Adding a complex maths equation to Latex

Question

I am trying to add the following equation to my paper.

This is my code and it is not producing desired output.

\begin{equation}
L_T(\vec{\lambda}) = \sum_(x,s)\elementof T \log P(s|X) - \sum_(i=1)^m \lamda_i^
\end{equation}
\subsection{Partition Function}

Any simple way to create this equation?

Answer 1

I kept to the OPs image rather than to his code to keep the result as required. an MWE could be

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm}
\begin{document}
  \[
    \mathcal L_{\mathcal T}(\vec{\lambda})
    = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T}
       \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m
       \frac{\lambda_i^2}{2\sigma^2}
  \]
\end{document}

In there, \mathcal defines the next letter to be caligraphic, \mathbfa bold face one. You should introduce semantic commands (for example I use bold for vectors and hence define \vectin mit documents. This defines globally how certain things should look like and makes the formulae semantically nicer.

However the result looks like

Answer 2

This doubts have to do with basic of how TeX (and LaTeX) operates, you should read an introduction.

Now, to your question, this will recreate exactly that output

\documentclass{article}
\begin{document}
\begin{equation} \textstyle 
  \mathcal{L}_{\mathcal{T}}(\vec{\lambda}) = \sum_{\mathbf{x},\mathbf{s}\in\mathcal{T}} \log P(\mathbf{x}|\mathbf{S}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2}
\end{equation}
\end{document}

But there's no reason for that \textstyle to be there, in centered equations super- or subscripts are usually placed above and below the sumation symbol. So better to leave it out (unless you specifically want to have that exact output).

In any case, I would define semantic commands for \mathcal, \mathbf, and even may be \mathcal{L} or \mathcal{T} or P. A few examples

• If in one document one wants the vectors to be written with bold fonts, rather than an arrow above (which is not the case in your code, but it's just an example) it's better to use \vec{x} (rather than \mathbf{x}) and define \renewcommand*\vec[1]{\mathbf{#1}}.

• If you want to use \mathbb{N} to denote number sets, may be it's better to use \numberset{N} or \numberset{K} in your document, rather than \mathbb{..}. That way you have a semantic macro which also gives you freedom to redefine the macro whenever you want;

• even more, you can, in turn, define \N or \naturals to be \numberset{N}, or \reals/\R to be \numberset{R}. That way you abstract even further. The document would be simpler to write and to read.

• And you can use \Pr for the \Pr(x|y) in case it's a probability, and may be redefine \Pr to your taste.

Of course, if you are using something once in a document, there's no need for this, but if you are using something again and again, it's definitely beneficial for your document to have semantic and symbolic macros, at a more higher level, rather than use the “core tools” directly.

Answer 3

Please note (mandatory) arguments to a LaTeX command have to be enclosed within braces, not parentheses.

I propose some improvements: using \mid or \,\vert\, instead of | for a better spacing. Similarly, \smashoperator (from mathtools) sets the problem of subscripts or superscripts in \sum which are larger than the sum symbol and result in wide spacings in equations. Finally I recommend using \vv from \esvect, rather than vect: it produces nicer arrow tips (8 variants!) and are extensible. Compare:

\documentclass{article}
\usepackage{mathtools}
\usepackage{array}
\usepackage[b]{esvect}

\begin{document}

\begin{equation}
  \mathcal{L}_T(\vv{λ}) = \smashoperator{∑_{\mathbf{x},\mathbf{s} ∈ \mathcal{T}}} \log P(\mathbf{s}\,\vert\, \mathbf{x}) - ∑_{i=1}^m \frac{\lambda_i²}{\sigma²}
\end{equation}

\begin{equation}
  \mathcal{L}_T(\vec{λ}) = ∑_{\mathbf{x},\mathbf{s} ∈ \mathcal{T}} \log P(\mathbf{s}| \mathbf{x}) - ∑_{i=1}^m \frac{\lambda_i²}{\sigma²}
\end{equation}

\end{document}