eval.FEM.time {fdaPDE}

Evaluate a FEM.time object at a set of point locations

Description

It evaluates a FEM.time object at the specified set of locations or regions. If space.time.locations is provided locations, incidence_matrix and time.instants must be NULL. Otherwise time.instants and one of locations and incidence_matrix must be given. In this case the evaluation is perform on the tensor grid time.instants-by-locations (or time.instants-by-areal domains).

Usage

eval.FEM.time(FEM.time, locations = NULL, time.instants = NULL, 
                     space.time.locations = NULL, incidence_matrix = NULL, lambdaS = 1, 
                     lambdaT = 1, search = "tree", bary.locations = NULL)

Arguments

FEM.time

A FEM.time object to be evaluated.

locations

A 2-columns (in case of planar mesh) or 3-columns(in case of 2D manifold in a 3D space or a 3D volume) matrix with the spatial locations where the FEM.time object should be evaluated.

time.instants

A vector with the time instants where the FEM.time object should be evaluated.

space.time.locations

A 3-columns (in case of planar mesh) or 4-columns(in case of 2D manifold in a 3D space or a 3D volume) matrix with the time instants and spatial locations where the FEM.time object should be evaluated. The first column is for the time instants. If given, locations, incidence_matrix and time.instants must be NULL.

incidence_matrix

In case of areal data, the #regions x #elements incidence matrix defining the regions.

lambdaS

The index of the lambdaS choosen for the evaluation.

lambdaT

The index of the lambdaT choosen for the evaluation.

search

a flag to decide the search algorithm type (tree or naive or walking search algorithm).

bary.locations

A list with three vectors: locations, location points which are same as the given locations options. (checks whether both locations are the same); element ids, a vector of element id of the points from the mesh where they are located; barycenters, a vector of barycenter of points from the located element.

Value

A matrix of numeric evaluations of the FEM.time object. Each row indicates the location where the evaluation has been taken, the column indicates the function evaluated.

References

Devillers, O. et al. 2001. Walking in a Triangulation, Proceedings of the Seventeenth Annual Symposium on Computational Geometry

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
time = 1:5
coeff = rep(fs.test(mesh$nodes[,1], mesh$nodes[,2]),5)*time
## Create the FEM.time object
FEM_time_function = FEM.time(coeff=coeff, time_mesh=1:5, FEMbasis=FEMbasis, FLAG_PARABOLIC=TRUE)

evaluations = eval.FEM.time(FEM_time_function, locations = matrix(c(-0.92,0), ncol=2), 
                            time.instants = time)