template<typename MatrixType> void triangular(const MatrixType& m) { typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; RealScalar largerEps = 10*test_precision<RealScalar>(); int rows = m.rows(); int cols = m.cols(); MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), m4(rows, cols), r1(rows, cols), r2(rows, cols), mzero = MatrixType::Zero(rows, cols), mones = MatrixType::Ones(rows, cols), identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> ::Identity(rows, rows), square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> ::Random(rows, rows); VectorType v1 = VectorType::Random(rows), v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows); MatrixType m1up = m1.template part<Eigen::UpperTriangular>(); MatrixType m2up = m2.template part<Eigen::UpperTriangular>(); if (rows*cols>1) { VERIFY(m1up.isUpperTriangular()); VERIFY(m2up.transpose().isLowerTriangular()); VERIFY(!m2.isLowerTriangular()); } // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2); // test overloaded operator+= r1.setZero(); r2.setZero(); r1.template part<Eigen::UpperTriangular>() += m1; r2 += m1up; VERIFY_IS_APPROX(r1,r2); // test overloaded operator= m1.setZero(); m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy(); m3 = m2.transpose() * m2; VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1); // test overloaded operator= m1.setZero(); m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy(); VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1); VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal()); m1 = MatrixType::Random(rows, cols); for (int i=0; i<rows; ++i) while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>(); Transpose<MatrixType> trm4(m4); // test back and forward subsitution m3 = m1.template part<Eigen::LowerTriangular>(); VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>())); VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>() .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>())); // check M * inv(L) using in place API m4 = m3; m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); m3 = m1.template part<Eigen::UpperTriangular>(); VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>())); VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>() .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>())); // check M * inv(U) using in place API m4 = m3; m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); m3 = m1.template part<Eigen::UpperTriangular>(); VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps)); m3 = m1.template part<Eigen::LowerTriangular>(); VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps)); VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular()); // test swap m1.setOnes(); m2.setZero(); m2.template part<Eigen::UpperTriangular>().swap(m1); m3.setZero(); m3.template part<Eigen::UpperTriangular>().setOnes(); VERIFY_IS_APPROX(m2,m3); }
template<typename MatrixType> void triangular_square(const MatrixType& m) { typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; RealScalar largerEps = 10*test_precision<RealScalar>(); typename MatrixType::Index rows = m.rows(); typename MatrixType::Index cols = m.cols(); MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), m4(rows, cols), r1(rows, cols), r2(rows, cols), mzero = MatrixType::Zero(rows, cols), mones = MatrixType::Ones(rows, cols), identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> ::Identity(rows, rows), square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> ::Random(rows, rows); VectorType v1 = VectorType::Random(rows), v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows); MatrixType m1up = m1.template triangularView<Upper>(); MatrixType m2up = m2.template triangularView<Upper>(); if (rows*cols>1) { VERIFY(m1up.isUpperTriangular()); VERIFY(m2up.transpose().isLowerTriangular()); VERIFY(!m2.isLowerTriangular()); } // VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2); // test overloaded operator+= r1.setZero(); r2.setZero(); r1.template triangularView<Upper>() += m1; r2 += m1up; VERIFY_IS_APPROX(r1,r2); // test overloaded operator= m1.setZero(); m1.template triangularView<Upper>() = m2.transpose() + m2; m3 = m2.transpose() + m2; VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1); // test overloaded operator= m1.setZero(); m1.template triangularView<Lower>() = m2.transpose() + m2; VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1); m1 = MatrixType::Random(rows, cols); for (int i=0; i<rows; ++i) while (ei_abs2(m1(i,i))<1e-1) m1(i,i) = ei_random<Scalar>(); Transpose<MatrixType> trm4(m4); // test back and forward subsitution with a vector as the rhs m3 = m1.template triangularView<Upper>(); VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps)); m3 = m1.template triangularView<Lower>(); VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps)); m3 = m1.template triangularView<Upper>(); VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps)); m3 = m1.template triangularView<Lower>(); VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps)); // test back and forward subsitution with a matrix as the rhs m3 = m1.template triangularView<Upper>(); VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps)); m3 = m1.template triangularView<Lower>(); VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps)); m3 = m1.template triangularView<Upper>(); VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps)); m3 = m1.template triangularView<Lower>(); VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps)); // check M * inv(L) using in place API m4 = m3; m3.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4); VERIFY(m4.cwiseAbs().isIdentity(test_precision<RealScalar>())); // check M * inv(U) using in place API m3 = m1.template triangularView<Upper>(); m4 = m3; m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4); VERIFY(m4.cwiseAbs().isIdentity(test_precision<RealScalar>())); // check solve with unit diagonal m3 = m1.template triangularView<UnitUpper>(); VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps)); // VERIFY(( m1.template triangularView<Upper>() // * m2.template triangularView<Upper>()).isUpperTriangular()); // test swap m1.setOnes(); m2.setZero(); m2.template triangularView<Upper>().swap(m1); m3.setZero(); m3.template triangularView<Upper>().setOnes(); VERIFY_IS_APPROX(m2,m3); }