Ising model for spatial data

Performs simulations based on the given parameters of the Ising model

kinetic_ising(
  x,
  B,
  J,
  updates = 1,
  iter,
  rule = "glauber",
  inertia = 0,
  version = 1,
  progress = FALSE,
  external_field = NULL
)

Arguments

x

SpatRaster or matrix containing two values: -1 and 1. NA cells are excluded from the simulation.

B

External pressure (positive or negative): it tries to align cells' values with its sign

J

Strength of the local autocorrelation tendency (always positive): it tries to align signs of neighboring cells

updates

Specifies how many sets of iterations are performed on the input object. The output of this function has as many layers as the updates value.

iter

Specifies how many iterations are performed on the input object. By default it equals to the number of values in the input object.

rule

IM temporal evolution rule: either "glauber" (default) or "metropolis"

inertia

Represents the modification of the algorithm aimed at suppressing the salt-and-pepper noise of the focus category present when simulating evolution of a coarse-textured pattern. With Q > 0, small patches of the focus category are not generated, thus eliminating the salt-and-pepper noise of the focus category

version

By default, 1, the x object is converted into a matrix (fast, but can be memory consuming); version = 2 has a lower RAM impact, but is much slower

progress

TRUE/FALSE

external_field

Optional spatial adjustment added to B at each cell. Values are on the same pressure scale as B: positive values favor 1, negative values favor -1, and zero has no effect. The field must be a matrix with the same dimensions as a matrix x, or a single-layer SpatRaster with the same geometry as a raster x. Values may be NA only where x is NA.

Value

Object of the same class as x with the number of layers specified by updates

Details

To derive external_field from a probability map p, first convert the probabilities to local pressure using external_field = 0.5 * log(p / (1 - p)) - B.

Exact probabilities of zero and one produce infinite pressure and therefore act as hard constraints. To keep the pressure finite, clip estimated probabilities before conversion. For a matrix, use p = pmin(pmax(p, eps), 1 - eps); for a SpatRaster, use p = terra::clamp(p, eps, 1 - eps). Smaller values of eps represent stronger classifier evidence.

References

Ising, E., 1924. Beitrag zur theorie des ferro-und paramagnetismus. Ph.D. thesis, Grefe & Tiedemann.

Onsager, L., 1944. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Physical Review 65 (3-4), 117.

Brush, S. G., 1967. History of the Lenz-Ising model. Reviews of modern physics 39 (4), 883.

Cipra, B. A., 1987. An introduction to the Ising model. The American Mathematical Monthly 94 (10), 937–959.

Examples

data(r_start, package = "spatialising")
ts1 = kinetic_ising(r_start, B = -0.3, J = 0.7)
ts10 = kinetic_ising(r_start, B = -0.3, J = 0.7, updates = 10)

# \donttest{
  r1 = terra::rast(system.file("raster/r_start.tif", package = "spatialising"))
  terra::plot(r1)

  r2 = kinetic_ising(r1, B = -0.3, J = 0.7)
  terra::plot(r2)


  library(terra)
  ri1 = kinetic_ising(r1, B = -0.3, J = 0.7, updates = 9)
  plot(ri1)


  ri2 = kinetic_ising(r1, B = 0.3, J = 0.7, updates = 9)
  plot(ri2)


  ri3 = kinetic_ising(r1, B = -0.3, J = 0.4, updates = 9)
  plot(ri3)

# }