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<a name="Stability-of-fastest-modes"></a>
<ul class="toc"><li><a href="mini_ker.html#Top">Miniker 102 manual</a> </li>
<li><ul class="toc"><li><a href="Dynamic-system-analysis.html#Dynamic-system-analysis">4. Dynamic analysis of systems in Miniker</a> </li>
</ul></li>
</ul>
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<a name="Stability-analysis-of-fastest-modes"></a>
<h2 class="section"> 4.5 Stability analysis of fastest modes </h2>
<ul class="toc">
<li> <a href="#SVD-with-cmz">4.5.1 Singular Value Decomposition with cmz</a> </li>
<li> <a href="#SVD-with-make">4.5.2 Singular Value Decomposition with make</a> </li>
<li> <a href="#SVD-run-and-output">4.5.3 Singular Value Decomposition run and output</a> </li>
</ul>
<a name="index-SVD"></a>
<a name="index-Singular-Value-Decomposition"></a>
<a name="index-state-matrix"></a>
<a name="index-sltc_002eexe"></a>
<p>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
<acronym title="Singular Value Decomposition">SVD</acronym> (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.
</p>
<p>The Singular value decomposition of a matrix is noted
</p>
<p>
<center class="math-display" >
<img
src="mini_ker_tex4ht_tex20x.png" alt=" †
UwV " class="math-display" ></center>
</p>
<p>An executable file, ‘<tt>sltc.exe</tt>’ is generated and running this file will
produce the corresponding results.
</p>
<hr size="2">
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<a name="Singular-Value-Decomposition-with-cmz"></a>
<h3 class="subsection"> 4.5.1 Singular Value Decomposition with cmz </h3>
<a name="index-smod"></a>
<p>The cmz macro <code>smod SLTC</code> prepares a main program
(‘<tt>circul</tt>’ of +PATCH SLTC), provided as a base for user’s own analysis,
in the directory ‘<tt>sltc/</tt>’.
</p>
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<a name="Singular-Value-Decomposition-with-make"></a>
<h3 class="subsection"> 4.5.2 Singular Value Decomposition with make </h3>
<a name="index-Makefile_002esltc"></a>
<p>To compile the singular value decomposition executable with <code>make</code> you
can do
</p><table><tr><td> </td><td><pre class="example">make sltc.exe
</pre></td></tr></table>
<p>If you want to have a separate directory for the SVD, you should copy
the sequence ‘<tt>dimetaphi.inc</tt>’ (or make a link to that file) to the
directory. You should also copy the file ‘<tt>Makefile.sltc</tt>’ from the
‘<tt>template/</tt>’ directory in this directory, rename it ‘<tt>Makefile</tt>’
and set the Miniker directory path in the
<code>miniker_dir</code> variable. For
example, if the Miniker directory is in ‘<tt>/u/src/mini_ker</tt>’:
</p>
<table><tr><td> </td><td><pre class="example">miniker_dir = /u/src/mini_ker
</pre></td></tr></table>
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<a name="Singular-Value-Decomposition-run-and-output"></a>
<h3 class="subsection"> 4.5.3 Singular Value Decomposition run and output </h3>
<a name="index-SVD-run"></a>
<a name="index-run_002c-SVD"></a>
<a name="index-SVD-output"></a>
<a name="index-output_002c-SVD"></a>
<a name="index-sltc_002eexe-1"></a>
<a name="index-title_002etex_002c-SVD"></a>
<a name="index-aspha_002edata_002c-SVD"></a>
<p>As it is, the ‘<tt>sltc.exe</tt>’ executable generated by the compilation
determines the SVD. This program requires ‘<tt>title.tex</tt>’ (see <a href="A-model-description.html#Title-file">Title file</a>) to
transmit a title for output and graphics, and ‘<tt>aspha.data</tt>’
(see <a href="Setting-and-running-a-model.html#Simulation-and-output">Running a simulation and using the output</a>)
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:
</p>
<table><tr><td> </td><td><pre class="example">./sltc.exe
</pre></td></tr></table>
<p>The files ‘<tt>u.data</tt>’, ‘<tt>w.data</tt>’, and ‘<tt>v.data</tt>’ holds the singular elements
for Ast ( U, w and V),
and ‘<tt>us.data</tt>’, ‘<tt>ws.data</tt>’, and ‘<tt>vs.data</tt>’
holds the singular elements of Ast + A†
st.
The corresponding macros ‘<samp>.kumac</samp>’ for PAW<a name="DOCF9" href="mini_ker_fot.html#FOOT9">(9)</a>
are also generated.
</p>
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