plotmath {graphics}R Documentation

Mathematical Annotation in R


If the text argument to one of the text-drawing functions (text, mtext, axis) 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 persp plots).


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 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:

Syntax Meaning
x + y x plus y
x - y x minus y
x*y juxtapose x and y
x/y x forwardslash y
x %+-% y x plus or minus y
x %/% y x divided by y
x %*% y x times y
x[i] x subscript i
x^2 x superscript 2
paste(x, y, z) juxtapose x, y, and z
sqrt(x) square root of x
sqrt(x, y) yth root of x
x == y x equals y
x != y x is not equal to y
x < y x is less than y
x <= y x is less than or equal to y
x > y x is greater than y
x >= y x is greater than or equal to y
x %~~% y x is approximately equal to y
x %=~% y x and y are congruent
x %==% y x is defined as y
x %prop% y x is proportional to y
plain(x) draw x in normal font
bold(x) draw x in bold font
italic(x) draw x in italic font
bolditalic(x) draw x in bolditalic font
list(x, y, z) comma-separated list
... ellipsis (height varies)
cdots ellipsis (vertically centred)
ldots ellipsis (at baseline)
x %subset% y x is a proper subset of y
x %subseteq% y x is a subset of y
x %notsubset% y x is not a subset of y
x %supset% y x is a proper superset of y
x %supseteq% y x is a superset of y
x %in% y x is an element of y
x %notin% y x is not an element of y
hat(x) x with a circumflex
tilde(x) x with a tilde
dot(x) x with a dot
ring(x) x with a ring
bar(xy) xy with bar
widehat(xy) xy with a wide circumflex
widetilde(xy) xy with a wide tilde
x %<->% y x double-arrow y
x %->% y x right-arrow y
x %<-% y x left-arrow y
x %up% y x up-arrow y
x %down% y x down-arrow y
x %<=>% y x is equivalent to y
x %=>% y x implies y
x %<=% y y implies x
x %dblup% y x double-up-arrow y
x %dbldown% y x double-down-arrow y
alphaomega Greek symbols
AlphaOmega uppercase Greek symbols
infinity infinity symbol
partialdiff partial differential symbol
32*degree 32 degrees
60*minute 60 minutes of angle
30*second 30 seconds of angle
displaystyle(x) draw x in normal size (extra spacing)
textstyle(x) draw x in normal size
scriptstyle(x) draw x in small size
scriptscriptstyle(x) draw x in very small size
x ~~ y put extra space between x and y
x + phantom(0) + y leave gap for "0", but don't draw it
x + over(1, phantom(0)) leave vertical gap for "0" (don't draw)
frac(x, y) x over y
over(x, y) x over y
atop(x, y) x over y (no horizontal bar)
sum(x[i], i==1, n) sum x[i] for i equals 1 to n
prod(plain(P)(X==x), x) product of P(X=x) for all values of x
integral(f(x)*dx, a, b) definite integral of f(x) wrt x
union(A[i], i==1, n) union of A[i] for i equals 1 to n
intersect(A[i], i==1, n) intersection of A[i]
lim(f(x), x %->% 0) limit of f(x) as x tends to 0
min(g(x), x > 0) minimum of g(x) for x greater than 0
inf(S) infimum of S
sup(S) supremum of S
x^y + z normal operator precedence
x^(y + z) visible grouping of operands
x^{y + z} invisible grouping of operands
group("(",list(a, b),"]") specify left and right delimiters
bgroup("(",atop(x,y),")") use scalable delimiters
group(lceil, x, rceil) special delimiters


Murrell, P. and Ihaka, R. (2000) An approach to providing mathematical annotation in plots. Journal of Computational and Graphical Statistics, 9, 582–599.

See Also

demo(plotmath), axis, mtext, text, title, substitute quote, bquote


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),
     lab = 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)))
for(i in 2:9)
    text(i,i+1, substitute(list(xi,eta) == group("(",list(x,y),")"),
                           list(x=i, y=i+1)))

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)

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