使用带有 matplotlib 的 brewer2mpl 发散颜色图，gamma 给出的结果很差，其值不同于 1

Question

Playing with colormaps in this question I was introduced to brewer2mpl in comments. For the diverging map (with zero in the middle) I noticed that gamma is implemented to work in a naive way and so gives unexpected ^† results when it is not equal to 1. The neutral tone meant to represent zero slides around so that values near zero are blue with gamma = 0.5 and orang when gamma = 1.5

Is there anyway to make a gamma-like parameter that operates symmetrically around zero in matplotlib or brewer2mpl or do I just have to do it manually somehow by raising np.abs(u) to some power then re-normalizing and re-introducing the sign?

^† expected behavior would be to apply gamma symmetrically about zero; at least that's what I had expected.

import numpy as np
import matplotlib.pyplot as plt
import brewer2mpl

Re = 6378137. # meters
J2 = 1.7555E+25 # m^5/s^2
hw = 400
x = np.linspace(-2.5*Re, 2.5*Re, 2*hw+1)
x, z = np.meshgrid(x, x)
r = np.sqrt(x**2 + z**2)
u = J2 * r**-5 * 0.5 * (3*z**2 - r**2)
u[r<Re] = np.nan

if True:
    umax = np.nanmax(np.abs(u))
    bmap = brewer2mpl.get_map('RdBu', 'Diverging', 9)
    gammas = 0.5, 1, 1.5
    plt.figure()
    for i, gamma in enumerate(gammas):
        cmap = bmap.get_mpl_colormap(N=100, gamma=gamma)
        plt.subplot(1, 3, i+1)
        plt.imshow(u, cmap=cmap, vmin=-umax, vmax=umax)
        plt.colorbar()
        plt.title('gamma = ' + str(gamma))
        plt.plot([hw, hw], [0.3*hw, 1.7*hw], '-k')
        plt.xlim(0, 2*hw+1)
        plt.ylim(0, 2*hw+1)
    plt.suptitle("Earth's geopotential's J2 component", fontsize=16)
    plt.show()

Answer 1

You can create two colormaps, one from red to white, one from white to blue. Then apply gamma to each of those. Finally get the colors from those colormaps and create a new one with the combined colors.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap
from copy import copy

cmap = plt.get_cmap("RdBu", lut=256)
# Create two new colormaps, each with one half of the original
cmap_lower = LinearSegmentedColormap.from_list("", cmap(np.arange(0,128)))
cmap_upper = LinearSegmentedColormap.from_list("", cmap(np.arange(128,256)))
gammas = [1, 0.5, 1.5]


fig, axs = plt.subplots(ncols=3, figsize=(8,5))

for ax, gamma in zip(axs, gammas):
    # copy each colormap and set the respective gamma
    cm1 = copy(cmap_lower)
    cm1.set_gamma(gamma)
    cm2 = copy(cmap_upper)
    cm2.set_gamma(gamma)
    # get the colors from the each
    colors = np.concatenate((cm1(np.arange(0,256)), cm2(np.arange(0,256))), axis=0) 
    this_cmap = LinearSegmentedColormap.from_list("", colors)

    im = ax.imshow(np.arange(300).reshape(30,10), cmap=this_cmap)
    fig.colorbar(im, ax=ax)
    ax.set_title(f"gamma={gamma}")

plt.show()