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// |
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// Copyright (c) 2017 CNRS |
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// |
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// This file is part of tsid |
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// tsid is free software: you can redistribute it |
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// and/or modify it under the terms of the GNU Lesser General Public |
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// License as published by the Free Software Foundation, either version |
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// 3 of the License, or (at your option) any later version. |
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// tsid is distributed in the hope that it will be |
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// useful, but WITHOUT ANY WARRANTY; without even the implied warranty |
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// of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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// General Lesser Public License for more details. You should have |
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// received a copy of the GNU Lesser General Public License along with |
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// tsid If not, see |
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// <http://www.gnu.org/licenses/>. |
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// |
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#include "tsid/solvers/solver-HQP-eiquadprog.hpp" |
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#include "tsid/math/utils.hpp" |
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#include "eiquadprog/eiquadprog.hpp" |
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#include "tsid/utils/stop-watch.hpp" |
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using namespace tsid::math; |
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using namespace tsid::solvers; |
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using namespace Eigen; |
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SolverHQuadProg::SolverHQuadProg(const std::string& name) |
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: SolverHQPBase(name), |
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m_hessian_regularization(DEFAULT_HESSIAN_REGULARIZATION) { |
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m_n = 0; |
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m_neq = 0; |
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m_nin = 0; |
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} |
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void SolverHQuadProg::sendMsg(const std::string& s) { |
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std::cout << "[SolverHQuadProg." << m_name << "] " << s << std::endl; |
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} |
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void SolverHQuadProg::resize(unsigned int n, unsigned int neq, |
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unsigned int nin) { |
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const bool resizeVar = n != m_n; |
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const bool resizeEq = (resizeVar || neq != m_neq); |
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const bool resizeIn = (resizeVar || nin != m_nin); |
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if (resizeEq) { |
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#ifndef NDEBUG |
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sendMsg("Resizing equality constraints from " + toString(m_neq) + " to " + |
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toString(neq)); |
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#endif |
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m_qpData.CE.resize(neq, n); |
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m_qpData.ce0.resize(neq); |
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} |
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if (resizeIn) { |
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#ifndef NDEBUG |
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sendMsg("Resizing inequality constraints from " + toString(m_nin) + " to " + |
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toString(nin)); |
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#endif |
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m_qpData.CI.resize(2 * nin, n); |
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m_qpData.ci0.resize(2 * nin); |
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} |
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if (resizeVar) { |
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#ifndef NDEBUG |
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sendMsg("Resizing Hessian from " + toString(m_n) + " to " + toString(n)); |
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#endif |
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m_qpData.H.resize(n, n); |
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m_qpData.g.resize(n); |
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m_output.x.resize(n); |
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} |
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m_n = n; |
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m_neq = neq; |
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m_nin = nin; |
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} |
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void SolverHQuadProg::retrieveQPData(const HQPData& problemData, |
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const bool /*hessianRegularization*/) { |
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if (problemData.size() > 2) { |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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false, "Solver not implemented for more than 2 hierarchical levels."); |
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} |
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// Compute the constraint matrix sizes |
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unsigned int neq = 0, nin = 0; |
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const ConstraintLevel& cl0 = problemData[0]; |
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if (cl0.size() > 0) { |
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const unsigned int n = cl0[0].second->cols(); |
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for (ConstraintLevel::const_iterator it = cl0.begin(); it != cl0.end(); |
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it++) { |
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auto constr = it->second; |
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assert(n == constr->cols()); |
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if (constr->isEquality()) |
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neq += constr->rows(); |
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else |
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nin += constr->rows(); |
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} |
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// If necessary, resize the constraint matrices |
