igl::spectra Namespace Reference

Functions
template<typename EigsScalar , typename DerivedU , typename DerivedS , typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>>>
bool	eigs (const Eigen::SparseMatrix< EigsScalar > &A, const Eigen::SparseMatrix< EigsScalar > &B, const int k, const igl::EigsType type, Eigen::PlainObjectBase< DerivedU > &U, Eigen::PlainObjectBase< DerivedS > &S)
	Act like MATLAB's eigs function.
template<typename EigsScalar , typename DerivedU , typename DerivedS , typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>>>
bool	eigs (const Eigen::SparseMatrix< EigsScalar > &A, const Eigen::SparseMatrix< EigsScalar > &B, const int k, const EigsScalar sigma, Eigen::PlainObjectBase< DerivedU > &U, Eigen::PlainObjectBase< DerivedS > &S)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
template<typename DerivedV , typename DerivedF , typename DerivedV_uv >
bool	lscm (const Eigen::MatrixBase< DerivedV > &V, const Eigen::MatrixBase< DerivedF > &F, Eigen::PlainObjectBase< DerivedV_uv > &V_uv)
	Compute a free-boundary least-squares conformal map parametrization.

Function Documentation

eigs() [1/2]

template<typename EigsScalar , typename DerivedU , typename DerivedS , typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>>>

bool igl::spectra::eigs	(	const Eigen::SparseMatrix< EigsScalar > &	A,
		const Eigen::SparseMatrix< EigsScalar > &	B,
		const int	k,
		const igl::EigsType	type,
		Eigen::PlainObjectBase< DerivedU > &	U,
		Eigen::PlainObjectBase< DerivedS > &	S
	)

Act like MATLAB's eigs function.

Compute the first/last k eigen pairs of the generalized eigen value problem:

 A u = s B u

Solutions are approximate and sorted.

Ideally one should use ARPACK and the Eigen unsupported ARPACK module. This implementation does simple, naive power iterations.

Parameters

[in]	A	#A by #A symmetric matrix
[in]	B	#A by #A symmetric positive-definite matrix
[in]	k	number of eigen pairs to compute
[in]	type	whether to extract from the high or low end
[out]	sU	#A by k list of sorted eigen vectors (descending)
[out]	sS	k list of sorted eigen values (descending)

eigs() [2/2]

template<typename EigsScalar , typename DerivedU , typename DerivedS , typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>>>

bool igl::spectra::eigs	(	const Eigen::SparseMatrix< EigsScalar > &	A,
		const Eigen::SparseMatrix< EigsScalar > &	B,
		const int	k,
		const EigsScalar	sigma,
		Eigen::PlainObjectBase< DerivedU > &	U,
		Eigen::PlainObjectBase< DerivedS > &	S
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

[in]

sigma

shift to apply to A, as in A ← A + sigma B

lscm()

template<typename DerivedV , typename DerivedF , typename DerivedV_uv >

bool igl::spectra::lscm	(	const Eigen::MatrixBase< DerivedV > &	V,
		const Eigen::MatrixBase< DerivedF > &	F,
		Eigen::PlainObjectBase< DerivedV_uv > &	V_uv
	)

Compute a free-boundary least-squares conformal map parametrization.

Equivalently derived in "Intrinsic Parameterizations of Surface Meshes" [Desbrun et al. 2002] and "Least Squares Conformal Maps for Automatic Texture Atlas Generation" [Lévy et al. 2002], though this implementation follows the derivation in: "Spectral Conformal Parameterization" [Mullen et al. 2008] Free boundary version. "Spectral Conformal Parameterization" using Eigen decomposition. Assumes mesh is a single connected component topologically equivalent to a chunk of the plane.

Parameters

[in]	V	#V by 3 list of mesh vertex positions
[in]	F	#F by 3 list of mesh faces (must be triangles)
[out]	UV	#V by 2 list of 2D mesh vertex positions in UV space

Returns

true only on solver success.