Tomographer::MathTools::SolveCLyap Namespace Reference

Definitions for solving the Complex Lyapunov Equation. More...

Classes
class	SolveError
	Error while attempting to solve complex Lyapunov/Sylvester equation. More...

Functions
template<bool debug_perform_check = false, typename LoggerType >
void	solve (Eigen::Ref< Eigen::MatrixXcd > X, const Eigen::Ref< const Eigen::MatrixXcd > &A, const Eigen::Ref< const Eigen::MatrixXcd > &C, LoggerType &logger, const double tol=1e-8)
	Solve complex Lyapunov equation of the form A'*X + X*A == C More...

Detailed Description

Definitions for solving the Complex Lyapunov Equation.

See SolveCLyap::solve().

Function Documentation

solve()

template<bool debug_perform_check = false, typename LoggerType >

void Tomographer::MathTools::SolveCLyap::solve	(	Eigen::Ref< Eigen::MatrixXcd >	X,
		const Eigen::Ref< const Eigen::MatrixXcd > &	A,
		const Eigen::Ref< const Eigen::MatrixXcd > &	C,
		LoggerType &	logger,
		const double	tol = 1e-8
	)

Solve complex Lyapunov equation of the form A'*X + X*A == C

Solves the Lyapunov equation "A.adjoint() * X + X * A == C" on the range of A. The matrices A, X and C must be square. A must be Hermitian.

The initial value of X is unimportant, and on output contains the solution of the given equation.

If an error occurs, a SolveError is thrown.

This function requires you to link to the LAPACK library (external symbol used is ztrsyl_).

Note that only complex double type is supported. In the future we might support other complex types, by calling the other LAPACK routines.

If the template parameter debug_perform_check is set to true, then some debugging consistency checks are performed.

Definition at line 130 of file solveclyap.h.