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resize(n, neq, nin); |
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int i_eq = 0, i_in = 0; |
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for (ConstraintLevel::const_iterator it = cl0.begin(); it != cl0.end(); |
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it++) { |
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auto constr = it->second; |
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if (constr->isEquality()) { |
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m_qpData.CE.middleRows(i_eq, constr->rows()) = constr->matrix(); |
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m_qpData.ce0.segment(i_eq, constr->rows()) = -constr->vector(); |
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i_eq += constr->rows(); |
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} else if (constr->isInequality()) { |
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m_qpData.CI.middleRows(i_in, constr->rows()) = constr->matrix(); |
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m_qpData.ci0.segment(i_in, constr->rows()) = -constr->lowerBound(); |
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i_in += constr->rows(); |
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m_qpData.CI.middleRows(i_in, constr->rows()) = -constr->matrix(); |
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m_qpData.ci0.segment(i_in, constr->rows()) = constr->upperBound(); |
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i_in += constr->rows(); |
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} else if (constr->isBound()) { |
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m_qpData.CI.middleRows(i_in, constr->rows()).setIdentity(); |
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m_qpData.ci0.segment(i_in, constr->rows()) = -constr->lowerBound(); |
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i_in += constr->rows(); |
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m_qpData.CI.middleRows(i_in, constr->rows()) = |
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-Matrix::Identity(m_n, m_n); |
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m_qpData.ci0.segment(i_in, constr->rows()) = constr->upperBound(); |
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i_in += constr->rows(); |
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} |
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} |
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} else |
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resize(m_n, neq, nin); |
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if (problemData.size() > 1) { |
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const ConstraintLevel& cl1 = problemData[1]; |
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m_qpData.H.setZero(); |
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m_qpData.g.setZero(); |
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for (ConstraintLevel::const_iterator it = cl1.begin(); it != cl1.end(); |
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it++) { |
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const double& w = it->first; |
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auto constr = it->second; |
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if (!constr->isEquality()) |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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false, "Inequalities in the cost function are not implemented yet"); |
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m_qpData.H += w * constr->matrix().transpose() * constr->matrix(); |
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m_qpData.g -= w * (constr->matrix().transpose() * constr->vector()); |
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} |
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m_qpData.H.diagonal() += m_hessian_regularization * Vector::Ones(m_n); |
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} |
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#ifdef ELIMINATE_EQUALITY_CONSTRAINTS |
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// eliminate equality constraints |
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const int r = m_neq; |
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Matrix Z(m_n, m_n - m_neq); |
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Matrix ZT(m_n, m_n); |
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m_ZT_H_Z.resize(m_n - r, m_n - r); |
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START_PROFILER("Eiquadprog eliminate equalities"); |
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if (m_neq > 0) { |
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START_PROFILER("Eiquadprog CE decomposition"); |
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// m_qpData.CE_dec.compute(m_qpData.CE, ComputeThinU | ComputeThinV); |
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m_qpData.CE_dec.compute(m_qpData.CE); |
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STOP_PROFILER("Eiquadprog CE decomposition"); |
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START_PROFILER("Eiquadprog get CE null-space basis"); |
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// get nullspace basis from SVD |
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// const int r = m_qpData.CE_dec.nonzeroSingularValues(); |
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// const Matrix Z = m_qpData.CE_dec.matrixV().rightCols(m_n-r); |
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// get null space basis from ColPivHouseholderQR |
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// Matrix Z = m_qpData.CE_dec.householderQ(); |
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// Z = Z.rightCols(m_n-r); |
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// get null space basis from COD |
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// P^{-1} * y => colsPermutation() * y; |
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// Z = m_qpData.CE_dec.matrixZ(); // * m_qpData.CE_dec.colsPermutation(); |
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ZT.setIdentity(); |
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// m_qpData.CE_dec.applyZAdjointOnTheLeftInPlace(ZT); |
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typedef tsid::math::Index Index; |
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const Index rank = m_qpData.CE_dec.rank(); |
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Vector temp(m_n); |
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for (Index k = 0; k < rank; ++k) { |
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if (k != rank - 1) ZT.row(k).swap(ZT.row(rank - 1)); |
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ZT.middleRows(rank - 1, m_n - rank + 1) |
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.applyHouseholderOnTheLeft( |
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m_qpData.CE_dec.matrixQTZ().row(k).tail(m_n - rank).adjoint(), |
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m_qpData.CE_dec.zCoeffs()(k), &temp(0)); |
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if (k != rank - 1) ZT.row(k).swap(ZT.row(rank - 1)); |
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} |
