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.

CC: @tscrim

Component: linear algebra

Keywords: parallelization, free module, tensor

Author: Marco Mancini

Branch: 21d1d70

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/18100

[man74cio]

Commit: 2f93525

[man74cio]

New commits:

4ca6874	merged parallelisation from SageManifold
2f93525	added paralellization

[man74cio]

Branch: public/18100-parallelization_tensors

[sagetrac-git]

Changed commit from 2f93525 to 2080154

[sagetrac-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

[sagetrac-git]

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

5659f29

Added parallelization on tensor product

[sagetrac-git]

Changed commit from 2080154 to 5659f29

[sagetrac-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__

[sagetrac-git]

Changed commit from 5659f29 to 325e832

[sagetrac-git]

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

256d268

changed name TensorParallelism to TensorParallelCompute

[sagetrac-git]

Changed commit from 325e832 to 256d268