R/ca.R
In fdschneider/caspr: Cellular Automata for Spatial Pressure in R
#' Run cellular automata simulation.
#'
#' @param x A landscape object.
#' @param model A valid object of class 'ca_model'. Defaults to musselbed. Valid
#' values are: \code{musselbed}, \code{grazing}.
#' @param parms A list of parameters with one or several parameters containing a
#' vector of parameter values. Those will be combined full-factorially using
#' \code{expand.grid()}. Will be checked against template parameters in
#' \code{model}. If not provided, template parameters will be used.
#' @param t_max Maximal number of timesteps. Model will be terminated even if
#' still in transient dynamics (i.e. model did not reach steady state)
#' @param t_eval Timespan of moving window that is evaluated for the end of
#' transient dynamics.
#' @param saveeach Timespan between timesteps at which a full snapshot of the
#' landscape is saved into the output of the simulation.
#' @param stopifsteady Binary parameter, defaults to FALSE. If TRUE, the
#' function provided in parameter \code{steady} will be applied to test in
#' each timestep if steady state is reached.
#' @param steady A function returning TRUE or FALSE, taking exactly the
#' parameters \code{i}, \code{result}, \code{steadyparms}. By default the
#' function returns TRUE if the difference in mean cover of the primary cell
#' state (i.e. the first in the vector provided in \code{model$states}) over
#' two subsequent timespans of length \code{steadyparms$t_eval} is smaller
#' than \code{steadyparms$accept}.
#' @param steadyparms a list of parameters that are required by the function
#' provided in \code{steady}.
#' @param seed An integer number serving as seed for random number generation.
#' @param plotting A binary variable. If TRUE, simulation is plotted into an animated gif.
#' @param filename A character string. Filename of animated gif (defaults to "modelrun.gif") which will be placed in current working directory.
#'
#'
#' If not provided global seeds of R apply.
#' @param ... Parameters handed over to update function in \code{model$update}.
#'
#' @return The output is returned as a list object of class \code{ca_result},
#' containing a full timeseries of global and local cover as well as snapshots
#' of the landscape.
#'
#' \describe{
#' \item{\code{$model}}{The entire model object
#' used to generate this simulation run, including the parameters at
#' \code{$model$parms}}
#' \item{\code{$time}}{Vector of timesteps.}
#' \item{\code{$issteady}}{Binary vector reporting for each timestep if the criterion for steady state was fulfilled. The criterion can be customized by adjusting parameter \code{steady}.}
#' \item{\code{$cover}}{A list of cover timeseries for each state of the model.}
#' \item{\code{$local}}{A list of local cover timeseries for each
#' state of the model.}
#' \item{\code{$snaps}}{A vector of indices of saved snapshots.}
#' \item{\code{$landscapes}}{A list of landscape objects at each
#' point in \code{$snaps}} \item{\code{$issteady}}{A binary vector of the
#' returned values of function \code{steady}}
#' }
#'
#' @details Runs iterations of the update function \code{model$update()} on the
#' initial landscape \code{x} until a \code{t_max} is reached. The function
#' saves the full timeseries, i.e. a value for each timestep, of the global
#' cover of each state as well as the average local cover of each state. The
#' full landscape object of each timestep is stored in a list
#' \code{result$landscapes} of the output object, but frequency of these
#' snapshots can be altered by increasing the parameter \code{saveeach}.
#'
#' @export
#'
#' @examples
#'
#' # 1. run simulation and save a snapshot each 50 timesteps. plot timeseries and snapshots.
#'
# # create initial landscape
#' l <- init_landscape(c("+","0","-"), c(0.6,0.2,0.2), width = 100)
#' p <- list(r = 0.4, d = 0.9, delta = 0.01) # set parameters
#' r <- ca(l, model = musselbed, parms = p, t_max = 200) # run simulation
#' plot(r)
#'
#' par(mfrow= c(2,3))
#' sapply(c(0,25,50,100,150,200)+1, function(i) plot(r$landscapes[[i]]) )
#'
#' # 2. run simulation and save full landsape at each timestep. create animated gif.
