DNDS::HardEigen Namespace Reference

Functions
real	EigenLeastSquareInverse (const Eigen::MatrixXd &A, Eigen::MatrixXd &AI, real svdTol=0)
	Moore-Penrose pseudoinverse via SVD, dropping singular values below svdTol (relative to the largest). Returns the largest / smallest ratio (condition number).
real	EigenLeastSquareInverse_Filtered (const Eigen::MatrixXd &A, Eigen::MatrixXd &AI, real svdTol=0, int mode=0)
	Pseudoinverse with a choice of singular-value filter.
Eigen::Matrix3d	Eigen3x3RealSymEigenDecomposition (const Eigen::Matrix3d &A)
	Analytic eigen-decomposition of a 3x3 real symmetric matrix. Returns the eigenvector matrix (columns = eigenvectors, scaled so that diagonal == eigenvalues).
Eigen::Matrix2d	Eigen2x2RealSymEigenDecomposition (const Eigen::Matrix2d &A)
	Analytic 2x2 analogue of Eigen3x3RealSymEigenDecomposition.
real	Eigen2x2RealSymEigenDecompositionGetCond (const Eigen::Matrix2d &A)
	2x2 analogue of Eigen3x3RealSymEigenDecompositionGetCond.
real	Eigen3x3RealSymEigenDecompositionGetCond (const Eigen::Matrix3d &A)
	Condition number of a 3x3 SPD matrix from its eigenvalues.
real	Eigen3x3RealSymEigenDecompositionGetCond01 (const Eigen::Matrix3d &A)
	Like Eigen3x3RealSymEigenDecompositionGetCond but returns lambda0 / lambda1 only (ignores the smallest eigenvalue).
Eigen::Matrix3d	Eigen3x3RealSymEigenDecompositionNormalized (const Eigen::Matrix3d &A)
	Eigen-decomposition with eigenvector columns normalised to unit length.
Eigen::Matrix2d	Eigen2x2RealSymEigenDecompositionNormalized (const Eigen::Matrix2d &A)
	2x2 analogue of Eigen3x3RealSymEigenDecompositionNormalized.
Eigen::Index	EigenLeastSquareSolve (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, Eigen::MatrixXd &AIB)
	Least-squares solve A * AIB ~= B via a rank-revealing QR-style decomposition; returns the computed rank of A.

Function Documentation

Eigen2x2RealSymEigenDecomposition()

Eigen::Matrix2d DNDS::HardEigen::Eigen2x2RealSymEigenDecomposition

(

const Eigen::Matrix2d &

A

)

Analytic 2x2 analogue of Eigen3x3RealSymEigenDecomposition.

Definition at line 88 of file HardEigen.cpp.

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Eigen2x2RealSymEigenDecompositionGetCond()

real DNDS::HardEigen::Eigen2x2RealSymEigenDecompositionGetCond

(

const Eigen::Matrix2d &

A

)

2x2 analogue of Eigen3x3RealSymEigenDecompositionGetCond.

Definition at line 104 of file HardEigen.cpp.

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Eigen2x2RealSymEigenDecompositionNormalized()

Eigen::Matrix2d DNDS::HardEigen::Eigen2x2RealSymEigenDecompositionNormalized

(

const Eigen::Matrix2d &

A

)

2x2 analogue of Eigen3x3RealSymEigenDecompositionNormalized.

Definition at line 145 of file HardEigen.cpp.

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Eigen3x3RealSymEigenDecomposition()

Eigen::Matrix3d DNDS::HardEigen::Eigen3x3RealSymEigenDecomposition

(

const Eigen::Matrix3d &

A

)

Analytic eigen-decomposition of a 3x3 real symmetric matrix. Returns the eigenvector matrix (columns = eigenvectors, scaled so that diagonal == eigenvalues).

Definition at line 72 of file HardEigen.cpp.

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Eigen3x3RealSymEigenDecompositionGetCond()

real DNDS::HardEigen::Eigen3x3RealSymEigenDecompositionGetCond

(

const Eigen::Matrix3d &

A

)

Condition number of a 3x3 SPD matrix from its eigenvalues.

Definition at line 112 of file HardEigen.cpp.

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Eigen3x3RealSymEigenDecompositionGetCond01()

real DNDS::HardEigen::Eigen3x3RealSymEigenDecompositionGetCond01

(

const Eigen::Matrix3d &

A

)

Like Eigen3x3RealSymEigenDecompositionGetCond but returns lambda0 / lambda1 only (ignores the smallest eigenvalue).

Definition at line 120 of file HardEigen.cpp.

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Eigen3x3RealSymEigenDecompositionNormalized()

Eigen::Matrix3d DNDS::HardEigen::Eigen3x3RealSymEigenDecompositionNormalized

(

const Eigen::Matrix3d &

A

)

Eigen-decomposition with eigenvector columns normalised to unit length.

Definition at line 129 of file HardEigen.cpp.

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EigenLeastSquareInverse()

real DNDS::HardEigen::EigenLeastSquareInverse	(	const Eigen::MatrixXd &	A,
		Eigen::MatrixXd &	AI,
		real	svdTol
	)

Moore-Penrose pseudoinverse via SVD, dropping singular values below svdTol (relative to the largest). Returns the largest / smallest ratio (condition number).

Todo:

test these eigen solvers !!

Definition at line 13 of file HardEigen.cpp.

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EigenLeastSquareInverse_Filtered()

real DNDS::HardEigen::EigenLeastSquareInverse_Filtered	(	const Eigen::MatrixXd &	A,
		Eigen::MatrixXd &	AI,
		real	svdTol = 0,
		int	mode = 0
	)

Pseudoinverse with a choice of singular-value filter.

Parameters

A	Input matrix.
AI	Output pseudoinverse.
svdTol	Filter tolerance (relative to the largest singular value).
mode	Filter selection: 0: standard "lsqminnorm" – drop smallest singular values below the tolerance (stabilises rank-deficient systems); 1: drop largest singular values above 1/svdTol relative to the smallest (inverse filtering, rarely needed).

Returns

Condition number of A (ratio of largest to smallest post-filter singular value).

note this filtering!

note this filtering!

Definition at line 25 of file HardEigen.cpp.

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EigenLeastSquareSolve()

Eigen::Index DNDS::HardEigen::EigenLeastSquareSolve	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		Eigen::MatrixXd &	AIB
	)

Least-squares solve A * AIB ~= B via a rank-revealing QR-style decomposition; returns the computed rank of A.

Definition at line 160 of file HardEigen.cpp.

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