Eigen::Matrix3d A = Eigen::Matrix3d::Identity();Eigen::Vector3d a(0.5, 3, -0.4);Eigen::Vector3d Aa = A * a;std::cout<<"The multiplication of A * a is "<< std::endl<< Aa << std::endl;Eigen::MatrixXd B = Eigen::MatrixXd::Identity(6, 5);Eigen::VectorXd b(5);b <<1, 4, 6, -2, 0.4;Eigen::VectorXd Bb = B * b;std::cout<<"The multiplication of B * b is "<< std::endl<< Bb << std::endl;
Transpose and inverse:
Eigen::MatrixXd A(3, 2);A << 1, 2,2, 3,3, 4;Eigen::MatrixXd B = A.transpose();// the transpose of A is a 2x3 matrixEigen::MatrixXd C = (B * A).inverse();// computer the inverse of BA, which is a 2x2 matrix
Dot product and cross product:
Eigen::Vector3d v(1, 2, 3);Eigen::Vector3d w(0, 1, 2);double vDotw = v.dot(w); // dot product of two vectorsEigen::Vector3d vCrossw = v.cross(w); // cross product of two vectors
Accessing matrix:
Eigen::MatrixXd A = Eigen::MatrixXd::Random(7, 9);std::cout<<"The element at fourth row and 7the column is "<< A(3, 6) << std::endl;Eigen::MatrixXd B = A.block(1, 2, 3, 3);std::cout<<"Take sub-matrix whose upper left corner is A(1, 2)"<< std::endl<< B << std::endl;Eigen::VectorXd a = A.col(1); // take the second column of AEigen::VectorXd b = B.row(0); // take the first row of BEigen::VectorXd c = a.head(3);// take the first three elements of aEigen::VectorXd d = b.tail(2);// take the last two elements of b
Quaternion:
Eigen::Quaterniond q(2, 0, 1, -3); std::cout << "This quaternion consists of a scalar " << q.w() << " and a vector " << std::endl << q.vec() << std::endl;q.normalize();std::cout << "To represent rotation, we need to normalize it such that its length is " << q.norm() << std::endl;Eigen::Vector3d v(1, 2, -1);Eigen::Quaterniond p;p.w() = 0;p.vec() = v;Eigen::Quaterniond rotatedP = q * p * q.inverse(); Eigen::Vector3d rotatedV = rotatedP.vec();std::cout << "We can now use it to rotate a vector " << std::endl << v << " to " << std::endl << rotatedV << std::endl;Eigen::Matrix3d R = q.toRotationMatrix(); // convert a quaternion to a 3x3 rotation matrixstd::cout << "Compare with the result using an rotation matrix " << std::endl << R * v << std::endl;Eigen::Quaterniond a = Eigen::Quterniond::Identity();Eigen::Quaterniond b = Eigen::Quterniond::Identity();Eigen::Quaterniond c; // Adding two quaternion as two 4x1 vectors is not supported by the EIgen API. That is, c = a + b is not allowed. We have to do this in a hard wayc.w() = a.w() + b.w();c.x() = a.x() + b.x();c.y() = a.y() + b.y();c.z() = a.z() + b.z();
