R/optimDIST.R

In Laboratorio-de-Pedometria/spsann-package: Optimization of Spatial Samples via Simulated Annealing

#' Optimization of sample configurations for spatial trend identification and estimation (II)
#'
#' @description
#' Optimize a sample configuration for spatial trend identification and estimation. A criterion is
#' defined so that the sample reproduces the frequency marginal distribution of the covariates
#' (FREQ).
#'
# @inheritParams spJitter
#' @template spSANN_doc
#' @template ACDC_doc
#' @template spJitter_doc
#'
#' @details
#' \subsection{Frequency marginal distribution of covariates}{
#' Reproducing the frequency marginal distribution of the numeric covariates depends upon the
#' definition of marginal sampling strata. These marginal sampling strata are also used to define
#' the factor levels of all numeric covariates that are passed together with factor covariates. Two
#' types of marginal sampling strata can be used: _equal-area_ and _equal-range_.
#'
#' Equal-area marginal sampling strata are defined using the sample quantiles estimated with
#' [stats::quantile()] using a discontinuous function(`type = 3`). Using a discontinuous function
#' avoids creating breakpoints that do not occur in the population of existing covariate values.
#'
#' Depending on the level of discretization of the covariate values, [stats::quantile()] produces
#' repeated breakpoints. A breakpoint will be repeated if that value has a relatively high frequency
#' in the population of covariate values. The number of repeated breakpoints increases with the
#' number of marginal sampling strata. Repeated breakpoints result in empty marginal sampling
#' strata. To avoid this, only the unique breakpoints are used.
#'
#' Equal-range marginal sampling strata are defined by breaking the range of covariate values into
#' pieces of equal size. Depending on the level of discretization of the covariate values, this
#' method creates breakpoints that do not occur in the population of existing covariate values. Such
#' breakpoints are replaced with the nearest existing covariate value identified using Euclidean
#' distances.
#'
#' Like the equal-area method, the equal-range method can produce empty marginal sampling strata.
#' The solution used here is to merge any empty marginal sampling strata with the closest non-empty
#' marginal sampling strata. This is identified using Euclidean distances as well.
#'
#' The approaches used to define the marginal sampling strata result in each numeric covariate
#' having a different number of marginal sampling strata, some of them with different area/size.
#' Because the goal is to have a sample that reproduces the frequency marginal distribution of the
#' covariate, each marginal sampling strata will have a different number of sample points. The
#' wanted distribution of the number of sample points per marginal strata is estimated empirically
#' as the proportion of points in the population of existing covariate values that fall in each
#' marginal sampling strata.
#' }
#'
#' @return
#' `optimFREQ` (`optimDIST`) returns an object of class `OptimizedSampleConfiguration`: the
#' optimized sample configuration with details about the optimization.
#'
#' `objFREQ` (`objDIST`) returns a numeric value: the energy state of the sample configuration --
#' the objective function value.
#'
#' @references
#' Hyndman, R. J.; Fan, Y. Sample quantiles in statistical packages. _The American Statistician_,
#' v. 50, p. 361-365, 1996.
#'
#' Everitt, B. S. _The Cambridge dictionary of statistics_. Cambridge: Cambridge University Press,
#' p. 432, 2006.
#'
#' @author Alessandro Samuel-Rosa \email{alessandrosamuelrosa@@gmail.com}
#' @seealso [spsann::optimACDC()]
#' @aliases optimFREQ objFREQ FREQ optimDIST objDIST DIST
#' @import Rcpp
#' @export
#' @examples
#' #####################################################################
#' # NOTE: The settings below are unlikely to meet your needs.         #
#' #####################################################################
#' if (interactive() & require(sp)) {
#'   data(meuse.grid, package = "sp")
#'   schedule <- scheduleSPSANN(
#'     initial.temperature = 1, chains = 1,
#'     x.max = 1540, y.max = 2060, x.min = 0,
#'     y.min = 0, cellsize = 40)
#'   set.seed(2001)
#'   res <- optimDIST(points = 10, candi = meuse.grid[, 1:2],
#'     covars = meuse.grid[, 5], use.coords = TRUE, schedule = schedule)
#'   objSPSANN(res) -
#'     objDIST(points = res, candi = meuse.grid[, 1:2],
#'     covars = meuse.grid[, 5],
#'     use.coords = TRUE)
#' }
# MAIN FUNCTION ####################################################################################
#' @rdname optimFREQ
optimFREQ <-
  function(points, candi,
            # FREQ
            covars, strata.type = "area", use.coords = FALSE,
            # SPSANN
            schedule, plotit = FALSE, track = FALSE,
            boundary, progress = "txt", verbose = FALSE) {
    # Objective function name
    objective <- "DIST"
    # Check spsann arguments
    eval(.check_spsann_arguments())
    # Check other arguments
    check <- .optimACDCcheck(
      candi = candi, covars = covars,
      use.coords = use.coords, strata.type = strata.type)
    if (!is.null(check)) stop (check, call. = FALSE)
    # Set plotting options
    eval(.plotting_options())
    # Prepare points and candi
    eval(.prepare_points())
    # Prepare for jittering
    eval(.prepare_jittering())
    
