在实验 https://github.com/int0x03/kernel-utils 的过程中, 我们最后通过 qemu 启动 img 文件, 然后通过我们预设的用户名/密码进入 shell. 但是这个shell 和启动VM 用的同一个tty, 所以系统的一些message 会源源不断的输出到这个tty, 如果你要在这个shell 改些东西, 会非常尴尬.

如何启动另外一个tty?

要启动另外一个tty, 我们可以通过 ssh 登录这个VM, 就需要安装 openssh-server, 所以我们更改 config/env.sh 在需要安装到软件那行, 加入 openssh-server.

改后:

packages_to_install="systemd-resolved bpftrace bpfcc-tools gdb iptables openssh-server"

另外需要本地端口做转换, 所以需要更改 qemu 的启动参数, 在 boot 文件改动如下:

netdev_args="user,id=network0,net=192.168.0.0/24 -device e1000,netdev=network0 -net nic -net user,hostfwd=tcp::2222-:22"

sshd server 默认是不让以 root 用户登录的, 所以要更改 /etc/ssh/sshd_config 运行root 访问:

PermitRootLogin yes

然后重启 sshd server

systemctl restart ssh

如何登录

在宿主机 ssh -p 2222 root@localhost

(本文最初发布在掘金 https://juejin.cn/post/7242312269887914041)
学习 Linux 内核的第一步就是下载 Linux 内核代码, 然后进行编译与运行.

下载内核源代码

内核源码除了 Linus 的官方 https://github.com/torvalds/linux git, 还有各家发布版的 Linux 内核. 最好去发布版的内核去下载, 这样编译过程中不容易出错.

我的 Linux 机器是 Ubuntu 22.04 TLS, 所以根据官方文档: https://wiki.ubuntu.com/Kernel/SourceCode, 可以 clone git 下载:

$ git clone --depth 1 -b master git://git.launchpad.net/~ubuntu-kernel/ubuntu/+source/linux/+git/jammy

这里为了减少下载文件的数量和大小, 选择只下载最新的代码, 只选择了master分支. 下载到 jammy 文件夹.

编译配置

编译之前先要安装编译内核需要的各种安装包:

$ sudo apt update 
$ sudo apt upgrade -y
$ sudo apt install git fakeroot build-essential ncurses-dev xz-utils libssl-dev bc flex bison libelf-dev -y 

配置并编译

$ cd jammy
# 此时并没有 .config 文件, 执行下面的命令会让你选择配置, 然后保存.
$ make menuconfig
# 生成 .config 文件
$ ls -lah .config
-rw-rw-r-- 1 sre sre 256K Jun  2 20:58 .config

我们可以看到 .config 文件里面的各种配置项目, 比如:

CONFIG_VERSION_SIGNATURE="Ubuntu 5.15.0-72.79-generic 5.15.98"
CONFIG_HAVE_KERNEL_GZIP=y
CONFIG_TSL2583=m

有些配置项表示一个纯文本的配置, 比如上面的版本号. 另外一些后面是 =y, =m 或者=n.

1. =y：当选项被设置为=y时，表示该选项将作为内核的一部分编译进内核映像（静态编译）。这意味着相关的功能将始终可用，并包含在生成的内核映像中。当系统启动时，这些功能将立即可用，无需加载额外的模块。选择=y是在构建内核时将特定功能编译到内核中的一种方式。
2. =m：当选项被设置为=m时，表示该选项将作为可加载模块编译（动态编译）。这意味着相关的功能将编译为独立的模块文件（通常是以.ko为扩展名），并在需要时由内核加载。使用=m选项可以将特定功能作为模块构建，以便在运行时根据需要加载和卸载。

选择=y或=m取决于您对系统需求的权衡。如果您确定某个功能始终需要在内核运行时可用，并且不希望依赖额外的模块加载过程，则选择=y。如果您希望能够根据需要加载和卸载某个功能，并且不会一直使用该功能，则选择=m。

请注意，对于某些选项，可能还有其他设置，例如=n，表示将完全排除该功能的编译。这意味着相关的功能将在内核映像和模块中都不可用。选择特定的设置取决于您的需求和系统配置。

文字界面配置如下, 最后选择 Save 到 .config 文件.

