Posts on Shaka

Installation of ArchLinux

Tue, 06 Oct 2026 00:00:00 +0000

This post aims to record the installation procedure of ArchLinux on my notebook, Thinkpad X1 Carbon (x1c) 2018, i.e., 6th generation.

Preparition

Download the installation image from the nearest mirror.

Burn the image into a USB stick.

 dd if=/path/to/image/ of=/dev/sdb status=progress bs=10M

The notebook has Windows 10 installed with 快速启动 enabled. Therefore, it needs to be disabled before the installation. Uncheck the option of 控制面板 -> 硬件和声音 -> 电源选项 -> 选择电源按钮的功能 -> 更改当前不可用的设置 -> 启用快速启动（推荐）.

Installation

Boot

Power on the notebook.
Press Enter and F1 to enter the BIOS configuration.
Disable the Security -> Secure Boot.
Enable Config -> Thunderbolt BIOS Assist Mode. This will significantly reduce the power consumption of CPU wakeups¹.
Insert the prepared USB and press F10 to save the change and reboot the notebook.
Press Enter and F12 to temporarily boot from the prepared USB stick.

Partition

For UEFI booting, a dedicated EFI system partition (ESP) is mandatory. EFI bootloaders, applications and drivers can be stored in an ESP and lauched by the UEFI firmware at the boot stage. In other words, it is completely independent of OS. Considering the potential support of dual-boot in the futher, I prepare a 1 GB partition for ESP. Accordingly, I created a primary partition (/dev/nvme0n1p1) of partion type EFI System. Taking fdisk for instance, the type can be selected by alias uefi.

In addition, I created two ext4 partitions for / and /home respectively.

Format the partitions

 mkfs.fat -F 32 /dev/nvme0n1p1
 mkfs.ext4 /dev/nvme0n1p2
 mkfs.ext4 /dev/nvme0n1p3

Mount the partitions

 mount /dev/nvme0n1p2 /mnt
 mount --mkdir /dev/nvme0n1p1 /mnt/boot
 mount --mkdir /dev/nvme0n1p3 /mnt/home

Connect to the Internet

 iwctl --passphrase PASSWORD station wlan0 connect-hidden SSID

Select the nearest mirror

Edit /etc/pacman.d/mirrorlist as below.

 Server = http://mirrors.aliyun.com/archlinux/$repo/os/$arch

Install the base system

 pacstrap /mnt base

Generate file system table

 genfstab -U /mnt >> /mnt/etc/fstab

The resultant /etc/fstab looks

 # Static information about the filesystems.
 # See fstab(5) for details.

 # <file system> <dir> <type> <options> <dump> <pass>
 # /dev/nvme0n1p2 LABEL=OS
 UUID=a2d1afa4-4a38-4849-a4e7-ab5a5c4dba8d	/ 	ext4 	rw,relatime	0 1

 # /dev/nvme0n1p1 LABEL=ESP
 UUID=019D-1686 	/boot 	vfat 	rw,relatime,fmask=0022,dmask=0022,codepage=437,iocharset=ascii,shortname=mixed,utf8,errors=remount-ro	0 2

 # /dev/nvme0n1p3 LABEL=DATA
 UUID=386c4fbc-f1fd-4147-98bb-547867e762f5	/home 	ext4 	rw,relatime	0 2

Chroot into the newly installed system

 arch-chroot -S /mnt

Host name

Create file /etc/hostname.

 notebook

Time zone

 ln -sf /usr/share/zoneinfo/Asia/Shanghai /etc/localtime
 hwclock --systohc
 systemctl enable systemd-timesyncd.service

Locale

Edit /etc/locale.gen and uncomment the following lines.

...
en_US.UTF-8 UTF-8
...
zh_CN.UTF-8 UTF-8
...

Generate and set locales.

locale-gen
echo LANG=en_US.UTF-8 > /etc/locale.conf

Kernel and microcode

 pacman -S linux linux-firmware intel-ucode

Initramfs

 mkinitcpio -P

CPU frequency scaling

 pacman -S cpupower
 systemctl enable cpupower.service

Network

 pacman -S networkmanager
 systemctl enable NetworkManager.service

Bootloader

I adopt systemd-boot as the UEFI boot manager, shipped with systemd.

Installation

 bootctl install

Configuration

/boot/loader/loader.conf
```
 default arch.conf
 timeout 3
```

/boot/loader/entries/arch.conf

 title	Arch Linux
 linux	/vmlinuz-linux
 initrd	/intel-ucode.img
 initrd	/initramfs-linux.img
 options	root=UUID=a2d1afa4-4a38-4849-a4e7-ab5a5c4dba8d rw

/boot/loader/entries/arch-fallback.conf

 title	Arch Linux (fallback)
 linux	/vmlinuz-linux
 initrd	/intel-ucode.img
 initrd	/initramfs-linux-fallback.img
 options	root=UUID=a2d1afa4-4a38-4849-a4e7-ab5a5c4dba8d rw

Password for root

 passwd

Unmount and reboot

 exit
 umount -R /mnt
 reboot

Python - UV

Sat, 15 Aug 2026 00:00:00 +0000

As another tool for Python, uv is written by rust and provides integrated experience, e.g.

interpretor management (by uv python)
virtual environment manangement (by uv venv)
package management (by uv pip)
project management (by uv init/add/lock/sync)

In Archlinux, uv can be easily installed by pacman, i.e.,

 pacman -S uv

Its usage can be summarized as follows. Note that, if a virtual environment has already activated, then the argument --python /PATH/TO/ENVIRONMENT below can be omitted.

Python interpretor management

List the interpretors.
```
 uv python list
```
Install an interpretor.
```
 uv python install x.y[.z]
```

Linux - Hyprland

Sun, 12 Jul 2026 00:00:00 +0000

Introduction

Hyprland is a dynamic tiling compositor based on wlroot. Compared to sway, hyprland provides better experience and easy configuration. What is exciting, its development is much active.

Hyprland's core components and necessary applications can be simply installed and configured, e.g.,

hyprland: core components
foot: a native terminal in wayland
fuzzel: an application launcher
light: a backlight controller
swaync: a notification utility
grim: a screenshot utility
slurp: a region selection utility in wayland
swaybg: a background setting utility
swaylock: a utility to lock screen
wdisplays: an arandr counterpart in wayland
waybar: a bar utility in wayland
ttf-font-awesome: a font to display icons in waybar
xdg-desktop-portal-hyprland: XDG desktop handler enabling D-Bus based communication for other applications
qt5-wayland/qt6-wayland: Wayland support for QT

Installation

 pacman -S hyprland waybar foot fuzzel swaybg swaylock light grim slurp ttf-font-awesome qt5-wayland qt6-wayland blueman network-manager-applet pipewire wireplumber xdg-desktop-portal-hyprland xdg-desktop-portal-gtk

Configuration

By default, all the configuration files are stored in directory ~/.config/hypr.

~/.config/hypr/hyprland.conf

 ########################################################################################
 AUTOGENERATED HYPR CONFIG.
 PLEASE USE THE CONFIG PROVIDED IN THE GIT REPO /examples/hypr.conf AND EDIT IT,
 OR EDIT THIS ONE ACCORDING TO THE WIKI INSTRUCTIONS.
 ########################################################################################

 #
 # Please note not all available settings / options are set here.
 # For a full list, see the wiki
 #

 # autogenerated = 1 # remove this line to remove the warning

 # See https://wiki.hyprland.org/Configuring/Monitors/
 # monitor=name,resolution,position,scale
 monitor=eDP-1,disable
 monitor=DP-1,preferred,auto,2
 
 # See https://wiki.hyprland.org/Configuring/Keywords/ for more

 # Execute your favorite apps at launch
 exec-once = waybar --config ~/.config/hypr/waybar/config --style ~/.config/hypr/waybar/style.css
 exec-once = swaybg -i /usr/share/backgrounds/archlinux/small.png
 exec-once = swaync --config ~/.config/hypr/swaync.json
 exec-once = fcitx5 -D
 exec-once = nm-applet
 exec-once = blueman-applet
 exec-once = /usr/lib/polkit-kde-authentication-agent-1

 # Source a file (multi-file configs)
 source = ~/.config/hypr/bind.conf
 source = ~/.config/hypr/env.conf

 # Window rules
 windowrulev2 = opacity 0.3, floating:1, class:foot

 misc {
 disable_hyprland_logo = true
 disable_splash_rendering = true
 focus_on_activate = true
 }

 # For all categories, see https://wiki.hyprland.org/Configuring/Variables/
 input {
 kb_layout = us
 kb_variant =
 kb_model =
 kb_options = caps:ctrl_modifier
 kb_rules =
 repeat_rate = 60
 repeat_delay = 300
 follow_mouse = 1
 touchpad {
 natural_scroll = yes
 disable_while_typing = true
 }
 sensitivity = 0 # -1.0 - 1.0, 0 means no modification.
 }

 general {
 # See https://wiki.hyprland.org/Configuring/Variables/ for more
 gaps_in = 1
 gaps_out = 1
 border_size = 3
 col.active_border = rgba(33ccffee) rgba(00ff99ee) 45deg
 col.inactive_border = rgba(595959aa)
 layout = dwindle
 }

 decoration {
 # See https://wiki.hyprland.org/Configuring/Variables/ for more
 rounding = 9
 drop_shadow = yes
 shadow_range = 3
 shadow_render_power = 3
 col.shadow = rgba(1a1a1aee)
 }

 animations {
 enabled = yes
 # Some default animations, see https://wiki.hyprland.org/Configuring/Animations/ for more
 bezier = myBezier, 0.05, 0.9, 0.1, 1.05
 animation = windows, 1, 8, default
 animation = windowsOut, 1, 8, default, slide
 animation = border, 1, 10, default
 animation = borderangle, 1, 8, default
 animation = fade, 1, 8, default
 animation = workspaces, 1, 8, default, fade
 }

 dwindle {
 # See https://wiki.hyprland.org/Configuring/Dwindle-Layout/ for more
 pseudotile = yes # master switch for pseudotiling. Enabling is bound to mainMod + P in the keybinds section below
 preserve_split = yes # you probably want this
 }

 master {
 # See https://wiki.hyprland.org/Configuring/Master-Layout/ for more
 new_is_master = true
 }

 gestures {
 # See https://wiki.hyprland.org/Configuring/Variables/ for more
 workspace_swipe = off
 }

 # Example per-device config
 # See https://wiki.hyprland.org/Configuring/Keywords/#executing for more
 device:epic-mouse-v1 {
 sensitivity = -0.5
 }

~/.config/hypr/bind.conf

 # See https://wiki.hyprland.org/Configuring/Keywords/ for more
 $mainMod = SUPER

 # Example binds, see https://wiki.hyprland.org/Configuring/Binds/ for more
 bind = $mainMod, Q, killactive
 bind = $mainMod SHIFT, SPACE, togglefloating
 bind = $mainMod, E, togglesplit # dwindle
 bind = $mainMod, T, toggleopaque
 bind = $mainMod, F, fullscreen

 bind = $mainMod, Return, exec, foot --config ~/.config/hypr/foot.ini
 bind = $mainMod, D, exec, fuzzel --config ~/.config/hypr/fuzzel.ini
 bind = , Print, exec, grim $(date +'%Y%m%d-%H%M%S.png')
 bind = SHIFT, Print, exec, grim -g "$(slurp)" $(date +'%Y%m%d-%H%M%S.png')

 # Move focus
 bind = $mainMod, O, cyclenext
 bind = $mainMod, left, movefocus, l
 bind = $mainMod, right, movefocus, r
 bind = $mainMod, up, movefocus, u
 bind = $mainMod, down, movefocus, d

 # Switch workspaces
 bind = $mainMod, 1, workspace, 1
 bind = $mainMod, 2, workspace, 2
 bind = $mainMod, 3, workspace, 3
 bind = $mainMod, 4, workspace, 4
 bind = $mainMod, 5, workspace, 5
 bind = $mainMod, 6, workspace, 6
 bind = $mainMod, 7, workspace, 7
 bind = $mainMod, 8, workspace, 8
 bind = $mainMod, 9, workspace, 9

 # Move active window to a workspace
 bind = $mainMod SHIFT, 1, movetoworkspacesilent, 1
 bind = $mainMod SHIFT, 2, movetoworkspacesilent, 2
 bind = $mainMod SHIFT, 3, movetoworkspacesilent, 3
 bind = $mainMod SHIFT, 4, movetoworkspacesilent, 4
 bind = $mainMod SHIFT, 5, movetoworkspacesilent, 5
 bind = $mainMod SHIFT, 6, movetoworkspacesilent, 6
 bind = $mainMod SHIFT, 7, movetoworkspacesilent, 7
 bind = $mainMod SHIFT, 8, movetoworkspacesilent, 8
 bind = $mainMod SHIFT, 9, movetoworkspacesilent, 9

 # Move/resize windows
 bind = $mainMod SHIFT, R, submap, resize_window
 submap = resize_window
 binde = , right, resizeactive, 10 0
 binde = , left, resizeactive, -10 0
 binde = , up, resizeactive, 0 -10
 binde = , down, resizeactive, 0 10
 bind = , escape, submap, reset
 submap = reset
 bindm = $mainMod, mouse:272, movewindow
 bindm = $mainMod, mouse:273, resizewindow

 # Adjust volume
 bindle = , XF86AudioRaiseVolume, exec, pactl set-sink-volume @DEFAULT_SINK@ +5%
 bindle = , XF86AudioLowerVolume, exec, pactl set-sink-volume @DEFAULT_SINK@ -5%
 bindle = , XF86AudioMute, exec, pactl set-sink-mute @DEFAULT_SINK@ toggle
 bindle = , XF86AudioMicMute, exec, pactl set-source-mute @DEFAULT_SOURCE@ toggle

 # Adjust Brightness
 bindle = , XF86MonBrightnessUp, exec, sudo light -A 5
 bindle = , XF86MonBrightnessDown, exec, sudo light -U 5

 # System submap: (E)xit, (H)alt, (R)eboot.
 bind = $mainMod SHIFT, E, submap, system
 submap = system
 bind = , E, exit
 bind = , L, exec, swaylock -i /usr/share/backgrounds/archlinux/small.png
 bind = , H, exec, systemctl poweroff
 bind = , R, exec, systemctl reboot
 bind = , escape, submap, reset
 submap = reset

~/.config/hypr/env.conf

 env = LANG,en_US.UTF-8
 env = XCURSOR_SIZE,32
 env = GTK_IM_MODULE,fcitx
 env = QT_IM_MODULE,fcitx
 env = XMODIFIERS,@im=fcitx
 env = QT_QPA_PLATFORM,wayland
 env = MOZ_ENABLE_WAYLAND,1
 env = XAPIAN_CJK_NGRAM,1
 env = EDITOR,/usr/bin/emacsclient -a "" -t
 env = LIBSEAT_BACKEND,logind

~/.config/hypr/foot.ini
```
 [main]
 font=JetBrains Mono:size=18
```

~/.config/hypr/fuzzel.ini

 font=JetBrains Mono
 dpi-aware=auto
 prompt=" "
 icon-theme=Arc
 icons-enabled=yes
 fuzzy=yes
 show-actions=no
 lines=9
 width=60
 vertical-pad=0
 line-height=32

 [colors]
 background=fbf1c7ff
 text=32302fff
 match=ae6962ff
 selection=d5c4a1ff
 selection-text=282828ff

 [border]
 width=0
 radius=12

~/.config/hypr/swaync.json

 {
 "$schema": "/etc/xdg/swaync/configSchema.json",
 "positionX": "right",
 "positionY": "top",
 "layer": "overlay",
 "control-center-layer": "top",
 "layer-shell": true,
 "cssPriority": "application",
 "control-center-margin-top": 0,
 "control-center-margin-bottom": 0,
 "control-center-margin-right": 0,
 "control-center-margin-left": 0,
 "notification-2fa-action": true,
 "notification-inline-replies": false,
 "notification-icon-size": 64,
 "notification-body-image-height": 100,
 "notification-body-image-width": 200,
 "timeout": 10,
 "timeout-low": 5,
 "timeout-critical": 0,
 "fit-to-screen": true,
 "control-center-width": 500,
 "control-center-height": 600,
 "notification-window-width": 300,
 "keyboard-shortcuts": true,
 "image-visibility": "when-available",
 "transition-time": 200,
 "hide-on-clear": false,
 "hide-on-action": true,
 "script-fail-notify": true,
 "scripts": {
 "example-script": {
 "exec": "echo 'Do something...'",
 "urgency": "Normal"
 },
 "example-action-script": {
 "exec": "echo 'Do something actionable!'",
 "urgency": "Normal",
 "run-on": "action"
 }
 },
 "notification-visibility": {
 "example-name": {
 "state": "muted",
 "urgency": "Low",
 "app-name": "Spotify"
 }
 },
 "widgets": [
 "inhibitors",
 "title",
 "dnd",
 "notifications"
 ],
 "widget-config": {
 "inhibitors": {
 "text": "Inhibitors",
 "button-text": "Clear All",
 "clear-all-button": true
 },
 "title": {
 "text": "Notifications",
 "clear-all-button": true,
 "button-text": "Clear All"
 },
 "dnd": {
 "text": "Do Not Disturb"
 },
 "label": {
 "max-lines": 5,
 "text": "Label Text"
 },
 "mpris": {
 "image-size": 96,
 "image-radius": 12
 }
 }
 }

~/.config/hypr/waybar/config

 {
 "layer": "top",
 "modules-left": ["hyprland/workspaces"],
 "modules-center": [],
 "modules-right": ["cpu", "memory", "temperature", "backlight", "battery", "pulseaudio", "clock", "tray", "notification"],
 // Modules configuration
 "hyprland/workspaces": {
 "format": "{name}{icon}",
 "on-click": "activate",
 "sort-by-number": true
 },
 "tray": {
 "spacing": 10,
 "icon-size": 30
 },
 "clock": {
 "format": "{: %Y-%m-%d %a %H:%M}",
 "tooltip": false
 },
 "cpu": {
 "format": "{usage}% ",
 "tooltip": false
 },
 "memory": {
 "format": "{}% ",
 "tooltip": true
 },
 "temperature": {
 "critical-threshold": 80,
 "format": "{temperatureC}°C {icon}",
 "format-icons": ["", "", ""]
 },
 "backlight": {
 "format": "{percent}% {icon} ",
 // "format-icons": ["", ""]
 "format-icons": ["", "", "", "", "", "", "", "", ""]
 },
 "battery": {
 "states": {
 // "good": 95,
 "warning": 30,
 "critical": 15
 },
 "format": "{capacity}% {icon} ",
 "format-charging": "{capacity}% ",
 "format-plugged": "{capacity}% ",
 "format-alt": "{time} {icon}",
 "tooltip": false,
 "format-icons": ["", "", "", "", ""]
 },
 "network": {
 "format-wifi": "{essid} ({signalStrength}%)  ",
 "format-ethernet": "{ifname}: {ipaddr}/{cidr}  ",
 "format-linked": "{ifname} (No IP)  ",
 "format-disconnected": "Disconnected ⚠ ",
 "format-alt": "{ifname}: {ipaddr}/{cidr}",
 "tooltip": false
 },
 "pulseaudio": {
 "scroll-step": 10, // %, can be a float
 "format": "{volume}% {icon} {format_source}",
 "format-bluetooth": "{volume}% {icon} {format_source}",
 "format-muted": "{volume}%  {format_source}",
 "format-source": "{volume}% ",
 "format-source-muted": "{volume}% ",
 "format-icons": {
 "headphones": "",
 "handsfree": "",
 "headset": "",
 "phone": "",
 "portable": "",
 "car": "",
 "default": ["", "", ""]
 },
 "on-click": "pavucontrol"
 },
 "notification": {
 "tooltip": false,
 "format": "{icon}",
 "format‐icons": {
 "notification": "<U+F0A2><span foreground=’red’><sup><U+F444></sup></span>",
 "none": "<U+F0A2>",
 "dnd‐notification": "<U+F1F7><span foreground=’red’><sup><U+F444></sup></span>",
 "dnd‐none": "<U+F1F7>",
 "inhibited‐notification": "<U+F0A2><span foreground=’red’><sup><U+F444></sup></span>",
 "inhibited‐none": "<U+F0A2>",
 "dnd‐inhibited‐notification": "<U+F1F7><span foreground=’red’><sup><U+F444></sup></span>",
 "dnd‐inhibited‐none": "<U+F1F7>"
 },
 "return‐type": "json",
 "exec‐if": "which swaync‐client",
 "exec": "swaync‐client ‐swb",
 "on‐click": "swaync‐client ‐t ‐sw",
 "on‐click‐right": "swaync‐client ‐d ‐sw",
 "escape": true
 }
 }

~/.config/hypr/waybar/style.css

 ,* {
 border: none;
 border-radius: 0;
 font-family: JetBrains Mono;
 font-size: 16px;
 min-height: 0;
 }

 window#waybar {
 background-color: transparent;
 }

 window#waybar.hidden {
 opacity: 0.3;
 }

 /*
 window#waybar.empty {
 background-color: transparent;
 }
 window#waybar.solo {
 background-color: #FFFFFF;
 }
 ,*/

 window#waybar.termite {
 background-color: #3F3F3F;
 }

 window#waybar.chromium {
 background-color: #000000;
 border: none;
 }

 #workspaces button {
 padding: 0 5px;
 background-color: transparent;
 color: #ffffff;
 border-bottom: 3px solid transparent;
 }

 /* https://github.com/Alexays/Waybar/wiki/FAQ#the-workspace-buttons-have-a-strange-hover-effect */
 #workspaces button:hover {
 background: rgba(0, 0, 0, 0.2);
 box-shadow: inherit;
 border-bottom: 3px solid #ffffff;
 }

 #workspaces button.active {
 background-color: #64727D;
 border-bottom: 3px solid #ffffff;
 }

 #workspaces button.urgent {
 background-color: #eb4d4b;
 }

 #mode {
 background-color: #64727D;
 border-bottom: 3px solid #ffffff;
 }

 #clock,
 #battery,
 #cpu,
 #memory,
 #temperature,
 #backlight,
 #network,
 #pulseaudio,
 #custom-media,
 #tray,
 #mode,
 #idle_inhibitor {
 padding: 0 10px;
 margin: 0 0px;
 color: #ffffff;
 }

 #clock {
 background-color: #64727D;
 }

 #battery {
 background-color: #ffffff;
 color: #000000;
 }

 #battery.charging {
 color: #ffffff;
 background-color: #26A65B;
 }

 @keyframes blink {
 to {
 background-color: #ffffff;
 color: #000000;
 }
 }

 #battery.critical:not(.charging) {
 background-color: #f53c3c;
 color: #ffffff;
 animation-name: blink;
 animation-duration: 0.5s;
 animation-timing-function: linear;
 animation-iteration-count: infinite;
 animation-direction: alternate;
 }

 label:focus {
 background-color: #000000;
 }

 #cpu {
 background-color: #2ecc71;
 color: #000000;
 }

 #memory {
 background-color: #9b59b6;
 }

 #backlight {
 background-color: #90b1b1;
 }

 #network {
 background-color: #2980b9;
 }

 #network.disconnected {
 background-color: #f53c3c;
 }

 #pulseaudio {
 background-color: #f1c40f;
 color: #000000;
 }

 #pulseaudio.muted {
 background-color: #90b1b1;
 color: #2a5c45;
 }

 #custom-media {
 background-color: #66cc99;
 color: #2a5c45;
 min-width: 100px;
 }

 #custom-media.custom-spotify {
 background-color: #66cc99;
 }

 #custom-media.custom-vlc {
 background-color: #ffa000;
 }

 #temperature {
 background-color: #f0932b;
 }

 #temperature.critical {
 background-color: #eb4d4b;
 }

 #tray {
 background-color: #2980b9;
 }

 #idle_inhibitor {
 background-color: #2d3436;
 }

 #idle_inhibitor.activated {
 background-color: #ecf0f1;
 color: #2d3436;
 }

 #mpd {
 background-color: #66cc99;
 color: #2a5c45;
 }

 #mpd.disconnected {
 background-color: #f53c3c;
 }

 #mpd.stopped {
 background-color: #90b1b1;
 }

 #mpd.paused {
 background-color: #51a37a;
 }

C++ - Span

Mon, 27 Apr 2026 00:00:00 +0000

std::span is a class template introduced in C++ 20. As one of the most paramount features, span is essentially a non-owning view of a sequence of objects, which is contiguously distributed in memory and can consequently be iterated and indexed, e.g., std::array, std::vector, std::string.

Constructors

span(ptr)
span(ptr, len)
span(starting_ptr, ending_ptr)

Member functions

first(num) returns a new span comprising the first num elements.
last(num) returns a new span comprising the last num elements.
front() / data() returns a reference to the first element.
back() returns a reference to the last element.
at(idx) / operator[idx] returns a reference to the idx th element.
subspan(starting_idx, len) returns a new span of length len starting from starting_idx th element.
size() returns the number of elements in the span.
empty() returns a boolean indicator whether the span is empty.
begin() returns the iterator to the beginning of the span.
end() returns the iterator to the ending (sentinel) of the span.

RIME Input Method Engine (RIME)

Sun, 12 Apr 2026 00:00:00 +0000

Rime input method engine (RIME) is an excellent input method application, which can be run on a variety of platforms, e.g., Linux, MacOS, and Windows.

RIME does not come with a frontend. Therefore, RIME as well as its frontend (e.g., fcitx5 or ibus) can be installed together.

 pacman -S librime fcitx5-im

Among the RIME solutions, wanxiang is a good choice. On ArchLinux, it can be easily installed by

 yay -S rime-wanxiang-updater

After the installation, run rime-wanxiang-updater to update the data and complete the configuration.

Linux - Network Bonding

Sat, 24 Jan 2026 00:00:00 +0000

Just as its name indicates, network bonding is a technique to bond a plurality of network interface together for load balance and a wider bandwidth.

The configuration of network bonding is simple. Taking ArchLinux for instance, the network bonding of 2 network interfaces (e.g., eth0 and eth1) can be configured as follows.

/etc/systemd/network/10-bond0-eth0.network

 [Match]
 Name=eth0

 [Network]
 Bond=bond0

/etc/systemd/network/10-bond0-eth1.network

 [Match]
 Name=eth1

 [Network]
 Bond=bond0

/etc/systemd/network/10-bond0.netdev

 [NetDev]
 Name=bond0
 Kind=bond

 [Bond]
 Mode=802.3ad
 LACPTransmitRate=fast
 MIIMonitorSec=100ms

/etc/systemd/network/10-bond0.network

 [Match]
 Name=bond0

 [Network]
 Address=xxx.xxx.xxx.xxx/24
 Gateway=xxx.xxx.xxx.xxx
 DNS=xxx.xxx.xxx.xxx

Mermaid

Mon, 19 Jan 2026 00:00:00 +0000

Mermaid is a JavaScript-based software to draw a wide variety of diagrams and charts, e.g., flowchart, sequence, state, block, class, mindmap, Gantt, git, pie, etc.

In Linux, mermaid can be directly installed via package manager. Taking ArchLinux for instance, it can be installed via pacman, i.e.,

 pacman -S mermaid-cli

Then, the mermaid utility mmdc is available which takes a mermaid file (with a .mmd extension) as input and outputs a diagram.

Slurm

Sun, 18 Jan 2026 00:00:00 +0000

Introduction

Slurm is the most popular open-source workload manager for Linux clusters released under GNU GPL v2. As a cluster manager, slurm is widely used all over the world, from academic circles to industrial areas. On one hand, it virtualizes the physically individual computing nodes as a supercomputer whereby the procedure and method of visiting resources can be greatly simplified. On other hand, it provides automatic job submission/queuing/scheduling/executing, as well as results collection.

Slurm is comprised of 3 daemons.

slurmctld is the controller daemon running on server.
slurmdbd is an optional but recommended daemon for database-based storage and statistics running on server. E.g., MySQL/mariadb can be installed.
slurmd is a client daemon running on each computing node.

Mathematics

Sat, 29 Nov 2025 00:00:00 +0000

As the titile indicates, this post is written to summarize the basic of mathematics.

Special functions

Gamma function
\begin{align*} \Gamma(x) \triangleq \int_0^{+\infty} e^{-t} t^{x - 1} dt \end{align*}
Particularly, $\forall x \in \mathbb{Z}^+$, $\Gamma(x) = (x-1)!$.
Bessel functions
- First kind
  \begin{align*} J_n(x) \triangleq \frac{1}{2\pi}\int_{-\pi}^{\pi} e^{j(x\sin\theta-n\theta)}d\theta \end{align*}
  Particularly, $\forall \phi \in [0, 2\pi)$, $J_0(x) = \dfrac{1}{2\pi} \int_\phi^{2\pi + \phi}e^{\pm jx\cos\theta}d\theta = \dfrac{1}{2\pi} \int_\phi^{2\pi + \phi}e^{\pm jx\sin\theta}d\theta$.
- Second kind
Q-function
\begin{align*} Q(x) &\triangleq \frac{1}{\sqrt{2\pi}}\int_x^{+\infty}e^{-\frac{t^2}{2}} dt \\ &= 1 - Q(-x) \end{align*}
Error function and complementary error function
\begin{align*} erf(x) &= \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt \\ &= 2Q(\sqrt{2}x) \\ erfc(x)&= \frac{2}{\sqrt{\pi}}\int_x^{+\infty} e^{-t^2} dt \\ &= 1 - erf(x) \\ &= 1 - 2Q(\sqrt{2}x) \end{align*}
Euler
\begin{align*} e^{j\theta} &= \cos\theta + j\sin\theta \\ \cos\theta &= \frac{e^{j\theta} + e^{-j\theta}}{2} \\ \sin\theta &= \frac{e^{j\theta} - e^{-j\theta}}{2j} \end{align*}

Linux - Add User in a Batch Way

Tue, 28 Oct 2025 00:00:00 +0000

Following script can be used to add users in a batch way.

 #!/bin/bash

 for u in `seq 9`; do
 useradd -m -G GROUP $u
 echo $u | passwd -s $u
 done

PBS and Maui

Tue, 21 Oct 2025 00:00:00 +0000

Introduction

Portable batch system (PBS) was originally developed by NASA, which is comprised of a resource manager, a scheduler and a client. What is different, a resource manager and a scheduler are usually running on server side, while clients running on computing nodes. For the softwares, both commercial PBS Pro and open-source Torque are available. But herein, we consider the open-source Torque only.

Just as their names indicate, a resource manager targets for resource management and configuration, responsible for checking the availability of resource, e.g. CPU, memory, etc., and resource assignment; a scheduler accept jobs from subscribers and maintains one or more queues.

The built-in scheduler is a simple FIFO scheduler. However, other schedulers can be adopted instead. For instance, Maui is a very popular and powerful scheduler, based on which advanced and complex strategies can be realized and customized.

C++ - Armadillo

Wed, 15 Oct 2025 00:00:00 +0000

Introduction

Armadillo¹ is an excellent C++ library, which provides efficient linear algebra related operations, based on a series of classes, e.g., for vectors, matrices, etc. Thanks to its friendly interfaces, similar to MATLAB, the library is very easy to use.

Armadillo is developped by Conrad Sanderson and Ryan Curtin, and released under Apache 2.0 license.

Installation & configuration

Installation

Above all, several third-party open source libraries (including OpenBLAS, LAPACK, ARPACK, SuperLU) should be installed as necessary dependencies. Taking ArchLinux for instance, these libraries can be simply installed by

 pacman -S openblas lapack arpack superlu

Then, armadillo can be installed by executing following commands.

 git clone --depth 1 https://gitlab.com/conradsnicta/armadillo-code.git
 cd armadillo-code
 cmake . -DCMAKE_INSTALL_PREFIX:PATH=/opt/armadillo
 make
 make install

Configuration

Create file /etc/ld.so.conf.d/arma.conf with its content as follows.
```
 /opt/armadillo/lib
```
Then, fresh the cache accordingly.
```
 ldconfig
```

Create a soft link for headers.

 ln -s /opt/armadillo/include/* /usr/local/include/

Building & linking

Due to the soft links in /usr/local/include, the headers can already be found.
Due to /etc/ld.so.conf.d/arma.conf, the object files in the library can be directly linked by option -larmadillo, e.g.,
```
 g++ main.cpp -o main -O2 -std=c++14 -larmadillo
```

K - Means Clustering

Sat, 27 Sep 2025 00:00:00 +0000

K - Means is a classical clustering algorithm, targeting intra-cluster close resemblance and inter-cluster difference.

Without loss of generality, the procedure of assigning $n$ samples to $k$ clusters can be listed as follows.

Initialize the cluster centers: Randomly select $k$ different samples as cluster centers.
Assign samples: For each sample, compute its distance to each cluster center, and assign the sample to its closest cluster.
Update cluster centers: For each cluster, update the mean value of intra-cluster samples as the new cluster center.
Repeat steps 2 and 3 until cluster centers do not change anymore or a maximum/expected number of iterations are reached.

