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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2022, University of Edinburgh, Heriot-Watt University |
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// Copyright note valid unless otherwise stated in individual files. |
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// All rights reserved. |
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/////////////////////////////////////////////////////////////////////////////// |
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#include "crocoddyl/core/solvers/box-qp.hpp" |
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namespace crocoddyl { |
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BoxQP::BoxQP(const std::size_t nx, const std::size_t maxiter, |
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const double th_acceptstep, const double th_grad, const double reg) |
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: nx_(nx), |
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maxiter_(maxiter), |
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th_acceptstep_(th_acceptstep), |
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th_grad_(th_grad), |
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reg_(reg), |
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fold_(0.), |
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fnew_(0.), |
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x_(nx), |
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xnew_(nx), |
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g_(nx), |
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dx_(nx), |
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xo_(nx), |
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dxo_(nx), |
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qo_(nx), |
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Ho_(nx, nx) { |
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// Check if values have a proper range |
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if (0. >= th_acceptstep && th_acceptstep >= 0.5) { |
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std::cerr << "Warning: th_acceptstep value should between 0 and 0.5" |
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<< std::endl; |
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} |
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if (0. > th_grad) { |
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std::cerr << "Warning: th_grad value has to be positive." << std::endl; |
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} |
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if (0. > reg) { |
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std::cerr << "Warning: reg value has to be positive." << std::endl; |
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} |
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// Initialized the values of vectors |
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x_.setZero(); |
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xnew_.setZero(); |
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g_.setZero(); |
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dx_.setZero(); |
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xo_.setZero(); |
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dxo_.setZero(); |
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qo_.setZero(); |
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Ho_.setZero(); |
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// Reserve the space and compute alphas |
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solution_.x = Eigen::VectorXd::Zero(nx); |
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solution_.clamped_idx.reserve(nx_); |
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solution_.free_idx.reserve(nx_); |
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const std::size_t n_alphas_ = 10; |
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alphas_.resize(n_alphas_); |
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for (std::size_t n = 0; n < n_alphas_; ++n) { |
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alphas_[n] = 1. / pow(2., static_cast<double>(n)); |
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} |
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} |
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BoxQP::~BoxQP() {} |
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const BoxQPSolution& BoxQP::solve(const Eigen::MatrixXd& H, |
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const Eigen::VectorXd& q, |
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const Eigen::VectorXd& lb, |
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const Eigen::VectorXd& ub, |
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const Eigen::VectorXd& xinit) { |
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if (static_cast<std::size_t>(H.rows()) != nx_ || |
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static_cast<std::size_t>(H.cols()) != nx_) { |
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throw_pretty("Invalid argument: " |
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<< "H has wrong dimension (it should be " + |
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std::to_string(nx_) + "," + std::to_string(nx_) + ")"); |
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} |
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if (static_cast<std::size_t>(q.size()) != nx_) { |
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throw_pretty( |
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"Invalid argument: " << "q has wrong dimension (it should be " + |
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std::to_string(nx_) + ")"); |
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} |
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if (static_cast<std::size_t>(lb.size()) != nx_) { |
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throw_pretty( |
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"Invalid argument: " << "lb has wrong dimension (it should be " + |
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std::to_string(nx_) + ")"); |
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} |
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if (static_cast<std::size_t>(ub.size()) != nx_) { |
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throw_pretty( |
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"Invalid argument: " << "ub has wrong dimension (it should be " + |
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std::to_string(nx_) + ")"); |
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} |
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if (static_cast<std::size_t>(xinit.size()) != nx_) { |
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throw_pretty( |
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"Invalid argument: " << "xinit has wrong dimension (it should be " + |
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std::to_string(nx_) + ")"); |
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} |
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// We need to enforce feasible warm-starting of the algorithm |
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for (std::size_t i = 0; i < nx_; ++i) { |
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x_(i) = std::max(std::min(xinit(i), ub(i)), lb(i)); |
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} |
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// Start the numerical iterations |
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for (std::size_t k = 0; k < maxiter_; ++k) { |
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solution_.clamped_idx.clear(); |
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solution_.free_idx.clear(); |
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// Compute the Cauchy point and active set |
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g_ = q; |
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g_.noalias() += H * x_; |
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for (std::size_t j = 0; j < nx_; ++j) { |
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const double gj = g_(j); |
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const double xj = x_(j); |
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const double lbj = lb(j); |
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const double ubj = ub(j); |
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if ((xj == lbj && gj > 0.) || (xj == ubj && gj < 0.)) { |
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solution_.clamped_idx.push_back(j); |
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} else { |
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solution_.free_idx.push_back(j); |
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} |
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} |
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// Compute the search direction as Newton step along the free space |
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nf_ = solution_.free_idx.size(); |
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nc_ = solution_.clamped_idx.size(); |
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Eigen::VectorBlock<Eigen::VectorXd> xf = xo_.head(nf_); |
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Eigen::VectorBlock<Eigen::VectorXd> xc = xo_.tail(nc_); |
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Eigen::VectorBlock<Eigen::VectorXd> dxf = dxo_.head(nf_); |
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Eigen::VectorBlock<Eigen::VectorXd> qf = qo_.head(nf_); |
