# utility functions
# functions for getting Q bounds.
#' Minimum across xs of max across time of width
#'
#' @param x a numeric matrix
minmax <- function(x)
min(apply(x, 1, max))
#' Maximum across xs of min across time of width
#'
#' @param x a numeric matrix
maxmin <- function(x) {
max(apply(x, 1, min))
}
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