Return explicit error for Matsubara sampling with non-centrosymmetric kernels

[shinaoka]

Summary

The Matsubara sampling point calculation (default_matsubara_sampling_points and related methods) relies on the assumption that basis functions in Matsubara space are either pure imaginary or pure real, which is only guaranteed for centrosymmetric kernels.

For non-centrosymmetric kernels, these methods would produce incorrect results silently or panic at runtime.

Current behavior

• FiniteTempBasis::default_matsubara_sampling_points() panics at runtime with a message about centrosymmetry (basis.rs:446-451)
• FiniteTempBasis::default_tau_sampling_points() also panics (basis.rs:335-340)
• MatsubaraSamplingPositiveOnly uses ComplexToRealFitter which assumes real coefficients — this is only valid when basis functions have definite parity (centrosymmetric case)

While FiniteTempBasis<K, S> requires K: CentrosymmKernel at the type level, the Basis<S> trait itself does not encode this constraint. Any future Basis implementation for a non-centrosymmetric kernel could reach these code paths.

Desired behavior

Return explicit errors (e.g., Result types or at minimum clear error messages) rather than relying on:

1. Runtime panics that may not clearly indicate the root cause
2. Silent incorrect results from MatsubaraSamplingPositiveOnly when coefficients are not real

Root cause

The Matsubara sampling algorithm uses sign_changes / find_extrema of uhat basis functions, which assumes each uhat_l(iωn) is either pure real or pure imaginary (a consequence of centrosymmetry). For non-centrosymmetric kernels, uhat_l are general complex-valued and these algorithms do not apply.

Affected code

• sparse-ir/src/basis.rs: default_matsubara_sampling_points, default_tau_sampling_points, default_matsubara_sampling_points_impl
• sparse-ir/src/matsubara_sampling.rs: MatsubaraSamplingPositiveOnly::new(), ::with_sampling_points()
• sparse-ir/src/polyfourier.rs: sign_changes, find_extrema