Parallelization of Wedge Product

[mjungmath]

Apparently, the wedge product is not performed on multiple cores when parallel computation is enabled. According to the compontent-wise computation of general tensors, I add this feature for the wedge product for alternate forms, too.

CC: @egourgoulhon @tscrim @mkoeppe

Component: geometry

Keywords: differential_forms, parallel

Author: Michael Jung

Branch/Commit: u/gh-mjungmath/wedge_product_parallel @ 6303e7c

Issue created by migration from https://trac.sagemath.org/ticket/29796

[mjungmath]

Author: Michael Jung

[mjungmath]

Changed keywords from none to mixed_forms

[mjungmath]

Changed keywords from mixed_forms to differential_forms, parallel

[mjungmath]

Branch: u/gh-mjungmath/wedge_product_parallel

[mjungmath]

Commit: d8ecedc

[mjungmath]

comment:7

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:

d8ecedc

Trac #29796: first parallelization approach

[sagetrac-git]

Changed commit from d8ecedc to 6303e7c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0961bdc	Trac #29796: further small improvements
6303e7c	Trac #29796: indentation fixed

[mjungmath]

comment:9

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 20-80% 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

[egourgoulhon]

comment:10

Replying to @mjungmath:

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 20-80% 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.

[mjungmath]

comment:11

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.

[mjungmath]

comment:12

Besides this odd fact, do you have any ideas how the summation can be parallelized, too?

[mkoeppe]

comment:15

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mjungmath]

comment:16

By the way, why don't we use MapReduce patterns (or similar) for parallelizations? The parallelization syntax used all over is hardly readable imho.

See for example: https://towardsdatascience.com/a-beginners-introduction-into-mapreduce-2c912bb5e6ac