It evaluates a FEM object at the specified set of locations or areal regions. The locations are used for pointwise evaluations and incidence matrix for areal evaluations. The locations and the incidence matrix cannot be both NULL or both provided.
A 2-columns (in 2D) or 3-columns (in 2.5D) matrix with the spatial locations where the FEM object should be evaluated.
In case of areal evaluations, the #regions-by-#elements incidence matrix defining the regions where the FEM object should be evaluated.
A vector or a matrix of numeric evaluations of the
FEM object contains multiple finite element functions the output is a matrix, and
each row corresponds to the location (or areal region) where the evaluation has been taken, while each column
corresponds to the function evaluated.
Sangalli, L. M., Ramsay, J. O., & Ramsay, T. O. (2013). Spatial spline regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(4), 681-703.
Azzimonti, L., Sangalli, L. M., Secchi, P., Domanin, M., & Nobile, F. (2015). Blood flow velocity field estimation via spatial regression with PDE penalization. Journal of the American Statistical Association, 110(511), 1057-1071.
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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$nodes[,2]) ## Create the FEM object FEMfunction = FEM(coeff, FEMbasis) ## Evaluate the finite element function in the location (1,0.5) eval.FEM(FEMfunction, locations = matrix(c(1, 0.5), ncol = 2)) ## Evaluate the mean of the finite element function over the fifth triangle of the mesh incidence_matrix = matrix(0, ncol = nrow(mesh$triangles)) incidence_matrix[1,5] = 1 eval.FEM(FEMfunction, incidence_matrix = incidence_matrix)
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