English Study

Wed, 09 Jul 2025 00:00:00 +0000

发音

元音字母和辅音字母

在英文的26个字母中，有5个元音字母，分别为 a, e, i, o, u; 剩下的21个字母为辅音字母。

开音节和闭音节

开音节单词: 以元音字母结尾的单词
闭音节单词: 以辅音字母结尾的单词

通常，辅音字母的发音较单一，而元音字母的发音相对复杂。元音字母的发音有长音(也即字母本身的音)和短音，通常在开音节单词中发长音，在闭音节单词中发短音。

元音字母	`a`	`e`	`i`	`o`	`u`
开音节	`[ei]`	`[i:]`	`[ai]`	`[əʊ]`	`[ju:]`
闭音节	`[æ]`	`[e]`	`[ɪ]`	`[ɒ]`	`[ʌ]`

音标

爆破音: [p], [b], [t], [d], [k], [g].

Misc.

I can't do it 中的 't 不发音，所以这句话读起来和I can do it相似，区别仅仅在于后者中的can弱读。
字母组合 ee 和 ea 均发 [i:] 音。不同在于， ee 喜欢和字母 b 和字母 p 在一起；而 ea 喜欢和字母 d 和字母 t 在一起。
字母组合 ai 和 ay 均发 [ei] 音。不同在于， ai 一般位于单词中间；而 ay 位于单词尾部。

单词

appointment: 预约
beverage: 饮料
classy: 优等的, 上等的, 有品味的.
disrupt：使瓦解
mind
- in one's mind: 表达某人记得某事，在某人的记忆里。
- on one's mind: 表达困扰某人的问题或事情，某人心里挂念担心的问题或事情。
pantsuit：衣裤套装
sale: 促销
stereotype：模式化形象，刻板印象。
stingy: 吝啬的, 小气的.
trendy: 流行的，时髦的，时尚的。
变化
- get: 逐渐变
- turn: 颜色变
- grow: 成长变
- become: 身份变
看
- look: 看的时间短
- watch: 看的时间长
- see: 强调看的结果
- read: 强调安静读
意识
- conscious/consciously: 有意识的/有意识地
- subconscious/subconsciously: 潜意识的/潜意识地
真
- very: 只能修饰形容词或副词。
- really: 能修饰动词、形容词、或副词。
动物
- mosquito: 蚊子
超市
- 查看促销活动: check promotions
- 自动扶梯: escalator
  - 乘坐扶梯: take the escalator
- 蔬菜
  - 香菜: coriander
  - 麻薯: mochi
- 水果
  - 榴莲: durian
- 瑞士卷: Swiss roll
盖子
- cap: 通常指紧密贴合的盖子，需要拧上或者扣上才能固定。一般用于瓶子、小容器、笔、牙膏等。
  - 打开: unscrew the cap, twist off the cap.
  - 关上: screw the cap, tighten the cap.
- lid: 通常是可以拿起来的盖子，盖在容器顶部。一般用于锅、盒子、罐子、垃圾桶等较大的容器。例如：垃圾桶盖子: trash can lid.
  - 打开/关上盖子: open/close the lid
租房
- 合同: contract
- 房东: landlord
- 押金: deposit
- 中介: broker
- 转租: sublet
- 租户: tenant
- 水电费: utilities
- 设施: amenities
- 租金: rent
- 带家具的: furnished
- 租期: tenancy period

Electromagnetic Field (EMF)

Sat, 24 May 2025 00:00:00 +0000

Maxwell's equations without free charge

\begin{align*} \nabla \times \mathbf{E} &= -\mu \frac{\partial \mathbf{H}}{\partial t} \\ \nabla \times \mathbf{H} &= \epsilon \frac{\partial \mathbf{E}}{\partial t} \\ \nabla \cdot \epsilon\mathbf{E} &= 0 \\ \nabla \cdot \mu\mathbf{H} &= 0 \end{align*}

where

$\mathbf{E}$ and $\mathbf{H}$ are strengths of electric and magnetic fields respectively;
$\epsilon$ and $\mu$ are permittivity and permeability respectively.

Wave equation

Both $\mathbf{E}$ and $\mathbf{H}$ fulfill wave equation in vector format, i.e.,

\begin{align*} \nabla^2 \mathbf{E} - \frac{n^2}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} &= 0\\ \nabla^2 \mathbf{H} - \frac{n^2}{c^2} \frac{\partial^2 \mathbf{H}}{\partial t^2} &= 0 \end{align*}

where

$n$ is the refractive index of the medium;
$c = \dfrac{1}{\sqrt{\epsilon_0 \mu_0}}$ is the propagation speed of wave in vacuum, with $\epsilon_0$ and $\mu_0$ the permittivity and permeability in vacuum respectively.

For any individual component, the wave equation in scalar format applies, i.e.,

\begin{align} \nabla^2 u(\mathbf{p}, t) - \frac{n^2}{c^2} \frac{\partial^2 u(\mathbf{p}, t)}{\partial t^2} = 0, \label{eq:wave-eq} \end{align}

where $u(\mathbf{p},t)$ can be $\mathbf{E}_x$, $\mathbf{E}_y$, $\mathbf{E}_z$, $\mathbf{H}_x$, $\mathbf{H}_y$, or $\mathbf{H}_z$.

For monochromatic wave, a scalar-field can be written as

\begin{align} u(\mathbf{r}, t) &= a(\mathbf{r}) \cos[2\pi ft + \phi(\mathbf{r})] \nonumber \\ &= \mathcal{R}\left[U(\mathbf{r}, t) \right] \nonumber \\ &= \mathcal{R}\left[U(\mathbf{r}) e^{j2\pi ft}\right] \label{eq:separable} \end{align}

where

$U(\mathbf{r}) \triangleq a(\mathbf{r}) e^{j \phi(\mathbf{r})}$, $a(\mathbf{r})$ and $\phi(\mathbf{r})$ are respectively the amplitude and phase at point $\mathbf{r}$;
$U(\mathbf{r},t) \triangleq U(\mathbf{r})e^{j2\pi ft}$.

LaTeX - Beamer

Tue, 18 Feb 2025 00:00:00 +0000

Beamer is a convenient \LaTeX package for high quality slides. A template can be shown as follows.

 \documentclass[t, compress, red, 10pt, aspectratio=169, allowframebreaks]{beamer}

 \usepackage{hyperref}
 \hypersetup{pdfpagemode=FullScreen,
 colorlinks=true,
 pdfauthor={Shaka},
 pdftitle={TITLE},
 pdfcreator={GNU Emacs},
 pdflang={English}}
 \usepackage{tikz}
 \usepackage{pgfplots}
 \usepackage{circuitikz}
 \usetikzlibrary{arrows, cd, shapes}
 \tikzstyle{every picture}+=[remember picture]
 \usepackage{amsmath, amssymb, amsfonts}
 \usepackage{caption, subcaption}
 \usepackage{fontawesome5}
 \usepackage{enumerate}
 \usepackage{cite}
 \usepackage{tabularx}
 \usepackage{fancybox}
 \usepackage{booktabs}

 \usepackage{biblatex}
 \addbibresource{~/ref/ref.bib}
 \newcounter{eg}
 \newcounter{prop}
 % \usepackage{xeCJK}
 % \setCJKsansfont{WenQuanYi Micro Hei}
 % \usepackage{helvet}
 % \usepackage{charter}
 % \usepackage{fourier}
 % \usepackage{Minion Pro}
 % \usepackage{mathdesign}
 % \usepackage{mathpazo}
 % \usepackage{newcent}
 % \usepackage{avant}
 % \usepackage{bookman}
 \DeclareMathOperator{\diag}{diag}
 \renewcommand{\emph}[1]{\textit{\textcolor{blue}{#1}}}

 %% Insert logo at top right corner of each slide
 % LaTeX
 \logo{\pgfputat{\pgfxy(0, 8.2)}{\pgfbox[right,bottom]{\includegraphics[height=0.8cm]{logo.png}}}}
 % XeLaTeX
 % \logo{\pgfputat{\pgfxy(0, 8.2)}{\includegraphics[height=0.7cm]{logo.jpg}}}

 %% Custom footer
 \usefoottemplate{\rightline{\textbf{\insertframenumber}}}

 %% Theme setting
 % \setbeamercolor{frametitle}{fg=black}
 \usetheme{default}
 \useinnertheme{circles}
 \useoutertheme{default}
 \setbeamercovered{transparent}
 \setbeamertemplate{caption}[numbered]
 \usefonttheme{professionalfonts}
 \setbeamerfont{title}{shape=\scshape,series=\bfseries}
 \setbeamerfont{frametitle}{shape=\scshape,series=\bfseries}

 \begin{document}

 \title{TITLE}
 \author{AUTHOR}
 \date{\today}
 \institute{INSTITUTE}
 \titlepage

 \begin{frame}
 \frametitle{Outline}
 \tableofcontents
 \end{frame}

 \AtBeginSection
 {
 \begin{frame}
 \frametitle{Outline}
 \tableofcontents[currentsection, hideallsubsections]
 \end{frame}
 }

 \begin{frame}
 \frametitle{References}
 \printbibliography
 \end{frame}

 \begin{frame}
 \frametitle{FRAME}
 \begin{itemize}
 \item Proposal\refstepcounter{prop}\theprop\label{prop:1}: xxx
 \item Example\refstepcounter{eg}\theeg\label{eg:1}: xxx
 \item Proposal \ref{prop:1} and Example\ref{eg:1} xxx
 \end{itemize}
 \end{frame}
 \end{document}

MMSE-based Channel Estimation

Tue, 18 Feb 2025 00:00:00 +0000

Regarding channel estimation, minimum mean square error (MMSE) is a popular algorithm widely utilized in a variety of applications. This short document is just written to reveal the rationale between the algorithm.

Without loss of generality, we take an OFDM system for instance. The received signals on pilot, a.k.a. reference signal (RS) resource elements (RE) can be written as $\mathbf{y}_p = \mathbf{X}_p \mathbf{h}_{p} + \mathbf{n}_p$, where

$\mathbf{X}_p \in \mathbb{C}^{P \times P}$ is a diagonal matrix with pilot symbols as its diagonal elements, $P \in \mathbb{Z}^+$ the number of pilot in the pattern.
$\mathbf{h}_p \in \mathbb{C}^P$ is the channel frequency response (CFR) on the pilot REs.
$\mathbf{n}_p \in \mathbb{C}^P \sim \mathcal{CN}(\mathbf{0}, \sigma^2\mathbf{I}_P)$ is the additive Gaussian white noise.

The CFR of the target RE can be denoted by $\tilde{\mathbf{h}} = \mathbf{G} \mathbf{y}_p$, where $\mathbf{h}$ is the target CFR and $\mathbf{G}$ is the MMSE channel estimator.

Orgmode - Beamer

Tue, 18 Feb 2025 00:00:00 +0000

Emacs's builtin utility, orgmode can export an orgmode file to beamer slides. A template for beamer can be used directly.

In the export, text between a pair of stars will not be exported to boldface stuff as expected by default. Instead, it is colored by red as alert. Following settings can be placed in preamble to correct the behavior.

 \setbeamercolor{alerted text}{fg=black}
 \setbeamerfont{alerted text}{series=\bfseries}

Python - Argument Parser

Tue, 18 Feb 2025 00:00:00 +0000

Package argparse is a convenient utility for argument parsing, in which class ArgumentParser is defined. Concerning its usage, a simple example can be given as follows.

 from argparse import ArgumentParser, ArgumentDefaultsHelpFormatter

 args = ArgumentParser(formatter_class=ArgumentDefaultsHelpFormatter, conflict_handler='resolve')

 # Arguments in the root
 args.add_argument("--ARGUMENT1", type=int, metavar='', help="DESCRIPTION OF ARGUMENT1", default=0)

 # Arguments in groups
 grp1 = args.add_argument_group("GROUP1", "DESCRIPTION OF GROUP1")
 grp1.add_argument("--ARGUMENT1INGROUP1", type=float, metavar='', help="DESCRIPTION OF ARGUMENT1 IN GROUP1", default=0)
 grp1.add_argument("--ARGUMENT2INGROUP1", type=int, nargs=2, metavar='', help="DESCRIPTION OF ARGUMENT2 IN GROUP1", default=[0, 1])
 grp1.add_argument("--ENABLEFEATURE1", help="DESCRIPTION OF ENABLEFEATURE1 IN GROUP1", action="store_true")
 ...
 grp2 = args.add_argument_group("GROUP2", "DESCRIPTION OF GROUP2")
 ...

 # Parse the arguments
 para = args.parse_args()

 # Use the arguments parsed
 arg1 = para.ARGUMENT1 # arg1 is an integer
 arg1_grp1 = para.ARGUMENT1INGROUP1 # arg1_grp1 is a float
 arg2_grp1 = para.ARGUMENT2INGROUP1 # arg2_grp2 is a list comprising of 2 integers
 ...
 feature1_enabler = para.ENABLEFEATURE1 # feature1_enabler is a boolean

Python - Concurrent

Tue, 18 Feb 2025 00:00:00 +0000

Python has 2 builtin concurrent utilities which is widely utilized, i.e., process pool and thread pool, dedicated to CPU intensity and I/O intensity respectively.

Due to global interpreter lock (GIL), a process pool should be used for a CPU intensive task. In this case, each CPU involved (e.g., all the CPU by default) can be fully utilized.
While for a I/O intensive task, a thread pool should be used instead.

A simple example can be found below.

Python - Virtual Environment

Sun, 12 Jan 2025 00:00:00 +0000

Python的虚拟环境（virtual environment）是一个独立的Python运行环境。在一个独立的环境中，可以正常安装所需要的数据包（如使用pip等）。既不受系统环境的影响，也不会对系统环境产生影响。具体地，创建虚拟环境就是把系统Python环境复制到所创建的独立环境中。当进入一个虚拟环境时，virtualenv会修改相关的环境变量，让python和pip指向当前的独立环境。

创建独立的环境

 python -m venv ENV_NAME

进入环境

 source ENV_NAME/bin/activate

安装/升级pip

 python -m ensurepip --upgrade

退出环境

 deactivate

删除环境

 rm -fr ENV_NAME

Emacs - Doxygen

Wed, 27 Nov 2024 00:00:00 +0000

Introduction

Doxygen¹ is a powerful tool to document the source codes. In principle, it parses the specially formated comments from the source codes and then produces very professional documents. Up to now, it is able to support almost all the popular programming languages, e.g. C/C++, Java, Python, and etc.

Syntax

Comment block

Multi-line comment blocks: Begin with /** or /*!, and end with */.
Single-line comment blocks: delimiters /// or //!.

Special command

Within code blocks, special commands can be used. They begin with a prefix @ or \ and optionally have arguments enclosed in braces. Moreover, different braces mean different scopes.

Angle braces < > mean the argument is a single word.
Round braces ( ) mean the argument extends to end of line.
Curly braces { } mean the argument extends to next paragraph.

List

Column aligned - → a unsorted/bulleted list item.
Column aligned -# → a sorted list item.

Hierachical lists can be created by using different indents for different levels.

Group

/** \defgroup <label> ''<title>'' */
/* @{ */
 // group memebers here ...
/* @} */

/** \defgroup <label> ''<title>'' */
// @{
 // group memebers here ...
// @}

where the title is optional while the label is mandatory and can be used for reference by

\ref <label> ''<link>''

Formula

Inline formula

\f$ ... \f$

Centered formula

\f[ ... \f]

Graph

Doxygen can automatically generate graphs by dot from Graphviz². Additionally, mannual dot commands are enclosed between \dot and \enddot.

Text

\a/\e <word>: word
\b <word>: word
\c <word>: word

Section

\attention {...}: an Attention paragraph
\author {...}: author list
\brief {...}: a brief description
\bug {...}: a bug description
\date {...}
\deprecated {...}: a Deprecated paragraph
\note {...}: a Note paragraph
\par (title) {...}: a paragraph with a optional title
\param <p> {...}: a description of parameter p
\return {...}: a description of return values
\remarks {...}: a Remarks paragraph
\sa/\see {ref}: a See Also paragraph
\todo {...}: a To Do paragraph
\version {...}: a paragraph including the version string
\warning {...}: a paragraph for warning messages

Python - TDoc

Sat, 07 Sep 2024 00:00:00 +0000

Introduction

In order to facilitate the tdoc. related processing, I wrote a simple module using Python, termed tdoc, based on

Builtin modules, os, functools, multiprocessing, argparse; and
3rd party libraries, pandas, pybtex, urllib.

Features

It takes a tdoc. list file, usually has a xlsx extension name, as input.
It optionally filters the target tdocs. with agenda item, title, and/or author (e.g., company).
It can download tdocs. interested from 3GPP using multithreading (with configurable thread number) to a specified directory.
It can build a database based on the tdocs. after necessary filtering, and export it to a bib file.

Syntax

Its syntax can be listed as follows by run python tdoc.py --help.

 usage: tdoc.py [-h] [--remote_dir REMOTE_DIR]
 [--output_dir OUTPUT_DIR] [--agenda_item AGENDA]
 [--title TITLE] [--author AUTHOR]
 [--bibtex_file BIBTEX_FILE]
 [--thread_num THREAD_NUM]
 tdoc_list

 positional arguments:
 tdoc_list

 options:
 -h, --help show this help message and exit
 --remote_dir REMOTE_DIR
 --output_dir OUTPUT_DIR
 --agenda_item AGENDA
 --title TITLE
 --author AUTHOR
 --bibtex_file BIBTEX_FILE
 --thread_num THREAD_NUM

Orthogonal Matching Pursuit (OMP)

Fri, 06 Sep 2024 00:00:00 +0000

Matching pursuit (MP) and its improvement orthogonal matching pursuit (OMP) are both popular algorithms in compressive sensing (CS). Compared to MP, OMP can offer better performance, e.g. in respects of higher precision and faster convergency. This post aims to summarize the detailed procedure of OMP.

Given a NP-hard problem

\begin{align*} \mathcal{L}:\quad &\arg\min_{\mathbf{x}}\|\mathbf{x}\|_0 \\ \mathrm{subject~to}\quad & \mathbf{Ax} = \mathbf{b} \end{align*}

where

$\mathbf{A} \in \mathbb{C}^{m \times n}$ is a short-fat matrix, i.e., $n \gg m$.
$\mathbf{b}\in\mathbb{C}^m$.
$\mathbf{x}\in\mathbb{C}^n$.
- $\|\mathbf{x}\|_0$ is $\ell_0$ norm of $\mathbf{x}$, i.e., the number of non-zero elements of $\mathbf{x}$, a.k.a. the sparsity of $\mathbf{x}$;
- The set comprising the indices of all non-zero elements in $\mathbf{x}$ is termed the support of $\mathbf{x}$, denoted by
  \begin{align*} \mathrm{supp}(\mathbf{x}) \triangleq \{i \mid [\mathbf{x}]_i \neq 0\}. \end{align*}

Linux - Makefile

Sat, 03 Aug 2024 00:00:00 +0000

As is well-known, makefile is a text file which specifies the behavior of make. According to the rules in makefile, a project can be automatically built in a fairly smart way.

Given a project, different from Windows platform, where the required makefile is implicitly generated by the IDE in use; in Unix/Linux, it is of the most importance to compose a makefile. Only in this way, we can control the building and linking of the given project to maximum extent.

Least Square and Its Iterative Approach (RLS)

Wed, 29 May 2024 00:00:00 +0000

Introduction

As is well-known, least square (LS) is the optimal linear unbiased estimator, which plays an extremely important role in the classic estimation theory. This document motivates to illustrate the fundamental of LS algorithm. However, LS algorithm suffers rather high complexity, especially for the operation of matrix inversion, which greatly limits its application in practice. In order to reduce the computational complexity, an iterative approach, a.k.a. recursive LS (RLS), has been proposed.

The remainder part of the document is structured as follows. In Section #sec:ls, the principle of LS algorithm is derived in detail. Then its iterative solution, i.e., RLS algorithm, follows in Section #sec:rls.

Fourier Transform

Thu, 02 May 2024 00:00:00 +0000

Fourier Series

Continuous Fourier Series

\begin{align*} \tilde{x}(t) &= \frac{1}{T} \sum_{k=-\infty}^{\infty}X_a \left( k\frac{2\pi}{T} \right) e^{j\frac{2\pi}{T}kt} \\ X_a \left( k\frac{2\pi}{T} \right) &= \int_{-\frac{T}{2}}^{\frac{T}{2}} \tilde{x}(t) e^{-j\frac{2\pi}{T}kt} dt \end{align*}

Discrete Fourier Series

\begin{align*} \tilde{x}(n) &= \frac{1}{N} \sum_{k=0}^{N-1} \tilde{X}(k)e^{j\frac{2\pi}{N}kn} \\ \tilde{X}(k) &= \sum_{n=0}^{N-1} \tilde{x}(n) e^{-j\frac{2\pi}{N}nk} \end{align*}

Properties

\begin{align*} \tilde{x}(n+m) &\leftrightarrow \tilde{X}(k)e^{j\frac{2\pi}{N}km} \\ \tilde{x}^{*}(n) &\leftrightarrow \tilde{X}^{*}(-k) \\ \tilde{x}(-n) &\leftrightarrow \tilde{X}(-k) \\ \sum_{m=0}^{N-1} \tilde{x}_1(m) \tilde{x}_2(n-m) &\leftrightarrow \tilde{X}_1(k) \tilde{X}_2(k) \\ \tilde{x}_1(n) \tilde{x}_2(n) &\leftrightarrow \frac{1}{N} \sum_{\ell=0}^{N-1} \tilde{X}_1(\ell) \tilde{X}_2(k-\ell) \\ \tilde{x}_e(n) &\leftrightarrow \tilde{X}_r(k) \\ \tilde{x}_o(n) &\leftrightarrow j\tilde{X}_i(k) \\ \tilde{x}_r(n) &\leftrightarrow \tilde{X}_e(k) \\ j\tilde{x}_i(n) &\leftrightarrow \tilde{X}_o(k) \end{align*}

where subscript $r$, $i$, $e$, and $o$ mean the real, imagnary, even, and odd parts of an expression, respectively, i.e,

\begin{align*} \tilde{x}(n) &= \tilde{x}_e(n) + \tilde{x}_o(n) \\ &= \tilde{x}_r(n) + j \tilde{x}_i(n) \\ \tilde{x}_e(n) &= \frac{\tilde{x}(n) + \tilde{x}(-n)}{2} \\ \tilde{x}_o(n) &= \frac{\tilde{x}(n) - \tilde{x}(-n)}{2} \\ \tilde{X}(k) &= \tilde{X}_e(k) + \tilde{X}_o(k) \\ &= \tilde{X}_r(k) + j \tilde{X}_i(k) \\ \tilde{X}_e(k) &= \frac{\tilde{X}(k) + \tilde{X}(-k)}{2} \\ \tilde{X}_o(k) &= \frac{\tilde{X}(k) - \tilde{X}(-k)}{2}. \end{align*}

Wide Sense Fourier Series

Continuous

Given a continuous time signal space $\mathcal{S}$ defined in range $(t_1, t_2)$, if $\{\phi_i(t) \mid i=1, 2, \ldots, N\}$ is a complete orthogonal basis in $\mathcal{S}$, $\forall x(t) \in \mathcal{S}$, it can be represented as a linear combination of the basis, i.e.,

\begin{align*} x(t) = \sum_{i=1}^N a_i \phi_i(t), \end{align*}

where

\begin{align*} a_i = \dfrac{\int_{t_1}^{t_2} x(t) \phi_i^{*}(t) dt}{\int_{t_1}^{t_2}|\phi_i(t)|^2dt}, \quad i = 1, 2, \ldots, N. \end{align*}

Discrete

Given a discrete time signal space $\mathcal{S}$ defined in range $(n_1, n_2)$, if $\{\phi_i[n] \mid i=1, 2, \ldots, N\}$ is a complete orthogonal basis in $\mathcal{S}$, $\forall x[n] \in \mathcal{S}$, it can be represented as a linear combination of the basis, i.e.,

\begin{align*} x[n] = \sum_{i=1}^N a_i \phi_i[n], \end{align*}

where

\begin{align*} a_i = \dfrac{\sum_{n=n_1}^{n_2} x[n] \phi_i^{*}[n]}{\sum_{n=n_1}^{n_2}|\phi_i[n]|^2}, \quad i = 1, 2, \ldots, N. \end{align*}

LaTeX - Pgf/Tikz

Sun, 25 Feb 2024 00:00:00 +0000

Introduction

Pgf/tikz is an excellent LaTeX package to plot high quality graphs. This post just summaries its basic usages.

Installation

Pgf/Tikz is a built-in package in the texlive. As long as texlive is ready, pgf/tikz is out-of-the-box.

Basic usage

Setting

\usepackage{tikz}
...
\tikz ...
\begin{tikzpicture}
...
\end{tikzpicture}

Style

Create a new style

\tikzstyle{newstylename}=[option1=value1, option2=value2, ...]

For example, following styles can be defined for nodes in a flowchart.

 \tikzstyle{startstop} = [rectangle, rounded corners, minimum width=3cm, minimum height=1cm, text centered, text width=5cm, draw=black, fill=red!30]
 \tikzstyle{io} = [trapezium, trapezium left angle=70, trapezium right angle=110, minimum width=3cm, minimum height=1cm, text centered, text width=5cm, draw=black, fill=blue!30]
 \tikzstyle{process} = [rectangle, minimum width=3cm, minimum height=1cm, text centered, text width=5cm, draw=black, fill=orange!30]
 \tikzstyle{decision} = [diamond, minimum width=3cm, minimum height=1cm, text centered, text width=5cm, draw=black, fill=green!30]
 \tikzstyle{arrow} = [thick, ->, >=stealth]

Modify an existing style

\tikzstyle{existingstylename}+=[option1=value1, option2=value2, ...]

Coordinate

(x, y)
(angle: radius)

List

% step length = 1
{a, ..., b}
...
% step length = d
{a, a + d, ..., b}

Arrow

Draw

Line

\draw (x1, y1) -- (x2, y2) -- (x3, y3) -- cycle

Curve

\draw (x1, y1) .. controls (x2, y2) and (x3, y3) .. (x4, y4);
\draw (x1, y1) .. controls (x2, y2) .. (x3, y3);

Grid

\draw [step=s] (x1, y1) grid (x2, y2);
\draw [xstep=x_s, ystep=y_s] (x1, y1) grid (x2, y2);

Arc

\draw (x1, y1) arc (start_angle: end_angle: radius);

Rectangle

\draw (x1, y1) rectangle (x2, y2);
\fill [color] (x1, y1) rectangle (x2, y2);
\filldraw [fill=color1, draw=color2] (x1, y1) rectangle (x2, y2);
\shade [inner/top/left color=color1, outer/bottom/right color=color2] (x1, y1) rectangle (x2, y2);
\shadedraw [inner/top/left color=color1, outer/bottom/right color=color2, draw=color3] (x1, y1) rectangle (x2, y2);
\clip (x1, y1) rectangle (x2, y2);

Circle

\draw (x1, y1) circle (radius);
\fill [color] (x1, y1) circle (radius);
\filldraw [fill=color1, draw=color2] (x1, y1) circle (radius);
\shade [inner/top/left color=color1, outer/bottom/right color=color2] (x1, y1) circle (radius);
\shadedraw [inner/top/left color=color1, outer/bottom/right color=color2, draw=color3] (x1, y1) circle (radius);
\clip (x1, y1) circle (radius);

Ellipse

\draw (x1, y1) ellipse (x_radius and y_radius);
\fill [color] (x1, y1) ellipse (x_radius and y_radius);
\filldraw [fill=color1, draw=color2] (x1, y1) ellipse (x_radius and y_radius);
\shade [inner/top/left color=color1, outer/bottom/right color=color2] (x1, y1) ellipse (x_radius and y_radius);
\shadedraw [inner/top/left color=color1, outer/bottom/right color=color2, draw=color3] (x1, y1) ellipse (x_radius and y_radius);
\clip (x1, y1) ellipse (x_radius and y_radius);

Node

(x0, y0) node [anchor=north/south/east/west, shape=circle/rectangle/ellipse, draw=color1, fill=color2, label=angle:node_label_angle] (node_name) {node_label};
...
\node at (x0, y0) (node_name) {node_label};

Connecting nodes with

Lines

\draw [arrow] (node_name_A) to (node_name_B);
\draw (node_name_A) edge [arrow, color] (node_name_B);

Curves

\draw [arrow] (node_name_A) to [bend left/right=30] (node_name_B);
\draw [arrow] (node_name_A) to [in=30, out=60] (node_name_B);
\draw (node_name_A) edge [arrow, color, in=30, out=60] (node_name_B);
\draw (node_name_A) edge [arrow, color, bend left/right=30] (node_name_B);

Refer to nodes outside current picture

\tikzstyle{every picture}+=[remember picture]
...
\tikz[overlay]
\begin{tikzpicture}[overlay]
...
\end{tikzpicture}

Mix tikz command with LaTeX

\tikz [baseline] ...

Cramer-Rao Bound

Mon, 19 Feb 2024 00:00:00 +0000

In parameter estimation, the performance of an estimator is usually evaluated in the respects of unbiasedness, efficiency, and consistency.

Take the estimation of parameter $\alpha$ for instance,

For an estimator $\hat{\alpha}$, if $\mathrm{E}[\hat{\alpha}] = \alpha$, then the estimator $\hat{\alpha}$ is unbiased.
- If $\lim\limits_{n\to\infty}\mathrm{E}[\hat{\alpha}] = \alpha$, then the estimator $\hat{\alpha}$ is progressively unbiased.
For two estimators $\hat{\alpha}_1$ and $\hat{\alpha}_2$, if $\mathrm{Var}[\hat{\alpha}_1] < \mathrm{Var}[\hat{\alpha}_2]$, then $\hat{\alpha}_1$ is more efficient than $\hat{\alpha}_2$.
For an estimator $\hat{\alpha}$, if $\forall \epsilon > 0$, $\exists N \in \mathbb{Z}^+$, when $n > N$, $\mathrm{Prob}[\|\hat{\alpha} - \alpha\| < \epsilon] = 1$; or equivalently $\lim\limits_{n\to\infty}\mathrm{Prob}[\|\hat{\alpha} - \alpha\| < \epsilon] = 1$ holds, then the estimator $\hat{\alpha}$ is consistent.

An unbiased estimator with minimal variance is termed minimal variance unbiased (MVU) estimator.

Emacs - RefTeX

Mon, 19 Feb 2024 00:00:00 +0000

RefTeX is a Emacs package dedicated for label, reference, citation, and index related operations in \LaTeX. What is exciting, RefTeX has been integrated into Emacs since version 20.2.

RefTeX is easy to use by providing 4 macros, \label, \ref, \cite, and \index. It can be configured as follows.

Loading the package
```
 (require 'reftex)
```

Turning on the mode

 (add-hook 'LaTeX-mode-hook 'turn-on-reftex); with AUCTeX LaTeX mode
 (add-hook 'latex-mode-hook 'turn-on-reftex); with Emacs latex mode

Integrating with AUCTeX
```
 (setq reftex-plug-into-AUCTeX t)
```

Targeting for quick operations, following keybindings are binded by default.

LaTeX - Biblatex

Mon, 19 Feb 2024 00:00:00 +0000

Biblatex is a new LaTeX package for bibliography management taking biber as backend, and more powerful than bibtex. For TeXLive users, biblatex is out-of-box.

LaTeX

… \usepackage[backend=biber, style=numeric]{biblatex} \addbibresource{PATH/TO/REF.bib} … \printbibliography …

Org

In orgmode, command org-cite-insert, binded to C-c C-x @ by default, is used to insert citation entries.

…

Python - QAM

Mon, 19 Feb 2024 00:00:00 +0000

Introduction

In order to structure the utility relating to constellation modulation, I wrote a class Quadrature_Amplitude_Modulation in Python.

Source code

 import numpy as np
 import matplotlib.pyplot as plt

 class Quadrature_Amplitude_Modulation:
 def __init__(self, mod_order: int) -> None:
 """! Constructor for quadrature amplitude modulation (QAM)
 @param mod_order Modulation order, e.g., 4 for QPSK.
 """
 self.mod_order = mod_order
 self.bit_num_sym = int(np.log2(mod_order))
 m = np.sqrt(mod_order)
 v = np.linspace(1 - m, m - 1, int(m))
 x, y = np.meshgrid(v, v)
 self.const = np.reshape(x + 1j * y, -1) / np.sqrt((mod_order - 1) * 2 / 3)
 self.name = "QPSK" if mod_order == 4 else f"{mod_order}QAM"
 def calc_mi(self, sinr: float, sample_num: int=1000) -> float:
 """! Calculate the per-symbol mutual information, a.k.a. RBIR, for the specified SINR.
 @param sinr SINR in dB
 @param sample_num Number of random samples
 @return Per-bit information
 """
 n_pwr = np.power(10, -0.1 * sinr)
 n = np.random.randn(sample_num) + 1j * np.random.randn(sample_num)
 n *= np.sqrt(n_pwr / 2)
 si = np.zeros((self.mod_order, sample_num))
 for sym_idx in range(self.mod_order):
 for sample_idx in range(sample_num):
 x = np.power(np.abs(self.const - self.const[sym_idx] + n[sample_idx]), 2) - np.power(np.abs(n[sample_idx]), 2)
 si[sym_idx][sample_idx] = np.sum(np.exp(-1 * x / n_pwr))
 return self.bit_num_sym - np.log2(si).mean()
 def visualize(self, ax: plt.Axes = None, **kwargs) -> None:
 """! Visualize the constellation
 @param ax An axis object
 @param kwargs Keyword argument for further customization
 """
 if ax is None:
 _, ax = plt.subplots()
 ax.scatter(self.const.real, self.const.imag, **kwargs)
 ax.set_xlabel('In-phase')
 ax.set_ylabel('Quadrature')
 ax.set_title(self.name)
 ax.set_aspect('equal')
 ax.grid(True)

TR38.901

Mon, 19 Feb 2024 00:00:00 +0000

3GPP TR38.901 offers the guidance and methodology of channel modelling, including both system-level simulation (SLS) and link-level simulation (LLS).

