61 lines
2.0 KiB
TeX
61 lines
2.0 KiB
TeX
\documentclass{standalone}
|
|
|
|
\usepackage[T1]{fontenc}
|
|
\usepackage{tikz}
|
|
\usepackage{amsmath,amssymb}
|
|
|
|
% matrices
|
|
\newcommand*{\mat}[1]{\boldsymbol{#1}}
|
|
% tensors (special case for lower case caligraphic letters)
|
|
\newcommand*{\ten}[1]{
|
|
\ifnum\pdfstrcmp{#1}{`}=1 % lowercase argument
|
|
\mathfrak{#1}
|
|
\else % uppercase argument
|
|
\mathcal{#1}
|
|
\fi
|
|
}
|
|
% matrix transpose
|
|
\renewcommand*{\t}[1]{{#1^{T}}}
|
|
% Expected Value
|
|
\newcommand{\E}{\operatorname{\mathbb{E}}}
|
|
|
|
|
|
\begin{document}
|
|
\begin{tikzpicture}[scale = 1.2, line width = 1pt]
|
|
|
|
\def\rect#1#2#3{
|
|
\draw (0, 0, 0) -- (#1, 0, 0) -- (#1, #2, 0) -- (0, #2, 0) -- cycle;
|
|
|
|
\draw[ ] (#1, 0, -#3) -- (#1, #2, -#3) -- (0, #2, -#3);
|
|
\draw[dashed] (#1, 0, -#3) -- (0, 0, -#3) -- (0, #2, -#3);
|
|
|
|
\draw[dashed] (0, 0, 0) -- (0, 0, -#3);
|
|
\draw[ ] (0, #2, 0) -- (0, #2, -#3);
|
|
\draw[ ] (#1, 0, 0) -- (#1, 0, -#3);
|
|
\draw[ ] (#1, #2, 0) -- (#1, #2, -#3);
|
|
}
|
|
|
|
\begin{scope}[yshift = 1cm, line width = 1pt]
|
|
\rect{1.5}{1}{2}
|
|
\node[font = \boldmath] at (1, 0.5) {$\ten{R}(\ten{X})$};
|
|
\end{scope}
|
|
\rect{3}{2}{4}
|
|
\node at (2, 0.5) {$\ten{X} - \E\ten{X}$};
|
|
|
|
\draw[lightgray, line width = 0.7pt] (-2.1, 2) arc (180:270:2);
|
|
\draw[fill = lightgray, fill opacity = 0.7] (-2.1, 1) rectangle +(2, 1)
|
|
node [pos = 0.5] {$\t{\mat{\beta}_1}$};
|
|
|
|
\draw[lightgray, line width = 0.7pt, domain = 0:1, smooth, variable = \t]
|
|
plot ({0}, {2.1 + 4 * cos(90 * \t)}, {-4 * sin(90 * \t)});
|
|
\draw[fill = lightgray, fill opacity = 0.7]
|
|
(0, 2.1, 0) -- (0, 2.1, -2) -- (0, 6.1, -2) -- (0, 6.1, 0) -- cycle;
|
|
\node[opacity = 0.7, cm={0.66, 0.66, 0, 1, (0, 0)}]
|
|
at (0, 5.3, -1.1) {$\t{\mat{\beta}_3}$};
|
|
|
|
\draw[lightgray, line width = 0.7pt] (0, 5.1) arc (90:0:3);
|
|
\draw[fill = lightgray, fill opacity = 0.7] (0, 2.1) rectangle +(1.5, 3)
|
|
node [pos = 0.5] {$\t{\mat{\beta}_2}$};
|
|
\end{tikzpicture}
|
|
\end{document}
|