\documentclass[xcolor=usenames,dvipsnames,svgnames,beamer]{standalone}

\usepackage{amsmath}
\usepackage{multirow}
\usepackage{color}
\usepackage{colortbl}
\usepackage{graphicx}
\usepackage{subcaption}

\usepackage{lmodern}
\usetheme{Warsaw}
\beamertemplatenavigationsymbolsempty%
\setbeamertemplate{footline}[frame number]
\setbeamertemplate{itemize item}[triangle]

\begin{document}

\begin{frame}
  \frametitle{TenStream Concept}

  \begin{columns}
    \column[c]{.4\textwidth}
    \only<1->{%
      \begin{figure}
        \begin{subfigure}[b]{.450\columnwidth}
          \includegraphics[width=\textwidth]{../../slides/tenstream_theory/direct-streams-schematic.pdf}
          \caption{\tiny direct streams}
          \label{fig:direct-schematic}
        \end{subfigure}%
        ~%
        \begin{subfigure}[b]{.450\columnwidth}
          \includegraphics[width=\textwidth]{../../slides/tenstream_theory/diffuse-streams-schematic.pdf}
          \caption{\tiny diffuse streams}
          \label{fig:diffuse-schematic}
        \end{subfigure}
      \end{figure}
    }
    \column[c]{.6\textwidth}
    \begin{itemize}
      \item{
          Finite Volume formalism:\\
          Discretize energy transport --- spatially and by angle
        }
    \end{itemize}
  \end{columns}



  \begin{columns}
    \column[c]{.4\textwidth}
    \fontsize{4}{4}\selectfont
    \newcommand{\mcolora}     {\cellcolor{Black!05} \boldsymbol}
    \newcommand{\mcolorb}     {\cellcolor{Black!20} \boldsymbol}
    \newcommand{\mcolorc}     {\cellcolor{Black!05} \boldsymbol}
    \newcommand{\mcolord}     {\cellcolor{Black!20} \boldsymbol}
    \newcommand{\mcolore}     {\cellcolor{Black!10} \boldsymbol}
    \newcommand{\mcolorf}     {\cellcolor{Black!25} \boldsymbol}
    \newcommand{\mcolorg}     {\cellcolor{Black!05} \boldsymbol}
    \newcommand{\mcolorh}     {\cellcolor{Black!00} \boldsymbol}
    \newcommand{\mcolori}     {\cellcolor{Black!05} \boldsymbol}
    \newcommand{\mcolorj}     {\cellcolor{Black!25} \boldsymbol}
    \newcommand{\mcolorbeta}  {\cellcolor{Black!10} \boldsymbol}
    \newcommand{\mcoloralpha} {\cellcolor{Black!30} \boldsymbol}

    {
      \setlength{\arraycolsep}{.5pt}
      \renewcommand\arraystretch{1.5}
      \begin{equation*}
        \label{eq:mat}
        \begin{bmatrix}
          \mathrm
          E_{\uparrow}   ^ {\mathrm T}  \\
          E_{\downarrow} ^ {\mathrm B}  \\
          E_{\swarrow}   ^ {\mathrm L}  \\
          E_{\searrow}   ^ {\mathrm R}  \\
          E_{\nwarrow}   ^ {\mathrm L}  \\
          E_{\nearrow}   ^ {\mathrm R}  \\

          S_{\downarrow}  ^ {\mathrm B}  \\
          S_{\rightarrow} ^ {\mathrm R}  \\
        \end{bmatrix}
        \hspace{-.5em}
        =
        \hspace{-.5em}
        \begin{bmatrix}
          \mathrm
          {\mcolora\gamma_{1}} & {\mcolorb\gamma_{2}} & {\mcolorc\gamma_{3}} & {\mcolorc\gamma_{3}}  & {\mcolord\gamma_{4}}  & {\mcolord\gamma_{4}}  & {\mcolorbeta \beta_{01} }  & {\mcolorbeta \beta_{11} } \\
          {\mcolorb\gamma_{2}} & {\mcolora\gamma_{1}} & {\mcolord\gamma_{4}} & {\mcolord\gamma_{4}}  & {\mcolorc\gamma_{3}}  & {\mcolorc\gamma_{3}}  & {\mcolorbeta \beta_{02} }  & {\mcolorbeta \beta_{12} } \\
          {\mcolore\gamma_{5}} & {\mcolorf\gamma_{6}} & {\mcolorg\gamma_{7}} & {\mcolorh\gamma_{8}}  & {\mcolori\gamma_{9}}  & {\mcolorj\gamma_{10}} & {\mcolorbeta \beta_{03} }  & {\mcolorbeta \beta_{13} } \\
          {\mcolore\gamma_{5}} & {\mcolorf\gamma_{6}} & {\mcolorh\gamma_{8}} & {\mcolorg\gamma_{7}}  & {\mcolorj\gamma_{10}} & {\mcolori\gamma_{9}}  & {\mcolorbeta \beta_{04} }  & {\mcolorbeta \beta_{14} } \\
          {\mcolorf\gamma_{6}} & {\mcolore\gamma_{5}} & {\mcolori\gamma_{9}} & {\mcolorj\gamma_{10}} & {\mcolorg\gamma_{7}}  & {\mcolorh\gamma_{8}}  & {\mcolorbeta \beta_{05} }  & {\mcolorbeta \beta_{15} } \\
          {\mcolorf\gamma_{6}} & {\mcolore\gamma_{5}} & {\mcolorj\gamma_{10}}& {\mcolori\gamma_{9}}  & {\mcolorh\gamma_{8}}  & {\mcolorg\gamma_{7}}  & {\mcolorbeta \beta_{06} }  & {\mcolorbeta \beta_{16} } \\
          {0}                 & {0}                 & {0}                 & {0}                  & {0}                  & {0}                  & {\mcoloralpha \alpha_{00}} & {\mcoloralpha \alpha_{10}} \\
          {0}                 & {0}                 & {0}                 & {0}                  & {0}                  & {0}                  & {\mcoloralpha \alpha_{01}} & {\mcoloralpha \alpha_{11}} \\
        \end{bmatrix}
        \hspace{-.5em}
        \begin{bmatrix}
          \mathrm
          E_{\uparrow}    ^ {\mathrm B}  \\
          E_{\downarrow}  ^ {\mathrm T}  \\
          E_{\swarrow}    ^ {\mathrm R}  \\
          E_{\searrow}    ^ {\mathrm L}  \\
          E_{\nwarrow}    ^ {\mathrm R}  \\
          E_{\nearrow}    ^ {\mathrm L}  \\

          S_{\downarrow}  ^ {\mathrm T}  \\
          S_{\rightarrow} ^ {\mathrm L}  \\
        \end{bmatrix}
      \end{equation*}
    }


    \column[c]{.6\textwidth}
    \normalsize
    \begin{itemize}
      \item{Transport coefficients from MonteCarlo}
      \item{Couple voxels in 3 dimensions\dots}
    \end{itemize}
  \end{columns}

  \begin{columns}
    \column[c]{.4\textwidth}
    \begin{center}
    \includegraphics[width=.56\textwidth]{../../slides/tenstream_theory/matview.pdf}\\
    \end{center}
    \column[c]{.6\textwidth}
    \begin{itemize}
      \item{
          \dots gives huge but sparse matrix
          $\Longrightarrow$ solve with iterative methods
        }
    \end{itemize}
  \end{columns}
\end{frame}

\end{document}
