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POEfficiently recalculating the gradient of a numpy array with unknown dimensionality
 

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  1. POEfficiently recalculating the gradient of a numpy array with unknown dimensionality
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    <p>I have an N-dimensional numpy array <code>S</code>. Every iteration, exactly one value in this array will change.</p> <p>I have a second array, <code>G</code> that stores the gradient of <code>S</code>, as calculated by numpy's <code>gradient()</code> function. Currently, my code unnecessarily recalculates all of <code>G</code> every time I update <code>S</code>, but this is unnecessary, as only one value in <code>S</code> has changed, and so I only should have to recalculate <code>1+d*2</code> values in <code>G</code>, where <code>d</code> is the number of dimensions in <code>S</code>. </p> <p>This would be an easier problem to solve if I knew the dimensionality of the arrays, but the solutions I have come up with in the absence of this knowledge have been quite inefficient (not substantially better than just recalculating all of <code>G</code>). </p> <p>Is there an efficient way to recalculate only the necessary values in <code>G</code>?</p> <p><strong>Edit: adding my attempt, as requested</strong></p> <p>The function returns a vector indicating the gradient of <code>S</code> at <code>coords</code> in each dimension. It calculates this without calculating the gradient of <code>S</code> at every point, but the problem is that it does not seem to be very efficient.</p> <p>It looks similar in some ways to the answers already posted, but maybe there is something quite inefficient about it?</p> <p>The idea is the following: I iterate through each dimension, creating a slice that is a vector only in that dimension. For each of these slices, I calculate the gradient and place the appropriate value from that gradient into the correct place in the returned vector <code>grad</code>.</p> <p>The use of <code>min()</code> and <code>max()</code> is to deal with the boundary conditions.</p> <pre><code> def getSGradAt(self,coords) : """Returns the gradient of S at position specified by the vector argument 'coords'. self.nDim : the number of dimensions of S self.nBins : the width of S (same in every dim) self.s : S """ grad = zeros(self.nDim) for d in xrange(self.nDim) : # create a slice through S that has size &gt; 1 only in the current # dimension, d. slices = list(coords) slices[d] = slice(max(0,coords[d]-1),min(self.nBins,coords[d]+2)) # take the middle value from the gradient vector grad[d] = gradient(self.s[sl])[1] return grad </code></pre> <p>The problem is that this doesn't run very quickly. In fact, just taking the gradient of the whole array <code>S</code> seems to run faster (for <code>nBins = 25</code> and <code>nDim = 4</code>).</p> <p><strong>Edited again, to add my final solution</strong></p> <p>Here is what i ended up using. This function updates <code>S</code>, changing the value at <code>X</code> by the amount <code>change</code>. It then updates <code>G</code> using a variation on the technique proposed by Jaime.</p> <pre><code> def changeSField(self,X,change) : # change s self.s[X] += change # update g (gradient field) slices = tuple(slice(None if j-2 &lt;= 0 else j-2, j+3, 1) for j in X) newGrads = gradient(self.s[slices]) for i in arange(self.nDim) : self.g[i][slices] = newGrads[i] </code></pre>
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    1. CO`gradient` returns an array if the input is 1-dimensional and a list of arrays if the input has a number of dimensions other than 1. It looks like it wasn't meant to be used with arrays of runtime-determined dimension, and the list is going to exclude most of the clever slice-assignments you could do with an array.
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      1. USuser2357112
 

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