diff --git a/CMakeLists.txt b/CMakeLists.txt
index 0a7fa430b091ed77c703da00cc95480831e80609..cc9322f017781ff734fe82ad5489092c76b4bc06 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -27,5 +27,6 @@ add_subdirectory(dune)
 add_subdirectory(doc)
 add_subdirectory(cmake/modules)
 
+
 # finalize the dune project, e.g. generating config.h etc.
 finalize_dune_project(GENERATE_CONFIG_H_CMAKE)
diff --git a/Matlab-Programs/BMatrix.txt b/Matlab-Programs/BMatrix.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a758f4e80ddfe98e31e5c55d78e482f3a6aeb9ad
--- /dev/null
+++ b/Matlab-Programs/BMatrix.txt
@@ -0,0 +1,3 @@
+1 1 -0.612883927868050238
+1 2 -0.599999999999977551
+1 3 -0.000197872958097770234
diff --git a/Matlab-Programs/MatlabDuneImport.m b/Matlab-Programs/MatlabDuneImport.m
new file mode 100644
index 0000000000000000000000000000000000000000..82c48dc450dce38e184734e4d5e11ece345f5983
--- /dev/null
+++ b/Matlab-Programs/MatlabDuneImport.m
@@ -0,0 +1,4 @@
+new_mat = spconvert(load('matlab.txt')); %Sparse Matrix type
+
+new_mat = full(new_mat)
+
diff --git a/Matlab-Programs/Minimization.mlx b/Matlab-Programs/Minimization.mlx
index 0f820d20422f81b36ace9cfbfc7399125274743f..19e2d2bcf44518829519b53b8f52ec2a2021c88e 100644
Binary files a/Matlab-Programs/Minimization.mlx and b/Matlab-Programs/Minimization.mlx differ
diff --git a/Matlab-Programs/Minimization_Script.m b/Matlab-Programs/Minimization_Script.m
index 034580b684ec6bd43202e33b2e8d72c0c2b5a7bf..3491941d010e513bc69181b401e0a8c401f10e1a 100644
--- a/Matlab-Programs/Minimization_Script.m
+++ b/Matlab-Programs/Minimization_Script.m
@@ -40,8 +40,7 @@ catch ME  % use relativePath
     Bmat = spconvert(load('../outputs/BMatrix.txt'));
     fprintf('Use relative Path')
 end
-Qmat = spconvert(load('../outputs/QMatrix.txt'));
-Bmat = spconvert(load('../outputs/BMatrix.txt'));
+
 
 
 %convert to full matrix... 
diff --git a/Matlab-Programs/Minimization_compare.mlx b/Matlab-Programs/Minimization_compare.mlx
new file mode 100644
index 0000000000000000000000000000000000000000..2e5e59307a2539c5f46fba1894abaea96a2d3d25
Binary files /dev/null and b/Matlab-Programs/Minimization_compare.mlx differ
diff --git a/Matlab-Programs/PD.py b/Matlab-Programs/PD.py
new file mode 100644
index 0000000000000000000000000000000000000000..1c2d99cf87752f5757f2a7b90d1e52546e69862d
--- /dev/null
+++ b/Matlab-Programs/PD.py
@@ -0,0 +1,146 @@
+# state file generated using paraview version 5.7.0
+
+# ----------------------------------------------------------------
+# setup views used in the visualization
+# ----------------------------------------------------------------
+
+# trace generated using paraview version 5.7.0
+#
+# To ensure correct image size when batch processing, please search 
+# for and uncomment the line `# renderView*.ViewSize = [*,*]`
+
+#### import the simple module from the paraview
+from paraview.simple import *
+#### disable automatic camera reset on 'Show'
+paraview.simple._DisableFirstRenderCameraReset()
+
+# Create a new 'Render View'
+renderView1 = CreateView('RenderView')
+renderView1.ViewSize = [964, 795]
+renderView1.AxesGrid = 'GridAxes3DActor'
+renderView1.CenterOfRotation = [20.0, 25.25, 19.999999225139618]
+renderView1.StereoType = 'Crystal Eyes'
+renderView1.CameraPosition = [19.716196756133453, -140.19818563854574, 19.725993950408547]
+renderView1.CameraFocalPoint = [19.716196756133453, 4.1990335064686235, 19.725993950408554]
+renderView1.CameraViewUp = [0.0, 0.0, 1.0]
+renderView1.CameraFocalDisk = 1.0
+renderView1.CameraParallelScale = 37.37275037457204
+renderView1.Background = [0.32, 0.34, 0.43]
+
+SetActiveView(None)
+
+# ----------------------------------------------------------------
+# setup view layouts
+# ----------------------------------------------------------------
+
+# create new layout object 'Layout #1'
+layout1 = CreateLayout(name='Layout #1')
+layout1.AssignView(0, renderView1)
+
+# ----------------------------------------------------------------
+# restore active view
+SetActiveView(renderView1)
+# ----------------------------------------------------------------
+
+# ----------------------------------------------------------------
+# setup the data processing pipelines
+# ----------------------------------------------------------------
+
+# create a new 'Legacy VTK Reader'
+phaseDiagramvtk = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/PhaseDiagram.vtk'])
+
+# create a new 'Legacy VTK Reader'
+phaseDiagramvtk_1 = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/PhaseDiagram.vtk'])
+
+# create a new 'Legacy VTK Reader'
+phaseDiagramvtk_2 = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/PhaseDiagram.vtk'])
+
+# create a new 'Legacy VTK Reader'
+legacyVTKReader1 = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/wind.vtk'])
+
+# create a new 'Transform'
+transform1 = Transform(Input=phaseDiagramvtk_2)
+transform1.Transform = 'Transform'
+
+# init the 'Transform' selected for 'Transform'
+transform1.Transform.Scale = [1.0, 1.0, 40.0]
+
+# create a new 'Legacy VTK Reader'
+phaseDiagramvtk_3 = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/PhaseDiagram.vtk'])
+
+# create a new 'Legacy VTK Reader'
+phaseDiagramvtk_4 = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/PhaseDiagram.vtk'])
+
+# ----------------------------------------------------------------
+# setup the visualization in view 'renderView1'
+# ----------------------------------------------------------------
+
+# show data from transform1
+transform1Display = Show(transform1, renderView1)
+
+# get color transfer function/color map for 'type'
+typeLUT = GetColorTransferFunction('type')
+typeLUT.RGBPoints = [0.0, 0.0, 0.0, 1.0, 0.0, 0.17254901960784313, 0.043137254901960784, 0.9215686274509803, 0.0, 0.785929, 0.247056, 0.295477, 0.0, 0.17254901960784313, 0.043137254901960784, 0.9215686274509803, 0.5332077132980828, 0.41568627450980394, 0.00392156862745098, 0.9686274509803922, 0.8393082088494452, 0.48627450980392156, 0.0, 0.9725490196078431, 1.5502514522630406, 1.0, 0.5215686274509804, 0.9607843137254902, 2.4093082613015326, 1.0, 0.043137254901960784, 0.5529411764705883, 3.140000104904175, 1.0, 0.0, 0.01568627450980392]
+typeLUT.ColorSpace = 'Lab'
+typeLUT.NanColor = [0.0, 1.0, 0.0]
+typeLUT.NumberOfTableValues = 593
+typeLUT.ScalarRangeInitialized = 1.0
+
+# get opacity transfer function/opacity map for 'type'
+typePWF = GetOpacityTransferFunction('type')
+typePWF.Points = [0.0, 1.0, 0.5, 0.0, 1.0269182920455933, 0.36764705181121826, 0.5, 0.0, 1.6292452668398216, 0.08088235557079315, 0.5, 0.0, 2.3500630855560303, 0.3602941334247589, 0.5, 0.0, 2.804276943206787, 0.6176470518112183, 0.5, 0.0, 3.140000104904175, 1.0, 0.5, 0.0]
+typePWF.ScalarRangeInitialized = 1
+
+# trace defaults for the display properties.