编译:

$ make all -j 4 # 使用 4个线程编译, 可能要等很久, 最后生成内核文件 arch/x86/boot/bzImage
...

$ ls -lah arch/x86/boot/bzImage
-rw-r--r-- 1 root root 11M Jun  5 08:59 arch/x86/boot/bzImage
Kernel: arch/x86/boot/bzImage is ready  (#1)
$ make help # 查看更多命令

如果遇到下面的出错:

sre@sre:~/work/exp/jammy$ make all -j 8
  ...
make[1]: *** No rule to make target 'debian/canonical-certs.pem', needed by 'certs/x509_certificate_list'.  Stop.
make[1]: *** Waiting for unfinished jobs....
make: *** [Makefile:1900: certs] Error 2

可以参看 https://askubuntu.com/questions/1329538/compiling-the-kernel-5-11-11 去掉里面证书的部分:

# 可以看到当前的配置, 改成=“”
sre@sre:~/work/exp/jammy$ cat .config | grep CONFIG_SYSTEM_TRUSTED_KEYS
CONFIG_SYSTEM_TRUSTED_KEYS="debian/canonical-certs.pem"

测试启动内核

首先安装 qemu, 然后启动内核:

$ sudo apt install qemu-system-x86 -y
$ qemu-system-x86_64 -kernel bzImage -append "console=tty0 console=ttyS0" -nographic
SeaBIOS (version 1.15.0-1)
iPXE (https://ipxe.org) 00:03.0 CA00 PCI2.10 PnP PMM+07F8B340+07ECB340 CA00
Booting from ROM...

Kernel Offset: disabled
---[ end Kernel panic - not syncing: No working init found.  Try passing init= option to kernel.

可以看到最后内核 panic, 因为没有任何 root 文件系统, 也没有 init 代码. 这时候, 我们可以通过 -initrd 来启动, 里面可以包含一个 busybox.

如何制作一个 initrd

使用 https://github.com/aweeraman/kernel-utils 提供的工具, 按照说明文档, 执行第一步 ./mk-initrd 就能生成 initramfs.cpio.gz, 里面包含了 initrc 和 busybox.

再次测试启动:

$ qemu-system-x86_64 -kernel bzImage -initrd initramfs.cpio.gz -append "console=tty0 console=ttyS0" -nographic

#这次成功启动

如何做一个最小的内核并启动进入命令行

制作最小内核

在 Linux 内核源代码根目录执行 make help, 你能看到各种有关配置的子命令, 比如:

1. defconfig: New config with default from ARCH supplied defconfig.
2. allnoconfig: New config where all options are answered with no.
3. allyesconfig: New config where all options are accepted with yes.
4. tinyconfig: Configure the tiniest possible kernel.

这里我们关注的是 tinyconfig, 于是我们先清理一下, 然后使用 tinyconfig 生成 .config 文件, 然后制作 image, 最后使用 qemu 去执行:

$ make mrproper
$ make tinyconfig
$ make all -j 8
    Kernel: arch/x86/boot/bzImage is ready

$ qemu-system-x86_64 -kernel bzImage  -append "console=tty0 console=ttyS0 init=/bin/sh" -nographic
SeaBIOS (version 1.15.0-1)
iPXE (https://ipxe.org) 00:03.0 CA00 PCI2.10 PnP PMM+07F8B340+07ECB340 CA00
Booting from ROM..

最后发现日志停在 Booting from ROM.. 就没有任何消息了.

这是因为 tinyconfig 包含的驱动或者配置太少, 导致没有后续输出, 我们需要在 tinyconfig 的基础上添加一些配置.

