matplotlib 等高线图：对数刻度中的比例颜色条级别

是否可以将颜色条的级别设置为对数比例，如下图所示？

这是一些可以实现的示例代码：

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LogNorm
delta = 0.025

x = y = np.arange(0, 3.01, delta)
X, Y = np.meshgrid(x, y)
Z1 = plt.mlab.bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
Z2 = plt.mlab.bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
Z = 1e6 * (Z1* Z2)

fig=plt.figure()
ax1 = fig.add_subplot(111)
lvls = np.logspace(0,4,20)
CF = ax1.contourf(X,Y,Z,
         norm = LogNorm(),
         levels = lvls
        )
CS = ax1.contour(X,Y,Z,
         norm = LogNorm(),
         colors = 'k',
         levels = lvls
        )
cbar = plt.colorbar(CF, ticks=lvls, format='%.4f')
plt.show()

我在 Windows 7 上使用 python 2.7.3 和 matplotlib 1.1.1。

我建议生成一个伪颜色条，如下所示（请参阅注释以获取解释）：

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LogNorm
import matplotlib.gridspec as gridspec

delta = 0.025

x = y = np.arange(0, 3.01, delta)
X, Y = np.meshgrid(x, y)
Z1 = plt.mlab.bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
Z2 = plt.mlab.bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
Z = 1e6 * (Z1 * Z2)

fig=plt.figure()

#
# define 2 subplots, using gridspec to control the 
# width ratios:
#
# note: you have to import matplotlib.gridspec for this
#
gs = gridspec.GridSpec(1, 2,width_ratios=[15,1])

# the 1st subplot
ax1 = plt.subplot(gs[0])

lvls = np.logspace(0,4,20)

CF = ax1.contourf(X,Y,Z,
                  norm = LogNorm(),
                  levels = lvls
                 )
CS = ax1.contour(X,Y,Z,
                 norm = LogNorm(),
                 colors = 'k',
                 levels = lvls
                )

#
# the pseudo-colorbar
#

# the 2nd subplot
ax2 = plt.subplot(gs[1])        

#
# new levels!
#
# np.logspace gives you logarithmically spaced levels - 
# this, however, is not what you want in your colorbar
#
# you want equally spaced labels for each exponential group:
#
levls = np.linspace(1,10,10)
levls = np.concatenate((levls[:-1],np.linspace(10,100,10)))
levls = np.concatenate((levls[:-1],np.linspace(100,1000,10)))
levls = np.concatenate((levls[:-1],np.linspace(1000,10000,10)))

#
# simple x,y setup for a contourf plot to serve as colorbar
#
XC = [np.zeros(len(levls)), np.ones(len(levls))]
YC = [levls, levls]
CM = ax2.contourf(XC,YC,YC, levels=levls, norm = LogNorm())
# log y-scale
ax2.set_yscale('log')  
# y-labels on the right
ax2.yaxis.tick_right()
# no x-ticks
ax2.set_xticks([])

plt.show()

这会给你一个像这样的情节：

EDIT

或者，使用诸如新级别和spacing='proportional'调用时的选项colorbar:

1. 替换这一行：

   lvls = np.logspace(0,4,20)  
   

   用这些：

   lvls = np.linspace(1,10,5)
   lvls = np.concatenate((lvls[:-1],np.linspace(10,100,5)))
   lvls = np.concatenate((lvls[:-1],np.linspace(100,1000,5)))
   lvls = np.concatenate((lvls[:-1],np.linspace(1000,10000,5)))
   

2. 替换这一行：

   cbar = plt.colorbar(CF, ticks=lvls, format='%.4f')
   

   有了这个：

   cbar = plt.colorbar(CF, ticks=lvls, format='%.2f', spacing='proportional')
   

你最终会得到这个情节：

(the format只是改变了，因为新的刻度不需要 4 位小数）

EDIT 2
如果您想自动生成像我使用的那样的关卡，您可以考虑这段代码：

levels = []
LAST_EXP = 4
N_LEVELS = 5
for E in range(0,LAST_EXP):
    levels = np.concatenate((levels[:-1],np.linspace(10**E,10**(E+1),N_LEVELS)))