+transform1Display.Representation = 'Points'
+transform1Display.ColorArrayName = ['POINTS', 'type']
+transform1Display.LookupTable = typeLUT
+transform1Display.OSPRayScaleArray = 'type'
+transform1Display.OSPRayScaleFunction = 'PiecewiseFunction'
+transform1Display.SelectOrientationVectors = 'None'
+transform1Display.ScaleFactor = 4.95
+transform1Display.SelectScaleArray = 'type'
+transform1Display.GlyphType = 'Arrow'
+transform1Display.GlyphTableIndexArray = 'type'
+transform1Display.GaussianRadius = 0.2475
+transform1Display.SetScaleArray = ['POINTS', 'type']
+transform1Display.ScaleTransferFunction = 'PiecewiseFunction'
+transform1Display.OpacityArray = ['POINTS', 'type']
+transform1Display.OpacityTransferFunction = 'PiecewiseFunction'
+transform1Display.DataAxesGrid = 'GridAxesRepresentation'
+transform1Display.PolarAxes = 'PolarAxesRepresentation'
+transform1Display.ScalarOpacityFunction = typePWF
+transform1Display.ScalarOpacityUnitDistance = 0.7474550074914409
+
+# init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+transform1Display.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+transform1Display.ScaleTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.6714465592330834, 0.625, 0.5, 0.0, 1.1355345914648751, 0.6691176295280457, 0.5, 0.0, 2.093228726131573, 0.8676470518112183, 0.5, 0.0, 2.310566008990662, 0.6911764740943909, 0.5, 0.0, 3.140000104904175, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+transform1Display.OpacityTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.6714465592330834, 0.625, 0.5, 0.0, 1.1355345914648751, 0.6691176295280457, 0.5, 0.0, 2.093228726131573, 0.8676470518112183, 0.5, 0.0, 2.310566008990662, 0.6911764740943909, 0.5, 0.0, 3.140000104904175, 0.8014705777168274, 0.5, 0.0]
+
+# setup the color legend parameters for each legend in this view
+
+# get color legend/bar for typeLUT in view renderView1
+typeLUTColorBar = GetScalarBar(typeLUT, renderView1)
+typeLUTColorBar.Position = [0.8796680497925311, 0.01509433962264151]
+typeLUTColorBar.Title = 'type'
+typeLUTColorBar.ComponentTitle = ''
+
+# set color bar visibility
+typeLUTColorBar.Visibility = 1
+
+# show color legend
+transform1Display.SetScalarBarVisibility(renderView1, True)
+
+# ----------------------------------------------------------------
+# setup color maps and opacity mapes used in the visualization
+# note: the Get..() functions create a new object, if needed
+# ----------------------------------------------------------------
+
+# ----------------------------------------------------------------
+# finally, restore active source
+SetActiveSource(phaseDiagramvtk_2)
+# ----------------------------------------------------------------
\ No newline at end of file
diff --git a/Matlab-Programs/PhaseDiagram.vtk b/Matlab-Programs/PhaseDiagram.vtk
new file mode 100644
index 0000000000000000000000000000000000000000..2fce7e1124d933bf59f4b7f813ac267dc70b32e5
--- /dev/null
+++ b/Matlab-Programs/PhaseDiagram.vtk
@@ -0,0 +1,11 @@
+# vtk DataFile Version 2.0
+VTK from Matlab
+ASCII
+DATASET STRUCTURED_GRID
+DIMENSIONS 1 30 30
+POINTS 900 float
+0.00 2.00 0.01 0.34 2.00 0.01 0.69 2.00 0.01 1.03 2.00 0.01 1.38 2.00 0.01 1.72 2.00 0.01 2.07 2.00 0.01 2.41 2.00 0.01 2.76 2.00 0.01 3.10 2.00 0.01 3.45 2.00 0.01 3.79 2.00 0.01 4.14 2.00 0.01 4.48 2.00 0.01 4.83 2.00 0.01 5.17 2.00 0.01 5.52 2.00 0.01 5.86 2.00 0.01 6.21 2.00 0.01 6.55 2.00 0.01 6.90 2.00 0.01 7.24 2.00 0.01 7.59 2.00 0.01 7.93 2.00 0.01 8.28 2.00 0.01 8.62 2.00 0.01 8.97 2.00 0.01 9.31 2.00 0.01 9.66 2.00 0.01 10.00 2.00 0.01 0.00 2.00 0.04 0.34 2.00 0.04 0.69 2.00 0.04 1.03 2.00 0.04 1.38 2.00 0.04 1.72 2.00 0.04 2.07 2.00 0.04 2.41 2.00 0.04 2.76 2.00 0.04 3.10 2.00 0.04 3.45 2.00 0.04 3.79 2.00 0.04 4.14 2.00 0.04 4.48 2.00 0.04 4.83 2.00 0.04 5.17 2.00 0.04 5.52 2.00 0.04 5.86 2.00 0.04 6.21 2.00 0.04 6.55 2.00 0.04 6.90 2.00 0.04 7.24 2.00 0.04 7.59 2.00 0.04 7.93 2.00 0.04 8.28 2.00 0.04 8.62 2.00 0.04 8.97 2.00 0.04 9.31 2.00 0.04 9.66 2.00 0.04 10.00 2.00 0.04 0.00 2.00 0.08 0.34 2.00 0.08 0.69 2.00 0.08 1.03 2.00 0.08 1.38 2.00 0.08 1.72 2.00 0.08 2.07 2.00 0.08 2.41 2.00 0.08 2.76 2.00 0.08 3.10 2.00 0.08 3.45 2.00 0.08 3.79 2.00 0.08 4.14 2.00 0.08 4.48 2.00 0.08 4.83 2.00 0.08 5.17 2.00 0.08 5.52 2.00 0.08 5.86 2.00 0.08 6.21 2.00 0.08 6.55 2.00 0.08 6.90 2.00 0.08 7.24 2.00 0.08 7.59 2.00 0.08 7.93 2.00 0.08 8.28 2.00 0.08 8.62 2.00 0.08 8.97 2.00 0.08 9.31 2.00 0.08 9.66 2.00 0.08 10.00 2.00 0.08 0.00 2.00 0.11 0.34 2.00 0.11 0.69 2.00 0.11 1.03 2.00 0.11 1.38 2.00 0.11 1.72 2.00 0.11 2.07 2.00 0.11 2.41 2.00 0.11 2.76 2.00 0.11 3.10 2.00 0.11 3.45 2.00 0.11 3.79 2.00 0.11 4.14 2.00 0.11 4.48 2.00 0.11 4.83 2.00 0.11 5.17 2.00 0.11 5.52 2.00 0.11 5.86 2.00 0.11 6.21 2.00 0.11 6.55 2.00 0.11 6.90 2.00 0.11 7.24 2.00 0.11 7.59 2.00 0.11 7.93 2.00 0.11 8.28 2.00 0.11 8.62 2.00 0.11 8.97 2.00 0.11 9.31 2.00 0.11 9.66 2.00 0.11 10.00 2.00 0.11 0.00 2.00 0.15 0.34 2.00 0.15 0.69 2.00 0.15 1.03 2.00 0.15 1.38 2.00 0.15 1.72 2.00 0.15 2.07 2.00 0.15 2.41 2.00 0.15 2.76 2.00 0.15 3.10 2.00 0.15 3.45 2.00 0.15 3.79 2.00 0.15 4.14 2.00 0.15 4.48 2.00 0.15 4.83 2.00 0.15 5.17 2.00 0.15 5.52 2.00 0.15 5.86 2.00 0.15 6.21 2.00 0.15 6.55 2.00 0.15 6.90 2.00 0.15 7.24 2.00 0.15 7.59 2.00 0.15 7.93 2.00 0.15 8.28 2.00 0.15 8.62 2.00 0.15 8.97 2.00 0.15 9.31 2.00 0.15 9.66 2.00 0.15 10.00 2.00 0.15 0.00 2.00 0.18 0.34 2.00 0.18 0.69 2.00 0.18 1.03 2.00 0.18 1.38 2.00 0.18 1.72 2.00 0.18 2.07 2.00 0.18 2.41 2.00 0.18 2.76 2.00 0.18 3.10 2.00 0.18 3.45 2.00 0.18 3.79 2.00 0.18 4.14 2.00 0.18 4.48 2.00 0.18 4.83 2.00 0.18 5.17 2.00 0.18 5.52 2.00 0.18 5.86 2.00 0.18 6.21 2.00 0.18 6.55 2.00 0.18 6.90 2.00 0.18 7.24 2.00 0.18 7.59 2.00 0.18 7.93 2.00 0.18 8.28 2.00 0.18 8.62 2.00 0.18 8.97 2.00 0.18 9.31 2.00 0.18 9.66 2.00 0.18 10.00 2.00 0.18 0.00 2.00 0.21 0.34 2.00 0.21 0.69 2.00 0.21 1.03 2.00 0.21 1.38 2.00 0.21 1.72 2.00 0.21 2.07 2.00 0.21 2.41 2.00 0.21 2.76 2.00 0.21 3.10 2.00 0.21 3.45 2.00 0.21 3.79 2.00 0.21 4.14 2.00 0.21 4.48 2.00 0.21 4.83 2.00 0.21 5.17 2.00 0.21 5.52 2.00 0.21 5.86 2.00 0.21 6.21 2.00 0.21 6.55 2.00 0.21 6.90 2.00 0.21 7.24 2.00 0.21 7.59 2.00 0.21 7.93 2.00 0.21 8.28 2.00 0.21 8.62 2.00 0.21 8.97 2.00 0.21 9.31 2.00 0.21 9.66 2.00 0.21 10.00 2.00 0.21 0.00 2.00 0.25 0.34 2.00 0.25 0.69 2.00 0.25 1.03 2.00 0.25 1.38 2.00 0.25 1.72 2.00 0.25 2.07 2.00 0.25 2.41 2.00 0.25 2.76 2.00 0.25 3.10 2.00 0.25 3.45 2.00 0.25 3.79 2.00 0.25 4.14 2.00 0.25 4.48 2.00 0.25 4.83 2.00 0.25 5.17 2.00 0.25 5.52 2.00 0.25 5.86 2.00 0.25 6.21 2.00 0.25 6.55 2.00 0.25 6.90 2.00 0.25 7.24 2.00 0.25 7.59 2.00 0.25 7.93 2.00 0.25 8.28 2.00 0.25 8.62 2.00 0.25 8.97 2.00 0.25 9.31 2.00 0.25 9.66 2.00 0.25 10.00 2.00 0.25 0.00 2.00 0.28 0.34 2.00 0.28 0.69 2.00 0.28 1.03 2.00 0.28 1.38 2.00 0.28 1.72 2.00 0.28 2.07 2.00 0.28 2.41 2.00 0.28 2.76 2.00 0.28 3.10 2.00 0.28 3.45 2.00 0.28 3.79 2.00 0.28 4.14 2.00 0.28 4.48 2.00 0.28 4.83 2.00 0.28 5.17 2.00 0.28 5.52 2.00 0.28 5.86 2.00 0.28 6.21 2.00 0.28 6.55 2.00 0.28 6.90 2.00 0.28 7.24 2.00 0.28 7.59 2.00 0.28 7.93 2.00 0.28 8.28 2.00 0.28 8.62 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diff --git a/Matlab-Programs/PhaseDiagram2D.vtk b/Matlab-Programs/PhaseDiagram2D.vtk
new file mode 100644
index 0000000000000000000000000000000000000000..7b2be226c432e118dd622e30bbb0de6b43adb06b
--- /dev/null
+++ b/Matlab-Programs/PhaseDiagram2D.vtk
@@ -0,0 +1,11 @@
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diff --git a/Matlab-Programs/PhaseDiagramNew.pvsm b/Matlab-Programs/PhaseDiagramNew.pvsm
new file mode 100644
index 0000000000000000000000000000000000000000..982ede4f4cd85b8bd1c411455ed0d591a0f65cc1
--- /dev/null
+++ b/Matlab-Programs/PhaseDiagramNew.pvsm
