LogLikelihood transformations and decompositions (FP32 prep)

[vhaasteren]

Add likelihood transform support and split varying/constant log-likelihood terms

Summary

Extends LogLikelihood to support transformed bases ("native", "Lw", "GtLw") and to optionally return the log-likelihood split into parameter-varying vs. constant terms (e.g., when white noise and delay params are fixed). This enables single-precision workflows and numerical verification.

Changes

• transform parameter on LogLikelihood: LogLikelihood now accepts a transform argument ("native", "Lw", "GtLw"). The transform selects how the rNr/logdet data term is computed via get_transformed_rNr_logdet.
• Unified get_transformed_rNr_logdet: All transforms (native, Lw, GtLw) go through a single get_transformed_rNr_logdet API. Each pulsar returns a tuple whose first element is the parameter-varying part and the rest are constant terms (e.g., dimension counts, log determinants).
• Return format: For transform="native" (default), returns a single scalar log-likelihood (backward compatible). For transform="Lw" or "GtLw", returns (loglike_varying, loglike_remainder) — the part that depends on the prior matrix B vs. the rest.
• TransformedLogLikelihood removed: Logic folded into LogLikelihood; the transform is controlled by the constructor argument.

Backward compatibility

Existing callers that do not pass transform get transform="native" and receive a scalar. PTAs built with lnlikelihood=LogLikelihood (or LogLikelihoodDenseCholesky) behave as before.

Usage

Default: scalar log-likelihood (unchanged behavior)

loglike = pta.get_lnlikelihood(params)

Transformed mode: returns (varying, remainder) for single-precision use

pta = PTA(models, lnlikelihood=lambda pta: LogLikelihood(pta, transform="GtLw"))
loglike_varying, loglike_remainder = pta.get_lnlikelihood(params)
total = loglike_varying + loglike_remainder