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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

    †
UwV

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 PAW9 are also generated.


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