NLHomoProblem.cpp

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#include "NLHomoProblem.hpp"
#include <polyfem/State.hpp>
#include "forms/PeriodicContactForm.hpp"
#include "forms/lagrangian/MacroStrainLagrangianForm.hpp"
#include <polyfem/assembler/MacroStrain.hpp>
#include <polyfem/io/Evaluator.hpp>
 
namespace polyfem::solver
{
    NLHomoProblem::NLHomoProblem(const int full_size,
                                 const assembler::MacroStrainValue &macro_strain_constraint,
                                 const State &state,
                                 const double t,
                                 const std::vector<std::shared_ptr<Form>> &forms,
                                 const std::vector<std::shared_ptr<AugmentedLagrangianForm>> &penalty_forms,
                                 const bool solve_symmetric_macro_strain,
                                 const std::shared_ptr<polysolve::linear::Solver> &solver)
        : NLProblem(full_size, state.periodic_bc, t, forms, penalty_forms, solver),
          state_(state),
          only_symmetric(solve_symmetric_macro_strain),
          macro_strain_constraint_(macro_strain_constraint)
    {
        init_projection();
    }
 
    void NLHomoProblem::init_projection()
    {
        const int dim = state_.mesh->dimension();
        if (only_symmetric)
        {
            macro_mid_to_full_.setZero(dim * dim, (dim * (dim + 1)) / 2);
            macro_full_to_mid_.setZero((dim * (dim + 1)) / 2, dim * dim);
            for (int i = 0, idx = 0; i < dim; i++)
            {
                for (int j = i; j < dim; j++)
                {
                    macro_full_to_mid_(idx, i * dim + j) = 1;
 
                    macro_mid_to_full_(j * dim + i, idx) = 1;
                    macro_mid_to_full_(i * dim + j, idx) = 1;
 
                    idx++;
                }
            }
        }
        else
        {
            macro_mid_to_full_.setIdentity(dim * dim, dim * dim);
            macro_full_to_mid_.setIdentity(dim * dim, dim * dim);
        }
        macro_mid_to_reduced_.setIdentity(macro_full_to_mid_.rows(), macro_full_to_mid_.rows());
    }
 
    Eigen::VectorXd NLHomoProblem::extended_to_reduced(const Eigen::VectorXd &extended) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        Eigen::VectorXd reduced(dof1 + dof2);
        reduced.head(dof1) = NLProblem::full_to_reduced(extended.head(extended.size() - dim * dim));
        reduced.tail(dof2) = macro_full_to_reduced(extended.tail(dim * dim));
 
        return reduced;
    }
 
    Eigen::VectorXd NLHomoProblem::reduced_to_extended(const Eigen::VectorXd &reduced, bool homogeneous) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
        assert(reduced.size() == dof1 + dof2);
 
        Eigen::VectorXd full = NLProblem::reduced_to_full(reduced.head(dof1));
        Eigen::VectorXd disp_grad = macro_reduced_to_full(reduced.tail(dof2), homogeneous);
        Eigen::VectorXd extended(full.size() + disp_grad.size());
        extended << full, disp_grad;
 
        return extended;
    }
 
    Eigen::VectorXd NLHomoProblem::extended_to_reduced_grad(const Eigen::VectorXd &extended) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        Eigen::VectorXd grad(dof1 + dof2);
        grad.head(dof1) = NLProblem::full_to_reduced_grad(extended.head(extended.size() - dim * dim));
        grad.tail(dof2) = macro_full_to_reduced_grad(extended.tail(dim * dim));
 
        return grad;
    }
 
    double NLHomoProblem::value(const TVector &x)
    {
        double val = FullNLProblem::value(reduced_to_full(x));
 
        if (penalty_problem_ && full_size() == current_size())
        {
            val += penalty_problem_->value(x);
        }
 
        for (auto &form : homo_forms)
            if (form->enabled())
                val += form->value(reduced_to_extended(x));
 
        return val;
    }
    void NLHomoProblem::gradient(const TVector &x, TVector &gradv)
    {
        FullNLProblem::gradient(reduced_to_full(x), gradv);
 
        if (full_size() != current_size())
        {
            gradv = full_to_reduced_grad(gradv);
        }
        else if (penalty_problem_)
        {
            TVector tmp;
            penalty_problem_->gradient(x, tmp);
            gradv += tmp;
        }
 