Coordinate systems

Global coordinate system (GCS) and local coordinate system (LCS) are linked by a rotational matrix $\mathbf{R}$, which can be decomposed as 3 successive primary rotations around Z/Y/X axes respectively. Accordingly, the composite rotational matrix $\mathbf{R}$ can be expressed as the product of 3 Givens rotation matrices.

Large-scale fading

In SLS, large scale attenuation needs to be modelled. Coupling loss is defined as the combination of distance-dependent path loss, shadow fading, antenna gain at the transmitter and receiver, outdoor-to-indoor (O2I) penetration loss¹.

Path loss is usually dependent on propagation types, i.e. line-of-sight (LOS) or non-line-of-sight (NLOS).
Propagation type, LOS/NLOS, is per site².
Location type, i.e. indoor or outdoor, is per user³.
Shadow fading is per site⁴.
O2I penetration loss is per user⁵.

Kalman Filter

Sat, 17 Feb 2024 00:00:00 +0000

Without loss of generality, the probability density function (pdf) of Gaussian distribution can be denoted by function

\begin{align*} N(x, \mu, \sigma) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}, \end{align*}

where $\mu$ and $\sigma$ are the mean and standard deviation repectively. Then, we have

\begin{align*} N(x, \mu_1, \sigma_1) N(x, \mu_2, \sigma_2) = \frac{e^{-\cfrac{(\mu_1-\mu_2)^2}{2(\sigma_1^2+\sigma_2^2)}}}{\sqrt{2\pi(\sigma_1^2+\sigma_2^2)}} N\left(x, \frac{\mu_1\sigma_2^2 + \mu_2\sigma_1^2}{\sigma_1^2 + \sigma_2^2}, \frac{\sigma_1^2\sigma_2^2}{\sigma_1^2+\sigma_2^2}\right) \end{align*}

Matplotlib

Sun, 03 Sep 2023 00:00:00 +0000

Background

Matplotlib is a popular python package for figure plot and data visualization.

Installation

 pip install matplotlib

Submodules

Matplotlib comes with a series of submodules, e.g.,

matplotlib.pyplot is the counterpart of Matlab in matplotlib, which is essentially a collection of functions similar to Matlab.
matplotlib.pylab is a convenience module which imports matplotlib.pyplot (for plotting) and numpy (for array related operations) in a single name space.

General Concepts

In Matplotlib, there are some important concepts which can be illustrated below.

Concepts in a figure in Matplotlib (from https://matplotlib.org/1.5.1/faq/usage_faq.html)

A typical matplotlib Figure is comprised of a variety of components, as show below.

Components of a figure in Matplotlib (from https://matplotlib.org/stable/tutorials/introductory/usage.html)

`Figure`

A Figure object is essentially a canvas on which plot operations are performed. Clearly, it consists of one or more Axes objects.

 import matplotlib.pyplot as plt

 # Create an empty Figure object without any Axes.
 fig = plt.figure()
 fig = plt.figure(figsize=(WIDTH, HEIGHT), dpi=DPI)

 # Create a Figure object including one Axes.
 fig, ax = plt.subplots()

 # Create a Figure object including 2 x 3 Axes.
 fig, ax = plt.subplots(2, 3)

matplotlib.pyplot.gcf() can get the current Figure object.

`Axes`

Create Axes objects.
- matplotlib.pyplot.subplots
- figure.add_axes
A Axes object consists of a multiplicity Axis objects, e.g.,
- 2 Axis objects in a 2-dimension plot, e.g.., X-axis and Y-axis.
- 3 Axis objects in a 3-dimension plot, e.g.., X-axis, Y-axis, and Z-axis.
A Figure object's member function gca() can get the current Axes object.
A Figure object's member function subplots can create one or more Axes objects.
Member functions
- plot(X, Y)
- set_xlabel("XLABEL")
- set_ylabel("YLABEL")
- set_title("TITLE")
- set_xticks("XTICKS")
- set_yticks("YTICKS")
- set_xlim([XMIN, XMAX])
- set_ylim([YMIN, YMAX])
- legend()
- set_prop_cycle() : Set the random seed of colors, e.g., None for reset to the default.

`Axis`

Just as its name indicates, a Axis object defines the properties and attributes of a axis, e.g., limits, ticks, and ticklabels.

C++ - Basic

Sat, 08 Jul 2023 00:00:00 +0000

本文是阅读 Professional C++, third edition 中文版¹的读书笔记.

预处理指令

预处理指令以 # 字符开始. 如 #pragma once 可以防止文件被包含多次.
头文件最常见的用途是声明在其他地方定义的函数.
宏是C遗留下来的, 类似于内联函数, 但不执行类型检测, 在调用宏时, 预处理器会自动用扩展式替换, 并不会真正地应用函数调用语义, 这一行为可能导致无法预测的结果. 应该全部用内联函数替代宏.

头文件

头文件是为子系统或者代码段提供抽象接口的一种机制. 使用头文件需要注意两个方面

避免循环引用. 使用前置声明(forward declarations).
避免多次引用同一个头文件. 使用头文件保护(include guards), 如 #ifndef 机制或者 #pragma once 指令.

建议尽可能使用前置声明, 而不是包含其他头文件. 这可以减少编译和重编译时间, 因为它破坏了一个头文件对其他头文件的依赖. 当然, 实现文件需要包含前置声明的类型的正确头文件, 否则无法编译.

函数

函数声明通常称为"函数原型"或"签名", 以强调其代表函数的访问方式, 而不是具体的代码.
函数参数的默认值只能存在于函数声明中, 不能放在函数定义中.
与C不同, 在C++中没有形参的函数仅需要一个空的圆括号, 不需要使用 void 指出此处没有形参. 然而, 如果没有返回值, 仍需要使用 void 来指明这一点.
main() 函数是程序的入口. main() 函数返回一个 int 值以指示程序的最终执行状态. main() 函数或者没有参数, 或者具有两个参数.

 int main(int argc, char* argv[])

自C++11以来, C++通过拖尾返回类型(trailing return type)支持一种替代的函数语法. 函数的返回类型不再位于开头, 而放在行尾的箭头 -> 后面. 这在指定模板函数的返回类型时非常有用.

 auto func(int i) -> int
 {
 return i + 1;
 }

C++14允许要求编译器自动推断出函数的返回类型. 为此, 需要指定返回类型为 auto, 并忽略所有拖尾返回类型.

类型

`typedef`

typedef 为已有的类型声明提供一个新名称. 可将 typedef 看成已有类型声明的同义词, typedef 不会创建新的类型.

typedef 的最常见用法是当实际类型的声明过于笨拙时, 提供易于管理的名称, 这一情形通常出现在模板中. STL广泛使用 typedef 提供类型的简短名称. 如 string 实际上是一个 typedef.

typedef basic_string<char, char_traits<char>, allocator<char>> string

typedef 可以包括作用域限定符.

类型别名

某些情况下, 类型别名比 typedef 更容易理解. 例如,

typedef int my_int;

可以重写为

using my_int = int;

NR - Cell Search

Tue, 04 Jul 2023 00:00:00 +0000

Synchronization signals

In NR, synchronization signals consist of primary synchronization signal (PSS) and secondary synchronization signal (SSS). Together with physical broadcast channel (PBCH), PSS and SSS are jointly termed synchronization signal block (SSB¹).

A SSB spans 4 OFDM symbols in the time domain and 240 subcarriers in the frequency domain. Within a SSB, the PSS and SSS lie in the 1st and 3rd symbol, respectively. The PBCH situates in the 2nd and 4th symbols, as well as the 48 subcarriers on the each side of the SSS (in the 3rd symbol), as shown in the figure below. Therefore, within a SSB, there are totally $240 + 48 \times 2 + 240 = 576$ RE's for PBCH transmission².

SSB

It should be noted that 60kHz numerology cannot be used for SSB transmission.

The SSB is periodically transmitted and the periodicity can be 5/10/20/40/80/160ms. But a UE always assumes that a SSB is repeated at least once every 20ms no matter whether it is the truth.

PSS

Similar to LTE, there are 3 PSS sequences, including a basic m-sequence of length 127, and its two cyclically shifted versions³. The initial values of the basic sequence are {0, 1, 1, 0, 1, 1, 1}. The subsequent values can be derived according to

\begin{align*} x_0(n) = x_0(n - 7) \oplus x_0(n - 3). \end{align*}

Then, the cyclically shifted sequences can be obtained by

\begin{align*} x_1(n) = x_0(n + 43 \mod 127), \\ x_2(n) = x_0(n + 86 \mod 127). \end{align*}

SSS

There are 336 SSS sequences which are the sums of two m-sequences with different shifts, i.e.,

\begin{align*} x_{m_1, m_2}(n) = x(n + m_1) + y(n + m_2), \end{align*}

where the two m-sequences can be obtained according to

\begin{align*} x(n) = x(n - 7) \oplus x(n - 3), \\ y(n) = y(n - 7) \oplus y(n - 6). \end{align*}

NR - Demodulation Reference Signal (DMRS)

Mon, 03 Jul 2023 00:00:00 +0000

Conceptions

Just as its name indicates, demodulation reference signal (DMRS) is the reference signal dedicated for demodulation. Different from LTE system, the DMRS in NR system is comprised of a frontloaded DMRS and a few optional additional DMRS.

Frontloaded DMRS

Frontloaded DMRS aims to reduce the duration of demodulation and decoding. There are a couple of mapping schemes.

Mapping type A: it lies the symbol second to the PDCCH region, e.g., in normal-slot-based transmission.
Mapping type B: it begins with the first data symbol scheduled, e.g., in mini-slot-based transmission.

Additional DMRS

Additional DMRS is proposed to support high speed mobility, e.g., 500km/h. Each additional DMRS is a simple repetition of the corresponding frontloaded DMRS, e.g., identical subcarriers and equal OFDM symbol number.

For single-symbol frontloaded DMRS, up to 3 additional DMRS can be supported.
For double-symbol frontloaded DMRS, at most 1 additional DMRS is supported.

Channel State Information Reference Signal (CSI-RS)

Sun, 02 Jul 2023 00:00:00 +0000

Introduction

In NR system, channel state information reference signal (CSI-RS) plays a variety of roles, including

CSI measurement
Beam management
Tracking
Mobility management
Rate match

Generally, there are two types of CSI-RS, termed non-zero-power (NZP) CSI-RS and zero-power (ZP) CSI-RS, respectively. The former is configured by .

Sequence Generation

CSI-RS symbols are a sequence of QPSK-modulated Gold sequence, which is initialized with

\begin{align*} c_{\text{init}} = \left[ 2^{10}(N_{\text{symb}}^{\text{slot}}n_{s,f}^{\mu} + \ell + 1)(2n_{\text{ID}}+1) + n_{\text{ID}} \right] \mod 2^{31} \end{align*}

where

$N_{\text{symb}}^{\text{slot}}$ is the number of symbols in a slot.
$n_{s,f}^{\mu}$ is the index of the slot within a frame.
$\ell$ is the index of the symbol within a slot.
$n_{\text{ID}}$ is configured by .

NR - Downlink Codebook

Sun, 02 Jul 2023 00:00:00 +0000

In NR release 15, there are roughly two types of codebooks for spatial-domain CSI acquisition, termed type I and type II, respectively. The former is comprised of a finite set of vectors or matrices, as the same as the codebook in LTE systems. While for the type II codebook, each precoding vector is represented as a linear weighted sum of an incomplete orthogonal basis vectors. Further, frequency-domain compression is introduced in NR release 16 for enhancement, which is expected to remarkably reduce the feedback overhead. Note that this section aims to reveal the rationale behind the codebook design, in lieu of covering everything detail related in the specifications.

Git

Sat, 01 Jul 2023 00:00:00 +0000

Introduction

Git is a famous and powerful open-source software for version control and management. It was developed by Linus Torvalds with C programing language. What is different from subversion, git adopts a completely distributed manner. Regarding its utilization, besides its built-in manual, there is also an excellent book, Pro Git, which can be obtained for free¹. This post just summarizes the preliminary usage of git, which is referred from the book.

Objects

In git, there are 3 types of objects defined, blob, tree, and commit. In order to view its properties, a dedicated command git cat-file is provided. Its type and content can be returned with option -t and -p respectively.

A blob keeps the content of a binary compressed file.
A tree represents a directory, including its hierarchy, permission, and the names of its componential files.
A commit is essentially a SHA-1 hash.

A branch or a tag is nothing but a pointer pointing at the SHA-1 hash of a commit. Moreover, HEAD is also a pointer, which always points the active branch at the time.

Areas

In the utilization of git, there are four important areas for storage, workspace, index (or stage), repository and remote. Their relationship can be illustrated by the figure below.

LTE - PCFICH

Sat, 01 Jul 2023 00:00:00 +0000

As its name implies, physical control format indicator channel (PCFICH) indicates the size of the control region, or equivalently the position where data region starts, of the instant subframe in terms of the number of OFDM symbols.

There are totally 2 bits for PCFICH corresponding to the three candidate control region sizes. As illustrated in Figure fig:lte-pcfich, the 2-bit payload is first coded into a 32-bit codeword, i.e. the code rate is 1/16, and then scrambled by a cell-specific and subframe-specific sequence to randomize and whiten the inter-cell interference (ICI). After that, the codeword is modulated as 16 QPSK symbols and mapped to 4 resource element groups (REG's)¹ in the first OFDM symbol of each subframe. Targetting for frequency diversity, the spacing between each two adjacent REG's is 1/4 of the bandwidth.

NR - Phase Tracking Reference Signal (PTRS)

Sat, 01 Jul 2023 00:00:00 +0000

Introduction

Targetting for the great goal of the 5th generation (5G) system, the new radio (NR) system, proposed by the 3rd generation partner project (3GPP), has employed a variety of cutting-edge technologies, including advanced channel coding schemes, e.g., low density parity code (LDPC) and polar code, higher-order modulation schemes, e.g., 256QAM, etc. Considering the fact that the lower frequency spectrum has already been so crowded and overutilized, NR decided to explore higher frequency band, e.g., million meter wave (mmWave). After all, much richer spectrum resources are available at higher frequency bands than lower frequency spectrum.

As is well-known, high frequency transmission suffers severe attenuation loss in the propagation, which remarkably limits the effective coverage and transmission distance. Fortunately, higher frequency spectrum has shorter wave length. Given an aperture size, much more antennas can be equipped in higher frequency transmission than those in lower frequency transmission. In this way, more antennas can yield larger beamforming gain and complement the attenuation loss in the transmission over the higher frequency bands. In a word, higher frequency enables the dense deployment of antennas, i.e., massive multi-input multi-output (M-MIMO), or equivalently large-scale MIMO (LS-MIMO); while M-MIMO extends the transmission distance and coverage of the higher frequency bands. Therefore, M-MIMO and higher frequency transmission are usually jointly utilized and have been the focus of the research and discussion in the 3GPP standardization.

Generally, an oscillator always produces phase noise, which is essentially an impairment of the oscillator. Nevertheless, the phase noise soars as the operation frequency grows. In the NR system, which operates on higher frequency spectrum, the impact of phase noise cannot be ignored. Instead, the phase noise must be accurately estimated and complemented before data detection. To this end, a dedicated reference signal, termed phase tracking reference signal (PTRS) has been proposed to track the fluctuation of the phase noise.

This report intends to cover the detail relating to PTRS. The remaining of this report is structured as follows. Section #sec:pn-model briefly introduces the models of phase noise, and Section #sec:presence-density provides the configuration of PTRS, including its presence and density in the time and frequency domain. The number of PTRS supported is given in Section #sec:port-num. The PTRS port association follows in Section #sec:port-association. Then, resource mapping and sequence generation are presented in Sections #sec:res-map and #sec:seq-gen respectively. In Section #sec:pn-estim-compl, the methodology of phase noise estimation and complementation are described in details. Finally, Section #sec:summary summarizes the report.

For clear description, following denotation conventions are adopted throughout the document. $\otimes$ is the operator of circular convolution. $\mathcal{F}_N \left\{ \cdot \right\} $ is the $N$-point fast Fourier transformation (FFT) operator. Radio resource control (RRC) signaling and downlink control indicator (DCI) parameters are illustrated as blue and orange phrases, respectively.

Linux - WiFi6

Tue, 09 May 2023 00:00:00 +0000

Today, I found the wireless network card (Intel Corporation Wi-Fi 6 AX201) is suffering random disconnection. Maybe there is something wrong with the driver in Linux.

After several rounds of searching and trying, the problem can be solved by disabling the 11n and 11ac modes, as well as power saving.

For ArchLinux, following two lines can be inserted in file /etc/modprobe.d/iwlwifi.conf.

 options iwlwifi power_save=0
 options iwlwifi 11n_disable=1 11ac_disable=1

NR - Multi-TRP Transmission

Tue, 09 May 2023 00:00:00 +0000

Introduction

Recently, multi-TRP transmission is one of the most remarkable features of NR and consequently the focus of discussion in the standardization of 3GPP, since it is able to efficiently improve the reliability or the efficiency of the transmission.

This document tries to provide an in-depth analysis and reveal the rationale behind the technology.

For clear description, following denotation conventions have been adopted throughout the document. Scalars, vectors, and matrices are respectively denoted by plain, lower-case boldfaced, and upper-case boldfaced letters. For a complex scalar, $(\cdot)^{*}$ means its conjugate, and $|\cdot|$ gets its absolute value. Given a matrix $\mathbf{A}$, $\mathbf{A}^H$ is its conjugate transposition, and $|\mathbf{A}|$ returns its determinant. Particularly, $\mathbf{I}$ stands for the entity matrix. $\mathbb{C}^{m \times n}$ represents the complex space of dimension $m \times n$. $\mathcal{E}(\cdot)$ is the expectation operator.

SLNR-based Beamforming

Tue, 09 May 2023 00:00:00 +0000

Introduction

In coordinatd scheduling and beamforming (CS/CB), one of coordinatd multipoint (CoMP) transmission schemes, signal leakage noise power ratio (SLNR)-based beamforming is widely used.

Just as its name indicates, SLNR aims to maximize the ratio of desired signal power to the undesired leakage power and noise power.

This page is just written to summarize this SLNR-based beamforming scheme.

System model

Without loss of generality, we consider a simple scenario as shown in the figure above. Taking UE0 for instance, the BS intends to send data to it, i.e. the received signals at other UE's, e.g. UE1, …, UEn are all leakage. The SLNR can be expressed as

\begin{align} \text{SLNR}_0 := \frac{\|\mathbf{H}_0 \mathbf{w}_0\|^2}{P_N + \sum_{i\neq 0}\|\mathbf{H}_i \mathbf{w}_0\|^2}, \end{align}

where

$P_N$ is the noise power at UE0.
$\mathbf{w}_0$ is the beamforming vector intended for UE0.
$\mathbf{H}_i$ is the channel matrix from the BS to UEi, $i=0,1,\ldots,n$.

Uniform Distribution in a Ring Area

Tue, 09 May 2023 00:00:00 +0000

This post aims to provide an efficient method of generating uniformly distributed coordinates in a given ring area.

Without loss of generality, the ring area is illustrated in Figure fig:ring. The inner and outer radii are $R_1$ and $R_2$, respectively, $R_1 < R_2$. The corresponding angular scope starts from $\Theta_1$ and ends at $\Theta_2$, $\Theta_1 < \Theta_2$.

In polar coordinate system, the joint probability density function (PDF) of the radius and angle can be written as

Whitening Filter

Tue, 09 May 2023 00:00:00 +0000

Usually, we need to filter a mixture of desired signal and colored noise, in order to make the spectrum of the noise become white.

Without loss of generality, $x(t)$ is a wide-sense stationary stochastic process. If it is taken as input by a linear time invariant (LTI) system $W$ and the output process $n(t)$ has white power spectrum, i.e., power spectrum density (PSD) equal to 1; then the system $W$ is termed the whitening filter of process $x(t)$, and $n(t)$ is termed the innovation process of $x(t)$. If $n(t)$ is input into the inverse system of $W$, denoted by $W^{-1}$, then the output is the original process $x(t)$ and system $W^{-1}$ is the corresponding innovation fitler, as shown in Figure whitening_innovation.

Linux - Sway

Sat, 11 Mar 2023 00:00:00 +0000

Introduction

Sway is a tiling compositor based on Wayland. It can be identified as a counterpart of i3 in Wayland, and as resource saving and lightweight as i3. Even, sway has a completely compatible configuration to i3.

Sway's core components and necessary applications can be simply installed and configured, e.g.,

sway: core components
swaylock: a screen locker
swayidle: an idle management daemon
foot: a native terminal in wayland
rofi: an application launcher and window switcher
waybar: a bar utility in wayland
light: a backlight controller
mako: a notification daemon
grim: a screenshot utility
slurp: a region selection utility in wayland
swaybg: a background setting utility

Installation

 pacman -S sway swaylock swayidle foot rofi waybar light mako grim slurp swaybg

Configuration

For centralized management, the configuration files can be gathered in directory ~/.config/sway.

`~/.config/sway/config`

 # Default config for sway
 #
 # Copy this to ~/.config/sway/config and edit it to your liking.
 #
 # Read `man 5 sway` for a complete reference.

 ### Variables
 set $mod Mod4
 set $term /usr/bin/foot --font=monospace:size=12
 set $menu /usr/bin/wofi -c ~/.config/sway/wofi.conf
 set $wallpaper /usr/share/backgrounds/sway/Sway_Wallpaper_Blue_1920x1080.png
 set $locker swaylock -f -i $wallpaper

 ### Appearance and behavior
 font pango: Source Code Pro 18
 workspace_layout default
 default_border none
 default_floating_border pixel
 popup_during_fullscreen smart
 focus_follows_mouse no

 ### Output
 output eDP-1 bg $wallpaper fill
 output DP-1 bg $wallpaper fill scale 2

 ### Idle configuration
 exec swayidle -w \
 timeout 300 $locker \
 timeout 600 'swaymsg "output * dpms off"' \
 resume 'swaymsg "output * dpms on"' \
 before-sleep $locker

 ### Key bindings
 #
 # Basics:
 #
 # start a terminal
 bindsym $mod+Return exec $term

 # kill focused window
 bindsym $mod+q kill

 # start your launcher
 bindsym $mod+d exec $menu

 # Drag floating windows by holding down $mod and left mouse button.
 # Resize them with right mouse button + $mod.
 # Despite the name, also works for non-floating windows.
 # Change normal to inverse to use left mouse button for resizing and right
 # mouse button for dragging.
 floating_modifier $mod normal

 # reload the configuration file
 bindsym $mod+Shift+c reload

 #
 # Moving around:
 #
 # Move your focus around
 bindsym $mod+o focus next
 bindsym $mod+Left focus left
 bindsym $mod+Down focus down
 bindsym $mod+Up focus up
 bindsym $mod+Right focus right

 # Move the focused window with the same, but add Shift
 bindsym $mod+Shift+Left move left
 bindsym $mod+Shift+Down move down
 bindsym $mod+Shift+Up move up
 bindsym $mod+Shift+Right move right
 
 #
 # Workspaces:
 #
 # define names for workspaces
 set $ws1 "1"
 set $ws2 "2"
 set $ws3 "3"
 set $ws4 "4"
 set $ws5 "5"
 set $ws6 "6"
 set $ws7 "7"
 set $ws8 "8"
 set $ws9 "9"

 # switch to workspace
 bindsym $mod+1 workspace $ws1
 bindsym $mod+2 workspace $ws2
 bindsym $mod+3 workspace $ws3
 bindsym $mod+4 workspace $ws4
 bindsym $mod+5 workspace $ws5
 bindsym $mod+6 workspace $ws6
 bindsym $mod+7 workspace $ws7
 bindsym $mod+8 workspace $ws8
 bindsym $mod+9 workspace $ws9
 
 # move focused container to workspace
 bindsym $mod+Shift+1 move container to workspace $ws1
 bindsym $mod+Shift+2 move container to workspace $ws2
 bindsym $mod+Shift+3 move container to workspace $ws3
 bindsym $mod+Shift+4 move container to workspace $ws4
 bindsym $mod+Shift+5 move container to workspace $ws5
 bindsym $mod+Shift+6 move container to workspace $ws6
 bindsym $mod+Shift+7 move container to workspace $ws7
 bindsym $mod+Shift+8 move container to workspace $ws8
 bindsym $mod+Shift+9 move container to workspace $ws9

 #
 # Layout stuff:
 #
 # Split
 bindsym $mod+h splith
 bindsym $mod+v splitv

 # Switch the current container between different layout styles
 bindsym $mod+s layout stacking
 bindsym $mod+w layout tabbed
 bindsym $mod+e layout toggle split

 # Make the current focus fullscreen
 bindsym $mod+f fullscreen toggle

 # Toggle the current focus between tiling and floating mode
 bindsym $mod+Shift+space floating toggle

 # Swap focus between the tiling area and the floating area
 bindsym $mod+space focus mode_toggle

 # Move focus to the parent container
 bindsym $mod+u focus parent

 ### System mode
 mode "system" {
 bindsym h exec systemctl poweroff, mode "default"
 bindsym l exec $locker, mode "default"
 bindsym r exec systemctl reboot, mode "default"
 bindsym s exec $locker && systemctl suspend, mode "default"
 bindsym Return mode "default"
 bindsym Escape mode "default"
 }
 bindsym $mod+Shift+e mode "system"

 ### Display mode
 set $mode_display (D)ouble, (M)irror, (I)nternal, (E)xternal
 mode "$mode_display" {
 bindsym d exec swaymsg output eDP1 enable DP1 enable, mode "default"
 bindsym i exec swaymsg output eDP1 enable DP1 disable, mode "default"
 bindsym e exec swaymsg output eDP1 disable DP1 enable, mode "default"
 bindsym Return mode "default"
 bindsym Escape mode "default"
 }
 bindsym $mod+Shift+x mode "$mode_display"

 ### Status Bar:
 # Read `man 5 sway-bar` for more information about this section.
 bar {
 swaybar_command "waybar -c ~/.config/sway/waybar/config -s ~/.config/sway/waybar/style.css"
 }

 ### Startup
 exec mako --anchor top-right --default-timeout 6000
 exec wl-paste -t text --watch clipman store --no-persist
 exec fcitx5 -r &

 ### Screenshot
 bindsym --release {
 Print exec grim $(date +'%Y%m%d-%H%M%S.png')
 Shift+Print exec grim -g "$(slurp)" $(date +'%Y%m%d-%H%M%S.png')
 }

 ### Keyboard
 input type:keyboard {
 xkb_options ctrl:nocaps
 }

 ### Touchpad of laptop
 input type:touchpad {
 dwt enable
 }

 ### Lid related event for laptop
 bindswitch {
 lid:on output eDP-1 disable
 lid:off output eDP-1 enable
 }

 ### Special keys for laptop
 bindsym {
 # Volume
 XF86AudioRaiseVolume exec pactl set-sink-volume @DEFAULT_SINK@ +5%
 XF86AudioLowerVolume exec pactl set-sink-volume @DEFAULT_SINK@ -5%
 XF86AudioMute exec pactl set-sink-mute @DEFAULT_SINK@ toggle
 XF86AudioMicMute exec pactl set-source-mute @DEFAULT_SOURCE@ toggle

 # Brightness
 XF86MonBrightnessUp exec sudo light -A 5
 XF86MonBrightnessDown exec sudo light -U 5
 }

 include /etc/sway/config.d/*
 xwayland enable

`~/.config/sway/wofi.conf`

 mode=drun
 allow_images=true
 allow_markup=true
 location=center
 lines=9
 filter_rate=1
 term=termite
 key_up=Control_L-p
 key_down=Control_L-n
 key_exit=Control_L-g
 no_actions=true
 width=300
 image_size=32

`~/.config/sway/waybar.style.css`

 ,* {
 border: none;
 border-radius: 0;
 font-family: Roboto, Helvetica, Arial, sans-serif;
 font-size: 18px;
 min-height: 0;
 }

 window#waybar {
 background-color: rgba(43, 48, 59, 0.5);
 border-bottom: 3px solid rgba(100, 114, 125, 0.5);
 color: #ffffff;
 transition-property: background-color;
 transition-duration: .5s;
 }

 window#waybar.hidden {
 opacity: 0.3;
 }

 /*
 window#waybar.empty {
 background-color: transparent;
 }
 window#waybar.solo {
 background-color: #FFFFFF;
 }
 ,*/

 window#waybar.termite {
 background-color: #3F3F3F;
 }

 window#waybar.chromium {
 background-color: #000000;
 border: none;
 }

 #workspaces button {
 padding: 0 5px;
 background-color: transparent;
 color: #ffffff;
 border-bottom: 3px solid transparent;
 }

 /* https://github.com/Alexays/Waybar/wiki/FAQ#the-workspace-buttons-have-a-strange-hover-effect */
 #workspaces button:hover {
 background: rgba(0, 0, 0, 0.2);
 box-shadow: inherit;
 border-bottom: 3px solid #ffffff;
 }

 #workspaces button.focused {
 background-color: #64727D;
 border-bottom: 3px solid #ffffff;
 }

 #workspaces button.urgent {
 background-color: #eb4d4b;
 }

 #mode {
 background-color: #64727D;
 border-bottom: 3px solid #ffffff;
 }

 #clock,
 #battery,
 #cpu,
 #memory,
 #temperature,
 #backlight,
 #network,
 #pulseaudio,
 #custom-media,
 #tray,
 #mode,
 #idle_inhibitor {
 padding: 0 10px;
 margin: 0 0px;
 color: #ffffff;
 }

 #clock {
 background-color: #64727D;
 }

 #battery {
 background-color: #ffffff;
 color: #000000;
 }

 #battery.charging {
 color: #ffffff;
 background-color: #26A65B;
 }

 @keyframes blink {
 to {
 background-color: #ffffff;
 color: #000000;
 }
 }

 #battery.critical:not(.charging) {
 background-color: #f53c3c;
 color: #ffffff;
 animation-name: blink;
 animation-duration: 0.5s;
 animation-timing-function: linear;
 animation-iteration-count: infinite;
 animation-direction: alternate;
 }

 label:focus {
 background-color: #000000;
 }

 #cpu {
 background-color: #2ecc71;
 color: #000000;
 }

 #memory {
 background-color: #9b59b6;
 }

 #backlight {
 background-color: #90b1b1;
 }

 #network {
 background-color: #2980b9;
 }

 #network.disconnected {
 background-color: #f53c3c;
 }

 #pulseaudio {
 background-color: #f1c40f;
 color: #000000;
 }

 #pulseaudio.muted {
 background-color: #90b1b1;
 color: #2a5c45;
 }

 #custom-media {
 background-color: #66cc99;
 color: #2a5c45;
 min-width: 100px;
 }

 #custom-media.custom-spotify {
 background-color: #66cc99;
 }

 #custom-media.custom-vlc {
 background-color: #ffa000;
 }

 #temperature {
 background-color: #f0932b;
 }

 #temperature.critical {
 background-color: #eb4d4b;
 }

 #tray {
 background-color: #2980b9;
 }

 #idle_inhibitor {
 background-color: #2d3436;
 }

 #idle_inhibitor.activated {
 background-color: #ecf0f1;
 color: #2d3436;
 }

 #mpd {
 background-color: #66cc99;
 color: #2a5c45;
 }

 #mpd.disconnected {
 background-color: #f53c3c;
 }

 #mpd.stopped {
 background-color: #90b1b1;
 }

 #mpd.paused {
 background-color: #51a37a;
 }

Remap CapsLock as Ctrl

Thu, 09 Mar 2023 00:00:00 +0000

Background

Usually, key CapsLock is seldom used in our daily utilization, while key Ctrl is frequently used, esp. for Emacs users. Therefore, we can turn CapsLock into an additional Ctrl.

