\(H\) components used in coherence.R

This function calculates the following terms used in coherence calculation.

• \(H_{h,2} = \int_{[-1/2,1/2]^d}h(\boldsymbol{x})^2d\boldsymbol{x}\)

• \(H_{h^2,\underline{\hat\lambda}} = \left(H_{h^2\hat{\lambda}^{(1)},1}, \ldots, H_{h^2\hat{\lambda}^{(m)},1}\right)^\intercal\)

• \(H_{h^2,\underline{\hat{\lambda}}\cdot\underline{\hat{\lambda}}^\intercal} = (H_{h^2\hat{\lambda}^{(i)}\hat{\lambda}^{(j)}})_{1\leq i,j\leq m}\)

Usage

Hmatrix(sp.est, ppp)

Arguments

sp.est

A list of kernel spectral estimate matrices of ppp calculated by periodogram_smooth().

ppp

Point pattern.

Value

A list containing \(H_{h,2}\), \(H_{h^2,\underline{\hat\lambda}}\), and \(H_{h^2,\underline{\hat{\lambda}}\cdot\underline{\hat{\lambda}}^\intercal}\).