<html>
<head>
<meta http-equiv="content-type" content="text/html;
charset=iso-8859-15">
</head>
<body text="#000000" bgcolor="#ffffff">
<font size="-1">Hi,<br>
<br>
i have used a programmable filter (find it below) to calculate the
lambda2-criterion from gradients of velocity. In serial mode this
works fine - running it in parallel an error message comes up. Any
idea what does it mean and whats wrong with the filter?<br>
<br>
Best regards,<br>
<br>
Stefan<br>
</font> <br>
<br>
<br>
<br>
<tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>Executing with:
0
</tt><tt><br>
</tt><tt>
</tt><tt><br>
</tt><tt>2385958
</tt><tt><br>
</tt><tt>2406377
</tt><tt><br>
</tt><tt>2220610
</tt><tt><br>
</tt><tt>2292001
</tt><tt><br>
</tt><tt>2144431
</tt><tt><br>
</tt><tt>2331490
</tt><tt><br>
</tt><tt>2061524
</tt><tt><br>
</tt><tt>2344595
</tt><tt><br>
</tt><tt>Traceback (most recent call
last):
</tt><tt><br>
</tt><tt> File "<string>", line 22, in
<module>
</tt><tt><br>
</tt><tt> File "<string>", line 76, in
RequestData
</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 358, in
max
</tt><tt><br>
</tt><tt> return _global_func(MaxImpl(), array, axis,
controller)
</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 199, in
_global_func
</tt><tt><br>
</tt><tt> max_dims, size = _reduce_dims(res,
comm)
</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 168, in
_reduce_dims
</tt><tt><br>
</tt><tt> comm.Allreduce([dims, mpitype], [max_dims, mpitype],
MPI.MAX)
</tt><tt><br>
</tt><tt> File "MPI/Comm.pyx", line 715, in
mpi4py.MPI.Comm.Allreduce
(/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0/VTK/ThirdParty/mpi4py/vtkmpi4py/src/mpi4py.MPI.c:99224)</tt><tt><br>
</tt><tt>mpi4py.MPI.Exception: MPI_ERR_OTHER: known error not in
list</tt><tt><br>
</tt><tt>Traceback (most recent call last):</tt><tt><br>
</tt><tt> File "<string>", line 22, in <module></tt><tt><br>
</tt><tt>Traceback (most recent call last):</tt><tt><br>
</tt><tt> File "<string>", line 76, in RequestData</tt><tt><br>
</tt><tt> File "<string>", line 22, in <module></tt><tt><br>
</tt><tt> File "<string>", line 76, in RequestData</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 358, in max</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 358, in max</tt><tt><br>
</tt><tt> return _global_func(MaxImpl(), array, axis, controller)</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 199, in _global_func</tt><tt><br>
</tt><tt> max_dims, size = _reduce_dims(res, comm)</tt><tt><br>
</tt><tt> return _global_func(MaxImpl(), array, axis, controller)</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 199, in _global_func</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 168, in _reduce_dims</tt><tt><br>
</tt><tt>max_dims, size = _reduce_dims(res, comm)</tt><tt><br>
</tt><tt> comm.Allreduce([dims, mpitype], [max_dims, mpitype],
MPI.MAX)</tt><tt><br>
</tt><tt> File "MPI/Comm.pyx", line 715, in
mpi4py.MPI.Comm.Allreduce
(/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0/VTK/ThirdParty/mpi4py/vtkmpi4py/src/mpi4py.MPI.c:99224)</tt><tt><br>
</tt><tt> File
"/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0.bin/lib/site-packages/vtk/numpy_interface/algorithms.py",
line 168, in _reduce_dims</tt><tt><br>
</tt><tt>mpi4py.MPI.Exception: MPI_ERR_OTHER: known error not in
list</tt><tt><br>
</tt><tt>comm.Allreduce([dims, mpitype], [max_dims, mpitype],
MPI.MAX)</tt><tt><br>
</tt><tt> File "MPI/Comm.pyx", line 715, in
mpi4py.MPI.Comm.Allreduce
(/opt/PARAVIEW_5_4_0_OpenGL2/ParaView-v5.4.0/VTK/ThirdParty/mpi4py/vtkmpi4py/src/mpi4py.MPI.c:99224)</tt><tt><br>
</tt><tt>mpi4py.MPI.Exception: MPI_ERR_OTHER: known error not in
list</tt><tt><br>
</tt><tt><br>
</tt><tt><br>
<br>
<br>
<br>
<br>
<br>
</tt><tt>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';">
</span></pre>
</tt><tt>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';">grad </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> inputs[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">]</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">PointData[</span><span style=" font-family:'Hack'; color:#ba2121;">"Gradients"</span><span style=" font-family:'Hack';">] </span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';">npoints </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#008000;">len</span><span style=" font-family:'Hack';">(grad)</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack'; font-weight:600; color:#008000;">print</span><span style=" font-family:'Hack';"> npoints </span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';">data </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> []</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack'; font-weight:600; color:#008000;">for</span><span style=" font-family:'Hack';"> i </span><span style=" font-family:'Hack'; font-weight:600; color:#aa22ff;">in</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#008000;">range</span><span style=" font-family:'Hack';">(npoints):</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># Gradients</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> dvx </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> grad[i,:][</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">]</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> dvy </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> grad[i,:][</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">]</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> dvz </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> grad[i,:][</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">]</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># Symmetrical part of flow tensor -> S</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s0 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> dvx[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">]</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s1 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvx[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvy[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s2 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvx[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvz[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s3 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvy[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvx[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s4 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> dvy[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">];</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s5 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvy[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvz[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s6 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvz[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvx[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s7 