::isSpecialization<NewtonRaphsonConfig, std::remove_cvref_t<NRConfig>>::value
auto createNonlinearSolver(NRConfig&& config, F&& f) {
  using LS           = std::remove_cvref_t<NRConfig>::LinearSolver;
  using UF           = std::remove_cvref_t<NRConfig>::UpdateFunction;
  auto solverFactory = []<class F2, class LS2, class UF2>(F2&& f2, LS2&& ls, UF2&& uf) {
    return std::make_shared<NewtonRaphson<std::remove_cvref_t<F2>, std::remove_cvref_t<LS2>, std::remove_cvref_t<UF2>>>(
        f2, std::forward<LS2>(ls), std::forward<UF2>(uf));
  };
 
  if constexpr (std::remove_cvref_t<F>::nDerivatives == 2) {
    auto solver = solverFactory(derivative(f), std::forward<NRConfig>(config).linearSolver,
                                std::forward<NRConfig>(config).updateFunction);
    solver->setup(config.parameters);
    return solver;
  } else {
    static_assert(std::remove_cvref_t<F>::nDerivatives >= 1,
                  "The number of derivatives in the differentiable function have to be more than 0");
    auto solver =
        solverFactory(f, std::forward<NRConfig>(config).linearSolver, std::forward<NRConfig>(config).updateFunction);
    ;
 
    solver->setup(std::forward<NRConfig>(config).parameters);
    return solver;
  }
}
 
template <typename F, typename LS, typename UF>
class NewtonRaphson : public NonlinearSolverBase<F>
{
public:
  using Settings        = NRSettings;
  using SignatureTraits = typename F::Traits;
  using CorrectionType  = typename SignatureTraits::template Range<0>; 
  using JacobianType    = typename SignatureTraits::template Range<1>;
  static constexpr bool isLinearSolver = Ikarus::Concepts::LinearSolverCheck<LS, JacobianType, CorrectionType>;
 
  using Domain = typename SignatureTraits::Domain; 
 
  using UpdateFunction         = UF; 
  using DifferentiableFunction = F;  
 
  template <typename LS2 = LS, typename UF2 = UF>
  explicit NewtonRaphson(const DifferentiableFunction& residual, LS2&& linearSolver = {}, UF2&& updateFunction = {})
      : residualFunction_{residual},
        jacobianFunction_{derivative(residualFunction_)},
        linearSolver_{std::forward<LS2>(linearSolver)},
        updateFunction_{std::forward<UF2>(updateFunction)} {}
 
  void setup(const Settings& settings) {
    if (settings.minIter > settings.maxIter)
      DUNE_THROW(Dune::InvalidStateException,
                 "Minimum number of iterations cannot be greater than maximum number of iterations");
    settings_ = settings;
  }
 
  [[nodiscard(
      "The solve method returns information of the solution process. You should store this information and check if "
      "it was successful")]] NonLinearSolverInformation
  solve(Domain& x) {
    using enum NonLinearSolverMessages;
 
    NonLinearSolverInformation solverInformation{};
    auto state = typename NewtonRaphson::State(x, correction_, solverInformation);
    this->notify(INIT, state);
    solverInformation.success = true;
 
    decltype(auto) rx              = residualFunction_(x);
    decltype(auto) Ax              = jacobianFunction_(x);
    auto rNorm                     = norm(rx);
    solverInformation.residualNorm = static_cast<double>(rNorm);
 
    decltype(rNorm) dNorm;
    int iter{0};
    if constexpr (isLinearSolver)
      linearSolver_.analyzePattern(Ax);
 
    while ((rNorm > settings_.tol && iter < settings_.maxIter) or iter < settings_.minIter) {
      this->notify(ITERATION_STARTED, state);
      if constexpr (isLinearSolver) {
        linearSolver_.factorize(Ax);
        linearSolver_.solve(correction_, -rx);
        dNorm = correction_.norm();
      } else {
        correction_ = -linearSolver_(rx, Ax);
        dNorm       = norm(correction_);
      }
      solverInformation.correctionNorm = static_cast<double>(dNorm);
 
      this->notify(CORRECTION_UPDATED, state);
      updateFunction_(x, correction_);
      this->notify(CORRECTIONNORM_UPDATED, state);
      this->notify(SOLUTION_CHANGED, state);
 
      rx                             = residualFunction_(x);
      Ax                             = jacobianFunction_(x);
      rNorm                          = norm(rx);
      solverInformation.residualNorm = static_cast<double>(rNorm);
      this->notify(RESIDUALNORM_UPDATED, state);
 
      ++iter;
      solverInformation.iterations = iter;
      this->notify(ITERATION_ENDED, state);
    }
    if (iter == settings_.maxIter)
      solverInformation.success = false;
    solverInformation.iterations = iter;
    if (solverInformation.success)
      this->notify(FINISHED_SUCESSFULLY, state);
    return solverInformation;
  }
 
  auto& residual() { return residualFunction_; }
 
private:
  DifferentiableFunction residualFunction_;
  typename DifferentiableFunction::Derivative jacobianFunction_;
  std::remove_cvref_t<CorrectionType> correction_;
  LS linearSolver_;
  UpdateFunction updateFunction_;
  Settings settings_;
};
 
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
auto makeNewtonRaphson(const F& f, LS&& linearSolver = {}, UF&& updateFunction = {}) {
  return std::make_shared<NewtonRaphson<F, LS, UF>>(f, std::forward<LS>(linearSolver), std::move(updateFunction));
}
 
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
NewtonRaphson(const F& f, LS&& linearSolver = {},
              UF&& updateFunction = {}) -> NewtonRaphson<F, std::remove_cvref_t<LS>, std::remove_cvref_t<UF>>;
 
} // namespace Ikarus