quadForm: Evaluate quadratic form

In decorrelate: Decorrelation Projection Scalable to High Dimensional Data

Evaluate quadratic form

Description

Evaluate quadratic form

Usage

quadForm(ecl, A, alpha = -1/2)

Arguments

ecl	estimate of covariance/correlation matrix from eclairs storing U, d_1^2, \lambda and \nu
A	matrix
alpha	default = -1/2. Exponent of eigen-values

Details

Evaluate quadratic form A^T \Sigma^{2\alpha} A

Value

scalar value

Examples

library(Rfast)
n <- 800 # number of samples
p <- 200 # number of features

# create correlation matrix
Sigma <- autocorr.mat(p, .9)

# draw data from correlation matrix Sigma
Y <- rmvnorm(n, rep(0, p), sigma = Sigma * 5.1, seed = 1)

# eclairs decomposition
ecl <- eclairs(Y)

# return scalar
quadForm(ecl, Y[1, ])

# return matrix
quadForm(ecl, Y[1:2, ])

decorrelate documentation built on Aug. 8, 2025, 7:55 p.m.