R help - Jul 2006 - SUMMARY: making contour plots using (x,y,z) data

Folks,

A few days ago, I had asked a question on this mailing list about
making a contour plot where a function z(x,y) is evaluated on a grid
of (x,y) points, and the data structure at hand is a simple table of
(x,y,z) points. As usual, R has wonderful resources (and subtle
complexity) in doing this, and the gurus of the list showed me the
way. Here's a complete working example. One might stumble on contour()
but lattice::contourplot() fits this task better since the former
requires a certain unusual data representation, while
lattice::contourplot() wants a more natural data representation.

            -ans.

# Setup an interesting data matrix of (x,y,z) points:
points <- structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05,
0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,
0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.15, 0.15, 0.15, 0.15, 0.15,
0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15,
0.15, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2,
0.2, 0.2, 0.2, 0.2, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.3, 0.3, 0.3, 0.3, 0.3,
0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.35,
0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35, 0.35,
0.35, 0.35, 0.35, 0.35, 0.35, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4,
0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45,
0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45, 0.45,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55,
0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6,
0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.65, 0.65,
0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65, 0.65,
0.65, 0.65, 0.65, 0.65, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7,
0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.7, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75,
0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75,
0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8,
0.8, 0.8, 0.8, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85,
0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.85, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9,
0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.95, 0.95,
0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95, 0.95,
0.95, 0.95, 0.95, 0.95, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180,
190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160,
170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140,
150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120,
130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100,
110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80,
90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60,
70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40,
50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20,
30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190,
200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170,
180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150,
160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130,
140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110,
120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90,
100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70,
80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30, 40, 50,
60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 20, 30,
40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200,
20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180,
190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160,
170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140,
150, 160, 170, 180, 190, 200, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120,
130, 140, 150, 160, 170, 180, 190, 200, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0.998, 0.124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 1, 1, 0.998, 0.71, 0.068, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
0.998, 0.898, 0.396, 0.058, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.998,
0.97, 0.726, 0.268, 0.056, 0.006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.996,
0.88, 0.546, 0.208, 0.054, 0.012, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.998,
0.964, 0.776, 0.418, 0.18, 0.054, 0.014, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.998, 0.906, 0.664, 0.342, 0.166, 0.056, 0.018, 0.006, 0.002, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0.986, 0.862, 0.568, 0.29, 0.15, 0.056, 0.022, 0.008, 0.002, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0.954, 0.778, 0.494, 0.26, 0.148, 0.056, 0.024, 0.012,
0.004, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.906, 0.712, 0.43, 0.242, 0.144,
0.058, 0.028, 0.012, 0.006, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.878, 0.642,
0.38, 0.222, 0.142, 0.066, 0.034, 0.014, 0.008, 0.004, 0.002, 0, 0, 0, 0, 0, 0,
0, 0, 0.846, 0.586, 0.348, 0.208, 0.136, 0.068, 0.034, 0.016, 0.012, 0.006,
0.004, 0.002, 0, 0, 0, 0, 0, 0, 0, 0.8, 0.538, 0.318, 0.204, 0.136, 0.07, 0.046,
0.024, 0.012, 0.008, 0.004, 0.002, 0.002, 0, 0, 0, 0, 0, 0, 0.762, 0.496, 0.294,
0.2, 0.138, 0.072, 0.05, 0.024, 0.014, 0.012, 0.006, 0.004, 0.002, 0.002, 0, 0,
0, 0, 0, 0.704, 0.472, 0.286, 0.198, 0.138, 0.074, 0.054, 0.028, 0.016, 0.012,
0.008, 0.006, 0.004, 0.002, 0.002, 0, 0, 0, 0, 0.668, 0.438, 0.276, 0.196,
0.138, 0.078, 0.054, 0.032, 0.024, 0.014, 0.012, 0.008, 0.004, 0.004, 0.002,
0.002, 0, 0, 0, 0.634, 0.412, 0.27, 0.194, 0.14, 0.086, 0.056, 0.032, 0.024,
0.016, 0.012, 0.01, 0.006, 0.004, 0.004, 0.002, 0.002, 0, 0, 0.604, 0.388, 0.26,
0.19, 0.144, 0.088, 0.058, 0.048, 0.026, 0.022, 0.014, 0.012, 0.008, 0.006,
0.004, 0.004, 0.002, 0.002, 0, 0.586, 0.376, 0.256, 0.19, 0.146, 0.094, 0.062,
0.052, 0.028, 0.024, 0.014, 0.012, 0.012, 0.008, 0.004, 0.004, 0.004, 0.002,
0.002, 0.566, 0.364, 0.254, 0.192, 0.148, 0.098, 0.064, 0.054, 0.032, 0.024,
0.022, 0.014, 0.012, 0.012, 0.008, 0.004, 0.004, 0.004, 0.002), .Dim = c(399,
3), .Dimnames = list(NULL, c("x", "y", "z")))

# Understand this object --
summary(points)
  # x is a grid from 0 to 1
  # y is a grid from 20 to 200
  # z is the interesting object which will be the 3rd dimension.

# Solution using contourplot() from package 'lattice'
library(lattice)
d3 <- data.frame(points)
contourplot(z ~ x+y, data=d3)
## or nicer
contourplot(z ~ x+y, data=d3, cuts=20, region = TRUE)
## or using logit - transformed z values:
contourplot(qlogis(z) ~ x+y, data=d3, pretty=TRUE, region = TRUE)

# An equally interesting alternative is levelplot()
levelplot(z ~ x+y, pretty=TRUE, contour=TRUE, data=d3)

# There is a contour() function in R. Even though it sounds obvious
# for the purpose, it is a bit hard to use. 
# contour() wants 3 inputs: vectors of x and y values, and a matrix of
# z values, where the x values correspond to the rows of z, and the y
# values to the columns.  A collection of points like `points' above
# needs to be turned into such a grid. It might sound odd, but contour()
# image() and persp() have used this kind of input for the longest time.
# 
# For irregular data, there's an interp function in the akima package
# that can do this in general.
#
# The `points' object that I have above - a list of (x,y,z) points -
# fits directly into the mentality of lattice::contourplot() 

-- 
Ajay Shah                                      http://www.mayin.org/ajayshah  
ajayshah at mayin.org                            
http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.