Changes between Version 1 and Version 2 of WorkingGroups/TAM/ReferenceManual/testing/adjoint

Timestamp:

2009-10-14T16:52:28+02:00 (15 years ago)

Author:

vigilant

Comment:

--

WorkingGroups/TAM/ReferenceManual/testing/adjoint

@@ -5 +5 @@
 
 == 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
+}}}
 
-== Requierement ==
+In practice, we apply the comparison to perturbations state vectors '''dx''' and '''dy'''. We have then to compare:
+{{{
+<Adx,dy>_F = <dx,A_ad dy>_E
+}}}
+
+== Requierements ==
 
 == Unitary Test ==