TikZ marking several blocks in a matrix

Question

I would like to mark a few blocks in a matrix and I followed directions from other similar questions but I get a weird TikZ behavior .. seems that I can not have more than one marked block in a matrix? What I would like to show is the stencil of a blocked Givens rotations to annihilate non-zero elements under the diagonal starting from some column, where I update a block (red color) over the diagonal and then can work on the trailing columns or row block on the right (green color).

UPDATE: Using the answer as input I implemented my final use case.

\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{calc,fit,matrix,arrows,automata,positioning}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
\newcommand{\tikzdrawbox}[3][]{%
    \tikz[overlay,remember picture]{
    \draw[#3,#1]
      ($(left#2)+(-0.2em,0.9em)$) rectangle
      ($(right#2)+(0.2em,-0.3em)$);}
}

\newcommand\x{\times}

\begin{equation}\label{eq:blockedgivens}
\newcommand\y{\colorbox{myred}{$\times$}}
\newcommand\z{\colorbox{mygray}{$\times$}}
  \left(\begin{array}{ccccccccccccccc}
    \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 & \tikzmark{left1}\x & \x & \x & \x & \tikzmark{left3}\x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 & \z & \tikzmark{left2} \x \tikzmark{right1} & \x & \x & \x & \tikzmark{left4} \x & \x & \x & \x \tikzmark{right3}\\
     0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x \tikzmark{right2} & \x & \x & \x \tikzmark{right4} \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x \\
  \end{array}\right)
  \tikzdrawbox[thick]{1}{red}
  \tikzdrawbox[thick]{2}{red}
  \tikzdrawbox[thick]{3}{green}
  \tikzdrawbox[thick]{4}{green}
\end{equation}

Answer 1

Each block need its own pair of marks; I changed the definition of \tikzdrawbox; the first mandatory argument is a number used for the marks; the second optional argument allows you to pass options to \draw and the optional argument allows you to specify some "correction" to the block dimensions to prevent some borders to overlap:

\documentclass{article}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{calc,fit,matrix,arrows,automata,positioning}

\newcommand\x{\times}
\newcommand\y{\colorbox{red}{$\times$}}
\newcommand\z{\colorbox{gray}{$\times$}}


\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
\newcommand{\tikzdrawbox}[3][(0pt,0pt)]{%
    \tikz[overlay,remember picture]{
    \draw[#3]
      ($(left#2)+(-0.3em,0.9em) + #1$) rectangle
      ($(right#2)+(0.2em,-0.4em) - #1$);}
}

\begin{document}

\begin{equation}\label{eq:blockedgivens}
  \left(\begin{array}{ccccccccccccccc}
    \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 & \tikzmark{left1}\x & \x & \x & \x & \tikzmark{left3}\x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 & \z & \tikzmark{left2} \x \tikzmark{right1} & \x & \x & \x & \tikzmark{left4} \x & \x & \x & \x \tikzmark{right3} \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x \tikzmark{right2} & \x & \x & \x \tikzmark{right4} \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x & \x \\
     0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 &  0 & \z & \x \\
  \end{array}\right)
  \tikzdrawbox{1}{thick,red}
  \tikzdrawbox{2}{thick,red}
  \tikzdrawbox[(-1pt,2pt)]{3}{thick,green}
  \tikzdrawbox[(-4pt,2pt)]{4}{thick,green}
\end{equation}

\end{document}

Answer 2

If you don't have too many special entries(for which you can include more if cases), you can shorten the code a bit.

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{equation}\label{eq:blockedgivens}
\left( 
\begin{tikzpicture}[baseline=(current bounding box.center)] 
\begin{scope}[xscale=0.6,yscale=0.4]
\foreach \x in {1,...,14}
    \foreach \y in {1,...,14}
    {
    \ifnum\x<\y
    \node (my-\y-\x) at (\x,-\y) {$0$};
    \else
    \node (my-\y-\x) at (\x,-\y) {$\times$};
    \fi
    }
\end{scope}
\draw[red] (my-4-4.north west) rectangle (my-8-8.south east);
\draw[red] (my-8-8.north west) rectangle (my-12-12.south east);
\end{tikzpicture}
\right)
\end{equation}
\end{document}