Finite-Hankel and model-reduction API

This page collects the public model-reduction entry points. The naming is intentional:

  • finite_hankel_reduce_* means a finite-section Hankel/Ho–Kalman-style reduction;

  • finite_nehari_* means a finite-dimensional Nehari/AAK teaching or validation helper;

  • finite_aak_siso_certificate means a finite-section Schmidt-pair certificate;

  • exact infinite-dimensional AAK/Nehari solvers are outside the current public API scope.

SISO finite-Hankel reduction

The compatibility names finite_hankel_aak_reduce_impulse and finite_hankel_aak_reduce_iir remain available as deprecated aliases, but new code uses the shorter finite_hankel_reduce_* names because the implementation is a finite Hankel/Ho–Kalman baseline rather than an exact AAK solver.

MIMO block-Hankel reduction

The MIMO reducer accepts Markov parameters with shape (samples, outputs, inputs) and returns state-space matrices A, B, C, D. It does not attempt to force a scalar numerator/denominator representation onto a MIMO system. The diagonal and coupled MIMO tutorials validate this baseline within the current MIMO scope. mimo_state_space_process_batch is a compiled C++/OpenMP helper for repeated simulation of the returned state-space models; it is a runtime kernel, not a reduction algorithm. The coupled MIMO benchmark therefore reports processing speedup separately from one-shot and amortized end-to-end speedup.

Finite Nehari/rational workflow

Current naming and stability policy

The public names are deliberately conservative. Use finite_hankel_reduce_* for the supported finite-Hankel/Ho–Kalman baselines. Use finite_aak_* for finite-section AAK/Nehari candidate and certificate workflows. These finite-section helpers are useful and tested; exact infinite-dimensional AAK/Nehari optimality is outside their scope.

The practical benchmark result is also conservative: finite-Hankel is currently the fastest baseline in many high-order examples, while finite-section AAK/Nehari candidates provide rank-selection and certification machinery that is valuable for diagnostics and selected high-quality reductions.

Tutorials and validation cases

The recommended reading order is:

  1. Finite Hankel SISO model reduction

  2. Finite block-Hankel MIMO model reduction

  3. Coupled MIMO finite-Hankel model reduction

  4. Coupled MIMO finite-Hankel reduction benchmark

  5. Nehari and AAK intuition from a finite SISO Hankel matrix

  6. Finite Nehari/AAK rank-sweep benchmark

  7. Finite Nehari tail to rational model

  8. AAK Schmidt-pair diagnostics for SISO Hankel approximation

  9. Selecting a finite SISO AAK/Nehari rational candidate

  10. Finite-section SISO AAK/Nehari certificate

  11. Exact rational-tail validation for finite Nehari candidates

  12. Finite-section AAK/Nehari reduction on a non-exact tail

  13. Finite-section AAK/Nehari reduction of a stable IIR filter