feat: add use_positive_taus parameter and statistics-dependent periodicity

[shinaoka]

Summary

This PR unifies the behavior of tau sampling points to use the positive range [0, β] by default and implements statistics-dependent periodicity for augmentation functions, ensuring consistency with the Julia implementation (SparseIR.jl).

Key Changes

1. Added use_positive_taus parameter to default_tau_sampling_points

   • Default value: True (use [0, β] range)
   • When True, applies np.mod(points, β) and sorts the result
   • Propagates through FiniteTempBasis, AugmentedBasis, DiscreteLehmannRepresentation, and TauSampling

2. Implemented statistics-dependent periodicity for augmentation functions

   • Added normalize_tau(statistics, tau, beta) function in _util.py
   • Handles Fermionic anti-periodic: G(τ + β) = -G(τ)
   • Handles Bosonic periodic: G(τ + β) = G(τ)
   • Follows Rust taufuncs.rs implementation for consistency

3. Updated augmentation functions with statistics support

   • TauConst(beta, statistics='B'): now accepts statistics parameter, handles [-β, β] range
   • TauLinear(beta, statistics='B'): now accepts statistics parameter, handles [-β, β] range
   • MatsubaraConst(beta, statistics=None): updated range check to accept [-β, β]
   • All augmentation functions use normalize_tau for proper periodicity handling

4. Added comprehensive tests

   • test_normalize_tau_bosonic/fermionic: tests for periodicity rules
   • test_tau_const/linear_periodicity: statistics-dependent behavior tests
   • test_matsubara_const_range: [-β, β] range verification
   • test_tau_const/linear_with_statistics: factory method and direct creation tests
   • test_backward_compatibility: ensures old API still works

Backward Compatibility

• Default constructors maintain compatibility: TauConst(beta), TauLinear(beta) default to statistics='B' (Bosonic)
• use_positive_taus defaults to True (consistent with Julia implementation)
• All existing tests pass (95 passed, 8 skipped)

Cross-language Consistency

This implementation ensures consistency with:

• SparseIR.jl (Julia): Same use_positive_taus parameter and default behavior
• sparse-ir-rs (Rust): Follows the same normalize_tau logic from taufuncs.rs

Files Changed

• src/sparse_ir/_util.py: Added normalize_tau function (73 lines)
• src/sparse_ir/basis.py: Added use_positive_taus parameter to default_tau_sampling_points
• src/sparse_ir/augment.py: Updated TauConst, TauLinear, MatsubaraConst with statistics support
• src/sparse_ir/sampling.py: Propagate use_positive_taus parameter
• src/sparse_ir/dlr.py: Accept kwargs in default_tau_sampling_points
• tests/test_augment.py: Added 10 new comprehensive tests

Test Plan

• Run full test suite: 95 passed, 8 skipped
• Verify normalize_tau function for both Bosonic and Fermionic cases
• Test statistics-dependent periodicity for TauConst and TauLinear
• Verify [-β, β] range acceptance for all augmentation functions
• Verify backward compatibility with old API
• Cross-check behavior with Julia implementation

Related Issues

This PR implements the same functionality as SparseIR.jl PR #100.