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Adjoint test

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,dy>_F = <dx,A_ad dy>_E

Requierements

Unitary Test

Global Test

MPP test