texlive[47227] Master: thucoursework (2apr18)
commits+karl at tug.org
commits+karl at tug.org
Mon Apr 2 00:28:35 CEST 2018
Revision: 47227
http://tug.org/svn/texlive?view=revision&revision=47227
Author: karl
Date: 2018-04-02 00:28:35 +0200 (Mon, 02 Apr 2018)
Log Message:
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thucoursework (2apr18)
Modified Paths:
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trunk/Master/tlpkg/bin/tlpkg-ctan-check
trunk/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc
Added Paths:
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trunk/Master/texmf-dist/doc/latex/thucoursework/
trunk/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md
trunk/Master/texmf-dist/doc/latex/thucoursework/Makefile
trunk/Master/texmf-dist/doc/latex/thucoursework/README.md
trunk/Master/texmf-dist/doc/latex/thucoursework/iihw.pdf
trunk/Master/texmf-dist/doc/latex/thucoursework/iihw.tex
trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk
trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.fls
trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.pdf
trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.tex
trunk/Master/texmf-dist/doc/latex/thucoursework/matlabscript.m
trunk/Master/texmf-dist/doc/latex/thucoursework/pdf_normal.eps
trunk/Master/texmf-dist/doc/latex/thucoursework/tl.profile
trunk/Master/texmf-dist/doc/latex/thucoursework/update.md
trunk/Master/texmf-dist/tex/latex/thucoursework/
trunk/Master/texmf-dist/tex/latex/thucoursework/iidef.sty
trunk/Master/tlpkg/tlpsrc/thucoursework.tlpsrc
Added: trunk/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md (rev 0)
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+This project is licensed by GPL version 2.1.
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/Makefile (rev 0)
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+# Makefile for thucoursework
+
+# Compiling method: xelatex/pdflatex
+
+INSTALL_PACKAGE = install-tl-unx.tar.gz
+INSTALL_DIR = ./install-texlive
+REMOTE_INSTALLER_URL = http://mirror.ctan.org/systems/texlive/tlnet
+
+.PHONY: all pre_install_dep install_dep after_install_dep clean test
+
+all: after_install_dep iihw.pdf ithw.pdf
+
+pre_install_dep: $(INSTALL_PACKAGE)
+
+after_install_dep: install_dep
+ # tricky, to make variable assignment in recipe, and to execute shell command and assign the print result to a variable.
+ $(eval PLATFORM1=`$(INSTALL_DIR)/install-tl --print-platform`)
+ $(eval PLATFORM2=$(shell echo $(PLATFORM1)))
+ $(eval PLATFORM3=$(shell pwd))
+ $(eval export PATH :=$(PLATFORM3)/texlive/bin/$(PLATFORM2):$(PATH))
+ echo $$PATH
+ # to make tlmgr work, we need perl
+ tlmgr install xkeyval matlab-prettifier caption doublestroke xcolor listings l3kernel l3packages ms ulem fontspec environ trimspaces booktabs moreenum mathtools oberdiek enumitem fmtcount etoolbox latex-bin
+install_dep: pre_install_dep
+ mkdir -p $(INSTALL_DIR)
+ tar -zxvf $(INSTALL_PACKAGE) -C $(INSTALL_DIR) --strip-components 1
+ $(INSTALL_DIR)/install-tl -profile tl.profile
+
+$(INSTALL_PACKAGE):
+ wget $(REMOTE_INSTALLER_URL)/$(INSTALL_PACKAGE)
+
+clean:
+ rm -fr $(INSTALL_DIR)
+
+iihw.pdf: iihw.tex after_install_dep
+ pdflatex iihw.tex
+
+ithw.pdf: ithw.tex after_install_dep
+ xelatex ithw.tex
+
+test:
+ # first clear out root texlive bin dir
+ $(eval export PATH := /bin:/usr/bin)
+ echo $$PATH
+ $(eval PLATFORM1=`$(INSTALL_DIR)/install-tl --print-platform`)
+ $(eval PLATFORM2=$(shell echo $(PLATFORM1)))
+ $(eval PLATFORM3=$(shell pwd))
+ $(eval export PATH := $(PLATFORM3)/texlive/bin/$(PLATFORM2):$(PATH))
+ echo $$PATH
+ tlmgr --version
Property changes on: trunk/Master/texmf-dist/doc/latex/thucoursework/Makefile
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/README.md (rev 0)
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+# THU coursework Template
+[](https://www.travis-ci.org/zhaofeng-shu33/THU-coursework-template)
+LaTeX package for students in Tsinghua University to write coursework more efficiently, also can be used by students from other university.
