Plotting a function of two variables

Plot a real-valued function f evaluated on a grid of points of the Cartesian plane, possibly with parameters specified by .... The type of graphical display can be regulated by selecting the plotting function among a set of available options.

plot_fxy(f, xlim, ylim, ..., npt=51, grf, grpar)

Arguments

f

either a function or a character string with the name of a real-valued function whose first argument represents the coordinates of points where f is evaluated; see ‘Details’ for additional information.

xlim

either a vector of abscissae where the f must be evaluated, or a length-two vector with the endpoints of such an interval, in which case npt[1] equally spaced points will be considered.

ylim

either a vector of ordinates where the f must be evaluated, or a length-two vector with the endpoints of such an interval, in which case npt[2] equally spaced points will be considered.

...

additional parameters to be supplied to f; these must be named as expected by the specification of f.

npt

either an integer value or a two-element integer vector with the number of equally-spaced points, within the endpoints of xlim and ylim, used to set up the grid of points where f is evaluated; default value: 51. When a single value is supplied, this is expanded into a length-2 vector. If length(xlim)>2 and length(ylim)>2, npt is ignored.

grf

an optional character string with the name of the function which produces the graphical display, selectable among "contour", "filled.contour", "persp", "image" of package graphics; if grf is unset, "contour" is used.

grpar

an optional character string with arguments supplied to the selected grf function, with items separated by , as in a regular call.

Details

Function f will be called with the first argument represented by a two-column matrix, where each row represents a point of the grid on the Cartesian plane identified by xlim and ylim; this set of coordinates is stored in matrix pts of the returned list. If present, arguments supplied as ... are also passed to f. It is assumed that f accepts this type of call.

The original motivation of plot_fxy was to plot instances of bivariate probability density functions specified by package mnormt, but it can be used for plotting any function fulfilling the above requirements, as illustrated by some of the examples below.

Value

an invisible list with the following components:

x	a vector of coordinates on the \(x\) axis
y	a vector of coordinates on the \(y\) axis
pts	a matrix of dimension (npt[1]*npt[2],2) with the coordinates of the evaluation points \((x,y)\)
f.values	the vector of f values at the pts points.

See also

contour, filled.contour, persp, image

Examples

Sigma <- matrix(c(1,1,1,2), 2, 2)
mean <- c(0, -1)
xlim <- c(-3, 5) 
ylim <- c(-5, 3)
#
# multivariate normal density, contour-level plot
gp <- 'col="blue", nlevels=6, main="bivariate normal density"'
u <- plot_fxy(dmnorm, xlim, ylim, mean=mean, varcov=Sigma,  grpar=gp)

cat(str(u))
#> List of 4
#>  $ x       : num [1:51] -3 -2.84 -2.68 -2.52 -2.36 -2.2 -2.04 -1.88 -1.72 -1.56 ...
#>  $ y       : num [1:51] -5 -4.84 -4.68 -4.52 -4.36 -4.2 -4.04 -3.88 -3.72 -3.56 ...
#>  $ pts     : num [1:2601, 1:2] -3 -2.84 -2.68 -2.52 -2.36 -2.2 -2.04 -1.88 -1.72 -1.56 ...
#>  $ f.values: num [1:51, 1:51] 0.00107 0.00144 0.00184 0.00222 0.00256 ...
#---
# multivariate normal density, filled-contour plot
plot_fxy(dmnorm,  xlim, ylim, mean=mean, varcov=Sigma,grf="filled.contour")

#---
# multivariate normal density, perspective plot
gp <- "theta = 10, phi = 25, r = 2.5"
plot_fxy(dmnorm, xlim, ylim, mean=mean, varcov=Sigma, grf="persp", grpar=gp)

#---
# multivariate Student's "t" density;
# the xlim argument passed to function 'grf' overrides the earlier xlim;
# xlim and ylim can be placed after the arguments of 'f', if one prefers so
grp <- 'xlim=c(-1, 3)'
plot_fxy(dmt, mean=mean, S=Sigma, df=8, xlim, ylim, npt=101, 
        grf="filled.contour", grpar=grp)

#---
# multivariate truncated normal density, 'image' plot
low <- c(-3, -5)
hi <- c(1, 0)
plot_fxy(dmtruncnorm, mean=mean, varcov=Sigma, lower=low, upper=hi,
        xlim, ylim, npt=81, grf="image")

#---
# multivariate truncated normal distribution function, 'image' plot;
# hence not a density function 
low <- c(-3, -5)
hi <- c(1, 0)
v <- plot_fxy(pmtruncnorm, mean=mean, varcov=Sigma, lower=low, upper=hi, 
              xlim, ylim, npt=c(61, 81), grf="image")        

#---
# a different sort of 'f' function (lbeta), not a component of this package
funct <- function(z) lbeta(a=z[,1], b=z[,2])
plot_fxy(funct, xlim=c(0.1, 2), ylim=c(0.1, 2), npt=41, 
         grpar='main="function log-beta(a,b)", xlab="a", ylab="b"')