Description Usage Arguments Value
These functions are Deprecated in this release of fdaPDE, they will be marked as Defunct and removed in a future version.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  R_mass(FEMbasis)
R_stiff(FEMbasis)
R_smooth.FEM.basis(
locations,
observations,
FEMbasis,
lambda,
covariates = NULL,
GCV
)
R_eval.FEM.basis(FEMbasis, locations, nderivs = matrix(0, 1, 2))
R_eval.FEM(FEM, locations)
smooth.FEM.basis(
locations = NULL,
observations,
FEMbasis,
lambda,
covariates = NULL,
BC = NULL,
GCV = FALSE,
CPP_CODE = TRUE
)
smooth.FEM.PDE.basis(
locations = NULL,
observations,
FEMbasis,
lambda,
PDE_parameters,
covariates = NULL,
BC = NULL,
GCV = FALSE,
CPP_CODE = TRUE
)
smooth.FEM.PDE.sv.basis(
locations = NULL,
observations,
FEMbasis,
lambda,
PDE_parameters,
covariates = NULL,
BC = NULL,
GCV = FALSE,
CPP_CODE = TRUE
)
create.MESH.2D(nodes, nodesattributes = NA, segments = NA, holes = NA,
triangles = NA, order = 1, verbosity = 0)
refine.MESH.2D(mesh, minimum_angle, maximum_area, delaunay, verbosity)
## S3 method for class 'MESH2D'
plot(x, ...)

FEMbasis 
A F 
locations 
A #observationsby2 matrix where each row specifies the spatial coordinates of the corresponding observations in the vector 
observations 
A #observations vector with the observed data values over the domain. The locations of the observations can be specified with the 
lambda 
A scalar or vector of smoothing parameters. 
covariates 
A #observationsby#covariates matrix where each row represents the covariates associated with the corresponding observed data value in 
GCV 
Boolean. If 
nderivs 
A vector of lenght 2 specifying the order of the partial derivatives of the bases to be evaluated. The vectors' entries can be 0,1 or 2, where 0 indicates that only the basis functions, and not their derivatives, should be evaluated. 
FEM 
A 
BC 
vector with the Dirichlet boundary conditions to be applied. 
CPP_CODE 
Boolean, indicates whether C++ implementation ha sto be used or not. 
PDE_parameters 
A list specifying the parameters of the elliptic PDE in the regularizing term. 
nodes 
A #nodesby2 matrix containing the x and y coordinates of the mesh nodes. 
nodesattributes 
A matrix with #nodes rows containing nodes' attributes. These are passed unchanged to the output. If a node is added during the triangulation process or mesh refinement, its attributes are computed by linear interpolation using the attributes of neighboring nodes. This functionality is for instance used to compute the value of a Dirichlet boundary condition at boundary nodes added during the triangulation process. 
segments 
A #segmentsby2 matrix. Each row contains the row's indices in 
holes 
A #holesby2 matrix containing the x and y coordinates of a point internal to each hole of the mesh. These points are used to carve holes in the triangulation, when the domain has holes. 
triangles 
A #trianglesby3 (when 
order 
Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints).
These are
respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements. Default is 
verbosity 
This can be '0', '1' or '2'. It indicates the level of verbosity in the triangulation process. When 
mesh 
A MESH2D object representing the triangular mesh, created by create.MESH.2D. 
minimum_angle 
A scalar specifying a minimun value for the triangles angles. 
maximum_area 
A scalar specifying a maximum value for the triangles areas. 
delaunay 
A boolean parameter indicating whether or not the output mesh should satisfy the Delaunay condition. 
x 
A MESH2D object defining the triangular mesh, as generated by 
... 
Arguments representing graphical options to be passed to par. 
A square matrix with the integrals of all the basis' functions pairwise products. The dimension of the matrix is equal to the number of the nodes of the mesh.
A square matrix with the integrals of all the basis functions' gradients pairwise dot products. The dimension of the matrix is equal to the number of the nodes of the mesh.
A list with the following quantities:

A 

A 

If covariates is not 

If GCV is 

If GCV is 

If GCV is 
A matrix of basis function values. Each row indicates the location where the evaluation has been taken, the column indicates the basis function evaluated
A matrix of numeric evaluations of the FEM
object. Each row indicates the location where the evaluation has been taken, the column indicates the
function evaluated.
An object of the class MESH2D with the following output:

A #nodesby2 matrix containing the x and y coordinates of the mesh nodes. 

A vector of length #nodes, with entries either '1' or '0'. An entry '1' indicates that the corresponding node is a boundary node; an entry '0' indicates that the corresponding node is not a boundary node. 

nodesattributes A matrix with #nodes rows containing nodes' attributes. These are passed unchanged to the output. If a node is added during the triangulation process or mesh refinement, its attributes are computed by linear interpolation using the attributes of neighboring nodes. This functionality is for instance used to compute the value of a Dirichlet boundary condition at boundary nodes added during the triangulation process. 

A #trianglesby3 (when 

A vector of length #segments with entries either '1' or '0'. An entry '1' indicates that the corresponding element in 

A #edgesby2 matrix containing all the edges of the triangles in the output triangulation. Each row contains the row's indices in 

A vector of lenght #edges with entries either '1' or '0'. An entry '1' indicates that the corresponding element in 

A #trianglesby3 matrix. Each row contains the indices of the three neighbouring triangles. An entry '1' indicates that one edge of the triangle is a boundary edge. 

A #holesby2 matrix containing the x and y coordinates of a point internal to each hole of the mesh. These points are used to carve holes in the triangulation, when the domain has holes. 

Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints).
These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements. Default is 
A MESH2D object representing the refined triangular mesh, with the following output:

A #nodesby2 matrix containing the x and y coordinates of the mesh nodes. 

A vector of length #nodes, with entries either '1' or '0'. An entry '1' indicates that the corresponding node is a boundary node; an entry '0' indicates that the corresponding node is not a boundary node. 

nodesattributes A matrix with #nodes rows containing nodes' attributes. These are passed unchanged to the output. If a node is added during the triangulation process or mesh refinement, its attributes are computed by linear interpolation using the attributes of neighboring nodes. This functionality is for instance used to compute the value of a Dirichlet boundary condition at boundary nodes added during the triangulation process. 

A #trianglesby3 (when 

A #edgesby2 matrix. Each row contains the row's indices of the nodes where the edge starts from and ends to. 

A vector of lenght #edges with entries either '1' or '0'. An entry '1' indicates that the corresponding element in 

A #trianglesby3 matrix. Each row contains the indices of the three neighbouring triangles. An entry '1' indicates that one edge of the triangle is a boundary edge. 

A #holesby2 matrix containing the x and y coordinates of a point internal to each hole of the mesh. These points are used to carve holes in the triangulation, when the domain has holes. 

Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints).
These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements. Default is 
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