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krotovscheme.tex
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krotovscheme.tex
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\documentclass{article}
\usepackage{amsmath}
\newcommand{\bra}[1]{\ensuremath{\langle #1 \vert}} % for normal text
\newcommand{\ket}[1]{\ensuremath{\vert #1 \rangle}} % for normal text
\newcommand{\Bra}[1]{\left\langle #1 \right\vert}
\newcommand{\KetBra}[2]{\Ket{#1}\kern-0.1em\Bra{#2}}
\newcommand{\Ket}[1]{\left\vert #1 \right\rangle}
\newcommand{\Op}[1]{\ensuremath{\boldsymbol{\mathsf{\hat{#1}}}}}
\usepackage{tikz}
\usepackage[psfixbb,graphics,tightpage,active]{preview}
\PreviewEnvironment{tikzpicture}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[
x=0.85cm,
y=1.0cm,
]
%\tikzset{help lines/.style=gray, ultra thin}
%\tikzset{help lines/.style=white, ultra thin}
%\draw[style=help lines, step=1cm] (0,0) grid (20,15);
\tikzstyle{every node}+=[font= \small ]
%%% propagation boxes
% lower
\draw[color=gray!20, fill=gray!20,rounded corners=10] (2,2.1) rectangle (16,4.40);
\node[align=center] at (9, 2.3){\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {2}}} forward-propagation with updated control};
%\draw[color=gray!20, fill=gray!20,rounded corners=10] (14,2.8) rectangle (16,4.75);
% upper
\draw[color=gray!20, fill=gray!20,rounded corners=10] (2,5.60) rectangle (16,7.9);
\node[align=center] at (9, 7.7){\raisebox{.5pt}{\textcircled{\raisebox{-.9pt} {1}}} backward-propagation and storage with guess control};
%\draw[color=gray!20, fill=gray!20,rounded corners=10] (14,5.25) rectangle (16,7.2);
%%% forward propagation
\node (psifw1) at (3,4) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,-0.25)--(1,0);
\node at (0.5,0.25) {$\phi_k(0)$};
\end{tikzpicture}
};
\node (psifw2) at (6,4) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,-0.25)--(1,0);
\node at (0.5,0.25) {$\phi_k(t_1)$};
\end{tikzpicture}
};
\draw[->] (psifw1) .. controls +(1,-1) and +(-1,-1) .. node(epsn1)[fill=gray!20]{$\epsilon^{(i)}_1$} (psifw2);
\node (psifw3) at (9,4) {%
\begin{tikzpicture}
\draw[color=gray!20] (0,0)--(0.5,-0.25)--(1,0);
\node[color=gray!20] at (0.5,0.25) {$\phi_k(t)$};
\node at (0.5,0.25) {\dots};
\end{tikzpicture}
};
\draw[->] (psifw2) .. controls +(1,-1) and +(-1,-1) .. node(epsn2)[fill=gray!20]{$\epsilon^{(i)}_2$} (psifw3);
\node (psifw4) at (12,4) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,-0.25)--(1,0);
\node at (0.5,0.25) {$\phi_k(t_{N_T-1})$};
\end{tikzpicture}
};
\draw[->] (psifw3) .. controls +(1,-1) and +(-1,-1) .. node(epsn3)[fill=gray!20]{$\epsilon^{(i)}_{N_T-1}$} (psifw4);
\node (psifw5) at (15,4) {%
\begin{tikzpicture}
%\draw[color=gray!20](0,0)--(0.5,-0.25)--(1,0);
\node at (0.5,0.25) {$\phi_k(T)$};
\end{tikzpicture}
};
\draw[->] (psifw4) .. controls +(1,-1) and +(-1,-1) .. node(epsn4)[fill=gray!20]{$\epsilon^{(i)}_{N_T}$} (psifw5);
%%% backward propagation
\node (chi1) at (3,6) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,0.25)--(1,0);
\node at (0.5,-0.25) {$\chi_k(0)$};
\end{tikzpicture}
};
\node (chi2) at (6,6) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,0.25)--(1,0);
\node at (0.5,-0.25) {$\chi_k(t_1)$};
\end{tikzpicture}
};
\draw[<-] (chi1) .. controls +(1,1) and +(-1,1) .. node[fill=gray!20]{$\epsilon^{(i-1)}_1$} (chi2);
\node (chi3) at (9,6) {%
\begin{tikzpicture}
\draw[color=gray!20] (0,0)--(0.5,0.25)--(1,0);
\node[color=gray!20] at (0.5,-0.25) {$\chi_k(t)$};
\node at (0.5,-0.25) {\dots};
\end{tikzpicture}
};
\draw[<-] (chi2) .. controls +(1,1) and +(-1,1) .. node[fill=gray!20]{$\epsilon^{(i-1)}_2$} (chi3);
\node (chi4) at (12,6) {%
\begin{tikzpicture}
\draw (0,0)--(0.5,0.25)--(1,0);
\node at (0.5,-0.25) {$\chi_k(t_{N_T-1})$};
\end{tikzpicture}
};
\draw[<-] (chi3) .. controls +(1,1) and +(-1,1) .. node[fill=gray!20]{$\epsilon^{(i-1)}_{N_T-1}$} (chi4);
\node (chi5) at (15,6) {%
\begin{tikzpicture}
\draw[color=gray!20] (0,0)--(0.5,0.25)--(1,0);
\node[] at (0.5,-0.25) {$\chi_k(T)$};
\end{tikzpicture}
};
\draw[<-] (chi4) .. controls +(1,1) and +(-1,1) .. node[fill=gray!20]{$\epsilon^{(i-1)}_{N_T}$} (chi5);
%%% mu
\node (mu1) at (3,5) {%
\begin{tikzpicture}
\draw (-0.5,0.4)--(0.5,0.4);
\node at (0,0) {$\frac{\partial H}{\partial \epsilon}$};
\draw (-0.5,-0.4)--(0.5,-0.4);
\end{tikzpicture}
};
\draw[->] (mu1) -| (epsn1);
\node (mu2) at (6,5) {%
\begin{tikzpicture}
\draw (-0.5,0.4)--(0.5,0.4);
\node at (0,0) {$\frac{\partial H}{\partial \epsilon}$};
\draw (-0.5,-0.4)--(0.5,-0.4);
\end{tikzpicture}
};
\draw[->] (mu2) -| (epsn2);
\node (mu3) at (9,5) {%
\begin{tikzpicture}
\draw[color=white] (-0.5,0.4)--(0.5,0.4);
\node[color=white] at (0,0) {$\frac{\partial H}{\partial \epsilon}$};
\node at (0,0) {\dots};
\draw[color=white] (-0.5,-0.4)--(0.5,-0.4);
\end{tikzpicture}
};
\draw[->] (mu3) -| (epsn3);
\node (mu4) at (12,5) {%
\begin{tikzpicture}
\draw (-0.5,0.4)--(0.5,0.4);
\node at (0,0) {$\frac{\partial H}{\partial \epsilon}$};
\draw (-0.5,-0.4)--(0.5,-0.4);
\end{tikzpicture}
};
\draw[->] (mu4) -| (epsn4);
%\node at (15,5) {%
% \begin{tikzpicture}
% \draw (-0.5,0)--(0.5,0);
% \end{tikzpicture}
%};
%\node at (16.1,5) {%
% \begin{tikzpicture}
% \node at (0,0) {$ = \; \tau$};
% \end{tikzpicture}
%};
%
\end{tikzpicture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}