geigen: Generalized eigenvalue decomposition
In derekbeaton/GSVD: The generalized singular value decomposition

Description Usage Arguments Value Author(s) See Also Examples

geigen takes in constraints (W), (usually diagonal matrices, but any positive semi-definite matrix) that are applied to the data (X). Constraints are used for the orthogonality conditions.

1	geigen(X, W, k = 0, tol = sqrt(.Machine$double.eps), symmetric)

`X`	a square, symmetric data matrix to decompose
`W`	Weights – the constraints applied to the matrix and thus the eigen vectors.
`k`	total number of components to return though the full variance will still be returned (see `d_full`). If 0, the full set of components are returned.
`tol`	default is `sqrt(.Machine$double.eps)`. A tolerance level for eliminating effectively zero (small variance), negative, imaginary eigen/singular value components.
`symmetric`	if `X` is symmetric, set as TRUE. See `eigen`.

A list with eight elements:

`d_full`	A vector containing the singular values of X above the tolerance threshold (based on eigenvalues).
`l_full`	A vector containing the eigen values of X above the tolerance threshold (`tol`).
`d`	A vector of length `min(length(d_full), k)` containing the retained singular values of X
`l`	A vector of length `min(length(l_full), k)` containing the retained eigen values of X
`v`	Eigenvectors. Dimensions are `ncol(X)` by k.
`q`	Generalized eigenvectors. Dimensions are `ncol(X)` by k.
`fj`	Component scores. Dimensions are `ncol(X)` by k.

Derek Beaton

tolerance_eigen, gsvd and gplssvd

## (Metric) Multidimensional Scaling
data(wine, package="GSVD")
D <- as.matrix(dist(wine$objective))
masses <- rep(1/nrow(D), nrow(D))
Xi <- diag(nrow(D)) - ( rep(1,nrow(D)) %o% masses )
S <- Xi %*% (-(D^2) / 2) %*% t(Xi)
mds.res_geigen <- geigen(S)

## Principal components analysis: "covariance"
cov_X <- as.matrix(cov(wine$objective))
cov_pca.res_geigen <- geigen(cov_X)

## Principal components analysis: "correlation"
cor_X <- as.matrix(cor(wine$objective))
cor_pca.res_geigen <- geigen(cor_X)