添加配置

添加配置使用 make menuconfig 来修改, 最后保存就好.

1. 64-bit kernel
   
2. Device Drivers -> Character devices -> Enable TTY
   
3. Device Drivers -> Character devices -> Serial drivers -> 8250/16550 and compatible serial support -> Console on 8250/16550 and compatible serial port
   
4. General setup > Configure standard kernel features (expert users) -> Enable support for printk
   

保存上面配置, 并且做一个新的image:

$ make all -j 8 
$ qemu-system-x86_64 -kernel bzImage  -append "console=tty0 console=ttyS0 init=/bin/sh" -nographic

SeaBIOS (version 1.15.0-1)
iPXE (https://ipxe.org) 00:03.0 CA00 PCI2.10 PnP PMM+07F8B340+07ECB340 CA00
Booting from ROM..
Run /bin/sh as init process
Kernel panic - not syncing: Requested init /bin/sh failed (error -2).
Kernel Offset: disabled
---[ end Kernel panic - not syncing: Requested init /bin/sh failed (error -2). ]---

可以看到 Kernel panic, 因为我们只是启动 kernel, 没有root 文件系统, 也没有使用 initrd 的ramdisk.

修改config 支持 initrd

使用 make menuconfig 继续修改

1. General setup -> Initial RAM filesystem and RAM disk (initramfs/initrd) support
   
2. Executable file formats -> Kernel support for ELF binaries
   

保存, 然后 make all -j 8 再次制作image, 然后运行:

$ qemu-system-x86_64 -kernel bzImage -initrd initramfs.cpio.gz -append "console=tty0 console=ttyS0 init=/bin/sh" -nographic

Run /init as init process
Failed to execute /init (error -8)
Run /bin/sh as init process
/bin/sh: can't access tty; job control turned off
/ # input: ImExPS/2 Generic Explorer Mouse as /devices/platform/i8042/serio1/input/input2
clocksource: tsc: mask: 0xffffffffffffffff max_cycles: 0x311fac54234, max_idle_ns: 440795352581 ns
clocksource: Switched to clocksource tsc
uname -a
Linux (none) 6.4.0-rc5+ #3 Wed Jun  7 08:19:32 PDT 2023 x86_64 GNU/Linux
/ # ls /bin/
...

/ # ps aux
PID   USER     TIME  COMMAND

可以看到 kernel 启动后执行了 /bin/sh, 我们使用 uname能看到 kernel 的版本号, 但是ps 没有任何输出. 那是因为我们没有挂载 proc 文件系统. 同时执行挂载 proc 文件系统的脚本在 initramfs.cpio.gz 内部的 init 文件里, 它是一个 shell, 所以要使 kernel 支持 shell 的 #!.

再次通过 make menuconfig 修改配置:

1. Executable file formats -> Kernel support for scripts starting with #!
   
   2. File systems > Pseudo filesystems -> (/proc file system support & sysfs file system support)
   

修改完保存, 然后重新制作 image, 并且运行:

$ qemu-system-x86_64 -kernel bzImage -initrd initramfs.cpio.gz -append "console=tty0 console=ttyS0 init=/bin/sh" -nographic

ps
PID   USER     TIME  COMMAND
    1 0         0:00 {init} /bin/sh /init
    2 0         0:00 [kthreadd]
    3 0         0:00 [kworker/0:0-eve]
    4 0         0:00 [kworker/0:0H]
    5 0         0:00 [kworker/u2:0-ev]
    6 0         0:00 [mm_percpu_wq]
    7 0         0:00 [ksoftirqd/0]
    8 0         0:00 [oom_reaper]
    9 0         0:00 [writeback]
   10 0         0:00 [kswapd0]
   11 0         0:00 [kworker/u2:1-ev]
   12 0         0:00 [kworker/0:1-eve]
   13 0         0:00 [kworker/u2:2-ev]
   14 0         0:00 [kworker/0:2]
   19 0         0:00 sh
   20 0         0:00 ps

