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// |
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// Copyright (c) 2015-2019 CNRS INRIA |
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// |
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/* |
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* Validate the sparse Cholesky decomposition of the mass matrix. The code |
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* tests both the numerical value and the computation time. For a strong |
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* computation benchmark, see benchmark/timings. |
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* |
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*/ |
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#include "pinocchio/spatial/se3.hpp" |
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#include "pinocchio/multibody/model.hpp" |
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#include "pinocchio/multibody/data.hpp" |
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#include "pinocchio/algorithm/crba.hpp" |
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#include "pinocchio/algorithm/cholesky.hpp" |
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#include "pinocchio/multibody/sample-models.hpp" |
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#include "pinocchio/utils/timer.hpp" |
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#include "pinocchio/algorithm/joint-configuration.hpp" |
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#include <iostream> |
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#ifdef NDEBUG |
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#include <Eigen/Cholesky> |
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#endif |
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#include <boost/test/unit_test.hpp> |
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#include <boost/utility/binary.hpp> |
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BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE) |
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BOOST_AUTO_TEST_CASE(test_cholesky) |
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{ |
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using namespace Eigen; |
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using namespace pinocchio; |
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pinocchio::Model model; |
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pinocchio::buildModels::humanoidRandom(model, true); |
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pinocchio::Data data(model); |
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model.lowerPositionLimit.head<3>().fill(-1.); |
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model.upperPositionLimit.head<3>().fill(1.); |
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VectorXd q = randomConfiguration(model); |
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data.M.fill(0); // Only nonzero coeff of M are initialized by CRBA. |
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crba(model, data, q, Convention::WORLD); |
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pinocchio::cholesky::decompose(model, data); |
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data.M.triangularView<Eigen::StrictlyLower>() = |
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data.M.triangularView<Eigen::StrictlyUpper>().transpose(); |
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const Eigen::MatrixXd & U = data.U; |
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const Eigen::VectorXd & D = data.D; |
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const Eigen::MatrixXd & M = data.M; |
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#ifndef NDEBUG |
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std::cout << "M = [\n" << M << "];" << std::endl; |
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std::cout << "U = [\n" << U << "];" << std::endl; |
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std::cout << "D = [\n" << D.transpose() << "];" << std::endl; |
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#endif |
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BOOST_CHECK(M.isApprox(U * D.asDiagonal() * U.transpose(), 1e-12)); |
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Eigen::VectorXd v = Eigen::VectorXd::Random(model.nv); |
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// std::cout << "v = [" << v.transpose() << "]';" << std::endl; |
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Eigen::VectorXd Uv = v; |
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pinocchio::cholesky::Uv(model, data, Uv); |
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BOOST_CHECK(Uv.isApprox(U * v, 1e-12)); |
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Eigen::VectorXd Utv = v; |
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pinocchio::cholesky::Utv(model, data, Utv); |
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BOOST_CHECK(Utv.isApprox(U.transpose() * v, 1e-12)); |
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Eigen::VectorXd Uiv = v; |
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pinocchio::cholesky::Uiv(model, data, Uiv); |
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BOOST_CHECK(Uiv.isApprox(U.inverse() * v, 1e-12)); |
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Eigen::VectorXd Utiv = v; |
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pinocchio::cholesky::Utiv(model, data, Utiv); |
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BOOST_CHECK(Utiv.isApprox(U.transpose().inverse() * v, 1e-12)); |
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Eigen::VectorXd Miv = v; |
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pinocchio::cholesky::solve(model, data, Miv); |
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BOOST_CHECK(Miv.isApprox(M.inverse() * v, 1e-12)); |
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Eigen::VectorXd Mv = v; |
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Mv = pinocchio::cholesky::Mv(model, data, Mv); |
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BOOST_CHECK(Mv.isApprox(M * v, 1e-12)); |
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Mv = v; |
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pinocchio::cholesky::UDUtv(model, data, Mv); |
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BOOST_CHECK(Mv.isApprox(M * v, 1e-12)); |
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} |
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/* The flag triger the following timers: |
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* 000001: sparse UDUt cholesky |
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* 000010: dense Eigen LDLt cholesky (with pivot) |
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* 000100: sparse resolution |
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* 001000: sparse U*v multiplication |
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* 010000: sparse U\v substitution |
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* 100000: sparse M*v multiplication without Cholesky |
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*/ |
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BOOST_AUTO_TEST_CASE(test_timings) |
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{ |
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using namespace Eigen; |
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using namespace pinocchio; |
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pinocchio::Model model; |
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pinocchio::buildModels::humanoidRandom(model, true); |
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pinocchio::Data data(model); |
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model.lowerPositionLimit.head<3>().fill(-1.); |
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model.upperPositionLimit.head<3>().fill(1.); |
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VectorXd q = randomConfiguration(model); |
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data.M.fill(0); // Only nonzero coeff of M are initialized by CRBA. |
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crba(model, data, q, Convention::WORLD); |
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long flag = BOOST_BINARY(1111111); |
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PinocchioTicToc timer(PinocchioTicToc::US); |
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#ifdef NDEBUG |
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#ifdef _INTENSE_TESTING_ |
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const size_t NBT = 1000 * 1000; |
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#else |
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const size_t NBT = 10; |
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#endif |
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#else |
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const size_t NBT = 1; |
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std::cout << "(the time score in debug mode is not relevant) "; |
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#endif |
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bool verbose = flag & (flag - 1); // True is two or more binaries of the flag are 1. |
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if (verbose) |
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std::cout << "--" << std::endl; |
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if (flag >> 0 & 1) |
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{ |
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timer.tic(); |
