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Generate integration points

Source: R/bru.integration.R
ipoints.Rd

This function generates points in one or two dimensions with a weight attached to each point. The weighted sum of a function evaluated at these points is the integral of that function approximated by linear basis functions. The parameter samplers describes the area(s) integrated over.

In case of a single dimension samplers is supposed to be a two-column matrix where each row describes the start and end points of the interval to integrate over. In the two-dimensional case samplers can be either a SpatialPolygon, an inla.mesh or a SpatialLinesDataFrame describing the area to integrate over. If a SpatialLineDataFrame is provided, it has to have a column called 'weight' in order to indicate the width of the line.

The domain parameter is an inla.mesh.1d or inla.mesh object that can be employed to project the integration points to the vertices of the mesh. This reduces the final number of integration points and reduces the computational cost of the integration. The projection can also prevent numerical issues in spatial LGCP models where each observed point is ideally surrounded by three integration point sitting at the corresponding mesh vertices. This is controlled by int.args$method="stable" (default) or "direct", where the latter uses the integration points directly, without aggregating to the mesh vertices.

For convenience, the domain parameter can also be a single integer setting the number of equally spaced integration points in the one-dimensional case.

Usage

ipoints(
  samplers = NULL,
  domain = NULL,
  name = NULL,
  group = NULL,
  int.args = NULL,
  project = NULL
)

Arguments

samplers

Description of the integration region boundary. In 1D, a length 2 vector or two-column matrix where each row describes an interval, or NULL In 2D either a SpatialPolygon or a SpatialLinesDataFrame with a weight column defining the width of the a transect line, and optionally further columns used by the group argument, or NULL. When domain is NULL, samplers may also be an inla.mesh.1d or inla.mesh object, that is then treated as a domain argument instead.

domain

Either

  • when samplers is a 1D interval(s) definition only, domain can be a single integer for the number of integration points to place in each 1D interval, overriding int.args[["nsub1"]], and otherwise

  • when samplers is NULL, domain can be a numeric vector of points, each given integration weight 1 (and no additional points are added in between),

  • an inla.mesh.1d object for continuous 1D integration, or

  • an inla.mesh.2d object for continuous 2D integration.

name

Character array stating the name of the domains dimension(s). If NULL, the names are taken from coordinate names from samplers for Spatial* objects, otherwise "x", "y", "z" for 2D regions and "x" for 1D regions

group

Column names of the samplers object (if applicable) for which the integration points are calculated independently and not merged when aggregating to mesh nodes.

int.args

List of arguments passed to bru_int_polygon.

  • 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

  • poly_method: if set to "legacy", selects an old polygon integration method that doesn't handle holes. Currently only used for debugging purposes.

project

Deprecated in favour of int.args(method=...). If TRUE, aggregate the integration points to mesh vertices. Default: project = (identical(int.args$method, "stable"))

Value

A data.frame or SpatialPointsDataFrame of 1D and 2D integration points, respectively.

Author

Fabian E. Bachl bachlfab@gmail.com and finn.lindgren@gmail.com

Examples

# \donttest{
if (require("INLA", quietly = TRUE) &&
  require("ggplot2", quietly = TRUE)) {
  # Create 50 integration points covering the dimension 'myDim' between 0 and 10.

  ips <- ipoints(c(0, 10), 50, name = "myDim")
  plot(ips)


  # Create integration points for the two intervals [0,3] and [5,10]

  ips <- ipoints(matrix(c(0, 3, 5, 10), nrow = 2, byrow = TRUE), 50)
  plot(ips)


  # Convert a 1D mesh into integration points
  mesh <- inla.mesh.1d(seq(0, 10, by = 1))
  ips <- ipoints(mesh, name = "time")
  plot(ips)


  # Obtain 2D integration points from a SpatialPolygon

  data(gorillas, package = "inlabru")
  ips <- ipoints(gorillas$boundary)
  ggplot() +
    gg(gorillas$boundary) +
    gg(ips, aes(size = weight))


  #' Project integration points to mesh vertices

  ips <- ipoints(gorillas$boundary, domain = gorillas$mesh)
  ggplot() +
    gg(gorillas$mesh) +
    gg(gorillas$boundary) +
    gg(ips, aes(size = weight))


  # Turn a 2D mesh into integration points

  ips <- ipoints(gorillas$mesh)
  ggplot() +
    gg(gorillas$boundary) +
    gg(ips, aes(size = weight))
}


#> Warning: Computing integration points from polygon; specify a mesh for better numerical control.
#> Regions defined for each Polygons
#> Regions defined for each Polygons
#> Regions defined for each Polygons


# }