nonlinear colormap, matplotlib

Question

Are there any colormaps or is there a simple way to transform a matplotlib colormap to provide a much bigger color range near 0.5 and a smaller one at the extremes? I am creating a bunch of subplots, one of which has color values of about 10 times the others, so it’s values dominate and the rest of the plots all look the same. For a simple example say we have:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(1,10,10)
y = np.linspace(1,10,10)

t1 = np.random.normal(2,0.3,10)
t2 = np.random.normal(9,0.01,10)
t2_max = max(t2)

plt.figure(figsize=(22.0, 15.50))

p = plt.subplot(1,2,1)
colors = plt.cm.Accent(t1/t2_max)
p.scatter(x, y, edgecolors=colors, s=15, linewidths=4)

p = plt.subplot(1,2,2)
colors = plt.cm.Accent(t2/t2_max)
p.scatter(x, y, edgecolors=colors, s=15, linewidths=4)

plt.subplots_adjust(left=0.2)
cbar_ax = plt.axes([0.10, 0.15, 0.05, 0.7])
sm = plt.cm.ScalarMappable(cmap=plt.cm.Accent, norm=plt.Normalize(vmin=0, vmax=t2_max))
sm._A = []
cbar = plt.colorbar(sm,cax=cbar_ax)

plt.show()

There is much more variation in t1 than in t2, however the variation can not be seen because of the high values of t2. What I want is a map the will provide a larger color gradient around the mean of t1 without transforming the data itself. I have found one solution here http://protracted-matter.blogspot.co.nz/2012/08/nonlinear-colormap-in-matplotlib.html but cant get it to work for my scatter plots.

EDIT: From answer below the class can be modified to take negative numbers, and fixed boundaries.

import numpy as np
import matplotlib.pyplot as plt

x = y = np.linspace(1, 10, 10)

t1mean, t2mean = -6, 9
sigma1, sigma2 = .3, .01
t1 = np.random.normal(t1mean, sigma1, 10)
t2 = np.random.normal(t2mean, sigma2, 10)

class nlcmap(object):
    def __init__(self, cmap, levels):
        self.cmap = cmap
        self.N = cmap.N
        self.monochrome = self.cmap.monochrome
        self.levels = np.asarray(levels, dtype='float64')
        self._x = self.levels
        self.levmax = self.levels.max()
        self.levmin = self.levels.min()
        self.transformed_levels = np.linspace(self.levmin, self.levmax,
             len(self.levels))

    def __call__(self, xi, alpha=1.0, **kw):
        yi = np.interp(xi, self._x, self.transformed_levels)
        return self.cmap(yi / (self.levmax-self.levmin)+0.5, alpha)

tmax = 10
tmin = -10
#the choice of the levels depends on the data:
levels = np.concatenate((
    [tmin, tmax],
    np.linspace(t1mean - 2 * sigma1, t1mean + 2 * sigma1, 5),
    np.linspace(t2mean - 2 * sigma2, t2mean + 2 * sigma2, 5),
    ))
levels = levels[levels <= tmax]
levels.sort()
print levels
cmap_nonlin = nlcmap(plt.cm.jet, levels)

fig, (ax1, ax2) = plt.subplots(1, 2)

ax1.scatter(x, y, edgecolors=cmap_nonlin(t1), s=15, linewidths=4)
ax2.scatter(x, y, edgecolors=cmap_nonlin(t2), s=15, linewidths=4)

fig.subplots_adjust(left=.25)
cbar_ax = fig.add_axes([0.10, 0.15, 0.05, 0.7])

#for the colorbar we map the original colormap, not the nonlinear one:
sm = plt.cm.ScalarMappable(cmap=plt.cm.jet, 
                norm=plt.Normalize(vmin=tmin, vmax=tmax))
sm._A = []

cbar = fig.colorbar(sm, cax=cbar_ax)
#here we are relabel the linear colorbar ticks to match the nonlinear ticks
cbar.set_ticks(cmap_nonlin.transformed_levels)
cbar.set_ticklabels(["%.2f" % lev for lev in levels])

plt.show()

Answer 1

You could use LinearSegmentedColormap:

With this, you need to set up a color lookup table within a dictionary e.g. 'cdict' below.

cdict = {'red':   [(0.0,  0.0, 0.0),
                   (0.15,  0.01, 0.01),
                   (0.35,  1.0, 1.0),
                   (1.0,  1.0, 1.0)],