    # Prepare 'covars' and create the starting sample matrix 'sm'
    eval(.prepare_acdc_covars())
    
    # Base data and initial energy state (energy)
    # Use 'n_pts + n_fixed_pts' to account for existing fixed points.
    # pop_prop <- .strataACDC(n.pts = n_pts, strata.type = strata.type,
    #                         covars.type = covars.type, covars = covars)
    # energy0 <- data.frame(
    #   obj = .objDIST(sm = sm, pop.prop = pop_prop, n.pts = n_pts,
    #                  n.cov = n_cov, covars.type = covars.type))
    pop_prop <- .strataACDC(
      n.pts = n_pts + n_fixed_pts, strata.type = strata.type, covars.type = covars.type,
      covars = covars)
    energy0 <- data.frame(
      obj = .objDIST(
        sm = sm, pop.prop = pop_prop, n.pts = n_pts + n_fixed_pts, n.cov = n_cov,
        covars.type = covars.type))
    # Other settings for the simulated annealing algorithm
    old_sm <- sm
    new_sm <- sm
    best_sm <- sm
    old_energy <- energy0
    best_energy <- data.frame(obj = Inf)
    actual_temp <- schedule$initial.temperature
    k <- 0 # count the number of jitters
    # Set progress bar
    eval(.set_progress())
    # Initiate the annealing schedule
    for (i in 1:schedule$chains) {
      n_accept <- 0
      
      for (j in 1:schedule$chain.length) { # Initiate one chain
        
        for (wp in 1:n_pts) { # Initiate loop through points
          k <- k + 1
          
          # Plotting and jittering
          eval(.plot_and_jitter())
          
          # Update sample and correlation matrices, and energy state
          # Use 'n_pts + n_fixed_pts' to account for existing fixed points.
          new_sm[wp, ] <- covars[new_conf[wp, 1], ]
          # new_energy <- data.frame(
            # obj = .objDIST(sm = new_sm, pop.prop = pop_prop, n.pts = n_pts,
                           # n.cov = n_cov, covars.type = covars.type))
          new_energy <- data.frame(
            obj = .objDIST(
              sm = new_sm, pop.prop = pop_prop, n.pts = n_pts + n_fixed_pts, n.cov = n_cov, 
              covars.type = covars.type))
          
          # Evaluate the new system configuration
          accept <- .acceptSPSANN(old_energy[[1]], new_energy[[1]], actual_temp)
          if (accept) {
            old_conf <- new_conf
            old_energy <- new_energy
            old_sm <- new_sm
            n_accept <- n_accept + 1
          } else {
            new_energy <- old_energy
            new_conf <- old_conf
            new_sm <- old_sm
          }
          if (track) energies[k, ] <- new_energy
          
          # Record best energy state
          if (new_energy[[1]] < best_energy[[1]] / 1.0000001) {
            best_k <- k
            best_conf <- new_conf
            best_energy <- new_energy
            best_old_energy <- old_energy
            old_conf <- old_conf
            best_sm <- new_sm
            best_old_sm <- old_sm
          }
          
