Tuesday, December 15, 2009

Matplotlib in OS X (4)


While hunting around for colors for heatmaps, I came across the matplotlib class matplotlib.colors.LinearSegmentedColormap. The way the colors are specified seemed a bit strange at first, but then it became clear.

The first thing is that, naturally, the red, green and blue components are handled separately. They may vary independently and don't even have to be split up into the same number of "intervals." Color values are specified corresponding to the numerical endpoints of each interval, and when it is desired to encode a number as a color, this is done by linear interpolation. Intervals and colors are specified by values between 0 and 1.

An example I found here splits the interval 0 to 1 into two parts for all three colors. The red values come from this array:

r = ((0.0, 0.0, 0.0), 
(0.5, 1.0, 0.7),
(1.0, 1.0, 1.0))


What is going on is that we have split the interval into two parts: 0 to 0.5 and 0.5 to 1.0. These are the entries [0][0], [1][0] and [2][0]. The manual calls these x. From there:

row i:   x  y0  y1
/
/
row i+1: x y0 y1
/
/
row i+2: x y0 y1


Suppose we encounter a number that lies between the x in row i and the x in row i+1. We grab the indicated values (y1 from row i, and y0 from row i+1), and just interpolate.

So we have 7 values of interest for this set of two intervals:

• the beginning and end of each interval
(where the beginning of the second equals the end of the first)

• red at the beginning and end of interval 1

• red at the beginning and end of interval 2

Two values are never used---y0 from the first row and y1 from the last. Check out the second link for lots more examples.

import matplotlib.pyplot as plt
import matplotlib
import numpy as np

r = ((0.0, 0.0, 0.0),
(0.5, 1.0, 0.7),
(1.0, 1.0, 1.0))

g = ((0.0, 0.0, 0.0),
(0.5, 1.0, 0.0),
(1.0, 1.0, 1.0))

b = ((0.0, 0.0, 0.0),
(0.5, 1.0, 0.0),
(1.0, 0.5, 1.0))

colors = {'red':r, 'green':g, 'blue':b}
f = matplotlib.colors.LinearSegmentedColormap
m = f('my_color_map', colors, 256)
plt.pcolor(np.random.rand(10,10),cmap=m)
plt.colorbar()
plt.savefig('example.png')

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