newtonraphsonwithscalarsubsidiaryfunction.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 <type_traits>
#include <utility>
 
#include <ikarus/controlroutines/pathfollowingfunctions.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>
 
namespace Ikarus {
 
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
class NewtonRaphsonWithSubsidiaryFunction;
 
struct NewtonRaphsonWithSubsidiaryFunctionSettings
{
  double tol{1e-8};
  int maxIter{20};
};
 
template <typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
struct NewtonRaphsonWithSubsidiaryFunctionConfig
{
  using LinearSolver   = LS;
  using UpdateFunction = UF;
  NewtonRaphsonWithSubsidiaryFunctionSettings parameters{};
  LS linearSolver{};
  UF updateFunction{};
 
  template <typename UF2>
  auto rebindUpdateFunction(UF2&& updateFunction) const {
    NewtonRaphsonWithSubsidiaryFunctionConfig<LS, UF2> settings{
        .parameters = parameters, .linearSolver = linearSolver, .updateFunction = std::forward<UF2>(updateFunction)};
    return settings;
  }
 
  template <typename F>
  using Solver = NewtonRaphsonWithSubsidiaryFunction<F, LS, UF>;
};
 
// THE CTAD is broken for designated initializers in clang 16, when we drop support this can be simplified
#ifndef DOXYGEN
NewtonRaphsonWithSubsidiaryFunctionConfig()
    -> NewtonRaphsonWithSubsidiaryFunctionConfig<utils::SolverDefault, utils::UpdateDefault>;
 
NewtonRaphsonWithSubsidiaryFunctionConfig(NewtonRaphsonWithSubsidiaryFunctionSettings)
    -> NewtonRaphsonWithSubsidiaryFunctionConfig<utils::SolverDefault, utils::UpdateDefault>;
 
template <typename LS>
NewtonRaphsonWithSubsidiaryFunctionConfig(NewtonRaphsonWithSubsidiaryFunctionSettings,
                                          LS) -> NewtonRaphsonWithSubsidiaryFunctionConfig<LS, utils::UpdateDefault>;
 
template <typename LS, typename UF>
NewtonRaphsonWithSubsidiaryFunctionConfig(NewtonRaphsonWithSubsidiaryFunctionSettings, LS,
                                          UF) -> NewtonRaphsonWithSubsidiaryFunctionConfig<LS, UF>;
 
template <typename UF>
NewtonRaphsonWithSubsidiaryFunctionConfig(NewtonRaphsonWithSubsidiaryFunctionSettings, utils::SolverDefault,
                                          UF) -> NewtonRaphsonWithSubsidiaryFunctionConfig<utils::SolverDefault, UF>;
#endif
template <typename F, typename NRConfig>
requires traits::isSpecialization<NewtonRaphsonWithSubsidiaryFunctionConfig, 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<NewtonRaphsonWithSubsidiaryFunction<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 NewtonRaphsonWithSubsidiaryFunction : public NonlinearSolverBase<F>
{
public:
  using Settings        = NewtonRaphsonWithSubsidiaryFunctionSettings;
  using SignatureTraits = typename F::Traits;
 
  using Domain         = typename SignatureTraits::Domain; 
  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 UpdateFunctionType     = UF;
  using DifferentiableFunction = F; 
 
  template <typename LS2 = LS, typename UF2 = UF>
  explicit NewtonRaphsonWithSubsidiaryFunction(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) { settings_ = settings; }
 
  template <typename SubsidiaryType>
  [[nodiscard(
      "The solve method returns information of the solution process. You should store this information and check if "
      "it was successful")]] NonLinearSolverInformation
  solve(Domain& req, SubsidiaryType&& subsidiaryFunction, SubsidiaryArgs& subsidiaryArgs) {
    using enum NonLinearSolverMessages;
 