+
+Notice that the package itself does not import ctex package, to use it with Chinese writing, see example file `ithw.tex` for detail.
+
+## Features
+
+ * support custom courseheader
+ * support coursework counter
+ * definition of common math symbols
+
+## ToDo
+
+ * automatic enumerate environment labeling and reference
+
+## Usage
+
+`\usepackage{iidef}` and you are ready to go!
+
+## Sample File
+
+ * `iihw.tex` is the homework of **Information Inference**
+ * `ithw.tex` is the homework of **Information Theory**, chinese version (to make it work, use `ctex` package in user file.)
+
+## Contributors
+
+ TA xiangxiangxu revised this template, zhaofeng-shu33 made it a latex package.
+
+
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/iihw.pdf 2018-04-01 22:26:39 UTC (rev 47226)
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/iihw.tex (rev 0)
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+% Sample tex file for usage of iidef.sty
+% Homework template for Inference and Information
+% UPDATE: October 12, 2017 by Xiangxiang
+% UPDATE: 22/03/2018 by zhaofeng-shu33
+\documentclass[a4paper]{article}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath, amssymb, amsthm}
+% amsmath: equation*, amssymb: mathbb, amsthm: proof
+\usepackage{moreenum}
+\usepackage{mathtools}
+\usepackage{url}
+\usepackage[outdir=./]{epstopdf}
+\usepackage{graphicx}
+\usepackage{subcaption}
+\usepackage{booktabs} % toprule
+\usepackage[mathcal]{eucal}
+\usepackage{dsfont}
+
+\usepackage[numbered,framed]{matlab-prettifier}
+\lstset{
+ style = Matlab-editor,
+ captionpos =b,
+ basicstyle = \mlttfamily,
+ escapechar = ",
+ mlshowsectionrules = true,
+}
+
+\usepackage[thehwcnt = 6]{iidef}
+\thecourseinstitute{Tsinghua-Berkeley Shenzhen Institute}
+\thecoursename{Information Inference}
+\theterm{Fall 2017}
+\hwname{Coursework}
+\begin{document}
+\courseheader
+\name{YOUR NAME}
+\rule{\textwidth}{1pt}
+\begin{itemize}
+\item {\bf Acknowledgments: \/}
+ This template takes some materials from course CSE 547/Stat 548 of Washington University: \small{\url{https://courses.cs.washington.edu/courses/cse547/17sp/index.html}}.
+
+ If you refer to other materials in your homework, please list here.
+\item {\bf Collaborators: \/}
+ I finish this template by myself. If you finish your homework all by yourself, make a similar statement. If you get help from others in finishing your homework, state like this:
+ \begin{itemize}
+ \item 1.2 (b) was solved with the help from \underline{\hspace{3em}}.
+ \item Discussion with \underline{\hspace{3em}} helped me finishing 1.3.
+ \end{itemize}
+\end{itemize}
+\rule{\textwidth}{1pt}
+
+\vspace{2em}
+
+You may use \texttt{enumerate} to generate answers for each question:
+
+\begin{enumerate}
+ \setlength{\itemsep}{3\parskip}
+
+ \item Type of commonly used notations. Use another \texttt{enumerate} to start generate answers for sub-questions:
+ \begin{enumerate}
+ \item Use \verb|$ $| to get an inline equation: $\Prob(A) = \E[\1_A(\omega)]$.
+ \item Use \texttt{equation} to have equation in display math mode:
+ \begin{equation}
+ \frac{a + b}{2} \geq \sqrt{ab}
+ \label{eq:1}
+ \end{equation}
+
+ \item Use \verb|\eqref| to get reference for equations: \eqref{eq:1} holds when $a\geq 0, b\geq 0$.
+
+ \item Now we would introduce some commonly used notations:
+ \begin{enumerate}
+ \item Use \verb|\mathbb{P}, \mathbb{R}, \mathbb{E}| to type $\mathbb{P}, \mathbb{R}, \mathbb{E}$.
+ \item Use \verb|\mathcal{A}, \mathcal{X}, \mathcal{Y}, \mathcal{N}| to type $\mathcal{A}, \mathcal{X}, \mathcal{Y}, \mathcal{N}$.
+ \item Use \verb|\underline{x}, \underline{y}| to type vectors $\underline{x}, \underline{y}$.
+ \item Use \verb|\mathsf{x}, \mathsf{y}, \mathsf{z}| to type random variables $\rvx, \rvy, \rvz$. For simplicity, I have defined several macros so you could simply type \verb|\rvx, \rvy, \rvz|. Don't forget \verb|$ $|!
