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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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The cmz macro smod SLTCIRC
prepares a main program
(‘circule’ of +PATCH SLTCIRC), in the directory ‘sltcirc/’.
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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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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:
var | file | ntuple | explanation |
---|---|---|---|
p(.,.) | ‘phit.data’ | 55 | propagator from 0 to t, Φ(t,0) |
up(.,.) | ‘uphit.data’ | 50 | Left singular vectors U in the SVD of Φ |
wp(.) | ‘wphit.data’ | 51 | singulat values w in the SVD of Φ |
vp(.,.) | ‘vphit.data’ | 52 | Right Singular Vectors V in the SVD of Φ |
wr(.) | ‘wr.data’ | 53 | real part of eigen values of Φ(t,0) |
wi(.) | ‘wi.data’ | 54 | imaginary part of eigen values of Φ(t,0) |
lwp(.) | ‘lwphit.data’ | 67 | Lyapunov exponents |
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