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Section05-Neural-Networks-and-Language-Modeling/section05-test.tex

@@ -18,6 +18,7 @@
 \usepackage{changepage}
 \usepackage{pgfplots}
 \usepackage{subfigure}
+ \usepackage{tikz-3dplot}
 
 \usetikzlibrary{arrows,decorations.pathreplacing}
 \usetikzlibrary{shadows} % LATEX and plain TEX when using Tik Z
@@ -145,13 +146,77 @@
     \item 如果它在同一个位置、从多个的方向上看，有不同的值，而且这个数恰好用矩阵乘观察方向来算出来，就是张量(rank$>$1)
     \end{itemize}
 \end{itemize}
+
+\vspace{-0.8em}
+\begin{center}
+\tdplotsetmaincoords{50}{140}
+\begin{tikzpicture}[scale=2,tdplot_main_coords]
+\visible<3->{
+\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$a$};
+\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$b$};
+\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$c$};
+}
+\pgfmathsetmacro{\ax}{2}
+\pgfmathsetmacro{\ay}{2}
+\pgfmathsetmacro{\az}{1}
+\tdplotsetrotatedcoords{20}{40}{00}
+\visible<4->{
+\draw[thick,color=red,tdplot_rotated_coords,->] (0,0,0)
+        -- (.7,0,0) node[anchor=east]{$a'$};
+\draw[thick,color=green!50!black,tdplot_rotated_coords,->] (0,0,0)
+        -- (0,.7,0) node[anchor=west]{$b'$};
+\draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0)
+        -- (0,0,.7) node[anchor=south]{$c'$};
+}
+\tdplottransformmainrot{\ax}{\ay}{\az}
+    
+\visible<3->{\node [anchor=west,inner sep=2pt] (coord1) at (-0.40in,-0.4in) {\footnotesize{方向$v=(a,b,c)$}};}
+\visible<4->{\node [anchor=north west,inner sep=2pt] (coord2) at (coord1.south west) {\footnotesize{方向$u=(\red{a'}\black{,}{\color{ugreen} b'}\black{,}\blue{c'}\black{)}$}};}
+    
+\begin{scope}[xshift=0.4in,yshift=0.35in]
+\visible<2->{
+\node [anchor=west,inner sep = 2pt] (description) at (0,0) {\small{$T(v,u)$是一个三维空间$(x,y,z)$上的}};
+\node [anchor=north west,inner sep = 2pt] (description2) at (description.south west) {\small{2阶张量，其中$v$和$u$是两个向量}};
+}
+
+\visible<5->{
+\node [anchor=north west,inner sep=2pt] (T) at ([yshift=-2em]description2.south west) {\small{$T(v,u)=$}};
+\node [anchor=west,inner sep=1pt] (T2) at (T.east) {\footnotesize{$\begin{pmatrix} v_x \\ v_y \\ v_z \end{pmatrix}^T$}};
+\node [anchor=west,inner sep=1pt] (T3) at ([xshift=2pt]T2.east) {\footnotesize{$\begin{pmatrix} T_{xx} & T_{xy} & T_{xz} \\ T_{yx} & T_{yy} & T_{yz} \\ T_{zx} & T_{zy} & T_{zz} \end{pmatrix}$}};
+\node [anchor=west,inner sep=1pt] (T4) at ([xshift=2pt]T3.east) {\footnotesize{$\begin{pmatrix} u_x \\ u_y \\ u_z \end{pmatrix}$}};
+}
+\begin{pgfonlayer}{background}
+\visible<7->{
+\node [rectangle,inner sep=0pt,fill=red!20,minimum height=3.5em] [fit = (T3) ] (TBox) {};
+}
+\visible<6->{
+\node [rectangle,inner sep=0pt,fill=green!20,minimum height=3.5em] [fit = (T2) ] (VBox) {};
+\node [rectangle,inner sep=0pt,fill=blue!20,minimum height=3.5em] [fit = (T4) ] (UBox) {};
+}
+\end{pgfonlayer}
+
+\visible<6->{
+\draw [<-] (VBox.north) -- ([yshift=0.3em]VBox.north);
+\node [anchor=south,align=left] (Vlabel) at ([yshift=0.3em]VBox.north) {\scriptsize{$v$在基向量上的投影}};
+\draw [<-] (UBox.north) -- ([yshift=0.3em]UBox.north);
+\node [anchor=south,align=left] (Ulabel) at ([yshift=0.3em,xshift=-1em]UBox.north) {\scriptsize{$u$在基向量上的投影}};
+}
+\visible<7->{
+\draw [<-] (TBox.south) -- ([yshift=-0.3em]TBox.south);
+\node [anchor=north,align=left] (Vlabel) at ([yshift=-0.3em]TBox.south) {\scriptsize{张量在$3 \times 3$个方向上的分量，记为$[T]$}};
+\node [anchor=north west,align=left] (Vlabel2) at ([yshift=0.2em]Vlabel.south west) {\scriptsize{想象一下坐标系的旋转}};
+}
+\end{scope}
+\end{tikzpicture}
+\end{center}
+
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
 %%% 如何在深度学习中定义一个张量
 \begin{frame}{在神经网络中使用张量}
 \begin{itemize}
-\item 但是前面说的可以忽略:) 在这个教程中，请记住``\alert{张量是多维数组}''
+\item 但是前面的可以忽略 - 在这里，``\alert{张量就是多维数组}''
 \end{itemize}
 \end{frame}