+ \item Thanks to these macros, we could have $\reals, \E[\rvx], \Var(\rvy), \Prob(A), \independent, \1$ by typing \verb|\reals, \E[\rvx], \Var(\rvy), \Prob(A),\independent,| \verb|\1|.
+ \item Now you can use \verb|\ux, \uy, \uz| to type vectors $\ux, \uy, \uz$, and use \verb|\urvx, \urvy, \urvz| to type random vectors $\urvx, \urvy, \urvz$.
+ \item Remember that $P_{\rvx|\rvy}(x|y) \defas \Prob(\rvx = x|\rvy = y)$.
+ \begin{enumerate}
+ \item Writing $\Prob(x)$ is wrong. $\Prob$ should only operate on events.
+ \item $\rvx$ is a random variable, while $x$ is a real number.
+ \end{enumerate}
+
+ \end{enumerate}
+ \item You may find \url{https://en.wikibooks.org/wiki/LaTeX} useful.
+ \item Writing \LaTeX\ online may be easier for beginners:
+ \begin{enumerate}
+ \item ShareLaTeX: \url{https://www.sharelatex.com/}.
+ \item Overleaf: \url{https://www.overleaf.com/}.
+ \end{enumerate}
+ \end{enumerate}
+ \item You may need aligned equations for your homework, here are several examples:
+
+ Total propability rule:
+ \begin{equation*}
+ \begin{aligned}
+ \Prob(\rvx = x)
+ &= \sum_{y \in \mathcal{Y}} \Prob(\rvx = x, \rvy = y)\\
+ &= \sum_{y \in \mathcal{Y}} \Prob(\rvx = x| \rvy = y) \Prob(\rvy = y),\\
+ \end{aligned}
+ \end{equation*}
+ or
+ \begin{equation*}
+ \begin{aligned}
+ &\quad~ P_{\rvx}(x)\\
+ &= \sum_{y \in \mathcal{Y}} P_{\rvx\rvy}(x,y)\\
+ &= \sum_{y \in \mathcal{Y}} P_{\rvx|\rvy}(x|y)P_{\rvy}(y).\\
+ \end{aligned}
+ \end{equation*}
+ Indicator function:
+ \begin{equation*}
+ \1_A(\omega)=
+ \left\{
+ \begin{aligned}
+ 1, &\quad\text{if}~ \omega \in A,\\
+ 0, &\quad\text{if}~ \omega \notin A.
+ \end{aligned}
+ \right.
+ \end{equation*}
+
+ \item You may need to add figure and source codes in your homework. Figure \ref{fig:1} is an example that compares the empirical distribution (histogram) and probability density function of the Gaussian random variable.
+ \begin{figure}[htbp]
+ \centering
+ \includegraphics[width = 0.8\textwidth]{pdf_normal.eps}
+ \caption{Gaussian PDF and histogram of samples}
+ \label{fig:1}
+ \end{figure}
+
+ The source code to plot Figure \ref{fig:1} could be found in Appendix \ref{sec:a:code}. Here are the core codes:
+ \lstinputlisting[firstline=4,lastline=4, firstnumber=4]{matlabscript.m}
+ \lstinputlisting[firstline=6,lastline=7, firstnumber=6]{matlabscript.m}
+ To understand line 6, note that if we have $n$ samples of $\rvx$ denoted by $x^{(i)}, i = 1, 2, \cdots, n$, then the probability density function $p_{\rvx}$ could be estimated as
+ \begin{equation*}
+ \begin{aligned}
+ p_{\rvx}(x_0) &= \left.\frac{\mathrm{d}}{\mathrm{d}x} \Prob(\rvx \leq x) \right|_{x = x_0} \\
+ &\approx \frac{\Prob(x_0 - \Delta x < \rvx \leq x_0)}{\Delta x}\\
+ &\approx \frac{1}{n\Delta x} \sum_{i = 1}^n \1_{x^{(i)} \in (x_0 - \Delta x, x_0]}.
+ \end{aligned}
+ \end{equation*}
+
+\item An example of hypothesis testing:
+ \begin{equation*}
+ \log \frac{\Prob(\rvH = H_1|\rvy = y)}{\Prob(\rvH = H_0|\rvy = y)}
+ \mathop{\gtreqless}_{\hat{\rvH} = H_0}^{\hat{\rvH} = H_1} \gamma
+ \end{equation*}
+
+ \end{enumerate}
+
+
+ \newpage
+
+ \appendix
+ \section{Source code}
+ \label{sec:a:code}
+ % \lstlistoflistings
+ Source code for plotting Figure \ref{fig:1} is shown as follows.