@@ -0,0 +1,52044 @@
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+  <ServerManagerState version="5.7.0">
+    <Proxy group="animation" type="AnimationScene" id="263" servers="16">
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+      <Property name="Cues" id="263.Cues" number_of_elements="1">
+        <Proxy value="265"/>
+        <Domain name="groups" id="263.Cues.groups"/>
+      </Property>
+      <Property name="Duration" id="263.Duration" number_of_elements="1">
+        <Element index="0" value="10"/>
+      </Property>
+      <Property name="EndTime" id="263.EndTime" number_of_elements="1">
+        <Element index="0" value="1"/>
+      </Property>
+      <Property name="FramesPerTimestep" id="263.FramesPerTimestep" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="263.FramesPerTimestep.range"/>
+      </Property>
+      <Property name="GoToFirst" id="263.GoToFirst"/>
+      <Property name="GoToLast" id="263.GoToLast"/>
+      <Property name="GoToNext" id="263.GoToNext"/>
+      <Property name="GoToPrevious" id="263.GoToPrevious"/>
+      <Property name="LockEndTime" id="263.LockEndTime" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="263.LockEndTime.bool"/>
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+      <Property name="LockStartTime" id="263.LockStartTime" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="263.LockStartTime.bool"/>
+      </Property>
+      <Property name="Loop" id="263.Loop" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="263.Loop.bool"/>
+      </Property>
+      <Property name="NumberOfFrames" id="263.NumberOfFrames" number_of_elements="1">
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+        <Domain name="range" id="263.NumberOfFrames.range"/>
+      </Property>
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+        <Domain name="range" id="15307.ArcMajorTickSize.range"/>
+      </Property>
+      <Property name="ArcMajorTickThickness" id="15307.ArcMajorTickThickness" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.ArcMajorTickThickness.range"/>
+      </Property>
+      <Property name="ArcMinorTickVisibility" id="15307.ArcMinorTickVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.ArcMinorTickVisibility.bool"/>
+      </Property>
+      <Property name="ArcTickRatioSize" id="15307.ArcTickRatioSize" number_of_elements="1">
+        <Element index="0" value="0.3"/>
+        <Domain name="range" id="15307.ArcTickRatioSize.range"/>
+      </Property>
+      <Property name="ArcTickRatioThickness" id="15307.ArcTickRatioThickness" number_of_elements="1">
+        <Element index="0" value="0.5"/>
+        <Domain name="range" id="15307.ArcTickRatioThickness.range"/>
+      </Property>
+      <Property name="ArcTickVisibility" id="15307.ArcTickVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.ArcTickVisibility.bool"/>
+      </Property>
+      <Property name="ArcTicksOriginToPolarAxis" id="15307.ArcTicksOriginToPolarAxis" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.ArcTicksOriginToPolarAxis.bool"/>
+      </Property>
+      <Property name="AutoSubdividePolarAxis" id="15307.AutoSubdividePolarAxis" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.AutoSubdividePolarAxis.bool"/>
+      </Property>
+      <Property name="AxisMinorTickVisibility" id="15307.AxisMinorTickVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.AxisMinorTickVisibility.bool"/>
+      </Property>
+      <Property name="AxisTickVisibility" id="15307.AxisTickVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.AxisTickVisibility.bool"/>
+      </Property>
+      <Property name="CustomBounds" id="15307.CustomBounds" number_of_elements="6">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Element index="3" value="1"/>
+        <Element index="4" value="0"/>
+        <Element index="5" value="1"/>
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+      <Property name="CustomRange" id="15307.CustomRange" number_of_elements="2">
+        <Element index="0" value="0"/>
+        <Element index="1" value="1"/>
+      </Property>
+      <Property name="DataBounds" id="15307.DataBounds" number_of_elements="6">
+        <Element index="0" value="0"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Element index="3" value="1"/>
+        <Element index="4" value="0"/>
+        <Element index="5" value="1"/>
+      </Property>
+      <Property name="DeltaAngleMajor" id="15307.DeltaAngleMajor" number_of_elements="1">
+        <Element index="0" value="10"/>
+        <Domain name="range" id="15307.DeltaAngleMajor.range"/>
+      </Property>
+      <Property name="DeltaAngleMinor" id="15307.DeltaAngleMinor" number_of_elements="1">
+        <Element index="0" value="5"/>
+        <Domain name="range" id="15307.DeltaAngleMinor.range"/>
+      </Property>
+      <Property name="DeltaRangeMajor" id="15307.DeltaRangeMajor" number_of_elements="1">
+        <Element index="0" value="1"/>
+      </Property>
+      <Property name="DeltaRangeMinor" id="15307.DeltaRangeMinor" number_of_elements="1">
+        <Element index="0" value="1"/>
+      </Property>
+      <Property name="DistanceLODThreshold" id="15307.DistanceLODThreshold" number_of_elements="1">
+        <Element index="0" value="0.7"/>
+        <Domain name="range" id="15307.DistanceLODThreshold.range"/>
+      </Property>
+      <Property name="DrawPolarArcsGridlines" id="15307.DrawPolarArcsGridlines" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.DrawPolarArcsGridlines.bool"/>
+      </Property>
+      <Property name="DrawRadialGridlines" id="15307.DrawRadialGridlines" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.DrawRadialGridlines.bool"/>
+      </Property>
+      <Property name="EnableCustomBounds" id="15307.EnableCustomBounds" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+      </Property>
+      <Property name="EnableCustomRange" id="15307.EnableCustomRange" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.EnableCustomRange.bool"/>
+      </Property>
+      <Property name="EnableDistanceLOD" id="15307.EnableDistanceLOD" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.EnableDistanceLOD.bool"/>
+      </Property>
+      <Property name="EnableViewAngleLOD" id="15307.EnableViewAngleLOD" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.EnableViewAngleLOD.bool"/>
+      </Property>
+      <Property name="Input" id="15307.Input" number_of_elements="1">
+        <Proxy value="15268" output_port="0"/>
+        <Domain name="input_type" id="15307.Input.input_type"/>
+      </Property>
+      <Property name="LastRadialAxisColor" id="15307.LastRadialAxisColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.LastRadialAxisColor.range"/>
+      </Property>
+      <Property name="LastRadialAxisMajorTickSize" id="15307.LastRadialAxisMajorTickSize" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.LastRadialAxisMajorTickSize.range"/>
+      </Property>
+      <Property name="LastRadialAxisMajorTickThickness" id="15307.LastRadialAxisMajorTickThickness" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.LastRadialAxisMajorTickThickness.range"/>
+      </Property>
+      <Property name="LastRadialAxisTickRatioSize" id="15307.LastRadialAxisTickRatioSize" number_of_elements="1">
+        <Element index="0" value="0.3"/>
+        <Domain name="range" id="15307.LastRadialAxisTickRatioSize.range"/>
+      </Property>
+      <Property name="LastRadialAxisTickRatioThickness" id="15307.LastRadialAxisTickRatioThickness" number_of_elements="1">
+        <Element index="0" value="0.5"/>
+        <Domain name="range" id="15307.LastRadialAxisTickRatioThickness.range"/>
+      </Property>
+      <Property name="MaximumAngle" id="15307.MaximumAngle" number_of_elements="1">
+        <Element index="0" value="90"/>
+        <Domain name="range" id="15307.MaximumAngle.range"/>
+      </Property>
+      <Property name="MinimumAngle" id="15307.MinimumAngle" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.MinimumAngle.range"/>
+      </Property>
+      <Property name="MinimumRadius" id="15307.MinimumRadius" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.MinimumRadius.range"/>
+      </Property>
+      <Property name="NumberOfPolarAxis" id="15307.NumberOfPolarAxis" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.NumberOfPolarAxis.range"/>
+      </Property>
+      <Property name="NumberOfRadialAxes" id="15307.NumberOfRadialAxes" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.NumberOfRadialAxes.range"/>
+      </Property>
+      <Property name="Orientation" id="15307.Orientation" number_of_elements="3">
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+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="15307.Orientation.range"/>
+      </Property>
+      <Property name="PolarArcsColor" id="15307.PolarArcsColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.PolarArcsColor.range"/>
+      </Property>
+      <Property name="PolarArcsVisibility" id="15307.PolarArcsVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.PolarArcsVisibility.bool"/>
+      </Property>
+      <Property name="PolarAxisColor" id="15307.PolarAxisColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.PolarAxisColor.range"/>
+      </Property>
+      <Property name="PolarAxisMajorTickSize" id="15307.PolarAxisMajorTickSize" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="15307.PolarAxisMajorTickSize.range"/>
+      </Property>
+      <Property name="PolarAxisMajorTickThickness" id="15307.PolarAxisMajorTickThickness" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.PolarAxisMajorTickThickness.range"/>
+      </Property>
+      <Property name="PolarAxisTickRatioSize" id="15307.PolarAxisTickRatioSize" number_of_elements="1">
+        <Element index="0" value="0.3"/>
+        <Domain name="range" id="15307.PolarAxisTickRatioSize.range"/>
+      </Property>
+      <Property name="PolarAxisTickRatioThickness" id="15307.PolarAxisTickRatioThickness" number_of_elements="1">
+        <Element index="0" value="0.5"/>
+        <Domain name="range" id="15307.PolarAxisTickRatioThickness.range"/>
+      </Property>
+      <Property name="PolarAxisTitle" id="15307.PolarAxisTitle" number_of_elements="1">
+        <Element index="0" value="Radial Distance"/>
+      </Property>
+      <Property name="PolarAxisTitleLocation" id="15307.PolarAxisTitleLocation" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="15307.PolarAxisTitleLocation.enum">
+          <Entry value="0" text="Bottom"/>
+          <Entry value="1" text="Extern"/>
+        </Domain>
+      </Property>
+      <Property name="PolarAxisTitleVisibility" id="15307.PolarAxisTitleVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.PolarAxisTitleVisibility.bool"/>
+      </Property>
+      <Property name="PolarAxisVisibility" id="15307.PolarAxisVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.PolarAxisVisibility.bool"/>
+      </Property>
+      <Property name="PolarLabelExponentLocation" id="15307.PolarLabelExponentLocation" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="enum" id="15307.PolarLabelExponentLocation.enum">
+          <Entry value="0" text="Bottom"/>
+          <Entry value="1" text="Extern"/>
+          <Entry value="2" text="Labels"/>
+        </Domain>
+      </Property>
+      <Property name="PolarLabelFormat" id="15307.PolarLabelFormat" number_of_elements="1">
+        <Element index="0" value="%-#6.3g"/>
+      </Property>
+      <Property name="PolarLabelVisibility" id="15307.PolarLabelVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.PolarLabelVisibility.bool"/>
+      </Property>
+      <Property name="PolarTicksVisibility" id="15307.PolarTicksVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.PolarTicksVisibility.bool"/>
+      </Property>
+      <Property name="Position" id="15307.Position" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="15307.Position.range"/>
+      </Property>
+      <Property name="RadialAxesOriginToPolarAxis" id="15307.RadialAxesOriginToPolarAxis" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.RadialAxesOriginToPolarAxis.bool"/>
+      </Property>
+      <Property name="RadialAxesVisibility" id="15307.RadialAxesVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.RadialAxesVisibility.bool"/>
+      </Property>
+      <Property name="RadialLabelFormat" id="15307.RadialLabelFormat" number_of_elements="1">
+        <Element index="0" value="%-#3.1f"/>
+      </Property>
+      <Property name="RadialLabelLocation" id="15307.RadialLabelLocation" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="15307.RadialLabelLocation.enum">
+          <Entry value="0" text="Bottom"/>
+          <Entry value="1" text="Extern"/>
+        </Domain>
+      </Property>
+      <Property name="RadialLabelVisibility" id="15307.RadialLabelVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.RadialLabelVisibility.bool"/>
+      </Property>
+      <Property name="RadialUnitsVisibility" id="15307.RadialUnitsVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="15307.RadialUnitsVisibility.bool"/>
+      </Property>
+      <Property name="Ratio" id="15307.Ratio" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.Ratio.range"/>
+      </Property>
+      <Property name="Scale" id="15307.Scale" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.Scale.range"/>
+      </Property>
+      <Property name="ScreenSize" id="15307.ScreenSize" number_of_elements="1">
+        <Element index="0" value="10"/>
+        <Domain name="range" id="15307.ScreenSize.range"/>
+      </Property>
+      <Property name="SecondaryPolarArcsColor" id="15307.SecondaryPolarArcsColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.SecondaryPolarArcsColor.range"/>
+      </Property>
+      <Property name="SecondaryRadialAxesColor" id="15307.SecondaryRadialAxesColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.SecondaryRadialAxesColor.range"/>
+      </Property>
+      <Property name="SmallestVisiblePolarAngle" id="15307.SmallestVisiblePolarAngle" number_of_elements="1">
+        <Element index="0" value="0.5"/>
+        <Domain name="range" id="15307.SmallestVisiblePolarAngle.range"/>
+      </Property>
+      <Property name="TickLocation" id="15307.TickLocation" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="enum" id="15307.TickLocation.enum">
+          <Entry value="0" text="Inside"/>
+          <Entry value="1" text="Outside"/>
+          <Entry value="2" text="Both"/>
+        </Domain>
+      </Property>
+      <Property name="Use2DMode" id="15307.Use2DMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.Use2DMode.bool"/>
+      </Property>
+      <Property name="UseLogAxis" id="15307.UseLogAxis" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.UseLogAxis.bool"/>
+      </Property>
+      <Property name="ViewAngleLODThreshold" id="15307.ViewAngleLODThreshold" number_of_elements="1">
+        <Element index="0" value="0.7"/>
+        <Domain name="range" id="15307.ViewAngleLODThreshold.range"/>
+      </Property>
+      <Property name="Visibility" id="15307.Visibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.Visibility.bool"/>
+      </Property>
+      <Property name="LastRadialAxisTextBold" id="15307.LastRadialAxisTextBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.LastRadialAxisTextBold.bool"/>
+      </Property>
+      <Property name="LastRadialAxisTextColor" id="15307.LastRadialAxisTextColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.LastRadialAxisTextColor.range"/>
+      </Property>
+      <Property name="LastRadialAxisTextFontFamily" id="15307.LastRadialAxisTextFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="15307.LastRadialAxisTextFontFamily.enum">
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+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
+        </Domain>
+      </Property>
+      <Property name="LastRadialAxisTextFontFile" id="15307.LastRadialAxisTextFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="LastRadialAxisTextFontSize" id="15307.LastRadialAxisTextFontSize" number_of_elements="1">
+        <Element index="0" value="12"/>
+        <Domain name="range" id="15307.LastRadialAxisTextFontSize.range"/>
+      </Property>
+      <Property name="LastRadialAxisTextItalic" id="15307.LastRadialAxisTextItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.LastRadialAxisTextItalic.bool"/>
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+      <Property name="LastRadialAxisTextOpacity" id="15307.LastRadialAxisTextOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.LastRadialAxisTextOpacity.range"/>
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+      <Property name="LastRadialAxisTextShadow" id="15307.LastRadialAxisTextShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.LastRadialAxisTextShadow.bool"/>
+      </Property>
+      <Property name="PolarAxisLabelBold" id="15307.PolarAxisLabelBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisLabelBold.bool"/>
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+      <Property name="PolarAxisLabelColor" id="15307.PolarAxisLabelColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.PolarAxisLabelColor.range"/>
+      </Property>
+      <Property name="PolarAxisLabelFontFamily" id="15307.PolarAxisLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="15307.PolarAxisLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
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+      </Property>
+      <Property name="PolarAxisLabelFontFile" id="15307.PolarAxisLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="PolarAxisLabelFontSize" id="15307.PolarAxisLabelFontSize" number_of_elements="1">
+        <Element index="0" value="12"/>
+        <Domain name="range" id="15307.PolarAxisLabelFontSize.range"/>
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+      <Property name="PolarAxisLabelItalic" id="15307.PolarAxisLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisLabelItalic.bool"/>
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+      <Property name="PolarAxisLabelOpacity" id="15307.PolarAxisLabelOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.PolarAxisLabelOpacity.range"/>
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+      <Property name="PolarAxisLabelShadow" id="15307.PolarAxisLabelShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisLabelShadow.bool"/>
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+      <Property name="PolarAxisTitleBold" id="15307.PolarAxisTitleBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisTitleBold.bool"/>
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+      <Property name="PolarAxisTitleColor" id="15307.PolarAxisTitleColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.PolarAxisTitleColor.range"/>
+      </Property>
+      <Property name="PolarAxisTitleFontFamily" id="15307.PolarAxisTitleFontFamily" number_of_elements="1">
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+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
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+      </Property>
+      <Property name="PolarAxisTitleFontFile" id="15307.PolarAxisTitleFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="PolarAxisTitleFontSize" id="15307.PolarAxisTitleFontSize" number_of_elements="1">
+        <Element index="0" value="12"/>
+        <Domain name="range" id="15307.PolarAxisTitleFontSize.range"/>
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+      <Property name="PolarAxisTitleItalic" id="15307.PolarAxisTitleItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisTitleItalic.bool"/>
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+      <Property name="PolarAxisTitleOpacity" id="15307.PolarAxisTitleOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="15307.PolarAxisTitleOpacity.range"/>
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+      <Property name="PolarAxisTitleShadow" id="15307.PolarAxisTitleShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.PolarAxisTitleShadow.bool"/>
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+      <Property name="SecondaryRadialAxesTextBold" id="15307.SecondaryRadialAxesTextBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="15307.SecondaryRadialAxesTextBold.bool"/>
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+      <Property name="SecondaryRadialAxesTextColor" id="15307.SecondaryRadialAxesTextColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="15307.SecondaryRadialAxesTextColor.range"/>
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+      <Property name="SecondaryRadialAxesTextFontFamily" id="15307.SecondaryRadialAxesTextFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="15307.SecondaryRadialAxesTextFontFamily.enum">
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+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
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+      </Property>
+      <Property name="SecondaryRadialAxesTextFontFile" id="15307.SecondaryRadialAxesTextFontFile" number_of_elements="1">
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+      <Property name="RenderPointsAsSpheres" id="9829.RenderPointsAsSpheres" number_of_elements="1">
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+        <Domain name="scalar_range" id="9829.ScaleFactor.scalar_range"/>
+        <Domain name="vector_range" id="9829.ScaleFactor.vector_range"/>
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+          <Entry value="1" text="Magnitude"/>
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+      <Property name="ScaleTransferFunction" id="9829.ScaleTransferFunction" number_of_elements="1">
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+      <Property name="SelectOrientationVectors" id="9829.SelectOrientationVectors" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionCellLabelColor.range"/>
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+          <Entry value="1" text="Courier"/>
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+      </Property>
+      <Property name="SelectionCellLabelFontFile" id="9829.SelectionCellLabelFontFile" number_of_elements="1">
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+      <Property name="SelectionCellLabelItalic" id="9829.SelectionCellLabelItalic" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionCellLabelItalic.bool"/>
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+      <Property name="SelectionCellLabelJustification" id="9829.SelectionCellLabelJustification" number_of_elements="1">
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+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
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+      </Property>
+      <Property name="SelectionCellLabelOpacity" id="9829.SelectionCellLabelOpacity" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionCellLabelOpacity.range"/>
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+      <Property name="SelectionCellLabelShadow" id="9829.SelectionCellLabelShadow" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionCellLabelShadow.bool"/>
