fm_basis: Compute mapping matrix between mesh function space and points

Description

Computes the basis mapping matrix between a function space on a mesh, and locations.

Usage

fm_basis(x, ..., full = FALSE)
# S3 method for default
fm_basis(x, ..., full = FALSE)
# S3 method for fm_mesh_1d
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)
# S3 method for fm_mesh_2d
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)
# S3 method for fm_mesh_3d
fm_basis(x, loc, weights = NULL, ..., full = FALSE)
# S3 method for fm_lattice_2d
fm_basis(x, loc, weights = NULL, ..., full = FALSE)
# S3 method for fm_lattice_Nd
fm_basis(x, loc, weights = NULL, ..., full = FALSE)
# S3 method for fm_tensor
fm_basis(x, loc, weights = NULL, ..., full = FALSE)
# S3 method for fm_collect
fm_basis(x, loc, weights = NULL, ..., full = FALSE)
# S3 method for matrix
fm_basis(x, ok = NULL, weights = NULL, ..., full = FALSE)
# S3 method for Matrix
fm_basis(x, ok = NULL, weights = NULL, ..., full = FALSE)
# S3 method for list
fm_basis(x, weights = NULL, ..., full = FALSE)
# S3 method for fm_basis
fm_basis(x, ..., full = FALSE)
# S3 method for fm_evaluator
fm_basis(x, ..., full = FALSE)

Value

A sparseMatrix object (if full = FALSE), or a fm_basis object (if full = TRUE or isTRUE(derivatives)). The fm_basis object contains at least the projection matrix A and logical vector ok; If x_j

denotes the latent basis coefficient for basis function j, the field is defined as u(loc_i)=sum_j A_ij x_j for all i where ok[i] is TRUE, and u(loc_i)=0.0 where ok[i] is FALSE.

Arguments

x: An function space object, or other supported object (matrix, Matrix, list)
...: Passed on to submethods
full: logical; if TRUE, return a fm_basis object, containing at least a projection matrix A and logical vector ok indicating which evaluations are valid. If FALSE, return only the projection matrix A. Default is FALSE.
loc: A location/value information object (numeric, matrix, sf, fm_bary, etc, depending on the class of x)
weights: Optional weight vector to apply (from the left, one weight for each row of the basis matrix)
derivatives: If non-NULL and logical, include derivative matrices in the output. Forces full = TRUE.
ok: numerical of length NROW(x), indicating which rows of x are valid/successful basis evaluations. If NULL, inferred as rep(TRUE, NROW(x)).

Methods (by class)

fm_basis(fm_mesh_1d): If derivatives=TRUE, the fm_basis object contains additional derivative weight matrices, d1A and d2A, du/dx(loc_i)=sum_j dx_ij w_i.
fm_basis(fm_mesh_2d): If derivatives=TRUE, additional derivative weight matrices are included in the full=TRUE output: Derivative weight matrices dx, dy, dz; du/dx(loc_i)=sum_j dx_ij w_i, etc.
fm_basis(fm_mesh_3d): fm_mesh_3d basis functions.
fm_basis(fm_lattice_2d): fm_lattice_2d bilinear basis functions.
fm_basis(fm_lattice_Nd): fm_lattice_Nd multilinear basis functions.
fm_basis(fm_tensor): Evaluates a basis matrix for a fm_tensor function space.
fm_basis(fm_collect): Evaluates a basis matrix for a fm_collect function space. The loc argument must be a list or tibble with elements loc (the locations) and index (the indices into the function space collection).
fm_basis(matrix): Creates a new fm_basis object with elements A and ok, from a pre-evaluated basis matrix, including optional additional elements in the ... arguments. If a ok is NULL, it is inferred as rep(TRUE, NROW(x)), indicating that all rows correspond to successful basis evaluations. If full = FALSE, returns the matrix unchanged.
fm_basis(Matrix): Creates a new fm_basis object with elements A and ok, from a pre-evaluated basis matrix, including optional additional elements in the ... arguments. If a ok is NULL, it is inferred as rep(TRUE, NROW(x)), indicating that all rows correspond to successful basis evaluations. If full = FALSE, returns the matrix unchanged.
fm_basis(list): Creates a new fm_basis object from a plain list containing at least an element A. If an ok element is missing, it is inferred as rep(TRUE, NROW(x$A)). If full = FALSE, extracts the A matrix.
fm_basis(fm_basis): If full is TRUE, returns x unchanged, otherwise returns the A matrix contained in x.
fm_basis(fm_evaluator): Extract fm_basis information from an fm_evaluator object. If full = FALSE, returns the A matrix contained in the fm_basis object.

Examples

Run this code

# Compute basis mapping matrix
dim(fm_basis(fmexample$mesh, fmexample$loc))
print(fm_basis(fmexample$mesh, fmexample$loc, full = TRUE))

# From precomputed `fm_bary` information:
bary <- fm_bary(fmexample$mesh, fmexample$loc)
print(fm_basis(fmexample$mesh, bary, full = TRUE))