+ \lstinputlisting[caption=FigurePlot]{matlabscript.m}
+
+\end{document}
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk (rev 0)
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+# Fdb version 3
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===================================================================
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Index: trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.pdf 2018-04-01 22:26:39 UTC (rev 47226)
+++ trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.pdf 2018-04-01 22:28:35 UTC (rev 47227)
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___________________________________________________________________
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--- trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/thucoursework/ithw.tex 2018-04-01 22:28:35 UTC (rev 47227)
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+% Homework template for Inference and Information
+% UPDATE: September 26, 2017 by Xiangxiang
+\documentclass[a4paper]{article}
+\usepackage{ctex}
+\ctexset{
+proofname = \heiti{证明}
+}
+\usepackage{amsmath, amssymb, amsthm}
+% amsmath: equation*, amssymb: mathbb, amsthm: proof
+\usepackage{moreenum}
+\usepackage{mathtools}
+\usepackage{url}
+\usepackage{bm}
+\usepackage{enumitem}
+\usepackage{graphicx}
+\usepackage{subcaption}
+\usepackage{booktabs} % toprule
+\usepackage[mathcal]{eucal}
+\usepackage[thehwcnt = 1]{iidef}
+
+\thecourseinstitute{清华大学深圳研究生院}
+\thecoursename{应用信息论}
+\theterm{2018年春季学期}
+\hwname{作业}
+\slname{\heiti{解}}
+\begin{document}
+\courseheader
+\name{YOUR NAME}
+
+\begin{enumerate}
+ \setlength{\itemsep}{3\parskip}
+
+ \item 设$X$和$Y$是各有均值$m_x,m_y$,方差为$\sigma_x^2,\sigma_y^2$，且相互独立的高斯随机变量，已知$U=X+Y,V=X-Y$。试求$I(U;V)$。
+\begin{solution}
+$U,V$的联合分布是均值为$[\mu_x+\mu_y,\mu_x-\mu_y]$，协方差矩阵为
+$$\Lambda_{U,V}=\begin{bmatrix}
+1 & 1\\
+1 & -1\\
+\end{bmatrix}
+\begin{bmatrix}
+\sigma_x^2 & 0\\
+0 & \sigma_x^2\\
+\end{bmatrix}
+\begin{bmatrix}
+1 & 1\\
+1 & -1\\
+\end{bmatrix}^T
+=\begin{bmatrix}
+\sigma_x^2+\sigma_y^2 & \sigma_x^2-\sigma_y^2\\
+\sigma_x^2-\sigma_y^2 & \sigma_x^2+\sigma_y^2\\
+\end{bmatrix}
+$$
+由多元高斯分布微分熵的公式
+$$
+h(U)=\frac{1}{2}\log ((2\pi e)^2 |\Lambda_{U,V}|)=\frac{1}{2}\log(16\pi^2 e^2 \sigma^2_x\sigma^2_y)
+$$
+$U|V=v$也是高斯分布,方差为$\frac{4\sigma_x^2\sigma_y^2}{\sigma_x^2+\sigma_y^2}$，与$v$无关，因此
+$$
+h(U|V)=\E_{V}[h(U|V=v)]=\frac{1}{2}\log(2\pi e \frac{4\sigma_x^2\sigma_y^2}{\sigma_x^2+\sigma_y^2})\Rightarrow
+$$
+\begin{align*}
+I(U;V)=& h(U)-h(U|V)\\
+=&\frac{1}{2}\log(16\pi^2 e^2 \sigma^2_x\sigma^
+2_y)-\frac{1}{2}\log(2\pi e \frac{4\sigma_x^2\sigma_y^2}{\sigma_x^2+\sigma_y^2})\\
+=&\frac{1}{2}\log(2\pi e (\sigma_x^2+\sigma_y^2))
+\end{align*}
+
+%$$
+%p(u,v)=\frac{1}{4\pi \sigma_x\sigma_y}\exp(-\frac{(\frac{u+v}{2}-\mu_x)^2+(\frac{u+v}{2}-\mu_y)^2}{2})
+%$$
+
+\end{solution}
+\item 设有随机变量$X,Y,Z$均取值于$\{0,1\}$,已知$I(X;Y)=0,I(X;Y|Z)=1$。求证$H(Z)=1,H(X,Y,Z)=2$
