multiline equation inside a matrix that is a part of multiline equation

Question

I have an equation split to multiple lines. But the last line of the multiline equation contains 2x1 vector with long equations that go out of margin. How do I further split the equations in the vector so that they do go over margin and look visually pleasing?

\begin{equation} \label{eq:7}
\begin{split}
\mathbf{y}(1)&=tanh(\mathbf{W}^{ro}\cdot\mathbf{h}(1)+\mathbf{W}^{io}\cdot\mathbf{x}(1)) \\
&=\begin{bmatrix} tanh\Big(w^{ro}_{1,1}\cdot\alpha\cdot tanh\big(w^{ir}_{1,1}\cdot x_{1}(1)+w^{ir}_{2,1}\cdot x_{2}(1)\big) + w^{ro}_{2,1}\cdot \alpha \cdot tanh\big(w^{ir}_{1,2}\cdot x_{1}(1)+w^{ir}_{2,2} \cdot x_{2}(1)\big) + w^{io}_{1,1} \cdot x_{1}(1)+w^{io}_{2,1} \cdot x_{2}(1)\Big) \\ tanh\Big(w^{ro}_{1,2}\cdot \alpha \cdot tanh\big(w^{ir}_{1,1}\cdot x_{1}(1)+w^{ir}_{2,1}\cdot x_{2}(1)\big) + w^{ro}_{2,2}\cdot \alpha \cdot tanh\big(w^{ir}_{1,2}\cdot x_{1}(1)+w^{ir}_{2,2} \cdot x_{2}(1)\big) + w^{io}_{1,2}\cdot x_{1}(1)+w^{io}_{2,2}\cdot x_{2}(1)\Big) \end{bmatrix}.
\end{split}
\end{equation}

Current output looks like below where good portion of equations go over margin:

Any help will be greatly appreciated

Answer 1

You can break lines within a matrix by useing of multlined from the mathtools package:

\documentclass{article}
\usepackage{geometry}
\usepackage{mathtools}

\begin{document}
\begin{equation} \label{eq:7}
\begin{split}
\mathbf{y}(1)&=\tanh(\mathbf{W}^{ro}\cdot\mathbf{h}(1)+\mathbf{W}^{io}\cdot\mathbf{x}(1)) \\
    & = \begin{bmatrix}
        \begin{multlined}
    \tanh\Bigl(w^{ro}_{1,1}{\cdot}\alpha{\cdot} \tanh\bigl(w^{ir}_{1,1}{\cdot} x_{1}(1) + w^{ir}_{2,1}{\cdot} x_{2}(1)\bigr)       \\[-2ex]
        + w^{ro}_{2,1}{\cdot} \alpha {\cdot} \tanh\bigl(w^{ir}_{1,2}{\cdot} x_{1}(1) + w^{ir}_{2,2} {\cdot} x_{2}(1)\bigr) + w^{io}_{1,1} {\cdot} x_{1}(1)+w^{io}_{2,1} {\cdot} x_{2}(1)\Bigr)
        \end{multlined}     \\[4ex]
    %
       \begin{multlined}
    \tanh\Bigl(w^{ro}_{1,2}{\cdot} \alpha {\cdot} \tanh\bigl(w^{ir}_{1,1}{\cdot} x_{1}(1) + w^{ir}_{2,1}{\cdot} x_{2}(1)\bigr)       \\[-2ex]
        + w^{ro}_{2,2}{\cdot} \alpha {\cdot} \tanh\bigl(w^{ir}_{1,2}{\cdot} x_{1}(1)+w^{ir}_{2,2} {\cdot} x_{2}(1)\bigr) + w^{io}_{1,2}{\cdot} x_{1}(1)+w^{io}_{2,2}{\cdot} x_{2}(1)\Bigr)
        \end{multlined}
        \end{bmatrix}.
\end{split}
\end{equation}
\end{document}

note: I try to fix of use \Big( and \big(. More correct is \Bigl( and \bigl( and \Bigr) and \bigr). most of the math operators are defined, so instead ˙tanh you should use \tanh which write it correct mathrm font. I also reduce width of \cdots enclosing them in curly braces. Do you really need them?

Answer 2

Here there is my proposal:

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage[left=1in,right=.3in]{geometry}

\begin{document}
\begin{equation} \label{eq:7}
\begin{aligned}
\mathbf{y}(1)&=\tanh(\mathbf{W}^{\mathrm{ro}}\cdot\mathbf{h}(1)+\mathbf{W}^{\mathrm{io}}\cdot\mathbf{x}(1)) \\
&=\begin{bmatrix} \tanh\Big((w^{\mathrm{\mathrm{ro}}}_{1,1}\cdot\alpha\cdot \tanh\mu) + w^{\mathrm{ro}}_{2,1}\cdot \alpha \cdot \tanh \lambda + w^{\mathrm{io}}_{1,1} \cdot x_{1}(1)+w^{\mathrm{io}}_{2,1} \cdot x_{2}(1)\Big) \\ 
\tanh \Big((w^{\mathrm{ro}}_{1,2}\cdot \alpha \cdot \tanh\mu) + w^{\mathrm{ro}}_{2,2}\cdot \alpha \cdot \tanh \lambda + w^{\mathrm{io}}_{1,2}\cdot x_{1}(1)+w^{\mathrm{io}}_{2,2}\cdot x_{2}(1)\Big) \end{bmatrix}
\end{aligned}
\end{equation}

where $\mu=(w^{\mathrm{ir}}_{1,1}\cdot x_{1}(1)+w^{\mathrm{ir}}_{2,1}\cdot x_{2}(1))$ and $\lambda=(w^{\mathrm{ir}}_{1,2}\cdot x_{1}(1)+w^{\mathrm{ir}}_{2,2} \cdot x_{2}(1))$
\end{document}

Answer 3

I propose this layout, which doesn't require multiline equations inside matrix. Instead, I suppressed the \cdots (unnecessary, from my point of view) and used the mmatrix (medium-size matrix) environment from nccmath, and the fleqn environment (same package). This size remains readable, as it is ~80 % of \displaystyle.

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{mathtools, nccmath}

\begin{document}
\vspace*{1cm}
\begin{fleqn}

\begin{equation}
\begin{aligned}[b] \label{eq:7}
&\mathbf{y}(1)=\tanh(\mathbf{W}^{ro}\cdot\mathbf{h}(1)+\mathbf{W}^{io}\cdot\mathbf{x}(1)) = \\
 & \begin{mmatrix} \begin{bmatrix}
    \tanh\Bigl(w^{ro}_{1,1} \alpha \tanh\bigl(w^{ir}_{1,1} x_{1}(1) + w^{ir}_{2,1} x_{2}(1)\bigr)
        + w^{ro}_{2,1} \alpha \tanh\bigl(w^{ir}_{1,2} x_{1}(1) + w^{ir}_{2,2} x_{2}(1)\bigr) + w^{io}_{1,1} x_{1}(1)+w^{io}_{2,1} x_{2}(1)\Bigr)
        \\
    %
          \tanh\Bigl(w^{ro}_{1,2} \alpha \tanh\bigl(w^{ir}_{1,1} x_{1}(1) + w^{ir}_{2,1} x_{2}(1)\bigr)
        + w^{ro}_{2,2} \alpha \tanh\bigl(w^{ir}_{1,2} x_{1}(1)+w^{ir}_{2,2} x_{2}(1)\bigr) + w^{io}_{1,2} x_{1}(1)+w^{io}_{2,2} x_{2}(1)\Bigr)
        \end{bmatrix}
\end{mmatrix}
\end{aligned}
\end{equation}
\end{fleqn}

\end{document}