        for (auto &form : homo_forms)
            if (form->enabled())
            {
                Eigen::VectorXd grad_extended;
                form->first_derivative(reduced_to_extended(x), grad_extended);
                gradv += extended_to_reduced_grad(grad_extended);
            }
    }
    void NLHomoProblem::extended_hessian_to_reduced_hessian(const THessian &extended, THessian &reduced) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        Eigen::MatrixXd A12, A22;
        {
            Eigen::MatrixXd tmp = Eigen::MatrixXd(extended.rightCols(dim * dim));
            A12 = macro_full_to_reduced_grad(tmp.topRows(tmp.rows() - dim * dim).transpose()).transpose();
            A22 = macro_full_to_reduced_grad(macro_full_to_reduced_grad(tmp.bottomRows(dim * dim)).transpose());
        }
 
        std::vector<Eigen::Triplet<double>> entries;
        entries.reserve(extended.nonZeros() + A12.size() * 2 + A22.size());
 
        for (int k = 0; k < full_size_; ++k)
            for (StiffnessMatrix::InnerIterator it(extended, k); it; ++it)
                if (it.row() < full_size_ && it.col() < full_size_)
                    entries.emplace_back(it.row(), it.col(), it.value());
 
        for (int i = 0; i < A12.rows(); i++)
        {
            for (int j = 0; j < A12.cols(); j++)
            {
                entries.emplace_back(i, full_size_ + j, A12(i, j));
                entries.emplace_back(full_size_ + j, i, A12(i, j));
            }
        }
 
        for (int i = 0; i < A22.rows(); i++)
            for (int j = 0; j < A22.cols(); j++)
                entries.emplace_back(i + full_size_, j + full_size_, A22(i, j));
 
        // Eigen::VectorXd tmp = macro_full_to_reduced_grad(Eigen::VectorXd::Ones(dim*dim));
        // for (int i = 0; i < tmp.size(); i++)
        //     entries.emplace_back(i + full_size_, i + full_size_, 1 - tmp(i));
 
        reduced.resize(0, 0);
        reduced.resize(full_size_ + dof2, full_size_ + dof2);
        reduced.setFromTriplets(entries.begin(), entries.end());
 
        {
            assert(dof1 == Q2_.cols());
            StiffnessMatrix Q2_extended(Q2_.rows() + dof2, Q2_.cols() + dof2);
 
            {
                entries.clear();
                for (int k = 0; k < Q2_.cols(); ++k)
                    for (StiffnessMatrix::InnerIterator it(Q2_, k); it; ++it)
                    {
                        entries.emplace_back(it.row(), it.col(), it.value());
                    }
 
                for (int k = 0; k < dof2; k++)
                {
                    entries.emplace_back(Q2_.rows() + k, dof1 + k, 1);
                }
 
                Q2_extended.setFromTriplets(entries.begin(), entries.end());
            }
 
            reduced = Q2_extended.transpose() * reduced * Q2_extended;
            // remove numerical zeros
            reduced.prune([](const Eigen::Index &row, const Eigen::Index &col, const Scalar &value) {
                return std::abs(value) > 1e-10;
            });
        }
    }
    Eigen::MatrixXd NLHomoProblem::reduced_to_disp_grad(const TVector &reduced, bool homogeneous) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        return utils::unflatten(macro_reduced_to_full(reduced.tail(dof2), homogeneous), dim);
    }
    void NLHomoProblem::hessian(const TVector &x, THessian &hessian)
    {
        FullNLProblem::hessian(reduced_to_full(x), hessian);
 
        full_hessian_to_reduced_hessian(hessian);
 
        for (auto &form : homo_forms)
            if (form->enabled())
            {
                THessian hess_extended;
                form->second_derivative(reduced_to_extended(x), hess_extended);
 
                THessian hess;
                extended_hessian_to_reduced_hessian(hess_extended, hess);
                hessian += hess;
            }
    }
 
    void NLHomoProblem::set_fixed_entry(const Eigen::VectorXi &fixed_entry)
    {
        const int dim = state_.mesh->dimension();
 
        Eigen::VectorXd fixed_mask;
        fixed_mask.setZero(dim * dim);
        fixed_mask(fixed_entry.array()).setOnes();
        fixed_mask = (macro_full_to_mid_ * fixed_mask).eval();
 
        fixed_mask_.setZero(fixed_mask.size());
        for (int i = 0; i < fixed_mask.size(); i++)
            if (abs(fixed_mask(i)) > 1e-8)
                fixed_mask_(i) = true;
 
        const int new_reduced_size = fixed_mask_.size() - fixed_mask_.sum();
        macro_mid_to_reduced_.setZero(new_reduced_size, fixed_mask_.size());
        for (int i = 0, j = 0; i < fixed_mask_.size(); i++)
            if (!fixed_mask_(i))
                macro_mid_to_reduced_(j++, i) = 1;
    }
 
    void NLHomoProblem::full_hessian_to_reduced_hessian(THessian &hessian) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
        const int full_size = hessian.rows();
 
