Implementation details

Manuscript/stochastic_triples.tex

@@ -176,7 +176,7 @@ multiplications,\cite{form_w_abc} which are among the most efficient operations
 executed on modern CPUs and
 accelerators.\cite{ma_2011,haidar_2015,dinapoli_2014,springer_2018}
 
-In the algorithm proposed by Rendell\cite{rendell_1991}, for each given triplet $(abc)$, the sub-tensors $W_{ijk}(abc)$ and $V_{ijk}(abc)$ are computed and immediately utilized to calculate their contribution to $E_{ijk}(abc)$. Here, we propose a similar approach but introduce a semi-stochastic algorithm to randomly select the triplets $(abc)$, circumventing the need to compute all contributions.
+In the algorithm proposed by Rendell\cite{rendell_1991}, for each given triplet $(abc)$, the sub-tensors $W^{abc}$ and $V^{abc}$ are computed and immediately utilized to calculate their contribution to $E^{abc}$. Here, we propose a similar approach but introduce a semi-stochastic algorithm to randomly select the triplets $(abc)$, circumventing the need to compute all contributions.
 
 %=================================================================%
 \section{Semi-Stochastic Algorithm}
@@ -206,6 +206,23 @@ In the algorithm proposed by Rendell\cite{rendell_1991}, for each given triplet
 
 The algorithm was implemented in the \textsc{Quantum Package} software.
 \cite{garniron_2019}
+The stochastic algorithm is implemented using OpenMP tasks, where each task
+consists in the computation of a single component $E^{abc}$.
+The computation of the running average and statistical error is executed every second,
+for printing or for exiting when the statistical error gets below a given threshold.
+
+The number of samples $N^{abc}$ of each triplet $(abc)$ is initialized to $-1$, to identify
+the contributions that have not been already computed.
+An outer \emph{for} loop runs over the maximum number of iteration, equal to
+$N_{abc}$, the number of different triplets $(abc)$.
+
+Within a loop iteration, the index of the first non-computed triplet $(abc)$ is identified, and the task associated with its computation is sent to the task queue.
+As this triplet has never been drawn, $N^{abc}$ is set to zero.
+Then, a triplet $(abc)$ is drawn randomly.
+If the $E^{abc}$ has not been computed (identified by $N^{abc}=-1$), the number of samples is set to zero and the task for the computation of this contribution is enqueued. 
+In any case, $N^{abc}$ is then incremented.
+
+
 
 %a. Description of the computational framework and software used
 %b. Discussion of any specific optimizations or parallelization techniques employed