plotmath {graphics} | 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 `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
`alpha` – `omega` | Greek symbols
`Alpha` – `Omega` | 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

### 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

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

### 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")
    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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