psvd (version 1.0-0)

psvd-package: Eigendecomposition, Singular-Values and the Power Method

Description

The power method is used to compute simultaneously the eigenvectors of a square symmetric matrix. Using the classical method, all eigenvectors are computed. The method used here allows to compute the first r eigenvectors using only matrix multiplications and the Gram-Schmidt orthogonalization algorithm. The relationships between the eigendecomposition factors, on the one hand, and the PCA factors or SVD factors, on the order hand, are used to get SVD or PCA results).

Author

Doulaye Dembele:

Details

Package:	psvd
Type:	Package
Version:	0.1-0
Date:	2024-10-02
License:	GPL (>= 2)

Package psvd has the following functions:

calcSVD():	Given a data matrix X of size (m,n), m >=n, this function allows to compute
	the singular value decomposition.
calcPCA():	Given a data matrix X of size (m,n), m >=n, this function allows to\ compute
	the principal component analysis.
mGS():	Modified Gramf-Schmidt orthogonalization method, R code, internal use.
mGSc():	Modified Gramf-Schmidt orthogonalization method, C code, internal use.
eigenV():	Computation of the eigenvectors matrix for a symmetric square matrix using
	the power method, R Code, internal use.
eigenVc():	Computation of the eigenvectors matrix for a symmetric square matrix using
	the power method, C Code, internal use.

References

Dembele D. (2024), Manuscript in preparation

Examples

data(iris)
X <- as.matrix(iris[,1:4])
rownames(X) <- iris[,5]
res <- calcSVD(X, r=4)
res$d
res$v
res$iter