R: Mathematical Annotation in R

plotmath {base}

R Documentation

Mathematical Annotation in R

Description

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.

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 example(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

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

alpha – omega Greek symbols

Alpha – Omega uppercase Greek symbols

infinity infinity 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

References

Murrell, P. and Ihaka, R. (2000) An approach to providing mathematical annotation in plots. Journal of Computational and Graphical Statistics (In press).

Examples

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))

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)

######
# create tables of mathematical annotation functionality
######
make.table <- function(nr, nc) {
    savepar <- par(mar=rep(0, 4), pty="s")
    plot(c(0, nc*2 + 1), c(0, -(nr + 1)), 
         type="n", xlab="", ylab="", axes=F)
    savepar
}

get.r <- function(i, nr) {
    i %% nr + 1
}

get.c <- function(i, nr) {
    i %/% nr + 1
}

draw.title.cell <- function(title, i, nr) {
    r <- get.r(i, nr)
    c <- get.c(i, nr)
    text(2*c - .5, -r, title)
    rect((2*(c - 1) + .5), -(r - .5), (2*c + .5), -(r + .5))
}

draw.plotmath.cell <- function(expr, i, nr, string = NULL) {
    r <- get.r(i, nr)
    c <- get.c(i, nr)
    if (is.null(string)) {
        string <- deparse(expr)
        string <- substr(string, 12, nchar(string) - 1)
    }
    text((2*(c - 1) + 1), -r, string, col="grey")
    text((2*c), -r, expr, adj=c(.5,.5))
    rect((2*(c - 1) + .5), -(r - .5), (2*c + .5), -(r + .5), border="grey")
}

nr <- 20
nc <- 2
oldpar <- make.table(nr, nc)
i <- 0
draw.title.cell("Arithmetic Operators", i, nr); i <- i + 1
draw.plotmath.cell(expression(x + y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x - y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x * y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x / y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %+-% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %/% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %*% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(-x), i, nr); i <- i + 1
draw.plotmath.cell(expression(+x), i, nr); i <- i + 1
draw.title.cell("Sub/Superscripts", i, nr); i <- i + 1
draw.plotmath.cell(expression(x[i]), i, nr); i <- i + 1
draw.plotmath.cell(expression(x^2), i, nr); i <- i + 1
draw.title.cell("Juxtaposition", i, nr); i <- i + 1
draw.plotmath.cell(expression(x * y), i, nr); i <- i + 1
draw.plotmath.cell(expression(paste(x, y, z)), i, nr); i <- i + 1
draw.title.cell("Lists", i, nr); i <- i + 1
draw.plotmath.cell(expression(list(x, y, z)), i, nr); i <- i + 1
# even columns up
i <- 20
draw.title.cell("Radicals", i, nr); i <- i + 1
draw.plotmath.cell(expression(sqrt(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(sqrt(x, y)), i, nr); i <- i + 1
draw.title.cell("Relations", i, nr); i <- i + 1
draw.plotmath.cell(expression(x == y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x != y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x < y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x <= y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x > y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x >= y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %~~% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %=~% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %==% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %prop% y), i, nr); i <- i + 1
draw.title.cell("Typeface", i, nr); i <- i + 1
draw.plotmath.cell(expression(plain(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(italic(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(bold(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(bolditalic(x)), i, nr); i <- i + 1

# Need fewer, wider columns for ellipsis ...
nr <- 20
nc <- 2
make.table(nr, nc)
i <- 0
draw.title.cell("Ellipsis", i, nr); i <- i + 1
draw.plotmath.cell(expression(list(x[1], ..., x[n])), i, nr); i <- i + 1
draw.plotmath.cell(expression(x[1] + ... + x[n]), i, nr); i <- i + 1
draw.plotmath.cell(expression(list(x[1], cdots, x[n])), i, nr); i <- i + 1
draw.plotmath.cell(expression(x[1] + ldots + x[n]), i, nr); i <- i + 1
draw.title.cell("Set Relations", i, nr); i <- i + 1
draw.plotmath.cell(expression(x %subset% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %subseteq% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %supset% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %supseteq% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %notsubset% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %in% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %notin% y), i, nr); i <- i + 1
draw.title.cell("Accents", i, nr); i <- i + 1
draw.plotmath.cell(expression(hat(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(tilde(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(ring(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(bar(xy)), i, nr); i <- i + 1
draw.plotmath.cell(expression(widehat(xy)), i, nr); i <- i + 1
draw.plotmath.cell(expression(widetilde(xy)), i, nr); i <- i + 1
draw.title.cell("Arrows", i, nr); i <- i + 1
draw.plotmath.cell(expression(x %<->% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %->% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %<-% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %up% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %down% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %<=>% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %=>% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %<=% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %dblup% y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x %dbldown% y), i, nr); i <- i + 1
draw.title.cell("Symbolic Names", i, nr); i <- i + 1
draw.plotmath.cell(expression(Alpha - Omega), i, nr); i <- i + 1
draw.plotmath.cell(expression(alpha - omega), i, nr); i <- i + 1
draw.plotmath.cell(expression(infinity), i, nr); i <- i + 1
draw.plotmath.cell(expression(32 * degree), i, nr); i <- i + 1
draw.plotmath.cell(expression(60 * minute), i, nr); i <- i + 1
draw.plotmath.cell(expression(30 * second), i, nr); i <- i + 1