#'
#' l <- init_landscape(c("1","0"), c(0.6,0.4), 100)
#' r <- ca(l, model = life, t_max = 400)
#' animate(r, "life01.gif")
ca <- function(x, model = grazing, parms = "default",
t_max = 200, saveeach = 1,
stopifsteady = FALSE,
steady = caspr::steady,
steadyparms = list(t_eval = 200, accept = 0.001),
t_min = 0, # min number of iterations
plotting = FALSE,
filename = "modelrun",
seed = NULL, ... ) {
# checking for valid input
## parms
if(class(parms) == "parms_timeseries") {
parms_temp <- as.list(parms[1,])
} else {
parms_temp <- parms # set temporary parameter object
}
if(parms_temp[1] != "default") {
if(!all(names(model$parms) %in% names(parms_temp))) {
stop(paste("missing parameter(s): ", names(parms_temp)[all(names(model$parms) %in% names(parms_temp))] , "! please specify!" ) )
}
} else {
parms <- model$parms
warning("you did not specify 'parms'! using default parameters of model!")
}
if(saveeach > t_max) {
warning(paste0("Parameter saveeach is larger than t_max: I will only save initial and final landscape! Increase t_max!") )
saveeach <- t_max
}
#if(stopifsteady && identical(steadyparms$dim, x$dim) ) {
# warning(paste0("steadyness criterion was defined for lattice of dimensions: ",steadyparms$dim[1], "x",steadyparms$dim[1], " and might be invalid! Please adjust parameter 'steadyparms'!" ))
#}
## states
if(!all(x$states %in% model$states)) stop("invalid cell states specified in landscape object!")
#notworking! if(!identical(model$states, x$states)) warning("one or several of the model's default cell states are not present in initial landscape object!")
## is interaction matrix provided? if not defaults to four cell neighborhood.
if(is.null(model$interact)) {
I <- matrix(c(0, 1, 0, 1, NA, 1, 0, 1, 0), ncol = 3, byrow = TRUE)
} else {
I <- model$interact
}
mapping(x$dim[1], x$dim[2], i_matrix = I )
xstats <- summary(x)
states <- levels(x$cells)
# calculate timesteps for snapshots:
snaps <- seq(0, as.integer(t_max), as.integer(saveeach))
# initialise result object:
result <- list() # generate list object
result$model <- model
result$model$parms <- parms
result$time <- seq(0, t_max) # add vector of realized timesteps
#result$evaluate <- c(t_min, t_min+2*t_eval)+1
result$issteady <- logical(length = t_max + 1 )
#result$steadyval <- numeric( length = t_max + 1 )
result$cover <- as.data.frame(t(xstats$cover))
result$cover <- result$cover[rep(1, t_max+1),] # preallocating memory
result$local <- as.data.frame(t(xstats$local))
result$local <- result$local[rep(1, t_max+1),] # preallocating memory
result$seed <- seed # save seed
result$ini_landscape <- x # save initial landscape object at t=0
result$snaps <- snaps
result$landscapes <- list()
result$landscapes <- lapply(1:length(snaps), function(i) x) # preallocating memory
