Still looks to me like MPI_Scan is what you want. Just need three additional 
communicators (one for each direction). With a recurive doubling MPI_Scan 
inplementation it is O(log n) compared to O(n) in time.



> On May 14, 2018, at 8:42 AM, Pierre Gubernatis <pierre.guberna...@gmail.com> 
> wrote:
> 
> Thank you to all of you for your answers (I was off up to now).
> 
> Actually my question was't well posed. I stated it more clearly in this post, 
> with the answer: 
> 
> https://stackoverflow.com/questions/50130688/mpi-cartesian-grid-cumulate-a-scalar-value-through-the-procs-of-a-given-axis-o?noredirect=1#comment87286983_50130688
> 
> Thanks again.
> 
> 
> 
> 
> 2018-05-02 13:56 GMT+02:00 Peter Kjellström <c...@nsc.liu.se>:
>> On Wed, 2 May 2018 11:15:09 +0200
>> Pierre Gubernatis <pierre.guberna...@gmail.com> wrote:
>> 
>> > Hello all...
>> > 
>> > I am using a *cartesian grid* of processors which represents a spatial
>> > domain (a cubic geometrical domain split into several smaller
>> > cubes...), and I have communicators to address the procs, as for
>> > example a comm along each of the 3 axes I,J,K, or along a plane
>> > IK,JK,IJ, etc..).
>> > 
>> > *I need to cumulate a scalar value (SCAL) through the procs which
>> > belong to a given axis* (let's say the K axis, defined by I=J=0).
>> > 
>> > Precisely, the origin proc 0-0-0 has a given value for SCAL (say
>> > SCAL000). I need to update the 'following' proc (0-0-1) by doing SCAL
>> > = SCAL + SCAL000, and I need to *propagate* this updating along the K
>> > axis. At the end, the last proc of the axis should have the total sum
>> > of SCAL over the axis. (and of course, at a given rank k along the
>> > axis, the SCAL value = sum over 0,1,   K of SCAL)
>> > 
>> > Please, do you see a way to do this ? I have tried many things (with
>> > MPI_SENDRECV and by looping over the procs of the axis, but I get
>> > deadlocks that prove I don't handle this correctly...)
>> > Thank you in any case.
>> 
>> Why did you try SENDRECV? As far as I understand your description above
>> data only flows one direction (along K)?
>> 
>> There is no MPI collective to support the kind of reduction you
>> describe but it should not be hard to do using normal SEND and RECV.
>> Something like (simplified psuedo code):
>> 
>> if (not_first_along_K)
>>  MPI_RECV(SCAL_tmp, previous)
>>  SCAL += SCAL_tmp
>> 
>> if (not_last_along_K)
>>  MPI_SEND(SCAL, next)
>> 
>> /Peter K
> 
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