The R Project SVN R

% File src/library/grDevices/man/plotmath.Rd

% Part of the R package, https://www.R-project.org

% Copyright 1995-2019 R Core Team

% Distributed under GPL 2 or later

\name{plotmath}

\alias{plotmath}

\alias{symbol}

\alias{plain}

\alias{bold}

\alias{italic}

\alias{bolditalic}

\alias{hat}

\alias{bar}

\alias{dot}

\alias{ring}

\alias{widehat}

\alias{widetilde}

\alias{displaystyle}

\alias{textstyle}

\alias{scriptstyle}

\alias{scriptscriptstyle}

\alias{underline}

\alias{phantom}

\alias{over}

\alias{frac}

\alias{atop}

\alias{integral}

\alias{inf}

\alias{sup}

\alias{group}

\alias{bgroup}

\title{Mathematical Annotation in R}

\description{

  If the \code{text} argument to one of the text-drawing functions

  (\code{\link{text}}, \code{\link{mtext}}, \code{\link{axis}},

  \code{\link{legend}}) in \R is an expression, the argument is

  interpreted as a mathematical expression and the output will be

  formatted according to TeX-like rules.  Expressions can also be used

  for titles, subtitles and x- and y-axis labels (but not for axis

  labels on \code{persp} plots).

  In most cases other language objects (names and calls, including

  formulas) are coerced to expressions and so can also be used.

}

\details{

  A mathematical expression must obey the normal rules of syntax for any

  \R expression, but it is interpreted according to very different rules

  than for normal \R expressions.

  It is possible to produce many different mathematical symbols, generate

  sub- or superscripts, produce fractions, etc.

  The output from \code{demo(plotmath)} includes several tables which

  show the available features.  In these tables, the columns of grey text

  show sample \R expressions, and the columns of black text show the

  resulting output.

  The available features are also described in the tables below:

