tricontour {excursions}

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 class 'inla.mesh'
tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)

## S3 method for class 'matrix'
tricontour(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  ...
)

## S3 method for class '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 class 'inla.mesh'
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  ...
)

## S3 method for class 'matrix'
tricontourmap(
  x,
  z,
  nlevels = 10,
  levels = pretty(range(z, na.rm = TRUE), nlevels),
  loc,
  ...
)

## S3 method for class '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"),
  ...
)

Arguments

x

An object generated by a call to inla.mesh.2d or inla.mesh.create, 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").

Value

For tricontour, a list with some of the fields that inla.mesh.segment 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 inla.mesh.segment objects defining countour curves (level sets)

map

A list of sp or inla.mesh.segment objects enclosing regions between level sets

Author(s)

Finn Lindgren [e-mail]

Examples

## Not run: 
if (require("fmesher")) {
  ## 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))
}

## End(Not run)