+\begin{proof}
+$I(X;Y|Z)=H(X|Z)-H(X|Y,Z)\leq H(X|Z)\leq H(X)\leq \log(2)=1$
+所以等号全都成立$\Rightarrow X\sim B(\frac{1}{2})$。
+同理可知$Y\sim B(\frac{1}{2})$。
+另外$H(Y|Z)=H(Y)\Rightarrow I(Y;Z)=0\Rightarrow H(Z|Y)=H(Z)$
+\begin{align*}
+&H(X|Y,Z)=0 \\
+\iff &H(X,Y,Z)=H(Y,Z)\\
+\iff &H(X,Y)+H(Z|X,Y)=H(Y)+H(Z|Y)\\
+\iff &2+H(Z|X,Y)=1+H(Z)\\
+\iff &H(Z)=1+H(Z|X,Y)
+\end{align*}
+由上式推出$H(Z)\geq 1$,又$H(Z)\leq 1\Rightarrow H(Z)=1\Rightarrow H(X,Y,Z)=2$
+\end{proof}
+\item
+设有信号$X$经过处理器$A$后获输出$Y$,$Y$再经处理器$B$后获输出$Z$。已知处理器$A$和$B$
+分别独立处理$X$和$Y$。试证：$I(X;Z)\leq I(X;Y)$
+\begin{proof}
+$I(X;Z)=H(Z)-H(Z|X)=H(Z);I(Y;Z)=H(Y)$因为$Z$是$Y$的函数$\Rightarrow H(Z)\leq H(Y) \Rightarrow I(X;Z)\leq I(X;Y)$
+\end{proof}
+\item 已知随机变量$X$和$Y$的联合概率密度$p(a_k,b_j)$满足
+$$
+p(a_1)=\frac{1}{2},p(a_2)=p(a_3)=\frac{1}{4},p(b_1)=\frac{2}{3},p(b_2)=p(b_3)=\frac{1}{6}
+$$
+试求能使$H(X,Y)$取得最大值的联合概率密度分布。
+\begin{solution}
+$H(X,Y)=H(X)+H(Y)-I(X;Y)\leq H(X)+H(Y)=\frac{7}{6}+\log 3$
+等号成立当且仅当$X,Y$相互独立$\Rightarrow p(x,y)=p(x)p(y)$
+\end{solution}
+\item 设随机变量$X,Y,Z$满足$p(x,y,z)=p(x)p(y|x)p(z|y)$。求证$I(X;Y)\geq I(X;Y|Z)$
+\begin{proof}
+因为$p(x,y,z)=p(x)p(y|x)p(z|y,x)\Rightarrow p(z|y,x)=p(z|x)\Rightarrow x$ 与$z$关于$y$条件独立$\Rightarrow I(X;Y|Z)=H(X|Z)-H(X|Y,Z)= H(X|Z)-H(X|Y)\leq H(X)-H(X|Y) =I(X;Y)$
+\end{proof}
+\item 求证$I(X;Y;Z)=H(X,Y,Z)-H(X)-H(Y)-H(Z)+I(X;Y)+I(Y;Z)+I(Z;X)$,其中
+$I(X;Y;Z)\triangleq I(X;Y)-I(X;Y|Z)$
+\begin{proof}
+\begin{align*}
+I(X;Y;Z) =& I(X;Y)-I(X;Y|Z) \\
+=& H(X)+H(Y)-H(X,Y)-(H(X|Z)-H(X|Y,Z))\\
+=& H(X)+H(Y)-H(X,Y)-(H(X,Z)-H(Z))+H(X,Y,Z)-H(Y,Z)\\
+=& H(X,Y,Z)-H(X)-H(Y)-H(Z)+(H(X)+H(Y)-H(X,Y))\\
++&(H(Y)+H(Z)-H(Y,Z))+(H(Z)+H(X)-H(X,Z))\\
+=& H(X,Y,Z)-H(X)-H(Y)-H(Z)+I(X;Y)+I(Y;Z)+I(Z;X)
+\end{align*}
+\end{proof}
+\item 令$p=(p_1,p_2,\dots,p_a)$是一个概率分布，满足$p_1\geq p_2\geq \dots p_a$,假设$\epsilon >0 $使得$p_1-\epsilon \geq p_2+\epsilon$成立，证明：$H(p_1,p_2,\dots,p_a)
+\leq H(p_1-\epsilon,p_2+\epsilon,p_3,\dots,p_a)$
+\begin{proof}
+设$f(\epsilon)=(p_1-\epsilon)\log(p_1-\epsilon)+(p_2+\epsilon)\log(p_2+\epsilon)$
+由已知$0\leq \epsilon \frac{p_2-p_1}{2}$
+$f'(\epsilon)=\log\frac{p_2+\epsilon}{p_1-\epsilon}\leq 0$
+$\Rightarrow f(\epsilon)\leq f(0)\Rightarrow H(p_1,p_2,\dots,p_a)\leq H(p_1-\epsilon,p_2+\epsilon,p_3,\dots,p_a)$
+\end{proof}
+\item 设$p_i(x)\sim N(\mu_i,\sigma_i^2)$,试求相对熵$D(p_2||p_1)$
+\begin{solution}
+\begin{align*}
+D(p_2||p_1)=& \int_{\mathbb{R}} p_2(x) \log \frac{p_2(x)}{p_1(x)}dx\\
+=& \int_{\mathbb{R}} p_2(x) \left(\log \frac{\sigma_1^2}{\sigma_2^2}+\frac{1}{2}((x-\mu_1)^2-(x-\mu_2)^2)\log e\right)dx\\
+=& 2\log \frac{\sigma_1}{\sigma_2}+\frac{1}{2}(\mu_1^2-\mu_2^2)\log e+(\mu_2-\mu_1)\mu_2\log e\\
+=& 2\log \frac{\sigma_1}{\sigma_2}+\frac{1}{2}(\mu_1-\mu_2)^2\log e
+\end{align*}
+\end{solution}
+\item 若$f(x)$分别是区间$(0,0.01),(0,0.5),(0,1),(0,2),(0,5)$上均匀分布的分布函数，计算$f(x)$的微分熵。
+\begin{solution}
+设$U_t$是$(0,t)$上的均匀分布，则$h(U_t)=\log t$
+\begin{itemize}
+\item $h(U_{0.01})=\log 0.01$
+\item $h(U_{0.5})=-1$
+\item $h(U_{1})=0$
+\item $h(U_{2})=1$
