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

Value

scalar value

Details

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

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, ])
#> [1] 175.8736

# return matrix
quadForm(ecl, Y[1:2, ])
#>           [,1]      [,2]
#> [1,] 175.87358  11.73997
#> [2,]  11.73997 139.87274