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. Expressions can also be used for titles, subtitles and x- and y-axis labels (but not for axis labels on `persp` plots).

### 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, 9, 582–599.

### See Also

`axis`, `mtext`, `text`, `title`

### 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))

    ## How to combine "math" and numeric variables :
    plot(1:10, type="n", xlab="", ylab="", main = "plot math & numbers")
    tt <- 1.23 ; mtext(substitute(hat(theta) == that, list(that= tt)))
    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)

    ######
    # 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=FALSE)
        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 = TRUE)
    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]