Opened 11 months ago
Last modified 3 months ago
#29796 new enhancement
Parallelization of Wedge Product
Reported by:  ghmjungmath  Owned by:  

Priority:  major  Milestone:  sage9.4 
Component:  geometry  Keywords:  manifolds, differential_forms, parallel 
Cc:  egourgoulhon, tscrim, mkoeppe  Merged in:  
Authors:  Michael Jung  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/ghmjungmath/wedge_product_parallel (Commits, GitHub, GitLab)  Commit:  6303e7c19f873255c82c0dd76721baa8c5721669 
Dependencies:  Stopgaps: 
Description (last modified by )
Apparently, the wedge product is not performed on multiple cores when parallel computation is enabled. According to the compontentwise computation of general tensors, I add this feature for the wedge product for alternate forms, too.
Change History (15)
comment:1 Changed 11 months ago by
 Cc egourgoulhon added
 Component changed from PLEASE CHANGE to geometry
 Description modified (diff)
 Keywords manifolds mixed_forms added
comment:2 Changed 11 months ago by
 Type changed from PLEASE CHANGE to enhancement
comment:3 Changed 11 months ago by
 Description modified (diff)
comment:4 Changed 11 months ago by
 Description modified (diff)
 Keywords differential_forms parallel added; mixed_forms removed
 Summary changed from Mixed Forms  Fast zero check to Parallelization of Wedge Product
comment:5 Changed 11 months ago by
 Description modified (diff)
comment:6 Changed 11 months ago by
 Branch set to u/ghmjungmath/wedge_product_parallel
comment:7 Changed 11 months ago by
 Cc tscrim added
 Commit set to d8ecedceb0f88de6afb5af3ad4f53a622552fec4
comment:8 Changed 11 months ago by
 Commit changed from d8ecedceb0f88de6afb5af3ad4f53a622552fec4 to 6303e7c19f873255c82c0dd76721baa8c5721669
comment:9 followup: ↓ 10 Changed 11 months ago by
Some computations in 4 dimensions made it slightly worse: from around 8 sec to 15 sec. In contrast, more complicated computations in 6 dimensions yield a good improvement.
However, I noticed that the cpus are not fully engaged and run around 2080% workload, varying all the time. Hence, there is much room for improvement.
I appreciate any suggestions. I feel a little bit lost here.
New commits:
0961bdc  Trac #29796: further small improvements

6303e7c  Trac #29796: indentation fixed

comment:10 in reply to: ↑ 9 Changed 11 months ago by
Replying to ghmjungmath:
Some computations in 4 dimensions made it slightly worse: from around 8 sec to 15 sec. In contrast, more complicated computations in 6 dimensions yield a good improvement.
However, I noticed that the cpus are not fully engaged and run around 2080% workload, varying all the time. Hence, there is much room for improvement.
I appreciate any suggestions. I feel a little bit lost here.
I would say that the behaviour that you observe is due to the computation being not fully parallelized in the current code. Indeed, in the final lines
for ii, val in paral_wedge(listParalInput): for jj in val: cmp_r[[jj[0]]] += jj[1]
the computation cmp_r[[jj[0]]] += jj[1]
is performed sequentially.
comment:11 Changed 11 months ago by
Interestingly, I dropped the summation completely, and still, the computation takes longer than without parallelization. This is odd, isn't it?
Even this modification doesn't improve anything:
ind_list = [(ind_s, ind_o) for ind_s in cmp_s._comp for ind_o in cmp_o._comp if len(ind_s+ind_o) == len(set(ind_s+ind_o))] nproc = Parallelism().get('tensor') if nproc != 1: # Parallel computation lol = lambda lst, sz: [lst[i:i + sz] for i in range(0, len(lst), sz)] ind_step = max(1, int(len(ind_list) / nproc)) local_list = lol(ind_list, ind_step) # list of input parameters: listParalInput = [(cmp_s, cmp_o, ind_part) for ind_part in local_list] @parallel(p_iter='multiprocessing', ncpus=nproc) def paral_wedge(s, o, local_list_ind): partial = [] for ind_s, ind_o in local_list_ind: ind_r = ind_s + ind_o partial.append([ind_r, s._comp[ind_s] * o._comp[ind_o]]) return partial for ii, val in paral_wedge(listParalInput): for jj in val: cmp_r[[jj[0]]] = jj[1] else: # Sequential computation for ind_s, ind_o in ind_list: ind_r = ind_s + ind_o cmp_r[[ind_r]] += cmp_s._comp[ind_s] * cmp_o._comp[ind_o]
If nproc
is set to 1, the original speed is preserved.
I am fully aware that this leads to wrong results and the summation should be covered within the parallelization, somehow. Nevertheless, this seems strange to me.
comment:12 Changed 11 months ago by
Besides this odd fact, do you have any ideas how the summation can be parallelized, too?
comment:13 Changed 10 months ago by
 Cc mkoeppe added
comment:14 Changed 9 months ago by
 Milestone changed from sage9.2 to sage9.3
comment:15 Changed 3 months ago by
 Milestone changed from sage9.3 to sage9.4
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
This is my very first approach simply copied from the previous ones. However, I noticed that in lower dimensions, the parallelization is even slower. Furthermore, one could improve this process a little bit further just my considering distinct indices from the beginning (see the check in the loop).
I appreciate any help since I am not familiar with effective parallelization.
New commits:
Trac #29796: first parallelization approach