eval.FEM.fd {SpatialfdaR}

Evaluate a functional data object with an FEM basis.

Description

A set of points is supplied, and the height of the surface is evaluated at these points.'

Usage

eval.FEM.fd(pts, fdobj, nderivs=rep(0,2))

Arguments

pts

A two column matrix of pts within a triangular mesh.

fdobj

A functional data object with an FEM basis.

“1

nderivs

A vector of length 2 containing derivative orders with respect to the X and Y coordinates of the triangular mesh. The derivative orders are restricted to 0, 1 or 2, and 2 can only be used for a quadratic basis system. The default is both orders being 0.

Value

A matrix with number of rows equal to the number of rows of pts containing the values of of one or more surfaces at these points.

Author(s)

Jim Ramsay

References

Sangalli, Laura M., Ramsay, James O., Ramsay, Timothy O. (2013), Spatial spline regression models, Journal of the Royal Statistical Society, Series B, 75, 681-703.

See Also

eval.FEM.basis

Examples

#  ----------------------------------------------------------------------------
#  Example 1:  smoothing data over a circular region
#  ----------------------------------------------------------------------------
#  Set up a FEM object with a approximatedly circular boundary with 12 sides,
#  and two rings of 12 points plus a point at the centre.
angle = seq(0,11*pi/6,len=12)
#  define the 24 point locations
rad = 2
ctr = c(0,0)
pts  = matrix(0,25,2);
pts[ 1:12,1] = rad*cos(angle)   + ctr[1]
pts[ 1:12,2] = rad*sin(angle)   + ctr[2]
pts[13:24,1] = rad*cos(angle)/2 + ctr[1]
pts[13:24,2] = rad*sin(angle)/2 + ctr[2]
#  define the edge indices
edg <- matrix(0,12,2)
for (i in 1:11) {
  edg[i,1] <- i
  edg[i,2] <- i+1
}
edg[12,] <- c(12,1)
#  use delaunay triangulation to define the triangles
tri = delaunayn(pts)
plotFEM.mesh(pts, tri, shift = 0.02)
title("A 25-point curcular mesh")
#  Create an order 1 basis
hexFEMbasis <- create.FEM.basis(pts, edg, tri, 1)
#  locations of data
obspts <- pts
npts <- dim(obspts)[1]
points(obspts[,1], obspts[,2], col=2, cex=2, lwd=2)
hexfd = fd(matrix(1-c(obspts[,1]^2+obspts[,2]^2),npts,1),hexFEMbasis)
#  heights of a hemisphere at these locations
hexhgts <- round(eval.FEM.fd(obspts,hexfd),2)