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+      <Property name="SelectionCellLabelVisibility" id="9829.SelectionCellLabelVisibility" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionCellLabelVisibility.bool"/>
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+      <Property name="SelectionColor" id="9829.SelectionColor" number_of_elements="3">
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+        <Element index="1" value="0"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="9829.SelectionColor.range"/>
+      </Property>
+      <Property name="SelectionLineWidth" id="9829.SelectionLineWidth" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionLineWidth.range"/>
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+      <Property name="SelectionMaximumNumberOfLabels" id="9829.SelectionMaximumNumberOfLabels" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionMaximumNumberOfLabels.range"/>
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+      <Property name="SelectionOpacity" id="9829.SelectionOpacity" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionOpacity.range"/>
+      </Property>
+      <Property name="SelectionPointLabelBold" id="9829.SelectionPointLabelBold" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionPointLabelBold.bool"/>
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+      <Property name="SelectionPointLabelColor" id="9829.SelectionPointLabelColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="9829.SelectionPointLabelColor.range"/>
+      </Property>
+      <Property name="SelectionPointLabelFontFamily" id="9829.SelectionPointLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="9829.SelectionPointLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
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+      </Property>
+      <Property name="SelectionPointLabelFontFile" id="9829.SelectionPointLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionPointLabelFontSize" id="9829.SelectionPointLabelFontSize" number_of_elements="1">
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+      <Property name="SelectionPointLabelFormat" id="9829.SelectionPointLabelFormat" number_of_elements="1">
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+      <Property name="SelectionPointLabelItalic" id="9829.SelectionPointLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="9829.SelectionPointLabelItalic.bool"/>
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+        <Domain name="enum" id="9829.SelectionPointLabelJustification.enum">
+          <Entry value="0" text="Left"/>
+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
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+      </Property>
+      <Property name="SelectionPointLabelOpacity" id="9829.SelectionPointLabelOpacity" number_of_elements="1">
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+        <Domain name="range" id="9829.SelectionPointLabelOpacity.range"/>
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+      <Property name="SelectionPointLabelShadow" id="9829.SelectionPointLabelShadow" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionPointLabelShadow.bool"/>
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+      <Property name="SelectionPointLabelVisibility" id="9829.SelectionPointLabelVisibility" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionPointLabelVisibility.bool"/>
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+      <Property name="SelectionPointSize" id="9829.SelectionPointSize" number_of_elements="1">
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+      <Property name="SelectionRepresentation" id="9829.SelectionRepresentation" number_of_elements="1">
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+        <Domain name="enum" id="9829.SelectionRepresentation.enum">
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+          <Entry value="1" text="Wireframe"/>
+          <Entry value="2" text="Surface"/>
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+      </Property>
+      <Property name="SelectionUseOutline" id="9829.SelectionUseOutline" number_of_elements="1">
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+        <Domain name="bool" id="9829.SelectionUseOutline.bool"/>
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+        <Element index="2" value=""/>
+        <Element index="3" value="0"/>
+        <Element index="4" value="type"/>
+        <Domain name="array_list" id="9829.SetScaleArray.array_list">
+          <String text="arc_length"/>
+          <String text="type"/>
+          <String text="vtkValidPointMask"/>
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+      <Property name="ShaderPreset" id="9829.ShaderPreset" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="enum" id="9829.ShaderPreset.enum">
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+          <Entry value="1" text="Sphere"/>
+          <Entry value="2" text="Black-edged circle"/>
+          <Entry value="3" text="Plain circle"/>
+          <Entry value="4" text="Triangle"/>
+          <Entry value="5" text="Square Outline"/>
+          <Entry value="6" text="Custom"/>
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+      <Property name="ShaderReplacements" id="9829.ShaderReplacements" number_of_elements="1">
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+      <Property name="UseGlyphCullingAndLOD" id="9829.UseGlyphCullingAndLOD" number_of_elements="1">
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+      <Property name="UseSeparateColorMap" id="9829.UseSeparateColorMap" number_of_elements="1">
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+        </Domain>
+      </Property>
+      <Property name="RepresentationTypesInfo" id="10845.RepresentationTypesInfo" number_of_elements="8">
+        <Element index="0" value="3D Glyphs"/>
+        <Element index="1" value="Feature Edges"/>
+        <Element index="2" value="Outline"/>
+        <Element index="3" value="Point Gaussian"/>
+        <Element index="4" value="Points"/>
+        <Element index="5" value="Surface"/>
+        <Element index="6" value="Surface With Edges"/>
+        <Element index="7" value="Wireframe"/>
+      </Property>
+      <Property name="SelectionCellFieldDataArrayName" id="10845.SelectionCellFieldDataArrayName" number_of_elements="1">
+        <Element index="0" value="vtkOriginalCellIds"/>
+        <Domain name="array_list" id="10845.SelectionCellFieldDataArrayName.array_list"/>
+      </Property>
+      <Property name="SelectionPointFieldDataArrayName" id="10845.SelectionPointFieldDataArrayName" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10845.SelectionPointFieldDataArrayName.array_list">
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionVisibility" id="10845.SelectionVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10845.SelectionVisibility.bool"/>
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+      <Property name="Visibility" id="10845.Visibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.Visibility.bool"/>
+      </Property>
+      <Property name="Ambient" id="10845.Ambient" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="10845.Ambient.range"/>
+      </Property>
+      <Property name="AmbientColor" id="10845.AmbientColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10845.AmbientColor.range"/>
+      </Property>
+      <Property name="BackfaceAmbientColor" id="10845.BackfaceAmbientColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10845.BackfaceAmbientColor.range"/>
+      </Property>
+      <Property name="BackfaceDiffuseColor" id="10845.BackfaceDiffuseColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10845.BackfaceDiffuseColor.range"/>
+      </Property>
+      <Property name="BackfaceOpacity" id="10845.BackfaceOpacity" number_of_elements="1">
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+        <Domain name="range" id="10845.BackfaceOpacity.range"/>
+      </Property>
+      <Property name="BackfaceRepresentation" id="10845.BackfaceRepresentation" number_of_elements="1">
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+        <Domain name="enum" id="10845.BackfaceRepresentation.enum">
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+          <Entry value="401" text="Cull Backface"/>
+          <Entry value="402" text="Cull Frontface"/>
+          <Entry value="0" text="Points"/>
+          <Entry value="1" text="Wireframe"/>
+          <Entry value="2" text="Surface"/>
+          <Entry value="3" text="Surface With Edges"/>
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+      </Property>
+      <Property name="BlockColor" id="10845.BlockColor"/>
+      <Property name="BlockColorsDistinctValues" id="10845.BlockColorsDistinctValues" number_of_elements="1">
+        <Element index="0" value="12"/>
+        <Domain name="range" id="10845.BlockColorsDistinctValues.range"/>
+      </Property>
+      <Property name="BlockOpacity" id="10845.BlockOpacity"/>
+      <Property name="BlockVisibility" id="10845.BlockVisibility"/>
+      <Property name="ColorArrayName" id="10845.ColorArrayName" number_of_elements="5">
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+        <Element index="3" value="0"/>
+        <Element index="4" value="type"/>
+        <Domain name="array_list" id="10845.ColorArrayName.array_list">
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="ColorByLODIndex" id="10845.ColorByLODIndex" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.ColorByLODIndex.bool"/>
+      </Property>
+      <Property name="CustomShader" id="10845.CustomShader" number_of_elements="1">
+        <Element index="0" value=" // This custom shader code define a gaussian blur&#xa; // Please take a look into vtkSMPointGaussianRepresentation.cxx&#xa; // for other custom shader examples&#xa; //VTK::Color::Impl&#xa;   float dist2 = dot(offsetVCVSOutput.xy,offsetVCVSOutput.xy);&#xa;   float gaussian = exp(-0.5*dist2);&#xa;   opacity = opacity*gaussian;&#xa;"/>
+      </Property>
+      <Property name="CustomTriangleScale" id="10845.CustomTriangleScale" number_of_elements="1">
+        <Element index="0" value="3"/>
+      </Property>
+      <Property name="Diffuse" id="10845.Diffuse" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.Diffuse.range"/>
+      </Property>
+      <Property name="DiffuseColor" id="10845.DiffuseColor" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10845.DiffuseColor.range"/>
+      </Property>
+      <Property name="EdgeColor" id="10845.EdgeColor" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0.5"/>
+        <Domain name="range" id="10845.EdgeColor.range"/>
+      </Property>
+      <Property name="Emissive" id="10845.Emissive" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.Emissive.bool"/>
+      </Property>
+      <Property name="GaussianRadius" id="10845.GaussianRadius" number_of_elements="1">
+        <Element index="0" value="0.49974999999627473"/>
+        <Domain name="range" id="10845.GaussianRadius.range"/>
+      </Property>
+      <Property name="GlyphTableIndexArray" id="10845.GlyphTableIndexArray" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10845.GlyphTableIndexArray.array_list">
+          <String text="None"/>
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="GlyphType" id="10845.GlyphType" number_of_elements="1">
+        <Proxy value="10688" output_port="0"/>
+        <Domain name="input_type" id="10845.GlyphType.input_type"/>
+        <Domain name="proxy_list" id="10845.GlyphType.proxy_list">
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+          <Proxy value="10721"/>
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+      <Property name="InterpolateScalarsBeforeMapping" id="10845.InterpolateScalarsBeforeMapping" number_of_elements="1">
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+        <Domain name="bool" id="10845.InterpolateScalarsBeforeMapping.bool"/>
+      </Property>
+      <Property name="Interpolation" id="10845.Interpolation" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="enum" id="10845.Interpolation.enum">
+          <Entry value="0" text="Flat"/>
+          <Entry value="1" text="Gouraud"/>
+        </Domain>
+      </Property>
+      <Property name="LODValues" id="10845.LODValues">
+        <Domain name="scalar_range" id="10845.LODValues.scalar_range"/>
+      </Property>
+      <Property name="LineWidth" id="10845.LineWidth" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.LineWidth.range"/>
+      </Property>
+      <Property name="LookupTable" id="10845.LookupTable" number_of_elements="1">
+        <Proxy value="9287"/>
+        <Domain name="groups" id="10845.LookupTable.groups"/>
+      </Property>
+      <Property name="Luminosity" id="10845.Luminosity" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="10845.Luminosity.range"/>
+      </Property>
+      <Property name="MapScalars" id="10845.MapScalars" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10845.MapScalars.bool"/>
+      </Property>
+      <Property name="Masking" id="10845.Masking" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.Masking.bool"/>
+      </Property>
+      <Property name="MeshVisibility" id="10845.MeshVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.MeshVisibility.bool"/>
+      </Property>
+      <Property name="MultiComponentsMapping" id="10845.MultiComponentsMapping" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.MultiComponentsMapping.bool"/>
+      </Property>
+      <Property name="NonlinearSubdivisionLevel" id="10845.NonlinearSubdivisionLevel" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.NonlinearSubdivisionLevel.range"/>
+      </Property>
+      <Property name="OSPRayMaterial" id="10845.OSPRayMaterial" number_of_elements="1">
+        <Element index="0" value="None"/>
+        <Domain name="string_list" id="10845.OSPRayMaterial.string_list"/>
+      </Property>
+      <Property name="OSPRayScaleArray" id="10845.OSPRayScaleArray" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10845.OSPRayScaleArray.array_list">
+          <String text="Normals"/>
+          <String text="type"/>
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+      </Property>
+      <Property name="OSPRayScaleFunction" id="10845.OSPRayScaleFunction" number_of_elements="1">
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+        <Domain name="groups" id="10845.OSPRayScaleFunction.groups"/>
+        <Domain name="proxy_list" id="10845.OSPRayScaleFunction.proxy_list">
+          <Proxy value="10833"/>
+        </Domain>
+      </Property>
+      <Property name="OSPRayUseScaleArray" id="10845.OSPRayUseScaleArray" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.OSPRayUseScaleArray.bool"/>
+      </Property>
+      <Property name="Opacity" id="10845.Opacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.Opacity.range"/>
+      </Property>
+      <Property name="OpacityArray" id="10845.OpacityArray" number_of_elements="5">
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+        <Element index="2" value=""/>
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+        <Element index="4" value="type"/>
+        <Domain name="array_list" id="10845.OpacityArray.array_list">
