pretty10exp: Nice 10 ** k Label Expressions

Description

Produce nice \(a \times 10^k\) expressions to be used instead of the scientific notation "a E<k>".

Usage


pretty10exp(x, drop.1 = FALSE, sub10 = FALSE, digits = 7, digits.fuzz,
            off = pmax(10^-digits, 2^-(l10x*log2(10)+1075)),
            lab.type = c("plotmath","latex"),
            lab.sep = c("cdot", "times"))

Value

For the default lab.type = "plotmath", an expression of the same length as x, typically with elements of the form a %*% 10 ^ k. Exceptions are 0 which is kept simple, if drop.1 is true and \(a = 1\), 10 ^ k is used, and if sub10

is not false, a %*% 10 ^ 0 as a, and a %*% 10 ^ k as as the corresponding formatted number a * 10^k independently of

drop.1.

Otherwise, a character vector of the same length as

x. For lab.type = "latex", currently the only alternative to the default, these strings are LaTeX (math mode) compatible strings.

Arguments

x

numeric vector (e.g. axis tick locations)

drop.1

logical indicating if \(1 \times\) should be dropped from the resulting expressions.

sub10

logical, "10", "100", an integer number or vector of length two, say \((k_1,k_2)\), indicating if some \(10^j\) expressions for \(j \in J\) should be formatted traditionally, notably e.g., \(10^0 \equiv 1\).
When a number, say \(k\), \(J = \{j; j \le k\}\) are all simplified, when a length--2 vector, \(J = \{j; k_1 \le j \le k_2\}\) are.

Special cases:

sub10 = TRUE:: use \(1\) instead of \(10^0\),

sub10 = "10":

short for c(-1,1), i.e., uses \(0.1\) for 10^{-1}, \(1\) for \(10^0\) and \(10\) for \(10^1\);

sub10 = "100":

short for c(-1,2), i.e., uses \(0.1\), \(1\), \(10\), and \(100\) for 10^{-1},..., 10^2.

sub10 = "1000":

short for c(-2,3), using \(0.01\), \(0.1\), ..., \(1000\) for 10^{-2},..., 10^3.

If it would not break back compatibility, the author would nowadays choose the default as sub10 = "1000".

digits

number of digits for mantissa (\(a\)) construction; the number of significant digits, see signif.

digits.fuzz

the old deprecated name for digits.

off

a numeric offset in eT <- floor(l10x + off) where l10x <- log10(abs(x)) and eT are the exponents \(k\) for label factors \(10^k\). Previously hardcoded to 10^-digits, the new default provides better results for subnormal abs(x) values.

lab.type

a string indicating how the result should look like. By default, (plotmath-compatible) expressions are returned. Alternatively, lab.type = "plotmath" returns LaTeX formatted strings for labels. (The latter is useful, e.g., when using the tikzDevice package to generate LaTeX-processed figures.)

lab.sep

character separator between mantissa and exponent for LaTeX labels; it will be prepended with a backslash, i.e., ‘"cdot"’ will use ‘"\cdot"’

Author

Martin Maechler; Ben Bolker contributed lab.type = "latex" and lab.sep.

Examples

Run this code

pretty10exp(-1:3 * 1000)
pretty10exp(-1:3 * 1000, drop.1 = TRUE)
pretty10exp(c(1,2,5,10,20,50,100,200) * 1e3)
pretty10exp(c(1,2,5,10,20,50,100,200) * 1e3, drop.1 = TRUE)

set.seed(17); lx <- rlnorm(10, m=8, s=6)
pretty10exp(lx, digits = 3)
pretty10exp(lx, digits = 3, sub10 = 2)

pretty10exp(lx, digits = 3, lab.type="latex")
pretty10exp(lx, digits = 3, lab.type="latex", lab.sep="times", sub10=2)

## use regular formatted numbers from 0.03 to 300 :
pretty10exp(3*10^(-3:4), sub10 = c(-2,2))
pretty10exp(3*10^(-3:4), sub10 = c(-2,2), lab.type = "l")

# \dontshow{
stopifnot(identical(pretty10exp(numeric(0)), expression()))
# }
ax <- 10^(-6:0) - 2e-16
pretty10exp(ax, drop.1=TRUE) # nice for plotting
pretty10exp(ax, drop.1=TRUE, sub10=TRUE)
pretty10exp(ax, drop.1=TRUE, sub10=c(-2,2))

## in sfsmisc version <= 1.0-16, no 'digits',
## i.e., implicitly had  digits := #{double precision digits} ==
(dig. <- .Machine$double.digits * log10(2)) # 15.95
pretty10exp(ax, drop.1=TRUE, digits= dig.)  # ''ugly''

## Subnormal numbers
x <- sort(c(outer(10^-(323:305), 1:9))); x <- c(x[1]/2, x)
tail(x, 12) # nice
head(x, 6)  # "ugly" (they are multiple's of 2^-1074):
head(x, 6) / 2^-1074  # nice

head(p0 <- pretty10exp(x, off = 10^-7), 30) # previous behavior {before 'off' existed}
str(head(pTen <- lapply(p0, `[[`, 3L)))
str(exTen <- sapply(pTen, `[[`, 3L)) # -324 -324 ..
head(f0 <- sapply(p0, `[[`, 2L), 17)

head(p1 <- pretty10exp(x))# new default
str(head(pTen1 <- lapply(p1, `[[`, 3L)))
str(exTen1 <- sapply(pTen1, `[[`, 3L)) # -324 -324 ..
head(f1 <- sapply(p1, `[[`, 2L), 17)   #

head(cbind(x, f0, f1, exTen, exTen1), 80)
(nEQ <- which(sapply(1:length(p0), function(i) p0[[i]] != p1[[i]])))
cbind(x, f0, f1, exTen, exTen1)[nEQ,]
stopifnot(is.finite(f1), 0.5 <= f1, f1 <= 9)