Midpoint of Color Palette

Question

For my current project I need a heat map. The heat map needs a scalable color palette, because the values are interesting only in a small range. That means, even if I have values from 0 to 1, interesting is only the part between 0.6 and 0.9; so I would like to scale the heat map colors accordingly, plus show the scale next to the chart.

In Matplotlib I had no way of setting the mid point of a color palette except for overloading the original class, like shown here in the matplotlib guide.

This is exactly what I need, but without the disadvantages of the unclean data structure in Matplotlib.

So I tried Bokeh. In five minutes I achieved more than with Matplotlib in an hour, however, I got stuck when I wanted to show the color scale next to the heatmap and when I wanted to change the scale of the color palette.

So, here are my questions:

How can I scale the color palette in Bokeh or Matplotlib?

Is there a way to display the annotated color bar next to the heatmap?

import pandas
scores_df = pd.DataFrame(myScores, index=c_range, columns=gamma_range)

import bkcharts
from bokeh.palettes import Inferno256
hm = bkcharts.HeatMap(scores_df, palette=Inferno256)
# here: how to insert a color bar?
# here: how to correctly scale the inferno256 palette?
hm.ylabel = "C"
hm.xlabel = "gamma"
bkcharts.output_file('heatmap.html')

Following Aarons tips, i now implemented it as follows:

import matplotlib.pyplot as plt
import matplotlib.colors as colors
from bokeh.palettes import Inferno256


def print_scores(scores, gamma_range, C_range):
    # load a color map
    # find other colormaps here
    # https://docs.bokeh.org/en/latest/docs/reference/palettes.html
    cmap = colors.ListedColormap(Inferno256, len(Inferno256))
    fig, ax = plt.subplots(1, 1, figsize=(6, 5))

    # adjust lower, midlle and upper bound of the colormap
    cmin = np.percentile(scores, 10)
    cmid = np.percentile(scores, 75)
    cmax = np.percentile(scores, 99)
    bounds = np.append(np.linspace(cmin, cmid), np.linspace(cmid, cmax))
    norm = colors.BoundaryNorm(boundaries=bounds, ncolors=len(Inferno256))

    pcm = ax.pcolormesh(np.log10(gamma_range),
                    np.log10(C_range),
                    scores,
                    norm=norm,
                    cmap=cmap)
    fig.colorbar(pcm, ax=ax, extend='both', orientation='vertical')
    plt.show()

Answer 1

ImportanceOfBeingErnest correctly pointed out that my first comment wasn't entirely clear (or accurately worded)..

Most plotting functions in mpl have a kwarg: norm= this denotes a class (subclass of mpl.colors.Normalize) that will map your array of data to the values [0 - 1] for the purpose of mapping to the colormap, but not actually impact the numerical values of the data. There are several built in subclasses, and you can also create your own. For this application, I would probably utilize BoundaryNorm. This class maps N-1 evenly spaced colors to the space between N discreet boundaries.

I have modified the example slightly to better fit your application:

#adaptation of https://matplotlib.org/users/colormapnorms.html#discrete-bounds

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as colors
from matplotlib.mlab import bivariate_normal

#example data
N = 100
X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)]
Z1 = (bivariate_normal(X, Y, 1., 1., 1.0, 1.0))**2  \
    - 0.4 * (bivariate_normal(X, Y, 1.0, 1.0, -1.0, 0.0))**2
Z1 = Z1/0.03

'''
BoundaryNorm: For this one you provide the boundaries for your colors,
and the Norm puts the first color in between the first pair, the
second color between the second pair, etc.
'''

fig, ax = plt.subplots(3, 1, figsize=(8, 8))
ax = ax.flatten()
# even bounds gives a contour-like effect
bounds = np.linspace(-1, 1)
norm = colors.BoundaryNorm(boundaries=bounds, ncolors=256)
pcm = ax[0].pcolormesh(X, Y, Z1,
                       norm=norm,
                       cmap='RdBu_r')
fig.colorbar(pcm, ax=ax[0], extend='both', orientation='vertical')

# clipped bounds emphasize particular region of data:
bounds = np.linspace(-.2, .5)
norm = colors.BoundaryNorm(boundaries=bounds, ncolors=256)
pcm = ax[1].pcolormesh(X, Y, Z1, norm=norm, cmap='RdBu_r')
fig.colorbar(pcm, ax=ax[1], extend='both', orientation='vertical')

# now if we want 0 to be white still, we must have 0 in the middle of our array
bounds = np.append(np.linspace(-.2, 0), np.linspace(0, .5))
norm = colors.BoundaryNorm(boundaries=bounds, ncolors=256)
pcm = ax[2].pcolormesh(X, Y, Z1, norm=norm, cmap='RdBu_r')
fig.colorbar(pcm, ax=ax[2], extend='both', orientation='vertical')

fig.show()