jaxvacua.sampling.tadpole_quadratic_hessian

jaxvacua.sampling.tadpole_quadratic_hessian#

tadpole_quadratic_hessian(eft, sampler, z, tau, mode)#

Return the tadpole quadratic as the Hessian of the reconstructed ISD-tadpole function.

The map u -> tadpole(ISD_sampling(u)) is quadratic in u, so its Hessian at the origin is the matrix M. This routine is slower than tadpole_quadratic() and is mainly useful as a verification oracle or fallback for future input modes.

Parameters:

  • eft (Any) – FluxEFT-like object exposing tadpole and periods.sigma.

  • sampler (Any) – data_sampler-like object exposing ISD_sampling.

  • z (Array) – Complex-structure moduli of shape (h12,).

  • tau (Array) – Axio-dilaton value.

  • mode (Literal['ISD+', 'ISD-', 'F', 'H']) – One of "ISD+", "ISD-", "F", "H".

Returns:

  • Array – Symmetric real matrix M of shape

  • `` (2*(h12+1), 2*(h12+1))

Return type:

Array