Originally Posted by

**earboth** Thank you for the reply. I did find those math 2 latex useful.

My initial problem was lacking how to represent, mathematically, a function operating over a subset of 2D data of particular range. I believe that the 2D matrix needs to be defined first:

$\displaystyle Y = \begin{pmatrix} y_{1,0} & \cdots & y_{cos \theta_i, 0} & \cdots & y_{0, 0} \\ \vdots & \ddots & \vdots & \ddots & \vdots \\ y_{1, cos \theta_o^{\prime}} & \cdots & y_{cos \theta_i, cos \theta_o^{\prime}} & \cdots & y_{0, cos \theta_o^{\prime}} \\ \vdots & \cdots & \vdots & \ddots & \vdots \\ y_{1, cos \theta_{o_{max}}^{\prime}} & \cdots & y_{cos \theta_i ,cos \theta_{o_{max}}^{\prime}} & \cdots & y_{0, cos \theta_{o_{max}}^{\prime}} \end{pmatrix} $

Code:

Y =
\begin{pmatrix}
y_{1,0} & \cdots & y_{cos \theta_i, 0} & \cdots & y_{0, 0} \\
\vdots & \ddots & \vdots & \ddots & \vdots \\
y_{1, cos \theta_o^{\prime}} & \cdots & y_{cos \theta_i, cos \theta_o^{\prime}} & \cdots & y_{0, cos \theta_o^{\prime}} \\
\vdots & \cdots & \vdots & \ddots & \vdots \\
y_{1, cos \theta_{o_{max}}^{\prime}} & \cdots & y_{cos \theta_i ,cos \theta_{o_{max}}^{\prime}} & \cdots & y_{0, cos \theta_{o_{max}}^{\prime}}
\end{pmatrix}

Then define the function on the range with subscripts:

$\displaystyle \begin{array}{l} B_{max} = min_{cos \theta_i, 0} \; Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\ B_{min} = min_{cos \theta_i, cos \theta_{o_{max}}^{\prime}} \; Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\ \end{array} $

Code:

\begin{array}{l}
B_{max} = min_{cos \theta_i, 0} \; Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\
B_{min} = min_{cos \theta_i, cos \theta_{o_{max}}^{\prime}} \; Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\
\end{array}

I believe it is a little clearer. Hopefully the reader will understand.

Comments welcome!