如何制作一个可运行的 ISO 文件

创建文件结构并且复制数据

$ mkdir -p iso/boot/grub
$ cp bzImage iso/boot/
$ cp initramfs.cpio.gz  iso/boot/

创建 grub.cfg 文件

 $ vim iso/boot/grub/grub.cfg

set default=0
set timeout=10# Load EFI video drivers. This device is EFI so keep the
# video mode while booting the linux kernel.
insmod efi_gop
insmod font
if loadfont /boot/grub/fonts/unicode.pf2
then
        insmod gfxterm
        set gfxmode=auto
        set gfxpayload=keep
        terminal_output gfxterm
fimenuentry 'myos' --class os {
    insmod gzio
    insmod part_msdos
    linux /boot/bzImage init=/bin/sh console=ttyS0 console=tty0
    initrd /boot/initramfs.cpio.gz
}

安装 xorriso, mtools 并且制作 ISO image:

$ sudo apt install xorriso mtools -y
$ grub-mkrescue -o myos.iso iso/

$ ls -lah myos.iso

使用 Qemu 测试新的 ISO image

$ qemu-system-x86_64 -boot d -cdrom myos.iso -nographic

看到一篇关于时序相似性检测的文章 How can we quantify similarity between time series?, 里面涉及了几种算法的对比, 非常有启发性. 于是问 ChatGPT 要了几个关于相似性的算法, 也做了相关的对比.

这里记录一下相关的代码和步骤. 这个内容是在 Jupyter Notebook 写的. 主要分为4部分.

定义几种算法

import numpy as np
import pywt

# 1. 欧拉距离 1.长度相同
def euclidean_similarity(actual, predic):
    return np.sqrt(np.sum((actual - predic) ** 2))

# 2. mean absolute percentage error (MAPE) 1.长度相同, 值不能为0
def mape_similarity(actual, predic):
    return np.mean(np.abs((actual - predic) / actual))

# 3. Pearson correlation coefficient 1.长度相同, 1.0 表示完全相同
def correlation_similarity(actual, predic):
    a_diff = actual - np.mean(actual)
    p_diff = predic - np.mean(predic)
    numerator = np.sum(a_diff * p_diff)
    denominator = np.sqrt(np.sum(a_diff ** 2)) * np.sqrt(np.sum(p_diff ** 2))
    return numerator / denominator

# 4. 余弦相似性, 1.长度相同, 1.0 表示完全相同
def cosine_similarity(x, y):
    numerator = sum([a * b for a,b in zip(x,y)])
    denominator = np.sqrt(sum([a**2 for a in x])) * np.sqrt(sum([b**2 for b in y]))
    return numerator / denominator

# 5. 基于傅立叶变换 再使用余弦相似
def fft_similarity(x, y):
    # 对两个时序数据进行傅里叶变换
    fft_x = np.fft.fft(x)
    fft_y = np.fft.fft(y)

    # 对频谱数据进行归一化处理
    norm_x = np.abs(fft_x) / len(x)
    norm_y = np.abs(fft_y) / len(y)

    # 计算余弦相似度
    numerator = np.dot(norm_x, norm_y)
    denominator = np.linalg.norm(norm_x) * np.linalg.norm(norm_y)
    similarity = numerator / denominator

    return similarity

# 6. 小波变换 -
def wavelet_similarity(x, y, wavelet='db4', level=3, threshold='soft', threshold_value=0.1):
    # 对两个时序数据进行小波变换
    coeffs_x = pywt.wavedec(x, wavelet=wavelet, level=level)
    coeffs_y = pywt.wavedec(y, wavelet=wavelet, level=level)

    # 对小波系数进行阈值处理
    if threshold == 'hard':
        thresh_coeffs_x = [pywt.threshold(c, threshold_value, mode='hard') for c in coeffs_x]
        thresh_coeffs_y = [pywt.threshold(c, threshold_value, mode='hard') for c in coeffs_y]
    elif threshold == 'soft':
        thresh_coeffs_x = [pywt.threshold(c, threshold_value, mode='soft') for c in coeffs_x]
        thresh_coeffs_y = [pywt.threshold(c, threshold_value, mode='soft') for c in coeffs_y]
    else:
        raise ValueError("Invalid threshold mode. Must be 'hard' or 'soft'.")

