Yihui Xie


谢益辉 / 2005-07-28


$$f(d,u)={1/(d-u)-(\log(d/u))*u/(d-u)^2},\quad d\in(0.5,1),,u\in(0,0.5)$$


:) d_seq(0.51,1,0.01)
:) u_seq(0,0.49,0.01)
:) f_function(d,u)
^^ {1/(d-u)-(log(d/u))*u/(d-u)^2}
:) d_seq(0.51,1,0.01)
:) u_seq(0,0.49,0.01)
:) persp(d,u,outer(d,u,FUN="f"),"d","u","f")








Performs an outer product operation given two arrays (or vectors) and, optionally, a function.


outer(X, Y, FUN="*", ...)

X %o% Y #operator form


X,Y   first and second arguments to the function FUN. Missing values (NAs) are allowed if FUN accepts them.


FUN   an S-PLUS function that takes at least two vectors as arguments and returns a single value. This may also be a character string giving the name of such a function.
   ...   other arguments to FUN, if needed.  The names of the arguments, if any, should be those meaningful to FUN.


array, whose dimension vector is the concatenation of the dimension vectors of X and Y, and such that FUN(X[i,j,k,...], Y[a,b,c,...]) is the value of the [i,j,k,...,a,b,c,...] element. (Vectors are considered to be one-dimensional arrays.)


outer forms two arrays corresponding to the data in X and Y, each of which has a dim attribute formed by concatenating the dim attributes of X and Y. It then calls FUN just once with these two arrays as arguments. Therefore, FUN should be a function that operates elementwise on vectors or arrays and expects (at least) two arguments.


crossprod, Matrix-product.


z <- x %o% y   # The outer product array

# dim(z) == c(dim(as.array(x)), dim(as.array(y)))

# simulate a two-way table

outer(c(3.1, 4.5, 2.8, 5.2), c(2.7, 3.1, 2.8),"+") + matrix(rnorm(12), nrow=4)

z <- outer(months, years, paste) # All month, year combinations pasted.




Creates a perspective plot given a matrix that represents heights on an evenly spaced grid. Axes and/or a box may be placed on the plot.


persp(x, y, z, xlab = "X", ylab = "Y", zlab = "Z", axes = T, 
      box = T, eye = <<SEE below="" />>, zlim = <<SEE below="" />>, ar = 1)


x   vector containing x coordinates of the grid over  which  z is evaluated. The values should be in sorted order; missing values are not accepted.
y   vector of grid y coordinates. The values should be in sorted order; missing values are not accepted.
z   matrix of size length(x) by length(y) giving  the  surface height  at grid points, i.e., z[i,j] is evaluated at x[i], y[j].  The rows of z are indexed by x, and the columns  by y.  Missing values (NAs) are allowed, but should generally not occur in the convex hull of the non-missing values.

The first argument may be a list with components x, y, and z. In particular, the result of interp is suitable.

If the first argument is a matrix, it is assumed to be the z matrix and vectors x and y are generated (x is 1:nrow(z), y is 1:ncol(z)).   The result of 
predict together with expand.grid is suitable as an argument to persp.


xlab   character label for the x axis.
ylab   character label for the y axis.
zlab   character label for the z axis.
eye   vector giving the x,y,z coordinates for the viewpoint. The default is c(-6, -8, 5) times the range of the x, y, and z values.
axes   logical flag: should axes be drawn around the surface?
box   logical flag: should a box be drawn around the surface?

zlim   vector of the desired minimum and maximum z axis values.  The default is the range(z, na.rm=T).  This range will be expanded to round numbers.  The values in the input matrix z will be truncated to the z axis limits.
ar   aspect ratio for plotting the x,y grid, i.e., (xmax-xmin)/(ymax-ymin).

Graphical parameters may also be supplied as arguments to this function (see par).


persp assumes that the grid vectors x and y are increasing and evenly spaced.  If this is not true, suppress the axes with axes=F or use par commands to customize the axes.


invisible list containing information about what was plotted.

rotation   integer flag between 1 and 4 describing the point of view based on which corner of the xy plane appears closest to the viewer.
proj   2 by 2 by 2 array describing the projection of vectors that span the data.
rangex   vector giving the min and max values for x.
rangey   vector giving the min and max values for y.
rangez   vector giving the min and max values for z.


a perspective plot is created on the current graphics device.


Use persp.setup to change the color, line width and line type of the perspective lines.  Use the perspp function to add information to a perspective plot.


For some plots (including the case where mfrow or mfcol is bigger than c(2,2)) parts of the axes are cut off.  You can solve this problem either by putting up fewer figures on the page, changing the perspective angle with the eye argument, or by expanding the margin in which the cut off occurs.

Lines with an endpoint outside the plot may not be drawn.


contour, expand.grid, image, interp, outer, par, persp.setup, perspp, predict.


#Example 1, a polynomial

poly1 <-function(x, y){x^2 + x * y + y^2}
y <- x <- seq(-25, 25, length = 50)
persp(x,y, outer(x,y, FUN =  poly1))

#Example 2, data at geographic points
i <- interp(ozone.xy$x,ozone.xy$y,ozone.median)
persp(i, xlab = "Longitude", ylab = "Latitude", zlab = "Ozone")
title(main = "Median Ozone Concentrations in the North East")

#Example 3, first argument is a matrix

#Example 4, a smooth surface
int.ak <- interp(akima.x, akima.y, akima.z)
r.ak <- sapply(int.ak, function(x) diff(range(x,na.rm = T)))

par(mfrow = c(2,2), oma = c(0,0,5,0))
persp(int.ak, eye = c(6,-8,5)*r.ak)
persp(int.ak, eye = c(6,8,5)*r.ak)
persp(int.ak, eye = c(-6,8,5)*r.ak)
mtext(outer = T, side = 3, line = 2, "WAVEFORM DISTORTION", cex = 1.5)

par(mfrow = c(1,1))
persp(int.ak, eye = c(6,8,5)*r.ak)