quadratic_form: Computes quadratic form x' A x

In ForeCA: Forecastable Component Analysis

Description

quadratic_form computes the quadratic form \mathbf{x}' \mathbf{A} \mathbf{x} for an n \times n matrix \mathbf{A} and an n-dimensional vector \mathbf{x}, i.e., a wrapper for t(x) %*% A %*% x.

fill_symmetric and quadratic_form work with real and complex valued matrices/vectors.

fill_hermitian fills up the lower triangular part (NA) of an upper triangular matrix to its Hermitian (symmetric if real matrix) version, such that it satisfies \mathbf{A} = \bar{\mathbf{A}}', where \bar{z} is the complex conjugate of z. If the matrix is real-valued this makes it simply symmetric.

Note that the input matrix must have a real-valued diagonal and NAs in the lower triangular part.

Usage

quadratic_form(mat, vec)

fill_hermitian(mat)

Arguments

mat	numeric; n \times n matrix (real or complex).
vec	numeric; n \times 1 vector (real or complex).

Value

A real/complex value \mathbf{x}' \mathbf{A} \mathbf{x}.

Examples

## Not run: 
 set.seed(1)
 AA <- matrix(1:4, ncol = 2)
 bb <- matrix(rnorm(2))
 t(bb) %*% AA %*% bb
 quadratic_form(AA, bb)

## End(Not run)


AA <- matrix(1:16, ncol = 4)
AA[lower.tri(AA)] <- NA
AA

fill_hermitian(AA)

ForeCA documentation built on July 1, 2020, 7:50 p.m.