Linux

Sway

For sway, the remapping can be directly realized by inserting following entry in ~/.config/sway/config.

 input type:keyboard {
 xkb_options ctrl:nocaps
 }

KDE

For KDE, the transformation can be directly finished in the system settings. Enter Input Devices -> Keyboard -> Advanced, and tick the radio Caps Lock is also a Ctrl in Caps Lock behavior and Caps Lock as Ctrl in Ctrl position.

Gnome

For Gnome, it is extremely easy to turn CapsLock into an additional Ctrl. Install package gnome-tweak-tool, e.g.

 pacman -S gnome-tweak-tool

and configure it in the installed Tweak Tool. Enter Keyboard & Mouse -> Keyboard -> Additional Layout Options -> Caps Lock behavior and tick the radio Make Caps Lock an additional Ctrl.

Xmodmap

xmodmap is a utility for remapping keys in Xorg. To turn CapsLock into another Ctrl, install package xorg-xmodmap, e.g.

 pacman -S xorg-xmodmap

and create ~/.Xmodmap with its contents as follows.

 clear lock
 clear control
 add control = Caps_Lock Control_L Control_R
 keycode 66 = Control_L

For display manager, e.g. GDM, KDM, XDM, based startup, that is all. For startx-based, add a following entry in ~/.xinitrc.

 [[ -f ~/.Xmodmap ]] && xmodmap ~/.Xmodmap

俗话说

Tue, 21 Feb 2023 00:00:00 +0000

俗话说：好马不吃回头草；可俗话又说：浪子回头金不换！
俗话说：兔子不吃窝边草；可俗话又说：近水楼台先得月！
俗话说：宰相肚里能撑船；可俗话又说：有仇不报非君子！
俗话说：男子汉大丈夫，宁死不屈；可俗话又说：男子汉大丈夫，能屈能伸！
俗话说：知无不言，言无不尽；可俗话又说：交浅勿言深，沉默是金！
俗话说：车到山前必有路；可俗话又说：不撞南墙不回头！
俗话说：人不犯我，我不犯人；可俗话又说：先下手为强，后下手遭殃！
俗话说：礼轻情谊重；可俗话又说：礼多人不怪！
俗话说：一个好汉三个帮；可俗话又说：靠人不如靠己！
俗话说：人往高处走；可俗话又说：爬得高，摔得重！
俗话说：瘦死的骆驼比马大；可俗话又说：拔了毛的凤凰不如鸡！
俗话说：宁为玉碎，不为瓦全；可俗话又说：留得青山在，不怕没柴烧！
俗话说：人不可貌相，海水不可斗量；可俗话又说：人靠衣裳马靠鞍！
俗话说：苦海无边，回头是岸；可俗话又说：开弓没有回头箭！
俗话说：退一步海阔天空；可俗话又说：狭路相逢勇者胜！
俗话说：三百六十行，行行出状元；可俗话又说：万般皆下品，唯有读书高！
俗话说：书到用时方恨少；可俗话又说：百无一用是书生！
俗话说：金钱不是万能的；可俗话又说：有钱能使鬼推磨！
俗话说：出淤泥而不染；可俗话又说：近朱者赤，近墨者黑。
俗话说：青出于蓝而胜于蓝；可俗话又说：姜还是老的辣！
俗话说：后生可畏；可俗话又说：嘴上无毛，办事不牢！
俗话说：有缘千里来相会；可俗话又说：不是冤家不聚头！
俗话说：在天愿作比翼鸟，在地愿为连理枝；可俗话又说：夫妻本是同林鸟，大难来时各自飞！
俗话说：得饶人处且饶人；可俗话又说：纵虎归山，后患无穷！
俗话说：善有善报，恶有恶报；可俗话又说：人善被人欺，马善被人骑！
俗话说：一分耕耘、一分收获；可俗话又说：人无横财不富，马无夜草不肥！
俗话说：小心驶得万年船；可俗话又说：撑死胆大的，饿死胆小的！
俗话说：量小非君子；可俗话又说：无毒不丈夫！
俗话说：小不忍则乱大谋；可俗话又说：不蒸馒头蒸（争）口气！
俗话说：人人为我，我为人人；可俗话又说：人不为己，天诛地灭！
俗话说：不入虎穴，焉得虎子；可俗话又说：老虎屁股摸不得！
俗话说：百善孝为先；可俗话又说：忠孝不能两全！
俗话说：人定胜天；可俗话又说：天意难违。
俗话说：明人不做暗事；可俗话又说：兵不厌诈！

Reference

《俗话说，俗话又说，谁写的，笑死我了！》，微信公众号: 假装学英语(PretendEnglish)。

Emacs - Dired

Wed, 15 Feb 2023 00:00:00 +0000

Introduction

Aside from editing files, including local and remote ones, Emacs can also play the role of a file manager, i.e., manipulating directories and the files by its directory editor, dired.

Enter dired buffer

Dired can be entered in following ways:

Command: M-x dired
Key bindings
- C-x d is equivalent to the command above.
- C-x 4 d open a dired buffer in another window.

View and navigation

Key	Description
`(`	Toggle detail information (`dired-hide-details-mode`).
`^`	Go up one directory (`dired-up-directory`).
`n/C-n`	Move the point down an entry (`dired-next-line`).
`p/C-p`	Move the point up an entry (`dired-previous-line`).
`q`	Quit dired (`quit-window`).

Marking & unmarking

Marking and unmarking enable operations on multiple files or directories.

Key	Description
`m`	Mark the active entry or the selected region (`dired-mark`).
`u`	Unmark the active entry or the selected region (`dired-unmark`).
`U`	Unmark everything (`dired-unmark-all-marks`).
`d`	Flag for deletion (`dired-flag-file-deletion`).
`~`	Mark backup files (`dired-flag-backup-files`).
`* %`	Mark files and directories by regexp (`dired-mark-files-regexp`).
`* c`	Change marks (`dired-change-marks`).
`t`	Toggle existing marking (`dired-toggle-marks`).

LTE - Downlink Control

Wed, 15 Feb 2023 00:00:00 +0000

Introduction

In LTE, following physical channels are involved in downlink control.

Physical downlink control channel (PDCCH) carries
- Downlink (DL) assignment
- Uplink (UL) grant
- TPC commands for a group of users
- Physical downlink shared channel (PDSCH) arrival time instance
- Paging indication
- SPS activation/release
- Etc.
Physical control format indicator channel (PCFICH) indicates the time-domain duration of the PDCCH in each subframe.
Physical HARQ indicator channel (PHICH) indicates the acknowledgement of PUSCH.

Resource hierarchy

Just as its name implies, the basic element for PDCCH is Control channel element (CCE), which is comprised of 9 resource element group (REG), and a REG consists of 4 RE's in an OFDM symbol without cell-specific reference signal (CRS), or 6 RE's in an OFDM symbol with CRS. Irrespective of the both cases, there are always 4 effective RE's/REG, which is favorable of space frequency block codes (SFBC) based transmit diversity for PDCCH.

An aggregation level number of CCE's compose one PDCCH. The value of aggregation level can be 1, 2, 4, 8.

NR - Downlink Control

Tue, 14 Feb 2023 00:00:00 +0000

Introduction

In NR system, the downlink control information (DCI) is carried by physical downlink control channel (PDCCH), which physically occupied a region in the 2-dimension resource grid, which is essentially comprised of a certain number of resource elements (RE's), a.k.a., control resource set (CORESET). Different from the counterpart in LTE, i.e., PDCCH region which always covers the whole frequency range, CORESET does not span the whole bandwidth, since the bandwidth in NR system is remarkably large while not all the NR UE's are able to perform reception over the whole bandwidth.

Due to the static feature of CORESET, the indication of its size is not necessary. Therefore, there is no PCFICH in NR system. Additionally, irrespective of downlink or uplink, asynchronous HARQ is utilized in NR. Hence, PHICH is not needed either.

In NR, the channel coding scheme for PDCCH is based on polar codes. It can support 512 coded bits (prior to rate matching¹) and up to 140 information bits. Targetting an enhanced coverage, a beamformed single layer transmission is adopted for PDCCH. In this sense, it is similar to ePDCCH in LTE system.

Python - Data Type

Thu, 09 Feb 2023 00:00:00 +0000

Python中的大部分对象，如列表、字典、 Numpy 数组都是可变对象，大多数用户定义的类型（类）也是可变的。可变对象中包含的对象和值是可以被修改的。但是有一些对象是不可变的，如字符串、元组。

标量

Python的标准库中有一个小的内建类型集合，用来处理数值、字符串、布尔值以及日期和时间。这类“单值”类型被称为标量。主要的标量类型有

int¹
- 前缀 0x 表示16进制整数。
- 整数除法会把结果自动转型为浮点数。
- 如果需要C风格的整数除法（去掉小数部分），可以使用整除操作符 // 。
float²
str
- 可以使用单引号 ' 或双引号 " 写一个字符串字面值。
- 字符串是Unicode字符的序列，是不可改变的。很多Python对象可以通过函数 str 转成字符串。
- 对于单个字符，函数 ord 把字符转换为其对应的整数表示；函数 chr 把编码转换为对应的字符。
- 对于含有换行的多行字符串，可以使用三个单引号（ ''' ）或三个双引号（ """ ）。
- 反斜杠 \ 是转移符号，它用来指明特殊符号。可以在字符串前面加上前缀符号 r （raw的简写）避免对字符串转义。
- 字符串对象有一个 format 方法，可以用来代替字符串中的格式化参数，并产生一个新的字符串。
- 带有前缀符号 f （format的简写）的字符串被称之为 f-string 。如果其包含 {xxx} ，就会以对应的变量替换。
bool
- 布尔值有两个： True 和 False 。
- 布尔运算符包括： and ， or ， not 。
None³
bytes
- 字符串在内存中以Unicode表示，每个字符对应若干个字节。
- 字符串在硬盘上存储或在网络上传输的时候，需要转换为以字节为单位的 bytes 类型。
- 在Python中， bytes 类型的数据为以前缀 b 开头的单引号（如 b'xyz' ， b"xyz" ）或双引号表示。
- str 的方法 encode 可以将其编码为制定的 bytes 。
- bytes 的方法 decode 可以将其转换为字符串（ str ）。
- 当Python源代码中包含中文时，必须指定UTF-8编码保存。为了让Python解释器按照UTF-8编码读取Python程序代码，通常在源代码文件指定UTF-8编码。例如，文件开头为
```
 #!/usr/bin/env python
 # -*- coding: utf-8 -*-
```
常量
- 常量就是不能变的变量。在Python中，通常用全部大写的变量名来表示常量。

Archlinux - A Non-Official Repository from Chinese Community

Sun, 29 Jan 2023 00:00:00 +0000

Introducation

Archlinux is an excellent Linux distribution, which follows the principle of keep it simple and stupid (KISS) closely. Besides the official repositories, its Chinese community provides a non-official repository, a.k.a. ArchlinuxCN.

Configuration

Using the ArchlinuxCN can be completed by two steps.

Append following lines to /etc/pacman.conf.

 [archlinuxcn]
 Server = https://repo.archlinuxcn.org/$arch

Optionally, there are many mirrors, which can be found at https://github.com/archlinuxcn/mirrorlist-repo, e.g.,

Aliyun

 [archlinuxcn]
 Server = https://mirrors.aliyun.com/archlinuxcn/$arch

Netease

 [archlinuxcn]
 Server = https://mirrors.163.com/archlinux-cn/$arch

Import the corresponding PGP keys by installing package archlinuxcn-keyring.
```
 pacman -S archlinuxcn-keyring
```

Archlinux - Clean Packages

Sun, 29 Jan 2023 00:00:00 +0000

Archlinux is an excellent Linux distribution, featured by light weight, flexibility, keep it simple and stupid (KISS), as well as well-documented wiki. Therefore, I have been using it for so many years. Unavoidably, there are some packages accumulated and remained after numerous package related operations, e.g., installing, removing, updating, etc. This post aims to clean the packages.

For each installed package, following command can keep the latest version and remove all the historical versions.
```
 pacman -Scc
```
For each isolated (not in use) package, following command can remove them automatically.
```
 pacman -Qqdt | pacman -Rs -
```

Python - Pytorch Lightning

Sat, 28 Jan 2023 00:00:00 +0000

Pytorch Lightning is a high level framework and encapsulation on top of pytorch, which provides simplified interfaces and elegant code structure relating to AI. Detailed usage can be found in its manual.

Installation

The installation of Pytorch Lightning is very simple. Taking pip for instance, following command completes the procedure.

 pip install pytorch-lightning

Usage

Neural network

The structure of neural network can be defined as a subclass of pytorch_lightning.LightningModule, which is essentially a subclass of torch.nn.Module. Besides the constructor __init__ and function forward, a series of hook functions has been defined and can be simply overridden, e.g.,

configure_optimizers can be used to further tweak the behavior of the optimizer, e.g., the initial value of learning rate and how it is decaying.
on_train_start, on_validation_start, and on_test_start are the hook functions provoked at the beginning of training, validating, and testing, respectively.
on_train_end, on_validation_end, and on_test_end are the hook functions provoked at the end of training, validating, and testing, respectively.
training_step, validation_step, and test_step are the hook functions provoked for each batch in training, validating, and testing respectively, e.g., in which loss function is calculated.
training_epoch_end, validation_epoch_end, and test_epoch_end are the hook functions provoked at the end of each epoch in training, validating, and testing respectively.

Data module

In python_lightning, a data module class is defined in python_lightning.LightningDataModule, which provides a unified interface for data loading for training, validating, and testing. We can simply define our own data module as a subclass of python_lightning.LightningDataModule, and override the following functions.

setup can define one or more datasets needed.
train_dataloader, val_dataloader, and test_dataloader return separate dataloaders for training, validating and testing, respectively.

Procedure

The main procedure is completed based on an instance of class python_lightning.Trainer. In its constructor, we can customize it via a series of keyword arguments, e.g.,

default_root_dir indicates the output directory.
max_epochs is the maximum number of epochs.
check_val_every_n_epoch is the period of validation in epoch number.
logger is object for logging, e.g., python_lightning.loggers.TensorBoardLogger.
enable_progress_bar is a boolean indicator of progress bar.
strategy defines the training type, e.g., DDP, DDP2.
gpus indicates the identities of selected GPU(s).

The training and testing can be finished by calling its member functions, e.g.,

fit for training.
test for testing.
save_checkpoint to save the state of the python_lightning.Trainer object, including the coefficients or weights of the trainable parameters in the neural network.

Wiener-Khinchin Theorem

Sun, 22 Jan 2023 00:00:00 +0000

Wiener-Khinchin Theorem

Given a wide-sense stationary (WSS) stochastic process, its autocorrelation function and its power spectral density function are a pair of Fourier transform.

Frequency domain correlation

The frequency domain correlation can be derived as

\begin{align} \mathcal{E}\left[ H(f_1) H^{*}(f_2) \right] &= \mathcal{E} \left[ \int_{-\infty}^{+\infty}h(\tau_1)e^{-j2\pi f_1\tau_1} d\tau_1 \cdot \int_{-\infty}^{+\infty}h^{*}(\tau_2)e^{j2\pi f_2\tau_2} d\tau_2 \right] \nonumber \\ &= \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} \mathcal{E}\left[ h(\tau_1)h^{*}(\tau_2)\right]e^{-j2\pi(f_1 \tau_1 - f_2 \tau_2)} d\tau_1 d\tau_2, \label{eq:corr-f} \end{align}

where $h(\tau)$ and $H(f)$ are the channel impulse response (CIR) and channel frequency response (CFR) of the channel, respectively.

If the individual paths of the channel are uncorrelated, i.e., uncorrelated scatering (US), $\mathcal{E}\left[h(\tau_1) h^{*}(\tau_2)\right] = h(\tau_1) h^{*}(\tau_2) \delta(\tau_1 - \tau_2)$, then equation \eqref{eq:corr-f} can be further written as

\begin{align} \mathcal{E}\left[ H(f_1) H^{*}(f_2) \right] &= \int_{-\infty}^{+\infty}|h(\tau)|^2 e^{-j2\pi(f_1-f_2)\tau}d\tau \nonumber \\ &=\int_{-\infty}^{+\infty}P_{\mathrm{delay}}(\tau) e^{-j2\pi(f_1-f_2)\tau}d\tau, \label{eq:corr-f-us} \end{align}

where $P_{\mathrm{delay}}(\tau) \triangleq |h(\tau)|^2$ is the power delay profile (PDP) of the channel.

Particularly, if PDP is uniformly distributed within cyclic prefix (CP), denoted by $L_{\mathrm{cp}}$, i.e.,

\begin{align*} P_{\mathrm{delay}}(\tau) &= \frac{1}{L_{\mathrm{cp}}}, \quad \tau \in [0, L_{\mathrm{cp}}]; \\ \mathcal{E}\left[ H(f_1) H^{*}(f_2) \right] &=\mathrm{sinc} \left[ \left( f_1 - f_2 \right)L_{\mathrm{cp}} \right] e^{-j\pi\left( f_1 - f_2 \right)L_{\mathrm{cp}}}. \end{align*}

AI - MLP-Mixer

Sun, 08 Jan 2023 00:00:00 +0000

Multi-layer perceptron mixer (MLP-Mixer) is a novel neural network model, which attracts the attentions of both academic circle and industrial area. Besides the proposal paper, I found another blog post providing an excellent illustration.

The structure of MLP-Mixer can be shown in Figure mlp_mixer.

The input and output tensors have the same size, denoted by $B\times C\times P$, where $B$ is the batch size, $C$ is the number of channels, $P$ is the size of each patch. Usually, the patch size is a product of patch size in each dimension. E.g., a 2-D image of size $H\times W$ can be partitioned into a multiplicity of patches, with each of size $P = P_h \times P_w$. Then different patches correspond to different channels, i.e., $C = \dfrac{H}{P_{h}} \cdot \dfrac{W}{P_{w}}$. Without loss of generality, we stretch each patch into 1-D irrespecitve of its dimensions.
Just as its name indicates, each MLP-Mixer layer has two MLP modules, targeting for intra-patch feature extraction, a.k.a. token mixing, and inter-patch feature processing, a.k.a. channel mixing, respectively. Of course, token mixing and channel mixing operates along the dimension of patch (of size $P$) and channel (of size $C$), respectively.

Linux - Ranger

Mon, 19 Dec 2022 00:00:00 +0000

Ranger is a popular and powerful file manager in console.

Installation

In archlinux, ranger can be directly installed using pacman.

 pacman -S ranger

Configuration

Ranger can be customized by 4 configuration files below.

rc.conf organizes various options and keybindings.
commands.py defines commands, which can be provoked via :.
rifle.conf defines the default programs to open each type of files.
scope.sh is a shell script to preview each type of files.

In fact, there are both global and local versions for each configuration above. The local versions are stored in ~/.config/ranger. Optionally, the global version of the configuration files can be copied as follows to ~/.config/ranger as a starting point before further customization, i.e.,

 ranger --copy-config=rc/rifle/commands/scope/all

For rc.conf and commands, ranger subsequently loads the global version first and then the local version. By default, only the options different from the default values in the global version need to be overridden in the local counterpart. The loading of global version can be skipped by setting environment variable RANGER_LOAD_DEFAULT_RC to FALSE.

For scope.sh and rifle.conf, what is different, ranger loads either the local or the global version.

Mathematica

Mon, 19 Dec 2022 00:00:00 +0000

Bracketing

Parenthesis (): change the priorities in computing.
Square bracket []: function parameters, e.g. f[x].
Curly brace {}: list, e.g. {a, b, c}.
Double bracket: abbreviation of Part, e.g. v[[i]].

Constants

Command	Value
Pi	$\pi$
E	$e$
I	$i = \sqrt{-1}$
Infinity	$\infty$

Data objects

Command	Meaning
2 + 8 I	complex
"text"	string

Defining variables, functions, and rules

Command	Meaning
x = value	assignment
x := value	delayed assignment
x = . or Clear[x]	remove value assigned to `x`
f[x_] := expression	define a function `f(x)`
expression /. x->a	replace `x` by a in expression
expression //. x->a	replace repeatedly
lhs :> rhs /; test	apply rule if `test` is True

Linear algebra

Command	Meaning
{a, b, c}	vector, list
{{a, b}, {c, d}}	2 × 2 matrix
n.m	matrix multiply
Inverse[m]	inverse of matrix
Transpose[m]	transpose
Det[m]	determinant
MatrixPower[m, n]	m^n
MatrixExp[m]	e^m
LinearSolve[m, b]	solve mx = b
Eigenvalues[m]	eigenvalues
Eigenvectors[m]	eigenvectors
Eigensystem[m]	eigenvalues and eigenvectors

Algebraic calculation

Command	Meaning
Solve[lhs==rhs, x]	solve algebraic equation for x
DSolve[eqn, y[x], x]	solve differential equation
Reduce[eqn, x]	reduce equations
Eliminate[eqn, x]	eliminate variable x

Calculus

Command	Meaning
D[f, x]	$\partial f/\partial x$
D[f, {x,n}	$\partial^n f/\partial x^n$
Dt[f]	$df$
Integrate[f, x]	$\int fdx$
Integrate[f, {x, a, b}]	$\int_a^b f dx$
Sum[f, {i, m, n}]	$\sum_{i=m}^n f$
Product[f, {i, m, n}]	$\prod_{i=m}^n f$
Limit[f, x->a]	$\lim_{x\to a} f$

Input and output

Command	Meaning
<<file	read expressions from `file`, return last expression.
expression>>file	write `expression` to `file`.
expression>>>file	append `expression` to `file`.
!!file	display the content of `file`.
Save["file", x]	save the definition of `x` to `file`.
!command	issue a UNIX command.

Expression in different formats

Command	Meaning
FullForm[e]	full form
InputForm[e]	input
OutputForm[e]	out
CForm[e]	C codes
FortranForm	fortran
MatrixForm[e]	matrix
StandardForm[e]	math
TeXForm[e]	TEX

Programming

Table[expression, {i, max}]: make a list of values of expression with i from 1 to max.
Module[{a, b, c}, expression1; expression2;…]: a procedure with local variables a, b, c return value of last expression.
Do[expression, {i, min, max, di}]: evaluate expression with i run from min to max in steps of di.
While[test, body]: evaluate body repeatedly, so long as test is True.
For[star,test,inc,body]: evaluate start, then repeatedly evaluate body and inc, until test fails.
If[test, then, else]: evaluate then if test is True, and else if it is False.
Which[test1,value1,test2,value2,…]: give the value associated with the first test that is True.
Switch[expression, form1, value1, form2, value2, …]: give the value associated with first form matching expression.
Function[x, body]: specify a pure function.
Nest[f, x, n]: apply the function f nested n times to x.
Apply[f, {a, b, c}]: f(a, b, c).
Map[f, {a, b, c}]: apply f to each elements, {f(a), f(b), f(c)}.

Multiple Signal Classification (MUSIC)

Mon, 19 Dec 2022 00:00:00 +0000

Multiple signal classification (MUSIC) is a popular algorithm for spectrum estimation. This post is just written as a brief summary.

MUSIC

An observation signal vector can be expressed as

\begin{align*} \mathbf{x} = \mathbf{A} \mathbf{s} + \mathbf{n}, \end{align*}

where

$\mathbf{A} = \begin{bmatrix} \mathbf{a}(\omega_1) & \mathbf{a}(\omega_2) & \ldots & \mathbf{a}(\omega_r) \end{bmatrix}$ is a $N \times r$ Vandermonde matrix, $N > r$; Each column is a steering vector, e.g., $\mathbf{a}(\omega) \triangleq \begin{bmatrix} 1 \\ e^{j\omega} \\ e^{j2\omega} \\ \vdots \\ e^{j(N-1)\omega} \end{bmatrix}$.
$\mathbf{s} = \begin{bmatrix} s_1 \\ s_2 \\ \vdots \\ s_r \end{bmatrix}$ is a signal vector.
$\mathbf{n} \sim \mathcal{CN}(0, \sigma^2\mathbf{I}_N)$ is a complex additive Gaussian noise vector.

Then autocorrelation matrix of observation can be obtained by

\begin{align*} \mathbf{R}_{\mathbf{x}} &= \mathbf{E}[ \mathbf{x} \mathbf{x}^H] \\ &= \mathbf{A} \mathbf{R}_{\mathbf{s}} \mathbf{A}^H + \sigma^2 \mathbf{I}_N, \end{align*}

where $\mathbf{R}_{\mathbf{s}} \triangleq \mathbf{E}[ \mathbf{s} \mathbf{s}^H]$ is the autocorrelation of signal vector $\mathbf{s}$. In practice, the autocorrelation of observation is usually calculated based on a series of observation samples, i.e., $\hat{\mathbf{R}}_{\mathbf{x}} = \dfrac{1}{M} \sum_{i=1}^M \mathbf{x}_i \mathbf{x}_i^H$, where $M$ is the number of observation samples available.

The autocorrelation matrix of observation can be eigen value decomposed (EVD) as

\begin{align*} \mathbf{R}_{\mathbf{x}} &= \begin{bmatrix} \mathbf{U}_{\mathbf{s}} & \mathbf{U}_{\mathbf{n}} \end{bmatrix} \begin{bmatrix} \mathbf{\Lambda}_{\mathbf{s}} & \mathbf{0} \\ \mathbf{0} & \sigma^2 \mathbf{I}_{N-r} \end{bmatrix} \begin{bmatrix} \mathbf{U}_{\mathbf{s}}^H \\ \mathbf{U}_{\mathbf{n}}^H \end{bmatrix}, \end{align*}

where

The eigen vectors in $\mathbf{U}_{\mathbf{s}}$ corresponding to $p$ largest eigen values span the signal subspace.
The eigen vectors in $\mathbf{U}_{\mathbf{n}}$ corresponding to the remaining $N - r$ eigen values (equal to $\sigma^2$) span the noise subspace.

Considering the fact that the signal subspace and noise subspace are orthogonal and complementary to each other, i.e. $\text{span}(\mathbf{U}_{\mathbf{s}}) \perp \text{span}(\mathbf{U}_{\mathbf{n}})$, $\forall \mathbf{v} \in \text{span}(\mathbf{U}_{\mathbf{s}})$, $\mathbf{U}_{\mathbf{n}}^H \mathbf{v} = \mathbf{0}$. In order to depict the orthogonality quantitatively, a squared norm is introduced as follows.

\begin{align*} d^2(\mathbf{v}) &= \| \mathbf{U}_{\mathbf{n}}^H \mathbf{v}\|^2 \\ &= \mathbf{v}^H \mathbf{U}_{\mathbf{n}} \mathbf{U}_{\mathbf{n}}^H \mathbf{v} \\ &= \mathbf{v}^H (\mathbf{I}_N - \mathbf{U}_{\mathbf{s}} \mathbf{U}_{\mathbf{s}}^H) \mathbf{v} \end{align*}

MUSIC uses the reciprocal of the squared norm $d^{-2}$ as the metric, in which case $r$ sharp peaks appear at the signal frequencies. The MUSIC spectrum can be expressed as

\begin{align*} P_{\text{music}}(\omega) &= \frac{1}{d^2(\mathbf{a}(\omega))} \\ &= \frac{1}{\mathbf{a}^H(\omega) \mathbf{U}_{\mathbf{n}} \mathbf{U}_{\mathbf{n}}^H \mathbf{a}(\omega)} \\ & = \frac{1}{\mathbf{a}^H(\omega) (\mathbf{I}_N - \mathbf{U}_{\mathbf{s}} \mathbf{U}_{\mathbf{s}}^H) \mathbf{a}(\omega)}, \end{align*}

where $\omega$ is the candidate frequency, and $\mathbf{a}(\omega)$ is the candidate steering vector.

So long as the number of component (e.g., $r$ above) is known in advance (as its drawback), MUSIC can outperforms DFT based schemes, since it can achieve superresolutional estimation for the spectrum, rather than the discrete DFT bins.

NR - Numerology

Mon, 19 Dec 2022 00:00:00 +0000

Since release 15, new radio (NR) system has explicitly proposed the concept of numerology, which is used to represent the scaling of subcarrier bandwidth, FFT size, etc.

Above all, a reference numerology is defined based on

\begin{align*} \Delta_{\mathrm{subc, ref}} &= 15 \text{ kHz}, \\ N_{\mathrm{FFT, ref}} &= 2048. \end{align*}

Accordingly, the sampling rate the sample duration can be written as

\begin{align*} f_{\mathrm{s, ref}} &= \Delta_{\mathrm{subc, ref}} N_{\mathrm{FFT, ref}}, \\ T_{\mathrm{s, ref}} &= \frac{1}{f_{\mathrm{s, ref}}} = \frac{1}{\Delta_{\mathrm{subc, ref}} N_{\mathrm{FFT, ref}}}. \end{align*}

Additionally, an extreme numerology is also defined based on

Python - Einops

Mon, 19 Dec 2022 00:00:00 +0000

Einstein-inspired notation for operations (Einops¹) is a python package which provides extremely flexible and powerful opertions on tensors, e.g., permuting/reordering, reshaping (combining and partitioning along axes), reducing, repeating. Moreover, it supports numpy, tensorflow, pytorch, etc.

Installation

Einops can be directly installed from pypi.

pip install einops

Usage

Basic functions

Basically, Einops provides 3 Functions, rearrange, reduce, repeat, which can be imported by

 from einops import rearrange, reduce, repeat

 rearrange(tensor, pattern: str, **axes_lengths)
 reduce(tensor: ~Tensor, pattern: str, reduction: Union[str, Callable[[~Tensor, List[int]], ~Tensor]], **axes_lengths: int) -> ~Tensor
 repeat(tensor: ~Tensor, pattern: str, **axes_lengths) -> ~Tensor

tensor is a tensor (e.g., numpy.ndarray, tensorflow, pytorch) or a list of tensors with the same type and shape.
pattern is a string indicating rearrangement/reduction pattern.
reduction can be one of 'max', 'min', 'mean', 'sum', 'prod'.
axes_lengths are dimension related specifications.

`rearrange`

rearrange does not change the number of elements inside, and can achieve the operations like transpose, reshape, stack, squeeze, unsqueeze, concatenate, etc.

`reduce`

reduce combines elements in one or more axes. So it reduces the total number of elements, but keeps the ordering.

`repeat`

repeat produces repetition and tiling.

Layers

Einops also provides two corresponding layers, which can be directly integrated into any neural network.

 from einops.layers.chainer import Rearrange, Reduce
 from einops.layers.gluon import Rearrange, Reduce
 from einops.layers.keras import Rearrange, Reduce
 from einops.layers.torch import Rearrange, Reduce
 from einops.layers.tensorflow import Rearrange, Reduce

Taking pytorch for instace, a Rearrange layer or a Reduce layer can be generated by

 Rearrange(pattern, **axes_lengths)
 Reduce(pattern, reduction, **axes_lengths)

Python - Function

Mon, 19 Dec 2022 00:00:00 +0000

在Python中，函数通过关键字 def 定义。

参数

从函数的角度，parameter指函数定义圆括号内的变量列表，而argument指当函数被调用时传递的值。

Parameter

变长参数(variable-length)

参数名前加 * 可以表示该参数可以接受任意数目的位置参数。这种情况下，函数会接受元组参数(a tuple of arguments)。以 * 开头的参数只能以最后一个位置参数的形式出现。
参数名前加 ** 可以表示该参数可以接受任意数目的关键字参数。这种情况下，函数会接受元组参数(a tuple of arguments)。以 ** 开头的参数只能以最后一个参数的形式出现。

默认参数（可选参数）

可以在函数定义时，为参数指定默认值。
值得注意的是，默认值生效是在函数定义的时候，而不是在函数调用的时候。
一旦某个参数有默认值，那么后续所有参数都必须有默认值。为此，需要把有默认值的参数放在没有默认值的参数后面。
参数默认值应该重视不可变的对象，比如 None, True, False, 数字或者字符串。
如果默认值是可变容器的话，比如列表、集合或者字典，应该把 None 作为默认值，并在函数体内增加对默认值的检查。

Argument

函数调用时的参数可以分为位置参数(positional argument)和关键字参数(keyword argument)。

位置参数

位置参数按照调用顺序为对应的参数赋值。

关键字参数

关键字参数的调用方式为 kwarg=value 。
函数调用时，关键字参数的顺序可以是任意的。
关键字参数必须放在位置参数之后。

调用方式的限制

 def fn(positional_only1, positional_only2, /, positional_or_keyword1, positional_or_keyword2, *, keyword_only1, keyword_only2):

如果 / 和 * 都没有，那么函数调用时参数赋值既可以是以位置参数的方式，也可以是关键字参数的方式。
/ 之前的参数赋值必须以位置参数的形式。
* 之后的参数赋值必须以关键字参数的形式。

Docstring

对函数功能以及参数的描述。

Sparse Array

Mon, 19 Dec 2022 00:00:00 +0000

Concepts

Given a sparse array, the locations of its component antennas/sensors can be normalized to a minimum inter-antenna distance, denoted by $d$, e.g., typically $d = \lambda / 2$. Accordingly, a sparse array can be simply denoted by an integer set $\mathbb{S}$, and the locations of the antennas are $nd$, $n \in \mathbb{S}$.

Given a sparse array $\mathbb{S}$, its difference coarray (DCA) is defined as

\begin{align*} \mathbb{D} \triangleq \{n_1 - n_2 \mid n_1, n_2 \in \mathbb{S}\}. \end{align*}

Each entry in $\mathbb{D}$ is termed a spatial lag.
The cardinality of DCA, i.e., $|\mathbb{D}|$, is termed degree of freedom (DoF) of the sparse array $\mathbb{S}$.
Clearly, DCA is symmetric, i.e., $\forall n \in \mathbb{D}$, $-n \in \mathbb{D}$.

Let $\mathbb{U}$ denote the central ULA segment of $\mathbb{D}$. Its cardinality $|\mathbb{U}|$ is termed uniform degree of freedom (UDoF). Then, the number of uncorrelated sources which can be identified is $\dfrac{|\mathbb{U}| - 1}{2}$.

Direction Cosine

Sat, 29 Jan 2022 00:00:00 +0000

In 3-dimension (3-D) space, a non-zero vector can be denoted by

\begin{align*} \mathbf{v} = v_x \mathbf{e}_x + v_y \mathbf{e}_y + v_z \mathbf{e}_z, \end{align*}

where

$\mathbf{e}_x = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$, $\mathbf{e}_y = \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}$, and $\mathbf{e}_z = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}$ are the unit vectors of the 3 axes, respectively.
$v_x$, $v_y$, and $v_z$ are the components of $\mathbf{v}$ projected to the 3 axes.

For vector $\mathbf{v}$, its direction cosine vector can be expressed as

Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT)

Sun, 09 Jan 2022 00:00:00 +0000

Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT), as its name indicates, is an algorithm to estimate the frequency of sinusoid waves from a noisy mixture of them. Additionally, it can also be used for direction of arrival (DoA) estimation in a multiantenna system. This post describes its principle.

An observation signal vector can be expressed as

\begin{align*} \mathbf{x} = \mathbf{A} \mathbf{s} + \mathbf{n}, \end{align*}

where

$\mathbf{A} = \begin{bmatrix} \mathbf{a}(\omega_1) & \mathbf{a}(\omega_2) & \ldots & \mathbf{a}(\omega_r) \end{bmatrix}$ is a $N \times r$ Vandermonde matrix, $N > r$; Each column is a steering vector, e.g., $\mathbf{a}(\omega) \triangleq \begin{bmatrix} 1 \\ e^{j\omega} \\ e^{j2\omega} \\ \vdots \\ e^{j(N-1)\omega} \end{bmatrix}$.
$\mathbf{s} = \begin{bmatrix} s_1 \\ s_2 \\ \vdots \\ s_r \end{bmatrix}$ is a signal vector.
$\mathbf{n} \sim \mathcal{CN}(0, \sigma^2\mathbf{I}_N)$ is a complex additive Gaussian noise vector.

Then autocorrelation matrix of observation can be obtained by

C++ - Standard Template Library (STL)

Sun, 02 Jan 2022 00:00:00 +0000

标准模板库(standard template library, STL)是C++标准库的子集, 其大量使用了模板.

容器

STL中的所有容器都是模板, 是泛型结构, 因此可以通过这些容器保存任意类型的数据. 除 array 和 bitset 外, 大部分STL容器的大小灵活多变, 都能自动增长或收缩, 以容纳更多或者更少的元素.
STL容器是同构的, 每个容器实例只允许一种类型的元素.
STL容器对元素使用值语义(value semantic)。因此，编写要用于STL的类时，一定要保证它们是可复制的。如果需要引用语义，必须自己实现。实现方法是保存元素指针，而不是保存元素本身。可以使用 unique_ptr, 使容器成为该指针所指对象的拥有者；或者使用 shared_ptr, 使容器与其他拥有者共享拥有权。
STL容器的一个模板类型参数是分配器(allocator)。该容器可以使用该分配器来为元素分配内存或释放内存。有些容器(例如 map)也接受将一个比较器(comparator)作为一个模板类型参数。比较器用作顺序元素。
所有的STL容器都包含了移动构造函数和移动赋值运算符, 从而实现了移动语义.
移动语义要正确地用于STL容器，必须把移动构造函数和移动复制运算符标记为 noexcept.
C++11在大部分STL容器中添加了对 emplace 操作的支持. emplace 的意思是放置到位, 就地构件对象.

顺序容器(sequential container)

顺序容器是元素的序列。

`vector`

定义在头文件 <vector> 中.
提供对元素的随机访问.
元素保存在连续的内存中.
能够在尾部快速插入和删除元素, 在其他部位插入和删除操作比较慢.
可以在本来需要使用数组的地方使用 vector.
在任何可能的情况下使用 vector 而不是C风格的数组.
vector 的默认构造函数会创建一个带有0个元素的 vector. 此外, 还提供了一个可以指定元素数量的构造函数, 和同时指定元素数目和元素值的构造函数. 如果没有提供默认值, 那么新对象通过0初始化——将原始的整型类型初始化为0, 将原始浮点类型初始化为0.0, 将指针类型初始化为 nullptr.
vector 存储对象的副本, 其析构函数调用每个对象的析构函数. vector 类的复制构造函数和赋值运算符对 vector 中的所有元素执行深度复制.
assign() 方法删除所有现有的元素, 并添加任意数目的新元素.
swap() 方法可以交换两个 vector 的内容.
vector 的 operator[] 没有提供边界检查功能. C++标准指出通过 operator[] 访问边界外元素得到的结果是未定义的. 不同的是, at() 方法会执行边界检查, 越界会抛出异常(out_of_range).
front() 和 back() 分别返回 vector 的第一个元素和最后一个元素的引用.
size() 返回 vector 中元素的数目.
capacity() 返回 vector 在重分配之前可以保存的元素个数. 因此, 在重分配之前还能插入的元素个数为 capacity() - size().
resize() 可以指定 vector 要保存的元素数目.
reserve() 可以预分配空间.
push_back() 可以向 vector 追加元素.
pop_back() 可以删除 vector 最后一个元素. 注意, 该方法不会返回已删除的元素. 如果要访问这个元素, 必须首先通过 back() 获得这个元素.
insert() 方法可以在 vector 中任意位置插入元素.
erase() 方法可以在 vector 中任意位置删除元素.
clear() 方法可以删除所有元素.

`list` (双向链表)

定义在头文件 <list> 中.
元素查找和访问很慢.
元素不一定保存在连续的内存中.
插入和删除很快.
不支持元素的随机访问, 访问元素的方法只有 front() 和 back(), 分别返回第一个元素和最后一个元素的引用. 访问其他的元素必须通过迭代器.
应该尽量使用 list 方法而不是泛型STL算法, 因为前者更高效.

`forward_list` (单向链表)

只支持前向迭代.
没有提供快速的随机访问.
内存需求比 list 小.

`deque` (双头队列)

定义在头文件 <deque> 中.
不要求元素保存在连续内存中.
提供了快速的元素访问.
在序列两端提供了快速的插入和删除(常量时间).
在序列中间插入和删除的速度较慢.
提供了 push_front(), pop_front() 和 emplace_front().

`array`

定义在头文件 <array> 中.
标准C风格数组的替代品, 实际上是对C风格数组的简单包装.
适合大小固定的集合. 不能增加或收缩.
没有提供插入和删除操作.
元素的访问速度极快.
要求两个模板参数: 第一个参数指定了元素类型; 第二个参数指定了元素的固定数量.

容器适配器(adaptor)

容器适配器只是构建在某种标准顺序容器上的简单接口。

`queue`

定义在头文件 <queue> 中.
提供了标准的先入先出(FIFO)语义.
从一端插入元素, 从另一端取出元素.
插入元素和删除元素都很快.
push() 和 emplace() 方法在 queue 尾部添加一个新元素
pop() 移除头部元素.
front() 和 back() 分别返回第一个元素和最后一个元素的引用, 而不会删除元素.

`priority_queue`

定义在头文件 <queue> 中.
插入删除比 queue 要慢.
其头元素的优先级最高。
push() 和 emplace() 方法可以插入元素。
pop() 可以删除元素。
top() 可以返回头元素的const引用。
支持 size(), empty 和 swap() 方法。

`stack`

定义在头文件 <stack> 中.
提供了标准的先入后出(FILO)语义，也称为后入先出语义.
push() 在stack顶部添加一个新元素。
pop() 从stack顶部删除一个元素。
top() 返回顶部元素的引用。
最新插入的元素第一个被删除.
提供了快速的元素插入和删除.
支持 size(), empty 和 swap() 方法和标准的比较运算符。

关联容器

关联容器是关联了键和值的容器。

`pair` 工具类

pair 是一个类模板，将两个可能属于不同类型的值组合起来。
通过 first 和 second 公共数据成员访问这两个值。
定义了 operator== 和 operator< ，用于比较 first 和 second 元素。
工具函数模板 make_pair() 用于从两个值构造一个 pair 。
在 pair 中使用一般指针是危险的，因为 pair 复制构造函数和赋值运算符只对指针类型进行浅复制和赋值。然而，在 pair 中保存 shared_ptr 这样的智能指针则是很安全的。

排序关联容器或有序关联容器

`map` 和 `multimap`

定义在头文件 <map> 中，保存的是键/值对。
map
- 向 map 添加元素的方法是 insert() ，其允许判断键是否已经存在。该方法必须将键/值指定为 pair 对象或 initializer_list ，返回值为迭代器和布尔值组成的 pair() 。布尔值指示是否真的插入了新的键/值对，迭代器引用的是 map 中带有指定键的元素。如果指定的键已经存在，那么 insert() 不会改写元素值。
- operator[] 也可以插入元素。但是 operator[] 总是成功。如果给定键没有对应的元素值，就会创建带有对应键值的新元素。如果具有给定键的元素已经存在，那么 operator[] 会将元素值替换为新指定的值。
- find() 方法可以查找给定键值的元素。如果元素存在，这个方法返回指向具有指定键值的元素的迭代器；如果元素不存在，则返回 end() 迭代器。此外， operator[] 可以查找给定键值的元素，但是如果不知道元素是否存在，就不能使用 operator[] 。因为如果元素不存在， operator[] 就会插入一个包含相应键值的新元素。
multimap
- multimap 是一个允许多个元素使用同一个键值的 map 。
- multimap 不提供 operator[]. 其将所有带有同一个键值的元素保存在一起, 并提供了方法获得这个子范围的迭代器: lower_bound() 和 upper_bound() 方法分别返回满足给定键值的第一个元素和最后一个元素之后一个元素的迭代器. 如果没有元素匹配这个键值, 那么 lower_bound() 和 upper_bound() 相等. 此外, equal_range() 方法返回两个迭代器的 pair, 分别是 lower_bound() 和 upper_bound() 返回的迭代器.

`set` 和 `multiset`

定义在头文件 <set> 中。
multiset 和 set 的关系等同于 multimap 和 map 的关系. multiset 支持 set 的所有操作, 但允许容器中同时保存多个相等的元素.

无序关联容器或哈希表(hash table)

unordered_map 和 unordered_multimap 定义在头文件 <unordered_map> 中, 都是类模板. unordered_multimap 是允许多个元素带有同一个键值的 unordered_map.
unordered_set 和 unordered_multiset 定义在头文件 <unordered_set> 中. 二者分别类似于 set 和 multiset.
无序关联容器使用了哈希函数(hash function), 所以也称为哈希表.
哈希表的实现通常会使用某种形式的数组, 数组中的每个元素都称为桶(bucket).
哈希函数的结果未必是唯一的. 两个或多个键哈希到同一个桶索引, 称为冲突(collision).
C++标准为指针和所有基本数据类型(例如 bool, char, int, float, double 等)提供了哈希函数, 也为 error_code, bitset, unique_ptr, shared_ptr, type_index, string, vector<bool> 和 thread 提供了哈希函数.

其他容器

定义在头文件 <bitset> 中的 bitset 并不是一个真正的STL容器: 固定大小(声明时指定大小), 不支持迭代器.
string 也可看做字符的顺序容器.
STL提供了名为 istream_iterator 和 ostream_iterator 的特殊迭代器, 用于"遍历"输入和输出流.

Linux - Bash

Sun, 02 Jan 2022 00:00:00 +0000

Running ways

Make the shell script executable: The script should begin with the shebang (e.g. #!/bin/bash).
Treat the shell script as the argument of sh: In this case, the shebang is not necessary.

Print

`echo`

By default, a line break is appended every time it is invoked.
The default line break can be avoided by option -n.

`printf`

Syntax

printf "format_list" content/variable_list

Format
- %s
  - %3s: 3-character wide and right alignment.
  - %-3s: 3-character wide and left alignment.
- %c
- \n: line break.
- %f
  - %5.2f: 5-character wide with 2 of them for decimal portion, right alignment.
  - %-5.2f: 5-character wide with 2 of them for decimal portion, left alignment.

Linux - Dynamic Window Manager (DWM)

Sun, 02 Jan 2022 00:00:00 +0000

Dynamic window manager (DWM), as one component of the suckless suite, is a flexible but lightweight window manager for X. This post just summarizes the procedure of installation and customization.

DWM

Download the source codes

 git clone --depth=1 https://git.suckless.org/dwm

Customization

Patch
- Addtional features are supported as patches, which can be downloaded from https://dwm.suckless.org/patches. E.g., alpha, hide_vacant_tags, pertag, rotatestack.
- In order to record and maintain the customization with git, patches can be applied by
```
 git apply PATCH.diff
```

config.def.h

Users can further tweak DWM's appearance and behaviors by editing this file. E.g.,

 /* See LICENSE file for copyright and license details. */
 #include <X11/XF86keysym.h>

 /* appearance */
 static const unsigned int borderpx = 1; /* border pixel of windows */
 static const unsigned int snap = 32; /* snap pixel */
 static const int showbar = 1; /* 0 means no bar */
 static const int topbar = 1; /* 0 means bottom bar */
 static const char *fonts[] = { "Sarasa Mono SC:size=18" };
 /* static const char dmenufont[] = "monospace:size=10"; */
 static const char col_gray1[] = "#222222";
 static const char col_gray2[] = "#444444";
 static const char col_gray3[] = "#bbbbbb";
 static const char col_gray4[] = "#eeeeee";
 static const char col_cyan[] = "#005577";
 static const unsigned int baralpha = 0xd0;
 static const unsigned int borderalpha = OPAQUE;
 static const char *colors[][3] = {
 /* fg bg border */
 [SchemeNorm] = { col_gray3, col_gray1, col_gray2 },
 [SchemeSel] = { col_gray4, col_cyan, col_cyan },
 };
 static const unsigned int alphas[][3] = {
 /* fg bg border */
 [SchemeNorm] = { OPAQUE, baralpha, borderalpha },
 [SchemeSel] = { OPAQUE, baralpha, borderalpha },
 };

 /* tagging */
 static const char *tags[] = { "1", "2", "3", "4", "5", "6", "7", "8", "9" };

 static const Rule rules[] = {
 /* xprop(1):
 ,*	WM_CLASS(STRING) = instance, class
 ,*	WM_NAME(STRING) = title
 ,*/
 /* class instance title tags mask isfloating monitor */
 /* { "Gimp", NULL, NULL, 0, 1, -1 }, */
 { "Chromium", NULL, NULL, 0, 0, -1 },
 };

 /* layout(s) */
 static const float mfact = 0.6; /* factor of master area size [0.05..0.95] */
 static const int nmaster = 1; /* number of clients in master area */
 static const int resizehints = 1; /* 1 means respect size hints in tiled resizals */

 static const Layout layouts[] = {
 /* symbol arrange function */
 { "T", tile }, /* first entry is default */
 { "F", NULL }, /* no layout function means floating behavior */
 { "M", monocle },
 };

 /* key definitions */
 #define MODKEY Mod4Mask
 #define TAGKEYS(KEY,TAG) \
 { MODKEY, KEY, view, {.ui = 1 << TAG} }, \
 { MODKEY|ControlMask, KEY, toggleview, {.ui = 1 << TAG} }, \
 { MODKEY|ShiftMask, KEY, tag, {.ui = 1 << TAG} }, \
 { MODKEY|ControlMask|ShiftMask, KEY, toggletag, {.ui = 1 << TAG} },

 /* helper for spawning shell commands in the pre dwm-5.0 fashion */
 #define SHCMD(cmd) { .v = (const char*[]){ "/bin/sh", "-c", cmd, NULL } }

 /* commands */
 static char dmenumon[2] = "0"; /* component of dmenucmd, manipulated in spawn() */
 static const char *dmenucmd[] = { "/usr/bin/rofi", "-show", "drun", "-show-icons", "-lines", "9", "-width", "100", "-location", "7", "-font", "Sarasa Mono SC 18", NULL };
 static const char *termcmd[] = { "/usr/bin/alacritty", "--option", "font.normal.family=Sarasa Mono SC", "font.size=13", NULL };
 static const char *volup[] = { "/usr/bin/amixer", "set", "Master", "5%+", "umute", NULL };
 static const char *voldown[] = { "/usr/bin/amixer", "set", "Master", "5%-", "umute", NULL };
 static const char *voltoggle[] = { "/usr/bin/amixer", "set", "Master", "toggle", NULL };
 static const char *brightup[] = { "/usr/bin/xbacklight", "-inc", "5", NULL };
 static const char *brightdown[] = { "/usr/bin/xbacklight", "-dec", "5", NULL };
 static const char *fullscreenshot[] = { "/usr/bin/scrot", NULL };
 static const char *selectscreenshot[] = { "/usr/bin/scrot", "-s", NULL };

 static Key keys[] = {
 /* modifier key function argument */
 { MODKEY, XK_d, spawn, {.v = dmenucmd } },
 { MODKEY, XK_Return, spawn, {.v = termcmd } },
 { MODKEY, XK_b, togglebar, {0} },
 { MODKEY|ShiftMask, XK_o, rotatestack, {.i = +1 } },
 { MODKEY, XK_o, focusstack, {.i = +1 } },
 /* { MODKEY, XK_i, incnmaster, {.i = +1 } }, */
 /* { MODKEY, XK_d, incnmaster, {.i = -1 } }, */
 { MODKEY, XK_h, setmfact, {.f = -0.05} },
 { MODKEY, XK_l, setmfact, {.f = +0.05} },
 { MODKEY, XK_z, zoom, {0} },
 { MODKEY, XK_Tab, view, {0} },
 { MODKEY, XK_q, killclient, {0} },
 { MODKEY, XK_t, setlayout, {.v = &layouts[0]} },
 /* { MODKEY, XK_f, setlayout, {.v = &layouts[1]} }, */
 { MODKEY, XK_m, setlayout, {.v = &layouts[2]} },
 { MODKEY, XK_space, setlayout, {0} },
 { MODKEY|ShiftMask, XK_space, togglefloating, {0} },
 { MODKEY, XK_0, view, {.ui = ~0 } },
 /* { MODKEY|ShiftMask, XK_0, tag, {.ui = ~0 } },
 { MODKEY, XK_comma, focusmon, {.i = -1 } },
 { MODKEY, XK_period, focusmon, {.i = +1 } },
 { MODKEY|ShiftMask, XK_comma, tagmon, {.i = -1 } },
 { MODKEY|ShiftMask, XK_period, tagmon, {.i = +1 } }, */
 TAGKEYS( XK_1, 0)
 TAGKEYS( XK_2, 1)
 TAGKEYS( XK_3, 2)
 TAGKEYS( XK_4, 3)
 TAGKEYS( XK_5, 4)
 TAGKEYS( XK_6, 5)
 TAGKEYS( XK_7, 6)
 TAGKEYS( XK_8, 7)
 TAGKEYS( XK_9, 8)
 { MODKEY|ShiftMask, XK_e, quit, {0} },
 { 0, XK_Print, spawn, {.v = fullscreenshot} },
 { ShiftMask, XK_Print, spawn, {.v = selectscreenshot} },
 { 0, XF86XK_AudioRaiseVolume, spawn, {.v = volup }},
 { 0, XF86XK_AudioLowerVolume, spawn, {.v = voldown }},
 { 0, XF86XK_AudioMute, spawn, {.v = voltoggle }},
 { 0, XF86XK_MonBrightnessUp, spawn, {.v = brightup }},
 { 0, XF86XK_MonBrightnessDown, spawn, {.v = brightdown }},
 };

 /* button definitions */
 /* click can be ClkTagBar, ClkLtSymbol, ClkStatusText, ClkWinTitle, ClkClientWin, or ClkRootWin */
 static Button buttons[] = {
 /* click event mask button function argument */
 { ClkLtSymbol, 0, Button1, setlayout, {0} },
 { ClkLtSymbol, 0, Button3, setlayout, {.v = &layouts[2]} },
 { ClkWinTitle, 0, Button2, zoom, {0} },
 { ClkStatusText, 0, Button2, spawn, {.v = termcmd } },
 { ClkClientWin, MODKEY, Button1, movemouse, {0} },
 { ClkClientWin, MODKEY, Button2, togglefloating, {0} },
 { ClkClientWin, MODKEY, Button3, resizemouse, {0} },
 { ClkTagBar, 0, Button1, view, {0} },
 { ClkTagBar, 0, Button3, toggleview, {0} },
 { ClkTagBar, MODKEY, Button1, tag, {0} },
 { ClkTagBar, MODKEY, Button3, toggletag, {0} },
 };

Build and install

Remove config.h if it exists.
Compile
```
 make
```
Install
```
 make install
```
Clean the temporary object files.
```
 make clean
```

Linux - Fonts

Sun, 02 Jan 2022 00:00:00 +0000

On Unix/Linux desktop, there are a rich number of open source projects for font rendering. This post lists some pretty excellent choices. Taking ArchLinux for instance, the installations are presented.

Infinality

Append following repositories to `/etc/pacman.conf`.

[infinality-bundle]
Server= http://bohoomil.com/repo/$arch
[infinality-bundle-multilib]
Server= http://bohoomil.com/repo/multilib/$arch
[infinality-bundle-fonts]
Server= http://bohoomil.com/repo/fonts

Install infinality fonts

For x86-64

pacman -S infinality-bundle ibfonts-meta-extended infinality-bundle-multilib

For x86-32

pacman -S infinality-bundle ibfonts-meta-extended

Adobe

pacman -S adobe-source-{code,sans,serif}-pro-fonts

Fira

Fira font is dedicated for Firefox operation system (OS).

pacman -S ttf-fira-{mono,sans}

Linux - GNU Debugger (GDB)

Sun, 02 Jan 2022 00:00:00 +0000

GDB is the world famous GNU debugger, which is very powerful. In this article, its elementary usages can be listed as follows.

b(reak) LINE_IDX: set breakpoint in line LINE_IDX.
b(reak) FUN_NAME: set breakpoint at the begin of function FUN_NAME.
b(reak) ... if ...: set conditional breakpoint.
delete breakpoints BP_IDX: delete breakpoint BP_IDX (if BP_IDX is omitted, all the breakpoints will be deleted).
disable breakpoints BP_IDX: disable breakpoint BP_IDX (if BP_IDX is omitted, all the breakpoints will be disabled).
enable breakpoints BP_IDX: enable breakpoint BP_IDX (if BP_IDX is omitted, all the breakpoints will be enabled).
display VAR_NAME: track varable VAR_NAME, every time the program stops, its value will be displayed.
undisplay VAR_NAME: cancel tracking of variable VAR_NAME.
start: start to excute the program and stop at the first statement of main.
r(un): excute the program from beginning continuously.
c(ontinue): excute the program from current position contiously.
s(tep): excute the program by one step and enter the function if available.
n(ext): excute the program by one step and don’t enter any function.
backtrace(or bt): view the function call of all the levels and their parameters.
f(rame) FRM_IDX: select the stack frame of index FRM_IDX.
watch: set observation point.
i(nfo) locals: view the values of local variables in current stack frame.
i(nfo) b(reakpoints): view current breakpoints.
i(nfo) watchpoints: view current observation points.
l(ist): list 10 lines of source code, continuing the last.
l(ist) LINE_IDX: list the source code around line LINE_IDX.
l(ist) FUN_NAME: list the source code of function FUN_NAME.
x: print part content of register from some position. All the contents are treated as bytes without consideration that which bytes correspond to which variable. For example, x/7b p will print the content of size 7 bytes after point variable p.
p(rint) expr: print the value of expr. This functionality can be used to change the values of variables or provoke a function.
finish: excute the current function until return, and then stop.

Linux - Network File System (NFS)

Sun, 02 Jan 2022 00:00:00 +0000

Network file system (NFS) is a simple approach for share and exchange files in Unix/Linux. This post summarizes its installation and configuration.

Installation

pacman -S nfs-utils

Configuration

Server

Edit /etc/exports, e.g.

# /etc/exports - exports(5) - directories exported to NFS clients
#
# Example for NFSv2 and NFSv3:
# /srv/home hostname1(rw,sync) hostname2(ro,sync)
# Example for NFSv4:
# /srv/nfs4	 hostname1(rw,sync,fsid=0)
# /srv/nfs4/home hostname1(rw,sync,nohide)
# Using Kerberos and integrity checking:
# /srv/nfs4 *(rw,sync,sec=krb5i,fsid=0)
# /srv/nfs4/home *(rw,sync,sec=krb5i,nohide)
#
# Use `exportfs -arv` to reload.

/home 192.168.2.0/24(rw,async,subtree_check,no_root_squash)
/opt 192.168.2.0/24(ro,async,subtree_check,no_root_squash)

And then enable and start the service.

systemctl enable nfs-server.service
systemctl start nfs-server.service

Client

Add the corresponding entries in /etc/fstab, e.g.

server:/opt /opt nfs4 ro,_netdev,soft,async 0 0
server:/home /home nfs4 rw,_netdev,soft,async 0 0

Linux - Network time protocol (NTP)

Sun, 02 Jan 2022 00:00:00 +0000

Network time protocol (NTP) is a very convenient service which can provide network time synchronized automatically and periodically. This post briefly describes the installation and configuration of NTP on Linux OS.

Installation

Without loss of generality, we take Arch Linux for instance here.

pacman -S ntp

Configuration

Prepend following line(s) to `/etc/ntp.conf`.

As server

server 127.127.1.1
fudge 127.127.1.1 stratum 12

As client

server IP_ADDRESS

Start and enable the service

systemctl enable ntpd.service
systemctl start ntpd.service

Linux - Zathura

Sun, 02 Jan 2022 00:00:00 +0000

Introduction

Zathura is a light PDF viewer, with Vi/Vim-like keybindings. It always reloads and refreshes documents automatically. In this sense, it is naturally capable of providing real time preview of a PDF file, e.g., produced by LaTeX. Additionally, it has the option of enabling inverse search based on synctex.

Installation

 pacman -S zathura zathura-pdf-mupdf

Keybindings

General

Keybinding	Functionality
h/j/k/l	Scroll left/down/up/right.
J/K	Go to the next/previous page.
gg	Go to the first page.
G	Go to the last page.
nG	Go to the nth page.
?//	Search backward/forward for the text.
n/N	Search backward/forward for the next result.
o/O	Open a document.
R	Reload document.
Tab	Show index and switch to index mode.
a	Fit page.
s	Fit width.
r	Rotate by 90 degrees.
d	Toggle dual-page view.
f	Follow links.
q	Quit
Ctrl-r	Invert color.
F5	Toggle to presentation mode.
F11	Toggle to fullscreen mode.
Ctrl-n	Toggle status bar.
+/-/=	Zoom in/out/to the origin size.
mX	Set a quickmark to X, a letter or a number.
'X	Goto quickmark saved at X.

Index mode

Keybinding	Functionality
j/k	Move to lower/upper entry.
h/l	Collapse/expand entry.
H/L	Collapse/expand all entries.
space/return	Select and open entry.

Linux - Zsh

Sun, 02 Jan 2022 00:00:00 +0000

Introduction

As is well-known, shell is an interface provided by the Unix/Linux operation systems (OS) to subscribers whereby a user can interact with the kernel of the OS efficiently and conveniently.

In fact, there are already a variety of shells, e.g., bash, csh, tcsh, zsh, etc. This post just presented a brief introduction to zsh.

Zsh is indeed a powerful shell. Perhaps this is just the reason why it is termed "shell terminator", as letter 'Z' is the letter terminator, the last one in the alphabeta.

NR - Uplink Control Information (UCI)

Sun, 02 Jan 2022 00:00:00 +0000

Introduction

Targetting for HARQ acknowledgement and scheduling request, similar to LTE, uplink control information (UCI) is transmitted on physical uplink control channel (PUCCH) or physical uplink shared channel (PUSCH).

Simultaneous transmission of PUCCH and PUSCH is not supported in release 15, but UCI can be pigged-back on PUSCH, i.e., UCI is multiplexed with data and transmitted on PUSCH.

In carrier aggregation (CA) case, UCI is only transmitted on the primary cell (PCell), to support asymmetric CA, i.e., different number of carriers in the downlink and uplink. To avoid overloading, PUCCH's can be divided into 2 groups. The feedback relating to the 1st group is transmitted in the uplink of the PCell, while the feedback corresponding to the 2nd group is delivered in the uplink of the primary second cell (PSCell).

For PUCCH, only a single antenna port is specified. Given a UE equipped with multiple antennas, how to make use of the antenna array is a UE implementation related issue.

Python - Tensorflow

Sun, 02 Jan 2022 00:00:00 +0000

Introducation

Tensorflow is a deep learning library, which provides two programming interfaces, C++ and Python. Moreover, The Python API integrates very well with numpy. In many places, Tensorflow tensors can be interchanged with numpy ndarrays.

Representation

In tensorflow, machine learning algorithms are represented as computational graphs, i.e. graph, in which a vertex/node and an edge represent an operation (op) and a data flowing, respectively.

Operation

An operation can have zero or more inputs and produce zero or more outputs.
An operation may stand for a mathematical equation, a variable, a constant, a control flow directive, a file I/O operation, or even a network communication port.

Tensor

A tensor is a multidimentional array or list, the generalization of scalars, 1-D vector, and 2-D matrices.
Tensors are the connecting edges, passed between nodes/ops in the flow diagram.
A tensor is a symbolic handle, which does not hold or store values in memory, but provides only an interface for retrieving the value referenced by the tensor.
Parameters

Rank

The number of dimensions, i.e., the depth of brackets.

Shape

The number of components in each dimension, e.g., the number of rows and columns. Tensorflow defines following shape-related functions, tensorflow.shape, tensorflow.size, tensorflow.rank, tensorflow.reshape, tensorflow.expand_dims.

Type

Data type assigned to the elements of the tensor, e.g., DT_FLOAT, DT_DOUBLE, DT_INT8, DT_UINT8, DT_INT16, DT_INT32, DT_INT64, DT_STRING, DT_BOOL, DT_COMPLEX64. Additionally, tensorflow provides following type transformation functions, e.g., tensorflow.string_to_number, tensorflow.to_double, tensorflow.to_float, tensorflow.to_int32, tensorflow.to_int64, tensorflow.cast.

Emacs - Ebib

Sat, 25 Dec 2021 00:00:00 +0000

Ebib is a tool inside Emacs for bibliography management, supporting BibTeX and biblatex files. This post is just a brief summary of the online manual.

Installation

Ebib can be easily installed via Melpa.

View

When ebib is started, the Emacs frame is divided into 2 windows, index buffer at the top and entry buffer at the bottom.

Index buffer

All the entries are listed in this buffer.

The fields or columns displayed in the buffer can be customized.
The entries are by default sorted in ascending order on the first column defined in ebib-index-columns, but the sorting rule can be specified by option ebib-index-default-sort.

Entry buffer

All the fields of the selected entry are shown in this buffer. The first field is type field, as the name indicates, it indicates the type of the entry, e.g., article, book. Besides, the remaining fields can be classified into 4 groups below. Required fields and optional fields are type-specific; while extra fields and undefined fields are not, but defined globally.

Required fields: Required by BibTeX/biblatex.
Optional fields
Extra fields: Usually ignored by BibTeX/biblatex.
Undefined fields

Emacs - Gnus

Sat, 25 Dec 2021 00:00:00 +0000

Gnus is the builtin mail client inside Emacs. As long as Emacs is installed, gnus is available.

The bahavior of gnus can be customized in following two files.

~/.gnus

 (setq user-full-name "NAME"
 user-mail-address "USERNAME")

 (setq gnus-select-method
 '(nnimap "ACCOUNT_NAME" (nnimap-address "IMAP.SERVER.COM")))

 (setq gnus-use-full-window nil
 gnus-message-archive-group nil
 gnus-fetch-old-headers t
 nnmail-expiry-wait 'never)

 (setq send-mail-function 'smtpmail-send-it
 smtpmail-smtp-server "SMTP.SERVER.COM")

~/.authinfo

 machine IMAP.SERVER.COM login USERNAME password PASSWORD port imap
 machine SMTP.SERVER.COM login USERNAME password PASSWORD port smtp

After the configuration above, gnus can be launched via M-x gnus inside Emacs.

Linux - Command Line Tools

Sat, 25 Dec 2021 00:00:00 +0000

Targetting for more features and conveniences, some extremely excellent command line tools are listed in this document, which is encouraged to use.

Starship

Starship can provide an exciting prompt to a variety of shells, e.g., bash, csh/tcsh, zsh, etc.

Installation (e.g., for Arch Linux)

 pacman -S starship

Configuration in ~/.bashrc (e.g., for bash)

 eval "$(starship init bash)"

File finder

fd

Fd is a replacement for classic find, which can be easily installed by

 pacman -S fd

fzf

Fzf stands for fuzzy finder, which can be easily installed by

 pacman -S fzf

Linux - Sed

Sat, 25 Dec 2021 00:00:00 +0000

简介

Sed 是著名的流编辑器，它能够对文本进行逐行处理，通常需要配合正则表达式使用。具体地， Sed 先把当前行的文本导入 模式空间(pattern space) 对其处理，然后输出处理后的文本。

命令格式

 sed [OPTIONS] 'COMMAND' FILE(S)
 sed [OPTIONS] -f 'SCRIPT' FILE(S)

选项

选项	含义
`-h/--help`	显示帮助信息。
`-V/--version`	显示版本信息。
`-n/--quiet/--silent`	仅显示经过处理的结果。
`-i`	原地(inplace)替换

选项

命令

命令	含义
`s`	替换
`p`	打印

命令

示例

替换命令 `s`

 # 替换每行的第一个匹配。
 sed 's/FROM/TO/' FILE

 # 通过后缀 =g= 替换每行的所有匹配。
 sed 's/FROM/TO/g' FILE

 # 通过后缀 =Ng= 对每行的第N处匹配开始替换。
 sed 's/FROM/TO/g' FILE

 # 通过选项 =-i= 对文件直接原地替换。
 sed -i 's/FROM/TO/[g]' FILE

Neural Network

Sat, 25 Dec 2021 00:00:00 +0000

Introducation

The network is composed of an input layer, an output layer, and optionally a series of hidden layers.
Input layer does not carry out any operation/function, but the hidden and output layers consist of functional neurons, i.e., have activation functions.

McCulloch and Pitts (M-P) model for neurons

\begin{align*} y = f(\mathbf{W} \mathbf{x} - \theta) \end{align*}

where $f$ is termed activation function.

Activation function

Activation function aims to introduce the non-linear capability, compensate the shortage of linear models.

Sign

\begin{align*} \text{sign}(x) = \begin{cases} 1, & x \ge 0; \\ 0, & x < 0. \end{cases} \end{align*}

Sigmoid

\begin{align*} \text{sigmoid}(x) = \frac{1}{1 + e^{-x}}. \end{align*}

Tanh

\begin{align*} \text{tanh}(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}. \end{align*}

ReLU

\begin{align*} \text{ReLU}(x) = \max(x, 0) \end{align*}

Softmax

Softmax function can transform scores/logits into a valid probability distribution.

\begin{align*} \text{softmax}(x_i) = \frac{e^{x_i}}{\sum_j e^{x_j}} \end{align*}

Python - Pandas

Sat, 25 Dec 2021 00:00:00 +0000

Pandas 支持大部分 numpy 语言风格的数组计算。尽管代码风格相似，但最大的不同在于前者是用来处理表格或不同类型数据的，而后者更适合处理相同类型数据的。

数据结构

Series

Series 是一维数组的对象，包含 index 序列和 values 序列，分别可以通过对象的 index 和 values 属性获得。
通常需要创建一个index序列来标识每个数据点。如果不显式指定，那么默认 index 为从0到N-1，其中N为Series对象的长度。
index 可以用来索引数据，在这种意义上， Series 就像一个有序的字典。另外，可以通过字典直接生成 Series 对象。
pandas 用 NaN (not a number) 来标记缺失或NA值，用 isnull 和 notnull 函数来检查 Series 对象。同时， isnull 和 notnull 也是 Series 类的成员函数。

DataFrame

DataFrame 是二维数据表，既有行索引，又有列索引。可以通过属性 T 进行转置。每一列可以是不同的类型（数值、字符串、布尔值等）。
和 Series 类似， DataFrame 的 values 属性会将数据以二维ndarray形式返回。
虽然 DataFrame 是二维的，但是可以通过分层索引扩展到更高维度的数据。
在将列表或数组赋值给某一列时，列表或数组的长度必须和 DataFrame 对象的长度相等。将 Series 对象赋值给某一列时，其索引会按照 DataFrame 对象的索引重新排序，并用缺失值填充空缺位置。

索引对象

Pandas 中的索引对象是用于存储轴标签和其他元数据的。构建 Series 或 DataFrame 对象时所使用的数组或标签序列都可以在内部转换为索引对象。
索引对象是不可变的，不能修改。
索引对象的 is_unique 属性可以返回其标签是否唯一。

基本功能

成员函数 reindex : 重建索引。支持如下参数：
- index : 作为新索引的序列。
- level : 匹配 MultiIndex 级别的简单索引。
成员函数 drop : 删除行或列，参数为行或列索引列表。在删除列时，需要增加参数axis=1或axis='columns'。
成员函数 head() 返回前五行。
成员函数 set_index (参数可以为单个列名或多个列名的列表) 将选中的列转换为索引。
成员函数 filter(regex=KEYWORD) 可以通过正则表达式对列名进行过滤筛选，返回一个符合筛选条件的新 DataFrame 。
成员函数 apply 可以将函数应用到一列或一行的一维数组上。特别地，如果应用到行，除了函数作为参数外，还需要增加参数axis='columns'。另外，传递给apply的函数并不一定要返回一个标量值，也可以返回带有多个值的Series。
成员函数 applymap 可以将函数应用到每一个元素上。

成员函数 plot 可以直接调用 matplotlib 绘图。默认地，以索引作为x轴，各个数据列为y轴，列名作为图例名称。但是其行为可以定制。例如，

 df.plot(ax=AX, x=COL1_NAME, y=COL2_NAME, title=TITLE, xlabel=XLABEL, ylabel=YLABEL, grid=True/False, legend=True/False, linestyle=LINESTYLE, xlim=[XMIN, XMAX], ylim=[YMIN, YMAX])

成员函数 sort_index 可以按照行索引或列索引进行字典型排序，该方法返回一个新的排序好的 DataFrame 对象。
- 默认为按行排序。可以通过参数 axis=1 来按列排序。
- 默认为升序排序，可以通过参数 ascending=False 来降序排列。
成员函数 sort_values 可以根据值来对 Series 对象或者 DataFrame 对象排序。
- 对于 DataFrame 对象，可以通过将列名或列名列表作为参数传给可选参数 by 来根据一列或者多列的值排序。
DataFrame 对象可以通过行索引返回 Series 对象，如 DataFrame.loc['index_name'] 或 DataFrame.iloc['index'] 。
DataFrame 对象可以通过列索引返回 Series 对象，如 DataFrame.loc[:, 'index_name'] 或 DataFrame.iloc[:, 'index'] 或 DataFrame['column_name'] ，如果列名无效，那么会新建列。此外， DataFrame.column_name 也能达到相同目的，但仅当列名存在时才有效时。值得注意的是，索引的列是数据的视图，而不是拷贝。因此，对返回 Series 对象的修改会映射到 DataFrame 对象。如果需要复制，需要调用 Series 类的 copy 成员函数。
DataFrame 对象可以通过行列索引来返回单个标量值，如 DataFrame.at['row_index_name', 'column_index_name'] 或 DataFrame.iat['row_index, 'column_index'] 。

concat : 合并多个Series或DataFrame。例如，

 import pandas as pd

 df = pd.concat([df1, df2], axis=1)

计算统计

可选参数

参数	描述
`axis`	归约轴，0为行，1为列。
`skipna`	是否跳过NaN ，默认值为 `True` 。
`level`	如果是多层索引（MultiIndex），该参数可以降低索引层数。

汇总

方法	描述
`count`	非NaN值的个数
`describe`	Series对象或DataFrame对象各列的统计汇总。
`min/max`	最小/大值
`argmin/argmax`	最小/大值的索引
`idxmin/idxmax`
`quantile`	计算0到1之间的分位数。
`sum`	和
`mean`	均值
`prod`	积
`median`	中位数（0.5分位数）
`mad`
`var`	方差
`std`	标准差
`skew`
`kurt`
`cumsum`	累加值
`cummin/cummax`
`cumprod`	累积值
`diff`
`pct_change`	百分比

Python - Pytorch

Sat, 25 Dec 2021 00:00:00 +0000

张量

在pytorch中，神经网络的输入、输出、以及网络的参数等都采用了“张量”的数据结构。张量与numpy中的多维数组(numpy.ndarray)非常类似，区别在于张量可以在GPU或其他硬件上运行。

成员函数名称末尾加上 _ ，会采用替换模式，也即该成员函数直接修改张量对象本身。
.item() 返回其具体数值，该方法仅适用于大小为1（也即只含有一个元素）的张量。
.view() 功能为reshape该张量（保持元素个数不变），其参数为新的shape。特别地，值为-1的维度可以通过元素总数不变推导得出。
定义一个张量时，可以通过参数 device 参数指定该张量存储于CPU还是GPU。也可以通过其成员函数 .to() 来转换。
定义一个张量时，参数 requires_grad=True 表示需要计算并存储对于该张量的梯度。该张量的函数均带有 grad_fn 属性。对于其任一函数，当调用其成员函数 .backward() 时，该函数对于该张量自变量的梯度将会被计算并保存在该张量的 .grad 属性中。
有时候需要停止跟踪记录某个张量（记为 x ）的梯度（比如在更新网络参数的权重系数时），可以采用以下任一方式：
1. 调用该张量的成员函数 x.requires_grad_(False) 。
2. 调用该张量的成员函数 x.detach() 会产生一个新的张量，其属性 requires_grad=False 。
3. 采用with语句，也即 with torch.no_grad(): 。

与 numpy.ndarray 相互转换

张量的成员函数 .numpy() 返回对应的 numpy.ndarray 。但是，该方法仅适用于存储在CPU的张量。
函数 torch.from_numpy() 可以将一个 numpy.ndarray 转换为张量。

值得注意的是，当一个张量存储在CPU上时，该张量与其对应的 numpy.ndarray 是连接着的，也即对其中一个的修改会导致另一个也会被修改。

神经网络

典型训练过程

构建含有一些可学习参数(或权重)的神经网络。
遍历训练数据集。
让输入通过网络得到输出。
计算预测误差(或损失函数)。
通过反向传播，计算并存储网络各个参数的梯度。
根据各个参数的梯度对其进行调整，如 weight = weight - learning_rate x gradient 。

正向传播与反向传播

神经网络的训练包括两个步骤

正向传播: 神经网络根据输入对输出进行最佳预测。
反向传播: 神经网络根据预测误差调整其参数。

当调用误差张量的成员函数 .backward() 时，开始反向传播，整个网络将被微分。Pytorch的自动差分引擎 torch.autograd 会对计算每个属性 requires_grad=True 的网络参数的梯度并将其累积在该网络参数的 .grad 属性中。所以，在反向传播开始之前，需要清空神经网络各个参数和反向传播的梯度缓冲区。

然后，需要从 torch.optim 中加载一个优化器(如随机梯度下降，SGD)。通过调用该优化器的 .step() 方法启动梯度下降，优化器会根据每个网络参数的梯度(存储于其 .grad 属性中)来对其进行调整。

定义网络

可以使用 torch.nn 包来构建神经网络。

基类 torch.nn.Module 包含
- 网络的各个层(作为类属性)，如输入层、输出层、隐藏层等。
- 成员函数 .forward 。
- 成员函数 .zero_grad ，用于清空神经网络中所有参数的梯度缓冲区。相当于整个网络中属性 requires_grad=True 的张量均调用成员函数 .grad.zero_() 。
构建神经网络可以通过定义以 torch.nn.Module 为基类的派生类完成。
只需要在派生类中重载成员函数 .forward ， torch.autograd 就会自动为网络各个参数定义 .backward() 函数。
所构建的神经网络的可学习参数由所述派生类的成员函数 .parameters() 返回。
torch.nn 包中定义了很多损失函数(如 torch.nn.MSELoss)。

下面是一个非常简单的神经网络。该神经网络只包含一个全连接层和一个激活函数relu。包括两个成员函数， TRAIN 和 TEST 。顾名思义，前者用于从训练数据集中加载数据，并训练神经网络中的可学习参数，并把所有可学习参数的最终权重（训练结果）保存在文件中；后者从权重文件中读取并加载所有可学习参数的权重，然后从测试数据集中加载数据，计算误差，从而完成对训练结果（可学习参数的权重）的测试。

 class NEURAL_NETWORK(torch.nn.Module):
 def __init__(self, IN_FEATURES, OUT_FEATURES):
 super(NEURAL_NETWORK, self).__init__()
 self.FC = torch.nn.Module.Linear(IN_FEATURES, OUT_FEATURES)

 def forward(self, INPUT):
 return torch.nn.function.relu(self.FC(INPUT))

 def TRAIN(self, DATALOADER_FOR_TRAIN):
 OPT = torch.optim.Adam(self.parameters(), LEARNING_RATE)
 LEARNING_RATE_SCHEDULER = torch.optim.lr_scheduler.ExponentialLR(OPT, gamma=0.9)
 for EPOCH_INDEX in range(EPOCH_NUM):
 for SAMPLE in DATALOADER_FOR_TRAIN:
 SAMPLE = SAMPLE.to(torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu"))
 VALUE_PREDICTED = self.forward(SAMPLE)
 VALUE_IDEAL = CALC_VALUE_IDEAL(SAMPLE)
 LOSS = torch.nn.MSELoss(VALUE_PREDICTED, VALUE_IDEAL)
 LOSS.requires_grad_(True)
 OPT.zero_grad()
 LOSS.backward()
 OPT.step()
 LEARNING_RATE_SCHEDULER.step()
 torch.save(self.state_dict(), "NEURAL_NETWORK_WEIGHT.pth")

 def TEST(self, DATALOADER_FOR_TEST):
 self.load_state_dict(torch.load("NEURAL_NETWORK_WEIGHT.pth", False))
 with torch.no_grad():
 for SAMPLE in DATALOADER_FOR_TEST:
 SAMPLE = SAMPLE.to(torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu"))
 VALUE_PREDICTED = self.forward(SAMPLE)
 VALUE_IDEAL = CALC_VALUE_IDEAL(SAMPLE)
 LOSS = torch.nn.MSELoss(VALUE_PREDICTED, VALUE_IDEAL)

Python - Basic

Tue, 04 May 2021 00:00:00 +0000

Python解释器

Python程序运行时，需要Python解释器去执行 .py 文件。下面是一些常见的Python解释器。

CPython

当Python安装好之后，CPython解释器就已经安装好了。该解释器是用C语言开发的，所以被称为CPython。在终端执行 python 命令后启动的就是该解释器。

PyPy

PyPy解释器采用JIT技术对Python程序代码进行动态编译，所以PyPy以执行速度见长。

Jython

Jython解释器可以将Python程序代码转换为Java字节码，在Java平台上运行。

IPython

IPython是基于CPython之上的一个交互式（interactive）Python解释器，所以被称为IPython。

没有内建到Python自身中的IPython特殊命令称为魔术命令，可以看作是IPython系统内部的命令行程序。魔术命令的前缀符号是百分号 % 。使用魔术命令也可以不加百分号，只要没有变量被定义与魔术函数名字相同即可。这种特性称为自动魔术，通过 %automagic 进行启动禁用。

命令	描述
`%quickref`	显示IPython快速参考卡。
`%magic`	显示所有可用魔术命令的详细文档。
`%debug`	从最后发生报错的底部进入交互式调试器。
`%hist`	打印历史命令输入。
`%pdb`	出现任意报错后自动进入调试器。
`%paste`	从剪贴板中执行已经预先格式化的Python代码。
`%cpaste`	打开一个特殊提示符，手动粘贴待执行的Python代码。
`%reset`	删除交互式命名空间中所有的变量、名称。
`%page OBJECT`	通过分页器更美观地打印显示一个对象。
`%run SCRIPT.py`	在IPython中运行一个Python脚本。
`%prun STATEMENT`	使用 `CProfile` 执行语句，并报告输出。
`%time STATEMENT`	报告单个语句的执行时间。
`%timeit STATEMENT`	多次运行单个语句计算平均执行时间（在估算代码最短执行时间时有用）。
`%who`, `%who_ls`, `%whos`	根据不同的详细程度，展示交互命名空间中定义的变量。
`%xdel VARIABLE`	在IPython内部删除一个变量，清除相关的引用。

在IPython会话中，可以使用 %run 命令运行任意的Python文件。IPython会在同一个进程内执行指定文件中的代码，确保在执行完成时可以立即得到结果。如果一个Python脚本需要命令行提供参数（通过 sys.argv 获得），那么则需要在命令行的文件路径后面加上参数进行传递。如果想让运行的脚本使用交互式IPython命名空间中已有的变量，需要使用 %run -i 替代 %run 。
%paste 会获得剪贴板中的所有文本，并作为代码块在命令行中执行； %cpaste 与之类似，只不过它会给出一个特殊的提示符提示粘贴代码。
%matplotlib 魔术函数可以设置matplotlib与IPython命令行或Jupyter notebook的集成。
在任意代码运行时按下 Ctrl-C ，无论脚本是通过 %run 或是其他长命令运行的，都将引起 KeyboardInterrupt ，导致所有的Python程序立即停止运行（某些特殊情况除外）。
IPython中大多数Python对象会被格式化为更可读、更美观的形式。
IPython还提供执行任意代码块（通过复制粘贴）和整个Python脚步的功能。
在一个变量名的前后使用问号(?)可以显示一些关于该对象的概要信息。使用双问号(??) 可以显示函数的源代码。 ? 可以像Unix命令行一样搜索IPython命名空间。把一些字符和通配符(*)结合在一起，会显示所有匹配通配符表达式的命令。

需要启动Jupyter时，可以在终端中运行如下命令。

 jupyter notebook

在很多平台上，Jupyter会自动默认网络浏览器（除非启动Jupyter时使用了 --no-browser 命令）。

Beam Pattern

Thu, 04 Mar 2021 00:00:00 +0000

Beamforming

Around the decades, multi-input multi-output (MIMO), a.k.a. multiantenna transmission, has been the focus of the research relating to wireless communications, and attracted the interests and attentions from both academic circle and industrial area. By deliberately designing the complex-valued coefficients of each antenna elements, the transmitted power or its majority can be limited to a specified direction or area. The operation is termed beamforming, and accordingly the weights of all the antenna elements involved are termed a beamforming vector or a beamformer. In this case, the SINR and the power of the received signal at the receiver can be remarkably enhanced.

C++ - Output Object

Sun, 14 Feb 2021 00:00:00 +0000

In object oriented programming (OOP) based C++ program, we usually need to output the properties and members of one or more objects. In this case, overriding the ostream operator, <<, is a convenient and intuitional method. Here is an example for class CLASS.

`class.h`

 #include <ostream>

 class CLASS
 {
 private:
 int mem_int;
 double mem_double;
 public:
 CLASS();
 friend std::ostream& operator<<(std::ostream& str, const CLASS& c);
 };

`class.cpp`

 #include <class.h>

 std::ostream& operator<<(std::ostream& str, const CLASS& c)
 {
 str << c.mem_int << ',' << c.mem_double;
 return str;
 }

Emacs - Notmuch

Thu, 11 Feb 2021 00:00:00 +0000

Introduction

Notmuch is a mail system¹. It can efficiently manage a fairly large number of emails. Particularly, it supports fast email searching and filtering based on tags, which is extremely similar to Gmail's tags whereby various virtual folders can be flexibly realized.

This post is composed just to summarize the basic installation and configuration of notmuch-based mail system.

Installation

pacman -S notmuch

Configuration

`~/.notmuch-config`

The basic configuration can be performed by either

an interactive guidance which can be provoked by

notmuch setup

or a manually composed ~/.notmuch-config as follows

[database]
# Mail storage in maildir format
path=/MAIL/REPO

[user]
name=NAME
primary_email=EMAILADDRESS

[new]
tags=unread;inbox;
ignore=

[search]
exclude_tags=deleted;spam;

[maildir]
synchronize_flags=true

[crypto]
gpg_path=gpg

`~/.emacs.d/init.el`

Add following content to the configuration of Emacs.

 (require 'notmuch)
 (setq user-full-name "NAME"
 user-mail-address "EMAILADDRESS")

 (setq mail-user-agent 'message-user-agent
 message-kill-buffer-on-exit t
 mm-text-html-renderer 'w3m)

 (setq notmuch-search-oldest-first nil
 notmuch-show-all-multipart/alternative-parts nil
 mail-interactive t
 notmuch-always-prompt-for-sender nil
 notmuch-show-indent-messages-width 3)

 (setq mail-specify-envelope-from t
 message-sendmail-envelope-from 'header
 mail-envelope-from 'header)

 (setq message-directory "."
 notmuch-fcc-dirs ".")

 (setq message-send-mail-function 'smtpmail-send-it
 smtpmail-smtp-server "SMTPSERVER"
 smtpmail-stream-type 'ssl
 smtpmail-smtp-service PORT)

 (setq notmuch-saved-searches '((:name "inbox"
 :query "tag:inbox"
 :count-query "tag:inbox and tag:unread"
 :sort-order newest-first)

Hooks

Additionally, notmuch supports hooks which are essentially scripts in /MAIL/REPO/.notmuch/hooks whereby users can specify and customize the behaviors of notmuch. Currently, following scripts and hooks are available.

pre-new: Hook/script provoked before command notmuch new, which is usually used to fetch mails.

#!/bin/sh
/usr/bin/offlineimap -c /PATH/TO/OFFLINEIMAPRC -a ACCOUNT

#!/bin/sh
/usr/bin/getmail --new --getmaildir=/PATH/TO/GETMAILRC --rcfile=GETMAILRC

post-new: Hook/script provoked after command notmuch new, which is usually used to tag the newly imported mails.

#!/bin/sh
notmuch tag -inbox +ML -- to:MAILLIST@EXAMPLE.COM
notmuch tag -inbox +SOMEONE -- from:SOMEONE@EXAMPLE.COM
/usr/bin/notmuch search --output=files tag:deleted OR tag:spam | xargs -r rm

post-insert: Hook/script called after command notmuch insert, which is provoked after mails are delivered, imported into database and labelled with initial tags.

#!/bin/sh
notmuch tag -inbox -unread +sent -- from:MYEMAILADDRESS
/usr/bin/notmuch search --output=files tag:deleted OR tag:spam | xargs -r rm

Automatics

Add new intended task by crontab -e with following content

*/5 * * * * /usr/bin/notmuch new

where the first line is for periodical fetching mail every 3 minutes and the second line to remove the mails deleted (tagged by deleted) at every boot.

Enable and start the service cronie.

systemctl enable cronie.service
systemctl start cronie.service

CJK Support

By default, notmuch cannot separate Chinese correctly, Japanese, or Korean words due to the non-space separator. A workaround is to set a environment variable as follows.

export XAPIAN_CJK_NGRAM=1

C++ - Singleton

Fri, 11 Dec 2020 00:00:00 +0000

Singleton plays an important role in program architecturing for its global visibility. For instance, system parameters are usually structured as a singleton. What deserves to be noticed, a singleton can be realized in a variety of manners.

Taking C++ for instance, a typical singleton can be simply defined as

`singleton.h`

 #ifndef SINGLETON_H
 #define SINGLETON_H

 class Singleton
 {
 private:
 static Singleton *instance;
 Singleton() = default;
 Singleton(const Singleton &rhs) = delete;
 Singleton& operator=(const Singleton &rhs) = delete;
 public:
 static Singleton* get_instance();
 };

 #endif /* SINGLETON_H */

`singleton.cpp`

 #include "singleton.h"

 Singleton *Singleton::instance = nullptr;

 Singleton* Singleton::get_instance()
 {
 if (instance == nullptr)
 instance = new Singleton;
 return instance;
 }

Gaussian Distribution

Sat, 01 Aug 2020 00:00:00 +0000

Probability density function

$X \sim \mathcal{N}(\mu, \sigma^2)$
\begin{align*} p(x) = \frac{1}{\sqrt{2\pi}\sigma} \exp\left[-\frac{(x-\mu)^2}{2\sigma^2}\right] \end{align*}

Distribution function

Q-function
- Definition
  \begin{align*} Q(x) \triangleq \int_x^{\infty} \frac{1}{\sqrt{2\pi}}\exp\left(-\frac{x^2}{2}\right)dx \end{align*}
- Properties
  \begin{align*} Q(-x) + Q(x) &= 1 \\ Q(0) &= \frac{1}{2} \end{align*}
Error function and complementary error function
- Definitions
  \begin{align*} \text{erf}(x) &\triangleq \frac{2}{\sqrt{\pi}} \int_0^x \exp\left(-x^2\right)dx \\ \text{erfc}(x) &\triangleq \frac{2}{\sqrt{\pi}} \int_x^{\infty} \exp\left(-x^2\right)dx \end{align*}
- Properties
  \begin{align*} \text{erf}(x) + \text{erfc}(x) &= 1 \\ \text{erf}(x) &= 1 - 2Q(\sqrt{2}x) \\ \text{erfc}(x) &= 2Q(\sqrt{2}x) \end{align*}

Laplace Transform

Mon, 06 Jul 2020 00:00:00 +0000

Given a time domain continuous signal, it can be represented in the complex frequency domain by Laplace transform. It is essentially an extension of Continuous Fourier transform.

Definition

Bilateral transform
\begin{align*} X(s) = \int_{-\infty}^{\infty} x(t) e^{-st} dt \end{align*}
Unilateral transform
\begin{align*} X(s) = \int_{0_-}^{\infty} x(t) e^{-st} dt \end{align*}
Inverse transform
\begin{align*} x(t) = \frac{1}{2\pi j} \int_{\sigma-j\infty}^{\sigma+j\infty} X(s) e^{st} ds \end{align*}
Region of convergence (ROC): Considering the fact that $X(s)$ is an infinite integration, the convergence must be ensured. To this end, ROC is defined, which is comprised of the candidate values of $s$ keeping the convergence. $s$ is termed complex frequency.

Properties (Unilateral Transform)

\begin{align*} x(t), t \ge 0_{-} &\leftrightarrow X(s) \\ x(at), a > 0 &\leftrightarrow \frac{1}{a}X \left( \frac{s}{a} \right) \\ x(t - t_0)\varepsilon(t - t_0), t_0>0 &\leftrightarrow X(s) e^{-st_0} \\ x(t)e^{s_0}t &\leftrightarrow X(s - s_0) \\ x^{(n)}(t) &\leftrightarrow s^nX(s) - s^{n-1}x(0_{-}) - \cdots - s^0x^{(n-1)}(0_{-}) \\ x_1(t) * x_2(t) &\leftrightarrow X_1(s) X_2(s) \\ x_1(t) x_2(t) &\leftrightarrow \frac{1}{2\pi j} \int_{C-j\infty}^{C+j\infty} X_1(\eta)X_2(s-\eta) d \eta \\ (-t)^nx(t) &\leftrightarrow \frac{d^nX(s)}{ds^{n}} \\ \frac{x(t)}{t} &\leftrightarrow \int_s^{\infty}X(\eta)d\eta \end{align*}

Initial Value Theorem

\begin{align*} x(0_{+}) = \lim_{s\to \infty}sX(s) \end{align*}

Final Value Theorem

\begin{align*} x(\infty) = \lim_{s\to 0} sX(s) \end{align*}

Transform Pairs (Unilateral Transform)

\begin{align*} x(t), t \ge 0_{-} &\leftrightarrow X(s) \\ \delta(t) &\leftrightarrow 1 \\ \varepsilon(t) &\leftrightarrow \frac{1}{s} \\ e^{-s_0t} &\leftrightarrow \frac{1}{s+s_0} \\ t^n, n \in \mathbb{Z}^+ &\leftrightarrow \frac{n!}{s^{n+1}} \\ \sin \omega t &\leftrightarrow \frac{\omega_0}{s^2 + \omega_0^2} \\ \cos \omega t &\leftrightarrow \frac{s}{s^2 + \omega_0^2} \end{align*}

Z Transform

Mon, 06 Jul 2020 00:00:00 +0000

Given a time domain discrete signal, i.e., a sequence, it can be represented in the complex frequency domain by Z transform. It is essentially an extension of discrete time Fourier transform (DTFT).

Definition

Bilateral transform
\begin{align*} X(z) = \sum_{n=-\infty}^{\infty} x(n) z^{-n} \end{align*}
Unilateral transform
\begin{align*} X(z) = \sum_{n=0}^{\infty} x(n) z^{-n} \end{align*}
Inverse transform
\begin{align*} x(n) &= \frac{1}{2\pi j}\oint_C X(z)z^{n-1} dz \\ &= \sum_{k} \text{Res} \left[ X(z)z^{n-1}, z_k \right]. \end{align*}
Region of convergence (ROC): Considering the fact that $X(z)$ is an infinite summation, the convergence must be ensured. To this end, ROC is defined, which is comprised of the candidate values of $z$ keeping the convergence. $z$ is termed complex frequency.

Properties

Denote the ROC as $\alpha < |z| < \beta$, $0 \le\alpha < \beta$.

Common to both bilateral and unilateral transforms
\begin{align*} a^n x(n), \quad a \neq 0. &\leftrightarrow X \left( \frac{z}{a} \right), \quad \alpha |a| < |z| < \beta |a|. \\ x_1(n) * x_2(n) &\leftrightarrow X_1(z) X_2(z), \quad \max(\alpha_1, \alpha_2) < |z| < \min(\beta_1, \beta_2). \\ n^mx(n), \quad m > 0. &\leftrightarrow \left(-z\frac{d}{dz}\right)^m X(z), \quad \alpha < |z| < \beta.\\ \frac{x(n)}{n+m}, \quad n+m > 0. &\leftrightarrow z^m \int_z^{\infty}X(\eta)\eta^{-(m+1)}d\eta, \quad \alpha < |z| < \beta. \\ x^*(n) &\leftrightarrow X^*(z^*) \\ x_1(n) * x_2(n) &\leftrightarrow X_1(z) X_2(z) \\ x(-n) &\leftrightarrow X\left(\frac{1}{z}\right), \quad \frac{1}{\beta} < |z| < \frac{1}{\alpha}.\\ \sum_{i=-\infty}^nx(i) &\leftrightarrow \frac{z}{z-1}X(z), \quad \max(\alpha, 1) < |z| < \beta. \end{align*}
Dedicated to bilateral transform
\begin{align*} x(n + m) \leftrightarrow z^m X(z), \quad \alpha < |z| < \beta \\ \end{align*}
Dedicated to unilateral transform
\begin{align*} x(n-m), \quad m > 0. &\leftrightarrow z^{-m}X(z) + \sum_{n=0}^{m-1}x(n-m)z^{-n}, \quad |z| > \alpha. \\ x(n+m), \quad m > 0. &\leftrightarrow z^mX(z) - \sum_{n=0}^{m-1}x(n)z^{m-n}, \quad |z| > \alpha. \end{align*}

Initial Value Theorem

\begin{align*} x(0) = \lim_{z\to\infty}X(z) \end{align*}

Final Value Theorem

\begin{align*} \lim_{n\to\infty}x(n) = \lim_{z\to 1}(z-1)X(z) \end{align*}

Aurora - A LaTeX Plugin for Microsoft Word

Sat, 29 Feb 2020 00:00:00 +0000

Aurora is an excellent LaTeX addon, which enables LaTeX based mathematical support, including a variety of symbols and equations.

For Microsoft Office-32, there is a dedicated tab for Aurora in Word. For Office-64, however, there is no tab at all. In this case, aurora has to be activated by insert → object. Clearly, the access is neither direct nor convenience. Targetting better convenience, macros can be defined and then placed in a card, e.g., following scripts define two macros, aurora_inline and aurora_display, to input inline and display style equations.

Blog on GitHub

Sat, 29 Feb 2020 00:00:00 +0000

It has been quite a long time for me not to write and publish blog since Google blogspot and WordPress were blocked. Recently, I have built a new blog site on GitHub. This post is just written to summarize the procedure.

Preparation

Softwares

Above all, you should have Emacs and Orgmode installed. Taking ArchLinux for instance, Emacs can be installed as follows

pacman -S emacs

The installation of Orgmode can be avoided since it has been already included as a built-in plugin.

In order to freely exchange data with GitHub, git is needed. Also taking ArchLinux for example, the installation can be performed by

pacman -S git

Account on GitHub

Of course, an account on GitHub is also indispensable. If you do not have an account, you have to sign up on http://github.com. According to the description of GitHub Pages, if your account is USERNAME, your blog site can be accessed via http://USERNAME.github.io.

C/C++ - switch

Sat, 29 Feb 2020 00:00:00 +0000

在C/C++语言中， switch 语句的通用格式为

switch (int_expr)
{
 case label1: statement(s)
 case label2: statement(s)
 ...
 default: statement(s)
}

顾名思义， int_expr 必须是一个结果为整数值的表达式。另外，每个标签都必须是整数常量表达式。最常见的标签是 int 或 char 常量（如1或‘a’），也可以是枚举常量。C++中的 case 标签只是行标签，而不是选项之间的界限。也就是说，程序跳到 switch 中特定代码后，将依次执行之后的所有语句，除非有明确的其他指示。程序不会执行到下一个 case 处自动停止，要让程序执行完一组特定语句后停止，必须使用 break 语句。这将导致程序跳到 switch 后面的语句处执行。

关于将枚举量用作标签，通常， cin 无法识别枚举类型（它不知道程序员是如何定义它们的），因此程序要求用户选择选项时输入整数。当 switch 语句将 int 值和枚举量标签进行比较时，将枚举量提升为 int 。另外，在 while 循环测试条件中，也会将枚举量提升为 int 类型。

C++ - IT++

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

IT++¹ is a powerful C++ library, which is widely employed in the area of communication, esp. in simulation programming and computing. It has provided a variety of useful classes, e.g. vector, matrix. With the aid of IT++, programming in C++ is very similar to programming in MATLAB.

IT++ is released under GPL, and can work on all the platforms, including Unix/Linux, Windows an Mac OS X.

Installation

Optionally, its functionality can be greatly extended based on existing open-source or commercial libraries, i.e.

Open-source libraries
- BLAS
- LAPACK
- FFTW
Commercial libraries
- ATLAS
- MKL
- ACML

Install the third-party libraries

Herein, we take the open-source libraries above for instance. For ArchLinux, the installation can be performed by

pacman -S blas lapack fftw

Install IT++

The lastest version of IT++ can be obtained via git, and installed to /opt/itpp by following commands.

git clone --depth=1 git://git.code.sf.net/p/itpp/git itpp-git
cd itpp-git
mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=/opt/itpp
make
make install
make clean
cd ..
rm -rf build

What deserves notice, the commands above installs the shared libraries. For the static version, option -DITPP_SHARED_LIB=off of cmake should be used.

BTW, HTML documentation will be installed by default. Therefore, doxygen needs to be installed in advance. Otherwise, the documentation installation should be disabled by -DHTML_DOCS=off option of cmake.

C++ - Multithread

Sat, 29 Feb 2020 00:00:00 +0000

背景

C++98/03不支持多线程编程, 所以必须借助第三方库或目标操作系统中的多线程API. 这使得编写跨平台的多线程程序很困难. C++11引入了标准的多线程库, 使得多线程程序跨平台更加容易. 目前的C++11标准仅针对CPU, 不支持GPU.

多线程编程的难点之一是将算法并行化, 这个过程和算法的类型高度相关. 此外, 要防止竞争条件和死锁, 并考虑缓存的一致性.

竞争条件: 当多个线程要读/写共享内存位置时, 可能会发生竞争条件.
死锁: 线程因为等待另一个阻塞线程锁定的资源而造成的无限阻塞.
撕裂: 部分数据已写入内存, 但还有部分数据没有写入. 如果另一个线程在此时读取数据, 就会得到不一致的数据.
缓存的一致性: 如果一个线程写入了一段数据, 该线程会立即看到新数据, 但这并不意味着所有线程都会立即看到新数据. 所以, 在读写多个线程时, 即使是最简单的数据类型, 也需要同步.

线程

C++线程库定义在头文件 <thread> 中.

通过函数指针创建线程

标准C++的 thread 类的构造函数是一个可变参数模板, 可以接受任意数目的参数. 第一个参数为函数名称, 其余参数为函数的参数. 如

 #include <thread>

 using namespace std;

 void f(int i, double j, bool k);

 int main(int argc, char *argv[])
 {
 thread t(f, 1, 2.0, true);
 t.join();
 return 0;
 }

默认情况下, 从不同线程中访问cout是线程安全的, 没有任何数据竞争, 除非在第一个输出或输入操作之前调用了 cout.sync_with_stdio(false).

通过函数对象创建线程

使用函数指针技术, 向线程传递信息的唯一方式是向函数传递参数. 而使用函数对象, 可向函数对象类添加成员变量, 并可以采用任何方式初始化和使用这些变量. 如

 #include <thread>

 using namespace std;

 class A
 {
 public:
 A(int i, double j, bool k);
 void operator()(int i);
 };

 int main(int argc, char *argv[])
 {
 thread t(A(1));
 t.join();
 return 0;
 }

函数对象总是复制到线程的某个内部存储中. 如果要在函数对象的某个特定实例上执行 operator() 而非进行复制, 那么应该使用头文件 <functional> 中的 std::ref() 或 std::cref() 传入该实例的引用或常引用.

通过lambda表达式创建线程

如

 #include <thread>

 using namespace std;

 int main(int argc, char *argv[])
 {
 int i = 3;
 thread t([&i]{i += 1;});
 t.join();
 return 0;
 }

通过成员函数创建线程

第一个参数为成员函数指针, 第二个参数为类对象指针, 其余参数为成员函数的参数.

 #include <thread>

 using namespace std;

 class A
 {
 public:
 A(int i, double j, bool k);
 void process(int i);
 };

 int main(int argc, char *argv[])
 {
 A a(1, 2.0, true);
 thread t{&A::process, &a, 3};
 return 0;
 }

线程本地存储

通过关键字 thread_local, 可将任何变量标记为线程本地数据, 即每个线程都有这个变量的独立副本, 而且这个变量能在线程的整个生命周期中持续存在. 对于每个线程, 该变量正好初始化一次.

如果 thread_local 变量在函数作用域中声明, 那么这个变量的行为和声明为静态变量是一致的, 只不过每个线程都有自己独立的副本, 而且不论这个函数在线程中调用多少次, 每个线程只初始化一次这个变量.

以下代码中, 多个线程共享唯一的j副本, 而每个线程都有自己的i副本.

 thread_local int i;
 int j;
 void process();

取消线程

标准没有在一个线程中取消另一个线程的机制. 实现这一目标的最好方法是提供两个线程都支持的某种通信机制. 最简单的机制是有一个共享变量, 目标线程定期检查这个变量, 判断是否应该终止. 其他线程可以设置这个共享变量, 间接指示线程关闭. 应避免读写这个共享变量带来的竞争条件和缓存一致性问题.

从线程获得结果

通过 future 能够方便地从线程获得结果, 也能方便地处理线程中发生的错误.

复制和重新抛出异常

每个线程都可以抛出自己的异常, 但它们必须在自己的线程内捕获异常. 一个线程抛出的异常不能在另一个线程中捕获. 使用 future 可以自动在线程之间传递异常.

C++ - Polymorphism

Sat, 29 Feb 2020 00:00:00 +0000

简介

多态是C++语言的一大特色。一个操作随着所传递或捆绑的对象类型的不同能够做出不同的反应，其行为模式称为多态¹。而且，仅仅对于对象的指针和引用的间接访问，才会发生多态。

虚函数

在使用类的C++语言中，抽象编程需要使用 虚函数 机制。基类与派生类的同名操作，只要标记上 virtual² ，则该操作（虚函数）便具有多态性。一旦标记基类的函数为虚函数，便有连锁反应，后面继承的类中一切同名成员函数都变成了虚函数。这样一来，如果实际对象是基类对象，那么调用的就是基类成员函数；如果实际对象是派生类对象，那么调用的就是派生类成员函数。

虚函数仅用于继承结构层次中的基类和派生类。除了基类和派生类的函数名必须相同外，连参数类型、个数和顺序都要相同。也就是说，基类和派生类的虚函数不能只是名字重载，而且要一模一样³。

只有类的成员函数才能声明为虚函数。
静态成员函数不能是虚函数。
内联函数不能是虚函数。
构造函数不能是虚函数。
析构函数可以是且通常声明为虚函数。

纯虚函数

纯虚函数是指被标明为不具体实现的虚函数。纯虚函数一旦声明，就不用定义。声明形式是在虚函数声明形式后跟“ = 0”。

抽象类

抽象类是指在类定义中至少声明一个纯虚函数的类。抽象类是不允许有实例对象的，即不能由抽象类创建实例对象，其用途只是为了继承。

总结

总之, 要想实现多态, 必须用虚函数(在基类中用关键字virtual). 对于派生类, 必须对虚函数进行实现. 对于基类, 有两个选择: 第一, 实现虚函数; 第二, 将虚函数声明为纯虚函数(相应地, 基类也就变成了抽象类).

Footnotes

钱能，“C++程序设计教程（第二版）”，清华大学出版社，2005年。

虚函数在继承层次结构中总是会自动地从基类传播下去。因此，派生类中的虚函数的标识（virtual）可以省略。

但是返回值可以不同。

C++ - 标准库

Sat, 29 Feb 2020 00:00:00 +0000

本文是阅读 Professional C++, third edition 中文版¹的读书笔记.

C++标准库的核心是泛型容器和泛型算法. 包括标准模板库(Standard Template Library, STL).

所有标准库类和函数都在 std 名称空间中声明. 包括如下组件:

字符串

定义在头文件 <string> 中的 string 类.

正则表达式

定义在头文件 <regex>.

I/O流

定义在头文件 <fstream>, <iomanip>, <ios>, <iosfwd>, <iostream>, <istream>, <ostream>, <sstream>, <streambuf> 和 <strstream> 中.

智能指针

定义在头文件 <memory> 中的 unique_ptr, shared_ptr, weak_ptr.

异常

定义在头文件 <exception>, <stdexcept> 和 <system_error>.

数学工具

定义在头文件 <complex> 中的复数类 complex.
定义在头文件 <ratio> 中的有理数运算库.
定义在头文件 <valarray> 中的 valarray 类(与 vector 类类似, 但是对高性能数值应用做了特别的优化).
定义在头文件 <limits> 中的 numeric_limits 类模板, 如
- numeric_limits<int>::max()
- numeric_limits<int>::min()
- numeric_limits<int>::lowest()
- numeric_limits<double>::max()
- numeric_limits<double>::min()
- numeric_limits<double>::lowest()

时间工具

定义在头文件 <chrono> 中的 Chrono 库.

随机数

定义在头文件 <random> 中的随机数库.

初始化列表

定义在头文件 <initializer_list> 中的初始化列表(用于编写参数数目可变的函数).

Pair

定义在头文件 <utility> 中的 pair 模板, 用于存储两种不同类型的元素. 这称为存储异构元素. 每个值的类型都应该在编译时确定. C++14添加了一个功能, 允许根据类型使用 std::get<T>() 从tuple中提取元素, 其中T是要提取的元素的类型(而不是索引). 创建tuple的另一种方法是使用 std::make_tuple() 工具函数. 这个函数只需要实际值, 在编译时会自动推导出类型(所以不能通过 & 来指定引用). 如果需要通过 make_tuple() 生成一个包含引用或常量引用的tuple, 那么需要分别使用定义在头文件 <functional> 中的 ref() 和 cref(). 通过 std::tuple_cat() 可将两个tuple串联为一个tuple.

Tuple

定义在头文件 <tuple> 中的 tuple 是 pair 的一种泛化, 它是固定大小的序列, 元组的元素可以是异构的, 其实例化的元素数目和类型在编译时固定不变.

函数对象

实现了函数调用运算符的类的对象称为函数对象. 函数对象可以用作某些STL算法的谓词. 头文件 <functional> 定义了一些预定义的函数对象, 支持根据已有的函数对象创建新函数对象.

多线程

单个线程可以用头文件 <thread> 中的 thread 类创建.
定义在头文件 <atomic> 中的原子性提供了对一段数据的线程安全的原子访问.
<condition_variable> 和 <mutex> 提供了其他线程同步机制.
如果只需计算某个数据得到结果, 并具有相应的异常处理, 使用定义在头文件 <future> 中的 async 和 future 要比直接使用 thread 类更容易.

类型特质

定义在头文件 <type_traits> 中的类型特质提供了编译期间的类型信息. 编写高级模板时可以使用它.

Footnotes

Marc Gregoire著, 张永强译. C++高级编程(第3版), 清华大学出版社, 2015.

Convex Optimization

Sat, 29 Feb 2020 00:00:00 +0000

A mathematical optimization problem can be expressed as

\begin{align*} \min & f_0(x) \\ \text{subject to} & f_i(x) \le b_i, \quad i=1, \ldots, m \end{align*}

where

$x = (x_1, \ldots, x_n)$ are optimization variables.
$f_0: \mathbf{R}^n \to \mathbf{R}$ is objective function.
$f_i: \mathbf{R}^n \to \mathbf{R}, i=1, \ldots, m$ are constraints functions.

Optimal solution $x^\star$ has the smallest value of $f_0$ among all vectors that satisfy the constraints.

In fact, a general optimization problem is very difficult to solve. Its solution cannot always be found. Even though it can, it suffers some compromise, e.g. very long computation time.

DOT

Sat, 29 Feb 2020 00:00:00 +0000

DOT ¹ is a language for drawing graphs. It has three main kinds of objects, graph, node and edge. Each object has a variety of attributes. Given a node or edge, its attribute(s) can be set as below respectively

NODE_NAME [ATTRIBUTE1=VALUE1, ATTRIBUTE2=VALUE2, ...];
NODE_NAME1 -> NODE_NAME2 [ATTRIBUTE1=VALUE1, ATTRIBUTE2=VALUE2, ...];

And the default values can be specified as below. And they will take effect afterwards.

node [ATTRIBUTE1=VALUE1, ATTRIBUTE2=VALUE2, ...];
edge [ATTRIBUTE1=VALUE1, ATTRIBUTE2=VALUE2, ...];

graph

A graph can be directed or undirected, corresponding to digraph and graph, respectively. Within a graph, a subgraph can be defined as a subset of nodes and edges.

rankdir

TB: from top to bottom (default value)
BT: from bottom to top
LR: from left to right
RL: from right to left

size

size="x,y"

ratio

rotate

nodesep

Separation between nodes of the same rank in inches.

ranksep

Separation between ranks in inches.

Emacs - Basic Configuration

Sat, 29 Feb 2020 00:00:00 +0000

As is well-known, Emacs is a powerful editor. Due to its infinite customizability and extensibility, in some sense, it is an operation system (OS) rather than an editor. This page briefly introduces how to customize it.

Set values for predefined variables

(setq variable value)

Bind shortcut keys

Set global shortcut key

(global-set-key key command)

where key is shortcut¹, e.g. M-SPC, <f7>, and command is the command name with a prefix of single quotation mark.

Set shortcut key for specific modes

(define-key keymap key command)

where keymap is associated to some mode, e.g. c-mode-map. Usually, each mode has its own keymap, which is the mode name appended with -map.

Emacs - C/C++ Programming

Sat, 29 Feb 2020 00:00:00 +0000

This page is written to summarize my configuration for C/C++ programming with Emacs.

Besides Emacs, following extensions are also needed. The installation can be finished by the built-in package manager, elpa. Before the installation, following configuration in ~/.emacs for elpa is necessary.

(setq package-archives '(("gnu" . "http://elpa.gnu.org/packages/")
 ("melpa" . "http://melpa.milkbox.net/packages/")))
(package-initialize)

Through elpa, install following extensions.

company: It represents complete anything. Just as its name implies, it is used for completion. It is similar to auto-complete, but I prefer company. In order to enable automatical completion in C/C++ programming, I use clang ¹ as backend in lieu of semantic, since semantic-based completion is too slow. However, as long as company is installed, semantic is already built-in, a.k.a. company-semantic. Moreover, it precedes clang-based backend. To deal with the problem, we remove semantic from the list of backend for company.

(global-company-mode t)
(setq company-idle-delay 0)
(setq company-backends (delete 'company-semantic company-backends))
(add-to-list 'company-backends 'company-c-headers)

BTW, for sake of completion based on other third-party libraries, we can create an elisp file .dir-locals.el in the project root. E.g. ITPP library installed in /opt/itpp.

Emacs - CDLaTeX

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

CDLaTeX¹ is a minor mode for fast LaTeX environment and macro insertion². In this sense, its functionalities are very similar to AUCTeX³. What's more, some of its convenience provided are also covered by AUCTeX.

Installation

The package of cdlatex is available at melpa, which can be easily installed.

Configuration

If AUCTeX is installed, CDLaTeX can be activated on top of it via

(add-hook 'LaTeX-mode-hook 'turn-on-cdlatex)

Otherwise, CDLaTeX can be directly turned on with latex mode, i.e.,

(add-hook 'latex-mode-hook 'turn-on-cdlatex)

Org

In org mode, instead of CDLaTeX itself, its light version org-cdlatex-mode should be used, which depends on cdlatex.el (in package CDLaTeX) and texmathp (in package AUCTeX). To automatically turn it on in a org file, add the following line in the emacs configuration file, e.g., ~/init.el.

(add-hook 'org-mode-hook 'turn-on-org-cdlatex)

Emacs - CEDET

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

CEDET¹ stands for collection of Emacs development environment tools, which is written to make Emacs become a perfect development environment. With the aid of CEDET, a variety of amazing features can be provided, e.g. code completion, browsing, tag jumping, drawing UML diagram, etc.

Installation

Through following commands, the latest version of CEDET can be installed into ~/.emacs.d/cedet.

cd ~/.emacs.d
git clone http://git.code.sf.net/p/cedet/git cedet
make

Configuration

;; load CEDET
(add-to-list 'load-path "~/.emacs.d/cedet")
(load-file "~/.emacs.d/cedet/cedet-devel-load.el")

;; enable the required features
(semantic-load-enable-minimum-features)
(semantic-load-enable-code-helpers)
(semantic-load-enable-gaudy-code-helpers)
(semantic-load-enable-excessive-code-helpers)
(semantic-load-enable-semantic-debugging-helpers)
(add-to-list 'semantic-default-submodes 'global-semantic-idle-summary-mode t) 
(add-to-list 'semantic-default-submodes 'global-semantic-idle-completions-mode t) 
(add-to-list 'semantic-default-submodes 'global-cedet-m3-minor-mode t) 
(add-to-list 'semantic-default-submodes 'global-semanticdb-minor-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-idle-scheduler-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-decoration-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-show-unmatched-syntax-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-show-parser-state-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-highlight-edits-mode t)
(add-to-list 'semantic-default-submodes 'global-semantic-highlight-func-mode t)

;; enable semantic mode
(semantic-mode 1)

;; enable semantic to access and parse the headers of system libaries, e.g. /usr/include, /usr/local/include, /opt/itpp/include.
(setq semantic-c-dependency-system-include-path (quote ("/usr/include" "/usr/local/include" "/opt/itpp/include")))
(require 'semantic/ia)
(require 'semantic/bovine/gcc)

;; jump to tags
(global-set-key (kbd "M-.") 'semantic-ia-fast-jump)

;; jump back from tags
(global-set-key (kbd "M-*") 'semantic-mrub-switch-tags)

Footnotes

http://cedet.sourceforge.net/

Emacs - Company

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Auto-completion is an important functionality in Emacs. It can greatly speed up our editing and programming. Generally speaking, the auto-completion can be divided into two parts, frontend and backend. As their names indicate, the former presents interface, while the latter provides contents. In a nutshell, the backend generates completion contents and feeds them to the frontend; then the frontend presents completion candidates to us for selection.

Up to now, there are a couple of popular frontends, auto-complete¹ and company². The word "company" stands for "complete anything". In fact, their functionalities are very similar. Both of them work well and their developments are fairly active. Both of them come with a variety of built-in backends. What's more, you can customize your own backends for your special requirements.

It should be noticed that each of the both above provides backend for C/C++ programming, e.g. company-clang is a powerful backend based on clang. It enables company completing based on the semantic analysis provided by clang. With the aid of this backend, the programming experience and efficiency can be remarkably improved.

For myself, I have been using company since I began to use Emacs. Therefore, I just summarize the installation and configuration of company in this post.

Emacs - Flycheck

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Flycheck¹ is a on-the-fly syntax checking extension of Emacs, which supports a variety number of programming languages. It greatly facilitates the programming experience.

Installation

Flycheck can be directly installed via ELPA.

M-x package-install
flycheck

Configuration

;; Enable global flycheck mode
(add-hook 'after-init-hook #'global-flycheck-mode)

;; Clang support (C++14)
(setq flycheck-clang-language-standard "c++14")

;; Elpy support (use flycheck instead of flymake)
(setq elpy-modules (delete 'elpy-module-flymake elpy-modules))
(add-hook 'elpy-mode-hook 'flycheck-mode)

Footnotes

http://www.flycheck.org/

Emacs - Helm

Sat, 29 Feb 2020 00:00:00 +0000

Helm¹ is a framework to narrow selection. It can be installed by ELPA

M-x package-install
helm

After that, it should be configured accordingly. Without loss of generality, following configurations can be used.

(require 'helm-config)
(helm-mode 1)
(define-key global-map [remap find-file] 'helm-find-files)
(define-key global-map [remap occur] 'helm-occur)
(define-key global-map [remap list-buffers] 'helm-buffers-list)
(define-key global-map [remap dabbrev-expand] 'helm-dabbrev)
(define-key global-map [remap switch-to-buffer] 'helm-mini)
(define-key global-map [remap yank-pop] 'helm-show-kill-ring)
(define-key global-map [remap execute-extended-command] 'helm-M-x)

;; fuzzy match
(setq helm-M-x-fuzzy-match t
 helm-buffers-fuzzy-matching t
 helm-recentf-fuzzy-match t)

;; follow mode
(helm-follow-mode-persistent t)

Alternatively, package helm-ag can be installed to accelerate the match, which is a the-silver-searcher-based multithread counterpart of ack. Helm-ag and the-silver-searcher can be installed by

Emacs - Language Server Protocol

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Language server protocol (LSP) offers a uniform specification between a client and a server¹.

The Language Server protocol is used between a tool (the client) and a language smartness provider (the server) to integrate features like auto complete, go to definition, find all references and alike into the tool

With LSP, different clients and development tools, e.g., integrated development environment (IDE), can share a common server. Taking C/C++ for instance, various clients, e.g., Emacs, Vim, Eclipse, etc. can communicate with a common server with their own clients. For Emacs, its client is enbodied as a mode, lsp-mode².

Maskray has provided a good summary of cquery for reference³. This post just records the installation and configuration of LSP for C/C++.

Emacs - Movement

Sat, 29 Feb 2020 00:00:00 +0000

Character-wise movement

Key binding	Purpose
`C-f`	Move forward by a character
`C-b`	Move backward by a character
`C-p`	Move to previous line
`C-n`	Move to next line

Word-wise movement

Key binding	Purpose
`M-f`	Move forward by a word
`M-b`	Move backward by a word

Line-wise movement

Key binding	Purpose
`C-a`	Move point to the beginning of the line
`C-e`	Move point to the end of the line
`M-m`	Move point to the first non-whitespace character on this line

Sexp-wise movement

Key binding	Purpose
`C-M-f`	Move forward by a s-expression (sexp)
`C-M-b`	Move backward by a sexp

List-wise movement

Key binding	Purpose
`C-M-p`	Move backward to the previous list
`C-M-n`	Move forward to the next list
`C-M-u`	Move up out of a list
`C-M-d`	Move down into a list

Sentence-wise movement

Key binding	Purpose
`M-a`	Move to the beginning of a sentence
`M-e`	Move to the end of a sentence

Paragraph-wise movement

Key binding	Purpose
`M-{`	Move to the beginning of a paragraph
`M-}`	Move to the end of a paragraph

Defun-wise movement

Key binding	Purpose
`C-M-a`	Move to the beginning of a defun
`C-M-e`	Move to the end of a defun

Page-wise movement

Key binding	Purpose
`C-x [`	Move backward by a page
`C-x ]`	Move forward by a page
`C-v`	Scroll down a page
`M-v`	Scroll up a page
`C-M-v`	Scroll down the other window
`C-M-S-v`	Scroll up the other window
`M-<`	Move to the beginning of the buffer
`M->`	Move to the end of the buffer

Emacs - Mu4e

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

mu4e is an excellent mail client for Emacs whereby sending/getting mails can be carried out in Emacs. For an Emacs user, the deep integration gives rise to great convenience and efficiency. This post provides a brief summary for the utilization of mu4e.

Installation

Dependencies

mu depends on xapian and gmime, which should be installed in advance.

pacman -S xapian-core gmime

`mu`¹

git clone --depth=1 git://github.com/djcb/mu.git
cd mu
autoreconf -i
./configure --prefix=/opt/mu
make
make install
ln -s /opt/mu/bin/mu /usr/local/bin

`getmail` and `procmail`

pacman -S getmail procmail

Configuration

`getmailrc`

 [retriever]
 type = SimplePOP3SSLRetriever
 server = POP_SERVER
 port = PORT_NUM
 username = USER_NAME
 password = PASSWORD

 [destination]
 type = MDA_external
 path = /usr/bin/procmail

 [options]
 read_all = false
 delete = false
 verbose = 0
 message_log = $HOME/.Mail/getmail.log

`~/.procmailrc`

 MAILDIR=$HOME/.Mail
 DEFAULT=$MAILDIR/inbox/
 LOGFILE=$MAILDIR/procmail.log
 VERBOSE=yes

 :0:
 ,* ^(To|Cc): 3GPP_TSG_RAN_WG1@LIST.ETSI.ORG
 r1/

 :0:
 ,* ^(To|Cc): 3GPP_TSG_RAN_WG1_NR@LIST.ETSI.ORG
 r1nr/

 :0:
 ,* ^(To|Cc): 3GPP_TSG_RAN@LIST.ETSI.ORG
 rp/

`~/.emacs.d/init.el`

 (add-to-list 'load-path "/opt/mu/share/emacs/site-lisp/mu4e")
 (require 'mu4e)
 (require 'org-mu4e)

 (setq user-full-name "NAME"
 user-mail-address "EMAIL_ADDRESS"
 mu4e-compose-signature "SIGNATURE")

 (setq mu4e-maildir "~/.Mail"
 mu4e-drafts-folder "/drafts"
 mu4e-sent-folder "/sent"
 mu4e-trash-folder "/trash")

 (setq mu4e-headers-fields '((:human-date . 12)
 (:flags . 6)
 (:mailing-list . 10)
 (:from . 22)
 (:thread-subject)))

 (setq message-send-mail-function 'smtpmail-send-it
 smtpmail-default-smtp-server "SMTP_SERVER"
 smtpmail-smtp-server "SMTP_SERVER"
 smtpmail-stream-type 'starttls
 smtpmail-smtp-service PORT_NUM)

 (setq mu4e-get-mail-command "getmail --getmaildir=GETMAIL_CONFIG_DIR -r getmailrc")

 (setq mail-user-agent 'mu4e-user-agent
 mu4e-user-mail-address-list '("EMAIL_ADDRESS")
 mu4e-completing-read-function (quote completing-read)
 mu4e-confirm-quit nil
 mu4e-attachment-dir "~/Downloads"
 mu4e-html2text-command "w3m -dump -T text/html -M"
 mu4e-use-fancy-chars t
 mu4e-view-show-images t
 mu4e-view-show-addresses t
 mu4e-update-interval 180
 mu4e-change-filenames-when-moving t
 message-kill-buffer-on-exit t
 org-mu4e-convert-to-html t)

`~/.authinfo`

machine SMTP_SERVER login USER password PASSWORD port PORT_NUM

Others

Create a maildir

mkdir .Mail

Get the mails

getmail --getmaildir=GETMAIL_CONFIG_DIR -r getmailrc

Index the mails

mu index --maildir=~/.Mail

Footnotes

mu4e is essentially a part of mu.

Emacs - Wanderlust

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Wanderlust is also a mail client within Emacs. This post aims to summarize the procedure of its installation and configurations.

Installation

Wanderlust can be directly installed via ELPA. APEL, SEMI and FLIM are also installed as dependency.

Configuration

We postulate that all the mails are stored in ~/.Mail, in which there are a plurality of Maildir folders, e.g., draft, queue, sent, trash, boc, edas, home, office, linkedin, r1, r1nr, rp. Mails are periodically fetched by getmail or offlineimap, e.g.,

 */10 * * * * /usr/bin/getmail --new --getmaildir=/PATH/TO/GETMAILRC --rcfile=GETMAILRC

 */10 * * * * /usr/bin/offlineimap -c /PATH/TO/OFFLINEIMAPRC -a ACCOUNT

In this case, following configurations are needed for wanderlust.

~/.config/emacs/init.el

 (use-package wl
 :ensure wanderlust
 :init
 (require 'mime-w3m)
 (autoload 'wl "wl" "Wanderlust" t)
 (autoload 'wl-other-frame "wl" "Wanderlust on new frame." t)
 (autoload 'wl-draft "wl-draft" "Write draft with Wanderlust." t)
 (autoload 'wl-user-agent-compose "wl-draft" nil t)
 :config
 (if (boundp 'mail-user-agent)
 (setq mail-user-agent 'wl-user-agent))
 (if (fboundp 'define-mail-user-agent)
 (define-mail-user-agent
 'wl-user-agent
 'wl-user-agent-compose
 'wl-draft-send
 'wl-draft-kill
 'mail-send-hook))
 :custom
 (wl-from "Shaka <shaka@company.com>")
 (org-mime-library 'semi)
 (wl-folder-check-async t)
 (wl-stay-folder-window t)
 (wl-fcc-force-as-read t)
 (wl-interactive-exit nil)
 (wl-insert-message-id nil)
 (wl-quicksearch-folder "[]")
 (elmo-search-default-engine 'notmuch)
 ;; Folders
 (wl-folder-desktop-name "xi")
 (wl-folders-file "~/.config/emacs/xi/folders")
 (elmo-maildir-folder-path "~/.Mail")
 (elmo-localdir-folder-path "~/.Mail")
 (wl-temporary-file-directory "/tmp")
 (wl-default-spec ".")
 (wl-trash-folder ".trash")
 (wl-fcc ".sent")
 (wl-draft-folder ".draft")
 (wl-queue-folder ".queue")
 (wl-summary-auto-refile-skip-marks nil)
 ;; Auto refile
 (wl-refile-rule-alist
 '((("To" "Cc")
 (".*3gpp_tsg_ran@list\\.etsi\\.org.*" . ".~/.Mail/rp")
 (".*3gpp_tsg_ran_wg1@list\\.etsi\\.org.*" . ".~/.Mail/r1")
 (".*3gpp_tsg_ran_wg1_nr@list\\.etsi\\.org.*" . ".~/.Mail/r1nr"))
 ("From"
 (".*personalservice@bank-of-china\\.com.*" . ".~/.Mail/boc")
 (".*10000bj@189\\.cn.*" . ".~/.Mail/telecomm")
 (".+@linkedin\\.com.*" . ".~/.Mail/linkedin"))
 ("Subject" (".*EDAS-CFP.*" . ".~/.Mail/edas"))
 ("To"
 (".*shaka@home\\.com.*" . ".~/.Mail/home")
 (".*shaka@company\\.com.*" . ".~/.Mail/office"))))
 ;; Send mail with msmtp.
 (wl-draft-send-mail-function 'wl-draft-send-mail-with-sendmail)
 (message-sendmail-envelope-from 'header)
 (mail-envelope-from 'header)
 (mail-specify-envelope-from t)
 (sendmail-program "/usr/bin/msmtp")
 ;; Appearance
 (mime-header-accept-quoted-encoded-words t)
 (wl-message-ignored-field-list '("."))
 (wl-message-visible-field-list '("^Subject:" "^Date:" "^From:" "^\\(To\\|Cc\\):"))
 (wl-summary-width 100)
 (wl-biff-check-folder-list '(".~/.Mail/home" ".~/.Mail/office"))
 (wl-summary-line-format "%5(%n%) %3(%T%P%) %15(%f%) %23(%Y-%M-%D(%W) %h:%m%) %t%C%s"))

~/.config/emacs/xi/folders

.~/.Mail/home "home"
home{
.~/.Mail/boc "boc"
.~/.Mail/telecomm "telecomm"
.~/.Mail/linkedin "linkedin"
.~/.Mail/edas "edas"
}

.~/.Mail/office "office"
office{
.~/.Mail/rp "rp"
.~/.Mail/r1 "r1"
.~/.Mail/r1nr "r1nr"
}

.~/.Mail/sent "sent"
.~/.Mail/draft "draft"
.~/.Mail/trash "trash"

# %INBOX:shaka/clear@imap.home.com:143 "home"
# %INBOX:shaka/clear@imap.company.com:993! "office"

Emacs - YCMD

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

YouCompleteMe (YCM) is originally a completion framework for VIM¹, and afterwards splitted into a general server and a client. The general server, namely YCM daemon (YCMD)², is able to provide interface to a variety of clients beyond VIM, e.g. Emacs. Moreover, both company and auto-complete can directly utilize what the server/daemon provides.

Installation

Emacs packages

Install the Emacs packages via ELPA, ycmd, company-ycmd, company.

Dependency

pacman -S boost

YCMD

Install the YCMD to ~/.emacs.d/ycmd.

cd ~/.emacs.d
git clone https://github.com/Valloric/ycmd.git
cd ycmd
git submodule update --init --recursive
./build.py --clang-completer --system-libclang --system-boost

Configurations

~/.emacs.d/ycmd/global_config.py

cp ~/.emacs.d/ycmd/examples/.ycm_extra_conf.py ~/.emacs.d/ycmd/global_config.py

After that, customize it to meet your requirements.