# --------------- start simulation -----------------
# initialise simulation variables:
x_old <- x # ghost matrix at t_i
x_new <- x_old
if(0 %in% snaps) {
result$landscapes[[match(0, snaps)]] <- x_new
}
i = 1 # iterator for simulation timesteps ([Alex] this should really start
# at 1 but I'm afraid of breaking something. The way it is now
# overwrites the initial state).
if(!is.null(seed)) set.seed(seed) # get seed from function call
# starting iterations:
while ( i <= t_min ||
i <= t_max &&
( !stopifsteady || !steady(i, result, steadyparms) ) ) {
# call update function:
if(class(parms) == "parms_timeseries") parms_temp <- as.list(parms[i,])
model$update(x_old, parms_temp, ...) -> x_new
# save stats of new landscape
xstats <- summary(x_new)
result$cover[i+1,] <- xstats$cover
result$local[i+1,] <- xstats$local
# save landscape if snapshot
if(i %in% snaps) {
result$landscapes[[match(i, snaps)]] <- x_new
}
result$issteady[i+1] <- steady(i, result, steadyparms)
# replace ghost matrix for next iteration
x_old <- x_new
i = i+1
}
# ------------ end simulation -----------------
#result$steady_state$issteady <- steadiness <= steady
#result$steady_state$steadiness <- steadiness
class(result) <- "ca_result"
if(plotting) ca_animate(result, filename = filename)
return(result)
}
#' @export
print.ca_result <- function(x) {
obj <- deparse(substitute(x))
cat(" \n ")
cat("Model run of ", x$model$name, " over ", max(x$time),
" timesteps. \n", sep = "")
#if(x$steady_state$issteady == TRUE) {
# cat("\n average cover reached steady state ('steadiness' <= ",
# x$steady_state$steady ,"): \n", sep = "")
#} else {
# cat("\n average cover did not reach steady state ('steadiness' = ",
# round(x$steady_state$steadiness, 6) ,"): \n", sep = "")
#}
cat("\n average cover: \n")
cat( " ", formatC(names(summary(x)$mean_cover), width = 6, flag = " " ) , "\n")
cat( " ", formatC(round(summary(x)$mean_cover, digits = 3), width = 6, flag = " " ) )
cat(" \n \n")
cat(" for more details call 'summary(", obj,")' or 'plot(", obj,")'! \n", sep = "")
cat( " access simulation results: \n")
cat( " '", obj,"$model$parms' : simulation parameters \n", sep = "")
cat( " '", obj,"$time' : a vector of timesteps \n", sep = "")
cat( " '", obj,"$cover' : a dataframe of the states' timeseries \n", sep = "")
cat( " '", obj,"$ini_landscape' : the initial landscape object \n", sep = "")
cat( " '", obj,"$snaps' : an index table of saved snapshots \n", sep = "")
cat( " '", obj,"$landscapes[[i]]' : extract snapshot from list of snapshots \n", sep = "")
cat(" \n ")
}
#' plot method for 'ca_result' objects
#'
#' @param x An output object obtained from running function \code{ca()}.
#' @param plotstates A logical vector of the same length as
#' \code{x$model$states}. TRUE activates plotting of other cell state populations.
#' @param cols A vector of valid colors to replace the default color vector.
#' @param lwd Line width for timeseries plot.
#' @param ... Parameters handed to standard plot function, e.g. `bty`, `xlab`.
#' See \link{par}.
#' @details This prompts a (series of) summary plot for the simulation run. By
#' default this is a timeseries of the primary cell state (i.e. the first state
#' given in \code{x$model$states}).
#'
#' @export
plot.ca_result <- function(x, plotstates = c(TRUE, rep(FALSE, length(x$model$states)-1)), snapshots = FALSE, cols = x$model$cols , lwd = 1, ...) {
if(snapshots) {
}
plot(NA,NA,
type = "l",
col = x$model$cols[1],
xlab = "time", ylab = paste("cover of", x$model$states[1]) ,
xlim = c(1, max(x$time)), ylim = c(0,1),
...)
if(length(plotstates) == length(x$model$states) ) {
for(i in (1:length(plotstates))[plotstates]) {
lines(x$time,x$cover[[i]], col = cols[i], lwd = lwd)
}
}
}
#' summary method for `ca_result`
#'
#' @param x
#'
#' @param length.eval Number of time steps at the end of the simulation to consider
#' when computing mean and sd of covers
#'
#' @return Returns a list \code{out} containing the model name, the final time,
#' the mean cover and standard deviation in the last 10 timesteps.
#'
#' @note The mean and sd are supposed to depend on the model being in steady
#' state dynamics, i.e. beyond transitory. Lacking a universal criterion for
#' that, we report the final 10 timesteps.
#'
#' @export
summary.ca_result <- function(x, length.eval = 10) {
out <- list()
class(out) <- "ca_summary"
eval <- tail(seq_along(x$time), length.eval)
out$name <- x$model$name
out$time <- c(min(x$time), max(x$time))
out$mean_cover <- colMeans(x$cover[eval,])
out$sd_cover <- sapply(x$cover[eval,], sd)
return(out)
}
#' Transfer output of ca() into a list of matrices.
#'
#' @param x
#'
#' @return a list of matrices.
#' @export
#'
as.list.ca_result <- function(x) {
lapply(x$landscapes, as.matrix)
}
#' Transfer output of runca() into an array.
#'
#' @param x
#'
#' @return an array with dimensions 'width', 'height' and 'snaps'.
#' @export
#'
as.array.ca_result <- function(x) {
width <- x$landscapes[[1]]$dim[1]
height <- x$landscapes[[1]]$dim[2]
snaps <- length(x$landscapes)
array(unlist(lapply(x$landscapes, as.matrix)), dim = c(width, height, snaps), dimnames = c("width", "height", "snaps"))
}
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#' Run cellular automata simulation.
