Rescale a matrix

Linearly rescale a matrix. Specifically, the values in the matrix are rescaled so that the maximum value in the matrix is equal to a new user-specified maximum value.

Usage

rescale_matrix(x, max = 1)

Arguments

x

matrix, array, Matrix::Matrix object.

max

numeric new maximum value in matrix. Defaults to 1.

Value

A matrix, array, or Matrix::Matrix object. The returned object is the same class as x.

Details

This function is particularly useful for rescaling data prior to optimization to avoid numerical issues. For example, boundary length (e.g., generated using boundary_matrix()) or connectivity data (e.g., generated using connectivity_matrix()) can contain very large values (e.g., values greater than 1,000,000) and such large values can, in turn, degrade the performance of exact algorithm solvers (see Details section in presolve_check() for more information on numerical issues). By using this function to rescale boundary length or connectivity data prior to optimization (e.g., before using add_boundary_penalties() or add_connectivity_penalties(), this can help avoid numerical issues during optimization.

Notes

In previous versions, the default value for max was 1000. This default value has since been changed to a value of 1 to help ensure that the default scaling provides a better range of values for optimization.

See also

See boundary_matrix() and connectivity_matrix() for details on creating boundary length and connectivity data. Also, see presolve_check() for information on numerical issues.

Examples

# rescale_matrix() is especially useful for re-scaling boundary length data
# prior to optimization, and so here we provide an example showing how
# this can be accomplished

# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# compute boundary data
bd <- boundary_matrix(sim_pu_raster)

# re-scale boundary data
bd <- rescale_matrix(bd)

# create problem with boundary penalties
p <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_boundary_penalties(0.01, data = bd) %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s <- solve(p)

# plot solution
plot(s)