    # 计算余弦相似度
    flat_x = np.concatenate(thresh_coeffs_x)
    flat_y = np.concatenate(thresh_coeffs_y)
    numerator = np.dot(flat_x, flat_y)
    denominator = np.linalg.norm(flat_x) * np.linalg.norm(flat_y)
    similarity = numerator / denominator

    return similarity

# 7. 傅立叶变换 
# 先通过快速傅立叶变换把时域信号转成频域信号, 然后把其中一个频域和另外一个频域的复共轭做乘积, 再把结果做快速傅立叶逆变换, 得到在时域信号的互相关. 
def compare_multiple_arrays_with_max_shift(reference_array, other_arrays, max_shift):
    start_ns = time.time_ns()
    fft_reference = np.fft.rfft(reference_array)
    reference_norm = np.linalg.norm(reference_array)

    results = []

    for array in other_arrays:
        fft_array = np.fft.rfft(array)

        cross_correlation = np.fft.irfft(fft_reference * np.conj(fft_array))

        max_shift_arr = np.concatenate((cross_correlation[-max_shift:], cross_correlation[:max_shift + 1]))
        max_shift_abs_arr = np.abs(max_shift_arr)
        lag_index = np.argmax(max_shift_abs_arr)
        max_correlation = max_shift_abs_arr[lag_index]
        lag = lag_index - max_shift

        array_norm = np.linalg.norm(array)
        norm = reference_norm * array_norm
        correlation_coefficient = 0 if norm == 0 else max_correlation / norm

        results.append((correlation_coefficient, lag))

    print("method 0 used: ", time.time_ns() - start_ns)
    return results

定义一些辅助函数

# 一些辅助函数
def __normalize(vals):
    min_v = min(vals)
    max_v = max(vals)
    return [(x - min_v) / (max_v - min_v) * 100 for x in vals]

def __fill_0_for_empty_ts(x_values, y_values):
    """
    x_values & y_values are 2 dimension array, the 1st column is the millisecond, the 2nd
    column is the value of that time, ex: [[], [], []]
    """
    start_time = round(min(min(x_values)[0], min(y_values)[0]) / 60000)  # the min minute
    end_time = round(max(max(x_values)[0], max(y_values)[0]) / 60000)  # the max minute

    count = int(end_time - start_time) + 1
    x_vals = np.zeros(count)
    y_vals = np.zeros(count)

    for element in x_values:
        minute = round(element[0] / 60000)
        x_vals[minute - start_time] = float(element[1])

    for element in y_values:
        minute = round(element[0] / 60000)
        y_vals[minute - start_time] = float(element[1])

    return x_vals, y_vals

定义对比和测试函数

import matplotlib.pyplot as plt
import pandas as pd
from IPython.display import display

def __prepare(ts_x, ts_y):
    x = ts_x[:,1]
    y = ts_y[:,1]

    fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(30, 8))

    ax1.plot(np.array(ts_x[:,0], dtype='datetime64[ms]'), x, color='blue', label='ts_x')
    ax2.plot(np.array(ts_y[:,0], dtype='datetime64[ms]'), y, color='red', label='ts_y')


    nx = np.array(__normalize(x))
    ny = np.array(__normalize(y))
    ax3.plot(np.array(ts_y[:,0], dtype='datetime64[ms]'), nx, color='blue', label='normalized_x')
    ax3.plot(np.array(ts_y[:,0], dtype='datetime64[ms]'), ny, color='red', label='normalized_y')
    ax3.set_title('normalized')
    plt.tight_layout()
    
    return x, y, nx, ny

def test_similarity(x, y, similarity_func):
    return similarity_func(x, y)

