function multiple lines into box

Question

I'm trying to write the Leapfrog integrator for Monte Carlo Hamiltonian, but I can not properly align each of the rows, any suggestions please.

Expected Output:

My code:

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}

\begin{document}
\[
\boxed{
  \!\begin{aligned}
  \textbf{function} & \ LEAPFROG ((\boldsymbol{q}_0, \boldsymbol{p}_0); h, L) \\
    & \boldsymbol{p}_{1/2} \leftarrow  \boldsymbol{p}_0 - \frac{1}{2} h \nabla_q U(q_0) \\
    & \textbf{for} \  i \leftarrow 1,2,...,L \\
    & \boldsymbol{q}_i \leftarrow \boldsymbol{q}_{i-1} + h \boldsymbol{M}^{-1} \boldsymbol{p}_{i-1/2}\\
    & \textbf{if} \ i \neq L \ \textbf{then}\\
    & \boldsymbol{p}_{i + 1/2} \leftarrow \boldsymbol{p}_{i-1/2} - h \nabla_\boldsymbol{q} U (\boldsymbol{q}_i)\\
    & \boldsymbol{p}_L \leftarrow \boldsymbol{p}_{L-1/2} - 1/2 h \nabla_\boldsymbol{q} U (\boldsymbol{q}_L) \\
    & \textbf{return} \ ((\boldsymbol{q}_L, \boldsymbol{p_L}) \ \text{as} \ ((\boldsymbol{q}^*, \boldsymbol{p}^*)
  \end{aligned}
}
\]
\end{document}

Answer 1

You should probably look at one of the algorithm packages, however with some minimal changes from what you have, you get

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}

\begin{document}
\[
\boxed{
  \begin{aligned}
  &\textbf{function} \ \textsc{Leapfrog}\  ((\boldsymbol{q}_0, \boldsymbol{p}_0); h, L) \\
    &\quad \boldsymbol{p}_{1/2} \leftarrow  \boldsymbol{p}_0 - \tfrac{1}{2} h \nabla_q U(q_0) \\
    &\quad \textbf{for} \  i \leftarrow 1,2,...,L \\
    &\qquad \boldsymbol{q}_i \leftarrow \boldsymbol{q}_{i-1} + h \boldsymbol{M}^{-1} \boldsymbol{p}_{i-1/2}\\
    &\qquad \textbf{if} \ i \neq L \ \textbf{then}\\
    &\quad\qquad \boldsymbol{p}_{i + 1/2} \leftarrow \boldsymbol{p}_{i-1/2} - h \nabla_{\boldsymbol{q}} U (\boldsymbol{q}_i)\\
    &\quad \boldsymbol{p}_L \leftarrow \boldsymbol{p}_{L-1/2} - 1/2 h \nabla_{\boldsymbol{q}} U (\boldsymbol{q}_L) \\
    &\quad \textbf{return} \ ((\boldsymbol{q}_L, \boldsymbol{p_L}) \ \text{as} \ ((\boldsymbol{q}^*, \boldsymbol{p}^*)
  \end{aligned}
}
\]
\end{document}