+\item $h(U_{5})=\log 5$
+\end{itemize}
+\end{solution}
+\item 设
+\begin{align*}
+p_1(x,y)=& \frac{1}{2\pi \sigma_x\sigma_y}\exp[-\frac{1}{2}(\frac{x^2}{\sigma_x^2}+\frac{y^2}{\sigma_y^2})]\\
+p_2(x,y)=& \frac{1}{2\pi \sigma_x\sigma_y\sqrt{1-\rho^2}}\exp[-\frac{1}{2(1-\rho^2)}(\frac{x^2}{\sigma_x^2}-2\rho\frac{xy}{\sigma_x\sigma_y}+\frac{y^2}{\sigma_y^2})]
+\end{align*}
+试求$D(p_2||p_1)$和$I(X;Y)$，其中$X,Y\sim p_2$
+\begin{solution}
+\begin{align*}
+D(p_2||p_1) = & \iint_{\mathbb{R}^2} p_2(x,y)\log \frac{p_2(x,y)}{p_1(x,y)}dxdy \\
+ -&\frac{1}{2}\log(1-\rho^2)\\
+-&\frac{1}{2}(\log e)\iint_{\mathbb{R}^2} p_2(x,y)\left[\frac{\rho^2 x^2}{\sigma_x^2(1-\rho^2)}+\frac{\rho^2 y^2}{\sigma_y^2(1-\rho^2)}-\frac{2\rho xy}{(1-\rho^2)\sigma_x\sigma_y}\right]dxdy\\
+=&-\frac{1}{2}\log(1-\rho^2)
+\end{align*}
+$X|Y=y$服从高斯分布，方差为$(1-\rho^2)\sigma_x^2$
+\begin{align*}
+I(X;Y) = & h(X)-h(X|Y)\\
+= & \frac{1}{2}\log(2\pi e \sigma_x^2) - \frac{1}{2}\log(2\pi e \sigma_x^2(1-\rho^2))\\
+= & \frac{1}{2}\log(\frac{2\pi e}{1-\rho^2})
+\end{align*}
+
+\end{solution}
+
+\end{enumerate}
+\end{document}
+\begin{equation}
+\end{equation}
+
+%%% Local Variables:
+%%% mode: late\rvx
+%%% TeX-master: t
+%%% End:
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Added: trunk/Master/texmf-dist/doc/latex/thucoursework/tl.profile
===================================================================
--- trunk/Master/texmf-dist/doc/latex/thucoursework/tl.profile (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/thucoursework/tl.profile 2018-04-01 22:28:35 UTC (rev 47227)
@@ -0,0 +1,14 @@
+selected_scheme scheme-basic
+collection-fontsrecommended 1
+collection-langchinese 1
+collection-latex 1
+collection-xetex 1
+tlpdbopt_install_docfiles 0
+tlpdbopt_install_srcfiles 0
+TEXDIR ./texlive
+TEXMFCONFIG ./texlive/texmf-config
+TEXMFHOME ./texlive
+TEXMFLOCAL ./texlive
+TEXMFSYSCONFIG ./texlive/texmf-config
+TEXMFSYSVAR ./texlive/texmf-var
+TEXMFVAR ./texlive/texmf-var
Added: trunk/Master/texmf-dist/doc/latex/thucoursework/update.md
===================================================================
--- trunk/Master/texmf-dist/doc/latex/thucoursework/update.md (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/thucoursework/update.md 2018-04-01 22:28:35 UTC (rev 47227)
@@ -0,0 +1,36 @@
+September 26, 2017 [Xiangxiang]
+v1.1
+- Add mathcal and eucal package
+- Add aligned equations
+
+October 9, 2017 [Xiangxiang]
+v1.2
+- Add example for figures
+- Add example for input matlab codes
+- No need to set counter style manually
+
+October 12, 2017 [Xiangxiang]
+v1.3
+- Add example for vector and random vectors (underline)
+
+October 30, 2017 [Xiangxiang]
+v1.4
+- Add an example of hypothesis testing
+
+March 22, 2018 [zhaofeng-shu33]
+v2.0
+- Make it a latex package(.sty)
+
+v2.1
+- Use kvoptions to set the coursework counter.
+
+27/03/2018 [zhaofeng-shu33]
+v2.2
+- Use fancyhdr to set the coursework user file header.
+
