distanceMatrix: Calculate generalised distances

In GPFDA: Gaussian Process for Functional Data Analysis

Calculate generalised distances

Description

Calculate the generalised distance between vectors t and t' using an anisotropy matrix A.

• distMat and distMatSq calculate:

  [(t - t')^{p/2}]^T A (t - t')^{p/2}

• distMatLinear and distMatLinearSq calculate:

  t^T A t'

Usage

distMat(input, inputNew, A, power)

distMatSq(input, A, power)

distMatLinear(input, inputNew, A)

distMatLinearSq(input, A)

Arguments

input	Vector of the input coordinate t
inputNew	Vector of the input coordinate t'
A	Anisotropy matrix A
power	Power value p

Details

The distMatSq and distMatLinearSq functions are used when input vectors t and t' are identical, returning a symmetric matrix.

When distMat and distMatSq functions are used in powered exponential kernels, power=1 gives the exponential kernel and power=2 gives the squared exponential one.

distMatLinear and distMatLinearSq functions are used in the linear covariance kernel.

Value

A matrix

GPFDA documentation built on Sept. 11, 2023, 1:08 a.m.