add a local search function

[bluest93]

Change

Implemented the simple local search algorithm

Description

under core/post_process

1. Added local_search.py

• Implements a new class IsingMatrix that represents the Ising model in matrix form (np.array)
  • Converts an IsingModel into matrix form with quadratic and linear components
  • Calculates the energy difference when flipping a bit in the Ising state
• Implements a new class LocalSearch that perform local search algorithms
  • Runs the local search algorithm until convergence or until a maximum number of iterations
  • Performs first-improvement local search
  • Performs best-improvement local search
  • Decodes the result into a jijmodeling SampleSet

2. Added __inti__.py
3. Added tutorial notebook local_search.ipynb

under tests/core/post_process

1. Added a test file test_local_search.py

[bluest93]

For the best_improvement and first_improvement, I choose to return the state instead of index because I think it is easier to understand

[bluest93]

Sorry I found out there is a bug for the result when using best_improvement

[Jacomichi]

Please write the test for all the functionality

[yuyamashiro]

use ruff for format.

Ex.

ruff format qamomile/core/post_process/local_search.py

If you use ruff, please do not format all of the code for the Qamomile project in this Pull Request, as there will be too many changes and the PR will not be able to be reviewed.

[bluest93]

@Jacomichi

Please write the test for all the functionality

I have a confusion for writing a test. For example, the function of run contains other functions _run_local_search, which contains first_improvement and best_improvement, and decode. I guess I need to check all the functions above? but my concern is run consists of _run_local_search and decode(and a error message), testing these two functions seems there is not necessary to do a test on run?

[yuyamashiro]

@bluest93
Please write in the docstring of each method what the function of each method is and how it is intended to be used.
In addition to checking the type, when testing, make sure that it works properly as a local search.

[bluest93]

@yuyamashiro For the test_local_search.py, I have added an assertion to check whether the energy after the local search has decreased or is equal to the original energy.

[yuyamashiro]

There is not enough testing and its reliability is still low, but since it is not used in core parts, we will merge it in as is for now.
Also, for local search, the algorithm itself can be improved, such as by efficiently updating it using second-order differences instead of recalculating the energy difference, but we will include these after merging as well.

[Jacomichi]

I left the comments.