Latex 建立带有竖线和编号的算法环境

documentclass{article}
usepackage{amssymb}
usepackage{amsmath}
usepackage[linesnumbered, ruled]{algorithm2e}
SetKwRepeat{Do}{do}{while}%
egin{document}
egin{algorithm}[!ht]
  caption{Algorithm for problem eqref{WWW} }
  SetKwInOut{Input}{Input}SetKwInOut{Output}{Output}
 Input  { data matrix ${f X}$, label matrix ${f Y}$ and ${f W}_0$, $k=0$}
  Output  {${f W}^*$}
Repeat{ADMM stopping criterion is satisfied}{
 Updating ${f W}^k$:
egin{equation*}
({f X}{f X}^{mathrm T}+mu{f I}){f W}={f B}^{k-1}
end{equation*}
where ${f B}^{k-1} ={f X}{f Y}+alpha{f A}^{k-1}-{f Sigma}^{k-1}+mu{f U}^{k-1}$;
Updating ${f U}^k$:
egin{equation*}
  {f u}^k_i=
  egin{cases}
  frac{mu|{f n}^{k-1}_i|_2-alpha}{mu|{f n}^{k-1}_i|_{2}}{f n}^{k-1}_i,& ~mbox{if} ~alpha<mu|{f n}^{k-1}_i|_2 \
  quad 0 & ~mbox{otherwise}\
  end{cases}
  end{equation*}
  
Updating ${f Sigma}^{k}$:
egin{equation*}
egin{split}
  {f Sigma}^k:=&{f Sigma}^{k-1}+mu({f W}^{k-1}-{f U}^{k-1})
  end{split}
end{equation*}\
$k=k+1$;}
end{algorithm}
end{document}