Evaluate a quadratic form using a Cholesky factor

Computes t(v) %*% solve(X) %*% v (for a vector v) or t(V) %*% solve(X) %*% V (for a matrix V) efficiently via the Cholesky factor of X, without forming the inverse.

Usage

quad_form(factor, v)

Arguments

factor

An amChol object from chol_factor.

v

Numeric vector or matrix. For a vector, the result is a scalar; for a matrix with p columns, the result is a p x p matrix.

Value

Scalar double (when v is a vector) or numeric matrix of dimensions ncol(v) x ncol(v) containing the quadratic form.

Examples

m <- crossprod(matrix(rnorm(16), 4, 4)) + diag(4)
A <- adgeMatrix(m)
fac <- chol_factor(A)
v <- rnorm(4)
quad_form(fac, v)
#> [1] 1.776342