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// |
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// Copyright (c) 2024 INRIA |
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// |
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#include <iostream> |
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#include <pinocchio/math/tridiagonal-matrix.hpp> |
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#include <boost/variant.hpp> // to avoid C99 warnings |
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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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using namespace pinocchio; |
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BOOST_AUTO_TEST_CASE(test_zero) |
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{ |
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const Eigen::DenseIndex mat_size = 20; |
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TridiagonalSymmetricMatrixTpl<double> tridiagonal_matrix(mat_size); |
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tridiagonal_matrix.setZero(); |
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BOOST_CHECK(tridiagonal_matrix.isZero(0)); |
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BOOST_CHECK(tridiagonal_matrix.isDiagonal(0)); |
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BOOST_CHECK(tridiagonal_matrix.matrix().isZero(0)); |
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} |
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BOOST_AUTO_TEST_CASE(test_identity) |
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{ |
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const Eigen::DenseIndex mat_size = 20; |
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TridiagonalSymmetricMatrixTpl<double> tridiagonal_matrix(mat_size); |
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typedef TridiagonalSymmetricMatrixTpl<double>::PlainMatrixType PlainMatrixType; |
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tridiagonal_matrix.setIdentity(); |
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BOOST_CHECK(tridiagonal_matrix.isIdentity(0)); |
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BOOST_CHECK(tridiagonal_matrix.isDiagonal(0)); |
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BOOST_CHECK(tridiagonal_matrix.rows() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.cols() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.diagonal().size() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.subDiagonal().size() == mat_size - 1); |
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BOOST_CHECK(tridiagonal_matrix.diagonal().isOnes(0)); |
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BOOST_CHECK(tridiagonal_matrix.subDiagonal().isZero(0)); |
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BOOST_CHECK(tridiagonal_matrix.matrix().isIdentity(0)); |
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// Fill matrix |
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{ |
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PlainMatrixType mat(mat_size, mat_size); |
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mat = tridiagonal_matrix; |
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BOOST_CHECK(mat.isIdentity(0)); |
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} |
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// Matrix multiplication left and right |
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for (int k = 0; k < 1000; ++k) |
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{ |
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PlainMatrixType mat = PlainMatrixType::Random(mat_size, mat_size); |
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PlainMatrixType plain(mat_size, mat_size); |
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plain = tridiagonal_matrix; |
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PlainMatrixType res_apply_on_the_right = tridiagonal_matrix * mat; |
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PlainMatrixType res_apply_on_the_right_ref = plain * mat; |
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BOOST_CHECK(res_apply_on_the_right.isApprox(res_apply_on_the_right_ref)); |
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PlainMatrixType res_apply_on_the_left = mat * tridiagonal_matrix; |
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PlainMatrixType res_apply_on_the_left_ref = mat * plain; |
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BOOST_CHECK(res_apply_on_the_left.isApprox(res_apply_on_the_left_ref)); |
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} |
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} |
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BOOST_AUTO_TEST_CASE(test_random) |
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{ |
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const Eigen::DenseIndex mat_size = 20; |
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TridiagonalSymmetricMatrixTpl<double> tridiagonal_matrix(mat_size); |
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typedef TridiagonalSymmetricMatrixTpl<double>::PlainMatrixType PlainMatrixType; |
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tridiagonal_matrix.setRandom(); |
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BOOST_CHECK(tridiagonal_matrix.rows() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.cols() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.diagonal().size() == mat_size); |
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BOOST_CHECK(tridiagonal_matrix.subDiagonal().size() == mat_size - 1); |
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// Fill matrix |
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{ |
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PlainMatrixType mat(mat_size, mat_size); |
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mat = tridiagonal_matrix; |
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BOOST_CHECK(mat.diagonal() == tridiagonal_matrix.diagonal()); |
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BOOST_CHECK(mat.diagonal<-1>() == tridiagonal_matrix.subDiagonal()); |