  \tabular{ll}{

    \bold{Syntax} \tab \bold{Meaning} \cr

    \code{x + y}   \tab x plus y   \cr

    \code{x - y}   \tab x minus y \cr

    \code{x*y}    \tab juxtapose x and y \cr

    \code{x/y}    \tab x forwardslash y \cr

    \code{x \%+-\% y}   \tab x plus or minus y \cr

    \code{x \%/\% y}   \tab x divided by y \cr

    \code{x \%*\% y}   \tab x times y \cr

    \code{x \%.\% y}   \tab x cdot y \cr

    \code{x[i]}   \tab x subscript i \cr

    \code{x^2}    \tab x superscript 2 \cr

    \code{paste(x, y, z)} \tab juxtapose x, y, and z \cr

    \code{sqrt(x)}   \tab square root of x \cr

    \code{sqrt(x, y)}   \tab yth root of x \cr

    \code{x == y}   \tab x equals y \cr

    \code{x != y}   \tab x is not equal to y \cr

    \code{x < y}   \tab x is less than y \cr

    \code{x <= y}   \tab x is less than or equal to y \cr

    \code{x > y}   \tab x is greater than y \cr

    \code{x >= y}   \tab x is greater than or equal to y \cr

    \code{!x} \tab not x \cr

    \code{x \%~~\% y}   \tab x is approximately equal to y \cr

    \code{x \%=~\% y}   \tab x and y are congruent \cr

    \code{x \%==\% y}   \tab x is defined as y \cr

    \code{x \%prop\% y}  \tab x is proportional to y \cr

    \code{x \%~\% y}  \tab x is distributed as y \cr

    \code{plain(x)}   \tab draw x in normal font \cr

    \code{bold(x)}   \tab draw x in bold font \cr

    \code{italic(x)}   \tab draw x in italic font \cr

    \code{bolditalic(x)} \tab draw x in bolditalic font \cr

    \code{symbol(x)} \tab draw x in symbol font \cr

    \code{list(x, y, z)} \tab comma-separated list \cr

    \code{...}    \tab ellipsis (height varies) \cr

    \code{cdots}   \tab ellipsis (vertically centred) \cr

    \code{ldots}   \tab ellipsis (at baseline) \cr

    \code{x \%subset\% y} \tab x is a proper subset of y \cr

    \code{x \%subseteq\% y} \tab x is a subset of y \cr

    \code{x \%notsubset\% y} \tab x is not a subset of y \cr

    \code{x \%supset\% y} \tab x is a proper superset of y \cr

    \code{x \%supseteq\% y} \tab x is a superset of y \cr

    \code{x \%in\% y}   \tab x is an element of y \cr

    \code{x \%notin\% y} \tab x is not an element of y \cr

    \code{hat(x)}   \tab x with a circumflex \cr

    \code{tilde(x)}   \tab x with a tilde \cr

    \code{dot(x)} \tab x with a dot \cr

    \code{ring(x)}   \tab x with a ring \cr

    \code{bar(xy)}   \tab xy with bar \cr

    \code{widehat(xy)}   \tab xy with a wide circumflex \cr

    \code{widetilde(xy)} \tab xy with a wide tilde \cr

    \code{x \%<->\% y}   \tab x double-arrow y \cr

    \code{x \%->\% y}   \tab x right-arrow y \cr

    \code{x \%<-\% y}   \tab x left-arrow y \cr

    \code{x \%up\% y}   \tab x up-arrow y \cr

    \code{x \%down\% y}  \tab x down-arrow y \cr

    \code{x \%<=>\% y}   \tab x is equivalent to y \cr

    \code{x \%=>\% y}   \tab x implies y \cr

    \code{x \%<=\% y}   \tab y implies x \cr

    \code{x \%dblup\% y}   \tab x double-up-arrow y \cr

    \code{x \%dbldown\% y} \tab x double-down-arrow y \cr

    \code{alpha} -- \code{omega} \tab Greek symbols \cr

    \code{Alpha} -- \code{Omega} \tab uppercase Greek symbols \cr

    \code{theta1, phi1, sigma1, omega1} \tab cursive Greek symbols\cr

    \code{Upsilon1} \tab capital upsilon with hook\cr

    \code{aleph} \tab first letter of Hebrew alphabet\cr

    \code{infinity}   \tab infinity symbol \cr

    \code{partialdiff} \tab partial differential symbol \cr

    \code{nabla} \tab nabla, gradient symbol\cr

    \code{32*degree}   \tab 32 degrees \cr

    \code{60*minute}   \tab 60 minutes of angle \cr

    \code{30*second}   \tab 30 seconds of angle \cr

    \code{displaystyle(x)} \tab draw x in normal size (extra spacing) \cr

    \code{textstyle(x)}  \tab draw x in normal size \cr

    \code{scriptstyle(x)} \tab draw x in small size \cr

    \code{scriptscriptstyle(x)} \tab draw x in very small size \cr

    \code{underline(x)}   \tab draw x underlined\cr

    \code{x ~~ y}        \tab put extra space between x and y \cr

    \code{x + phantom(0) + y} \tab leave gap for "0", but don't draw it \cr

    \code{x + over(1, phantom(0))} \tab leave vertical gap for "0" (don't draw) \cr

    \code{frac(x, y)}   \tab x over y \cr

    \code{over(x, y)}   \tab x over y \cr

    \code{atop(x, y)}   \tab x over y (no horizontal bar) \cr

    \code{sum(x[i], i==1, n)} \tab sum x[i] for i equals 1 to n \cr

    \code{prod(plain(P)(X==x), x)} \tab product of P(X=x) for all values of x \cr

    \code{integral(f(x)*dx, a, b)} \tab definite integral of f(x) wrt x \cr

    \code{union(A[i], i==1, n)} \tab union of A[i] for i equals 1 to n \cr

    \code{intersect(A[i], i==1, n)} \tab intersection of A[i] \cr

    \code{lim(f(x), x \%->\% 0)} \tab limit of f(x) as x tends to 0 \cr

    \code{min(g(x), x > 0)} \tab minimum of g(x) for x greater than 0 \cr

    \code{inf(S)}        \tab infimum of S \cr

    \code{sup(S)}   \tab supremum of S \cr

    \code{x^y + z}   \tab normal operator precedence \cr

    \code{x^(y + z)}    \tab visible grouping of operands \cr

    \code{x^{y + z}}  \tab invisible grouping of operands \cr

    \code{group("(",list(a, b),"]")} \tab specify left and right delimiters \cr

    \code{bgroup("(",atop(x,y),")")} \tab use scalable delimiters \cr

    \code{group(lceil, x, rceil)} \tab special delimiters \cr

    \code{group(lfloor, x, rfloor)} \tab special delimiters \cr

  }

  The supported \sQuote{scalable delimiters} are \code{| ( [ \{},

  \code{lceil}, \code{lfloor} and their right-hand versions.