# calc shift 
def test_similarity_with_move(ts_x, ts_y, similarity_func):
    steps = 8
    length = len(ts_x)
    best_score = similarity_func(ts_x, ts_y)
    best_shift = 0
    for move in range(1, steps):
        score = similarity_func(ts_x[move:], ts_y[:(length - move)])
        # print(f"{best_score} vs {score} with {similarity_func.__name__} shift: {move}")
        best_score, best_shift = (score, move) if score > best_score else (best_score, best_shift)
        
        score = similarity_func(ts_y[move:], ts_x[:(length - move)])
        # print(f"{best_score} vs {score} with {similarity_func.__name__} shift: {-move}")
        best_score, best_shift = (score, move) if score > best_score else (best_score, best_shift)
    
    return best_score, best_shift

def compare(ts_x, ts_y):
    algorithms = [correlation_similarity, cosine_similarity, fft_similarity, wavelet_similarity]
    x, y, nx, ny = __prepare(ts_x, ts_y)
    result = {"algorithm":[], "raw":[], "normalized":[], "rawWithShift":[], "normalizedWithShift":[]}
    for algorithm in algorithms:
        result["algorithm"].append(algorithm.__name__)
        result["raw"].append(test_similarity(x, y, algorithm))
        result["normalized"].append(test_similarity(nx, ny, algorithm))
        result["rawWithShift"].append(test_similarity_with_move(x, y, algorithm))
        result["normalizedWithShift"].append(test_similarity_with_move(nx, ny, algorithm))

    df = pd.DataFrame(result)
    display(df)
    