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvz[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> dvy[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> s8 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> dvz[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">]</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># Antisymmetrical part of flow tensor -> Omega</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega0 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega1 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvx[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvy[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega2 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvx[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvz[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega3 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvy[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvx[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega4 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega5 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvy[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvz[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega6 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvz[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvx[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega7 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.5</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> (dvz[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> dvy[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">])</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> Omega8 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">0.0</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack'; color:#666666;">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># Matrix M = (S^2 + Omega^2)</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># M is symmetric</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># | m0 m1 m2 |</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># M = | m1 m3 m4 |</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># | m2 m4 m5 |</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m0 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s0 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s3 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s6 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega3 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega6</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m1 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s1 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s4 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s7 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega7</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m2 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s5 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s8 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega5</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m3 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s1 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s4</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s4 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s5</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s7 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega1 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega5</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega7</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m4 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s4</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s5 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s5</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s8 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega2</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> m5 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> s6</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s7</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s5 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> s8</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">s8 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega6</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> Omega7</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">Omega5</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># computing now the eigenvalues of M</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># | M - lambda I | = 0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># returns the characteristic equation:</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># lambda^3 + p*lambda^2 + q*lambda + r = 0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># due to symmetric Matrix the following assumption can be made:</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># all three eigenvalues will be real root values ( no imaginary parts )</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> p </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">-1*</span><span style=" font-family:'Hack';">( m0 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> m3 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> m5)</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> q </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">-1*</span><span style=" font-family:'Hack';">( m1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m1 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> m2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> m4</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m4 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m3 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m5 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m5)</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> r </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">-1*</span><span style=" font-family:'Hack';">( m0</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m3</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m5 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">2*</span><span style=" font-family:'Hack';">m1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m4 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m2</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m3 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m4</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m4</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m0 </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> m1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">m5)</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># computing now the reduced equation</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># lambda^3 + s*lambda + t = 0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> sx </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> (</span><span style=" font-family:'Hack'; color:#666666;">3.0</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> q </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> p</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">p) </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> t </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> (</span><span style=" font-family:'Hack'; color:#666666;">2.0</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">pow(p, </span><span style=" font-family:'Hack'; color:#666666;">3.0</span><span style=" font-family:'Hack';">) </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">27.0</span><span style=" font-family:'Hack';">) </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> (p </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> q </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span><span style=" font-family:'Hack';">) </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> r</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># calculate unordered eigenvalues (Cardano's method)</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># -> at first check if ( 1.0 / sqrtt(-s^3) ) can be computed</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> l </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> [</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">,</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">,</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">]</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-weight:600; color:#008000;">if</span><span style=" font-family:'Hack';"> ((sx </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> sx </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> sx) </span><span style=" font-family:'Hack'; color:#666666;"><</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">-1e-16</span><span style=" font-family:'Hack';">):</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> tmp1 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">sqrt( </span><span style=" font-family:'Hack'; color:#666666;">-1*</span><span style=" font-family:'Hack';"> sx </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span><span style=" font-family:'Hack';"> )</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> tmp2 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">-1*</span><span style=" font-family:'Hack';"> t </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> (</span><span style=" font-family:'Hack'; color:#666666;">2.0</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> tmp1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">tmp1</span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';">tmp1)</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> c1 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">2.0</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> tmp1 </span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> c2 </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">acos( </span><span style=" font-family:'Hack'; color:#008000;">min</span><span style=" font-family:'Hack';">((</span><span style=" font-family:'Hack'; color:#666666;">1.</span><span style=" font-family:'Hack';">, </span><span style=" font-family:'Hack'; color:#008000;">max</span><span style=" font-family:'Hack';">((</span><span style=" font-family:'Hack'; color:#666666;">-1.</span><span style=" font-family:'Hack';">, tmp2))) ) ) </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack'; color:#666666;">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> l[</span><span style=" font-family:'Hack'; color:#666666;">0</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> c1 </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">cos(c2) </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> p </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> l[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> c1 </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">cos(c2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">2.*</span><span style=" font-family:'Hack';">math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">pi</span><span style=" font-family:'Hack'; color:#666666;">/3.</span><span style=" font-family:'Hack';">) </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> p </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> l[</span><span style=" font-family:'Hack'; color:#666666;">2</span><span style=" font-family:'Hack';">] </span><span style=" font-family:'Hack'; color:#666666;">=</span><span style=" font-family:'Hack';"> c1 </span><span style=" font-family:'Hack'; color:#666666;">*</span><span style=" font-family:'Hack';"> math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">cos(c2 </span><span style=" font-family:'Hack'; color:#666666;">+</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">4.*</span><span style=" font-family:'Hack';">math</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">pi</span><span style=" font-family:'Hack'; color:#666666;">/3.</span><span style=" font-family:'Hack';">) </span><span style=" font-family:'Hack'; color:#666666;">-</span><span style=" font-family:'Hack';"> p </span><span style=" font-family:'Hack'; color:#666666;">/</span><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; color:#666666;">3.0</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack'; color:#666666;">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># sort eigenvalues</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># lambda1 <= lambda2 <= lambda3</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> l</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">sort()</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> </span><span style=" font-family:'Hack'; font-style:italic; color:#408080;"># save second eigenvalue</span></pre>
<pre style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';"> data</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">append(l[</span><span style=" font-family:'Hack'; color:#666666;">1</span><span style=" font-family:'Hack';">])</span></pre>
<pre style="-qt-paragraph-type:empty; margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; font-family:'Hack';">
</pre>
<pre style=" margin-top:0px; margin-bottom:12px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;"><span style=" font-family:'Hack';">output</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">PointData</span><span style=" font-family:'Hack'; color:#666666;">.</span><span style=" font-family:'Hack';">append(data, </span><span style=" font-family:'Hack'; color:#ba2121;">"lambda2"</span><span style=" font-family:'Hack';">) </span></pre>
<br>
<br>
<br>
</tt><tt><br>
</tt><tt><br>
</tt><tt><br>
</tt><tt><br>
</tt><tt><br>
</tt><br>
</body>
</html>