pathfollowingfunctions.hh

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// SPDX-FileCopyrightText: 2021-2024 The Ikarus Developers mueller@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 <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;               
  };
 
  struct ArcLength {
    void operator()(SubsidiaryArgs& args) const {
      if (psi) {
        const auto root = sqrt(args.DD.squaredNorm() + psi.value() * psi.value() * args.Dlambda * args.Dlambda);
        args.f          = root - args.stepSize;
        args.dfdDD      = args.DD / root;
        args.dfdDlambda = (psi.value() * psi.value() * args.Dlambda) / root;
      } else {
        DUNE_THROW(Dune::InvalidStateException,
                   "You have to call initialPrediction first. Otherwise psi is not defined");
      }
    }
 
    template <typename NonLinearOperator>
    void initialPrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      SolverTypeTag solverTag;
      using JacobianType = std::remove_cvref_t<typename NonLinearOperator::DerivativeType>;
      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;
 
      nonLinearOperator.lastParameter() = 1.0;  // lambda =1.0
      nonLinearOperator.template update<0>();
      const auto& R = nonLinearOperator.value();
      const auto& K = nonLinearOperator.derivative();
 
      static constexpr bool isLinearSolver
          = Ikarus::Concepts::LinearSolverCheck<decltype(LinearSolver(solverTag)),
                                                typename NonLinearOperator::DerivativeType,
                                                typename NonLinearOperator::ValueType>;
      static_assert(isLinearSolver,
                    "Initial predictor step in the standard arc-length method doesn't have a linear solver");
 
      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.value() * psi.value() + DD2);
 
      args.DD      = args.DD * args.stepSize / s;
      args.Dlambda = args.stepSize / s;
 
      nonLinearOperator.firstParameter() = args.DD;
      nonLinearOperator.lastParameter()  = args.Dlambda;
    }
 
    template <typename NonLinearOperator>
    void intermediatePrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      nonLinearOperator.firstParameter() += args.DD;
      nonLinearOperator.lastParameter() += args.Dlambda;
    }
 
    constexpr auto name() const { return std::string("Arc length"); }
 
  private:
    std::optional<double> psi;
  };
 
  struct LoadControlSubsidiaryFunction {
    void operator()(SubsidiaryArgs& args) const {
      args.f = args.Dlambda - args.stepSize;
      args.dfdDD.setZero();
      args.dfdDlambda = 1.0;
    }
 
    template <typename NonLinearOperator>
    void initialPrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      args.Dlambda                      = args.stepSize;
      nonLinearOperator.lastParameter() = args.Dlambda;
    }
 
    template <typename NonLinearOperator>
    void intermediatePrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      nonLinearOperator.lastParameter() += args.Dlambda;
    }
 
    constexpr auto name() const { return std::string("Load Control"); }
  };
 
  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 NonLinearOperator>
    void initialPrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      args.DD(controlledIndices).array() = args.stepSize;
      nonLinearOperator.firstParameter() = args.DD;
    }
 
    template <typename NonLinearOperator>
    void intermediatePrediction(NonLinearOperator& nonLinearOperator, SubsidiaryArgs& args) {
      nonLinearOperator.firstParameter() += args.DD;
    }
 
    constexpr auto name() const { return std::string("Displacement Control"); }
 
  private:
    std::vector<int> controlledIndices; 
  };
}  // namespace Ikarus