Compute mapping matrix between mesh function space and points

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

Usage

fm_basis(x, ..., full = FALSE)

# Default S3 method
fm_basis(x, ..., full = FALSE)

# S3 method for class 'fm_mesh_1d'
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)

# S3 method for class 'fm_mesh_2d'
fm_basis(x, loc, weights = NULL, derivatives = NULL, ..., full = FALSE)

# S3 method for class 'inla.mesh.1d'
fm_basis(x, ...)

# S3 method for class 'inla.mesh'
fm_basis(x, ...)

# S3 method for class 'fm_evaluator'
fm_basis(x, ..., full = FALSE)

# S3 method for class 'fm_basis'
fm_basis(x, ..., full = FALSE)

# S3 method for class 'fm_tensor'
fm_basis(x, loc, weights = NULL, ..., full = FALSE)

Arguments

x

fm_tensor() object

...

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 (vector, matrix, sf, 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.

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; u(loc_i)=sum_j A_ij w_i

Methods (by class)

• fm_basis(fm_mesh_1d): 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.

See also

fm_raw_basis()

Examples

# Compute basis mapping matrix
str(fm_basis(fmexample$mesh, fmexample$loc))
#> Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   ..@ i       : int [1:30] 1 9 3 7 8 5 0 6 4 2 ...
#>   ..@ p       : int [1:280] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..@ Dim     : int [1:2] 10 279
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:30] 0.3065 0.0477 0.0831 0.6947 0.4188 ...
#>   ..@ factors : list()
print(fm_basis(fmexample$mesh, fmexample$loc), full = TRUE)
#> <S4 Type Object>
#> attr(,"i")
#>  [1] 1 9 3 7 8 5 0 6 4 2 3 1 5 1 0 3 9 5 0 6 6 7 8 2 4 2 4 9 7 8
#> attr(,"p")
#>   [1]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [26]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [51]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [76]  0  0  0  0  0  0  0  0  0  1  2  2  2  3  5  5  5  5  5  5  5  5  6  6  6
#> [101]  6  6  6  7  7  7  7  7  7  7  7  8  9  9 10 10 10 10 10 10 10 10 10 10 10
#> [126] 11 11 11 11 11 12 12 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 15
#> [151] 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 17 17 18 18 19 19 20
#> [176] 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 24 24 25
#> [201] 26 26 26 26 26 26 26 26 26 26 26 26 26 27 28 30 30 30 30 30 30 30 30 30 30
#> [226] 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
#> [251] 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
#> [276] 30 30 30 30 30
#> attr(,"Dim")
#> [1]  10 279
#> attr(,"Dimnames")
#> attr(,"Dimnames")[[1]]
#> NULL
#> 
#> attr(,"Dimnames")[[2]]
#> NULL
#> 
#> attr(,"x")
#>  [1] 0.30649174 0.04765979 0.08314353 0.69474011 0.41877998 0.02530602
#>  [7] 0.03552982 0.33316542 0.02108322 0.21657062 0.58669638 0.13670741
#> [13] 0.41395969 0.55680084 0.89457972 0.33016010 0.91911732 0.56073430
#> [19] 0.06989045 0.36303944 0.30379514 0.27939227 0.37184709 0.48518787
#> [25] 0.62452377 0.29824151 0.35439301 0.03322289 0.02586761 0.20937293
#> attr(,"factors")
#> list()
#> attr(,"class")
#> [1] "dgCMatrix"
#> attr(,"class")attr(,"package")
#> [1] "Matrix"