plotmath                package: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)

