Breaking lines of array matrix

Question

I have a line of matrix arrays such as the next figure

Below the code of that matrix.

\begin{figure}
\[
 P=\left(\left\{\begin{array}{l}
 p^{(1)}(x_1,x_2,\cdots,x_{r_1})  \\
\vdots\\
p^{(m_1)}(x_1,x_2,\cdots,x_{r_1})
\end{array}
\right.%%%%%%%%%%%%%
\left\{\begin{array}{l}
 p^{(m_1+1)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2})  \\
\vdots\\
 p^{(m_1+m_2)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2}) 
 \end{array}
\right.%%%%%%%%%%%%
\right).
\]
\end{figure}

Could you help me to break each system such that the new figure approximately will be in this way (with the braces):

Answer 1

You need to nest array or matrix.

\documentclass{article}
\usepackage{mathtools}

    \begin{document}
\begin{figure}[h]
    \centering
\[
P = \left(\begin{array}{l}
    \left\{\begin{array}{l}
            p^{(1)}(x_1,x_2,\cdots,x_{r_1})  \\
            \vdots  \\
            p^{(m_1)}(x_1,x_2,\cdots,x_{r_1})
    \end{array}\right.      \\
    \left\{\begin{array}{l}
            p^{(m_1+1)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2})  \\
            \vdots\\
            p^{(m_1+m_2)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2})
    \end{array}\right.  
    \end{array}\right)
\]
\caption{nested arrays}
\end{figure}

\begin{figure}[h]
    \centering
\[
P = \begin{pmatrix*}[l]
    \left\{\begin{array}{l}
            p^{(1)}(x_1,x_2,\cdots,x_{r_1})  \\
            \vdots  \\
            p^{(m_1)}(x_1,x_2,\cdots,x_{r_1})
    \end{array}\right.      \\
    \left\{\begin{array}{l}
            p^{(m_1+1)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2})  \\
            \vdots\\
            p^{(m_1+m_2)}(x_1,x_2,\cdots,x_{r_1}, x_{r_1+1},x_{r_1+2},\cdots,x_{r_2})
    \end{array}\right.
    \end{pmatrix*}
\]
\caption{Arrays nested in matrix}
\end{figure}
    \end{document}

Answer 2

Using the dcases environment inside a pmatrix:

\documentclass{article}
\usepackage{mathtools}
\usepackage{eqparbox}

\begin{document}

\[
  P = \begin{pmatrix*}[l]
  \begin{dcases}
    \eqmakebox[V][l]{$ p^{(1)}(x_1,x_2,\dots,x_{r_1}) $} \\
    \eqmakebox[V]{$ \vdots $} \\
    \eqmakebox[V][l]{$ p^{(m_1)}(x_1,x_2,\dots,x_{r_1}) $}
  \end{dcases} \\
  \begin{dcases}
    p^{(m_1+1)}(x_1,x_2,\dots,x_{r_1}, x_{r_1+1},x_{r_1+2},\dots,x_{r_2}) \\
    \eqmakebox[V]{$ \vdots $} \\
    p^{(m_1+m_2)}(x_1,x_2,\dots,x_{r_1}, x_{r_1+1},x_{r_1+2},\dots,x_{r_2})
  \end{dcases}\\[-0.8ex]
  \hskip1em \vdots \\[-1.54ex]
  \hskip1em \vdots \\
  \begin{dcases}
    p^{(\sum_{i=1}^{\ell-1} m_i+1)}(x_1,x_2,\dots,x_{r_1}, \dots \dots, x_{r_{\ell-1}}, x_{r_{\ell-1}+1},\dots,x_{r_\ell }) \\
    \eqmakebox[V]{$ \vdots $} \\
    p^{(\sum_{i=1}^{\ell-1} m_i+m_\ell )}(x_1,x_2,\dots,x_{r_1}, \dots \dots, x_{r_{\ell-1}}, x_{r_{\ell-1}+1},\dots,x_{r_\ell })
  \end{dcases}
  \end{pmatrix*}
\]

\end{document}