fs.test: FELSPLINE test function

In fdaPDE: Physics-Informed Spatial and Functional Data Analysis

FELSPLINE test function

Description

Implements a finite area test function based on one proposed by Tim Ramsay (2002) proposed by Simon Wood (2008).

Usage

fs.test(x, y, r0 = 0.1, r = 0.5, l = 3, b = 1, exclude = FALSE)

Arguments

x, y	Points at which to evaluate the test function.
r0	The test domain is a sort of bent sausage. This is the radius of the inner bend.
r	The radius of the curve at the centre of the sausage.
l	The length of an arm of the sausage.
b	The rate at which the function increases per unit increase in distance along the centre line of the sausage.
exclude	Should exterior points be set to NA?

Value

Returns function evaluations, or NAs for points outside the horseshoe domain.

References

• Ramsay, T. 2002. Spline smoothing over difficult regions. J.R.Statist. Soc. B 64(2):307-319

• Wood, S. N., Bravington, M. V., & Hedley, S. L. (2008). Soap film smoothing. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(5), 931-955.

Examples

library(fdaPDE)

## Upload the horseshoe2D data
data(horseshoe2D)
boundary_nodes = horseshoe2D$boundary_nodes
boundary_segments = horseshoe2D$boundary_segments
locations = horseshoe2D$locations

## Create the 2D mesh
mesh = create.mesh.2D(nodes = rbind(boundary_nodes, locations), segments = boundary_segments)
## Create the FEM basis
FEMbasis = create.FEM.basis(mesh)
## Compute the coeff vector evaluating the desired function at the mesh nodes
## In this case we consider the fs.test() function introduced by Wood et al. 2008
coeff = fs.test(mesh$nodes[,1], mesh$nodes[,2], exclude = FALSE)
## Create the FEM object
FEMfunction = FEM(coeff, FEMbasis)
## Plot it
plot(FEMfunction)

fdaPDE documentation built on March 7, 2023, 5:28 p.m.