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STOP_PROFILER("Eiquadprog get CE null-space basis"); |
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// find a solution for the equalities |
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Vector x0 = m_qpData.CE_dec.solve(m_qpData.ce0); |
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x0 = -x0; |
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// START_PROFILER("Eiquadprog project Hessian full"); |
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// m_ZT_H_Z.noalias() = Z.transpose()*m_qpData.H*Z; // this is too slow |
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// STOP_PROFILER("Eiquadprog project Hessian full"); |
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START_PROFILER("Eiquadprog project Hessian incremental"); |
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const ConstraintLevel& cl1 = problemData[1]; |
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m_ZT_H_Z.setZero(); |
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// m_qpData.g.setZero(); |
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Matrix AZ; |
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for (ConstraintLevel::const_iterator it = cl1.begin(); it != cl1.end(); |
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it++) { |
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const double& w = it->first; |
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auto constr = it->second; |
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if (!constr->isEquality()) |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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false, "Inequalities in the cost function are not implemented yet"); |
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AZ.noalias() = constr->matrix() * Z.rightCols(m_n - r); |
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m_ZT_H_Z += w * AZ.transpose() * AZ; |
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// m_qpData.g -= w*(constr->matrix().transpose()*constr->vector()); |
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} |
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// m_ZT_H_Z.diagonal() += 1e-8*Vector::Ones(m_n); |
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m_qpData.CI_Z.noalias() = m_qpData.CI * Z.rightCols(m_n - r); |
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STOP_PROFILER("Eiquadprog project Hessian incremental"); |
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} |
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STOP_PROFILER("Eiquadprog eliminate equalities"); |
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#endif |
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} |
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const HQPOutput& SolverHQuadProg::solve(const HQPData& problemData) { |
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// #ifndef NDEBUG |
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// PRINT_MATRIX(m_qpData.H); |
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// PRINT_VECTOR(m_qpData.g); |
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// PRINT_MATRIX(m_qpData.CE); |
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// PRINT_VECTOR(m_qpData.ce0); |
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// PRINT_MATRIX(m_qpData.CI); |
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// PRINT_VECTOR(m_qpData.ci0); |
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// #endif |
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SolverHQuadProg::retrieveQPData(problemData); |
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// min 0.5 * x G x + g0 x |
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// s.t. |
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// CE^T x + ce0 = 0 |
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// CI^T x + ci0 >= 0 |
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m_objValue = eiquadprog::solvers::solve_quadprog( |
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m_qpData.H, m_qpData.g, m_qpData.CE.transpose(), m_qpData.ce0, |
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m_qpData.CI.transpose(), m_qpData.ci0, m_output.x, m_activeSet, |
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m_activeSetSize); |
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if (m_objValue == std::numeric_limits<double>::infinity()) |
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m_output.status = HQP_STATUS_INFEASIBLE; |
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else { |
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m_output.status = HQP_STATUS_OPTIMAL; |
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#ifndef NDEBUG |
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const Vector& x = m_output.x; |
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const ConstraintLevel& cl0 = problemData[0]; |
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if (cl0.size() > 0) { |
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for (ConstraintLevel::const_iterator it = cl0.begin(); it != cl0.end(); |
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it++) { |
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auto constr = it->second; |
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if (constr->checkConstraint(x) == false) { |
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if (constr->isEquality()) { |
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sendMsg("Equality " + constr->name() + " violated: " + |
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toString((constr->matrix() * x - constr->vector()).norm())); |
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} else if (constr->isInequality()) { |
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sendMsg( |
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"Inequality " + constr->name() + " violated: " + |
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toString( |
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(constr->matrix() * x - constr->lowerBound()).minCoeff()) + |
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"\n" + |
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toString( |
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(constr->upperBound() - constr->matrix() * x).minCoeff())); |
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} else if (constr->isBound()) { |
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sendMsg("Bound " + constr->name() + " violated: " + |
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toString((x - constr->lowerBound()).minCoeff()) + "\n" + |
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toString((constr->upperBound() - x).minCoeff())); |
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} |
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} |
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} |
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} |
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#endif |
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} |
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return m_output; |
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} |
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double SolverHQuadProg::getObjectiveValue() { return m_objValue; } |
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