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SpatialfdaR (version 1.0.0)

Spatial Functional Data Analysis

Description

Finite element modeling (FEM) uses meshes of triangles to define surfaces. A surface within a triangle may be either linear or quadratic. In the order one case each node in the mesh is associated with a basis function and the basis is called the order one finite element basis. In the order two case each edge mid-point is also associated with a basis function. Functions are provided for smoothing, density function estimation point evaluation and plotting results. Two papers illustrating the finite element data analysis are Sangalli, L.M., Ramsay, J.O., Ramsay, T.O. (2013) and Bernardi, M.S, Carey, M., Ramsay, J. O., Sangalli, L. (2018). Modelling spatial anisotropy via regression with partial differential regularization Journal of Multivariate Analysis, 167, 15-30.

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Version

Install

install.packages('SpatialfdaR')

Monthly Downloads

24

Version

1.0.0

License

GPL (>= 2)

Maintainer

James Ramsay

Last Published

October 11th, 2022

Functions in SpatialfdaR (1.0.0)

create.FEM.basis

Create a FEM Basis with Triangular Finite Element Basis Functions
randomFEMpts

Generate Random Locations in a Mesh with a Specified Density
eval.FEM.basis

Values of a Finite Element Functional Data Object
makenodes

Compute the matrix nodes containing all the nodes in the mesh.
tricoefCal

Compute the coefficient matrix required to test of a point is inside a triangle.
plotFEM.fd

Plots an FEM functional data object.
plotFEM.mesh

Plot a finite element mesh.
stiff.FEM

Compute the stiffness matrix for a finite element basis.
triquad

Set up Gaussian quadrature points and weights for a triangular domain.
triDensity

Compute the probabilities that a random location will be within one of the triangles of an FEM mesh.
squareMesh_RL

Generate a Triangulation of a Square.
mass.FEM

Compute the mass matrix for a finite element basis.
smooth.FEM.basis

Construct a functional data object by smoothing spatial data distributed over a region with a complicated boundary using a roughness penalty.
squareMesh

Generate a Triangulation of a Square.
smooth.FEM.density

Compute a smooth FEM density surface of a triangulated region.
insideIndex

Index of the triangle containing a point.
eval.FEM.fd

Evaluate a functional data object with an FEM basis.
FEMdensity

Evaluate the function value and gradient for a penalized likelihood estimate of spatial density.
MeuseData

Objects Defining Meuse River Mesh