Compute a collection of Boltzmann–Lotka–Volterra model solutions

This function computes a collection of flows between origin locations and destination locations using blvim() on a grid of parameters. The flows use the same costs, same production constraints and same attractivenesses. Each flow is computed using one of all the pairwise combinations between the alpha values given by alphas and the beta values given by betas. The function returns an object of class sim_list which contains the resulting flows.

Usage

grid_blvim(
  costs,
  X,
  alphas,
  betas,
  Z,
  bipartite = TRUE,
  origin_data = NULL,
  destination_data = NULL,
  epsilon = 0.01,
  iter_max = 50000,
  conv_check = 100,
  precision = 1e-06,
  quadratic = FALSE,
  progress = FALSE
)

Arguments

costs

a cost matrix

X

a vector of production constraints

alphas

a vector of return to scale parameters

betas

a vector of cost inverse scale parameters

Z

a vector of initial destination attractivenesses

bipartite

when TRUE (default value), the origin and destination locations are considered to be distinct. When FALSE, a single set of locations plays the both roles. This has only consequences in functions specific to this latter case such as terminals().

origin_data

NULL or a list of additional data about the origin locations (see details)

destination_data

NULL or a list of additional data about the destination locations (see details)

epsilon

the update intensity

iter_max

the maximal number of steps of the BLV dynamic

conv_check

number of iterations between to convergence test

precision

convergence threshold

quadratic

selects the update rule, see details.

progress

if TRUE, a progress bar is shown during the calculation (defaults to FALSE)

Value

an object of class sim_list

Location data

While models in this package do not use location data beyond X and Z, additional data can be stored and used when analysing spatial interaction models.

Origin and destination location names

Spatial interaction models can store names for origin and destination locations, using origin_names<-() and destination_names<-(). Names are taken by default from names of the cost matrix costs. More precisely, rownames(costs) is used for origin location names and colnames(costs) for destination location names.

Origin and destination location positions

Spatial interaction models can store the positions of the origin and destination locations, using origin_positions<-() and destination_positions<-().

Specifying location data

In addition to the functions mentioned above, location data can be specified directly using the origin_data and destination_data parameters. Data are given by a list whose components are not interpreted excepted the following ones:

• names is used to specify location names and its content has to follow the restrictions documented in origin_names<-() and destination_names<-()

• positions is used to specify location positions and its content has to follow the restrictions documented in origin_positions<-() and destination_positions<-()

Examples

positions <- matrix(rnorm(10 * 2), ncol = 2)
distances <- as.matrix(dist(positions))
production <- rep(1, 10)
attractiveness <- c(2, rep(1, 9))
all_flows <- grid_blvim(distances, production, c(1.25, 1.5), c(1, 2, 3), attractiveness)
all_flows
#> Collection of 6 spatial interaction models with 10 origin locations and 10
#> destination locations computed on the following grid:
#> • alpha: 1.25 and 1.5
#> • beta: 1, 2, and 3
length(all_flows)
#> [1] 6
all_flows[[2]]
#> Spatial interaction model with 10 origin locations and 10 destination locations
#> • Model: Wilson's production constrained
#> • Parameters: return to scale (alpha) = 1.5 and inverse cost scale (beta) = 1
#> ℹ The BLV model converged after 1800 iterations.