Miniker 102 manual: 4.5 Stability analysis of fastest modes

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## 4.5 Stability analysis of fastest modes

The preceding analyses are done along with a simulation. One has also the possibility of using in a more classical fashion the state advance matrix Ast, after the end of the simulation. Code to perform the SVD (Singular Value Decomposition) of the state matrix Ast and also of Ast + A† st is provided with Miniker. The singular elements of these two matrices correspond to the most rapid modes of instability of the perturbed system.

The Singular value decomposition of a matrix is noted

An executable file, ‘`sltc.exe`’ is generated and running this file will produce the corresponding results.

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### 4.5.1 Singular Value Decomposition with cmz

The cmz macro `smod SLTC` prepares a main program (‘`circul`’ of +PATCH SLTC), provided as a base for user’s own analysis, in the directory ‘`sltc/`’.

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### 4.5.2 Singular Value Decomposition with make

To compile the singular value decomposition executable with `make` you can do

    make sltc.exe

If you want to have a separate directory for the SVD, you should copy the sequence ‘`dimetaphi.inc`’ (or make a link to that file) to the directory. You should also copy the file ‘`Makefile.sltc`’ from the ‘`template/`’ directory in this directory, rename it ‘`Makefile`’ and set the Miniker directory path in the `miniker_dir` variable. For example, if the Miniker directory is in ‘`/u/src/mini_ker`’:

    miniker_dir = /u/src/mini_ker

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### 4.5.3 Singular Value Decomposition run and output

As it is, the ‘`sltc.exe`’ executable generated by the compilation determines the SVD. This program requires ‘`title.tex`’ (see Title file) to transmit a title for output and graphics, and ‘`aspha.data`’ (see Running a simulation and using the output) to access the state matrix. 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:

    ./sltc.exe

The files ‘`u.data`’, ‘`w.data`’, and ‘`v.data`’ holds the singular elements for Ast ( U, w and V), and ‘`us.data`’, ‘`ws.data`’, and ‘`vs.data`’ holds the singular elements of Ast + A† st. The corresponding macros ‘`.kumac`’ for PAW(9) are also generated.

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