Determinant(2)

Posted on 2017-12-24 | Edited on 2020-06-16 | In math

Exchange

定理一一个排列的任意两个元素对换，排列改变奇偶性

对相邻元素对换有：
- 如果 a > b，则a的逆序数不变，b的逆序数-1
- 如果 a < b，则a的逆序数+1，b的逆序数不变
 得到相邻元素兑换排列改变奇偶性
基于以上相邻元素对一般情况对换有：
- 将b对换到a后需要n次对换 $a_1 a_2 ... a_n a b b_1 b_2 ... b_n$
- 将a对换到 $b_n$ 后需要n+1次对换 $a_1 a_2 ... a_n b b_1 b_2 ... b_n a$ 对换a b对应2n+1次奇偶性改变，排列的奇偶性改变

推论奇排列变成标准排列，对换次数是奇数次；偶排列变成标准排列，对换次数是偶数次

$(-1)^ta_{1p_1}a_{2p_2}...a_{ip_i}...a_{jp_j}...a_{np_n}$

对行列式的排列做一次对换，其中 1 2 … i … j … n 是自然顺序，
p1 p2 … pi … pj …pn 是列的某个排列。对换后有：

$(-1)^ta_{1p_1}a_{2p_2}...a_{jp_j}...a_{ip_i}...a_{np_n}$

其中 1 2 … j … i … n 的逆序数的奇数r，p1 p2 … pj … pi …pn 的逆序数将反转设其逆序数为t1

$(-1)^{t_1} = -(-1)^t \Longrightarrow (-1)^t = (-1)^{t_1 + r}$

同时改变行号列号不改变奇偶性，即对调行列式排列元素不会改变符号。

$p_i = j \to q_j = i$

由此可得出存唯一行序列q1 q2 … qn，使得列序列标准化：

$\sum_{}{(-1)^ta_{q_11}a_{q_22}...a_{q_nn}}$

定理二 n阶行列式也可定义为 $\sum_{}{(-1)^ta_{p_11}a_{p_22}...a_{p_nn}}$

Property

性质1 行列式和它的转置行列式相等

所有元素行列互换，并不影响行列式的值

$D^T = \sum_{}{(-1)^ta_{1p_1}a_{2p_2}...a_{np_n}} = \sum_{}{(-1)^ta_{p_11}a_{p_22}...a_{p_nn}}$

性质2 互换行列式的两行（列），行列式变号

换行后的行列式表示为

$D1 = \sum_{}{(-1)^ta_{1p_1}a_{2p_2}...a_{jP_i}...a_{iP_j}...a_{np_n}} = -D$

互换的行（列）排列变奇偶性，求和后即整体变号

推论如果有两行（列）完全相同，行列式为0

互换两行（列）后有 D = -D1，行列式为0

性质3 行列式某行（列）都乘以k，等于k乘以该行列式

记作 $r_i * k , c_i * k$
提出公因子后记作 $r_i \div k , c_i \div k$

性质4 行列式中如果有两行（列）成比例，行列式为等于零

根据性质3提出公因子后，两行（列）相同。根据性质2，行列式为0

性质5 如果行列式某行（列）都是两数的和，则可分为两行列式的和

$\begin{vmatrix} a_{11} & a_{12} & ... & (a_{1i} + a'_{1i}) & ... & a_{1n}\\ a_{21} & a_{22} & ... & (a_{2i} + a'_{2i}) & ... & a_{2n}\\ ... & ... & ... & ... & ... & ... \\ a_{n1} & a_{n2} & ... & (a_{ni} + a'_{ni}) & ... & a_{nn} \end{vmatrix}$ $D = \begin{vmatrix} a_{11} & a_{12} & ... & a_{1i} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2i} & ... & a_{2n}\\ ... & ... & ... & ... & ... & ... \\ a_{n1} & a_{n2} & ... & a_{ni} & ... & a_{nn} \end{vmatrix} + \begin{vmatrix} a_{11} & a_{12} & ... & a'_{1i} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a'_{2i} & ... & a_{2n}\\ ... & ... & ... & ... & ... & ... \\ a_{n1} & a_{n2} & ... & a'_{ni} & ... & a_{nn} \end{vmatrix}$

假设组合的第i行元素都可分两数之和：

$D = \sum_{}{(-1)^ta_{1p_1}a_{2p_2}...(a_{iP_i} + a'_{iP_i})...a_{np_n}}$ $D = \sum_{}{(-1)^ta_{1p_1}a_{2p_2}...a_{iP_i}...a_{np_n}} + \sum_{}{(-1)^ta_{1p_1}a_{2p_2}...a'_{iP_i}...a_{np_n}}$

性质6 把行列式某行（列）的元素乘以同一数，加到另一行（列），行列式不变

根据性质4 和性质5，将加上的等比例数拆分出另一个行列式，值为0，即不改变行列式

Determinant (1)

Posted on 2017-12-22 | Edited on 2020-06-16 | In math

Primary

$\begin{cases} a_{11}x_1 + a_{12}x_2 = b_1 \\ a_{21}x_1 + a_{22}x_2 = b_2 \end{cases}$

消去后当 $a_{11}a_{22} - a_{12}a_{21} \neq 0$ 时得到：

$x1 = \frac {b_1 a_{22} - a_{12} b_2}{a_{11} a_{22} - a_{12} a_{21}} , x2 = \frac {a_{11} b_2 - b_1 a_{21}}{a_{11}a_{22} - a_{12}a_{21}}$

按方程组中的顺序排好行列：

$\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{vmatrix}$

分母即是行列式的主对角线”积” - 副对角线”积”
如果定义：

$D = \begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{vmatrix}, D_1 = \begin{vmatrix} b_{1} & a_{12} \\ b_{2} & a_{22} \end{vmatrix}, D_2 \begin{vmatrix} a_{11} & b_{1} \\ a_{21} & b_{2} \end{vmatrix},$

则有：

$x_1 = \frac{D_1}{D}, x_2 = \frac{D_2}{D}$

example

$\begin{cases} 3x_1 - 2x_2 = 1 \\ 6x_1 + 5x_2 = -4 \end{cases}$ $D = \begin{vmatrix} 3 & -2 \\ 6 & 5 \end{vmatrix} = 27 \neq 0 D_1 = \begin{vmatrix} 1 & -2 \\ -4 & 5 \end{vmatrix} D_2 = \begin{vmatrix} 3 & 1 \\ 6 & -4 \end{vmatrix}$ $x_1 = \frac{D_1}{D} = \frac{13}{27}, x_2 = \frac{D_2}{D} = \frac{-30}{27}$

n Factorial determinant

In 3 factorial determinant:

$\begin{vmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{vmatrix} = a_{11}a_{22}a_{33} + a_{13}a_{21}a_{32} + a_{12}a_{23}a_{31} - a_{13}a_{22}a_{31} - a_{12}a_{21}a_{33} - a_{11}a_{23}a_{32}$

带负号系数的组合都是逆序数为奇数的组合，用p1p2p3来代表某组合矩阵位置有

$\begin{vmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{vmatrix} = \sum_{}{(-1)^ta_{1p_1}a_{2p_2}a_{3p_3}}$

t表示p1p2p3组合时的逆序数，取和即使为矩阵的表示

More generalizate

$\sum_{}{(-1)^ta_{1p_1}a_{2p_2}...a_{np_n}}$

简记作$det(a{ij})$, 数$a{ij}$为D的(i, j)元

Prove

$\begin{vmatrix} & & & \lambda_1 \\ & & \lambda_2 & \\ & ... & & \\ \lambda_n & & & \end{vmatrix} = (-1)^{\frac{n(n-1)}{2}}\lambda_1\lambda_2...\lambda_n$

符号代表着副对角线的元素，对$\lambdai$可以用$a{i, n-i+1}$来表示。

$\begin{vmatrix} & & & \lambda_1 \\ & & \lambda_2 & \\ & ... & & \\ \lambda_n & & & \end{vmatrix} = \begin{vmatrix} & & & a_{1n} \\ & & a_{2,n-1} & \\ & ... & & \\ a_{n1} & & & \end{vmatrix} = (-1)^{\frac{n(n-1)}{2}}a_{1n}a_{2,n-1}...a{n1}$

对n n-1 n-2 … 1 组合的元素求逆序数

$t = 0 + 1 + 2 ... n-1 = \frac{n(n-1)}{2}$

Abbreviations and symbols

Posted on 2017-12-21 | Edited on 2020-06-16 | In ml

缩写

a	b	c
AR	autoregressive	自回归
BBTT	back propagation through time	通过时间的反向传播
BM	Boltzmann machine	Boltzmann机
BP	back propagation	反向传播
b/s	bit per second	每秒比特率
BSB	bran-state-in-a-box	盒中脑状态
BSS	blind source(signal) separation	盲源（信号）分离
cmm	correlation matrix memory	相关矩阵记忆
CV	cross-validation	交叉验证
DFA	deterministic finite-state automata	确定性有限状态自动机
EKF	extended Kalman filter	扩展卡尔曼滤波器
EM	expectation-maximization	期望最大化
FIR	finite-duration impulse response	有限时间冲击响应
FM	frequency-modulated(singal)	频率调制（信号）
GCV	generalized cross-validation	广义交叉验证
GHA	generalized Hebbian algorithm	广义Hebb算法
GSLC	generalized sodelobe canceler	广义旁瓣消除器
Hz	hertz	赫兹
ICA		独立分量分析
Infomax		最大互信息
Imax		最大互信息的变体
Imin		最大互信息的另一变体
KSOM		核自组织映射
KHA		核Hebb算法
LMS	least-mean-square	最小均方
LR		似然比
LS	Least-squares	最小二乘
LS-TD	Least-squares, temporal-difference	最小二乘，时序差分
LTP		长期增强
LTD		长期衰减
LRT		似然比测试
MAP		最大后验估计
MCA		次分量分析
MCMC	Markov Chain Monte Carlo	马尔可夫链蒙特卡洛
MDL		最小描述长度
MIMO		多输入多输出
ML		最大似然
MLP	Multilayer perceptron	多层感知器
MRC		模型参考控制
NARMA		非线性自回归平滑平均
NARX		具有外部输入的非线性自回归
NDP		神经动态规划
NW		Nadaraya-Watson(估计器)
NWKR		Nadaraya-Watson核回归
OBD		最优脑损伤
OBS		最优脑外科
OCR	optical character recognition	光学字符识别
PAC		可能近似正确
PCA		主分量分析
PF		粒子滤波器
pdf	probability density function	概率密度函数
pmf	probability mass function	概率质量函数
QP
RBF
RLS
RLS
RMLP
RTRL
SIMO
SIR
SIS
SISO
SNR
SOM
SRN
SVD
SVM
TD
TDNN
TLFN
VC
VLSI
XOR	exclusive OR	异或

符号

a	b	c
$\mathrm{a}$	action	动作
$\mathbf{a}^T\mathbf{b}$		向量a和b的内积
$\mathbf{ab}^T$		向量a和b的外积
$\dbinom{l}{m}$		二项式系数
$\mathrm{A}\bigcup\mathrm{B}$		A和B的并集
$\mathrm{B}$		温度的逆
$\mathrm{b}_k$		神经元k的偏置
$\cos(\mathbf{a},\mathbf{b})$		向量a的b夹角余弦
$\mathit{c}_{ u, v } (\mathit{u, v})$		系词的概率密度函数
$\mathit{D}$		记忆深度
$\mathit{D}_{ f \| g }$		概率密度函数f和g之间的Kullback-Leibler散度
$\tilde{\mathbf{D}}$		算子D的伴随矩阵
$\mathit{E}$		能量函数
$\mathit{E}_i$		统计力学中的状态i的能量
$\mathbb{E}$		统计期望算子
$\left\langle \mathit{E} \right\rangle$		平均能量
$\exp$		指数
$\varepsilon_{av}$		平均平方误差或平方误差和
$\varepsilon(n)$		平方误差和的瞬间值
$\varepsilon_{total}$		总平方误差和
$\mathit{F}$		自由能量
$\mathscr{F}*$		经验风险最小的子集（网络）
$\mathbf{H}$		Hessian矩阵
$\mathbf{H}^{-1}$		Hessian矩阵H的逆
$\mathit{i}$		-1的平方根，亦记作j
$\mathbf{I}$		单位矩阵
$\mathbf{I}$		Fisher信息矩阵
$\mathit{J}$		均方误差
$\mathbf{J}$		Jacobi矩阵
$\mathbf{P}^{1/2}$		矩阵P的方根
$\mathbf{P}^{T/2}$		矩阵P的方根转置
$\mathbf{P}_{n, n-1}$		卡尔曼滤波理论中的误差协方差矩阵
$\mathit{k}_B$		Boltzmann常数
$\log$		对数
$\mathit{L}(\mathbf{w})$		权值向量w的对数似然函数
$\mathscr{L}(\mathbf{w})$		但样本的权值向量w的对数似然函数
$\mathbf{M}_c$		可控矩阵
$\mathbf{M}_o$		可观察矩阵
$\mathrm{n}$		离散时间
$\mathit{P}_i$		统计力学中的状态i的概率
$\mathit{P}_{ij}$		从状态i到状态j的转移概率
$\mathbf{P}$		随机矩阵
$\mathrm{P}(e\|\mathscr{C})$		从类C中输入时e的条件概率
$\mathrm{P}_\alpha^+$		假设网络处于钳制状态（正向阶段）时，Blotzmann机的可见神经元状态为α的概率
$\mathrm{P}_\alpha^-$		假设网络处自有运行条件（负向阶段）时，Blotzmann机的可见神经元状态为α的概率
$\hat{r}_x(j, k; n)$		xi(n)和xk(n)的自相关函数估计
$\hat{r}_{dx}(k; n)$		d(n)和xk(n)的交叉相关函数估计
$\mathbf{R}$		输入向量的相关矩阵
$\mathrm{t}$		连续时间
$\mathit{T}$		温度
$\mathscr{T}$		训练集（样本）
$\mathrm{tr}$		表示矩阵迹的算子
$\mathrm{var}$		方差算子
$\mathit{V}(x)$		状态向量x的Lyapunov函数
$\mathit{v}_i$		神经元j的诱导局部域或激活位势
$\mathbf{w}_v$		突出权值向量的最优值
$\mathscr{w}_{kj}$		属于神经元k的突触j的突触权值
$\mathbf{w}^*$		最优向量x的平衡值
$\bar{\mathbf{x}}$		状态向量x的平衡值
$\left\langle \mathit{x}_i \right\rangle$		“热”意义下状态xj的平均
$\hat{\mathit{x}}$		x的估计，用加字符号^表示
$\|\mathit{x}\|$		x的绝对值(幅度)
$\mathit{x}^*$		状态x的复共轭，用*作上标
$\|\|\mathbf{x}\|\|$		向量x的欧几里得范数
$\mathbf{x}^T$		向量x的转置，用上标T表示
$\mathit{z}^{-1}$		单位时间延迟算子
$\mathrm{Z}$		部分函数
$\delta_j(n)$		神经元j在时刻n的局部梯度
$\Delta\mathit{w}$
$\nabla$		梯度算子
$\nabla^2$		拉普拉斯算子
$\nabla_w\mathit{J}$		J关于w的梯度
$\nabla \centerdot \mathbf{F}$		向量F的散度
$\eta$		学习率参数
$\kappa$		累积量
$\mu$		策略
$\theta_k$		神经元k的阀值（偏置bk的负值）
$\lambda$		正则化参数
$\lambda_k$		方阵的第k个特征值
$\varphi_k(\centerdot)$		神经元k的非线性激活函数
$\in$		“属于”符号
$\bigcup$		“并”符号
$\bigcap$		“交”符号
$*$		卷积符号
$+$		矩阵伪逆的上标符号
$+$		更新估计的上标符号

Thread security

Posted on 2017-12-02 | Edited on 2018-12-16 | In java

Security problem in java web

In tradition web develop, Servlet implement response to http request.
Servlet is one of the important standard of J2EE, it set how java response to Http request.
In project, classpath need relay on servlet-api.jar of j2ee.jar.
We can interact with web container through HttpServletRequest and HttpServletResponse object.

When container receive a request, container will dispatch a thread that
define in advance from main thread(tomcat observer pattern), to deal the mapping servlet implement.
When another request come in, main thread will choose thread from threadpool to serve,
but it do not care is there other threads using this implement.

So web container use singleton pattern to implement service object.
This pattern can reduce the servlet space waste, and improve response performance.
But it lead to security problem, the servlet in container is not thread security save.

HashMap and HashTable

HashMap implement Map interface from java 1.2
a light weight implement of HashTable, no contains method(avoid confusion)
All key / value in HaspMap entry are object(can be null).
not security save
HashTable is security save, it’s method is Synchronized
HashTable & HashMap hash implement is same, so performance in Synchronized is same too.

Theory

if multi-thread program run in same code result is same with single thread expect,
then thread secure. Thread security is caused by global or static changeable variable.
If only read operation on these variable in program, then no thread security problem in regular.

Thread security

In multi-thread environment, a class execute method, obtain independent resource

method signature variable is save(???)
local variable in method is save

ThreadLocal

ThreadLocal is self is not a thread, it’s static class.
It maintain thread’s independent copy ThreadLocalMap.

one side: all thread visit it’s own ThreadLocalMap
another side: one thread visit it’s own ThreadLocal

Summary

ThreadLocal maintain thread’s variable, to deal visit conflict.
Synchronized use JVM lock mechanism to make sure resource atomicity(one thread visit in time).

ThreadLocal use space to exchange time, provide every thread a variable copy, make sure visit concurrent but no conflict.
Synchronized use time to exchange space, monitor a target, to make thread visit in queue.

http://blog.51cto.com/dongisland/1369375

sleep in c++

Posted on 2017-11-15 | Edited on 2018-12-16 | In c++

Introduce

hang up thread for a while
unsigned sleep(unsigned seconds);

In VC++ add head file #include <windows.h> or #include "stdafx.h"
In GCC add head file #include <unistd.h>

Caution

In windows Sleep() is first letter upper case, and unit in milliseconds
In Linux sleep() is first letter lower case, and unit in seconds

List

a	b
Dos	sleep(1); //停留1秒 </br>delay(100); //停留100毫秒
Windows	Sleep(100); //停留100毫秒
Linux	sleep(1); //停留1秒 </br>usleep(1000); //停留1毫秒

sleep function

Think in Develop

Posted on 2017-10-27 | Edited on 2018-12-16 | In theory

Split front and backgroud

Now adays the front develop framwork has a great progress,
more and more web develop use model/ scriptable develop framwork.

Backgroud no need forcus on how to deal page staff, much more backgroud.
More and more POST style backgroud, restructure to REST style.

Front emphasize in rendering

App’s rendering got a great progress, thanks to mobile equipment popular.
Front developer now have more power to deal business with customer,
no need to care how hard backgroud gay work.

Backgroud emphasize in usability

Backgroud’s structure is important, it’s stability/ usability affect
user feeling a lot.

Backgroud developer more forcus on data/ model/ resource/ performan…

Develop now

For front developer, MVC is relatively balance.
For backgroud developer, V is steal useable in some old style develop
project, use script style backgroud language PHP JSP ASP …

But for robust modern business application, B/G have been splitted

https://segmentfault.com/a/1190000004213733

Linux memory

Posted on 2017-10-16 | Edited on 2018-12-16 | In linux

get top memory process

1 2	# +3[CPU] ps aux\|head -1;ps aux\|grep -v PID\|sort -rn -k +4\|head

free

free -m
free -b -s5
free -h

              total       used       free     shared    buffers     cached
Mem:          7.7G       7.6G       133M       164K       190M       3.1G
-/+ buffers/cache:       4.2G       3.5G
Swap:           0B         0B         0B

from the point of view of OS buffers and cached memory is used
available memory size = free + buffers + cached

ps
1
2
ps aux --sort -rss
ps aux | grep xxx

USER process’ user
PID process id
%CPU cpu proportion
%MEM memory proportion
VSZ total VM size in kB
RSS resident set size
TTY terminal
STAT
- R Running or runnable (on run queue)
- S Interruptible sleep (waiting for an event to complete)
START time the command started
TIME run cpu time
COMMAND string as arguments

/proc

cat /proc/pid/status

VmPeak:	 5033936 kB
VmSize:	 5033620 kB
VmLck:	       0 kB
VmHWM:	 1151928 kB
VmRSS:	 1151644 kB
VmData:	 4875980 kB
VmStk:	      88 kB
VmExe:	      36 kB
VmLib:	  127412 kB
VmPTE:	    2724 kB
VmSwap:	       0 kB
Threads:	72

VmSize(KB) task’s virtual address space size (total_vm-reserved_vm)
VmLck(KB) been locked physical memory size, can’t exchange to hard drive(locked_vm)
VmRSS(KB) resident set size, physical memory. (rss in ps)
VmData(KB) program’s data paragraph size (virtual), store initialized data(total_vm-shared_vm-stack_vm)
VmStk(KB) task’s stack size in user(stack_vm)
VmExe(KB) executable virtual memory size, (exclude lib) (end_code-start_code)
VmLib(KB) lib mapping to task memory space size(exec_lib)
VmPTE(KB) this process’s page size
Threads share this signal’s task number(POSIX multi app, thread group use same signal)

top

# [shit+m sort by memory]
top -p 6506

top - 11:14:20 up 125 days,  1:47,  1 user,  load average: 0.00, 0.00, 0.00
Tasks:   1 total,   0 running,   1 sleeping,   0 stopped,   0 zombie
Cpu(s):  0.2%us,  0.1%sy,  0.0%ni, 99.7%id,  0.0%wa,  0.0%hi,  0.0%si,  0.0%st
Mem:   8061396k total,  7925220k used,   136176k free,   194748k buffers
Swap:        0k total,        0k used,        0k free,  3291676k cached

  PID USER      PR  NI  VIRT  RES  SHR S %CPU %MEM    TIME+  COMMAND  
 3825 root      20   0  164m  41m 1020 S  0.0  0.5 146:54.42 redis-server

Cpu(s): 0.2%us, 0.1%sy, 0.0%ni, 99.7%id, 0.0%wa, 0.0%hi, 0.0%si, 0.0%st

us user space cup proportion
sy system core space cup proportion
ni priority changed task cup proportion
id idle cpu proportion
wa waiting IO cpu proportion
hi hard ware cost
si soft ware cost
st steal time

PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ COMMAND

PR priority rank
NI nice value
VIRT virtual memory size
RES not be exchanged memory size
SHR share meory size

find command

Posted on 2017-09-27 | Edited on 2018-12-16 | In linux

find [-H] [-L] [-P] [-D debugopts] [-Olevel] [path…] [expression]

find [path path …]

Option

-depth step into sub files first, then current directory
.The -delete action also implies -depth
-name [-iname] find file by name
find /etc /root -name passwd
-type
- d directory
- f regular file
-size
- b for 512-byte blocks (this is the default if no suffix is used)
- c for bytes
- w for two-byte words
- k for Kilobytes (units of 1024 bytes)
- M for Megabytes (units of 1048576 bytes)
- G for Gigabytes (units of 1073741824 bytes)
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3
4
# find files bigger than 30 kilobytes
# %k %b in printf represent different block size

find -size +30k -printf '%p %k %b \r\n'

-a[and] -o[or] -not logic option

# find files name end with sh, and belong to user
# ubuntu or group id is 1000
find /usr -name '*.sh' -a -user ubuntu -o -gid 1000

# find files name not end with class
find . -not -name '*.class'

-atime -mtime -ctime -amin -mmin -cmin
a access file
m modify file
c change property
time days
min minutes

# find files be accessed in last 19 days
find -atime -19 -printf '%p %a %t \r\n'

# find files not be accessed in last 19 days
find -atime +19 -printf '%p %a %t \r\n'

-newer -anewer -cnewer
based on parameter file modify time
-newer File was modified more recently than file
-anewer File was last accessed more recently than file was modified.
-cnewer File’s status was last changed more recently than file was modified.

-perm
find files based on privilege

# find files in current directory which
# permissions is -rwxr-xr-x
find -perm 755

# at least a kind of user have write privilege
find -perm +444

# all kind user have write privilege
find -perm -444

Action

-printf format out put

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#   name  depth  space[512-kbytes]  space[1024-kbytes]
#   permissions  access_time  change_time  modify_time
find -user ubuntu -printf '%p %d %b %k %M %a %c %t \r\n'

-ls
list in ls command
-ok
ask user yes/no execute command

-exec command {} +
execute command no asking

# delete files in current directory no accessed in 30 days
find . -atime +30 –exec rm –rf {}
# same effect
find . -atime +30 | xargs rm -rf

linux find

Tomcat Container

Posted on 2017-09-20 | Edited on 2018-12-16 | In java

Tomcat container is a typical case of Chain of Responsibility pattern
Container composed by Engine Host Context Wrapper

connector.getService().getContainer().getPipeline().getFirst().invoke(request, response);

every container have it’s own pip and valve
getPipeline() got pipline determine data direction
getFirst() got valve determine door open or close
Interface Valve have method invoke

Engine

engine is top level container, it dispatch request to host

Host

a host represent a virtual machine like ‘localhost’, it store host reference info.

Context

context represent a web project in webapps

Wrapper

wrapper response for a servlet, like load/ init/ resource recycle

at javax.servlet.http.HttpServlet.service(HttpServlet.java:727)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:303)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at org.springframework.web.filter.CharacterEncodingFilter.doFilterInternal(CharacterEncodingFilter.java:88)
at org.springframework.web.filter.OncePerRequestFilter.doFilter(OncePerRequestFilter.java:76)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:220)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:122)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:503)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:170)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:103)
at org.apache.catalina.valves.AccessLogValve.invoke(AccessLogValve.java:950)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:116)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:421)
at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1070)
at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:611)
at org.apache.tomcat.util.net.JIoEndpoint$SocketProcessor.run(JIoEndpoint.java:314)
at java.util.concurrent.ThreadPoolExecutor$Worker.runTask(ThreadPoolExecutor.java:886)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:908)
at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
at java.lang.Thread.run(Thread.java:662)

log4j configuration

Posted on 2017-09-18 | Edited on 2020-09-17 | In java

level

log4j.rootLogger = [level],appenderName,appenderName2,…

level show log’s privilege, OFF,TRACE,DEBUG,INFO,WARN,ERROR,FATAL,ALL
log4j recommand 4 level, from low to high : DEBUG, INFO, WARN, ERROR

output

appenderName point logs’ output target
log4j.appender.xxx
log4j.appender.T.xxx

appender have these

org.apache.log4j.ConsoleAppender
to console
org.apache.log4j.FileAppender
to file
org.apache.log4j.DailyRollingFileAppender
create a file everyday
org.apache.log4j.RollingFileAppender
to some size make a new file
org.apache.log4j.WriterAppender
stream to everywhere

ConsoleAppender

-Threshold = DEBUG:log lowest output level
-ImmediateFlush = TRUE:default is true, all log will output immediately
-Target = System.err:default is System.out, out put to console(err is red,out is black)

FileAppender

-Threshold = INFO:log lowest output level
-ImmediateFlush = TRUE:default is true, all log will output immediately
-File = log/log4j.log:output file path
-Append = FALSE:default true, add message to file, false override file
-Encoding = UTF-8:appoint file encoding

DailyRollingFileAppender

-Threshold = WARN:log lowest output level
-ImmediateFlush = TRUE:default is true, all log will output immediately
-File = log/log4j.log:output file path
-Append = FALSE:default true, add message to file, false override file
-DatePattern=’.’yyyy-ww:every week
‘.’yyyy-MM:month
‘.’yyyy-ww:week
‘.’yyyy-MM-dd:day
‘.’yyyy-MM-dd-a:twice a day
‘.’yyyy-MM-dd-HH:hour
‘.’yyyy-MM-dd-HH-mm:minute
-Encoding = UTF-8:appoint file encoding

RollingFileAppender

-Threshold = ERROR:log lowest output level
-ImmediateFlush = TRUE:default is true, all log will output immediately
-File = log/log4j.log:output file path
-Append = FALSE:default true, add message to file, false override file
-MaxFileSize = 100KB:suffix can be KB MB GB when file met the threshold,
new file will be created like log4j.log.1 log4j.log.2
-MaxBackupIndex = 2:appoint rolling files’ up limit
-Encoding = UTF-8:appoint file encoding

layout

org.apache.log4j.HTMLLayout
org.apache.log4j.PatternLayout
customized layout
org.apache.log4j.SimpleLayout
contain log level, string so on
org.apache.log4j.TTCCLayout
contain time/ thread/ class info so on
org.apache.log4j.xml.XMLLayout

HTMLLayout

-LocationInfo = TRUE:default false, output java file and row num
-Title=Struts Log Message:默认值 Log4J Log Messages

PatternLayout

-ConversionPattern = %m%n:formatting message [reference to Format]

XMLLayout

-LocationInfo = TRUE:default false, output java file and row num

Format

similar with c style
| a | b |
| —- | —- |
| %m | message in code |
| %p | level:DEBUG,INFO,WARN,ERROR,FATAL |
| %r | Millisecond from code to file |
| %c | class full name |
| %t | Thread |
| %n | Windows \r\n Unix \n Max \r |
| %d | ISO8601 in default or %d{yyyy-MM-dd HH\:mm\:ss,SSS} like: 2017-09-18 22:10:28,921 |
| %l | detail in event like: Testlog.main(TestLog.java:10)|
| %F | file name |
| %L | code row num |
| %x | 输出和当前线程相关联的NDC(嵌套诊断环境),像java servlets多客户多线程的应用中 |
| %% | “%” |
| %5c | min width right alignment in default |
| %-5c | min width - left alignment |
| %.5c | max width split left char |
| %20.30c | less than 20 add blank, more than 30 split from left |

Demo

#OFF,systemOut,logFile,logDailyFile,logRollingFile,logMail,logDB,ALL
log4j.rootLogger =ALL,systemOut,logFile,logDailyFile,logRollingFile,logMail,logDB

#输出到控制台
log4j.appender.systemOut = org.apache.log4j.ConsoleAppender
log4j.appender.systemOut.layout = org.apache.log4j.PatternLayout
log4j.appender.systemOut.layout.ConversionPattern = [%-5p][%-22d{yyyy/MM/dd HH:mm:ssS}][%l]%n%m%n
#log4j.appender.systemOut.layout.ConversionPattern = %d{yyyy-MM-dd HH\:mm\:ss} %5p %c{1}\: %m%n
#log4j.appender.systemOut.layout.ConversionPattern = %d{yyyy-MM-dd HH\:mm\:ss,SSS} %5p [%t] (%F\:%L) - %m%n
log4j.appender.systemOut.Threshold = DEBUG
log4j.appender.systemOut.ImmediateFlush = TRUE
log4j.appender.systemOut.Target = System.out

#输出到文件
log4j.appender.logFile = org.apache.log4j.FileAppender
log4j.appender.logFile.layout = org.apache.log4j.PatternLayout
log4j.appender.logFile.layout.ConversionPattern = [%-5p][%-22d{yyyy/MM/dd HH:mm:ssS}][%l]%n%m%n
log4j.appender.logFile.Threshold = DEBUG
log4j.appender.logFile.ImmediateFlush = TRUE
log4j.appender.logFile.Append = TRUE
log4j.appender.logFile.File = ../Struts2/WebRoot/log/File/log4j_Struts.log
log4j.appender.logFile.Encoding = UTF-8

#按DatePattern输出到文件
log4j.appender.logDailyFile = org.apache.log4j.DailyRollingFileAppender
log4j.appender.logDailyFile.layout = org.apache.log4j.PatternLayout
log4j.appender.logDailyFile.layout.ConversionPattern = [%-5p][%-22d{yyyy/MM/dd HH:mm:ssS}][%l]%n%m%n
log4j.appender.logDailyFile.Threshold = DEBUG
log4j.appender.logDailyFile.ImmediateFlush = TRUE
log4j.appender.logDailyFile.Append = TRUE
log4j.appender.logDailyFile.File = ../Struts2/WebRoot/log/DailyFile/log4j_Struts
log4j.appender.logDailyFile.DatePattern = '.'yyyy-MM-dd-HH-mm'.log'
log4j.appender.logDailyFile.Encoding = UTF-8

#设定文件大小输出到文件
log4j.appender.logRollingFile = org.apache.log4j.RollingFileAppender
log4j.appender.logRollingFile.layout = org.apache.log4j.PatternLayout
log4j.appender.logRollingFile.layout.ConversionPattern = [%-5p][%-22d{yyyy/MM/dd HH:mm:ssS}][%l]%n%m%n
log4j.appender.logRollingFile.Threshold = DEBUG
log4j.appender.logRollingFile.ImmediateFlush = TRUE
log4j.appender.logRollingFile.Append = TRUE
log4j.appender.logRollingFile.File = ../Struts2/WebRoot/log/RollingFile/log4j_Struts.log
log4j.appender.logRollingFile.MaxFileSize = 1MB
log4j.appender.logRollingFile.MaxBackupIndex = 10
log4j.appender.logRollingFile.Encoding = UTF-8

#用Email发送日志
log4j.appender.logMail = org.apache.log4j.net.SMTPAppender
log4j.appender.logMail.layout = org.apache.log4j.HTMLLayout
log4j.appender.logMail.layout.LocationInfo = TRUE
log4j.appender.logMail.layout.Title = Struts2 Mail LogFile
log4j.appender.logMail.Threshold = DEBUG
log4j.appender.logMail.SMTPDebug = FALSE
log4j.appender.logMail.SMTPHost = SMTP.163.com
log4j.appender.logMail.From = xxx@163.com
log4j.appender.logMail.To = xxx@gmail.com
#log4j.appender.logMail.Cc = xxx@gmail.com
#log4j.appender.logMail.Bcc = xxx@gmail.com
log4j.appender.logMail.SMTPUsername = leon
log4j.appender.logMail.SMTPPassword = 123456
log4j.appender.logMail.Subject = Log4j Log Messages
#log4j.appender.logMail.BufferSize = 1024
#log4j.appender.logMail.SMTPAuth = TRUE

#将日志登录到MySQL数据库
log4j.appender.logDB = org.apache.log4j.jdbc.JDBCAppender
log4j.appender.logDB.layout = org.apache.log4j.PatternLayout
log4j.appender.logDB.Driver = com.mysql.jdbc.Driver
log4j.appender.logDB.URL = jdbc:mysql://127.0.0.1:3306/xxx
log4j.appender.logDB.User = root
log4j.appender.logDB.Password = 123456
log4j.appender.logDB.Sql = INSERT INTOT_log4j(project_name,create_date,level,category,file_name,thread_name,line,all_category,message)values('Struts2','%d{yyyy-MM-ddHH:mm:ss}','%p','%c','%F','%t','%L','%l','%m')

log4j.properties

Exchange

定理一 一个排列的任意两个元素对换，排列改变奇偶性

推论 奇排列变成标准排列，对换次数是奇数次；偶排列变成标准排列，对换次数是偶数次

定理二 n阶行列式也可定义为\sum_{}{(-1)^ta_{p_11}a_{p_22}...a_{p_nn}}

Property

性质1 行列式和它的转置行列式相等

性质2 互换行列式的两行（列），行列式变号

推论 如果有两行（列）完全相同，行列式为0

性质3 行列式某行（列）都乘以k，等于k乘以该行列式

性质4 行列式中如果有两行（列）成比例，行列式为等于零

性质5 如果行列式某行（列）都是两数的和，则可分为两行列式的和

性质6 把行列式某行（列）的元素乘以同一数，加到另一行（列），行列式不变

Primary

example

n Factorial determinant

More generalizate

Prove

缩写

符号

Security problem in java web

HashMap and HashTable

Theory

Thread security

ThreadLocal

Summary

Introduce

Caution

List

Split front and backgroud

Front emphasize in rendering

Backgroud emphasize in usability

Develop now

Option

Action

Engine

Host

Context

Wrapper

level

output

ConsoleAppender

FileAppender

DailyRollingFileAppender

RollingFileAppender

layout

HTMLLayout

PatternLayout

XMLLayout

Format

Demo

定理一一个排列的任意两个元素对换，排列改变奇偶性

推论奇排列变成标准排列，对换次数是奇数次；偶排列变成标准排列，对换次数是偶数次

定理二 n阶行列式也可定义为 $\sum_{}{(-1)^ta_{p_11}a_{p_22}...a_{p_nn}}$

推论如果有两行（列）完全相同，行列式为0