PgfPlots：非线性缩放 X 轴

Question

我想以非线性方式缩放 x 轴。也就是说，例如，我想让刻度 1、2、45、100、400 之间相等距离。1 和 2、2 和 45 等之间的比例应该是线性的。我在互联网上搜索了很多次，但找不到线索。

Answer 1

虽然可能仅使用 LaTeX 就可以完成此操作，但我很懒，所以我使用 Python 和 Numpy 来创建新的 x 值。假设您有一个包含两列数字的数据文件，分别为x和y。我在 Python 代码中添加了注释，如果有任何不清楚的地方可以询问。

# I'm using Python 3, but I think this line will make it work with Python 2.x
from __future__ import division
# numpy for number juggling, sys to get arguments from command line
import numpy as np
import sys

# read the two columns from the specified file into x and y
x,y = np.loadtxt(sys.argv[1],unpack=True)

# read tick locations from second argument and convert from str to float
ticks = sys.argv[2]
ticks = [float(i) for i in ticks.split(',')]


# in the case that the data are outside the specified tick locations,
# add a new tick for the smallest and/or largest x-value
if x[0] < ticks[0]:
    ticks = [x[0]] + ticks
if x[-1] > ticks[-1]:
    ticks = ticks + [x[-1]]

# make a new x-vector including tick locations, and interpolate y-values to tick locs
newx = np.unique((np.concatenate((x,ticks))))
newy = np.interp(newx,x,y)

# set up array for new x-values
weirdx = np.empty_like(newx)

for i in range(len(ticks)-1):
    # find all x-values that are between two adjacent ticks
    I = np.where( (ticks[i] <= newx) & (newx <= ticks[i+1]) )[0]
    if len(I) > 0:
        # Algorithm:
        #   take x values in range and subtract the first value (at first tick), so they start at 0
        #   divide by the last value (at last tick), so values run from 0 to 1
        #   add i, where i is the number of the first tick (counting from 0)
        subx = newx[I]
        subx -= subx[0]
        subx /= subx[-1]
        subx += i
        weirdx[I] = subx

# if the ticks are outside the data range, remove the x and y values at the first/last ticks
if x[-1] < ticks[-1]:
    weirdx = np.delete(weirdx, -1)
    newy = np.delete(newy,-1)
if x[0] > ticks[0]:
    weirdx = np.delete(weirdx, 0)
    newy = np.delete(newy,0)

# save new data file, and file with tick labels
np.savetxt('newdata.dat',np.hstack(( weirdx[:,np.newaxis], newy[:,np.newaxis] )), '%.8f')
np.savetxt('ticks.dat', ticks, '%u')

将脚本保存在与数据文件相同的文件夹中并运行

python ticks.py data.dat 1,2,45,200,450

其中ticks.py是脚本文件的名称，data.dat是数据文件的名称，1,2,...是刻度位置列表。请注意，刻度列表中不能有空格。

作为测试，我为直线生成了一些数字y = 2x，x 介于 0 到 495 之间。输出和 LaTeX 代码如下。请注意，必须手动指定刻度的位置。

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotstableread{newdata.dat}\data
\pgfplotstableread{ticks.dat}\ticky
\begin{document}

\begin{tikzpicture}
\begin{axis}[
  xticklabels from table={\ticky}{[index]0},
  xtick={0,...,6},
  grid]
\addplot [black] table[x index=0,y index=1] {\data};
\end{axis}
\end{tikzpicture}

\end{document}