frobenius_piece: Frobenius Norm of a rank-3 Matrix

In TMasak/surfcov: Random Surfaces' Covariance Estimation beyond Separability

Frobenius Norm of a rank-3 Matrix

Description

Calculates the Frobenius norm of a single sub-matrix of the difference of the Van Loan's permutations of a separable-plus-banded covariance, which must be at most rank 3, with left factors a1, b1 and 1, and right factors a2, b2, 1. Gram-Schmidt orthogonalization can be used to calculate the Frobenius norm of such a matrix of size K x K in only 3*K operations, where K is the dimension of the matrix.

Usage

frobenius_piece(a1, b1, a2, b2, beta)

Arguments

a1	left singular vector of the minuend
b1	right singular vector of the minuend
a2	left singular vector of the subtrahend
b2	left singular vector of the minuend
beta	corresponding to the constant matrix 1 otimes 1

Value

a number, the Frobenius norm

Examples

a1 <- runif(5)
b1 <- runif(10)
a2 <- runif(5)
b2 <- runif(10)
beta <- runif(1)
frobenius_piece(a1,b1,a2,b2,beta)

TMasak/surfcov documentation built on April 25, 2022, 12:15 a.m.