如何在密度图中使用matplotlib设置对数坐标轴？

Question

我正在尝试使用matplotlib制作一个二维密度图（来自一些模拟数据）。我的x和y数据是一些量的以10为底的对数。请问我该如何设置坐标轴为对数坐标（并且有对数的次刻度）呢？

下面是我的代码示例：

import numpy as np
import matplotlib.pyplot as plt

Data = np.genfromtxt("data") # A 2-column data file
x = np.log10(Data[:,0])
y = np.log10(Data[:,1])

xmin = x.min()
xmax = x.max()
ymin = y.min()
ymax = y.max()

fig = plt.figure()
ax = fig.add_subplot(111)

hist = ax.hexbin(x,y,bins='log', gridsize=(30,30), cmap=cm.Reds)
ax.axis([xmin, xmax, ymin, ymax])

plt.savefig('plot.pdf')

Answer 1

@gcalmettes的回答提到了pyplot.hist，而pyplot.hexbin的用法稍微有点不同：

hexbin(x, y, C = None, gridsize = 100, bins = None,
             xscale = 'linear', yscale = 'linear',
             cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None,
             edgecolors='none', reduce_C_function = np.mean, mincnt=None, marginals=True,
             **kwargs)

你需要关注的是xscale这个参数：

*xscale*: [ 'linear' | 'log' ]
    Use a linear or log10 scale on the horizontal axis.

Answer 2

根据matplotlib.pyplot.hist的说明，如果你想在坐标轴上使用对数刻度，可以把'log'这个参数设置为'True'。

hist(x, bins=10, range=None, normed=False, cumulative=False,
     bottom=None, histtype='bar', align='mid',
     orientation='vertical', rwidth=None, log=False, **kwargs)

log:
If True, the histogram axis will be set to a log scale. If log is True and x is a 1D
array, empty bins will be filtered out and only the non-empty (n, bins, patches) will be
returned.

另外，还有一个pyplot.loglog函数，可以用来绘制x轴和y轴都使用对数刻度的图。

Answer 3

非常感谢大家的建议。

下面我分享一下我自己的解决方案。虽然这不算是一个“最小可工作示例”，但我已经把我的代码简化了不少！

简单来说，我使用了 imshow 来绘制“图像”（一个带有对数区间的二维直方图），并且我去掉了坐标轴。然后，我在第一个图的正上方画了一个第二个空白（透明）的图，只是为了得到对数坐标轴，因为 imshow 似乎不支持这个功能。说实话，这样做挺复杂的！

我的代码可能还远远不够好，因为我刚开始学习 python 和 matplotlib……

顺便提一下，我不使用 hexbin 有两个原因： 1) 对于像我这样的超大数据文件，它运行得太慢。 2) 在我使用的版本中，六边形的大小稍微有点大，也就是说它们会重叠，导致“像素”形状和大小不规则。 另外，我还想把直方图的数据以文本格式写入文件。

#!/usr/bin/python

# How to get log axis with a 2D colormap (i.e. an "image") ??
#############################################################
#############################################################

import numpy as np
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import math

# Data file containing 2D data in log-log coordinates.
# The format of the file is 3 columns : x y v
# where v is the value to plotted for coordinate (x,y)
# x and y are already log values
# For instance, this can be a 2D histogram with log bins.
input_file="histo2d.dat"

# Parameters to set space for the plot ("bounding box")
x1_bb, y1_bb, x2_bb, y2_bb = 0.125, 0.12, 0.8, 0.925

# Parameters to set space for colorbar
cb_fraction=0.15
cb_pad=0.05

# Return unique values from a sorted list, will be required later
def uniq(seq, idfun=None): 
    # order preserving
    if idfun is None:
        def idfun(x): return x
    seen = {}
    result = []
    for item in seq:
        marker = idfun(item)
        # in old Python versions:
        # if seen.has_key(marker)
        # but in new ones:
        if marker in seen: continue
        seen[marker] = 1
        result.append(item)
    return result

# Read data from file. The format of the file is 3 columns : x y v
# where v is the value to plotted for coordinate (x,y)

Data = np.genfromtxt(input_file)
x = Data[:,0]
y = Data[:,1]
v = Data[:,2]

# Determine x and y limits and resolution of data

x_uniq = np.array(uniq(np.sort(x)))
y_uniq = np.array(uniq(np.sort(y)))

x_resolution = x_uniq.size
y_resolution = y_uniq.size

x_interval_length = x_uniq[1]-x_uniq[0]
y_interval_length = y_uniq[1]-y_uniq[0]

xmin = x.min()
xmax = x.max()+0.5*x_interval_length
ymin = y.min()
ymax = y.max()+0.5*y_interval_length

# Reshape 1D data to turn it into a 2D "image"

v = v.reshape([x_resolution, y_resolution])
v = v[:,range(y_resolution-1,-1,-1)].transpose()

# Plot 2D "image" 
# ---------------

# I use imshow which only work with linear axes.
# We will have to change the axes later...

axis_lim=[xmin, xmax, ymin, ymax]

fig = plt.figure()
ax = fig.add_subplot(111)
extent = [xmin, xmax, ymin, ymax]
img = plt.imshow(v, extent=extent, interpolation='nearest', cmap=cm.Reds, aspect='auto')
ax.axis(axis_lim)

# Make space for the colorbar
x2_bb_eff = (x2_bb-(cb_fraction+cb_pad)*x1_bb)/(1.0-(cb_fraction+cb_pad))
ax.set_position([x1_bb, y1_bb, x2_bb_eff-x1_bb, y2_bb-y1_bb])
position = ax.get_position()

# Remove axis ticks so that we can put log ticks on top
ax.set_xticks([])
ax.set_yticks([])

# Add colorbar
cb = fig.colorbar(img,fraction=cb_fraction,pad=cb_pad)
cb.set_label('Value [unit]')

# Add logarithmic axes
# --------------------

# Empty plot on top of previous one. Only used to add log axes.
ax = fig.add_subplot(111,frameon=False)
ax.set_xscale('log')
ax.set_yscale('log')
plt.plot([])
ax.set_position([x1_bb, y1_bb, x2_bb-x1_bb, y2_bb-y1_bb])

axis_lim_log=map(lambda x: 10.**x, axis_lim)
ax.axis(axis_lim_log)

plt.grid(b=True, which='major', linewidth=1)
plt.ylabel('Some quantity [unit]')
plt.xlabel('Another quantity [unit]')

plt.show()