# Math/Latex to represent getting a minimum value in a 2D range subset

• Aug 17th 2012, 04:54 AM
lordmule
Math/Latex to represent getting a minimum value in a 2D range subset
Hi everyone,

I would really appreciate some suggestions on what I am trying to say mathematically, and how to write it in Latex.

I have Data as a 2D table of values. I wish to obtain the minimum value of one particular row while considering the all columns of the table (happens to be zero to pi/2).

e.g.
 B_max=4 7 4 5 # # # # # # # # B_min=2 3 3 2

what I had originally
$\displaystyle B_{max} = min(Y_i, Y_j) \quad \forall i,j \epsilon Data_{cos \theta_o^{\prime} = 0}\\ B_{min} = min(Y_i, Y_j) \quad \forall i,j \epsilon Data_{cos \theta_o^{\prime} = cos \theta_{o_{max}}^{\prime}}$

maybe this one is better

$\displaystyle B_{max} = min(Y_{i,{cos \theta_o^{\prime} = 0}} , B_{max}) \forall i \epsilon Data_{[0,\frac{\pi}{2}], [0,0] }$

If you noticed, I am more a programmer than a math guy. But if there is a programmers approach to writing math, i'd be very keen on reading it.
• Aug 17th 2012, 06:59 AM
earboth
Re: Math/Latex to represent getting a minimum value in a 2D range subset
Quote:

Originally Posted by lordmule
Hi everyone,

I would really appreciate some suggestions on what I am trying to say mathematically, and how to write it in Latex.

...

If you noticed, I am more a programmer than a math guy. But if there is a programmers approach to writing math, i'd be very keen on reading it.

Maybe this is of some help: Help:Displaying a formula - Wikipedia, the free encyclopedia
• Aug 20th 2012, 01:15 AM
lordmule
Re: Math/Latex to represent getting a minimum value in a 2D range subset
Quote:

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.