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  1. PO
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    <p>I think I managed to do it with this single disgusting line:</p> <pre><code>cast(aggregate(value ~ X1 + X2, rbind(melt(M1), melt(M2)), sum), X1 ~ X2)[,-1] </code></pre> <p>This makes use of the <code>reshape</code> package. Returned as a data frame so convert to matrix as necessary.</p> <p>If you want it in the format you suggested in your example, try this:</p> <pre><code>"%ms%" &lt;- function(m1, m2) { m &lt;- as.matrix(cast(aggregate(value ~ X1 + X2, rbind(melt(m1), melt(m2)), sum), X1 ~ X2)[,-1]) mn &lt;- unique(colnames(m1), colnames(m2)) rownames(m) &lt;- mn colnames(m) &lt;- mn return (m) } </code></pre> <p>Then you can do:</p> <pre><code>M1 %ms% M2 </code></pre> <p><hr /> EDIT:</p> <h2>EXPLANATION</h2> <p>Obviously should have some explanation sorry.</p> <pre><code>melt(M1) </code></pre> <p>Converts <code>M1</code> from its original form into a format like this (row, col, value). E.g.</p> <pre><code> 1 3 4 5 7 8 1 0 0 1 0 0 0 3 0 0 0 0 0 0 4 1 0 0 0 0 0 5 0 0 0 0 0 0 7 0 0 0 0 1 0 8 0 0 0 0 0 0 </code></pre> <p>Is converted to:</p> <pre><code> X1 X2 value 1 1 1 0 2 3 1 0 3 4 1 1 </code></pre> <p>etc. Combining <code>M1</code> and <code>M2</code> lists every possible (row, col, value) across both matrix into one single matrix. Now this:</p> <pre><code>aggregate(value ~ X1 + X2, rbind(melt(M1), melt(M2)), sum) </code></pre> <p>Sums values where the row and column are the same. So it will sum (1, 1) across both matrices for example. And (3, 1) etc. It won't do anything that doesn't exist e.g. <code>M2</code> doesn't have a 7th column/row.</p> <p>Finally <code>cast</code> transforms the matrix so that it is written with the result of <code>aggregate</code>'s first column as rows, its second column as columns. Effectively undoing the melt from earlier. The <code>[,-1]</code> is taking off an unnecessary column leftover from <code>cast</code> (I think there is probably a better way of doing that but I don't know how).</p> <p>As I said, it's returned as a data frame so use <code>as.matrix()</code> on the result if that's what you wish.</p>
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    1. POJoin and sum not compatible matrices
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    1. PTAnswer
    1. USMadScone
    1. USMadScone
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      1. VTUpMod
    1. COOh, that's nice. I think you could have the `cast` function do the aggregation, so the `aggregate` function would be unneeded. Using the `reshape2` package so that we can choose to get a matrix back instead of a data frame, it would be `acast(rbind(melt(M1), melt(M2)), Var1~Var2, fun.aggregate=sum)`.
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      1. USAaron
    2. COIt is a good solution: thanks! However, I've done a little benchmark and reported results in the question.
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      1. USleodido
    3. COGood stuff @Aaron. I'm still stuck using `reshape` for some reason. Time to upgrade methinks.
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      1. USMadScone
 

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