#include <utility>
#include <Eigen/Core>
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| Eigen::MatrixXd | DecomposePSDmatrixIntoXtransposeTimesX (const Eigen::Ref< const Eigen::MatrixXd > &Y, double zero_tol, bool return_empty_if_not_psd=false) |
| | 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...
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| 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...
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| 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...
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