Correct numpy tolerence

[atxy-blip]

In commit 254b981, atol for numpy backend was wrongly set to 1e-5 in mps/backend.py, instead of the original value 1e-8. Meanwhile, in this version only atol was set up.

https://github.com/shuaigroup/Renormalizer/blob/254b9819d0e9124736d9c1681de0ec7bc60792bb/renormalizer/mps/backend.py#L136-L140

As for numpy, the basic logic for considering two numbers a and b close in is:

abs(a - b) <= max(rtol * max(abs(a), abs(b)), atol)

The existence of rtol allows for the comparison of large numbers, e.g., 10001 and 10000, which may emerge in imaginary time-evolution. Therefore, I propose adding back the rtol parameter.

---

This commit does the following things:

• Correct the values of mps.backend.canonical_rtol and mps.backend.canonical_atol
• Add a setter for the above properties
• Use the tols as default parameter values in mps.matrix.check_lortho, mps.mp.check_left_canonical, mps.mp.ensure_left_canonical and their right counterparts

I am not sure whether rtol set to 1e-2 is appropriate for 32-bits. Discussions are welcome for any issue concerned : )

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 94.54545% with 3 lines in your changes are missing coverage. Please review.

Project coverage is 87.23%. Comparing base (07b639f) to head (2c37a67).

:exclamation: Current head 2c37a67 differs from pull request most recent head 24626e1

Please upload reports for the commit 24626e1 to get more accurate results.

Files	Patch %	Lines
renormalizer/mps/mp.py	85.00%	3 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #167 +/- ## ========================================== + Coverage 85.87% 87.23% +1.35% ========================================== Files 117 118 +1 Lines 12342 13710 +1368 ========================================== + Hits 10599 11960 +1361 - Misses 1743 1750 +7 ```

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[liwt31]

In general the PR is OK, but I'm curious if this setting has a practical effect on the calculations you've carried out?

[atxy-blip]

if this setting has a practical effect on the calculations you've carried out

Nope. Code from the lastest master branch still messes up our Holstein test after I set $RENO_NUM_THREADS to 1 and appied the new atol. I am still investigating on why it happens on my setup.

Anyway, proposing a fix on atol is the least thing I can do at this stage : (

[jiangtong1000]

What do you mean by messing up?

On Thu, May 9, 2024 at 6:03 AM Yu Xiong @.***> wrote:

if this setting has a practical effect on the calculations you've carried out

Nope. Code from the lastest master branch still messes up our Holstein test after I set $RENO_NUM_THREADS to 1 and appied the new atol. I am still investigating on why it happens on my setup.

Anyway, proposing a fix on atol is the least thing I can do at this stage : (

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[atxy-blip]

@jiangtong1000 I intend to open a new issue for discussion of the current problem. Please check #168 : D

[liwt31]

@atxy-blip ready to merge if you fix my review comment. It'll be better if you can solve the codecov issue.

[atxy-blip]

ready to merge if you fix my review comment

Fixed.

[liwt31]

Thanks for the contribution! Looking forward to more of your PRs 😄

[liwt31]

Note that this branch has been rebased and its commits are different from your local version @atxy-blip