Parallelization of computations on tensors on free modules

[egourgoulhon]

This ticket implements parallelization of basic operations (arithmetics, contractions) on tensors on free modules of finite rank. The parallelization is performed by means of Python's module multiprocessing, via the decorator @parallel. It is implemented in computational methods of classes handling tensor components: sage.tensor.modules.comp.Components and sage.tensor.modules.comp.CompWithSym. The user can control the number of processes involved in the parallelization via the singleton class Parallelism. The latter, introduced in this ticket, is actually generic and can be used in other parts of Sage.

This work is an extension of #15916, within the ​SageManifolds project (actually the code in this ticket is the basis for parallelization in SageManifolds 0.8). See the metaticket #18528 for an overview.

[mmancini]

New commits:

​4ca6874	merged parallelisation from SageManifold
​2f93525	added paralellization

[git]

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

​2080154

Renamed class for parallelism in the Singleton class TensorParallelism. Added doc/test for TensorParallelism

[git]

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

​5659f29

Added parallelization on tensor product

[git]

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

​325e832

Corrected error in parallelisation of __mul__. Added parallism for the symmetric __add__

[git]

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

​256d268

changed name TensorParallelism to TensorParallelCompute

[git]

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

​bea739d

Added Eric corrections to parallelism

[git]

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

​a6d4bd4	Merge branch 'public/18100-parallelization_tensors' into Sage 6.7
​81f662c	Improve documentation of class TensorParallelCompute.

[git]

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

​ea38c84

In doc, changed processor with process

[vdelecroix]

Hello,

The name set_nproc is not appropriate for a function that is intended to be used only for tensor products. Secondly, why are you duplicating the interface with a class TensorParallelCompute and functions set_nproc, get_nproc?

Vincent

[mmancini]

Replying to vdelecroix: Hello Vincent,

Thanks to review our work.

We try to reply to the two points: 1) You are right, the names set_nproc and get_nproc are generic names and not clearly referred to tensors, so we propose to changes them in set_nproc_tensor and get_nproc_tensor.

2) The functions set_nproc and get_nproc were introduced in order to avoid to the users to typing the two more verbose (and less clear) functions TensorParallelCompute().set(nproc) and TensorParallelCompute._nproc Note that the singleton TensorParallelCompute is not in the global namespace but only the functions set_nproc and get_nproc.

Best regards,

Marco

Hello,

The name set_nproc is not appropriate for a function that is intended to be used only for tensor products. Secondly, why are you duplicating the interface with a class TensorParallelCompute and functions set_nproc, get_nproc?

Vincent

[git]

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

​819661d

Changed variables name : set_nproc to set_nproc_tensor, get_nproc to get_nproc_tensor

[git]

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

​53c248c

Parallelization: corrected doc

[mmancini]

In the last 2 commits we modified the variables name set_nproc get_nproc in set_nproc_tensor and get_nproc_tensor as proposed.

[egourgoulhon]

This ticket is now the basis for parallelization of demanding computations involving affine connections on differentiable manifolds (#19147), as well as in pseudo-Riemannian manifolds (#19209).

[vdelecroix]

Some more questions:

• I still don't understand why there is an object oriented interface and a function interface. Why not only one?

• Wouldn't it be better to gather everything related to parallelism in a single place? You could mimic what is done for proofs (sage.structure.proof.proof) or global options (sage.structure.global_options). These two are not perfect but at least they intend to be general and reusable. The object oriented interface could be something like:

  sage: Parallelism().get('tensor')
  1
  sage: Parallelism().set('tensor', 3)
  sage: Parallelism().set_default(3)
  sage: Parallelism().get_default()
  3
  sage: Parallellism().get_all()
  {
   'tensor': 3,
   'xyz': 2
  }
  

(though that could be postponed to some other tickets)

• The functions get_nproc_tensor and set_nproc_tensor should definitely not be in the global namespace as they are very much specialized.

[git]

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

​ade22b1

Created Singleton class Parallelism more generic. Persist problem with doc and tests

[git]

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

​4e64db3

Fix doctests and documentation issues in class Parallelism

[vdelecroix]

Thanks for the heavy changes! If you are done with your changes and want a review again you need to switch the status of the ticket from "needs info" to "needs review".

You also need to update the ticket description.

It would be good to advertise this ticket on sage-devel. Other people might be interested (e.g. #18987 for which the parallelization option can use some default).

[egourgoulhon]

Replying to vdelecroix:

Thanks for the heavy changes! If you are done with your changes and want a review again you need to switch the status of the ticket from "needs info" to "needs review".

Actually a few improvements in the documentation are under way and will be committed soon.

You also need to update the ticket description.

Yes indeed.

It would be good to advertise this ticket on sage-devel. Other people might be interested (e.g. #18987 for which the parallelization option can use some default).

OK.

[git]

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

​b033297

Improvements in the documentation of class Parallelism

[egourgoulhon]

Note that the documentation of class Parallelism has been added to the Parallel Computing section of the reference manual.

[git]

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

​21d1d70

Minor modification in the doctests of parallel computation in class Components

[vdelecroix]

Hello,

All right. This is a good start for further improvements...

Vincent

[mmancini]

Replying to vdelecroix:

Hello,

All right. This is a good start for further improvements...

Vincent

Hello Vincent,

Thanks a lot for the review, advices and suggestions. Regards, Marco