Filtered Lanczos Algorithm for Eigenvalues / Eigenvectors of a Symmetric Matrix

Classes
struct	FilteredLanczosOptions
	An instance of this class, taken by FilteredLanczosEigenSolver(), is a collection of options for the filtered Lanczos procedure to solve symmetric eigenvalue problems. More...
struct	FilteredLanczosInfo
	FilteredLanczosEigenSolver() returns an instance of this class which gives the information of the filtered Lanczos procedure. More...

Functions
FilteredLanczosInfo	FilteredLanczosEigenSolver (Vector &eigVal, Matrix &eigVec, const SparseMatrix &S, Vector &frame, mkIndex polyDegree, mkIndex baseDegree, FilteredLanczosOptions &opts)
	This routine computes the eigenvalues in the requested window and the corresponding eigenvectors. More...

Detailed Description

Function Documentation

FilteredLanczosEigenSolver()

FilteredLanczosInfo FilteredLanczosEigenSolver	(	Vector &	eigVal,
		Matrix &	eigVec,
		const SparseMatrix &	S,
		Vector &	frame,
		mkIndex	polyDegree,
		mkIndex	baseDegree,
		FilteredLanczosOptions &	opts
	)

This routine computes the eigenvalues in the requested window and the corresponding eigenvectors.

• The window can contain the largest or smallest eigenvalues, in which case the requested are the extreme eigenvalues.
• The window can also be well inside the interval of the spectrum, in which case it is often referred to as an interior eigenvalue problem.

Parameters

eigVal	is a vector which contains the computed eigenvalues (if opts.wantEigVal==true).
eigVec	is a matrix whose columns are computed eigenvectors. More precisely, eigVec(:,j) is the eigenvector corresponding to the eigenvalue eigVal(j).
S	is the sparse matrix whose eigenvalues / eigenvectors are to be sought.
frame	is a vector of 2 or 4 elements: If frame consists of 2 elements, then [frame(1),frame(2)] is the window in which the eigenvalues are sought. If frame consists of 4 elements, then [frame(2),frame(3)] is the window in which the eigenvalues are sought, and [frame(1),frame(4)] is the interval which (tightly) contains all eigenvalues. In the former case, an interval which contains (tightly) all eigenvalues is not given, and will be determined by a standard Lanczos procedure. See also FilteredLanczosOptions::numIterForEigenRange.
polyDegree	is the degree of s(z), with z*s(z) the polynomial filter.
baseDegree	is the left-and-right degree of the base filter for each interval.
opts	is a collection of options for the filtered Lanczos procedure.

Returns

An instance of class FilteredLanczosInfo which gives the information of the filtered Lanczos procedure.