Update progress bar

[ASKabalan]

This pull request updates the jax_grid_search package to remove its internal ProgressBar and instead use the new jax_progress library for progress tracking. All documentation, examples, and code have been refactored to use TqdmProgressMeter from jax_progress. The optimizer API is simplified, and progress tracking is now more robust and compatible with JAX transformations and parallelization.

Progress tracking migration and API changes:

• Removed the internal ProgressBar and replaced all progress tracking with the TqdmProgressMeter and related abstractions from the jax_progress library. The optimize function now accepts an AbstractProgressMeter instead of a ProgressBar, and progress tracking is handled via the new interface. ([[1]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R9-L12), [[2]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R41-R73), [[3]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971L96-R94), [[4]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971L111-R119), [[5]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971L158-R157), [[6]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R167), [[7]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971L179-R185), [[8]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-e9356f19204a5e43d969451ba2e0e9154a2acdc2da94f7df0b9d5a3f480cc1d8L12-R20), [[9]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-e9356f19204a5e43d969451ba2e0e9154a2acdc2da94f7df0b9d5a3f480cc1d8L43-R44), [[10]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L202-R203), [[11]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L212-R220), [[12]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L232-R233), [[13]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L248-R253), [[14]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5R263-R275), [[15]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L284-R294), [[16]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L318-R336), [[17]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L344-L352), [[18]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L362-R366), [[19]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L385-R395), [[20]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-49aaa2819e35a856818ecec8c9fa7e1c79ad028d3f44bd749736353cfb51bac9L66-R74))

• Updated the optimizer state to include progress_state for tracking the internal state of the progress meter, ensuring compatibility with JAX transformations and parallel execution. ([[1]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R30), [[2]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R167))

Documentation and example updates:

• Revised all documentation and example usages to demonstrate progress tracking using TqdmProgressMeter from jax_progress instead of the removed ProgressBar. This includes changes to code snippets in README.md and examples/README.md. ([[1]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L202-R203), [[2]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L212-R220), [[3]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L232-R233), [[4]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L248-R253), [[5]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5R263-R275), [[6]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L284-R294), [[7]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L318-R336), [[8]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L344-L352), [[9]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L362-R366), [[10]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L385-R395), [[11]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-49aaa2819e35a856818ecec8c9fa7e1c79ad028d3f44bd749736353cfb51bac9L66-R74), [[12]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-e9356f19204a5e43d969451ba2e0e9154a2acdc2da94f7df0b9d5a3f480cc1d8L12-R20))

Dependency and import updates:

• Added jax-progress and supporting libraries (optimistix, lineax, equinox) as dependencies in pyproject.toml, and removed rich since it is no longer used. Updated type ignore settings to include jax_progress. ([[1]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-50c86b7ed8ac2cf95bd48334961bf0530cdc77b5a56f852c5c61b89d735fd711L18-R21), [[2]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-50c86b7ed8ac2cf95bd48334961bf0530cdc77b5a56f852c5c61b89d735fd711L106-R109))

API and interface improvements:

• The optimize function signature is simplified: removed progress_id (now handled internally by jax_progress), and the progress callback is now more flexible. Added a new default_desc_cb for progress description formatting. ([[1]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971R41-R73), [[2]](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-4e119a63b792ddddff254e19a8e258582cf57ad193225b5b445e837701066971L96-R94))

Minor corrections:

• Fixed typos and improved clarity in documentation and comments. ([README.mdL318-R336](https://github.com/CMBSciPol/jax-grid-search/pull/18/files#diff-b335630551682c19a781afebcf4d07bf978fb1f8ac04c6bf87428ed5106870f5L318-R336))

These changes make progress tracking more robust, consistent, and compatible with modern JAX workflows.