    Ikarus::NonLinearSolverInformation solverInformation{};
    auto state = typename NewtonRaphsonWithSubsidiaryFunction::State{
        .domain = req, .correction = correction_, .information = solverInformation};
    this->notify(INIT, state);
 
    solverInformation.success = true;
 
    auto& lambda = req.parameter();
    auto& x      = req.globalSolution();
 
 
    auto lambdaDummy = lambda;
    auto DDummy      = x;
    x.setZero();
    lambda            = 1.0;
    decltype(auto) rx = residualFunction_(req);
    const auto Fext0  = (-rx).eval(); // dRdlambda(lambda)
    lambda            = lambdaDummy;
    x                 = DDummy;
 
    rx                = residualFunction_(req);
    decltype(auto) Ax = jacobianFunction_(req);
 
    Eigen::VectorXd deltaD;
    deltaD.resizeLike(rx);
    deltaD.setZero();
 
    subsidiaryArgs.dfdDD.resizeLike(Fext0);
 
    subsidiaryFunction(subsidiaryArgs);
    auto rNorm                     = sqrt(rx.dot(rx));
    solverInformation.residualNorm = static_cast<double>(rNorm);
    decltype(rNorm) dNorm;
    int iter{0};
    if constexpr (isLinearSolver)
      linearSolver_.analyzePattern(Ax);
 
    Eigen::MatrixX2<double> residual2d, sol2d;
 
    while (rNorm > settings_.tol && iter < settings_.maxIter) {
      this->notify(ITERATION_STARTED, state);
 
      residual2d.resize(rx.rows(), 2);
      residual2d << -rx, Fext0;
      sol2d.resize(rx.rows(), 2);
 
      if constexpr (isLinearSolver) {
        linearSolver_.factorize(Ax);
        linearSolver_.solve(sol2d, residual2d);
      } else {
        sol2d = linearSolver_(residual2d, Ax);
      }
 
      subsidiaryFunction(subsidiaryArgs);
 
      const double deltalambda = (-subsidiaryArgs.f - subsidiaryArgs.dfdDD.dot(sol2d.col(0))) /
                                 (subsidiaryArgs.dfdDD.dot(sol2d.col(1)) + subsidiaryArgs.dfdDlambda);
      deltaD = sol2d.col(0) + deltalambda * sol2d.col(1);
 
      this->notify(CORRECTION_UPDATED, state);
 
      updateFunction_(x, deltaD);
      updateFunction_(subsidiaryArgs.DD, deltaD);
 
      lambda += deltalambda;
      subsidiaryArgs.Dlambda += deltalambda;
 
      dNorm                            = sqrt(deltaD.dot(deltaD) + deltalambda * deltalambda);
      solverInformation.correctionNorm = static_cast<double>(dNorm);
 
      rx                             = residualFunction_(req);
      Ax                             = jacobianFunction_(req);
      rNorm                          = sqrt(rx.dot(rx) + subsidiaryArgs.f * subsidiaryArgs.f);
      solverInformation.residualNorm = static_cast<double>(rNorm);
 
      this->notify(SOLUTION_CHANGED, state);
      this->notify(CORRECTIONNORM_UPDATED, state);
      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_;
  UF updateFunction_;
  Settings settings_;
};
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
auto makeNewtonRaphsonWithSubsidiaryFunction(const F& f, LS&& linearSolver = {}, UF&& updateFunction = {}) {
  return std::make_shared<NewtonRaphsonWithSubsidiaryFunction<F, LS, UF>>(f, std::forward<LS>(linearSolver),
                                                                          std::move(updateFunction));
}
 
template <typename F, typename LS = utils::SolverDefault, typename UF = utils::UpdateDefault>
NewtonRaphsonWithSubsidiaryFunction(const F& f, LS&& linearSolver = {}, UF&& updateFunction = {})
    -> NewtonRaphsonWithSubsidiaryFunction<F, std::remove_cvref_t<LS>, std::remove_cvref_t<UF>>;
 
} // namespace Ikarus