+30/03/2018 [zhaofeng-shu33]
+v2.3
+- User configuration of Homework
+- Add solution environment
+- User configuration of solution environment name
+- Add sample file `hthw.tex`
Property changes on: trunk/Master/texmf-dist/doc/latex/thucoursework/update.md
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/thucoursework/iidef.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/thucoursework/iidef.sty (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/thucoursework/iidef.sty 2018-04-01 22:28:35 UTC (rev 47227)
@@ -0,0 +1,136 @@
+%% GPL v2.1
+%% version 2.3
+%% UPDATE: 30/03/2018 by zhaofeng-shu33
+%% This package requires package kvoptions,enumitems
+\ProvidesPackage{iidef}
+% semester
+\def\@term{term}
+\newcommand{\theterm}[1]{\renewcommand\@term{#1}}
+% institute
+\newcommand{\@courseinstitute}[1]{institute}
+\newcommand{\thecourseinstitute}[1]{\renewcommand\@courseinstitute{#1}}
+% coursename
+\newcommand{\@coursename}[1]{coursename}
+\newcommand{\thecoursename}[1]{\renewcommand\@coursename{\textsc{#1}}}
+
+% configuration of nested enumerate env
+\RequirePackage{enumitem}
+% set hwcount key-value option
+\RequirePackage{kvoptions}
+% required by macro DeclareMathOperator
+\RequirePackage{amsmath}
+
+% \iidef at thehwcnt = 1
+\DeclareStringOption[1]{thehwcnt}
+
+\ProcessKeyvalOptions*
+\def\thehwcnt{\iidef at thehwcnt}
+% enumitem related configuration
+\setlist[enumerate,1]{label=\thehwcnt.\arabic*.}
+\setlist[enumerate,2]{label=(\alph*)}
+\setlist[enumerate,3]{label=\roman*.}
+\setlist[enumerate,4]{label=\greek*)}
+
+% user can rewrite homework name
+\def\@hwname{Homework}
+\def\hwname#1{\renewcommand\@hwname{#1}}
+
+% page header setup, distinguish between first page(plain style) and second page on (runningpage style)
+%*****************************************************************************************************
+\newcommand{\courseheader}{
+\thispagestyle{plain}%first page use native plain style to suppress header
+\vspace*{-1in}
+\begin{center}
+\@courseinstitute\\
+\@coursename\\
+\@term
+\vspace*{0.1in}
+\hrule
+\end{center}
+\begin{center}
+ \underline{\bf \@hwname\;\thehwcnt} \\
+\end{center}
+}
+% Set up page headers using with fancyhdr
+\RequirePackage{fancyhdr}
+\fancypagestyle{runningpage}
+{
+ \fancyhead[L]{\small\@coursename}
+ \fancyhead[R]{\small\@courseinstitute}
+}
+% use runningpage style from second page on
+\pagestyle{runningpage}
+% *********************************************************************************************
+
+%common math symbols go here
+%*************************************************
+\def\v#1{\underline{#1}}
+\newcommand{\uc}{\underline{c}} % c, vec
+\newcommand{\uv}{\underline{v}} % x, vec
+\newcommand{\uw}{\underline{w}} % w, vec
+\newcommand{\ux}{\underline{x}} % x, vec
+\newcommand{\uy}{\underline{y}} % y, vec
+\newcommand{\uz}{\underline{z}} % z, vec
+\newcommand{\um}{\underline{m}} % m, vec
+\newcommand{\rvx}{\mathsf{x}} % x, r.v.
