\HeaderA{pretty}{Pretty Breakpoints}{pretty}
\keyword{dplot}{pretty}
\begin{Description}\relax
Compute a  sequence of about \code{n+1} equally spaced \sQuote{round}
values which cover the range of the values in \code{x}.
The values are chosen so that they are 1, 2 or 5 times a power of 10.
\end{Description}
\begin{Usage}
\begin{verbatim}
pretty(x, n = 5, min.n = n %/% 3,  shrink.sml = 0.75,
       high.u.bias = 1.5, u5.bias = .5 + 1.5*high.u.bias,
       eps.correct = 0)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] an object coercible to numeric by \code{\LinkA{as.numeric}{as.numeric}}.
\item[\code{n}] integer giving the \emph{desired} number of
intervals.  Non-integer values are rounded down.
\item[\code{min.n}] nonnegative integer giving the \emph{minimal} number of
intervals.  If \code{min.n == 0}, \code{pretty(.)} may return a
single value.
\item[\code{shrink.sml}] positive numeric
by a which a default scale is shrunk in the case when
\code{range(x)} is very small (usually 0).
\item[\code{high.u.bias}] non-negative numeric, typically \eqn{> 1}{}.
The interval unit is determined as \{1,2,5,10\} times \code{b}, a
power of 10.  Larger \code{high.u.bias} values favor larger units.
\item[\code{u5.bias}] non-negative numeric
multiplier favoring factor 5 over 2.  Default and \sQuote{optimal}:
\code{u5.bias = .5 + 1.5*high.u.bias}.
\item[\code{eps.correct}] integer code, one of \{0,1,2\}. If non-0, an
\emph{epsilon correction} is made at the boundaries such that
the result boundaries will be outside \code{range(x)}; in the
\emph{small} case, the correction is only done if \code{eps.correct >=2}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
\code{pretty} ignores non-finite values in \code{x}.

Let \code{d <- max(x) - min(x)} \eqn{\ge 0}{>= 0}.
If \code{d} is not (very close) to 0, we let \code{c <- d/n},
otherwise more or less \code{c <- max(abs(range(x)))*shrink.sml / min.n}.
Then, the \emph{10 base} \code{b} is
\eqn{10^{\lfloor{\log_{10}(c)}\rfloor}}{10^(floor(log10(c)))} such
that \eqn{b \le c < 10b}{}.

Now determine the basic \emph{unit} \eqn{u}{} as one of
\eqn{\{1,2,5,10\} b}{}, depending on \eqn{c/b \in [1,10)}{} and the two
\sQuote{\emph{bias}} coefficients, \eqn{h =}{}\code{high.u.bias} and
\eqn{f =}{}\code{u5.bias}.

\dots\dots\dots
\end{Details}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{axTicks}{axTicks}} for the computation of pretty axis tick
locations in plots, particularly on the log scale.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
pretty(1:15)     # 0  2  4  6  8 10 12 14 16
pretty(1:15, h=2)# 0  5 10 15
pretty(1:15, n=4)# 0  5 10 15
pretty(1:15 * 2) # 0  5 10 15 20 25 30
pretty(1:20)      # 0  5 10 15 20
pretty(1:20, n=2) # 0 10 20
pretty(1:20, n=10)# 0  2  4 ... 20

for(k in 5:11) {
  cat("k=",k,": "); print(diff(range(pretty(100 + c(0, pi*10^-k)))))}

##-- more bizarre, when  min(x) == max(x):
pretty(pi)

add.names <- function(v) { names(v) <- paste(v); v}
utils::str(lapply(add.names(-10:20), pretty))
utils::str(lapply(add.names(0:20),   pretty, min.n = 0))
sapply(    add.names(0:20),   pretty, min.n = 4)

pretty(1.234e100)
pretty(1001.1001)
pretty(1001.1001, shrink = .2)
for(k in -7:3)
  cat("shrink=", formatC(2^k, width=9),":",
      formatC(pretty(1001.1001, shrink.sml = 2^k), width=6),"\n")
\end{ExampleCode}
\end{Examples}

