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POmatlab: exp(X) gives inf even though exp(max(X)) does not
 

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  1. POmatlab: exp(X) gives inf even though exp(max(X)) does not
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    <p><em>[Edit: The whole thing has a very simple solution: the matrix used the single datatype instead of the default double]</em></p> <p>I have just noticed a somewhat peculiar (I think) behaviour in matlab and wonder what's causing it. I have a 10000x500 matrix M with values ranging from </p> <pre><code>min(min(M)) = -226.9723 to max(max(M)) = 92.8173 </code></pre> <p>and</p> <pre><code>exp(-227) = 2.6011e-99 exp(93) = 2.4512e+40 </code></pre> <p>but if I exp the entire matrix, this matrix has inf values:</p> <pre><code>ii = isinf(exp(M)); sum(sum(ii)) ans = 2 </code></pre> <p>How does Matlab store the values in the matrix so that operations on individual elements can give a different result than when doing the same operation on the matrix itself?</p> <p>I.e. </p> <pre><code>expM = exp(M); exp(M(1)) == expM(1) ; %can be false, which I find surprising </code></pre> <p>I know I have to change the algorithm anyway as the high exponents will give inexact results even if I can avoid inf values. It happens in a formula for a artificial neural network calculation like: </p> <pre><code> sum(log(1+exp(ones(numcases,1)*b_h + data*w_vh)),2); </code></pre> <p>so my plan is to split this up into two cases, first where the exponent is small I do the calculation as above, for high values I approximate </p> <pre><code>log(1+exp(ones(numcases,1)*b_h + data*w_vh) </code></pre> <p>with </p> <pre><code>ones(numcases,1)*b_h + data*w_vh </code></pre> <p>Does that sound reasonable? My reasoning of course is that </p> <pre><code>log(1+exp(x)) ≈ log(exp(x)) ≈ x, for large x </code></pre> <p>btw: is there a better way to get the maximum element of a matrix other than doing max twice as in max(max(M))?</p>
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    1. COInteresting issue... I can't seem to reproduce it on my machine using R2010a, I'm not getting any inf and exp(a) always == expa where expa = exp(a)
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    2. COYeah, I couldn't find a simple code example that generates a matrix that shows this behaviour either :/ I'll upload a mat file for anyone curious enough to care :)
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    3. COStrange indeed. I can tell you this does not happen in GNU Octave, or at least I couldn't replicate this.
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      1. USOfri Raviv
 

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