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SMOOTH(NBT) |
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{ |
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pinocchio::cholesky::decompose(model, data); |
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} |
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if (verbose) |
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std::cout << "Decompose =\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 1 & 1) |
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{ |
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timer.tic(); |
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Eigen::VectorXd v = Eigen::VectorXd::Random(model.nv); |
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Eigen::VectorXd res(model.nv); |
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SMOOTH(NBT) |
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{ |
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Eigen::LDLT<Eigen::MatrixXd> Mchol(data.M); |
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res = Mchol.solve(v); |
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} |
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if (verbose) |
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std::cout << "Eigen::LDLt =\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 2 & 31) |
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{ |
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std::vector<Eigen::VectorXd> randvec(NBT); |
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for (size_t i = 0; i < NBT; ++i) |
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randvec[i] = Eigen::VectorXd::Random(model.nv); |
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Eigen::VectorXd zero = Eigen::VectorXd::Zero(model.nv); |
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Eigen::VectorXd res(model.nv); |
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if (flag >> 2 & 1) |
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{ |
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timer.tic(); |
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SMOOTH(NBT) |
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{ |
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pinocchio::cholesky::solve(model, data, randvec[_smooth]); |
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} |
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if (verbose) |
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std::cout << "solve =\t\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 3 & 1) |
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{ |
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timer.tic(); |
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SMOOTH(NBT) |
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{ |
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pinocchio::cholesky::Uv(model, data, randvec[_smooth]); |
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} |
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if (verbose) |
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std::cout << "Uv =\t\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 4 & 1) |
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{ |
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timer.tic(); |
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SMOOTH(NBT) |
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{ |
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pinocchio::cholesky::Uiv(model, data, randvec[_smooth]); |
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} |
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if (verbose) |
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std::cout << "Uiv =\t\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 5 & 1) |
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{ |
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timer.tic(); |
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Eigen::VectorXd res; |
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SMOOTH(NBT) |
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{ |
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res = pinocchio::cholesky::Mv(model, data, randvec[_smooth]); |
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} |
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if (verbose) |
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std::cout << "Mv =\t\t"; |
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timer.toc(std::cout, NBT); |
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} |
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if (flag >> 6 & 1) |
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{ |
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timer.tic(); |
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SMOOTH(NBT) |
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{ |
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pinocchio::cholesky::UDUtv(model, data, randvec[_smooth]); |
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} |
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if (verbose) |
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std::cout << "UDUtv =\t\t"; |
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timer.toc(std::cout, NBT); |
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} |
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} |
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} |
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BOOST_AUTO_TEST_CASE(test_Minv_from_cholesky) |
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{ |
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using namespace Eigen; |
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using namespace pinocchio; |
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pinocchio::Model model; |
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pinocchio::buildModels::humanoidRandom(model, true); |
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pinocchio::Data data(model); |
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model.lowerPositionLimit.head<3>().fill(-1.); |
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model.upperPositionLimit.head<3>().fill(1.); |
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VectorXd q = randomConfiguration(model); |
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crba(model, data, q, Convention::WORLD); |
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data.M.triangularView<Eigen::StrictlyLower>() = |
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data.M.triangularView<Eigen::StrictlyUpper>().transpose(); |
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MatrixXd Minv_ref(data.M.inverse()); |
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cholesky::decompose(model, data); |
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VectorXd v_unit(VectorXd::Unit(model.nv, 0)); |
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VectorXd Ui_v_unit(model.nv); |
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VectorXd Ui_v_unit_ref(model.nv); |
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for (int k = 0; k < model.nv; ++k) |
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{ |
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v_unit = VectorXd::Unit(model.nv, k); |
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Ui_v_unit.setZero(); |
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cholesky::internal::Miunit(model, data, k, Ui_v_unit); |
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Ui_v_unit_ref = v_unit; |
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cholesky::Uiv(model, data, Ui_v_unit_ref); |
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Ui_v_unit_ref.array() *= data.Dinv.array(); |
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cholesky::Utiv(model, data, Ui_v_unit_ref); |
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BOOST_CHECK(Ui_v_unit.head(k + 1).isApprox(Ui_v_unit_ref.head(k + 1))); |
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Ui_v_unit_ref = v_unit; |
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cholesky::solve(model, data, Ui_v_unit_ref); |
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BOOST_CHECK(Ui_v_unit.head(k + 1).isApprox(Ui_v_unit_ref.head(k + 1))); |
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} |
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MatrixXd Minv(model.nv, model.nv); |
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Minv.setZero(); |
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cholesky::computeMinv(model, data, Minv); |
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BOOST_CHECK(Minv.isApprox(Minv_ref)); |
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// Check second call to cholesky::computeMinv |
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cholesky::computeMinv(model, data, Minv); |
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BOOST_CHECK(Minv.isApprox(Minv_ref)); |
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// Call the second signature of cholesky::computeMinv |
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Data data_bis(model); |
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crba(model, data_bis, q, Convention::WORLD); |
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cholesky::decompose(model, data_bis); |
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cholesky::computeMinv(model, data_bis); |
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BOOST_CHECK(data_bis.Minv.isApprox(Minv_ref)); |
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} |
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BOOST_AUTO_TEST_SUITE_END() |
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