对比测试

明显区分度测试

# 测试1 明显区分度 原始数据
ts_x = 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ts_y = np.array([[1682638320000,1.2999976391715666],[1682638380000,1.3445933616363022],[1682638440000,0.8513891645166145],[1682638500000,0.580030734376455],[1682638560000,0.5366737829361838],[1682638620000,0.29213584265117487],[1682638680000,0.06666666666666667],[1682638740000,0.016666666666666666],[1682638800000,0.016666666666666666],[1682638860000,0],[1682638920000,0.016666666666666666],[1682638980000,0.041666666666666664],[1682639040000,0.049999999999999996],[1682639100000,0.14999968754412588],[1682639160000,0.16110728963202783],[1682639220000,0.15000013889120378],[1682639280000,0.14438552780642439],[1682639340000,0.3352488269002545],[1682639400000,0.4791106494858955],[1682639460000,0.4670988185285921],[1682639520000,0.47477976942200895],[1682639580000,0.4166843529964785],[1682639640000,0.5047513306649607],[1682639700000,1.1145315261277136],[1682639760000,1.3657446685411132],[1682639820000,1.3118932804610217],[1682639880000,1.3502069581635667],[1682639940000,0.8249999312100912],[1682640000000,0.5749947576282455],[1682640060000,0.425062421275175],[1682640120000,0.39166635418185697],[1682640180000,0.5333356252965927],[1682640240000,0.5416674308240772],[1682640300000,0.5416659377744454],[1682640360000,0.5499998959440148],[1682640420000,0.46666524316478064],[1682640480000,0.6336589514654256],[1682640540000,0.6913314113839778],[1682640600000,0.5028315836111288],[1682640660000,0.38466392611255945],[1682640720000,0.19999944449045007],[1682640780000,0.10833336810662474],[1682640840000,0.03333333333333333],[1682640900000,0.0250005208514185],[1682640960000,0.2667035720031638],[1682641020000,0.40833451392505926],[1682641080000,0.5416680904110321],[1682641140000,0.6833330295489726],[1682641200000,0.45832292308947503],[1682641260000,0.5583323612227931],[1682641320000,0.46665854636552123],[1682641380000,0.34166541686573676],[1682641440000,0.33333107679551194],[1682641500000,0.08333326388946759],[1682641560000,0.05000010416796876],[1682641620000,0.024999999999999998],[1682641680000,0.016666666666666666],[1682641740000,0.024999999999999998],[1682641800000,0.041669619101209456],[1682641860000,0.049999999999999996],[1682641920000,0.05833302083926493],[1682641980000,0.15000000000000005],[1682642040000,0.1333332638938078],[1682642100000,0.2083326042501437],[1682642160000,0.6653442813240605],[1682642220000,1.0819944200907627],[1682642280000,1.3986757640109924],[1682642340000,1.6500266144000366],[1682642400000,1.4083953201740684],[1682642460000,1.1167151023096336],[1682642520000,0.9916681947057309],[1682642580000,0.7666733685670183],[1682642640000,0.7583336112326406],[1682642700000,0.59166618062355],[1682642760000,0.6583337847718469],[1682642820000,0.5999875460015153],[1682642880000,0.6166656945127288],[1682642940000,0.6166678820895601],[1682643000000,0.4499863662297911],[1682643060000,0.9416896769371015],[1682643120000,0.9832976874844609],[1682643180000,0.9333240658929527],[1682643240000,1.0750055964431735],[1682643300000,0.600000903022002],[1682643360000,0.39173132611068756],[1682643420000,0.40000562689957914],[1682643480000,0.4916728171698435],[1682643540000,0.5500227058301577],[1682643600000,0.9166703126734733],[1682643660000,1.0583296540822842],[1682643720000,0.8999965974380644],[1682643780000,1.1166663542753188],[1682643840000,0.7916661458777478],[1682643900000,0.76667354487317],[1682643960000,0.7722229090747322],[1682644020000,0.4666662500708899],[1682644080000,0.7416511215169792],[1682644140000,0.8249939602133775],[1682644200000,0.7083330903728287],[1682644260000,0.8083158526792605],[1682644320000,0.6416650001313566],[1682644380000,0.724999757219176],[1682644440000,0.8166649654408255],[1682644500000,0.7666740378807257],[1682644560000,0.6083323959263589],[1682644620000,0.37500145838802307],[1682644680000,0.4499981251539282],[1682644740000,0.48333923941052465],[1682644800000,0.5333367363136681],[1682644860000,0.4833325347750283],[1682644920000,0.37500076390596115],[1682644980000,0.400000000050347],[1682645040000,0.3833338194904531],[1682645100000,0.4333312848965507],[1682645160000,0.3416668750176507],[1682645220000,0.24166645841926884],[1682645280000,0.21666690978081724],[1682645340000,0.15833458338599746],[1682645400000,0.14166677085546953],[1682645460000,0.12500935008019612],[1682645520000,0.5833696574822261],[1682645580000,1.3166618058052564],[1682645640000,1.7416512586793633],[1682645700000,2.066650247736495],[1682645760000,1.791559029251039],[1682645820000,1.1082862688662387],[1682645880000,0.7999629530472216],[1682645940000,0.44166684035257686],[1682646000000,0.4416632989306695],[1682646060000,0.39166559063438255],[1682646120000,0.29166784727343953],[1682646180000,0.3500004167204877],[1682646240000,0.1333350349949652],[1682646300000,0.1416661805839104],[1682646360000,0.11666652778009254],[1682646420000,0.049999999999999996],[1682646480000,0.05000045141334044],[1682646540000,0.0583330208398436],[1682646600000,0.15833333336313743],[1682646660000,0.30833399308608334],[1682646720000,0.45000006944965304],[1682646780000,0.5250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compare(ts_x, ts_y)

结果:

不明显区分度

# 测试2 一般区分度 
ts_x = 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compare(ts_x, ts_y)

结果: