Quadratic Form of the inverse of a matrix and a vector

Source: R/helper.r

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 \(q = x' A^{-1} x\).

quadform_inv(A, x)

Arguments

A

matrix that is p x p and nonsingular
x

vector of length p

Value

scalar value

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: http://tolstoy.newcastle.edu.au/R/help/05/11/14989.html