plotmath              package:grDevices              R Documentation

Mathematical Annotation in R

Description:

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

     In most cases other language objects (names and calls, including
     formulas) are coerced to expressions and so can also be used.

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 %.% y'                       x cdot 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
       'symbol(x)'                     draw x in symbol 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
       'theta1, phi1, sigma1, omega1'  cursive Greek symbols
       'Upsilon1'                      capital upsilon with hook
       'aleph'                         first letter of Hebrew alphabet
       'infinity'                      infinity symbol
       'partialdiff'                   partial differential symbol
       'nabla'                         nabla, gradient 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
       'underline(x)'                  draw x underlined
       '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

     The symbol font uses Adobe Symbol encoding so, for example, a
     lower case mu can be obtained either by the special symbol 'mu' or
     by 'symbol("m")'.  This provides access to symbols that have no
     special symbol name, for example, the universal, or forall, symbol
     is 'symbol("\042")'.

     Note to TeX users: TeX's '\Upsilon' is 'Upsilon1', TeX's
     '\varepsilon' is close to 'epsilon', and there is no equivalent of
     TeX's '\epsilon'.  TeX's '\varpi' is close to 'omega1'. 
     'vartheta', 'varphi' and 'varsigma' are allowed as synonyms for
     'theta1', 'phi1' and 'sigma1'.

     'sigma1' is also known as 'stigma', its Unicode name.

     Control characters (e.g. '\n') are not interpreted in character
     strings in plotmath, unlike normal plotting.

     The fonts used are taken from the current font family, and so can
     be set by 'par(family=)' in base graphics, and 'gpar(fontfamily=)'
     in package 'grid'.

Other symbols:

     On many OSes and some graphics devices many other symbols are
     available as part of the standard text font, and all of the
     symbols in the Adobe Symbol encoding are in principle available
     _via_ changing the font face or (see 'Details') plotmath: see the
     examples section of 'points' for a function to display them.  ('In
     principle' because some of the glyphs are missing from some
     implementations of the symbol font.)  Unfortunately, 'postscript'
     and 'pdf' have support for little more than European and CJK
     characters and the Adobe Symbol encoding (and in a few fonts, also
     Cyrillic characters).

     In a UTF-8 locale any Unicode character can be entered, perhaps as
     a '\uxxxx' or '\Uxxxxxxxx' escape sequence, but the issue is
     whether the graphics device is apply to display the character. 
     The widest range of characters is likely to be available in the
     'X11' device using cairo: see its help page for how installing
     additional fonts can help.

     In non-UTF-8 locales there is normally no support for symbols not
     in the languages for which the current encoding was intended.

References:

     Murrell, P. and Ihaka, R. (2000) An approach to providing
     mathematical annotation in plots. _Journal of Computational and
     Graphical Statistics_, *9*, 582-599.

     The symbol codes can be found in octal in the Adobe reference
     manuals, e.g. for Postscript <URL:
     http://www.adobe.com/products/postscript/pdfs/PLRM.pdf> or PDF
     <URL:
     http://www.adobe.com/devnet/acrobat/pdfs/pdf_reference_1-7.pdf>
     and in decimal, octal and hex at <URL:
     http://www.stat.auckland.ac.nz/~paul/R/CM/AdobeSym.html>.

See Also:

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

Examples:

     require(graphics)

     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),
          labels = 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)))
     ## note that both of these use calls rather than expressions.

     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)

     ## some other useful symbols
     plot.new(); plot.window(c(0,4), c(15,1))
     text(1, 1, "universal", adj=0); text(2.5, 1,  "\\042")
     text(3, 1, expression(symbol("\042")))
     text(1, 2, "existential", adj=0); text(2.5, 2,  "\\044")
     text(3, 2, expression(symbol("\044")))
     text(1, 3, "suchthat", adj=0); text(2.5, 3,  "\\047")
     text(3, 3, expression(symbol("\047")))
     text(1, 4, "therefore", adj=0); text(2.5, 4,  "\\134")
     text(3, 4, expression(symbol("\134")))
     text(1, 5, "perpendicular", adj=0); text(2.5, 5,  "\\136")
     text(3, 5, expression(symbol("\136")))
     text(1, 6, "circlemultiply", adj=0); text(2.5, 6,  "\\304")
     text(3, 6, expression(symbol("\304")))
     text(1, 7, "circleplus", adj=0); text(2.5, 7,  "\\305")
     text(3, 7, expression(symbol("\305")))
     text(1, 8, "emptyset", adj=0); text(2.5, 8,  "\\306")
     text(3, 8, expression(symbol("\306")))
     text(1, 9, "angle", adj=0); text(2.5, 9,  "\\320")
     text(3, 9, expression(symbol("\320")))
     text(1, 10, "leftangle", adj=0); text(2.5, 10,  "\\341")
     text(3, 10, expression(symbol("\341")))
     text(1, 11, "rightangle", adj=0); text(2.5, 11,  "\\361")
     text(3, 11, expression(symbol("\361")))

