First a quick description of my usecase:
I have an array of 81x81x81 complex values which represent a wavefunction in real space. I have 200 values of vector k, for which I need to calculate various things using these 81x81x81 arrays, after calculating the discrete fourier transforms of each of them. This is done for 1 array, by taking it, shifting it a certain amount of indices (basically shifting it by -2:2 times the primary vector in all 3 dimensions), and taking the sum of these shifted values * exp(i dot(k,R)). In the end I arrive at an 81x81x81 array, where the elements are some variation of:
c1 exp(i dot(k,-2R))+c2 exp(i dot(k,-R) + c3 +c4 exp(i dot(k,R)) + c5 exp(i dot(k,2R)) +…, where the c’s are the values coming from the shifted arrays, and the R representing the shifting vector.
Obviously this is quite a lot of shuffling around and looking up different parts of memory and that is the main bottleneck of my program at the moment.
However, the only varying thing is this k-vector, meaning that all the c’s and R’s are the same for every k-point. So i feel that instead of taking my basis 81x81x81 arrays, then creating the new ones for every k-point, there might be a better strategy.
Is this a possible usecase for lazy evaluation? Basically that the sum for each point of the array is not done until I use it specifying some value of k? Is using lazy evaluation on such a scale going to be performant and manageable memory-wise?
I tried by using metaprogramming, creating an 81x81x81 array of code that represents the sums, but this results in arrays of over 6gb of data which is not manageable since I have more than 8 of those arrays to work with, and also causes a significant overhead in the evaluation when I loop through the points during various calculations.
As an idea of the speed it takes to construct the summed arrays, it takes about 0.7s for each of the 8 arrays, and this has to be done at each of my 200 k values. So it’s not painstakingly slow by any means, I just feel like there might be a better solution and like to learn more about cool features of the language, so if there are better ways of doing this using Julia please let me know!