  \code{"."} is equivalent to \code{""}: the corresponding delimiter

  will be omitted. Delimiter \code{||} is supported but has the same

  effect as \code{|}.

  The symbol font uses Adobe Symbol encoding so, for example, a lower

  case mu can be obtained either by the special symbol \code{mu} or by

  \code{symbol("m")}.  This provides access to symbols that have no

  special symbol name, for example, the universal, or forall, symbol is

  \code{symbol("\\042")}.  To see what symbols are available in this way

  use \code{TestChars(font=5)} as given in the examples for

  \code{\link{points}}: some are only available on some devices.

  Note to TeX users: TeX's \samp{\\Upsilon} is \code{Upsilon1}, TeX's

  \samp{\\varepsilon} is close to \code{epsilon}, and there is no

  equivalent of TeX's \samp{\\epsilon}.  TeX's \samp{\\varpi} is close to

  \code{omega1}.  \code{vartheta}, \code{varphi} and \code{varsigma} are

  allowed as synonyms for \code{theta1}, \code{phi1} and \code{sigma1}.

  \code{sigma1} is also known as \code{stigma}, its Unicode name.

  Control characters (e.g., \samp{\\n}) are not interpreted in character

  strings in plotmath, unlike normal plotting.

  The fonts used are taken from the current font family, and so can be

  set by \code{\link{par}(family=)} in base graphics, and

  \code{\link{gpar}(fontfamily=)} in package \pkg{grid}.

  Note that \code{bold}, \code{italic} and \code{bolditalic} do not

  apply to symbols, and hence not to the Greek \emph{symbols} such as

  \code{mu} which are displayed in the symbol font.  They also do not

  apply to numeric constants.

}

\section{Other symbols}{

  On many OSes and some graphics devices many other symbols are

  available as part of the standard text font, and all of the symbols in

  the Adobe Symbol encoding are in principle available \emph{via}

  changing the font face or (see \sQuote{Details}) plotmath: see the

  examples section of \code{\link{points}} for a function to display

  them.  (\sQuote{In principle} because some of the glyphs are missing

  from some implementations of the symbol font.)  Unfortunately,

  \code{\link{postscript}} and \code{\link{pdf}} have support for little

  more than European (not Greek) and CJK characters and the Adobe Symbol

  encoding (and in a few fonts, also Cyrillic characters).

  \describe{

    \item{On Unix-alikes:}{

  In a UTF-8 locale any Unicode character can be entered, perhaps as a

  \samp{\\uxxxx} or \samp{\\Uxxxxxxxx} escape sequence, but the issue is

  whether the graphics device is able to display the character.  The

  widest range of characters is likely to be available in the

  \code{\link{X11}} device using cairo: see its help page for how

  installing additional fonts can help.  This can often be used to

  display Greek \emph{letters} in bold or italic.

  In non-UTF-8 locales there is normally no support for symbols not in

  the languages for which the current encoding was intended.

    }

    \item{On Windows:}{

  Any Unicode character can be entered into a text string \emph{via} a

  \samp{\\uxxxx} escape, or used by number in a call to

  \code{\link{points}}.  The \code{\link{windows}} family of devices can

  display such characters if they are available in the font in use.

  This can often be used to display Greek \emph{letters} in bold or italic.

  A good way to both find out which characters are available in a font

  and to determine the Unicode number is to use the \sQuote{Character

  Map} accessory (usually on the \sQuote{Start} menu under

  \sQuote{Accessories->System Tools}).  You can also copy-and-paste

  characters from the \sQuote{Character Map} window to the \code{Rgui}

  console (but not to \code{Rterm}).

    }

 }

}

\references{

  Murrell, P. and Ihaka, R. (2000).

  An approach to providing mathematical annotation in plots.

  \emph{Journal of Computational and Graphical Statistics},

  \bold{9}, 582--599.

  \doi{10.2307/1390947}.

