百分位分布图

Question

有谁知道如何更改 X 轴刻度和刻度以显示如下图所示的百分位数分布？此图片来自 MATLAB，但我想使用 Python（通过 Matplotlib 或 Seaborn）来生成。

从@paulh 的指针来看，我现在离我更近了。这段代码

import matplotlib
matplotlib.use('Agg')

import numpy as np
import matplotlib.pyplot as plt
import probscale
import seaborn as sns

clear_bkgd = {'axes.facecolor':'none', 'figure.facecolor':'none'}
sns.set(style='ticks', context='notebook', palette="muted", rc=clear_bkgd)

fig, ax = plt.subplots(figsize=(8, 4))

x = [30, 60, 80, 90, 95, 97, 98, 98.5, 98.9, 99.1, 99.2, 99.3, 99.4]
y = np.arange(0, 12.1, 1)

ax.set_xlim(40, 99.5)
ax.set_xscale('prob')

ax.plot(x, y)
sns.despine(fig=fig)

生成以下图（注意重新分布的 X 轴）

我发现它比标准量表更有用：

我联系了原始图表的作者，他们给了我一些指示。它实际上是一个对数比例图，x 轴反转，值为 [100-val]，手动标记 x 轴刻度。下面的代码使用与此处其他图表相同的示例数据重新创建原始图像。

import matplotlib
matplotlib.use('Agg')

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

clear_bkgd = {'axes.facecolor':'none', 'figure.facecolor':'none'}
sns.set(style='ticks', context='notebook', palette="muted", rc=clear_bkgd)

x = [30, 60, 80, 90, 95, 97, 98, 98.5, 98.9, 99.1, 99.2, 99.3, 99.4]
y = np.arange(0, 12.1, 1)

# Number of intervals to display.
# Later calculations add 2 to this number to pad it to align with the reversed axis
num_intervals = 3
x_values = 1.0 - 1.0/10**np.arange(0,num_intervals+2)

# Start with hard-coded lengths for 0,90,99
# Rest of array generated to display correct number of decimal places as precision increases
lengths = [1,2,2] + [int(v)+1 for v in list(np.arange(3,num_intervals+2))]

# Build the label string by trimming on the calculated lengths and appending %
labels = [str(100*v)[0:l] + "%" for v,l in zip(x_values, lengths)]


fig, ax = plt.subplots(figsize=(8, 4))

ax.set_xscale('log')
plt.gca().invert_xaxis()
# Labels have to be reversed because axis is reversed
ax.xaxis.set_ticklabels( labels[::-1] )

ax.plot([100.0 - v for v in x], y)

ax.grid(True, linewidth=0.5, zorder=5)
ax.grid(True, which='minor', linewidth=0.5, linestyle=':')

sns.despine(fig=fig)

plt.savefig("test.png", dpi=300, format='png')

这是结果图：

Answer 1

这些类型的图表在低延迟社区中很受欢迎，用于绘制延迟分布。在处理延迟时，大多数有趣的信息往往位于较高的百分位数，因此对数视图往往效果更好。我第一次看到https://github.com/giltene/jHiccup 和https://github.com/HdrHistogram/ 中使用的这些图表。

引用的图由以下代码生成

n = ceil(log10(length(values)));          
p = 1 - 1./10.^(0:0.01:n);
percentiles = prctile(values, p * 100);
semilogx(1./(1-p), percentiles);

x 轴用下面的代码标记

labels = cell(n+1, 1);
for i = 1:n+1
  labels{i} = getPercentileLabel(i-1);
end
set(gca, 'XTick', 10.^(0:n));
set(gca, 'XTickLabel', labels);

% {'0%' '90%' '99%' '99.9%' '99.99%' '99.999%' '99.999%' '99.9999%'}
function label = getPercentileLabel(i)
    switch(i)
        case 0
            label = '0%';
        case 1
            label = '90%';
        case 2
            label = '99%';
        otherwise
            label = '99.';
            for k = 1:i-2
                label = [label '9'];
            end
            label = [label '%'];
    end
end

Answer 2

以下 Python 代码使用 Pandas 读取包含已记录延迟值列表（以毫秒为单位）的 csv 文件，然后将这些延迟值（以微秒为单位）记录在 HdrHistogram 中，并将 HdrHistogram 保存到hgrm 文件，然后将由 Seaborn 到 plot 使用延迟分布图。

import pandas as pd
from hdrh.histogram import HdrHistogram
from hdrh.dump import dump
import numpy as np
from matplotlib import pyplot as plt
import seaborn as sns
import sys
import argparse

# Parse the command line arguments.

parser = argparse.ArgumentParser()
parser.add_argument('csv_file')
parser.add_argument('hgrm_file')
parser.add_argument('png_file')
args = parser.parse_args()

csv_file = args.csv_file
hgrm_file = args.hgrm_file
png_file = args.png_file

# Read the csv file into a Pandas data frame and generate an hgrm file.

csv_df = pd.read_csv(csv_file, index_col=False)

USECS_PER_SEC=1000000
MIN_LATENCY_USECS = 1
MAX_LATENCY_USECS = 24 * 60 * 60 * USECS_PER_SEC # 24 hours
# MAX_LATENCY_USECS = int(csv_df['response-time'].max()) * USECS_PER_SEC # 1 hour
LATENCY_SIGNIFICANT_DIGITS = 5
histogram = HdrHistogram(MIN_LATENCY_USECS, MAX_LATENCY_USECS, LATENCY_SIGNIFICANT_DIGITS)
for latency_sec in csv_df['response-time'].tolist():
    histogram.record_value(latency_sec*USECS_PER_SEC)
    # histogram.record_corrected_value(latency_sec*USECS_PER_SEC, 10)
TICKS_PER_HALF_DISTANCE=5
histogram.output_percentile_distribution(open(hgrm_file, 'wb'), USECS_PER_SEC, TICKS_PER_HALF_DISTANCE)

# Read the generated hgrm file into a Pandas data frame.

hgrm_df = pd.read_csv(hgrm_file, comment='#', skip_blank_lines=True, sep=r"\s+", engine='python', header=0, names=['Latency', 'Percentile'], usecols=[0, 3])

# Plot the latency distribution using Seaborn and save it as a png file.

sns.set_theme()
sns.set_style("dark")
sns.set_context("paper")
sns.set_color_codes("pastel")

fig, ax = plt.subplots(1,1,figsize=(20,15))
fig.suptitle('Latency Results')

sns.lineplot(x='Percentile', y='Latency', data=hgrm_df, ax=ax)
ax.set_title('Latency Distribution')
ax.set_xlabel('Percentile (%)')
ax.set_ylabel('Latency (seconds)')
ax.set_xscale('log')
ax.set_xticks([1, 10, 100, 1000, 10000, 100000, 1000000, 10000000])
ax.set_xticklabels(['0', '90', '99', '99.9', '99.99', '99.999', '99.9999', '99.99999'])

fig.tight_layout()
fig.savefig(png_file)