Spatial Functional Data Analysis
Create a FEM Basis with Triangular Finite Element Basis Functions
Values of a Finite Element Functional Data Object
Evaluate a functional data object with an FEM basis.
Evaluate the function value and gradient for a penalized likelihood es...
Index of the triangle containing a point.
Compute the matrix nodes containing all the nodes in the mesh.
Compute the mass matrix for a finite element basis.
Plots an FEM functional data object.
Plot a finite element mesh.
Generate Random Locations in a Mesh with a Specified Density
Construct a functional data object by smoothing spatial data distribut...
Compute a smooth FEM density surface of a triangulated region.
Generate a Triangulation of a Square.
Generate a Triangulation of a Square.
Compute the stiffness matrix for a finite element basis.
Compute the coefficient matrix required to test of a point is inside a...
Compute the probabilities that a random location will be within one of...
Set up Gaussian quadrature points and weights for a triangular domain.
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)<http://www.mox.polimi.it/~sangalli> and Bernardi, M.S, Carey, M., Ramsay, J. O., Sangalli, L. (2018)<http://www.mox.polimi.it/~sangalli>. Modelling spatial anisotropy via regression with partial differential regularization Journal of Multivariate Analysis, 167, 15-30.