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POFaster way to initialize arrays via empty matrix multiplication? (Matlab)
 

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  1. POFaster way to initialize arrays via empty matrix multiplication? (Matlab)
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    <p>I've stumbled upon the weird way (in my view) that Matlab is dealing with <a href="http://www.mathworks.com/help/matlab/math/empty-matrices-scalars-and-vectors.html" rel="noreferrer">empty matrices</a>. For example, if two empty matrices are multiplied the result is:</p> <pre><code>zeros(3,0)*zeros(0,3) ans = 0 0 0 0 0 0 0 0 0 </code></pre> <p>Now, this already took me by surprise, however, a quick search got me to the link above, and I got an explanation of the somewhat twisted logic of why this is happening. </p> <p><strong>However</strong>, nothing prepared me for the following observation. I asked myself, how efficient is this type of multiplication vs just using <code>zeros(n)</code> function, say for the purpose of initialization? I've used <a href="http://www.mathworks.com/matlabcentral/fileexchange/18798" rel="noreferrer"><code>timeit</code></a> to answer this:</p> <pre><code>f=@() zeros(1000) timeit(f) ans = 0.0033 </code></pre> <p>vs:</p> <pre><code>g=@() zeros(1000,0)*zeros(0,1000) timeit(g) ans = 9.2048e-06 </code></pre> <p>Both have the same outcome of 1000x1000 matrix of zeros of class <code>double</code>, but the empty matrix multiplication one is ~350 times faster! (a similar result happens using <code>tic</code> and <code>toc</code> and a loop)</p> <p>How can this be? are <code>timeit</code> or <code>tic,toc</code> bluffing or have I found a faster way to initialize matrices? (this was done with matlab 2012a, on a win7-64 machine, intel-i5 650 3.2Ghz...)</p> <p><strong>EDIT:</strong></p> <p>After reading your feedback, I have looked more carefully into this peculiarity, and tested on 2 different computers (same matlab ver though 2012a) a code that examine the run time vs the size of matrix n. This is what I get:</p> <p><img src="https://i.stack.imgur.com/DSZn7.png" alt="enter image description here"></p> <p>The code to generate this used <code>timeit</code> as before, but a loop with <code>tic</code> and <code>toc</code> will look the same. So, for small sizes, <code>zeros(n)</code> is comparable. However, around <code>n=400</code> there is a jump in performance for the empty matrix multiplication. The code I've used to generate that plot was:</p> <pre><code>n=unique(round(logspace(0,4,200))); for k=1:length(n) f=@() zeros(n(k)); t1(k)=timeit(f); g=@() zeros(n(k),0)*zeros(0,n(k)); t2(k)=timeit(g); end loglog(n,t1,'b',n,t2,'r'); legend('zeros(n)','zeros(n,0)*zeros(0,n)',2); xlabel('matrix size (n)'); ylabel('time [sec]'); </code></pre> <p>Are any of you experience this too?</p> <p><strong>EDIT #2:</strong></p> <p>Incidentally, empty matrix multiplication is not needed to get this effect. One can simply do:</p> <pre><code>z(n,n)=0; </code></pre> <p>where n> some threshold matrix size seen in the previous graph, and get the <strong>exact</strong> efficiency profile as with empty matrix multiplication (again using timeit). </p> <p><img src="https://i.stack.imgur.com/EZVOI.png" alt="enter image description here"></p> <p>Here's an example where it improves efficiency of a code:</p> <pre><code>n = 1e4; clear z1 tic z1 = zeros( n ); for cc = 1 : n z1(:,cc)=cc; end toc % Elapsed time is 0.445780 seconds. %% clear z0 tic z0 = zeros(n,0)*zeros(0,n); for cc = 1 : n z0(:,cc)=cc; end toc % Elapsed time is 0.297953 seconds. </code></pre> <p>However, using <code>z(n,n)=0;</code> instead yields similar results to the <code>zeros(n)</code> case.</p>
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    1. CO@natan, you can try the [kronecker](http://www.mathworks.it/it/help/matlab/ref/kron.html) product of zero matrices also. Somehow it can even be *quadratically* fast.
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    2. CO@natan - if you are going to create tag wiki entries such as [this one](http://stackoverflow.com/tags/economics/info) by copying and pasting verbatim from Wikipedia, please including a source attributation at the end of the wiki; otherwise, [you are plagiarizing text](http://meta.stackexchange.com/a/79002/148949).
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