fdaPDE-deprecated: Deprecated Functions

Description Usage Arguments Value

Description

These functions are Deprecated in this release of fdaPDE, they will be marked as Defunct and removed in a future version.

Usage

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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, ...)

Arguments

FEMbasis

A FEMbasis object describing the Finite Element basis, as created by create.FEM.basis.

locations

A #observations-by-2 matrix where each row specifies the spatial coordinates of the corresponding observations in the vector observations.

observations

A #observations vector with the observed data values over the domain. The locations of the observations can be specified with the locations argument. Otherwise if only the vector of observations is given, these are consider to be located in the corresponding node in the table nodes of the mesh. In this last case, an NA value in the observations vector indicates that there is no observation associated to the corresponding node.

lambda

A scalar or vector of smoothing parameters.

covariates

A #observations-by-#covariates matrix where each row represents the covariates associated with the corresponding observed data value in observations.

GCV

Boolean. If TRUE the following quantities are computed: the trace of the smoothing matrix, the estimated error standard deviation, and the Generalized Cross Validation criterion, for each value of the smoothing parameter specified in lambda.

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 FEM object to be evaluated

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 #nodes-by-2 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 #segments-by-2 matrix. Each row contains the row's indices in nodes of the vertices where the segment starts from and ends to. Segments are edges that are not splitted during the triangulation process. These are for instance used to define the boundaries of the domain. If this is input is NULL, it generates a triangulation over the convex hull of the points specified in nodes.

holes

A #holes-by-2 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 #triangles-by-3 (when order = 1) or #triangles-by-6 (when order = 2) matrix. This option is used when a triangulation is already available. It specifies the triangles giving the row's indices in nodes of the triangles' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as described at
https://www.cs.cmu.edu/~quake/triangle.highorder.html. In this case the function create.MESH.2D is used to produce a complete MESH2D object.

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 order = 1.

verbosity

This can be '0', '1' or '2'. It indicates the level of verbosity in the triangulation process. When verbosity = 0 no message is returned during the triangulation. When verbosity = 2 the triangulation process is described step by step by displayed messages. Default is verbosity = 0.

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 create.Mesh.2D or refine.Mesh.2D.

...

Arguments representing graphical options to be passed to par.

Value

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:

fit.FEM

A FEM object that represents the fitted spatial field.

PDEmisfit.FEM

A FEM object that represents the Laplacian of the estimated spatial field.

beta

If covariates is not NULL, a vector of length #covariates with the regression coefficients associated with each covariate.

edf

If GCV is TRUE, a scalar or vector with the trace of the smoothing matrix for each value of the smoothing parameter specified in lambda.

stderr

If GCV is TRUE, a scalar or vector with the estimate of the standard deviation of the error for each value of the smoothing parameter specified in lambda.

GCV

If GCV is TRUE, a scalar or vector with the value of the GCV criterion for each value of the smoothing parameter specified in lambda.

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:

nodes

A #nodes-by-2 matrix containing the x and y coordinates of the mesh nodes.

nodesmarkers

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

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.

triangles

A #triangles-by-3 (when order = 1) or #triangles-by-6 (when order = 2) matrix. This option is used when a triangulation is already available. It specifies the triangles giving the indices in nodes of the triangles' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as described at
https://www.cs.cmu.edu/~quake/triangle.highorder.html.

segmentsmarker

A vector of length #segments with entries either '1' or '0'. An entry '1' indicates that the corresponding element in segments is a boundary segment; an entry '0' indicates that the corresponding segment is not a boundary segment.

edges

A #edges-by-2 matrix containing all the edges of the triangles in the output triangulation. Each row contains the row's indices in nodes, indicating the nodes where the edge starts from and ends to.

edgesmarkers

A vector of lenght #edges with entries either '1' or '0'. An entry '1' indicates that the corresponding element in edge is a boundary edge; an entry '0' indicates that the corresponding edge is not a boundary edge.

neighbors

A #triangles-by-3 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.

holes

A #holes-by-2 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.

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 order = 1.

A MESH2D object representing the refined triangular mesh, with the following output:

nodes

A #nodes-by-2 matrix containing the x and y coordinates of the mesh nodes.

nodesmarkers

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

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.

triangles

A #triangles-by-3 (when order = 1) or #triangles-by-6 (when order = 2) matrix. This option is used when a triangulation is already available. It specifies the triangles giving the row's indices in nodes of the triangles' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as described at
https://www.cs.cmu.edu/~quake/triangle.highorder.html.

edges

A #edges-by-2 matrix. Each row contains the row's indices of the nodes where the edge starts from and ends to.

edgesmarkers

A vector of lenght #edges with entries either '1' or '0'. An entry '1' indicates that the corresponding element in edge is a boundary edge; an entry '0' indicates that the corresponding edge is not a boundary edge.

neighbors

A #triangles-by-3 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.

holes

A #holes-by-2 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.

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 order = 1.


fdaPDE documentation built on July 2, 2020, 2:22 a.m.