data redistribution

Figure 1: Illustration of the data redistribution procedure.

In the cases of both transforms one needs to redistribute the intermediate data object, $\Delta\left(\theta\left(r\right)\right)$. The redistribution process is sketched graphically in Fig 1. For the map2alm transform the black lines show the data division prior and red - post the redistribution. For alm2map - otherwise. Note that in the actual implementation there is no constraint on what and how many values of $m$ are assigned to each proc and thus the figure is oversimplified and in practice requires data re-mapping prior to the data exchange. The communication is then accomplished by a single (per map) call to the MPI routine MPI_Alltoallv.