          # Update progress bar
          eval(.update_progress())
          
        } # End loop through points
        
      } # End the chain
      
      # Check the proportion of accepted jitters in the first chain
      eval(.check_first_chain())
      
      # Count the number of chains without any change in the objective function.
      # Restart with the previously best configuration if it exists.
      if (n_accept == 0) {
        no_change <- no_change + 1
        if (no_change > schedule$stopping) {
          # if (new_energy[[1]] > best_energy[[1]] * 1.000001) {
            # old_conf <- old_conf
            # new_conf <- best_conf
            # old_energy <- best_old_energy
            # new_energy <- best_energy
            # no_change <- 0
            # new_sm <- best_sm
            # old_sm <- best_old_sm
            # cat("\nrestarting with previously best configuration\n")
          # } else { 
            break 
          # }
        }
        if (verbose) {
          cat("\n", no_change, "chain(s) with no improvement... stops at",
              schedule$stopping, "\n")
        }
      } else {
        no_change <-  0
      }
      # Update control parameters
      # Testing new parametes 'x_min0' and 'y_min0' (used with finite 'candi')
      actual_temp <- actual_temp * schedule$temperature.decrease
      x.max <- x_max0 - (i / schedule$chains) * (x_max0 - x.min) + cellsize[1] + x_min0
      y.max <- y_max0 - (i / schedule$chains) * (y_max0 - y.min) + cellsize[2] + y_min0
    } # End the annealing schedule
    # Prepare output
    eval(.prepare_output())
  }
# INTERNAL FUNCTION - CALCULATE THE CRITERION VALUE ################################################
# Arguments:
# sm: sample matrix
# n.pts: number of points
# n.cov: number of covariates
# pop.prop: the sampling strata and population proportion, for numeric 
#           covariates, and the population proportion, for factor covariates
# covars.type: the type of covariate (numeric or factor)
.objDIST <-
  function(sm, n.pts, n.cov, pop.prop, covars.type) {
    if (covars.type == "numeric") {
      # Count the number of points per marginal sampling strata
      count <- lapply(1:n.cov, function(i) {
        graphics::hist(sm[, i], pop.prop[[1]][[i]], plot = FALSE)$counts
      })
      # Compute the sample proportions
      samp.prop <- lapply(1:n.cov, function(i) count[[i]] / n.pts)
      # Compare the sample and population proportions
      samp.prop <- sapply(1:n.cov, function(i) 
        sum(abs(samp.prop[[i]] - pop.prop[[2]][[i]])))
    } else { # Factor covariates
      # Compute the sample proportions
      samp.prop <- lapply(sm, function(x) table(x) / n.pts)
      # Compare the sample and population proportions
      samp.prop <- sapply(1:n.cov, function(i)
        sum(abs(samp.prop[[i]] - pop.prop[[i]])))
    }
    # Compute the energy value
    energy <- sum(samp.prop)
    return(energy)
  }
# CALCULATE OBJECTIVE FUNCTION VALUE ###############################################################
#' @rdname optimFREQ
#' @export
objFREQ <-
  function(points, candi,
    # FREQ
    covars, strata.type = "area", use.coords = FALSE) {
    # Check other arguments
    check <- .optimACDCcheck(
      candi = candi, covars = covars, use.coords = use.coords, strata.type = strata.type)
    if (!is.null(check)) stop (check, call. = FALSE)
    # Prepare points and candi
    eval(.prepare_points())
    # Prepare 'covars' and create the starting sample matrix 'sm'
    eval(.prepare_acdc_covars())
    # Calculate the energy state
    pop_prop <- .strataACDC(
      n.pts = n_pts, strata.type = strata.type, covars = covars, covars.type = covars.type)
    energy <- .objDIST(sm = sm, pop.prop = pop_prop, n.pts = n_pts, n.cov = n_cov,
      covars.type = covars.type)
    # Output
    return(energy)
  }
####################################################################################################
#' @rdname optimFREQ
#' @export
optimDIST <- optimFREQ
#' @rdname optimFREQ
#' @export
objDIST <- objFREQ