svdcpp: Singular Value Decomposition of a Matrix

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

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:

• d: A vector containing the singular values of X.

• U: A matrix whose columns contain the left singular vectors of X.

• V: A matrix whose columns contain the right singular vectors of X.

Author(s)

Kaifeng Lu, [e-mail]

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)

lrstat documentation built on April 4, 2025, 2:24 a.m.