# R/adapt_seq.R In ProjectMOSAIC/mosaic: Project MOSAIC Statistics and Mathematics Teaching Utilities

```#' Adaptively generate sequences in an interval
#'
#' selecting points equally spaced along an interval, it selects points
#' such that the values of a function applied at those points are
#' (very) roughly equally spaced.  This can be useful for sampling
#' a function in such a way that it can be plotted more smoothly,
#' for example.
#'
#'
#' @param from start of interval
#' @param to end of interval
#' @param length.out desired length of sequence
#' @param f a function
#' @param args arguments passed to `f`
#' @param quiet suppress warnings about NaNs, etc.
#' @return a numerical vector
#' @examples
#'
#' @export
length.out=200,
f=function(x,...){ 1 },
args=list(),
quiet=FALSE
)
{
n <- round(sqrt(length.out))
n <- max(n,10)
s <- seq(from, to, length.out=n)
iteration <- 0
keepers <- s

repeat{
iteration <- iteration + 1
# clean up: remove bad s values
if (quiet) {
suppressWarnings(y <- do.call(f, args=c(list(s), args)))
} else {
y <- do.call(f, args=c(list(s), args))
}
w <- which(is.finite(y))
a <- min(w) - 1
a <- max(a,1)
b <- max(w) + 1
b <- min(b,length(s))
w <- sort(unique(c(w, 1, length(s), a, b )))
s <- s[w]; y <- y[w]

# quit if we have enough or reach edge condition
# print(list(i=iteration, a=s[a], b=s[b], start=head(s,4), end=tail(s,4)))
if ((length(s) < 2) || (iteration > 20) || (length(s) > length.out))
return(s[is.finite(y)])

# keep best points + previous keepers
ds <- ediff(s)
dy <- ediff(y)
angle <- atan(dy/ds)
wsum <- cumsum(is.finite(y))
a <- which.min( wsum== 1) - 1  # last non-finite
a <- max(a,1)
b <- which.min( wsum == max(wsum) ) # first of last run of non-finites
b < min(b,length(s))
score[c(a,b)] <- Inf     # keep a and b

w <- which( s %in% keepers | score > quantile(score, probs=0.2, na.rm=TRUE))
# be sure to keep left and right ends
w <- sort(unique(c(w, 1, length(s))))
s <- s[w]
keepers <- s

# create some more s values at midpoints
ds <- diff(s)
mid.s <- s[-1] - .5 * ds
s <- sort( c(s, mid.s) )
if (quiet) {
suppressWarnings(y <- do.call(f, args=c(list(s), args)))
} else {
y <- do.call(f, args=c(list(s), args))
}
}