Make a tensor product function space

Tensor product function spaces. The interface and object storage model is experimental and may change.

Usage

fm_tensor(x, ...)

Arguments

x

list of function space objects, such as fm_mesh_2d().

...

Currently unused

Value

A fm_tensor or fm_tensor_list object. Elements of fm_tensor:

fun_spaces

fm_list of function space objects

manifold

character; manifold type summary. Regular subset of Rd "Rd", if all function spaces have type "R", torus connected "Td" if all function spaces have type "S", and otherwise "Md" In all cases, d is the sum of the manifold dimensions of the function spaces.

See also

Other object creation and conversion: fm_as_collect(), fm_as_fm(), fm_as_lattice_2d(), fm_as_lattice_Nd(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_mesh_3d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_collect(), fm_lattice_2d(), fm_lattice_Nd(), fm_mesh_1d(), fm_mesh_2d(), fm_segm(), fm_simplify()

Examples

m <- fm_tensor(list(
  space = fmexample$mesh,
  time = fm_mesh_1d(1:5)
))
m2 <- fm_as_tensor(m)
m3 <- fm_as_tensor_list(list(m, m))
c(fm_dof(m$fun_spaces$space) * fm_dof(m$fun_spaces$time), fm_dof(m))
#> [1] 1460 1460
str(fm_evaluator(m, loc = list(space = cbind(0, 0), time = 2.5)))
#> List of 1
#>  $ proj:List of 2
#>   ..$ A :Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   .. .. ..@ i       : int [1:6] 0 0 0 0 0 0
#>   .. .. ..@ p       : int [1:1461] 0 0 0 0 0 0 0 0 0 0 ...
#>   .. .. ..@ Dim     : int [1:2] 1 1460
#>   .. .. ..@ Dimnames:List of 2
#>   .. .. .. ..$ : NULL
#>   .. .. .. ..$ : NULL
#>   .. .. ..@ x       : num [1:6] 0.135 0.3242 0.0408 0.135 0.3242 ...
#>   .. .. ..@ factors : list()
#>   ..$ ok: logi TRUE
#>   ..- attr(*, "class")= chr "fm_basis"
#>  - attr(*, "class")= chr "fm_evaluator"
str(fm_basis(m, loc = list(space = cbind(0, 0), time = 2.5)))
#> Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   ..@ i       : int [1:6] 0 0 0 0 0 0
#>   ..@ p       : int [1:1461] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..@ Dim     : int [1:2] 1 1460
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:6] 0.135 0.3242 0.0408 0.135 0.3242 ...
#>   ..@ factors : list()
str(fm_fem(m))
#> List of 3
#>  $ cc:Formal class 'dgTMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:1460] 0 1 2 3 4 5 6 7 8 9 ...
#>   .. ..@ j       : int [1:1460] 0 1 2 3 4 5 6 7 8 9 ...
#>   .. ..@ Dim     : int [1:2] 1460 1460
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:1460] 0.1745 0.1268 0.0722 0.1806 0.0717 ...
#>   .. ..@ factors : list()
#>  $ g1:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:12176] 0 1 33 286 289 292 0 1 2 262 ...
#>   .. ..@ p       : int [1:1461] 0 6 12 17 23 28 34 41 48 53 ...
#>   .. ..@ Dim     : int [1:2] 1460 1460
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:12176] 1.26418 -0.35484 -0.17096 -0.00842 -0.38105 ...
#>   .. ..@ factors : list()
#>  $ g2:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:44746] 0 1 2 32 33 239 246 262 285 286 ...
#>   .. ..@ p       : int [1:1461] 0 18 37 53 72 87 105 130 155 170 ...
#>   .. ..@ Dim     : int [1:2] 1460 1460
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:44746] 11.317 -6.118 1.065 0.213 -2.766 ...
#>   .. ..@ factors : list()