#'
#' @param x A landscape object.
#' @param model A valid object of class 'ca_model'. Defaults to musselbed. Valid
#' values are: \code{musselbed}, \code{grazing}.
#' @param parms A list of parameters with one or several parameters containing a
#' vector of parameter values. Those will be combined full-factorially using
#' \code{expand.grid()}. Will be checked against template parameters in
#' \code{model}. If not provided, template parameters will be used.
#' @param t_max Maximal number of timesteps. Model will be terminated even if
#' still in transient dynamics (i.e. model did not reach steady state)
#' @param t_eval Timespan of moving window that is evaluated for the end of
#' transient dynamics.
#' @param saveeach Timespan between timesteps at which a full snapshot of the
#' landscape is saved into the output of the simulation.
#' @param stopifsteady Binary parameter, defaults to FALSE. If TRUE, the
#' function provided in parameter \code{steady} will be applied to test in
#' each timestep if steady state is reached.
#' @param steady A function returning TRUE or FALSE, taking exactly the
#' parameters \code{i}, \code{result}, \code{steadyparms}. By default the
#' function returns TRUE if the difference in mean cover of the primary cell
#' state (i.e. the first in the vector provided in \code{model$states}) over
#' two subsequent timespans of length \code{steadyparms$t_eval} is smaller
#' than \code{steadyparms$accept}.
#' @param steadyparms a list of parameters that are required by the function
#' provided in \code{steady}.
#' @param seed An integer number serving as seed for random number generation.
#' @param plotting A binary variable. If TRUE, simulation is plotted into an animated gif.
#' @param filename A character string. Filename of animated gif (defaults to "modelrun.gif") which will be placed in current working directory.
#'
#'
#' If not provided global seeds of R apply.
#' @param ... Parameters handed over to update function in \code{model$update}.
#'
#' @return The output is returned as a list object of class \code{ca_result},
#' containing a full timeseries of global and local cover as well as snapshots
#' of the landscape.
#'
#' \describe{
#' \item{\code{$model}}{The entire model object
#' used to generate this simulation run, including the parameters at
#' \code{$model$parms}}
#' \item{\code{$time}}{Vector of timesteps.}
#' \item{\code{$issteady}}{Binary vector reporting for each timestep if the criterion for steady state was fulfilled. The criterion can be customized by adjusting parameter \code{steady}.}
#' \item{\code{$cover}}{A list of cover timeseries for each state of the model.}
#' \item{\code{$local}}{A list of local cover timeseries for each
#' state of the model.}
#' \item{\code{$snaps}}{A vector of indices of saved snapshots.}
#' \item{\code{$landscapes}}{A list of landscape objects at each
#' point in \code{$snaps}} \item{\code{$issteady}}{A binary vector of the
#' returned values of function \code{steady}}
#' }
#'
#' @details Runs iterations of the update function \code{model$update()} on the
#' initial landscape \code{x} until a \code{t_max} is reached. The function
#' saves the full timeseries, i.e. a value for each timestep, of the global
#' cover of each state as well as the average local cover of each state. The
#' full landscape object of each timestep is stored in a list
#' \code{result$landscapes} of the output object, but frequency of these
#' snapshots can be altered by increasing the parameter \code{saveeach}.
#'
#' @export
#'
#' @examples
#'
#' # 1. run simulation and save a snapshot each 50 timesteps. plot timeseries and snapshots.
#'
# # create initial landscape
#' l <- init_landscape(c("+","0","-"), c(0.6,0.2,0.2), width = 100)
#' p <- list(r = 0.4, d = 0.9, delta = 0.01) # set parameters
#' r <- ca(l, model = musselbed, parms = p, t_max = 200) # run simulation
#' plot(r)
#'
#' par(mfrow= c(2,3))
#' sapply(c(0,25,50,100,150,200)+1, function(i) plot(r$landscapes[[i]]) )
#'
#' # 2. run simulation and save full landsape at each timestep. create animated gif.