~/.emacs

...

;;; Company
(add-hook 'after-init-hook 'global-company-mode) 
(setq company-idle-delay 0) 
(company-auctex-init) 

;;; Ycmd
(add-hook 'after-init-hook #'global-ycmd-mode)
(set-variable 'ycmd-server-command '("python2" "/home/shaka/.emacs.d/ycmd/ycmd"))
(set-variable 'ycmd-global-config "/home/shaka/.emacs.d/ycmd/global_config.py") 
(company-ycmd-setup)

...

GitLab

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Gitlab is a code management service based on git. It is very powerful and suitable to collaborated development within a team.

Installation

Generally speaking, the deployment of gitlab is very difficult since it depends on many compenents, e.g., database, http server, etc. However, there is corresponding docker image of gitlab, which are ready. Consequently, gitlab can be easily deployed via docker. The procedure can be summarized as follows.

pacman -S docker
systemctl enable docker
systemctl start docker
docker pull gitlab/gitlab-ce:latest
sudo docker run --detach --hostname localhost --net host --publish 443:443 --publish 80:80 --publish 22:22 --name gitlab --restart always --volume /srv/gitlab/config:/etc/gitlab --volume /srv/gitlab/logs:/var/log/gitlab --volume /srv/gitlab/data:/var/opt/gitlab gitlab/gitlab-ce:latest

GRUB

Sat, 29 Feb 2020 00:00:00 +0000

GRUB is a powerful bootloader which can boot a variety of operation systems, including Unix, Linux and Windows. It is usually installed in the MBR of a disk. This article presents the method how to repair it if it is corrupted.

Above all, open a terminal or switch to a tty, then input commands below step by step:

type grub to enter the interface of GRUB.
if separate /boot partition exists, input find /grub/stage1; otherwise, input find /boot/grub/stage1 instead.
indicate the location for GRUB installation, root (hdX, Y).
set up GRUB to hdX ’s MBR, setup (hdX).
quit the GRUB program, quit.

LaTeX - Gantt Chart

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Today, I found an interesting $\LaTeX$ package, pgfgantt. This package provides a ganttchart environment and, as its name indicates, can produce Gantt charts.

Usage

The framework of using the package can be illustrated as

 \usepackage{pgfgantt}
 ...
 \begin{ganttchart}[OPTIONS]{STARTING}{ENDING}
 TITLE
 CHARTELEMENT
 \end{ganttchart}

where

OPTIONS can be
- time slot format with candidates: simple / isodate / isodate-yearmonth / isodate-year / little-endian / middle-endian / big-endian.
- newline shortcut can turn \\ into a new line break, equivalent to \ganttnewline.
- vgrid / hgrid specifies the presence and appearance of the vertical/horizontal grids.
- today can indidate the current day/month/year by a vertical rule at the provided time.
- today label can specify the label for today.
- inline can put the labels inside the corresponding bars.
- x unit / y unit
- x unit title / y unit title
- x unit chart / y unit chart
- expand chart can automatically expand the chart horizontally, e.g., \textwidth.
STARTING is the starting date of the chart.
ENDING is the ending date of the chart.
TITLE can be
- \gantttitle[OPTIONS]{LABEL}{NUMBEROFTIMESLOTS}
- \gantttitlelist[OPTIONS]{LABELLIST}{LENGTHOFEACHELEMENT} defines a series of \gantttitle in a batch way.
- \gantttitlecalendar[OPTIONS]{CALENDARLINES} with CALENDARLINES a comma-separated list of lines, e.g., decade, year, month=name/shortname, day, week, weekday=name/shortname, etc.
- \gantttitlecalendar*[OPTIONS]{STARTING}{ENDING}{CALENDARLINES} is similar to \gantttitlecalendar[OPTIONS]{CALENDARLINES} but constrained to a range defined by STARTING and ENDING.
CHARTELEMENT is predefined chart elements as follows.
- \ganttgroup[OPTIONS]{LABEL}{STARTING}{ENDING} combines several subtasks (bars) into a single task.
- \ganttbar[OPTIONS]{LABEL}{STARTING}{ENDING} indicates the duration of a task/subtask.
- \ganttmilestone[OPTIONS]{LABEL}{TIME} signifies a milestone, e.g., the completion of a task.
- \ganttlinkedgroup[OPTIONS]{LABEL}{STARTING}{ENDING} is similar to \ganttgroup[OPTIONS]{LABEL}{STARTING}{ENDING} but additionally draws a link from the previous element.
- \ganttlinkedbar[OPTIONS]{LABEL}{STARTING}{ENDING} is similar to \ganttbar[OPTIONS]{LABEL}{STARTING}{ENDING} but additionally draws a link from the previous element.
- \ganttlinkedmilestone[OPTIONS]{LABEL}{TIME} is similar to \ganttmilestone[OPTIONS]{LABEL}{TIME} but additionally draws a link from the previous element.
CHARTELEMENT has an interesting option progress, whose value can be none / today / PERCENTILE.

LaTeX - Pgfplots

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Pgfplots is an excellent LaTeX package to plot high quality graphs. This post just summaries its basic usages.

Installation

Pgfplots is a built-in package in the texlive. As long as texlive is ready, pgfplots is out-of-the-box.

Usage

Pgfplots depends on pgf/tikz, and the statements are encapsulated in the environment of tikzpicture. The basic plot commands are \addplot and \addplot3 for 2D or 3D plot purpose, respectively. It should be noticed that each of them has a variant, i.e. \addplot+ and \addplot3+. \addplot/\addplot3 uses the provided local options only, while \addplot+/\addplot3+ adopts both the global and local options.

Templates for pgfplots usage can be presented as follows.

 \usepackage{pgfplots}
 \pgfplotsset{GLOBAL-OPTIONS}
 ...
 % For single curve plot
 \begin{tikzpicture}
 \begin{AXIS-TYPE}[AXIS-OPTIONS]
 \addplot/\addplot3[PLOT-OPTIONS] {FORMULA};
 \legend{LABEL};
 \end{AXIS-TYPE}
 \end{tikzpicture}

 % For multi-curve plot
 \begin{tikzpicture}
 \begin{AXIS-TYPE}[AXIS-OPTIONS]
 \addplot/\addplot3[PLOT-OPTIONS] {FORMULA1};
 \addlegendentry{LABEL1};
 \node at (AXIS-TYPE cs:x1,y1) {TEXT}; % Annotation for the curve.
 
 \addplot/\addplot3[PLOT-OPTIONS] {FORMULA2};
 \addlegendentry{LABEL2};
 ...
 \end{AXIS-TYPE}
 \end{tikzpicture}

`AXIS-TYPE`

The candidate values are axis/semilogxaxis/semilogyaxis/loglogaxis/polaraxis¹.

`FORMULA`

plain function², e.g.

\addplot {f(x)};

parameter function, e.g.

\addplot ({x(t)}, {y(t)});

coordinates, e.g.

\addplot coordinates{(x1, y1)(x2, y2)...(xn, yn)}

data in a file, e.g.

\addplot table [x = COLUMN1, y = COLUMN2]{DATA-FILE};

with the content of DATA-FILE as below.

COLUMN1 COLUMN2 COLUMN3
a1 b1 c1
a2 b2 c2
... ... ...

shade a region, e.g.

\addplot [...] {...} \closedcycle;

Options

AXIS-OPTIONS and PLOT-OPTIONS are basically the same, and the latter overrides the former.

title={TITLE}
domain=START: END specifies the range of the variable x.
blue/red/brown/green/cyan/magenta/yellow/black/gray/white/darkgray/lightgray/lime/olive/orange/pink/purple/teal/violet can be mixed by COLOR1!PERCENTAGE!COLOR2.
xlabel/ylabel={LABEL}
xtick/ytick={START, START+DELTA, ..., END} separates the ticks between START and END with step length DELTA.
xticklabels/yticklabels={a, b, c, ...}
axis equal image equally scales the axes, and trims the width or height to suit.
axis lines=box/left/middle/center/right/none³ specified the way the axes are drawn, e.g. middle make the axes intersect at the origin.
grid
grid style=solid/dashed
xmajorgrids/ymajorgrids=true/false enables/disables grid lines at the tick positions on the x/y axis.
legend pos=outer north east/north west/north east/south west/south east
legend cell align=left/right
xmin/xmax/ymin/ymax=BOUND
data cs=cart/polar specifies the coordinate, e.g. (x, y) or (angle, radius).
line width=WIDTH, e.g. line width=1pt.
thin/ultra thin/very thin/thick/semithick/ultra thick/very thick
solid/dashed/dotted/dashdotted/dashdotdotted
customize font size

tick label style={font=\normalsize\small\footnotesize\tiny}
label style={font=\normalsize\small\footnotesize\tiny}
legend style={font=\normalsize\small\footnotesize\tiny}

samples=SAMPLE_NUMBER defines the number of points in the domain.
smooth is an alternative to samples, which makes a smooth curves between data points.
mark=*/x/+/|/o/asterisk/star/10-pointed star/oplus/oplus*/otimes/otimes*/square/square*/triangle/triangle*/diamond/halfdiamond*/halfsquare*/right*/left*/halfcircle/halfcircle*/pentagon/pentagon*/cubes⁴
no marks
mark repeat=N marks the data points every N ones instead of every one.
only marks hides the line joining the data points.
opacity=FRACTION makes something not transparent, e.g. fill opacity=0.6.
xbar/ybar for bar plot.

Linux - Customize Console

Sat, 29 Feb 2020 00:00:00 +0000

Nowdays, a modern console can display many colors other than black and white. For example, 256-color can be enabled by adding the following entry into ~/.bashrc.

[[ $TERM=="xterm" ]] && export TERM=xterm-256color

Linux - Microcode

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Microcode is a technique that imposes an interpreter between the hardware and the architectural level of a computer. Processor vendors, e.g., Intel and AMD, release updates to the processor microcode for some reasons, e.g., bug fixes, which can be applied by the Linux kernel during boot.

For AMD processors, the microcode is covered by package linux-firmware which is installed as part of the base system. Therefore, no specific processing is needed. While for Intel processors, it is not the truth. Package intel-ucode must be manually installed.

LTE - D2D

Sat, 29 Feb 2020 00:00:00 +0000

Overview

In LTE-Advanced systems, the link for D2D communication is termed sidelink ¹. A sidelink carries two physical signals

DMRS
Synchronization signal

and four physical channels

Physical sidelink shared channel (PSSCH)
Physical sidelink control channel (PSCCH)
Physical sidelink discovery channel (PSDCH)
Physical sidelink broadcast channel (PSBCH)

PSSCH, PSCCH and PSDCH are all on the same antenna port, R1000. PSBCH and synchronization signals are on R1010 and R1020, respectively.

Physical channels

Scrambling

The data stream is first scrambled by a random sequence. The scrambling sequence shall be initialized at the beginning of every PSSCH/PSCCH/PSDCH/PSBCH subframe. The corresponding random seeds are

PSSCH: $c_\text{init} = n_\text{ID}^\text{SA} \cdot 2^{14} + n_\text{ssf}^\text{PSSCH} \cdot 2^9 + 510$, where $n_\text{ID}^\text{SA}$ is destination ID which can be obtained from PSDCH.
PSCCH/PSDCH: $c_\text{init} = 510$.
PSBCH: $c_\text{init} = N_\text{ID}^\text{SL}$.

Modulation

The scrambled sequence is then modulated as constellation symbols. The modulation schemes for the physical channels are

Physical channel	Modulation scheme
PSSCH	QPSK/16QAM
PSCCH/PSDCH/PSBCH	QPSK

Layer mapping

There is only one layer for each physical channel above. Namely, for each physical channel, the single codeword is mapped to a single layer.

Transform precoding

Similar to uplink transmission, SC-FDMA is adopted for sidelinks. For the 4 physical channels above, every $M_\text{sc}^\text{PSSCH}$ / $M_\text{sc}^\text{PSCCH}$ / $M_\text{sc}^\text{PSDCH}$ / $M_\text{sc}^\text{PSBCH}$ complex-valued symbols are FFT-processed.

Precoding

As mentioned above, there is only one layer for each physical channel over a sidelink. Therefore, the single layer can be directly mapped to the corresponding antenna port, i.e. R1000 for PSSCH, and R1010 for PSCCH/PSDCH/PSBCH.

Mapping to physical resources

The complex symbols are first scaled by $\beta_\text{PSSCH}$ / $\beta_\text{PSCCH}$ / $\beta_\text{PSDCH}$ / $\beta_\text{PSBCH}$ before mapping to the physical resource blocks (PRB's). The mapping shall be in increasing order of first the index k, and then the index l, starting with the first slot in the subframe. Moreover, the PRB's used for reference signal (RS's) will be avoided in the mapping. Resource elements in the last SC-FDMA symbol within a subframe shall be counted in the mapping process but not transmitted.

Particularly for PSSCH, frequency hopping is supported. The details can be referred to the specification.

For PSBCH, the available PRB's are in the central 6 PRB's, i.e. 72 subcarriers, as synchronization signals.

LTE - Discovery Signal

Sat, 29 Feb 2020 00:00:00 +0000

Just as its name indicates, discovery signal is transmitted by a cell to be discovered and measured by UE's. According to the standard¹, a discovery signal occasion for a cell consists of

1~5 consecutive subframes for FDD
2~5 consecutive subframes for TDD

Discovery signal is comprised of

CRS on antenna port 0 (R0)
PSS
- in the 1st subframe for FDD
- in the 2nd subframe for TDD
SSS in the 1st subframe
NZP CSI-RS in zero or more subframes

Footnotes

Section 6.11A in 3GPP TS36.211

LTE - Frequency Domain Location of Carriers

Sat, 29 Feb 2020 00:00:00 +0000

An LTE carrier, in principle, can be positioned anywhere within the spectrum range. In order to save the time consumption of carrier search for UE's, it is necessary to introduce additional restrictions on top of the specification.

Within each supported frequency band, LTE carriers always exist on a 100 kHz carrier grid/raster, i.e., the center of a carrier frequency can be written as $n \cdot 100$ kHz, where $n$ is an integer.

LTE - Mobility Management

Sat, 29 Feb 2020 00:00:00 +0000

The most remarkable character of mobile communication, which differs from other communication methods, is its mobility. The mobility can fall into two categories, intra-radio access technology (RAT) and inter-RAT mobility. Just as its name indicates, intra-RAT mobility means that the UE moves within one RAT, while inter-RAT mobility is the case that the UE move from one RAT to another. Namely, the source cell and the destination cell belong to two different RATs. Moreover, according to whether the destination cell operates on the same frequency as the serving cell, intra-RAT mobility can be further divided into intra-frequency and inter-frequency mobility two types.

LTE - PDCCH & EPDCCH

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

This post provides a brief summary on physical downlink control channel (PDCCH) and enhanced physical downlink control channel (EPDCCH) in long term evolution (LTE). Note the summary is based on the famous book, 4G, LTE-Advanced Pro and the Road to 5G¹.

PDCCH

PDCCH carries downlink control information (DCI), e.g. scheduling decisions and power control commands. Since each scheduling message is transmitted on a separate PDCCH, there are multiple simultaneous PDCCH transmission within each cell. From a UE perspective, each UE can receive multiple DCI messages in the same subframe, e.g. it is scheduled simultaneously in uplink and downlink.

Different control information can be categorized into different DCI formats, each of which corresponds with a certain message size² and usage.

A DCI payload is first attached with a CRC which is scrambled by a radio network temporary identifier (RNTI)³, and then coded with a 1/3 tail-biting convolutional code⁴ and rate-matched to fit the amount of resources for PDCCH transmission. After the rate matching, the bit sequence is scrambled by a cell-specific and subframe-specific scrambling sequence to whiten and randomize the inter-cell interference (ICI) before QPSK modulation and mapping to resource elements (RE's).

The mapping of PDCCH is based on a conception of control channel element (CCE), which is essentially a simple representation of 9 REG's, i.e. 36 RE's. Each PDCCH can take up 1, 2, 4 or 8 CCE's for link adaptation. The number of CCE's used for a PDCCH is termed aggregation level. The number of CCE's available for PDCCH depends on the size of control region, the cell bandwidth, the number of antenna ports in the downlink, and the resources occupied by PHICH.

Since a UE is not signalled about the aggregation level of each PDCCH, it has to blindly decode it. In order to reduce the computational complexity, some restrictions are imposed, e.g. each aggregated CCE can only start with the CCE's with their indices divisible by its aggregation level.

Machine Learning

Sat, 29 Feb 2020 00:00:00 +0000

Introducation

Machine learning (ML) is a subfield of artificial intelligence (AI).

Application

Image processing

Image tagging
Optical character recognition (OCR)
Self-driving cars

Text analysis

Spam filtering
Sentiment analysis
Information extract

Data mining

Discover patterns and make predictions from data.

Anomaly detection
Association rules
Grouping
Predictions

Video games & robotics

Algorithms

ML algorithms try to solve the same problem: learn to transform every input to the correct output.
ML algorithms try to make generalizations, and create the simplest hypothesis (with fewest assumptions) that explains most of the training examples.

Algorithms

Support vector machines (SVM's)

The model tries to build a set of hyperplanes in a high dimensional space which tries to separate instances of different classes by getting the largest separation between the nearest instances from different classes.

Probabilistic models

The models try to predict the correct response by modeling the problem with a probability distribution, e.g., Naive Bayes classifiers.
It returns the prediction as well as the corresponding degree of certainty.

Deep learning

It is based on the artificial neural network models. They try to emulate (in a very simplified way) the way the brain works.
The network consist of a huge set of interconnected neurons, i.e., the basic processing unit, organized in various layers.

Feature engineering

Feature extraction

Before fed to the ML algorithms, the raw data should be tranformed into a vector of features.

Feature selection

Score each feature and return only the most valuable ones.
Do not use huge feature sets.

Performance metric

The instances for training and testing must be disjoint.

Matched Filter

Sat, 29 Feb 2020 00:00:00 +0000

设时间$[0, T]$内的观察信号$r(t)$为信号$s(t)$和噪声$n(t)$的叠加，也即

\begin{align*} r(t) = s(t) + n(t), \quad t \in [0, T] \end{align*}

如果要设计一个冲激响应为$h(t)$的滤波器，使得其输出在$t = T$时的信噪比(signal to noise power ratio, SNR)最大，这样的滤波器称为匹配滤波器(matched filter, MF)。其冲激响应为

\begin{align*} h(t) = C s^*(T - t), \end{align*}

其中，$C$为非零常数。

证明过程如下: 滤波器在$t = T$时的SNR为

\begin{align*} \gamma(T) = \frac{\left|\int_{-\infty}^{\infty}S(f)H(f)e^{j2 \pi f T}df\right|^2} {N_0 \left|\int_{-\infty}^{\infty}H(f)e^{j2 \pi f T}df\right|^2}, \end{align*}

其中，$S(f)$和$H(f)$分别为$s(t)$和$h(t)$的Fourier变换，$N_0$为噪声的功率谱密度。

根据Cauchy-Schwartz不等式有

\begin{align*} \gamma(T) &\le \frac{\left|\int_{-\infty}^{\infty}S(f)e^{j2 \pi f T}df\right|^2 \cdot \left|\int_{-\infty}^{\infty}H(f)e^{j2 \pi f T}df\right|^2} {N_0 \left|\int_{-\infty}^{\infty}H(f)e^{j2 \pi f T}df\right|^2} \\ &= \frac{\left|\int_{-\infty}^{\infty}S(f)e^{j2 \pi f T}df\right|^2}{N_0} \end{align*}

当且仅当$H(f) = C S^*(f) e^{-j 2 \pi f T}$也即$h(t) = C s^{*}(T - t)$时等号成立，其中，$C$为非零常数。

MATLAB - Figure Data Abstraction

Sat, 29 Feb 2020 00:00:00 +0000

Provided a MATLAB figure file, e.g. FILE.fig, the original data can be abstracted by following procedure.

open('FILE.fig'); % open the figure file
fig_handle = findall(gca, 'type', 'line'); % get figure handle
x = get(fig_handle, 'xdata'); % get data of X-axis
y = get(fig_handle, 'ydata'); % get data of Y-axis

MATLAB over SSH

Sat, 29 Feb 2020 00:00:00 +0000

If MATLAB is installed on a secure shell (SSH) server, which is avaiable for access, we can run MATLAB remotely through SSH. In this way, MATLAB is running in symbol environment without X display, and the results can be saved in a file for further post-processing. What's important, MATLAB keeps running after logout (SSH) until the MATLAB script ends or error happens.

Running MATLAB remotely can be realized by the command

Mutt

Sat, 29 Feb 2020 00:00:00 +0000

Mutt is a text-based but powerful mail user agent (MUA) in the world of Unix/Linux. Originally, it is nothing but a MUA. However, it can make use of other programs to edit, send and receive mails. For example, it uses vim to edit mails, msmtp to send mails and getmail to receive mails. This is just the philosophy of Unix.

In ArchLinux operation system (OS), the mutt package is compiled with interactive mail access protocol (IMAP), post office protocol (POP) 3 and simple message transfer protocol (SMTP) support. In this case, mutt not only can manage mails, but also can send and receive mails. At least for me, it’s the best choice.

Orgmode - Export to HTML5 Slide

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

As is well-known, orgmode is a famous major mode of Emacs. What deserves notice, it can export org files to a variety of formats, e.g. \LaTeX, pdf, text, freemind.

Today, I found an interesting export backend, ox-ioslide, whereby org files can be directly exported to html5 slides.

Installation

It can be easily installed via Emacs's ELPA system.

M-x package-install ox-ioslide

After that, the backend can be automatically loaded by adding the following line in .emacs.

(require 'ox-ioslide)

Orgmode - Link

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Orgmode is an extremely powerful tool for get thing done (GTD), project planning, note keeping, etc.

Orgmode makes it fairly easy to insert, edit, and reference to a variety types of links.

Format

The general format for a link looks like [[link][description]] or [[link]]. If the description is a file name or URL that points to an image, HTML export will inline the image as a clickable button. If there is no description and the link points to an image, the image will be inlined into the exported HTML file.

Internal links

An internal link is used to mark an object and assign it a number. The marked object can be referenced by links pointing to it. Particularly, links without description appear as the number assigned.

An entry with the CUSTOM_ID property of my-custom-id can be referenced to as [[#my-custom-id]].
[[My Target]] or [[My Target][Find my target]] leads to a text search in the current file for the corresponding target <<My Target>>.

Targeted links

File links can contain additional information for more precise jumping, which can be a line number or a search option after a double colon.

Link	Target
`[[file:/path/to/filename::9]]`	Line 9 of the target file.
`[[file:/path/to/filename::My Target]]`	Find `<<My Target>>` in the target file.
`[[file:/path/to/filename::*My Target]]`	Find headline `My Target` in the target file.
`[[file:/path/to/filename::#my-custom-id]]`	Find entry with the `CUSTOM_ID` property of `my-custom-id`.
`[[file:/path/to/filename::/regexp/]]`	Find regular expression `regexp` in the target file.

Orgmode - Table

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

Orgmode provides a minor mode orgtbl-mode, which makes table creating and editing extremely easy.

Any line with | as the first non-whitespace character is treated as a part of a table.

The fastest way to create a table is to directly type |Column1|Column2|Column3 followed by C-c RET. Then a 3-column table will be created immediately, with the head of Column1, Column2, and Column3 respectively.

Keybinding

Keybinding	Functionality
`C-c` \|	Convert the active region to a table.
`C-c SPC`	Clear the current cell.
`C-c C-c`	Re-align the table.
`TAB`	Re-align the table move to the next column.
`S-TAB`	Re-align the table move to the previous column.
`M-a`	Move the beginning of the current cell, or on to the previous cell.
`M-e`	Move the end of the current cell, or on to the next cell.
`RET`	Re-align the table and move to the next row.
`M-left/right`	Move the current column left/right.
`M-up/down`	Move the current row up/down.
`M-S-left`	Kill the current column.
`M-S-up`	Kill the current row.
`M-S-right`	Insert a new column to the right.
`M-S-down`	Insert a new row above.
`C-c -`	Insert a horizontal line below.
`C-u C-c -`	Insert a horizontal line above.
`C-c +`	Sum the numbers in the current column, or a active region.

Alignment and width

<l>, <r>, and <c> can align the column at point to the left, right, and center respectively.
<N> can fix the width of the column at point to N characters.

Reference

Symbol	Reference
`@r`	r-th row
`$c`	c-th column
`@r$c`	The cell in r-th row c-th column
`@r1..@r2`	The rows from r1 to r2
`$c1..$c2`	The columns from c1 to c2

Orgmode - Tikz

Sat, 29 Feb 2020 00:00:00 +0000

Tikz/pgf is an excellent LaTeX package to draw pictures. It can be used in Emacs org mode. An example can be provided as follows.

 ,#+BEGIN_SRC latex :file FILE.png :imagemagick yes :headers '("\\usepackage{tikz}") :fit yes :iminoptions -density 600
 \begin{tikzpicture}
 tikz statements;
 \end{tikzpicture}
 ,#+END_SRC

Python - Package Management

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

One of the most charmful characters of Python is its a rich number of packages. Accordingly, package managers emerge, e.g., pip, setuptools. This post just briefly introduce the usage of pip.

Installation

In ArchLinux system, pip can be easily installed by

 pacman -S python-pip

As a dependency, python will also be installed if it has not yet.

Configuration

Similar to the package manager of Linux operation systems, pip connects with, synchronizes to, and downloads from websites. For the sake of download speed maximization, pip is encouraged to visit the nearest mirror site, which can be configured by editing /etc/pip.conf, e.g.,

 [global]
 index-url = https://mirrors.163.com/pypi/simple

Regular Expression

Sat, 29 Feb 2020 00:00:00 +0000

正则表达式是指用于字符串匹配的一种模式,最早出现于20世纪40年代.

字符集(字符组) `[]`

[0-9] 可以匹配0到9范围内的任意数字.可以简写为 \d.
\D 可以匹配非数字字符.相当于 [^0-9] 或 [^\d].
\t 可以匹配水平制表符.
\v 可以匹配垂直制表符.
\f 可以匹配换页符.
\n 可以匹配换行符.
\r 可以匹配回车符.
\s 可以匹配空白字符.相当于 [\t\n\r].
\S 可以匹配非空白字符.相当于 [^\t\n\r] 或 [^\s].

通配符

. 可以匹配任意字符¹.
^ 行起始符.
$ 行结束符.
\b 单词边界².
\B 非单词边界.

捕获与反向引用

可以使用圆括号 () 创建捕获分组,之后可以对其进行反向引用,如 $1.

量词

{} 中的数字表示确切的匹配次数.
+ 表示一次或者多次.
? 表示零次或者一次.
* 表示零次或者多次.

Footnotes

某些情况下不能匹配行起始符.

在旧语法中,指定单词首尾边界分别使用 \< 和 \>.

SSH

Sat, 29 Feb 2020 00:00:00 +0000

Secure shell (SSH) is the most popular and efficient method for remote access. This post introduces SSH relevant issues, from installation to configuration.

Installation

Take Archlinux for instance here.

pacman -S openssh

Transmission over asymmetrical encryption

Generate key pair on the client

ssh-keygen -t rsa

Copy the public key to the server

scp ~/.ssh/id_rsa.pub USERNAME@SERVER:~/.ssh/authorized_keys
#or
ssh-copy-id -i ~/.ssh/id_rsa.pub USERNAME@SERVER

Enable `X11 forwarding` to run GUI programs over SSH

On server

Installation

pacman -S xorg-xauth

Configuration

Add following line in /etc/ssh/sshd_config

X11Forwarding yes

On client

Add following lines in /etc/ssh/ssh_config

ForwardAgent yes
ForwardX11 yes
ForwardX11Trusted yes

Virtual Console Switch

Sat, 29 Feb 2020 00:00:00 +0000

Unix and Linux operation systems (OS) originally provided textual interfaces only, but now, we can already enjoy the perfect graphic experience through their desktop systems, e.g. Gnome, KDE, XFCE. This post only aims to present the methods of switching between textual and graphical interfaces.

Switch from graphical interface to textual interface: press Ctrl + Alt + Fn, where n = 1, 2, ...
Switch from textual interface to graphical interface: press Alt + Fm, where the value of integer m is different from OS to OS. For most Linux OS, m = 7.
Switch from textual interface i to textual interface j: press Alt + Fj.

Wiener Filter

Sat, 29 Feb 2020 00:00:00 +0000

设观测信号$x(t)$为期望信号$s(t)$和噪声信号$n(t)$的叠加，也即

\begin{align*} x(t) = s(t) + n(t). \end{align*}

其中，$s(t)$和$n(t)$是宽平稳过程，且相互联合宽平稳，观测信号$x(t)$和期望信号$s(t)$的自相关函数和互相关函数分别为$R_x(\tau)$、$R_s(\tau)$和$R_{sx}(\tau)$，功率谱密度函数及其互功率谱密度函数分别为$S_x(f)$、$S_s(f)$和$S_{sx}(f)$。

如果要设计一个冲激响应为$h(t)$的滤波器，使得其输出信号和期望信号$s(t)$的均方误差达到最小，这样的滤波器称为Wiener滤波器，又称均方滤波器。其冲激响应$h(t)$满足Wiener-Hopf方程。

\begin{align*} \int_{-\infty}^{\infty}R_{x}(t - \tau) h^*(\tau)d\tau = R_{sx}(t). \end{align*}

相应地，其传递函数为

\begin{align*} H^*(f) = \frac{S_{sx}(f)}{S_x(f)}. \end{align*}

ZC

Sat, 29 Feb 2020 00:00:00 +0000

Introduction

The Zadoff-Chu (ZC) sequence¹ is named after Solomon A. Zadoff and D. C. Chu, which is a constant amplitude zero auto-correlation (CAZAC) sequence² with its cylically shifted versions are zero correlated, i.e. orthogonal to each other. A ZC sequence without cyclic shift is termed a root sequence, which can be expressed as

\begin{align*} x_u(n) = e^{-j\frac{\pi u n (n+1+2q)}{L}}, \quad n = 0, 1, \ldots, L-1, \end{align*}

where $u$ is the index of the root sequence, $L$ is the length and $q \in \mathbb{Z}$.

归去来兮辞

Sat, 29 Feb 2020 00:00:00 +0000

序

余家贫，耕植不足以自给。幼稚盈室，瓶无储粟，生生所资，未见其术。亲故多劝余为长吏，脱然有怀，求之靡途。会有四方之事，诸侯以惠爱为德，家叔以余贫苦，遂见用于小邑。于时风波未静，心惮远役，彭泽去家百里，公田之利，足以为酒。故便求之。及少日，眷然有归欤之情。何则？质性自然，非矫厉所得。饥冻虽切，违己交病。尝从人事，皆口腹自役。于是怅然慷慨，深愧平生之志。犹望一稔，当敛裳宵逝。寻程氏妹丧于武昌，情在骏奔，自免去职。仲秋至冬，在官八十余日。因事顺心，命篇曰《归去来兮》。乙巳岁十一月也。

正文

归去来兮，田园将芜胡不归？既自以心为形役，奚惆怅而独悲？悟已往之不谏，知来者之可追。实迷途其未远，觉今是而昨非。舟遥遥以轻飏，风飘飘而吹衣。问征夫以前路，恨晨光之熹微。

乃瞻衡宇，载欣载奔。僮仆欢迎，稚子候门。三径就荒，松菊犹存。携幼入室，有酒盈樽。引壶觞以自酌，眄庭柯以怡颜。倚南窗以寄傲，审容膝之易安。园日涉以成趣，门虽设而常关。策扶老以流憩，时矫首而遐观。云无心以出岫，鸟倦飞而知还。景翳翳以将入，抚孤松而盘桓。

归去来兮，请息交以绝游。世与我而相违，复驾言兮焉求？悦亲戚之情话，乐琴书以消忧。农人告余以春及，将有事于西畴。或命巾车，或棹孤舟。既窈窕以寻壑，亦崎岖而经丘。木欣欣以向荣，泉涓涓而始流。善万物之得时，感吾生之行休。

已矣乎！寓形宇内复几时？曷不委心任去留？胡为乎遑遑欲何之？富贵非吾愿，帝乡不可期。怀良辰以孤往，或植杖而耘耔。登东皋以舒啸，临清流而赋诗。聊乘化以归尽，乐夫天命复奚疑！

C++ - Thread Pool

Thu, 19 Dec 2019 00:00:00 +0000

Introduction

Threadpool is a C++ thread pool written by Philipp Henkel based on boost library. It provides a variety of thread pools with easy usage.

Installation

As a prequisite, boost library should be installed in advance, e.g.,

 pacman -S boost

Threadpool consists only of header files, and therefore the building operation is not needed. The only operation is to copy the header file threadpool.hpp and folder threadpool/ to directory /usr/include/boost.