excursions (version 2.5.11)

tricontour: Calculate contour curves on a triangulation

Description

Calculates contour curves and/or regions between them, for functions defined on a triangulation

Usage

tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)
# S3 method for fm_mesh_2d
tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)
# S3 method for matrix
tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  ...
)
# S3 method for list
tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  type = c("+", "-"),
  tol = 1e-07,
  ...
)
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)
# S3 method for fm_mesh_2d
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)
# S3 method for matrix
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  ...
)
# S3 method for list
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  type = c("+", "-"),
  tol = 1e-07,
  output = c("sp", "fm", "inla.mesh.segment"),
  ...
)

Value

For tricontour, a list with some of the fields that fm_segm objects have:

loc

A coordinate matrix

idx

Contour segment indices, as a 2-column matrix, each row indexing a single segment

grp

A vector of group labels. Each segment has a label, in 1,...,nlevels*2+1, where even labels indicate interior on-level contour segments, and odd labels indicate boundary segments between levels.

For tricontourmap, a list:

contour

A list of sp or fm_segm objects defining countour curves (level sets)

map

A list of sp or fm_segm objects enclosing regions between level sets

Arguments

x

An object generated by a call to fm_mesh_2d or fm_rcdt_2d, a triangle-vertex index matrix, or a list of triangulation information, list(loc, graph=list(tv)).

z

A vector containing the values to be contoured (NAs are allowed).

nlevels

Number of contour levels desired, if and only if levels is not supplied.

levels

Numeric vector of levels at which to calculate contour lines.

...

Additional arguments passed to the other methods.

loc

coordinate matrix, to be supplied when x is given as a triangle-vertex index matrix only.

type

"+" or "-", indicating positive or negative association. For +, the generated contours enclose regions where \(u_1 \leq z < u_2\), for - the regions fulfil \(u_1 < z \leq u_2\).

tol

tolerance for determining if the value at a vertex lies on a level.

output

The format of the generated output. Implemented options are "sp" (default) and "fm" (and deprecated "inla.mesh.segment", converted to "fm").

Author

Finn Lindgren

Examples

if (FALSE) {
if (require("fmesher") &&
  require("sp")) {
  ## Generate mesh and SPDE model
  n.lattice <- 20 # increase for more interesting, but slower, examples
  x <- seq(from = 0, to = 10, length.out = n.lattice)
  lattice <- fm_lattice_2d(x = x, y = x)
  mesh <- fm_rcdt_2d_inla(lattice = lattice, extend = FALSE, refine = FALSE)

  ## Generate an artificial sample
  sigma2.e <- 0.1
  n.obs <- 1000
  obs.loc <- cbind(
    runif(n.obs) * diff(range(x)) + min(x),
    runif(n.obs) * diff(range(x)) + min(x)
  )
  Q <- fm_matern_precision(mesh, alpha = 2, rho = 3, sigma = 1)
  x <- fm_sample(n = 1, Q = Q)
  A <- fm_basis(mesh, loc = obs.loc)
  Y <- as.vector(A %*% x + rnorm(n.obs) * sqrt(sigma2.e))

  ## Calculate posterior
  Q.post <- (Q + (t(A) %*% A) / sigma2.e)
  mu.post <- as.vector(solve(Q.post, (t(A) %*% Y) / sigma2.e))

  ## Calculate continuous contours
  tric <- tricontour(mesh,
    z = mu.post,
    levels = as.vector(quantile(x, c(0.25, 0.75)))
  )

  ## Discrete domain contours
  map <- contourmap(
    n.levels = 2, mu = mu.post, Q = Q.post,
    alpha = 0.1, compute = list(F = FALSE), max.threads = 1
  )

  ## Calculate continuous contour map
  setsc <- tricontourmap(mesh,
    z = mu.post,
    levels = as.vector(quantile(x, c(0.25, 0.75)))
  )

  ## Plot the results
  reo <- mesh$idx$lattice
  idx.setsc <- setdiff(names(setsc$map), "-1")
  cols2 <- contourmap.colors(map,
    col = heat.colors(100, 0.5, rev = TRUE),
    credible.col = grey(0.5, 0)
  )
  names(cols2) <- as.character(-1:2)

  par(mfrow = c(1, 2))
  image(matrix(mu.post[reo], n.lattice, n.lattice),
    main = "mean", axes = FALSE, asp = 1
  )
  plot(setsc$map[idx.setsc], col = cols2[idx.setsc])
  par(mfrow = c(1, 1))
}
}