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Multi-domain integration

Source: R/integration.R
fm_int.Rd

Construct integration points on tensor product spaces

Usage

fm_int(domain, samplers = NULL, ...)

# S3 method for class 'list'
fm_int(domain, samplers = NULL, ..., extra = NULL)

# S3 method for class 'numeric'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'character'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'factor'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'SpatRaster'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'fm_lattice_2d'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'fm_mesh_1d'
fm_int(
  domain,
  samplers = NULL,
  name = "x",
  int.args = NULL,
  format = NULL,
  ...
)

# S3 method for class 'fm_mesh_2d'
fm_int(
  domain,
  samplers = NULL,
  name = NULL,
  int.args = NULL,
  format = NULL,
  ...
)

Arguments

domain

Functional space specification; single domain or a named list of domains

samplers

For single domain fm_int methods, an object specifying one or more subsets of the domain, and optional weighting in a weight variable. For fm_int.list, a list of sampling definitions, where data frame elements may contain information for multiple domains, in which case each row represent a separate tensor product integration subspace.

...

Additional arguments passed on to other methods

extra

Optional character vector with names of variables other than the integration domains to be included from the samplers. If NULL (default), all additional variables are included.

name

For single-domain methods, the variable name to use for the integration points. Default 'x'

int.args

List of arguments passed to line and integration methods.

  • method: "stable" (to aggregate integration weights onto mesh nodes) or "direct" (to construct a within triangle/segment integration scheme without aggregating onto mesh nodes)

  • nsub1, nsub2: integers controlling the number of internal integration points before aggregation. Points per triangle: (nsub2+1)^2. Points per knot segment: nsub1

format

character; determines the output format, as either "sf" (default for fm_mesh_2d when the sampler is NULL), "numeric" (default for fm_mesh_1d), "bary", or "sp". When NULL, determined by the domain and sampler types.

Value

A tibble, sf, or SpatialPointsDataFrame of 1D and 2D integration points, including a weight column, a.block column, and a matrix column .block_origin. The .block column is used to identify the integration blocks defined by the samplers. The .block_origin collects the original subdomain block information for tensor product blocks.

Methods (by class)

  • fm_int(list): Multi-domain integration

  • fm_int(numeric): Discrete double or integer space integration

  • fm_int(character): Discrete character space integration

  • fm_int(factor): Discrete factor space integration

  • fm_int(SpatRaster): SpatRaster integration. Not yet implemented.

  • fm_int(fm_lattice_2d): fm_lattice_2d integration. Not yet implemented.

  • fm_int(fm_mesh_1d): fm_mesh_1d integration. Supported samplers:

    • NULL for integration over the entire domain;

    • A vector defining points for summation (up to 0.5.0, length 2 vectors were interpreted as intervals. From 0.6.0 intervals must be specified as rows of a 2-column matrix);

    • A 2-column matrix with a single interval in each row;

    • A list of such vectors or matrices

    • A tibble with a named column containing a vector/matrix/list as above, and optionally a weight column.

  • fm_int(fm_mesh_2d): fm_mesh_2d integration. Any sampler class with an associated fm_int_mesh_2d() method is supported.

Examples

# Integration on the interval (2, 3.5) with Simpson's rule
ips <- fm_int(fm_mesh_1d(0:4), samplers = cbind(2, 3.5))
plot(ips$x, ips$weight)


# Create integration points for the two intervals [0,3] and [5,10]
ips <- fm_int(
  fm_mesh_1d(0:10),
  rbind(c(0, 3), c(5, 10))
)
plot(ips$x, ips$weight)


# Convert a 1D mesh into integration points
mesh <- fm_mesh_1d(seq(0, 10, by = 1))
ips <- fm_int(mesh, name = "time")
plot(ips$time, ips$weight)


if (require("ggplot2", quietly = TRUE)) {
  #' Integrate on a 2D mesh with polygon boundary subset
  ips <- fm_int(fmexample$mesh, fmexample$boundary_sf[[1]])
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh, multi = TRUE), alpha = 0.5) +
    geom_sf(data = fmexample$boundary_sf[[1]], fill = "red", alpha = 0.5) +
    geom_sf(data = ips, aes(size = weight)) +
    scale_size_area()
}


# Individual sampling points:
(ips <- fm_int(0:10, c(0, 3, 5, 6, 10)))
#> # A tibble: 5 × 4
#>       x weight .block .block_origin[,"x"]
#>   <int>  <dbl>  <int>               <int>
#> 1     0      1      1                   1
#> 2     3      1      2                   2
#> 3     5      1      3                   3
#> 4     6      1      4                   4
#> 5    10      1      5                   5
# Sampling blocks:
(ips <- fm_int(0:10, list(c(0, 3), c(5, 6, 10))))
#> # A tibble: 5 × 4
#>       x weight .block .block_origin[,"x"]
#>   <int>  <dbl>  <int>               <int>
#> 1     0      1      1                   1
#> 2     3      1      1                   1
#> 3     5      1      2                   2
#> 4     6      1      2                   2
#> 5    10      1      2                   2

# Continuous integration on intervals
ips <- fm_int(
  fm_mesh_1d(0:10, boundary = "cyclic"),
  rbind(c(0, 3), c(5, 10))
)
plot(ips$x, ips$weight)