+\newcommand{\rvy}{\mathsf{y}} % y, r.v.
+\newcommand{\rvz}{\mathsf{z}} % z, r.v.
+\newcommand{\rvw}{\mathsf{w}} % w, r.v.
+\newcommand{\rvH}{\mathsf{H}} % H, r.v.
+\newcommand{\urvx}{\underline{\mathsf{x}}} % x, r.v. vec
+\newcommand{\urvy}{\underline{\mathsf{y}}} % y, r.v. vec
+\newcommand{\urvz}{\underline{\mathsf{z}}} % z, r.v. vec
+\newcommand{\urvw}{\underline{\mathsf{w}}} % w, r.v. vec
+
+\newcommand{\defas}{\triangleq} %\coloneqq
+\newcommand{\reals}{\mathbb{R}}
+\newcommand{\TT}{\mathrm{T}} % transpose
+\DeclareMathOperator*{\argmax}{arg\,max}
+\DeclareMathOperator*{\argmin}{arg\,min}
+\DeclareMathOperator*{\argsup}{arg\,sup}
+\DeclareMathOperator*{\arginf}{arg\,inf}
+\DeclareMathOperator{\diag}{diag}
+\DeclareMathOperator{\Var}{Var}
+\DeclareMathOperator{\Cov}{Cov}
+\DeclareMathOperator{\MSE}{MSE}
+\DeclareMathOperator{\1}{\mathds{1}}
+\DeclareMathOperator{\In}{\mathbb{I}}
+\DeclareMathOperator{\E}{\mathbb{E}}
+\DeclareMathOperator{\Prob}{\mathbb{P}}
+\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}}
+\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}
+%************************************************************************************
+
+%name command macro
+%*************************
+\newcommand{\name}[1]{
+\begin{flushleft}
+ #1\hfill
+ \today
+\end{flushleft}
+\hrule
+
+\vspace{2em}
+
+\flushleft
+}
+%*************************
+
+%define the solution env with amsthm proof
+%******************************
+\RequirePackage{amsthm}
+
+\def\@slname{Solution}
+\def\slname#1{\renewcommand\@slname{#1}}
+
+\newenvironment{solution}
+{
+\proof[\@slname]
+}
+{
+% no qed symbol in solution env
+\renewcommand{\qedsymbol}{}
+\endproof
+}
+%******************************
+\endinput
Property changes on: trunk/Master/texmf-dist/tex/latex/thucoursework/iidef.sty
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Modified: trunk/Master/tlpkg/bin/tlpkg-ctan-check
===================================================================
--- trunk/Master/tlpkg/bin/tlpkg-ctan-check 2018-04-01 22:26:39 UTC (rev 47226)
+++ trunk/Master/tlpkg/bin/tlpkg-ctan-check 2018-04-01 22:28:35 UTC (rev 47227)
@@ -618,7 +618,7 @@
tfrupee thaienum thaispec thalie theatre theoremref
thesis-ekf thesis-gwu thesis-titlepage-fhac
thinsp thmbox thmtools threadcol threeddice threeparttable threeparttablex
- thumb thumbpdf thumbs thumby thuthesis
+ thucoursework thumb thumbpdf thumbs thumby thuthesis
ticket ticollege
tikz-bayesnet tikz-cd tikz-3dplot tikz-dependency tikz-dimline
tikz-feynhand tikz-feynman tikz-inet
Modified: trunk/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc
===================================================================
--- trunk/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc 2018-04-01 22:26:39 UTC (rev 47226)
+++ trunk/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc 2018-04-01 22:28:35 UTC (rev 47227)
@@ -152,6 +152,7 @@
depend thesis-ekf
depend thesis-gwu
depend thesis-titlepage-fhac
+depend thucoursework
depend thuthesis
depend timbreicmc
depend toptesi
Added: trunk/Master/tlpkg/tlpsrc/thucoursework.tlpsrc
===================================================================
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