        Eigen::MatrixXd tmp = constraint_grad();
        Eigen::MatrixXd A12 = hessian * tmp.transpose();
        Eigen::MatrixXd A22 = tmp * A12;
 
        std::vector<Eigen::Triplet<double>> entries;
        entries.reserve(hessian.nonZeros() + A12.size() * 2 + A22.size());
 
        for (int k = 0; k < hessian.outerSize(); ++k)
            for (StiffnessMatrix::InnerIterator it(hessian, k); it; ++it)
                entries.emplace_back(it.row(), it.col(), it.value());
 
        for (int i = 0; i < A12.rows(); i++)
            for (int j = 0; j < A12.cols(); j++)
            {
                entries.emplace_back(i, full_size + j, A12(i, j));
                entries.emplace_back(full_size + j, i, A12(i, j));
            }
 
        for (int i = 0; i < A22.rows(); i++)
            for (int j = 0; j < A22.cols(); j++)
                entries.emplace_back(i + full_size, j + full_size, A22(i, j));
 
        hessian.resize(0, 0);
        hessian.resize(full_size + dof2, full_size + dof2);
        hessian.setFromTriplets(entries.begin(), entries.end());
        // NLProblem::full_hessian_to_reduced_hessian(hessian);
 
        {
            assert(dof1 == Q2_.cols());
            StiffnessMatrix Q2_extended(Q2_.rows() + dof2, Q2_.cols() + dof2);
 
            {
                entries.clear();
                for (int k = 0; k < Q2_.cols(); ++k)
                    for (StiffnessMatrix::InnerIterator it(Q2_, k); it; ++it)
                    {
                        entries.emplace_back(it.row(), it.col(), it.value());
                    }
 
                for (int k = 0; k < dof2; k++)
                {
                    entries.emplace_back(Q2_.rows() + k, dof1 + k, 1);
                }
 
                Q2_extended.setFromTriplets(entries.begin(), entries.end());
            }
 
            hessian = Q2_extended.transpose() * hessian * Q2_extended;
            // remove numerical zeros
            hessian.prune([](const Eigen::Index &row, const Eigen::Index &col, const Scalar &value) {
                return std::abs(value) > 1e-10;
            });
        }
    }
 
    NLHomoProblem::TVector NLHomoProblem::full_to_reduced(const TVector &full) const
    {
        log_and_throw_error("Invalid function!");
        return TVector();
    }
 
    NLHomoProblem::TVector NLHomoProblem::full_to_reduced(const TVector &full, const Eigen::MatrixXd &disp_grad) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        TVector reduced;
        reduced.setZero(dof1 + dof2);
 
        reduced.head(dof1) = NLProblem::full_to_reduced(full - io::Evaluator::generate_linear_field(state_.n_bases, state_.mesh_nodes, disp_grad));
        reduced.tail(dof2) = macro_full_to_reduced(utils::flatten(disp_grad));
 
        return reduced;
    }
    NLHomoProblem::TVector NLHomoProblem::full_to_reduced_grad(const TVector &full) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        TVector reduced;
        reduced.setZero(dof1 + dof2);
        reduced.head(dof1) = NLProblem::full_to_reduced_grad(full);
        reduced.tail(dof2) = constraint_grad() * full;
 
        return reduced;
    }
    NLHomoProblem::TVector NLHomoProblem::reduced_to_full(const TVector &reduced) const
    {
        const int dim = state_.mesh->dimension();
        const int dof2 = macro_reduced_size();
        const int dof1 = reduced_size();
 
        Eigen::MatrixXd disp_grad = utils::unflatten(macro_reduced_to_full(reduced.tail(dof2)), dim);
        return NLProblem::reduced_to_full(reduced.head(dof1)) + io::Evaluator::generate_linear_field(state_.n_bases, state_.mesh_nodes, disp_grad);
    }
 
    int NLHomoProblem::macro_reduced_size() const
    {
        return macro_mid_to_reduced_.rows();
    }
    NLHomoProblem::TVector NLHomoProblem::macro_full_to_reduced(const TVector &full) const
    {
        return macro_mid_to_reduced_ * macro_full_to_mid_ * full;
    }
    Eigen::MatrixXd NLHomoProblem::macro_full_to_reduced_grad(const Eigen::MatrixXd &full) const
    {
        return macro_mid_to_reduced_ * macro_mid_to_full_.transpose() * full;
    }
    NLHomoProblem::TVector NLHomoProblem::macro_reduced_to_full(const TVector &reduced, bool homogeneous) const
    {
        TVector mid = macro_mid_to_reduced_.transpose() * reduced;
        const TVector fixed_values = homogeneous ? TVector::Zero(macro_full_to_mid_.rows()) : TVector(macro_full_to_mid_ * utils::flatten(macro_strain_constraint_.eval(t_)));
        for (int i = 0; i < fixed_mask_.size(); i++)
            if (fixed_mask_(i))
                mid(i) = fixed_values(i);
 
