I am looking to produce a matrix multiplication where one of the matrices consists of coloured blocks. Much like:
Is there any way to produce something like this in Latex?
[Tex/LaTex] Matrix color blocks
matrices
Related Solutions
I recommend to use TikZ and its matrix library, specifically the matrix of math nodes feature. TikZ offers a great and comprehensive manual.
Have a look at this example and its source code, written by Alain Matthes, in the TikZ example gallery: Matrix multiplication. It deals exactly with your subject.
The following example calculates the contents of the matrix for the diagonal boxes automatically, given the number of rows.
The environments for tables are a little tricky, because each cell is put in a group. Therefore the example first collects the contents of the matrix in a global macro \DiagonalMatrixLines and uses this macro inside the matrix environment. Macro \foreach of package pgffor is used for the loop.
(There are many other possibilities.)
The square is determined by the height and depth of the row. The matrix environments are based on the environment array which inserts a special
strut \@arstrut to set a minimum height and depth of the row. The additioal white space added by environment array is removed by setting \arraycolsep to zero.
\vdots occupies a little more than one line, but it seems that the matrix
with the diagonal boxes should not contain a row with \vdots. Therefore
is a matrix with four blocks smaller in height and with five blocks larger.
The next example uses the inner part of the left matrix to get the height
of the matrix and uses this height to resize the matrix with the diagonal blocks. The vertical middle of a matrix lies on the math axis.Therefore
we must move the middle of the matrix to the baseline before resizing.
\documentclass{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{pgf,pgffor,graphicx}
\makeatletter
\newcommand*{\DiagonalMatrixBlock}{%
\begingroup
\setlength{\fboxsep}{0pt}%
\colorbox{red}{%
\@arstrut
\kern\dp\@arstrutbox
\kern\ht\@arstrutbox
}%
\endgroup
}
\newcommand*{\@DiagonalMatrix}[1]{%
\begingroup
\setlength{\arraycolsep}{0pt}%
\global\let\DiagonalMatrixLines\@empty
\foreach[count=\xi] \x in {1,...,#1} {%
\ifnum\xi>1 %
\g@addto@macro\DiagonalMatrixLines{\\}%
\fi
\foreach \x in {1,...,\xi} {
\g@addto@macro\DiagonalMatrixLines{&}%
}%
\g@addto@macro\DiagonalMatrixLines{\DiagonalMatrixBlock}%
}%
\endgroup
}
\newcommand*{\DiagonalMatrix}[1]{%
\begingroup
\setlength{\arraycolsep}{0pt}%
\@DiagonalMatrix{#1}%
\begin{pmatrix}\DiagonalMatrixLines\end{pmatrix}%
\endgroup
}
\newcommand*{\ScaledDiagonalMatrix}[2]{%
\begingroup
\sbox0{$\begin{matrix}#2\end{matrix}$}%
\sbox2{$\vcenter{}$}
\setlength{\arraycolsep}{0pt}%
\@DiagonalMatrix{#1}%
\left(%
\raisebox{\ht2}{%
\resizebox{!}{\dimexpr\ht0-\ht2\relax}{%
\raisebox{-\ht2}{%
$\begin{matrix}\DiagonalMatrixLines\end{matrix}$%
}%
}%
}%
\right)%
\endgroup
}
\makeatother
\begin{document}
\[
\begin{pmatrix}
b_1 \\ b_2 \\ \vdots \\ b_n
\end{pmatrix}
=
\DiagonalMatrix{5}
\begin{pmatrix}
a_1 \\ a_2 \\ \vdots \\ a_n
\end{pmatrix}
\]
\[
\newcommand*{\MatrixB}{b_1 \\ b_2 \\ \vdots \\ b_n}
\begin{pmatrix}\MatrixB\end{pmatrix}
=
\ScaledDiagonalMatrix{8}{\MatrixB}
\begin{pmatrix}
a_1 \\ a_2 \\ \vdots \\ a_n
\end{pmatrix}
\]
\end{document}
Best Answer
I did this with stacks. Unfortunately, there is some tailoring that one must do, depending on the arrangement of boxes, so each particular image must be thought through. The
\colblock[color]{rows}{content}is the basic unit.\belowbaseline[length]{}is used in\colblockto align boxes at their top. That and\belowbaseline[length]{}can be used in the code to shift/align boxes. Passing either of them a multiple of\baselineskipwould allow some staggering in the vertical box placement.If the
\colblocks are allowed to be rectangular (I assumed square), let me know so that I may correct the answer.