From a90952824018c8cc8372c913f1778fc7a7ed2e37 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Sun, 1 Apr 2018 22:28:35 +0000 Subject: thucoursework (2apr18) git-svn-id: svn://tug.org/texlive/trunk@47227 c570f23f-e606-0410-a88d-b1316a301751 --- .../texmf-dist/doc/latex/thucoursework/LICENSE.md | 1 + Master/texmf-dist/doc/latex/thucoursework/Makefile | 50 + .../texmf-dist/doc/latex/thucoursework/README.md | 30 + Master/texmf-dist/doc/latex/thucoursework/iihw.pdf | Bin 0 -> 309084 bytes Master/texmf-dist/doc/latex/thucoursework/iihw.tex | 162 ++ .../doc/latex/thucoursework/ithw.fdb_latexmk | 244 ++ Master/texmf-dist/doc/latex/thucoursework/ithw.fls | 359 +++ Master/texmf-dist/doc/latex/thucoursework/ithw.pdf | Bin 0 -> 83095 bytes Master/texmf-dist/doc/latex/thucoursework/ithw.tex | 177 ++ .../doc/latex/thucoursework/matlabscript.m | 14 + .../doc/latex/thucoursework/pdf_normal.eps | 2944 ++++++++++++++++++++ .../texmf-dist/doc/latex/thucoursework/tl.profile | 14 + .../texmf-dist/doc/latex/thucoursework/update.md | 36 + .../texmf-dist/tex/latex/thucoursework/iidef.sty | 136 + Master/tlpkg/bin/tlpkg-ctan-check | 2 +- Master/tlpkg/tlpsrc/collection-publishers.tlpsrc | 1 + Master/tlpkg/tlpsrc/thucoursework.tlpsrc | 0 17 files changed, 4169 insertions(+), 1 deletion(-) create mode 100644 Master/texmf-dist/doc/latex/thucoursework/LICENSE.md create mode 100644 Master/texmf-dist/doc/latex/thucoursework/Makefile create mode 100644 Master/texmf-dist/doc/latex/thucoursework/README.md create mode 100644 Master/texmf-dist/doc/latex/thucoursework/iihw.pdf create mode 100644 Master/texmf-dist/doc/latex/thucoursework/iihw.tex create mode 100644 Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk create mode 100644 Master/texmf-dist/doc/latex/thucoursework/ithw.fls create mode 100644 Master/texmf-dist/doc/latex/thucoursework/ithw.pdf create mode 100644 Master/texmf-dist/doc/latex/thucoursework/ithw.tex create mode 100644 Master/texmf-dist/doc/latex/thucoursework/matlabscript.m create mode 100644 Master/texmf-dist/doc/latex/thucoursework/pdf_normal.eps create mode 100644 Master/texmf-dist/doc/latex/thucoursework/tl.profile create mode 100644 Master/texmf-dist/doc/latex/thucoursework/update.md create mode 100644 Master/texmf-dist/tex/latex/thucoursework/iidef.sty create mode 100644 Master/tlpkg/tlpsrc/thucoursework.tlpsrc (limited to 'Master') diff --git a/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md b/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md new file mode 100644 index 00000000000..ba9bcd4a044 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/LICENSE.md @@ -0,0 +1 @@ +This project is licensed by GPL version 2.1. diff --git a/Master/texmf-dist/doc/latex/thucoursework/Makefile b/Master/texmf-dist/doc/latex/thucoursework/Makefile new file mode 100644 index 00000000000..f134f1121ea --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/Makefile @@ -0,0 +1,50 @@ +# 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 diff --git a/Master/texmf-dist/doc/latex/thucoursework/README.md b/Master/texmf-dist/doc/latex/thucoursework/README.md new file mode 100644 index 00000000000..886f42b68f3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/README.md @@ -0,0 +1,30 @@ +# THU coursework Template +[![Build Status](https://www.travis-ci.org/zhaofeng-shu33/THU-coursework-template.svg?branch=master)](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. + + diff --git a/Master/texmf-dist/doc/latex/thucoursework/iihw.pdf b/Master/texmf-dist/doc/latex/thucoursework/iihw.pdf new file mode 100644 index 00000000000..a9582fec984 Binary files /dev/null and b/Master/texmf-dist/doc/latex/thucoursework/iihw.pdf differ diff --git a/Master/texmf-dist/doc/latex/thucoursework/iihw.tex b/Master/texmf-dist/doc/latex/thucoursework/iihw.tex new file mode 100644 index 00000000000..b444b3d01b0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/iihw.tex @@ -0,0 +1,162 @@ +% 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: diff --git a/Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk b/Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk new file mode 100644 index 00000000000..0063e388ab8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/ithw.fdb_latexmk @@ -0,0 +1,244 @@ +# Fdb version 3 +["pdflatex"] 1522547377 "/home/zhaofeng-shu33/Documents/thucoursework/ithw.tex" "ithw.pdf" "ithw" 1522547377 + "/dev/null" 1522494856 0 d41d8cd98f00b204e9800998ecf8427e "" + "/home/zhaofeng-shu33/Documents/thucoursework/ithw.tex" 1522547374 6662 87ff0172d0cfc13dabfbe212eef557a8 "" + "/usr/local/texlive/2017/texmf-dist/fonts/map/fontname/texfonts.map" 1511824771 3332 103109f5612ad95229751940c61aada0 "" + 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+\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: diff --git 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+617 121 L +cp +S +GR +%%Trailer +%%Pages: 1 +%%EOF diff --git a/Master/texmf-dist/doc/latex/thucoursework/tl.profile b/Master/texmf-dist/doc/latex/thucoursework/tl.profile new file mode 100644 index 00000000000..78ff318a839 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/tl.profile @@ -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 diff --git a/Master/texmf-dist/doc/latex/thucoursework/update.md b/Master/texmf-dist/doc/latex/thucoursework/update.md new file mode 100644 index 00000000000..5111cde5e5f --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/update.md @@ -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` diff --git a/Master/texmf-dist/tex/latex/thucoursework/iidef.sty b/Master/texmf-dist/tex/latex/thucoursework/iidef.sty new file mode 100644 index 00000000000..bf20d1d025c --- /dev/null +++ b/Master/texmf-dist/tex/latex/thucoursework/iidef.sty @@ -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@thehwcnt = 1 +\DeclareStringOption[1]{thehwcnt} + +\ProcessKeyvalOptions* +\def\thehwcnt{\iidef@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 diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index a8ca636ec69..80dedc28132 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -618,7 +618,7 @@ my @TLP_working = qw( 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 diff --git a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc index d6760647dac..ecbd659df06 100644 --- a/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-publishers.tlpsrc @@ -152,6 +152,7 @@ depend texilikecover depend thesis-ekf depend thesis-gwu depend thesis-titlepage-fhac +depend thucoursework depend thuthesis depend timbreicmc depend toptesi diff --git a/Master/tlpkg/tlpsrc/thucoursework.tlpsrc b/Master/tlpkg/tlpsrc/thucoursework.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d -- cgit v1.2.3