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Eigen::Block<Eigen::MatrixXd> Hff = Ho_.topLeftCorner(nf_, nf_); |
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Eigen::Block<Eigen::MatrixXd> Hfc = Ho_.topRightCorner(nf_, nc_); |
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for (std::size_t i = 0; i < nf_; ++i) { |
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const std::size_t fi = solution_.free_idx[i]; |
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qf(i) = q(fi); |
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xf(i) = x_(fi); |
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for (std::size_t j = 0; j < nf_; ++j) { |
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Hff(i, j) = H(fi, solution_.free_idx[j]); |
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} |
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for (std::size_t j = 0; j < nc_; ++j) { |
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const std::size_t cj = solution_.clamped_idx[j]; |
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xc(j) = x_(cj); |
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Hfc(i, j) = H(fi, cj); |
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} |
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} |
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if (reg_ != 0.) { |
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Hff.diagonal().array() += reg_; |
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} |
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Hff_inv_llt_.compute(Hff); |
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const Eigen::ComputationInfo& info = Hff_inv_llt_.info(); |
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if (info != Eigen::Success) { |
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throw_pretty("backward_error"); |
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} |
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solution_.Hff_inv.setIdentity(nf_, nf_); |
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Hff_inv_llt_.solveInPlace(solution_.Hff_inv); |
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qf.noalias() += Hff * xf; |
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if (nc_ != 0) { |
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qf.noalias() += Hfc * xc; |
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} |
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dxf = -qf; |
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Hff_inv_llt_.solveInPlace(dxf); |
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dx_.setZero(); |
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for (std::size_t i = 0; i < nf_; ++i) { |
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dx_(solution_.free_idx[i]) = dxf(i); |
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g_(solution_.free_idx[i]) = -qf(i); |
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} |
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// Try different step lengths |
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fold_ = 0.5 * x_.dot(H * x_) + q.dot(x_); |
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for (std::vector<double>::const_iterator it = alphas_.begin(); |
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it != alphas_.end(); ++it) { |
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double steplength = *it; |
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for (std::size_t i = 0; i < nx_; ++i) { |
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xnew_(i) = |
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std::max(std::min(x_(i) + steplength * dx_(i), ub(i)), lb(i)); |
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} |
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fnew_ = 0.5 * xnew_.dot(H * xnew_) + q.dot(xnew_); |
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if (fold_ - fnew_ > th_acceptstep_ * g_.dot(x_ - xnew_)) { |
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x_ = xnew_; |
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break; |
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} |
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} |
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// Check convergence |
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if (qf.lpNorm<Eigen::Infinity>() <= th_grad_) { |
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solution_.x = x_; |
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return solution_; |
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} |
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} |
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solution_.x = x_; |
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return solution_; |
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} |
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const BoxQPSolution& BoxQP::get_solution() const { return solution_; } |
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std::size_t BoxQP::get_nx() const { return nx_; } |
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std::size_t BoxQP::get_maxiter() const { return maxiter_; } |
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double BoxQP::get_th_acceptstep() const { return th_acceptstep_; } |
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double BoxQP::get_th_grad() const { return th_grad_; } |
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double BoxQP::get_reg() const { return reg_; } |
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const std::vector<double>& BoxQP::get_alphas() const { return alphas_; } |
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void BoxQP::set_nx(const std::size_t nx) { |
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nx_ = nx; |
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x_.conservativeResize(nx); |
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xnew_.conservativeResize(nx); |
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g_.conservativeResize(nx); |
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dx_.conservativeResize(nx); |
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xo_.conservativeResize(nx); |
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dxo_.conservativeResize(nx); |
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qo_.conservativeResize(nx); |
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Ho_.conservativeResize(nx, nx); |
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} |
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void BoxQP::set_maxiter(const std::size_t maxiter) { maxiter_ = maxiter; } |
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void BoxQP::set_th_acceptstep(const double th_acceptstep) { |
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if (0. >= th_acceptstep && th_acceptstep >= 0.5) { |
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throw_pretty( |
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"Invalid argument: " << "th_acceptstep value should between 0 and 0.5"); |
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} |
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th_acceptstep_ = th_acceptstep; |
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} |
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void BoxQP::set_th_grad(const double th_grad) { |
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if (0. > th_grad) { |
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throw_pretty("Invalid argument: " << "th_grad value has to be positive."); |
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} |
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th_grad_ = th_grad; |
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} |
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void BoxQP::set_reg(const double reg) { |
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if (0. > reg) { |
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throw_pretty("Invalid argument: " << "reg value has to be positive."); |
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} |
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reg_ = reg; |
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} |
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void BoxQP::set_alphas(const std::vector<double>& alphas) { |
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double prev_alpha = alphas[0]; |
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if (prev_alpha != 1.) { |
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std::cerr << "Warning: alpha[0] should be 1" << std::endl; |
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} |
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for (std::size_t i = 1; i < alphas.size(); ++i) { |
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double alpha = alphas[i]; |
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if (0. >= alpha) { |
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throw_pretty("Invalid argument: " << "alpha values has to be positive."); |
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} |
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if (alpha >= prev_alpha) { |
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throw_pretty( |
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"Invalid argument: " << "alpha values are monotonously decreasing."); |
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} |
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prev_alpha = alpha; |
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} |
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alphas_ = alphas; |
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} |
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} // namespace crocoddyl |
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