l2.norm: Calculates L2 norm among functions

In geofd: Spatial Prediction for Function Value Data

Description

Calculates the integral of the squared differences between functions

Usage

  l2.norm(s, datafd, M)

Arguments

s	number of sites where the original dataset was measured
datafd	a functional data object representing a smoothed dataset. See DETAILS below.
M	symmetric matrix defining the roughness penalty for functions expressed in terms of a B-spline or Fourier basis. See DETAILS below.

Details

Roughness penalty matrix

This matrix is the output of one of the following functions: fourierpen y bsplinepen. The used function depends upon the smoothing type which is going to be applied.

When the roughness penalty matrix is being calculated, the following considerations are taked in count:

• The differential operator passed as parameter for both fourierpen and bsplinepen is always zero.

• When the selected smooth method is bsplines, the basis object passed to bsplinepen is the output of the function create.bspline.basis using argvals as the rangeval parameter, nbasis as the number of basis functions parameter and the default order of b-splines, which is four, a cubic spline, as the norder parameter.

• When the selected smooth method is fourier, the basis object is the output of the function fourierpen. The parameters rangeval and nbasis are the same as for create.bspline.basis, and the period parameter as the number of observations on each curve.

Value

The calculated matrix of squared differences between each observation for each measured site. This matrix has two properties:

• Is symmetric.

• It's diagonal is filled with zeros.

See Also

okfd for doing Ordinary Kriging for function-value data, trace.variog for functional empirical trace variogram calculation, fit.tracevariog for fitting a variogram model in the functional scenario.

geofd documentation built on Jan. 29, 2020, 5:08 p.m.