R: Eigensolver

fm.eigen

R Documentation

Eigensolver

Description

fm.eigen computes eigenvalues/vectors of a square matrix. fm.cal.residul computes the residual of the eigenvalues.

Usage

fm.eigen(mul, k, n, which = "LM", sym = TRUE, options = NULL,
  env = parent.frame())

fm.cal.residul(mul, values, vectors)

Arguments

`mul`	The function to perform the matrix-vector multiplication.
`k`	Integer. The number of eigenvalues to compute.
`which`	String. Selection criteria.
`sym`	Logical scalar, whether the input matrix is symmetric.
`options`	List. Additional options to the eigensolver.
`env`	The environment in which `mul` will bevaluated.
`values`	The eigenvalues
`vectors`	The eigenvectors The `options` argument specifies what kind of computation to perform. It is a list with the following members, which correspond directly to Anasazi parameters: solver String. The name of the eigensolver to solve the eigenproblems. Currently, it supports three eigensolvers: KrylovSchur, Davidson and LOBPCG. KrylovSchur is the default eigensolver. tol Numeric scalar. Stopping criterion: the relative accuracy of the Ritz value is considered acceptable if its error is less than `tol` times its estimated value. block_size Numeric scalar. The eigensolvers use a block extension of an eigensolver algorithm. The block size determines the number of the vectors that operate together. num_blocks Numeric scalar. The number of blocks to compute eigenpairs.

Details

fm.eigen uses Anasazi package of Trilinos, if Anasazi is compiled into FlashR, or eigs to compute eigenvalues.

The which specify which eigenvalues/vectors to compute, character constant with exactly two characters. Possible values for symmetric input matrices:

"LA"Compute nev largest (algebraic) eigenvalues.
"SA"Compute nev smallest (algebraic) eigenvalues.
"LM"Compute nev largest (in magnitude) eigenvalues.
"SM"Compute nev smallest (in magnitude) eigenvalues.

Value

fm.eigen returns a named list with the following members: values: Numeric vector, the desired eigenvalues. vectors: Numeric matrix, the desired eigenvectors as columns. fm.cal.residul returns the corresponding residuals for the eigenvalues.

Author(s)

Da Zheng <dzheng5@jhu.edu>

Examples

mat <- fm.load.sparse.matrix("./spm123.mat", "./spm123.mat_idx")
res <- fm.eigen(mul, 10, nrow(mat))
fm.cal.residul(mul, res$values, res$vectors)