# Need even fewer, wider columns for typeface and style ...
nr <- 20
nc <- 1
make.table(nr, nc)
i <- 0
draw.title.cell("Style", i, nr); i <- i + 1
draw.plotmath.cell(expression(displaystyle(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(textstyle(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(scriptstyle(x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(scriptscriptstyle(x)), i, nr); i <- i + 1
draw.title.cell("Spacing", i, nr); i <- i + 1
draw.plotmath.cell(expression(x ~~ y), i, nr); i <- i + 1

# Need fewer, taller rows for fractions ...
# cheat a bit to save pages
par(new =T)
nr <- 10
nc <- 1
make.table(nr, nc)
i <- 4
draw.plotmath.cell(expression(x + phantom(0) + y), i, nr); i <- i + 1
draw.plotmath.cell(expression(x + over(1, phantom(0))), i, nr); i <- i + 1
draw.title.cell("Fractions", i, nr); i <- i + 1
draw.plotmath.cell(expression(frac(x, y)), i, nr); i <- i + 1
draw.plotmath.cell(expression(over(x, y)), i, nr); i <- i + 1
draw.plotmath.cell(expression(atop(x, y)), i, nr); i <- i + 1

# Need fewer, taller rows and fewer, wider columns for big operators ...
nr <- 10
nc <- 1
make.table(nr, nc)
i <- 0
draw.title.cell("Big Operators", i, nr); i <- i + 1
draw.plotmath.cell(expression(sum(x[i], i=1, n)), i, nr); i <- i + 1
draw.plotmath.cell(expression(prod(plain(P)(X == x), x)), i, nr); i <- i + 1
draw.plotmath.cell(expression(integral(f(x) * dx, a, b)), i, nr); i <- i + 1
draw.plotmath.cell(expression(union(A[i], i==1, n)), i, nr); i <- i + 1
draw.plotmath.cell(expression(intersect(A[i], i==1, n)), i, nr); i <- i + 1
draw.plotmath.cell(expression(lim(f(x), x %->% 0)), i, nr); i <- i + 1
draw.plotmath.cell(expression(min(g(x), x >= 0)), i, nr); i <- i + 1
draw.plotmath.cell(expression(inf(S)), i, nr); i <- i + 1
draw.plotmath.cell(expression(sup(S)), i, nr); i <- i + 1

make.table(nr, nc)
i <- 0
draw.title.cell("Grouping", i, nr); i <- i + 1
draw.plotmath.cell(expression((x + y)*z), i, nr); i <- i + 1
draw.plotmath.cell(expression(x^y + z), i, nr); i <- i + 1
draw.plotmath.cell(expression(x^(y + z)), i, nr); i <- i + 1
# have to do this one by hand
draw.plotmath.cell(expression(x^{y + z}), i, nr, string="x^{y + z}"); i <- i + 1
draw.plotmath.cell(expression(group("(", list(a, b), "]")), i, nr); i <- i + 1
draw.plotmath.cell(expression(bgroup("(", atop(x, y), ")")), i, nr); i <- i + 1
draw.plotmath.cell(expression(group(lceil, x, rceil)), i, nr); i <- i + 1
draw.plotmath.cell(expression(group(lfloor, x, rfloor)), i, nr); i <- i + 1
draw.plotmath.cell(expression(group("|", x, "|")), i, nr); i <- i + 1

par(oldpar)

[Package Contents]

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
`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
`alpha` – `omega`	Greek symbols
`Alpha` – `Omega`	uppercase Greek symbols
`infinity`	infinity 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

Mathematical Annotation in R

Description

Details

References

See Also

Examples