RSDFT-CIPSI-QMC/Data/algorithm.tex

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5.5 KiB
TeX

\documentclass{standalone}
\usepackage{graphicx,bm,microtype,hyperref,algpseudocode,subfigure,algorithm,algorithmicx,multirow,footnote,xcolor,physics,lipsum,wasysym,physics}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning,shapes.geometric}
\usetikzlibrary{decorations.pathmorphing}
\tikzset{snake it/.style={
decoration={snake,
amplitude = .4mm,
segment length = 2mm},decorate}
}
%\usepackage{tgchorus}
%\usepackage[T1]{fontenc}
\begin{document}
\begin{tikzpicture}[scale=2.3]
\begin{scope}[very thick
,node distance=2cm,on grid,>=stealth'
,Op1/.style={rectangle,draw,fill=yellow!40}
,Ring1/.style={rectangle,draw,fill=red!40}
,Ring2/.style={rectangle,draw,fill=blue!40}
,Ring12/.style={rectangle,draw,fill=purple!40}
,Ring1Test/.style={diamond,draw,fill=red!40}
,Ring12Test/.style={diamond,draw,fill=purple!40}
,Output/.style={ellipse,draw,fill=orange!40}
,Input/.style={circle,draw,fill=green!40}
]
\node [Input, align=center] (H) at (-3.052250,2.221211) { $\Psi^{(0)}$ };
\node [Op1, align=center] (He) at (-2.258396,0.948498) { Compute \\ one-$e$ \\ density };
\node [Op1, align=center] (Li) at (-0.793853,1.272713) { Compute \\ RS-DFT \\ Hamiltonian };
\node [Ring1, align=center] (Be) at (-0.000001,-0.000000) { CIPSI };
\node [Ring1, align=center] (B) at (-0.935138,-1.172476) { Compute \\ one-$e$ \\ density };
\node [Ring1, align=center] (C) at (-0.601539,-2.634910) { DIIS$_k$ };
\node [Ring1, align=center] (N) at (0.749849,-3.285870) { Compute \\ RS-DFT \\ Hamiltonian };
\node [Ring12, align=center] (O) at (2.101351,-2.635146) { Find \\ lowest \\ eigenvector };
\node [Ring2, align=center] (F) at (3.388986,-3.404559) { Compute \\ one-e \\ density};
\node [Ring2, align=center] (Ne) at (4.518642,-2.417707) { DIIS$_l$ };
\node [Ring2, align=center] (Na) at (3.929174,-1.038386) { Compute \\ RS-DFT \\ Hamiltonian };
\node [Ring12Test, align=center] (Mg) at (2.435205,-1.172771) { $\Delta E^{(k,l)} < \tau_2$ };
\node [Ring1Test, align=center] (Al) at (1.500000,0.000000) { $\Delta E^{(k)} < \tau_1$ };
\node [Input, align=center] (Si) at (2.250000,1.299038) { $\Psi^\mu$ };
\node [Output, align=center] (X1) at (-0.663664,2.334763) { $E^{(0)}$ };
\node [Output, align=center] (X2) at (0.633384,-4.349513) { $E^{(k)}$ };
\node [Output, align=center] (X3) at (4.716656,-0.313975) { $E^{(k,l)}$ };
\path
(H) edge [->,color=black ] node [above,black] {} (He)
(He) edge [->,color=black ] node [above,black] { $n^{(0)}$ } (Li)
(Li) edge [->,color=black ] node [below,black,sloped,align=left] { $\hat{H}^{\mu\,(k)}$ }
node [above,black,sloped] { $k\leftarrow 0$ }(Be)
(Be) edge [->,color=black ] node [above,sloped,black] { $\Psi^{\mu\,(k)}$ } (B)
(Al) edge [->,color=black ] node [above,sloped,black] { no} (Be)
(B) edge [->,color=black ] node [below,sloped,black] { $n^{(k)}$ } (C)
(C) edge [->,color=black ] node [below,sloped,black] { $\tilde{n}^{(k)}$ } (N)
(N) edge [->,color=black ] node [below,sloped,black] { $\hat{H}^{\mu\,(k)}$ }
node [above,sloped,black] { $l\leftarrow 0$ } (O)
(O) edge [->,color=black ] node [below,sloped,black] { $\Psi^{\mu\,(k,l)}$ }(F)
(F) edge [->,color=black ] node [below,sloped,black] { $n^{(k,l)}$ } (Ne)
(Ne) edge [->,color=black ] node [above,sloped,black] { $\tilde{n}^{(k,l)}$ } (Na)
(Na) edge [->,color=black ] node [above,sloped,black] { $\hat{H}^{\mu\,(k,l)}$ } (Mg)
(Mg) edge [->,color=black ] node [right,black] { yes } (Al)
(Mg) edge [->,color=black ] node [right,black] { no } (O)
(Al) edge [->,color=black ] node [above,sloped,black] {yes} (Si)
(Li) edge [->,color=black,snake it ] node [above,sloped,black] {} (X1)
(N) edge [->,color=black,snake it ] node [above,sloped,black] {} (X2)
(Na) edge [->,color=black,snake it ] node [above,sloped,black] {} (X3)
;
%\node[arr] at (2.5,-1)
%\node[arr] at (-1.,2) { $l\leftarrow l+1$ };
%\node[arr] at (-1.3,1.5) { $\tilde{H}^{(k,l)}$ };
%\node[tst] (n14) at (1,-4)
%\node[arr] at (-4.,4.5) { $k\leftarrow k+1$ };
%\node[arr] at (-3.6,4) { $\tilde{H}^{(k)}$ };
%\node[arr] at (2.2,-5)
%\node [Input, align=center] (In) [above=of G] {};
%\node [Output, align=center] (Out) [above=of Sigma] {};
%\node [Input, align=center] (In) [above=of G, yshift=1cm] {KS-DFT};
%\node [Output, align=center] (Out) [above=of Sigma, yshift=1cm] {BSE};
%\path
%(G) edge [->,color=gray!50] node [above,sloped,black] {$\Gamma = 1 + \fdv{\Sigma}{G} GG \Gamma$} (Gamma)
%(Gamma) edge [->,color=gray!50] node [below,sloped,black] {$P = - i GG \Gamma$} (P)
%(P) edge [->,color=black] node [above,sloped,black] {$W = v + vPW$} (W)
%(W) edge [->,color=black] node [above,sloped,black] {$\Sigma = i GW\Gamma$} (Sigma)
%(Sigma) edge [->,color=black] node [above,sloped,black] {$G = G_\text{0} + G_\text{0} \Sigma G$} (G)
%(G) edge [->,color=black] node [above,sloped,black] {$P = - i GG \quad (\Gamma = 1)$} (P)
%(In) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{KS}$} (G)
%(Sigma) edge [->,color=black] node [above,sloped,black] {$W(\omega)$ \& $\varepsilon^\text{GW}$} (Out)
%;
\end{scope}
\end{tikzpicture}
\end{document}
% Nodes