/[MITgcm]/manual/s_autodiff/text/doc_ad_2.tex

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-revision 1.16 by heimbach,
Tue May 11 21:55:14 2004 UTC
+revision 1.20 by edhill,
Wed Apr  5 02:27:33 2006 UTC
 Line 1
  % $Header$
  % $Name$
+ Author: Patrick Heimbach
  {\sf Automatic differentiation} (AD), also referred to as algorithmic
  (or, more loosely, computational) differentiation, involves
- automatically deriving code to calculate
+ automatically deriving code to calculate partial derivatives from an
- partial derivatives from an existing fully non-linear prognostic code.
+ existing fully non-linear prognostic code.  (see \cite{gri:00}).  A
- (see \cite{gri:00}).
+ software tool is used that parses and transforms source files
- A software tool is used that parses and transforms source files
+ according to a set of linguistic and mathematical rules.  AD tools are
- according to a set of linguistic and mathematical rules.
+ like source-to-source translators in that they parse a program code as
- AD tools are like source-to-source translators in that
+ input and produce a new program code as output.  However, unlike a
- they parse a program code as input and produce a new program code
+ pure source-to-source translation, the output program represents a new
- as output.
+ algorithm, such as the evaluation of the Jacobian, the Hessian, or
- However, unlike a pure source-to-source translation, the output program
+ higher derivative operators.  In principle, a variety of derived
- represents a new algorithm, such as the evaluation of the
+ algorithms can be generated automatically in this way.
- Jacobian, the Hessian, or higher derivative operators.
- In principle, a variety of derived algorithms
+ MITgcm has been adapted for use with the Tangent linear and Adjoint
- can be generated automatically in this way.
+ Model Compiler (TAMC) and its successor TAF (Transformation of
+ Algorithms in Fortran), developed by Ralf Giering (\cite{gie-kam:98},
- The MITGCM has been adapted for use with the
+ \cite{gie:99,gie:00}).  The first application of the adjoint of MITgcm
- Tangent linear and Adjoint Model Compiler (TAMC) and its successor TAF
+ for sensitivity studies has been published by \cite{maro-eta:99}.
- (Transformation of Algorithms in Fortran), developed
+ \cite{sta-eta:97,sta-eta:01} use MITgcm and its adjoint for ocean
- by Ralf Giering (\cite{gie-kam:98}, \cite{gie:99,gie:00}).
+ state estimation studies.  In the following we shall refer to TAMC and
- The first application of the adjoint of the MITGCM for sensitivity
+ TAF synonymously, except were explicitly stated otherwise.
- studies has been published by \cite{maro-eta:99}.
- \cite{sta-eta:97,sta-eta:01} use the MITGCM and its adjoint
+ TAMC exploits the chain rule for computing the first derivative of a
- for ocean state estimation studies.
+ function with respect to a set of input variables.  Treating a given
- In the following we shall refer to TAMC and TAF synonymously,
+ forward code as a composition of operations -- each line representing
- except were explicitly stated otherwise.
+ a compositional element, the chain rule is rigorously applied to the
+ code, line by line. The resulting tangent linear or adjoint code,
- TAMC exploits the chain rule for computing the first
+ then, may be thought of as the composition in forward or reverse
- derivative of a function with
+ order, respectively, of the Jacobian matrices of the forward code's
- respect to a set of input variables.
+ compositional elements.
- Treating a given forward code as a composition of operations --
- each line representing a compositional element, the chain rule is
- rigorously applied to the code, line by line. The resulting
- tangent linear or adjoint code,
- then, may be thought of as the composition in
- forward or reverse order, respectively, of the
- Jacobian matrices of the forward code's compositional elements.
  %**********************************************************************
  \section{Some basic algebra}
  \label{sec_ad_algebra}
+ \begin{rawhtml}
+ <!-- CMIREDIR:sec_ad_algebra: -->
+ \end{rawhtml}
  %**********************************************************************
  Let $ \cal{M} $ be a general nonlinear, model, i.e. a
-Line 676 
 Schematic view of intermediate dump and
+Line 674 
 Schematic view of intermediate dump and
  %**********************************************************************
  \section{TLM and ADM generation in general}
  \label{sec_ad_setup_gen}
+ \begin{rawhtml}
+ <!-- CMIREDIR:sec_ad_setup_gen: -->
+ \end{rawhtml}
  %**********************************************************************
  In this section we describe in a general fashion
-Line 685 
 differentiation using the software tool
+Line 686 
 differentiation using the software tool
  \input{part5/doc_ad_the_model}
  The basic flow is depicted in \ref{fig:adthemodel}.
- If CPP option {\tt ALLOW\_AUTODIFF\_TAMC} is defined, the driver routine
+ If CPP option \texttt{ALLOW\_AUTODIFF\_TAMC} is defined,
+ the driver routine
  {\it the\_model\_main}, instead of calling {\it the\_main\_loop},
- invokes the adjoint of this routine, {\it adthe\_main\_loop},
+ invokes the adjoint of this routine, {\it adthe\_main\_loop}
- which is the toplevel routine in terms of automatic differentiation.
+ (case \texttt{\#define ALLOW\_ADJOINT\_RUN}), or
- The routine {\it adthe\_main\_loop} has been generated by TAF.
+ the tangent linear of this routine {\it g\_the\_main\_loop}
+ (case \texttt{\#define ALLOW\_TANGENTLINEAR\_RUN}),
+ which are the toplevel routines in terms of automatic differentiation.
+ The routines {\it adthe\_main\_loop} or {\it g\_the\_main\_loop}
+ are generated by TAF.
  It contains both the forward integration of the full model, the
  cost function calculation,
  any additional storing that is required for efficient checkpointing,
-Line 942 
 The flow directives for the core MITgcm
+Line 948 
 The flow directives for the core MITgcm
  {\tt eesupp/src/} and {\tt model/src/}
  reside in {\tt pkg/autodiff/}.
  This directory also contains hand-written adjoint code
- for the MITgcm WRAPPER (see Section ???).
+ for the MITgcm WRAPPER (section \ref{chap:sarch}).
  Flow directives for package-specific routines are contained in
  the corresponding package directories in the file
-Line 1196 
 and their gradients: {\it ctrl\_unpack}
+Line 1202 
 and their gradients: {\it ctrl\_unpack}
  \\
  %
  Two important issues related to the handling of the control
- variables in the MITGCM need to be addressed.
+ variables in MITgcm need to be addressed.
  First, in order to save memory, the control variable arrays
  are not kept in memory, but rather read from file and added
  to the initial fields during the model initialization phase.
-Line 1271 
 when calling TAMC:
+Line 1277 
 when calling TAMC:
  tamc -input 'xx_tr1 ...' ...
  \end{verbatim}
  %
- Now, as mentioned above, the MITGCM avoids maintaining
+ Now, as mentioned above, MITgcm avoids maintaining
  an array for each control variable by reading the
  perturbation to a temporary array from file.
  To ensure the symbolic link to be recognized by TAMC, a scalar

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