  The symbol codes can be found in octal in the Adobe reference manuals,

  e.g.\sspace{}for Postscript

  % \url{https://www.adobe.com/products/postscript/pdfs/PLRM.pdf} now points to

  \url{https://www.adobe.com/content/dam/acom/en/devnet/actionscript/articles/PLRM.pdf}

  or PDF

  \url{https://www.adobe.com/devnet/acrobat/pdfs/pdf_reference_1-7.pdf}

  and in decimal, octal and hex at

  \url{http://www.stat.auckland.ac.nz/~paul/R/CM/AdobeSym.html}.

}

\seealso{

  \code{demo(plotmath)},

  \code{\link{axis}},

  \code{\link{mtext}},

  \code{\link{text}},

  \code{\link{title}},

  \code{\link{substitute}}

  \code{\link{quote}}, \code{\link{bquote}}

}

\examples{

require(graphics)

x <- seq(-4, 4, len = 101)

y <- cbind(sin(x), cos(x))

matplot(x, y, type = "l", xaxt = "n",

        main = expression(paste(plain(sin) * phi, "  and  ",

                                plain(cos) * phi)),

        ylab = expression("sin" * phi, "cos" * phi), # only 1st is taken

        xlab = expression(paste("Phase Angle ", phi)),

        col.main = "blue")

axis(1, at = c(-pi, -pi/2, 0, pi/2, pi),

     labels = expression(-pi, -pi/2, 0, pi/2, pi))

## How to combine "math" and numeric variables :

plot(1:10, type="n", xlab="", ylab="", main = "plot math & numbers")

theta <- 1.23 ; mtext(bquote(hat(theta) == .(theta)), line= .25)

for(i in 2:9)

    text(i, i+1, substitute(list(xi, eta) == group("(",list(x,y),")"),

                            list(x = i, y = i+1)))

## note that both of these use calls rather than expressions.

##

text(1, 10,  "Derivatives:", adj = 0)

text(1, 9.6, expression(

 "             first: {f * minute}(x) " == {f * minute}(x)), adj = 0)

text(1, 9.0, expression(

 "     second: {f * second}(x) "        == {f * second}(x)), adj = 0)

plot(1:10, 1:10)

text(4, 9, expression(hat(beta) == (X^t * X)^{-1} * X^t * y))

text(4, 8.4, "expression(hat(beta) == (X^t * X)^{-1} * X^t * y)",

     cex = .8)

text(4, 7, expression(bar(x) == sum(frac(x[i], n), i==1, n)))

text(4, 6.4, "expression(bar(x) == sum(frac(x[i], n), i==1, n))",

     cex = .8)

text(8, 5, expression(paste(frac(1, sigma*sqrt(2*pi)), " ",

                            plain(e)^{frac(-(x-mu)^2, 2*sigma^2)})),

     cex = 1.2)

## some other useful symbols

plot.new(); plot.window(c(0,4), c(15,1))

text(1, 1, "universal", adj = 0); text(2.5, 1,  "\\\\042")

text(3, 1, expression(symbol("\\042")))

text(1, 2, "existential", adj = 0); text(2.5, 2,  "\\\\044")

text(3, 2, expression(symbol("\\044")))

text(1, 3, "suchthat", adj = 0); text(2.5, 3,  "\\\\047")

text(3, 3, expression(symbol("\\047")))

text(1, 4, "therefore", adj = 0); text(2.5, 4,  "\\\\134")

text(3, 4, expression(symbol("\\134")))

text(1, 5, "perpendicular", adj = 0); text(2.5, 5,  "\\\\136")

text(3, 5, expression(symbol("\\136")))

text(1, 6, "circlemultiply", adj = 0); text(2.5, 6,  "\\\\304")

text(3, 6, expression(symbol("\\304")))

text(1, 7, "circleplus", adj = 0); text(2.5, 7,  "\\\\305")

text(3, 7, expression(symbol("\\305")))

text(1, 8, "emptyset", adj = 0); text(2.5, 8,  "\\\\306")

text(3, 8, expression(symbol("\\306")))

text(1, 9, "angle", adj = 0); text(2.5, 9,  "\\\\320")

text(3, 9, expression(symbol("\\320")))

text(1, 10, "leftangle", adj = 0); text(2.5, 10,  "\\\\341")

text(3, 10, expression(symbol("\\341")))

text(1, 11, "rightangle", adj = 0); text(2.5, 11,  "\\\\361")

text(3, 11, expression(symbol("\\361")))

}

\keyword{aplot}