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_fm(), fm_as_lattice_2d(), fm_as_mesh_1d(), fm_as_mesh_2d(), fm_as_segm(), fm_as_sfc(), fm_as_tensor(), fm_lattice_2d(), 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] 1395 1395
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 [1:1396] 0 0 0 0 0 0 0 0 0 0 ...
#>   .. .. ..@ Dim     : int [1:2] 1 1395
#>   .. .. ..@ Dimnames:List of 2
#>   .. .. .. ..$ : NULL
#>   .. .. .. ..$ : NULL
#>   .. .. ..@ x       : num [1:6] 0.2394 0.2112 0.0494 0.2394 0.2112 ...
#>   .. .. ..@ 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 [1:1396] 0 0 0 0 0 0 0 0 0 0 ...
#>   ..@ Dim     : int [1:2] 1 1395
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:6] 0.2394 0.2112 0.0494 0.2394 0.2112 ...
#>   ..@ factors : list()
str(fm_fem(m))
#> List of 3
#>  $ cc:Formal class 'dgTMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:1395] 0 1 2 3 4 5 6 7 8 9 ...
#>   .. ..@ j       : int [1:1395] 0 1 2 3 4 5 6 7 8 9 ...
#>   .. ..@ Dim     : int [1:2] 1395 1395
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:1395] 0.171 0.271 0.213 0.282 0.22 ...
#>   .. ..@ factors : list()
#>  $ g1:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:11677] 0 1 25 257 279 0 1 2 226 257 ...
#>   .. ..@ p       : int [1:1396] 0 5 11 16 22 28 33 39 45 51 ...
#>   .. ..@ Dim     : int [1:2] 1395 1395
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:11677] 1.337 -0.174 -0.113 -0.708 -0.343 ...
#>   .. ..@ factors : list()
#>  $ g2:Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
#>   .. ..@ i       : int [1:42761] 0 1 2 24 25 225 226 229 233 245 ...
#>   .. ..@ p       : int [1:1396] 0 17 36 53 73 91 107 127 147 167 ...
#>   .. ..@ Dim     : int [1:2] 1395 1395
#>   .. ..@ Dimnames:List of 2
#>   .. .. ..$ : NULL
#>   .. .. ..$ : NULL
#>   .. ..@ x       : num [1:42761] 11.9277 -1.7904 0.2465 0.0254 -1.1944 ...
#>   .. ..@ factors : list()