TAF: Transformation of Algorithms in Fortran

Overview of Applications:

Model	Model Reference	Lines	Language	Main Loop	TLM	ADM	comment	HES	AD References
NSC2KE	Mohamadi (1994)	2,500	F77	steady	2.4	3.4	iteration directive	9.8	Giering et al. (2005)
NS-Solver	Hinze (1999)	1,000	F77	steady	-	2.0	flow directives	-	Hinze and Slawig (2002)
IMBETHY	Knorr (2001)	5,000	F90	evolving	1.5	3.6	2 level checkpointing	12.7/5	Rayner et al. (2001)
MOM3	Pacanowski and Griffes (1999)	50,000	F77	evolving	yes	4.6	2 level checkpointing	-	Galanti et al. (2001)
MITGCM	Marshall et al. (1995)	100,000	F77	evolving	1.8	5.5	3 level checkpointing	11.0	Marotzke et al. (1999), Stammer (2000), Stammer et al. (2002), Heimbach et al. (2002), Stammer et al. (2002), Online Manual (2002)
Biomag code	Buecker et al. (2001)	83	F77		548/1098	3.1	-	-	Bischof et al. (2001)
NASA-DAO	Lin and Rood (1996), Lin and Rood (1997), Lin (1997)	87,000	F90	evolving	2.7	8.4	2 level checkpointing	-	Todling et al. (2003) Giering et al. (2005)
HB_AIRFOIL	Thomas et al. (2002), Thomas et al. (2002a), Hall et al. (2002a)	8,000	F90	steady+unsteady	yes	3	-	-	Thomas et al. (2003), Hall et al. (2002)
EULSOLDO	Cusdin and Müller (2003)	423	F77	-	2-3	2-3	AD restricted to kernel	-	Cusdin and Müller (2003), Cusdin and Müller (2003), Cusdin (2003)
3D N-S CFD code	Moinier et al. (2002)	699	F77	steady	1.2-3.4	1.2-3.4	flow and iteration directives	-	Cusdin and Müller (2003)
Rot-Disk	Beeson (2001), Timoshenko and Goodier (1970)	289	F77	-	7/6	7/6	iteration directive, (yet faster with structured AD)	-	Akkaram et al. (2003)
ARPS	Xue et al. ( 2000 , 2001)	40000	F90	evolving	2	11	2-level checkpointing	-	Xiao et al. (2004)
NAST2D	Griebel et al. (1998)	2700	F90	steady	90/289	1.8	iteration directive	-	-
NAST2D in 3D	Griebel et al. (1998)	3500	F90	steady	1.4	1.8	iteration directive	-	Othmer et al. (2006) and Kaminski et al. (2006)
NIRE-CTM	Taguchi ( 1993 , 1996)	860	F77	evolving	1.0	1.5	-	-	Taguchi (2005)

# of Fortran source code lines with comments and blank lines removed.

Describes the main time integration loop, if any.

steady state: converges to a steady state
evolving: integrates a system forward in time

Column TLM shows CPU time for evaluating function (model) plus first derivative in forward mode (tangent linear model, TLM) in multiples of the CPU time to evaluate the function only (CPU time ratio).

In most of the applications the TLM computes the product of Jacobian times one vector. Whereever there is more than one vector we print: CPU time ratio / # of vectors.

The entry "Yes" means that there is a TLM, but we don't have the performance, whereas "-" means that there is no TLM.

Column ADM shows CPU time for evaluating function (model) plus first derivative in reverse mode (adjoint model, ADM) in multiples of the CPU time to evaluate the function only (CPU time ratio).

In all examples the CPU time for the derivative of a scalar valued function is given.

Note that a 2 level checkpointing scheme (see, e.g. Giering and Kaminski, 2002) consumes the CPU time of about one additional function evaluation. For example the adjoint of IMBETHY has a CPU time ratio of about 3.6 - 1 = 2.6 for short integrations, which do not require a checkpointing scheme. 3 level checkpointing costs two additional function evaluations.

Comments on the selected strategy to increase the performance:

iteration directive: arranges memory efficient handling for integrations that converge to a steady state.
flow directive: are used to provide information about routines the source code of which is either not available or shall not be differentiated. TAF generates the interfaces to derivative code provided by the user. Self adjoint routines are an example for which it is more efficient to provide the derivative (the routine itself) instead of having TAF generate the adjoint.
checkpointing: A scheme to allow multiple use of tape space at the cost of additional function evaluations. Generation of such a scheme can be triggered by TAF directives (see e.g. Giering and Kaminski, 2002)

Column HES shows CPU time for evaluating columns of the Hessian (second derivative) in multiples of the CPU time for evaluating the function (CPU time ratio).

If the number of columns is not equal one, we print: CPU time ratio / # of columns.

"-" means that there is no Hessian code.