Drake
Drake C++ Documentation
quadratic_form.h File Reference
#include <utility>
#include <Eigen/Core>
Include dependency graph for quadratic_form.h:

Namespaces

 drake
 
 drake::math
 

Functions

Eigen::MatrixXd DecomposePSDmatrixIntoXtransposeTimesX (const Eigen::Ref< const Eigen::MatrixXd > &Y, double zero_tol)
 For a symmetric positive semidefinite matrix Y, decompose it into XᵀX, where the number of rows in X equals to the rank of Y. More...
 
std::pair< Eigen::MatrixXd, Eigen::MatrixXd > DecomposePositiveQuadraticForm (const Eigen::Ref< const Eigen::MatrixXd > &Q, const Eigen::Ref< const Eigen::VectorXd > &b, double c, double tol=0)
 Rewrite a quadratic form xᵀQx + bᵀx + c to (Rx+d)ᵀ(Rx+d) where. More...
 
Eigen::MatrixXd BalanceQuadraticForms (const Eigen::Ref< const Eigen::MatrixXd > &S, const Eigen::Ref< const Eigen::MatrixXd > &P)
 Given two quadratic forms, x'Sx > 0 and x'Px, (with P symmetric and full rank), finds a change of variables x = Ty, which simultaneously diagonalizes both forms (as inspired by "balanced truncation" in model-order reduction [1]). More...