Add parallelism for two tensor calculus functions

[mmancini]

1. Computation of tensor components in a new frame

In FreeModuleTensor.components()
loop for ind_new in new_comp.non_redundant_index_generator():
line 1101, file src/sage/tensor/modules/free_module_tensor.py

2. Pullback of a tensor field

In DiffMap.pullback()
loop for ind_new in ptcomp.non_redundant_index_generator():
line 980, file src/sage/manifolds/differentiable/diff_map.py

[git]

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

[git]

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

​84c61a7

_pullback_chart function in class DiffMap parallelized

[git]

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

​c89779b	Merge branch 'public/26168-adding_parallelism_2_functions' of git://trac.sagemath.org/sage into develop
​5f8eaa6	Paralleized also loop on new_comp.non_redundant_index_generator(): in FreeModuleTensor.components()

[mmancini]

Please, the loop functions in the title are parallelized. Please review this ticket.

[slelievre]

For one instance of Parallel computation::, a blank line is missing after it.

[chapoton]

Doc does not build

missing empty line here:

+        Parallel computation::
+           sage: Parallelism().set('tensor', nproc=2)

[git]

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

​a30055a

Doc corrected

[egourgoulhon]

Replying to git:

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

​a30055a

Doc corrected

Could you please also correct the pyflakes error reported in ​https://patchbot.sagemath.org/log/26168/Gentoo%20Base%20System/2.2/x86_64/4.4.26-gentoo/sage4/2018-11-20%2013:42:02?plugin=pyflakes, namely src/sage/manifolds/differentiable/diff_map.py:37: 'operator.itemgetter' imported but unused

[git]

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

​2ec62c8

deleted import of unused module

[mmancini]

Replying to egourgoulhon:

import was deleted , thanks

Replying to git:

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

​a30055a

Doc corrected

Could you please also correct the pyflakes error reported in ​https://patchbot.sagemath.org/log/26168/Gentoo%20Base%20System/2.2/x86_64/4.4.26-gentoo/sage4/2018-11-20%2013:42:02?plugin=pyflakes, namely src/sage/manifolds/differentiable/diff_map.py:37: 'operator.itemgetter' imported but unused

[egourgoulhon]

The doctests regarding the change of basis in src/sage/tensor/modules/free_module_tensor.py are not valid because the tensor components are cached. One must introduce a copy of the tensor t to trigger a new computation of the components in the basis f, i.e. one shall write something like

sage: Parallelism().set('tensor', nproc=2)
sage: t2 = v*w  # identical to t but initialized only in basis e
sage: t2.display(f)
v*w = -6 f_1*f^1 - 20/3 f_1*f^2 + 27/8 f_2*f^1 + 15/4 f_2*f^2
sage: t2[f,:] == t[f,:]  # check of the parallel computation
True
sage: Parallelism().set('tensor', nproc=1)  # switch off parallelization

But then t2.display(f) results in

ValueError: Cannot pickle code objects from closures

The doctest in display_comp() is also not valid, but I suggest to simply remove it because it is redundant with that in display().

[git]

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

​d1fb9d5

Error in parallel part: corrected. DocTest improved

[mmancini]

Replying to egourgoulhon: There was an error in the parallel function: it is corrected. I also applied the suggested changes in the doctest thank

The doctests regarding the change of basis in src/sage/tensor/modules/free_module_tensor.py are not valid because the tensor components are cached. One must introduce a copy of the tensor t to trigger a new computation of the components in the basis f, i.e. one shall write something like

sage: Parallelism().set('tensor', nproc=2)
sage: t2 = v*w  # identical to t but initialized only in basis e
sage: t2.display(f)
v*w = -6 f_1*f^1 - 20/3 f_1*f^2 + 27/8 f_2*f^1 + 15/4 f_2*f^2
sage: t2[f,:] == t[f,:]  # check of the parallel computation
True
sage: Parallelism().set('tensor', nproc=1)  # switch off parallelization

But then t2.display(f) results in

ValueError: Cannot pickle code objects from closures

The doctest in display_comp() is also not valid, but I suggest to simply remove it because it is redundant with that in display().

[egourgoulhon]

Replying to mmancini:

Replying to egourgoulhon: There was an error in the parallel function: it is corrected. I also applied the suggested changes in the doctest

Thanks.

The doctest in display_comp() is also not valid, but I suggest to simply remove it because it is redundant with that in display().

Could you remove that doctest?

[git]

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

​2ba9267

removed ridundant test

[mmancini]

Replying to egourgoulhon:

Replying to mmancini:

Replying to egourgoulhon: There was an error in the parallel function: it is corrected. I also applied the suggested changes in the doctest

Thanks.

The doctest in display_comp() is also not valid, but I suggest to simply remove it because it is redundant with that in display().

Could you remove that doctest?

Done.

[egourgoulhon]

Replying to mmancini:

Could you remove that doctest?

Done.

Thanks. I've tested the changes both in python2 and python3. Everything is OK and I thing it is ready to go. Thanks for this improvement!

[mmancini]

Replying to egourgoulhon:

Thanks to you for the review

Replying to mmancini:

Could you remove that doctest?

Done.

Thanks. I've tested the changes both in python2 and python3. Everything is OK and I thing it is ready to go. Thanks for this improvement!