        return macro_mid_to_full_ * mid;
    }
 
    void NLHomoProblem::init(const TVector &x0)
    {
        for (auto &form : homo_forms)
            form->init(reduced_to_extended(x0));
        FullNLProblem::init(reduced_to_full(x0));
    }
 
    bool NLHomoProblem::is_step_valid(const TVector &x0, const TVector &x1)
    {
        bool flag = NLProblem::is_step_valid(x0.head(reduced_size()), x1.head(reduced_size()));
        for (auto &form : homo_forms)
            if (form->enabled())
                flag &= form->is_step_valid(reduced_to_extended(x0), reduced_to_extended(x1));
 
        return flag;
    }
    bool NLHomoProblem::is_step_collision_free(const TVector &x0, const TVector &x1)
    {
        bool flag = NLProblem::is_step_collision_free(x0.head(reduced_size()), x1.head(reduced_size()));
        for (auto &form : homo_forms)
            if (form->enabled())
                flag &= form->is_step_collision_free(reduced_to_extended(x0), reduced_to_extended(x1));
 
        return flag;
    }
    double NLHomoProblem::max_step_size(const TVector &x0, const TVector &x1)
    {
        double size = NLProblem::max_step_size(x0.head(reduced_size()), x1.head(reduced_size()));
        for (auto &form : homo_forms)
            if (form->enabled())
                size = std::min(size, form->max_step_size(reduced_to_extended(x0), reduced_to_extended(x1)));
        return size;
    }
 
    void NLHomoProblem::line_search_begin(const TVector &x0, const TVector &x1)
    {
        NLProblem::line_search_begin(x0.head(reduced_size()), x1.head(reduced_size()));
        for (auto &form : homo_forms)
            form->line_search_begin(reduced_to_extended(x0), reduced_to_extended(x1));
    }
    void NLHomoProblem::post_step(const polysolve::nonlinear::PostStepData &data)
    {
        NLProblem::post_step(polysolve::nonlinear::PostStepData(data.iter_num, data.solver_info, reduced_to_full(data.x.head(reduced_size())), reduced_to_full(data.grad.head(reduced_size()))));
        for (auto &form : homo_forms)
            form->post_step(polysolve::nonlinear::PostStepData(
                data.iter_num, data.solver_info, reduced_to_extended(data.x), reduced_to_extended(data.grad)));
    }
 
    void NLHomoProblem::solution_changed(const TVector &new_x)
    {
        NLProblem::solution_changed(new_x.head(reduced_size()));
        for (auto &form : homo_forms)
            form->solution_changed(reduced_to_extended(new_x));
    }
 
    void NLHomoProblem::init_lagging(const TVector &x)
    {
        NLProblem::init_lagging(x.head(reduced_size()));
        for (auto &form : homo_forms)
            form->init_lagging(reduced_to_extended(x));
    }
    void NLHomoProblem::update_lagging(const TVector &x, const int iter_num)
    {
        NLProblem::update_lagging(x.head(reduced_size()), iter_num);
        for (auto &form : homo_forms)
            form->update_lagging(reduced_to_extended(x), iter_num);
    }
 
    void NLHomoProblem::update_quantities(const double t, const TVector &x)
    {
        NLProblem::update_quantities(t, x.head(reduced_size()));
        for (auto &form : homo_forms)
            form->update_quantities(t, reduced_to_extended(x));
    }
 
    Eigen::MatrixXd NLHomoProblem::constraint_grad() const
    {
        const int dim = state_.mesh->dimension();
        Eigen::MatrixXd jac; // (dim*dim) x (dim*n_bases)
 
        Eigen::MatrixXd X = io::Evaluator::get_bases_position(state_.n_bases, state_.mesh_nodes);
 
        jac.setZero(dim * dim, full_size_);
        for (int i = 0; i < X.rows(); i++)
            for (int j = 0; j < dim; j++)
                for (int k = 0; k < dim; k++)
                    jac(j * dim + k, i * dim + j) = X(i, k);
 
        return macro_full_to_reduced_grad(jac);
    }
} // namespace polyfem::solver