svdcpp {lrstat}R Documentation

Singular Value Decomposition of a Matrix

Description

Computes the singular-value decomposition of a rectangular matrix.

Usage

svdcpp(X, outtransform = 1L, decreasing = 1L)

Arguments

X

A numeric matrix whose SVD decomposition is to be computed.

outtransform

Whether the orthogonal matrices composing of the left and right singular vectors are to be computed.

decreasing

Whether the singular values should be sorted in decreasing order and the corresponding singular vectors rearranged accordingly.

Details

Given A \in R^{m\times n} (m \geq n), the following algorithm overwrites A with U^T A V = D, where U\in R^{m\times m} is orthogonal, V \in R^{n\times n} is orthogonal, and D \in R^{m\times n} is diagonal.

Value

A list with the following components:

Author(s)

Kaifeng Lu, kaifenglu@gmail.com

References

Gene N. Golub and Charles F. Van Loan. Matrix Computations, second edition. Baltimore, Maryland: The John Hopkins University Press, 1989, p.434.

Examples


A <- matrix(c(1,0,0,0, 1,2,0,0, 0,1,3,0, 0,0,1,4), 4, 4)
svdcpp(A)


[Package lrstat version 0.2.15 Index]