add lazy_string in matrix2.pyx

[xcaruso]

📚 Description

Formatting verbose messages in the method right_kernel could be quite slow (even when the message is never printed). We use the functionality lazy_string in order to avoid the formatting.

Also, just calling verbose() is slow when just a cache lookup is needed.

Timings

Before:

sage: K.<a> = NumberField(x^2 - 2, embedding=1)
sage: A = MatrixSpace(K, 1, 1).one()
sage: %time _ = A.right_kernel()
CPU times: user 23 ms, sys: 3 ms, total: 26 ms
Wall time: 26.1 ms
sage: %timeit A.right_kernel()  # cache lookup
2.16 µs ± 70.3 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

After:

sage: K.<a> = NumberField(x^2 - 2, embedding=1)
sage: A = MatrixSpace(K, 1, 1).one()
sage: %time _ = A.right_kernel()
CPU times: user 11 ms, sys: 10 µs, total: 11 ms
Wall time: 11.2 ms
sage: %timeit A.right_kernel()  # cache lookup
103 ns ± 1.55 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion. No, this was discussed at SageDays 117, we have no linked issue on GitHub for this.
• I have created tests covering the changes. No, there are already tests testing that verbose still works correctly.
• I have updated the documentation accordingly. No, there are no user-facing changes.

[saraedum]

@xcaruso it seems that this does not do the trick yet. See timings.

[xcaruso]

Yes, I saw.

[saraedum]

That's a bit better now. Let's ask py-spy what's going on now.

[saraedum]

That's funny:

[saraedum]

The value is taken from the cache now, so all the cost we are paying is the empty call to verbose at the top.

[saraedum]

So, that's a bit sad: @roed314 @videlec

sage: %timeit verbose("")
1.58 µs ± 10.6 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)

verbose returns cputime so that we can in later calls print the elapsed time…we should probably disable this when the verbosity level is not reached. This breaks constructions like this:

tm = verbose("", level=999)
verbose("shows elapsed time", level=1, t=tm)

[saraedum]

Should we come up with a plan later today to add regression testing to SageMath so we have some chance to catch things like that in the future? @fchapoton @roed314 @videlec

[fchapoton]

looks good

[seblabbe]

Looks good to me