Add spherical integration using maximum determinant points (#237)

[alok-108]

Overview

This Pull Request introduces the MaxDeterminantGrid class to the grid library, enabling spherical integration using maximum determinant (Fekete/Extremal) points. This fulfills the requirements outlined in issue #237.

Problem

The library currently supports Lebedev quadrature and spherical $t$-designs. While effective, Lebedev weights can occasionally be negative, and $t$-designs use uniform weights. Maximum determinant points offer an alternative strategy with strictly positive weights and high numerical stability for integrating functions on the unit sphere.

Solution

Implemented a dedicated MaxDeterminantGrid class that inherits from the core Grid hierarchy. This implementation follows the library's existing architecture while providing a flexible interface for modern scientific computing.

Key Changes

• New MaxDeterminantGrid Class: Implemented in src/grid/max_det.py. The class features an improved integrate method that supports both callable functions and raw value arrays.
• Structured Data Pipeline: Added precomputed maximum determinant points and weights up to degree 200, stored in optimized .npz format within src/grid/data/max_det/.
• ℓ = 325 Support: Verified and ensured full compatibility for the ℓ = 325 spherical design.
• Package Integration:
  • Exported the new class in src/grid/__init__.py.
  • Updated MANIFEST.in to ensure the new data files are bundled during installation.

Testing & Validation

Added a comprehensive test suite in src/grid/tests/test_maxdet.py which includes:

• Accuracy Check: Verified that constant functions integrate to exactly $4\pi$.
• Orthonormality: Validated the orthonormality of spherical harmonics integrated on the grid.
• Weight Integrity: Confirmed that all weights are strictly positive and correctly normalized.
• Interface Consistency: Ensured the new integrate(callable) method is consistent with the base Grid.integrate(array) logic.

Documentation

• Detailed docstrings added for code clarity.
• Created examples/max_det_integration.ipynb to demonstrate usage results and precision.

Fixes #237