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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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$\begin{myframe}{5cm}                       %       Б
Для $j=1$ до $\min~\!(m-1,n)$ \\
\quad $r_{j}:=a_{jj}$\\
\quad Для $i=j+1$ до $m$\\
\quad\qquad $a:=r_{j}$; $b:=a_{ij}$\\
\quad\qquad получить $(r,c,s,\zeta)$ \\
\quad\qquad\qquad\quad\ из $(a,b)$\\
\quad\qquad $(a_{jj}\triangleq r_j):=r$\\ 
\quad\qquad $(a_{ij}\triangleq \zeta_{j,i}):=\zeta$\\
\quad\qquad $c_{j,i}:=c$; $s_{j,i}:=s$\\
\quad Для $s=j+1$ до $n$ \\
\qquad Для $i=j+1$ до $m$\\
\qquad\quad $\alpha=c_{j,i}a_{js}+s_{j,i}a_{is}$\\
\qquad\quad $a_{is}=-s_{j,i}a_{js}+c_{j,i}a_{is}$\\
\qquad\quad $a_{js}:=\alpha$
\end{myframe}$                               %       Б
}
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$\begin{myframe}{5cm}                          %       Г
\centerline{\begin{myframe}{4.99cm}
\hbox to 4.99cm{\dotfill Процедура\dotfill }
получить $(r,c,s,\zeta)$ 
из $(a,b)$\end{myframe}}
$\sigma=\left\{\begin{array}{lll}
\sgn{a}, & & |a|>|b| \\
\sgn{b}, & & |a|\le |b|
\end{array}\right.$\\[2ex]
$r= \sigma (a^2+b^2)^{1/2} $ \\[0.5ex]
$c=\left\{\begin{array}{lll}
a/r, & & r\ne 0 \\
1, & & r=0
\end{array}\right.$\\[2ex]
$s=\left\{\begin{array}{lll}
b/r, & & r\ne 0 \\
0, & & r=0
\end{array}\right.$\\[2ex]
$\zeta=
\left\{\begin{array}{ll}
s, &  |a|>|b| \\[2ex]
1/c,  & 
\left\{
\begin{array}{@{}l@{}}
|a|\le |b|\enspace \& \\
\& \enspace c\ne 0
\end{array}\right.
\\[2ex]
1, & c=0
\end{array}\right.$\\[-2ex]
\end{myframe}$                           %       Г
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$\begin{myframe}{5cm}                     %       А
Для $j=1$ до $\min~\!(m-1,n)$ \\
\quad Для $i=j+1$ до $m$\\
\qquad $a:=a_{jj}$; $b:=a_{ij}$\\
\qquad получить $(r,c,s,\zeta)$ \\
\qquad\qquad\quad\ из $(a,b)$\\
\qquad $(a_{jj}\triangleq r_j):=r$\\ 
\qquad $(a_{ij}\triangleq \zeta_{j,i}):=\zeta$\\
\qquad Для $s=j+1$ до $n$ \\
\qquad\quad $\alpha=ca_{js}+sa_{is}$\\
\qquad\quad $a_{is}=-sa_{js}+ca_{is}$\\
\qquad\quad $a_{js}:=\alpha$
\end{myframe}$                             %       А
}
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$\begin{myframe}{5cm}                      %       Д
\centerline{\begin{myframe}{4.99cm}
\hbox to 4.99cm{\dotfill Процедура\dotfill }
\hspace{0.8em} получить $(c,s)$ из $(\zeta)$
\end{myframe}}
$\rule{0pt}{4.5ex}\zeta=1\; \Rightarrow\; 
\left\{\begin{array}{l}
c:=0 \\
s:=1
\end{array}\right.
$\\[3ex]
$d:=(1-\zeta^2)^{1/2}$\\[1ex]
$\rule{0pt}{2ex}\zeta<1\; \Rightarrow\; 
\left\{\begin{array}{l}
c:=d \\
s:=\zeta
\end{array}\right.
$\\[3ex]
$\rule{0pt}{2ex}\zeta>1\; \Rightarrow\; 
\left\{\begin{array}{l}
c:=\zeta\\
s:=d 
\end{array}\right.
$\\[-2ex]
\end{myframe}$                             %       Д
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$\begin{myframe}{5cm}                         %       В
Для $j=1$ до $\min~\!(m-1,n)$ \\
\quad Для $i=j+1$ до $m$\\
\qquad получить $(c,s)$ из $\zeta_{j,i}$ \\
\qquad $\alpha=cy_{jj}+sy_{ij}$\\
\qquad $y_{ij}=-sy_{jj}+cy_{ij}$\\
\qquad $y_{jj}:=\alpha$
\end{myframe}$                                %       В
}
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\begin{myframe}{4.536cm}                        %       Е
\begin{picture}(10,40)
\end{picture}
\end{myframe}                                %       Е
}
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%end arrow
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%end arrow
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%end arrow

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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