pathfollowingfunctions.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 <cmath>
#include <optional>
#include <string>
#include <utility>
#include <vector>
 
#include <dune/common/exceptions.hh>
#include <dune/common/float_cmp.hh>
 
#include <Eigen/Core>
 
#include <ikarus/solver/linearsolver/linearsolver.hh>
#include <ikarus/utils/concepts.hh>
#include <ikarus/utils/defaultfunctions.hh>
#include <ikarus/utils/traits.hh>
 
namespace Ikarus {
struct SubsidiaryArgs
{
  double stepSize;              
  Eigen::VectorX<double> DD;    
  double Dlambda;               
  double f;                     
  Eigen::VectorX<double> dfdDD; 
  double dfdDlambda;            
  int currentStep;              
 
  void setZero(const Concepts::EigenType auto& firstParameter) {
    stepSize = 0.0;
    DD.resizeLike(firstParameter);
    DD.setZero();
    Dlambda = 0.0;
    f       = 0.0;
    dfdDD.resizeLike(firstParameter);
    dfdDD.setZero();
    dfdDlambda  = 0.0;
    currentStep = 0;
  }
};
 
struct ArcLength
{
  void operator()(SubsidiaryArgs& args) const {
    const auto root = sqrt(args.DD.squaredNorm() + psi * psi * args.Dlambda * args.Dlambda);
    args.f          = root - args.stepSize;
    if (not computedInitialPredictor) {
      args.dfdDD.setZero();
      args.dfdDlambda = 0.0;
    } else {
      args.dfdDD      = args.DD / root;
      args.dfdDlambda = (psi * psi * args.Dlambda) / root;
    }
  }
 
  template <typename F>
  requires(Ikarus::Concepts::LinearSolverCheck<Ikarus::LinearSolver, typename F::Traits::template Range<1>,
                                               typename F::Domain::SolutionVectorType>)
  void initialPrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    SolverTypeTag solverTag;
    using JacobianType = std::remove_cvref_t<typename F::Traits::template Range<1>>;
    static_assert((traits::isSpecializationTypeAndNonTypes<Eigen::Matrix, JacobianType>::value) or
                      (traits::isSpecializationTypeNonTypeAndType<Eigen::SparseMatrix, JacobianType>::value),
                  "Linear solver not implemented for the chosen derivative type of the non-linear operator");
 
    if constexpr (traits::isSpecializationTypeAndNonTypes<Eigen::Matrix, JacobianType>::value)
      solverTag = SolverTypeTag::d_LDLT;
    else
      solverTag = SolverTypeTag::sd_SimplicialLDLT;
 
    req.parameter()  = 1.0;
    decltype(auto) R = residual(req);
    decltype(auto) K = derivative(residual)(req);
 
    auto linearSolver = LinearSolver(solverTag); // for the linear predictor step
    linearSolver.analyzePattern(K);
    linearSolver.factorize(K);
    linearSolver.solve(args.DD, -R);
 
    const auto DD2 = args.DD.squaredNorm();
 
    psi    = sqrt(DD2);
    auto s = sqrt(psi * psi + DD2);
 
    args.DD      = args.DD * args.stepSize / s;
    args.Dlambda = args.stepSize / s;
 
    req.globalSolution()     = args.DD;
    req.parameter()          = args.Dlambda;
    computedInitialPredictor = true;
  }
 
  template <typename F>
  void intermediatePrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    req.globalSolution() += args.DD;
    req.parameter() += args.Dlambda;
  }
 
  constexpr std::string name() const { return "Arc length"; }
 
private:
  double psi{0.0};
  bool computedInitialPredictor{false};
};
 
struct LoadControlSubsidiaryFunction
{
  void operator()(SubsidiaryArgs& args) const {
    args.f = args.Dlambda - args.stepSize;
    args.dfdDD.setZero();
    args.dfdDlambda = 1.0;
  }
 
  template <typename F>
  void initialPrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    args.Dlambda             = args.stepSize;
    req.parameter()          = args.Dlambda;
    computedInitialPredictor = true;
  }
 
  template <typename F>
  void intermediatePrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    req.parameter() += args.Dlambda;
  }
 
  constexpr std::string name() const { return "Load Control"; }
 
private:
  bool computedInitialPredictor{false};
};
 
struct DisplacementControl
{
  explicit DisplacementControl(std::vector<int> p_controlledIndices)
      : controlledIndices{std::move(p_controlledIndices)} {}
 
  void operator()(SubsidiaryArgs& args) const {
    const auto controlledDOFsNorm = args.DD(controlledIndices).norm();
    args.f                        = controlledDOFsNorm - args.stepSize;
    args.dfdDlambda               = 0.0;
    args.dfdDD.setZero();
    args.dfdDD(controlledIndices) = args.DD(controlledIndices) / controlledDOFsNorm;
  }
 
  template <typename F>
  void initialPrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    args.DD(controlledIndices).array() = args.stepSize;
    req.globalSolution()               = args.DD;
    computedInitialPredictor           = true;
  }
 
  template <typename F>
  void intermediatePrediction(typename F::Domain& req, F& residual, SubsidiaryArgs& args) {
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    req.globalSolution() += args.DD;
  }
 
  constexpr std::string name() const { return "Displacement Control"; }
 
private:
  std::vector<int> controlledIndices; 
  bool computedInitialPredictor{false};
};
} // namespace Ikarus