#'
#' l <- init_landscape(c("1","0"), c(0.6,0.4), 100)
#' r <- ca(l, model = life, t_max = 400)
#' animate(r, "life01.gif")
ca <- function(x, model = grazing, parms = "default",
t_max = 200, saveeach = 1,
stopifsteady = FALSE,
steady = caspr::steady,
steadyparms = list(t_eval = 200, accept = 0.001),
t_min = 0, # min number of iterations
plotting = FALSE,
filename = "modelrun",
seed = NULL, ... ) {
# checking for valid input
## parms
if(class(parms) == "parms_timeseries") {
parms_temp <- as.list(parms[1,])
} else {
parms_temp <- parms # set temporary parameter object
}
if(parms_temp[1] != "default") {
if(!all(names(model$parms) %in% names(parms_temp))) {
stop(paste("missing parameter(s): ", names(parms_temp)[all(names(model$parms) %in% names(parms_temp))] , "! please specify!" ) )
}
} else {
parms <- model$parms
warning("you did not specify 'parms'! using default parameters of model!")
}
if(saveeach > t_max) {
warning(paste0("Parameter saveeach is larger than t_max: I will only save initial and final landscape! Increase t_max!") )
saveeach <- t_max
}
#if(stopifsteady && identical(steadyparms$dim, x$dim) ) {
# warning(paste0("steadyness criterion was defined for lattice of dimensions: ",steadyparms$dim[1], "x",steadyparms$dim[1], " and might be invalid! Please adjust parameter 'steadyparms'!" ))
#}
## states
if(!all(x$states %in% model$states)) stop("invalid cell states specified in landscape object!")
#notworking! if(!identical(model$states, x$states)) warning("one or several of the model's default cell states are not present in initial landscape object!")
## is interaction matrix provided? if not defaults to four cell neighborhood.
if(is.null(model$interact)) {
I <- matrix(c(0, 1, 0, 1, NA, 1, 0, 1, 0), ncol = 3, byrow = TRUE)
} else {
I <- model$interact
}
mapping(x$dim[1], x$dim[2], i_matrix = I )
xstats <- summary(x)
states <- levels(x$cells)
# calculate timesteps for snapshots:
snaps <- seq(0, as.integer(t_max), as.integer(saveeach))
# initialise result object:
result <- list() # generate list object
result$model <- model
result$model$parms <- parms
result$time <- seq(0, t_max) # add vector of realized timesteps
#result$evaluate <- c(t_min, t_min+2*t_eval)+1
result$issteady <- logical(length = t_max + 1 )
#result$steadyval <- numeric( length = t_max + 1 )
result$cover <- as.data.frame(t(xstats$cover))
result$cover <- result$cover[rep(1, t_max+1),] # preallocating memory
result$local <- as.data.frame(t(xstats$local))
result$local <- result$local[rep(1, t_max+1),] # preallocating memory
result$seed <- seed # save seed
result$ini_landscape <- x # save initial landscape object at t=0
result$snaps <- snaps
result$landscapes <- list()
result$landscapes <- lapply(1:length(snaps), function(i) x) # preallocating memory
