RSDFT-CIPSI-QMC/Data/algo.org

#+HEADER: :file ../Manuscript/algorithm.pdf
#+HEADER: :results output silent :headers '("\\usepackage{tikz}")
#+HEADER: :fit yes :imoutoptions -geometry 400 :iminoptions -density 600
#+BEGIN_SRC latex



\begin{tikzpicture}[<->]
\usetikzlibrary{shapes.geometric}
% Nodes
\tikzstyle{inst}=[rectangle,draw,fill=yellow!50]
\tikzstyle{res}=[rectangle,draw,fill=blue!20,rounded corners=4pt]
\tikzstyle{tst}=[draw,thick,fill=red!20]
% Arrows
\tikzstyle{nxt}=[->,>=stealth,thick,rounded corners=4pt]
\tikzstyle{arr}=[]
% Arrows

%\node[inst] (dm0) at (0,8.5) { $n^{(0)} = n(\Psi^{(0)})$ };
%\node[inst] (h0) at (0,7) { $\tilde{H}^{(0)} = \tilde{H}(n^{(0)})$ };
%\node[res] (h0) at (3,7) { $E^{(0)}$ };
%\node[inst] (h0) at (0,5.5) { $\text{CIPSI}(\tilde{H}^{(k)}) \longrightarrow \Psi^{(k)}$ };
%\node[inst] (dm0) at (0,4) { $n^{(k)} = n(\Psi^{(k)})$ };
%\node[inst] (h0) at (0,2.5) { $\tilde{H}^{(k)} = \tilde{H}(n^{(k)})$ };
%\node[res] (h0) at (3,2.5) { $E^{(k)}$ };

Na   ( 3.929174,-1.038386)    0.000000
Mg   ( 2.435205,-1.172771)    0.000000
 O   ( 2.101351,-2.635146)    0.000000
 F   ( 3.388986,-3.404559)    0.000000
Ne   ( 4.518642,-2.417707)    0.000000
Al   ( 1.500000, 0.000000)    0.000000
Si   ( 2.250000, 1.299038)    0.000000
 N   ( 0.749849,-3.285870)    0.000000
 C   (-0.601539,-2.634910)    0.000000
 B   (-0.935138,-1.172476)    0.000000
Be   (-0.000001,-0.000000)    0.000000
Li   (-0.793853, 1.272713)    0.000000
 H   (-3.052250, 2.221211)    0.000000
He   (-2.258396, 0.948498)    0.000000
XX   (-0.663664, 2.334763)    0.000000
XX   ( 0.633384,-4.349513)    0.000000
XX   ( 4.716656,-0.313975)    0.000000


node distance=2cm,on grid,>=stealth',
Op1/.style={circle,draw,fill=yellow!40},
		Op2/.style={circle,draw,fill=orange!40},
		Op3/.style={circle,draw,fill=red!40},
		Op4/.style={circle,draw,fill=violet!40},
		DeadOp/.style={circle,draw,fill=gray!40},
		Input/.style={fill=white!40},
		Output/.style={fill=white!40}]
		\node [Op1, align=center]		(G)		at (3*0.587785, 3*0.809017)		{$G$};
		\node [DeadOp, align=center] 		(Gamma)	at (3*0.951057, -3*0.309017)		{$\Gamma$};
		\node [Op2, align=center]		(P)		at (3*0, -3*1.00000)				{$P$};
		\node [Op3, align=center]		(W)		at (-3*0.951057, -3*0.309017)		{$W$};
		\node [Op4, align=center] 		(Sigma)	at (-3*0.587785, 3*0.809017)		{$\Sigma$};
		\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{tikzpicture}
#+END_SRC


% Nodes
\node[arr] at () { $\Psi^{(0)}$ };
\node[inst] (n0) at (0,18) { Compute one-$e$ density };
\draw[nxt]  (0,19.5) -- (n0) ;

\node[inst] (n1) at (0,16) { Compute RSDFT Hamiltonian };
\draw[nxt]  (n0) -- (n1) ;
\node[arr] at (.5,17) { $n^{(0)}$ };

\node[res]  (n2) at (4.5,16) { $E^{(0)}$ };
\draw[nxt]  (n1) -- (n2) ;

\node[inst] (n3) at (1,14) { CIPSI };
\draw[nxt]  (n1) -- (n3) ;
\node[arr] at (1.1,15) { $\tilde{H}^{(k)}$ };
\node[arr] at (-0.2,15) { $k\leftarrow 0$ };

\node[inst] (n4) at (1,12) { Compute one-e density};
\draw[nxt]  (n3) -- (n4) ;
\node[arr] at (1.5,13) { $\Psi^{(k)}$ };

\node[inst] (n5) at (1,10) { DIIS$_k$ };
\draw[nxt]  (n4) -- (n5) ;
\node[arr] at (1.5,11) { $n^{(k)}$ };

\node[inst] (n6) at (1,8) { Compute RSDFT Hamiltonian };
\draw[nxt]  (n5) -- (n6) ;
\node[arr] at (1.5,9) { $n'^{(k)}$ };

\node[res]  (n7) at (5.5,8) { $E^{(k)}$ };
\draw[nxt]  (n6) -- (n7) ;

\node[inst] (n8) at (2,6) { Find lowest eigenvector };
\draw[nxt]  (n6) -- (n8) ;
\node[arr] at (2.2,7) { $\tilde{H}^{(k,l)}$ };
\node[arr] at (0.8,7) { $l\leftarrow 0$ };


\node[inst] (n9) at (2,4) { Compute one-e density};
\draw[nxt]  (n8) -- (n9) ;
\node[arr] at (2.5,5) { $\Psi^{(k,l)}$ };

\node[inst] (n10) at (2,2) { DIIS$_l$ };
\draw[nxt]  (n9) -- (n10) ;
\node[arr] at (2.5,3) { $n^{(k,l)}$ };

\node[inst] (n11) at (2,0) { Compute RSDFT Hamiltonian };
\draw[nxt]  (n10) -- (n11) ;
\node[arr] at (2.5,1) { $n'^{(k,l)}$ };

\node[res]  (n12) at (6.5,0) { $E^{(k,l)}$ };
\draw[nxt]  (n11) -- (n12) ;

\node[tst] (n13) at (2,-2) { $l>0$ and $|E^{(k,l)}-E^{(k,l-1)}| < \tau_2$ ? };
\draw[nxt]  (n11) -- (n13) ;
\node[arr]  at (2.5,-1) { $E^{(k,l)}$ };
\draw[nxt]  (n13.west) -| (-2.,-2) -| (-2,6) -- (n8.west) ;
\node[arr]  at (-1.3,-1.7) { no };
\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) { $k>0$ and $|E^{(k)}-E^{(k-1)}| < \tau_1$ ? };
\node[arr]  at (2.,-3) { yes };
\draw[nxt]  (n13) -- (n14);
\draw[nxt]  (n14.west) -| (-3.,-4) -| (-3,14) -- (n3.west) ;
\node[arr]  at (-2.3,-3.7) { no };
\node[arr]  at (-4.,4.5) { $k\leftarrow k+1$ };
\node[arr]  at (-3.6,4) { $\tilde{H}^{(k)}$ };

\draw[nxt]  (n14) -- (1., -5.5);
\node[arr]  at (2.2,-5) { $\Psi_\text{RSDFT-CIPSI}$ };