Miniker 102 manual: 4.6 Generalized linear tangent system analysis

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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:

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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