Shared operations

All three map families share the following target/reference convention:

• evaluate(x) maps target coordinates to reference coordinates.

• inverse(z) maps reference coordinates back to target coordinates.

• sample(n) draws target samples by drawing from the reference and inverting.

• pullback_pdf(x) and pullback_logpdf(x) evaluate the learned target density.

• pushforward_pdf(z, target) and pushforward_logpdf(z, target) evaluate a supplied target after mapping it to reference coordinates.

• log_det(x) evaluates the log absolute Jacobian determinant.

conditional_sample and conditional_pullback_* operate on leading fixed indices, for example fixed_indices=[0, 1]. Inputs are batches with shape (n_samples, d); a single point should be reshaped to (1, d).

Inverse calls support InverseOptions for bracket, evaluation, and time limits. Set return_diagnostics=True to receive an InverseResult containing values and structured failure diagnostics instead of only an array.

The diagnostics functions compare mapped samples with Gaussian reference samples using moment errors, MMD, and Forstner distance. They are evaluation helpers, not training objectives.