Nonlinear colormap biased by rare large values in matplotlib/seaborn

Question

I consider large matrices attaining values in between -1 to 1 and I wish to plot their heatmaps in python. Most values are very small, let's say around 10^{-8} but one or two entries are close to the edges. When I try the codes from the answers for this question I always get an image which is mostly unicolor with some points. For instance in this image the image is mostly red with some black points. I did try playing with vmin=np.amin(data),vmax=np.amax(data) but of course it does not solve the issue. I also tried some divergent colormaps but they didn't help much.

I wonder if matplotlib or seaborn can handle such type of data and if it is possible changing the scale/colormap so it will be wider based on the frequency of values (in the photo, that would mean I want more hues of red while keeping black points).

Minimal example which yields mostly white plot:

import numpy as np
import seaborn as sns
import matplotlib.pylab as plt
uniform_data = np.random.rand(1200, 1200)
uniform_data /= 10 ** 8
uniform_data[42,42] += 2
uniform_data[442,442] -= 2
ax = sns.heatmap(uniform_data)
plt.show()

Answer 1

(Note that you should import matplotlib.pyplot as pylab is now discouraged.)

If your data is uniformly distributed in a small interval, you could use the minimum and maximum of that interval for the color range. You could change these limits by, say, 10% so the extreme values still get another color (or use cmap.set_over() and cmap.set_under() to give the extreme values a completely different color).

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

uniform_data = np.random.rand(1200, 1200)
uniform_data /= 10 ** 8
uniform_data[42, 42] += 2
uniform_data[442, 442] -= 2
vmin = uniform_data[np.abs(uniform_data) < 0.1].min()
vmin = vmin * 0.9 if vmin > 0 else vmin * 1.1
vmax = uniform_data[np.abs(uniform_data) < 0.1].max()
vmmax = vmax * 0.9 if vmax < 0 else vmax * 1.1
ax = sns.heatmap(uniform_data, vmin=vmin, vmax=vmax)
plt.show()

If the values have very different orders of magnitude, you might use their logarithm to decide the color. With positive and negative values could be drawn in separate passes:

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

data = np.random.randn(20, 20) ** 9
pos_data = np.where(data > 0, data, np.nan)
neg_data = np.where(data < 0, data, np.nan)
fig, ax = plt.subplots()
sns.heatmap(np.log(pos_data), cmap='Blues_r', cbar=False, ax=ax)
sns.heatmap(np.log(-neg_data), cmap='Reds_r', cbar=False, ax=ax)
plt.show()