latex大括号公式编辑「建议收藏」

\begin{equation} \label{eqn11}%%\label
\begin{aligned}
  f_{k}^{-d,n}\left ( x_{dn}=w \right )  & =
\frac{\int _{\phi _{k}^{G}}p\left ( x_{dn}| \phi _{k}^{G} \right )\prod _{
  
  {d}'{n}'\neq dn,z_{
  
  {d}'{n}'=k}}p\left ( x_{
  
  {d}'{n}'}| \phi _{k}^{G} \right )p\left ( \phi _{k}^{G}|\varphi  \right )d\phi _{k}^{G}}{\int _{\phi _{k}^{G}}\prod _{
  
  {d}'{n}'\neq dn,z_{
  
  {d}'{n}'=k}}p\left ( x_{
  
  {d}'{n}'}| \phi _{k}^{G} \right )p\left ( \phi _{k}^{G}|\varphi  \right )d\phi _{k}^{G}} \\
 &=\left\{
             \begin{array}{lr}
          \frac{N_{k,w}+\varphi }{N_{k,\bullet }+V\varphi },  \: \: \: \: \: if \,\, k \,\, exists &  \\

             \frac{ 1 }{V }  \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: if \,\, k \,\,is \,\,new &  \\
             \end{array}
\right.
\end{aligned}
\end{equation}