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= ''' Adjoint test ''' =

[[PageOutline]]

== Principle ==
The adjoint test checks that the adjoint is the adjoint of the tangent using the adjoint definition. By definition, given a linear operator '''A''' going from a space '''E''' to a spece '''F''', and scalar products <.,.>_E, and <.,.>_F in these respective spcaces, the adjoint of '''A''' is the linear operator '''A_ad''' such that for any vectors (x,y) in the suitable spaces,
{{{
<Ax,y>_F = <x,A_ad y>_E
}}}

In practice, we apply the comparison to perturbations state vectors '''dx''' and '''dy'''. We have then to compare:
{{{
<Adx,Wdy>_F = <dx,A_ad Wdy>_E
}}}
W: diagonal matrix of scale factors

== Requierements ==
To run the some adjoint test we need the following features:
 * a direct trajectory (computed with NEMO)
 * additionnal namelist (for instance ''namtst'' to setup adjoint test parameter (off or on)

== Initialization ==
discuss about:
 * tangent and adjoint variables initalization
 * ramdom noise generation (repeatability)

== Unitary Test ==
We call ''unitary test'' some test involving only one subroutine (or at least a limited set of subroutines). It is performed on a single pertubation state vector '''dX'''. There is no time evolution. When needed several configuration are tested (for instance ''n_cla''=0/1, ''nn_fwb''=1/2...)

discuss about:
 * _tan and _adj initialization (means "why we should do _tan(nit000) vs. _adj(nitend)" for instance
 
== Global Test ==
The ''global test'' involves time evolution by reading foward the trajectory (for the tangent) and then backward (for the adjoint). It concerns mainly the ''step_tam'' routine. It is more conmplex as it stressed out:
 * initializations
 * interactions between routines
 * handling of direct trajectory

== MPP test ==
discuss about:
 * handling of domain/domain border for MPP test

== Test Pass Criteria ==
With the above notations, we note (if exists) the reltive error Err = |<Adx,dy>_F - <dx,A_ad dy>_E | / |<Adx,dy>_F| 
We compare the relative error (Err) to the epsilon machine Eps. It is '''passed''' when Err < 100*Eps and '''failed''' otherwise.
The adjoint test results output are gathered in the file '''adjoint_test.output_xxx''' with the following labels:
{{{
 * Test status is OK               if Err < Eps
 * Test status is WARNING   if Eps <= Err < 100*Eps
 * Test status is RED ALERT if Err >= 100 *Eps
}}} 


== Results ==
Currently we perform 51 tests (unitary routines and step_tam routine) with 100% passed rate on the different machines (see list below).

{{{
Test Layout:
 - configuration ORCA2 / GYRE
 - monodomain
 - ndays = 1/2/3/10
}}}
 
=== Machines description ===
|| '''Name''' || '''CPU type''' || '''RAM (per node)''' || '''OS''' ||'''Compiler'' ||
||Mirage ||Itanium   1.4 GHz || 4 Go || SuSe || Intel 9.0 ||
||Abel  ||  Itanium 1.4 GHz || 4 Go || SuSe || Intel 8.1 ||
|| Marvin || Core2Duo 2.8 GHz || 4 Go || OS X || g95 0.91 ||