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4.6 Generalized linear tangent system analysis

The state matrix Ast may also be used to compute the GTLS propagator (or state transition matrix applied to perturbation), after the simulation. The algorithm is a finite product of 5th order development of Φ(t + δt,t) = expAstδt. Numerous element of analysis are given, in particular the determination of the Lyapunov exponents of the system.

An executable file, sltcirc.exe is generated and running this file will produce the corresponding results.


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4.6.1 Generalized tangent linear system with cmz

The cmz macro smod SLTCIRC prepares a main program (circule of +PATCH SLTCIRC), in the directory sltcirc/.


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4.6.2 Generalized tangent linear system with make

To compile the GTLS analysis executable with make you can do

make sltcirc.exe

If you want to have a separate directory for the GTLS analysis, you should copy the sequence dimetaphi.inc (or make a link to that file) to the directory. You should also copy the file Makefile.sltcirc from the template/ directory in this directory and rename it Makefile and set the Miniker directory path in the miniker_dir variable.


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4.6.3 Generalized tangent linear system analysis run and output

The sltcirc.exe executable generated by the compilation computes the elements of analysis of the system. This program requires title.tex to transmit a title for output and graphics (see Title file), aspha.data to access the state matrix and dres.data, because time-step can be changed along the simulation (see Running a simulation and using the output) 10. To get access to these files (in case they are not in the current directory) it is possible to make a link to the corresponding files in the model directory. Once it is done the program may be run:

./sltcirc.exe

The following table gives the correspondence between variable name, result file and ntuple number, with a short explanation:

varfilentupleexplanation
p(.,.)phit.data55propagator from 0 to t, Φ(t,0)
up(.,.)uphit.data50Left singular vectors U in the SVD of Φ
wp(.)wphit.data51singulat values w in the SVD of Φ
vp(.,.)vphit.data52Right Singular Vectors V in the SVD of Φ
wr(.)wr.data53real part of eigen values of Φ(t,0)
wi(.)wi.data54imaginary part of eigen values of Φ(t,0)
lwp(.)lwphit.data67Lyapunov exponents

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