quadform_inv {sparsediscrim}

Quadratic Form of the inverse of a matrix and a vector

Description

We compute the quadratic form of a vector and the inverse of a matrix in an efficient manner. Let x be a real vector of length p, and let A be a p x p nonsingular matrix. Then, we compute the quadratic form q = x' A^{-1} x.

Usage

quadform_inv(A, x)

Arguments

A

matrix that is p x p and nonsingular

x

vector of length p

Details

A naive way to compute the quadratic form is to explicitly write ⁠t(x) \%*\% solve(A) \%*\% x⁠, but for large p, this operation is inefficient. We provide a more efficient method below.

Note that we have adapted the code from: https://stat.ethz.ch/pipermail/r-help/2005-November/081940.html

Value

scalar value