         'green': [(0.0,  0.0, 0.0),
                   (1.0,  0.0, 1.0)],

         'blue':  [(0.0,  0.0, 1.0),
                   (0.9,  0.01, 0.01),
                   (1.0,  0.0, 1.0)]}

This shows the transistions between values. I have set red to vary a lot around the values of t1/t2_max (0.15 to 0.35) and blue to vary a lot around the values of t2/t2_max (0.9 to 1.0). Green does nothing. I'd recommend reading the docs to see how this works. (Note this could be automated to automatically vary around your values). I then tweaked your code to show the graph:

import matplotlib.colors as col

my_cmap = col.LinearSegmentedColormap('my_colormap', cdict)

plt.figure(figsize=(22.0, 15.50))

p = plt.subplot(1,2,1)
colors = my_cmap(t1/t2_max)

p.scatter(x, y, edgecolors=colors, s=15, linewidths=4)

p = plt.subplot(1,2,2)
colors = my_cmap(t2/t2_max)

p.scatter(x, y, edgecolors=colors, s=15, linewidths=4)

plt.subplots_adjust(left=0.2)
cbar_ax = plt.axes([0.10, 0.15, 0.05, 0.7])
sm = plt.cm.ScalarMappable(cmap=my_cmap, norm=plt.Normalize(vmin=0, vmax=t2_max))
sm._A = []
cbar = plt.colorbar(sm,cax=cbar_ax)

plt.show()

Answer 2

Your link provides quite a good solution for the colormap. I edited a bit, but it contained al the necessary. You need to pick some sensible levels for your nonlinear colormap. I used two ranges centered around the mean values, between +- 4 the standard deviation of your sample. by changing that to another number you obtain a different local gradient in the color around the two mean values.

For the colorbar, you

• either leave the colors nonlinearly spaced with linearly spaced labels
• you have linearly spaced colors with nonlinearly spaced labels.

The second allows greater resolution when looking at the data, looks nicer and is implemented below:

import numpy as np
import matplotlib.pyplot as plt

x = y = np.linspace(1, 10, 10)

t1mean, t2mean = 2, 9
sigma1, sigma2 = .3, .01
t1 = np.random.normal(t1mean, sigma1, 10)
t2 = np.random.normal(t2mean, sigma2, 10)

class nlcmap(object):
    def __init__(self, cmap, levels):
        self.cmap = cmap
        self.N = cmap.N
        self.monochrome = self.cmap.monochrome
        self.levels = np.asarray(levels, dtype='float64')
        self._x = self.levels
        self.levmax = self.levels.max()
        self.transformed_levels = np.linspace(0.0, self.levmax,
             len(self.levels))

    def __call__(self, xi, alpha=1.0, **kw):
        yi = np.interp(xi, self._x, self.transformed_levels)
        return self.cmap(yi / self.levmax, alpha)

tmax = max(t1.max(), t2.max())
#the choice of the levels depends on the data:
levels = np.concatenate((
    [0, tmax],
    np.linspace(t1mean - 4 * sigma1, t1mean + 4 * sigma1, 5),
    np.linspace(t2mean - 4 * sigma2, t2mean + 4 * sigma2, 5),
    ))

levels = levels[levels <= tmax]
levels.sort()

cmap_nonlin = nlcmap(plt.cm.jet, levels)

fig, (ax1, ax2) = plt.subplots(1, 2)

ax1.scatter(x, y, edgecolors=cmap_nonlin(t1), s=15, linewidths=4)
ax2.scatter(x, y, edgecolors=cmap_nonlin(t2), s=15, linewidths=4)

fig.subplots_adjust(left=.25)
cbar_ax = fig.add_axes([0.10, 0.15, 0.05, 0.7])

#for the colorbar we map the original colormap, not the nonlinear one:
sm = plt.cm.ScalarMappable(cmap=plt.cm.jet, 
                norm=plt.Normalize(vmin=0, vmax=tmax))
sm._A = []

cbar = fig.colorbar(sm, cax=cbar_ax)
#here we are relabel the linear colorbar ticks to match the nonlinear ticks
cbar.set_ticks(cmap_nonlin.transformed_levels)
cbar.set_ticklabels(["%.2f" % lev for lev in levels])

plt.show()

In the result, notice that the ticks of the colorbar are NOT equispaced: