========
Examples
========

Worked examples of the inverse problems fips solves, as Jupyter notebooks. They
run when the documentation is built, so the output you see is what the current
code produces.

.. toctree::
   :maxdepth: 1

   gravity_2d
   flux_regional
   synthetic_truth
   data_worth

:doc:`gravity_2d`
   The density of buried prisms from the gravity measured above them: a small,
   self-contained problem with a correlated prior kept as Kronecker factors, and
   a sweep over the regularization factor.

:doc:`flux_regional`
   A year of monthly methane fluxes on a grid from daily concentrations at three
   sites: a sparse forward operator, a background as the offset, maps from
   ``to_xarray``, and the posterior of monthly totals.

:doc:`synthetic_truth`
   Does the inversion recover a known flux? A world makes the data and the
   inversion solves them: coverage of the monthly totals, a mismatch assumed too
   small or too large, a bias on one site, and a truth of 1.5 times the prior.

:doc:`data_worth`
   Which observations constrain a regional total? The prior and posterior
   uncertainty of a region's annual total and of a seasonal difference, what
   each site and each month of observations contributes, and which candidate
   site would help most.