[Tex/LaTex] piecewise function

math-mode

So this is a piecewise defined function I have that I need to talk about:

   f(a,b) = \left\{
     \begin{array}{lr}
       \text{open} & : \text{RMSD}_\text{s-open}\ge6, \text{RMSD}_\text{closed}\ge6\\
       \text{closed} & : \text{RMSD}_\text{closed}\le2 \\
       \text{semiopen} & : \text{RMSD}_\text{s-open}\le2\\
       \text{transition} & :f(a,b)\notin\{\text{open}, \text{closed}, \text{semiopen}\} \\

     \end{array}
   \right.

So what's the way to align up the colons (conditions) so that it looks all nice and pretty?

Also, if I want to describe transition to be the value of the function when none of the conditions of the previous 3 are satisfied, is the way I wrote it out with f(a,b) not belonging to the set {open,closed,semiopen} a good way of writing it? seems really unprofessional…

Best Answer

You can use the cases environment from amsmath:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[   
f(a,b) = 
     \begin{cases}
       \text{open,} &\quad\text{if RMSD}_\text{s-open}\ge6, \text{RMSD}_\text{closed}\ge6\\
       \text{closed,} &\quad\text{if RMSD}_\text{closed}\le2 \\
       \text{semiopen,} &\quad\text{if RMSD}_\text{s-open}\le2\\
       \text{transition,} &\quad\text{otherwise.} \\ 
     \end{cases}
\]

\end{document}

enter image description here

Regarding the other issue, it is usual to write "otherwise".

Related Solutions

[Tex/LaTex] How to write a function (piecewise) with bracket outside

This situation is exactly what the cases environment from the amsmath package was designed for. If you put

\usepackage{amsmath}

in your preamble then you can wite

\[ \begin{cases} 
      0 & x\leq 0 \\
      \frac{100-x}{100} & 0\leq x\leq 100 \\
      0 & 100\leq x 
   \end{cases}
\]

to adapt your example with the correct size bracket.

As for not being able to use TeX-like syntax to write equations on this site: this is a deliberate choice. Most of the time we actually want to talk about the TeX source here rather than the equations (or whatever) it produces; and there are times when it could be actively confusing to have a TeX-like process to produce images that isn't actually TeX (in its full, Turing-complete, confusing glory...)

(See the discussion on meta for more on this, if you're interested.)

[Tex/LaTex] How to get more space in piecewise function on LaTeX

Don't use $$ for display math.

\displaystyle is not needed.

Option -1:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\[
P(Y_i = j) = \left\{
        \begin{array}{ll}
            \frac{1}{1+\sum_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad k=K \\[1em]
            \frac{e^{\beta_j\cdot x_i}}{1+\sum_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad 1 \leq k \leq K-1
        \end{array}
    \right.,
\]
\end{document}

enter image description here

Option - 2

You can use cases.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\[
P(Y_i = j) = \begin{cases}
            \frac{1}{1+\sum_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad k=K \\[1em]   %%% <--- here
            \frac{e^{\beta_j\cdot x_i}}{1+\sum_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad 1 \leq k \leq K-1
        \end{cases}
\]
\end{document}

In either case, you can use \\[<dimen>] to change the vertical separation.

Beautification

To make your sums to look less cramped, you can use \limits as in

\sum\limits_{k=1}^{K-1}

Code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\[
P(Y_i = j) = \begin{cases}
            \frac{1}{1+\sum\limits_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad k=K \\[2em]
            \frac{e^{\beta_j\cdot x_i}}{1+\sum\limits_{k=1}^{K-1}e^{\beta_k\cdot x_i}} & \quad 1 \leq k \leq K-1
        \end{cases}
\]
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] How to write a function (piecewise) with bracket outside

[Tex/LaTex] How to get more space in piecewise function on LaTeX

Option -1:

Option - 2

Beautification

Related Question