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BOOST_CHECK(mat.diagonal<+1>().conjugate() == tridiagonal_matrix.subDiagonal().conjugate()); |
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} |
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// Matrix multiplication |
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for (int k = 0; k < 1000; ++k) |
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{ |
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PlainMatrixType rhs_mat = PlainMatrixType::Random(mat_size, mat_size); |
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PlainMatrixType plain(mat_size, mat_size); |
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plain = tridiagonal_matrix; |
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PlainMatrixType res = tridiagonal_matrix * rhs_mat; |
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PlainMatrixType res_ref = plain * rhs_mat; |
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BOOST_CHECK(res.isApprox(res_ref)); |
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BOOST_CHECK((tridiagonal_matrix * PlainMatrixType::Identity(mat_size, mat_size)) |
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.isApprox(tridiagonal_matrix.matrix())); |
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} |
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} |
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BOOST_AUTO_TEST_CASE(test_inverse) |
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{ |
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typedef TridiagonalSymmetricMatrixTpl<double> TridiagonalSymmetricMatrixd; |
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const Eigen::DenseIndex mat_size = 10; |
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TridiagonalSymmetricMatrixTpl<double> tridiagonal_matrix(mat_size); |
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typedef TridiagonalSymmetricMatrixTpl<double>::PlainMatrixType PlainMatrixType; |
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tridiagonal_matrix.setRandom(); |
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PlainMatrixType plain_mat(mat_size, mat_size); |
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plain_mat = tridiagonal_matrix; |
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const PlainMatrixType plain_mat_inverse = plain_mat.inverse(); |
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const TridiagonalSymmetricMatrixInverse<TridiagonalSymmetricMatrixd> & |
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tridiagonal_matrix_inverse = tridiagonal_matrix.inverse(); |
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BOOST_CHECK(tridiagonal_matrix_inverse.rows() == tridiagonal_matrix.rows()); |
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BOOST_CHECK(tridiagonal_matrix_inverse.cols() == tridiagonal_matrix.cols()); |
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const auto & tridiagonal_matrix_ref = tridiagonal_matrix_inverse.inverse(); |
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BOOST_CHECK(&tridiagonal_matrix_ref == &tridiagonal_matrix); |
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const PlainMatrixType tridiagonal_matrix_inverse_plain = tridiagonal_matrix_inverse; |
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BOOST_CHECK(tridiagonal_matrix_inverse_plain.isApprox(plain_mat_inverse)); |
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// Matrix multiplication |
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for (int k = 0; k < 1; ++k) |
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{ |
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PlainMatrixType rhs_mat = PlainMatrixType::Random(mat_size, mat_size); |
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PlainMatrixType res(mat_size, mat_size); |
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res = tridiagonal_matrix_ref * rhs_mat; |
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BOOST_CHECK(res.isApprox((plain_mat * rhs_mat).eval())); |
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res = tridiagonal_matrix_inverse * rhs_mat; |
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const PlainMatrixType res_ref = plain_mat_inverse * rhs_mat; |
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BOOST_CHECK(res.isApprox(res_ref)); |
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} |
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// Test diagonal |
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{ |
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Eigen::MatrixXd sub_diagonal_matrix = Eigen::MatrixXd::Zero(mat_size, mat_size); |
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sub_diagonal_matrix.diagonal<1>().setRandom(); |
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sub_diagonal_matrix.diagonal().setRandom(); |
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sub_diagonal_matrix.diagonal<-1>().setRandom(); |
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const Eigen::MatrixXd test_mat = Eigen::MatrixXd::Random(mat_size, mat_size); |
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const Eigen::MatrixXd res_ref = sub_diagonal_matrix * test_mat; |
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Eigen::MatrixXd res(mat_size, mat_size); // res.setZero(); |
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res.noalias() = sub_diagonal_matrix.diagonal().asDiagonal() * test_mat; |
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res.topRows(mat_size - 1) += |
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sub_diagonal_matrix.diagonal<1>().asDiagonal() * test_mat.bottomRows(mat_size - 1); |
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res.bottomRows(mat_size - 1) += |
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sub_diagonal_matrix.diagonal<-1>().asDiagonal() * test_mat.topRows(mat_size - 1); |
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BOOST_CHECK(res.isApprox(res_ref)); |
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} |
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} |
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BOOST_AUTO_TEST_SUITE_END() |
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