A long equation: how to adapt the font size to the page width?

Question

I would like to reduce the size of the following equation just exactly as needed in order to fit the page. Is there some sort of command to adapt the font size to the page width?

Here's my latex:

\begin{equation}
    d\left(\begin{array}{c}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{array}\right)
    =
    \left(\begin{array}{ccc}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{array}\right)
    \left(\begin{array}{c}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{array}\right)
    +
    \left(\begin{array}{ccc}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{array}\right)
    d \left(\begin{array}{c}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{array}\right)
\end{equation}

And here's the result I get (as you can see the equation gets out of the right page bound):

Note: I tried using

\resizebox{.9 \textwidth}{!} 
{
    \begin{equation}
    [...] % My equation here
    \end{equation}
}

But I get a compilation error.

Answer 1

As others have said it is best to avoid scaling. In this case you can most likely make it fit on one line without scaling. You are loading amsmath but not using its matrix environments which means that you have a lot more space around the large brackets than needed. That change and a small squeezing of the column spacing is all you need to make things fit here:

\documentclass[a4paper]{article}
\addtolength\textwidth{10mm}% try to get initial position like image shown No test file provided :(((
\usepackage{amsmath}

\begin{document}

original
\begin{equation}
    d\left(\begin{array}{c}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{array}\right)
    =
    \left(\begin{array}{ccc}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{array}\right)
    \left(\begin{array}{c}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{array}\right)
    +
    \left(\begin{array}{ccc}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{array}\right)
    d \left(\begin{array}{c}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{array}\right)
\end{equation}


ams matrices
\begin{equation}\setlength\arraycolsep{4pt}
    d\begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    =
   \begin{pmatrix}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{pmatrix}
    \begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    +
    \begin{pmatrix}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{pmatrix}
    d \begin{pmatrix}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{pmatrix}
\end{equation}
\end{document}

Answer 2

The environment of choice for this case is multline.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{multline}
    d\begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    =
    \begin{pmatrix}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{pmatrix}
    \begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix} \\
    +
    \begin{pmatrix}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{pmatrix}
    d \begin{pmatrix}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{pmatrix}
\end{multline}

\end{document}

Note the usage of pmatrix.

The objection that this doesn't directly answer the question should be rejected, but it's not difficult to make an example so you can judge for yourself.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\newenvironment{scaledequation}
 {\begin{equation}\begin{lrbox}{\scaledequationbox}$\displaystyle}
 {$\end{lrbox}%
  \resizebox{0.9\displaywidth}{!}{\usebox{\scaledequationbox}}%
  \end{equation}
  \ignorespacesafterend}
\newsavebox{\scaledequationbox}

\begin{document}

This is how a long equation should be treated when it's too wide for
fitting the given text width
\begin{multline}
    d\begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    =
    \begin{pmatrix}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{pmatrix}
    \begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix} \\
    +
    \begin{pmatrix}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{pmatrix}
    d \begin{pmatrix}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{pmatrix}
\end{multline}
On the other hand, you could rescale the material to fit, with a
dubious result, which you can compare to the previous one
\begin{scaledequation}
    d\begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    =
    \begin{pmatrix}
        -\alpha_{D} & 1 & 0 \\
        0 & -\alpha_{\Pi} & 0 \\
        0 & 0 & -\alpha_{\Theta}
    \end{pmatrix}
    \begin{pmatrix}
        D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    +
    \begin{pmatrix}
        \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
        0 & \sigma_{\Pi,\Pi}& 0 \\
        \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{pmatrix}
    d \begin{pmatrix}
        w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{pmatrix}
\end{scaledequation}
I have no doubt whatsoever as to which one I'd choose.

\end{document}

Answer 3

It is never a good solution to start adjusting the font size of math, (1) it gives an inconsistent design, and (2) hurts readability. Instead learn to break mathematics it will become an important tool in your future documents.

\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}
  \begin{aligned}
    d\begin{pmatrix}{c} D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    = {} & % note the {} in front of & in this case
    \begin{pmatrix}
      -\alpha_{D} & 1 & 0 \\
      0 & -\alpha_{\Pi} & 0 \\
      0 & 0 & -\alpha_{\Theta}
    \end{pmatrix}
    \begin{pmatrix}
      D(t) \\ \Pi(t) \\ \Theta(t)
    \end{pmatrix}
    \\
    & +
    \begin{pmatrix}
      \sigma_{D,D} & \sigma_{D,\Pi} & 0 \\
      0 & \sigma_{\Pi,\Pi}& 0 \\
      \sigma_{\Theta,D} & 0 & \sigma_{\Theta,\Theta}
    \end{pmatrix}
    d \begin{pmatrix} w_{D}(t)\\ w_{\Pi}(t) \\ w_{\Theta}(t)
    \end{pmatrix}
  \end{aligned}
 \end{equation}

\end{document}

here I've also used the pmatrix env as it gives less typing.

Note also how I provide a full minimal example including document class and appropriate preamble. This makes it a lot easier for others to test the code.