# --------------- start simulation -----------------
# initialise simulation variables:
x_old <- x # ghost matrix at t_i
x_new <- x_old
if(0 %in% snaps) {
result$landscapes[[match(0, snaps)]] <- x_new
}
i = 1 # iterator for simulation timesteps ([Alex] this should really start
# at 1 but I'm afraid of breaking something. The way it is now
# overwrites the initial state).
if(!is.null(seed)) set.seed(seed) # get seed from function call
# starting iterations:
while ( i <= t_min ||
i <= t_max &&
( !stopifsteady || !steady(i, result, steadyparms) ) ) {
# call update function:
if(class(parms) == "parms_timeseries") parms_temp <- as.list(parms[i,])
model$update(x_old, parms_temp, ...) -> x_new
# save stats of new landscape
xstats <- summary(x_new)
result$cover[i+1,] <- xstats$cover
result$local[i+1,] <- xstats$local
# save landscape if snapshot
if(i %in% snaps) {
result$landscapes[[match(i, snaps)]] <- x_new
}
result$issteady[i+1] <- steady(i, result, steadyparms)
# replace ghost matrix for next iteration
x_old <- x_new
i = i+1
}
# ------------ end simulation -----------------
#result$steady_state$issteady <- steadiness <= steady
#result$steady_state$steadiness <- steadiness
class(result) <- "ca_result"
if(plotting) ca_animate(result, filename = filename)
return(result)
}
#' @export
print.ca_result <- function(x) {
obj <- deparse(substitute(x))
cat(" \n ")
cat("Model run of ", x$model$name, " over ", max(x$time),
" timesteps. \n", sep = "")
#if(x$steady_state$issteady == TRUE) {
# cat("\n average cover reached steady state ('steadiness' <= ",
# x$steady_state$steady ,"): \n", sep = "")
#} else {
# cat("\n average cover did not reach steady state ('steadiness' = ",
# round(x$steady_state$steadiness, 6) ,"): \n", sep = "")
#}
cat("\n average cover: \n")
cat( " ", formatC(names(summary(x)$mean_cover), width = 6, flag = " " ) , "\n")
cat( " ", formatC(round(summary(x)$mean_cover, digits = 3), width = 6, flag = " " ) )
cat(" \n \n")
cat(" for more details call 'summary(", obj,")' or 'plot(", obj,")'! \n", sep = "")
cat( " access simulation results: \n")
cat( " '", obj,"$model$parms' : simulation parameters \n", sep = "")
cat( " '", obj,"$time' : a vector of timesteps \n", sep = "")
cat( " '", obj,"$cover' : a dataframe of the states' timeseries \n", sep = "")
cat( " '", obj,"$ini_landscape' : the initial landscape object \n", sep = "")
cat( " '", obj,"$snaps' : an index table of saved snapshots \n", sep = "")
cat( " '", obj,"$landscapes[[i]]' : extract snapshot from list of snapshots \n", sep = "")
cat(" \n ")
}
#' plot method for 'ca_result' objects
#'
#' @param x An output object obtained from running function \code{ca()}.
#' @param plotstates A logical vector of the same length as
#' \code{x$model$states}. TRUE activates plotting of other cell state populations.
#' @param cols A vector of valid colors to replace the default color vector.
#' @param lwd Line width for timeseries plot.
#' @param ... Parameters handed to standard plot function, e.g. `bty`, `xlab`.
#' See \link{par}.
#' @details This prompts a (series of) summary plot for the simulation run. By
#' default this is a timeseries of the primary cell state (i.e. the first state
#' given in \code{x$model$states}).
#'
#' @export
plot.ca_result <- function(x, plotstates = c(TRUE, rep(FALSE, length(x$model$states)-1)), snapshots = FALSE, cols = x$model$cols , lwd = 1, ...) {
if(snapshots) {
}
plot(NA,NA,
type = "l",
col = x$model$cols[1],
xlab = "time", ylab = paste("cover of", x$model$states[1]) ,
xlim = c(1, max(x$time)), ylim = c(0,1),
...)
if(length(plotstates) == length(x$model$states) ) {
for(i in (1:length(plotstates))[plotstates]) {
lines(x$time,x$cover[[i]], col = cols[i], lwd = lwd)
}
}
}
#' summary method for `ca_result`
#'
#' @param x
#'
#' @param length.eval Number of time steps at the end of the simulation to consider
#' when computing mean and sd of covers
#'
#' @return Returns a list \code{out} containing the model name, the final time,
#' the mean cover and standard deviation in the last 10 timesteps.
#'
#' @note The mean and sd are supposed to depend on the model being in steady
#' state dynamics, i.e. beyond transitory. Lacking a universal criterion for
#' that, we report the final 10 timesteps.
#'
#' @export
summary.ca_result <- function(x, length.eval = 10) {
out <- list()
class(out) <- "ca_summary"
eval <- tail(seq_along(x$time), length.eval)
out$name <- x$model$name
out$time <- c(min(x$time), max(x$time))
out$mean_cover <- colMeans(x$cover[eval,])
out$sd_cover <- sapply(x$cover[eval,], sd)
return(out)
}
#' Transfer output of ca() into a list of matrices.
#'
#' @param x
#'
#' @return a list of matrices.
#' @export
#'
as.list.ca_result <- function(x) {
lapply(x$landscapes, as.matrix)
}
#' Transfer output of runca() into an array.
#'
#' @param x
#'
#' @return an array with dimensions 'width', 'height' and 'snaps'.
#' @export
#'
as.array.ca_result <- function(x) {
width <- x$landscapes[[1]]$dim[1]
height <- x$landscapes[[1]]$dim[2]
snaps <- length(x$landscapes)
array(unlist(lapply(x$landscapes, as.matrix)), dim = c(width, height, snaps), dimnames = c("width", "height", "snaps"))
}
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