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="OpacityArrayComponent" id="10845.OpacityArrayComponent" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="comps" id="10845.OpacityArrayComponent.comps">
+          <Entry value="0" text=""/>
+        </Domain>
+      </Property>
+      <Property name="OpacityByArray" id="10845.OpacityByArray" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.OpacityByArray.bool"/>
+      </Property>
+      <Property name="OpacityTransferFunction" id="10845.OpacityTransferFunction" number_of_elements="1">
+        <Proxy value="10798"/>
+        <Domain name="proxy_list" id="10845.OpacityTransferFunction.proxy_list">
+          <Proxy value="10798"/>
+        </Domain>
+      </Property>
+      <Property name="Orient" id="10845.Orient" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.Orient.bool"/>
+      </Property>
+      <Property name="Orientation" id="10845.Orientation" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10845.Orientation.range"/>
+      </Property>
+      <Property name="OrientationMode" id="10845.OrientationMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.OrientationMode.enum">
+          <Entry value="0" text="Direction"/>
+          <Entry value="1" text="Rotation"/>
+          <Entry value="2" text="Quaternion"/>
+        </Domain>
+      </Property>
+      <Property name="Origin" id="10845.Origin" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10845.Origin.range"/>
+      </Property>
+      <Property name="Pickable" id="10845.Pickable" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10845.Pickable.bool"/>
+      </Property>
+      <Property name="PointSize" id="10845.PointSize" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="range" id="10845.PointSize.range"/>
+      </Property>
+      <Property name="Position" id="10845.Position" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10845.Position.range"/>
+      </Property>
+      <Property name="RenderLinesAsTubes" id="10845.RenderLinesAsTubes" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.RenderLinesAsTubes.bool"/>
+      </Property>
+      <Property name="RenderPointsAsSpheres" id="10845.RenderPointsAsSpheres" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.RenderPointsAsSpheres.bool"/>
+      </Property>
+      <Property name="Scale" id="10845.Scale" number_of_elements="3">
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+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
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+      <Property name="ScaleArrayComponent" id="10845.ScaleArrayComponent" number_of_elements="1">
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+      <Property name="ScaleByArray" id="10845.ScaleByArray" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.ScaleByArray.bool"/>
+      </Property>
+      <Property name="ScaleFactor" id="10845.ScaleFactor" number_of_elements="1">
+        <Element index="0" value="9.994999999925495"/>
+        <Domain name="bounds" id="10845.ScaleFactor.bounds"/>
+        <Domain name="scalar_range" id="10845.ScaleFactor.scalar_range"/>
+        <Domain name="vector_range" id="10845.ScaleFactor.vector_range"/>
+      </Property>
+      <Property name="ScaleMode" id="10845.ScaleMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.ScaleMode.enum">
+          <Entry value="0" text="No Data Scaling Off"/>
+          <Entry value="1" text="Magnitude"/>
+          <Entry value="2" text="Vector Components"/>
+        </Domain>
+      </Property>
+      <Property name="ScaleTransferFunction" id="10845.ScaleTransferFunction" number_of_elements="1">
+        <Proxy value="10799"/>
+        <Domain name="proxy_list" id="10845.ScaleTransferFunction.proxy_list">
+          <Proxy value="10799"/>
+        </Domain>
+      </Property>
+      <Property name="Scaling" id="10845.Scaling" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.Scaling.bool"/>
+      </Property>
+      <Property name="SelectMaskArray" id="10845.SelectMaskArray" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectOrientationVectors" id="10845.SelectOrientationVectors" number_of_elements="1">
+        <Element index="0" value="None"/>
+        <Domain name="array_list" id="10845.SelectOrientationVectors.array_list">
+          <String text="None"/>
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectScaleArray" id="10845.SelectScaleArray" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10845.SelectScaleArray.array_list">
+          <String text="None"/>
+          <String text="Normals"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionCellLabelBold" id="10845.SelectionCellLabelBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionCellLabelBold.bool"/>
+      </Property>
+      <Property name="SelectionCellLabelColor" id="10845.SelectionCellLabelColor" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10845.SelectionCellLabelColor.range"/>
+      </Property>
+      <Property name="SelectionCellLabelFontFamily" id="10845.SelectionCellLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.SelectionCellLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
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+      </Property>
+      <Property name="SelectionCellLabelFontFile" id="10845.SelectionCellLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionCellLabelFontSize" id="10845.SelectionCellLabelFontSize" number_of_elements="1">
+        <Element index="0" value="18"/>
+        <Domain name="range" id="10845.SelectionCellLabelFontSize.range"/>
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+      <Property name="SelectionCellLabelFormat" id="10845.SelectionCellLabelFormat" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionCellLabelItalic" id="10845.SelectionCellLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionCellLabelItalic.bool"/>
+      </Property>
+      <Property name="SelectionCellLabelJustification" id="10845.SelectionCellLabelJustification" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.SelectionCellLabelJustification.enum">
+          <Entry value="0" text="Left"/>
+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionCellLabelOpacity" id="10845.SelectionCellLabelOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.SelectionCellLabelOpacity.range"/>
+      </Property>
+      <Property name="SelectionCellLabelShadow" id="10845.SelectionCellLabelShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionCellLabelShadow.bool"/>
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+      <Property name="SelectionCellLabelVisibility" id="10845.SelectionCellLabelVisibility" number_of_elements="1">
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+        <Domain name="bool" id="10845.SelectionCellLabelVisibility.bool"/>
+      </Property>
+      <Property name="SelectionColor" id="10845.SelectionColor" number_of_elements="3">
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+        <Element index="1" value="0"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10845.SelectionColor.range"/>
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+      <Property name="SelectionLineWidth" id="10845.SelectionLineWidth" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="range" id="10845.SelectionLineWidth.range"/>
+      </Property>
+      <Property name="SelectionMaximumNumberOfLabels" id="10845.SelectionMaximumNumberOfLabels" number_of_elements="1">
+        <Element index="0" value="100"/>
+        <Domain name="range" id="10845.SelectionMaximumNumberOfLabels.range"/>
+      </Property>
+      <Property name="SelectionOpacity" id="10845.SelectionOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.SelectionOpacity.range"/>
+      </Property>
+      <Property name="SelectionPointLabelBold" id="10845.SelectionPointLabelBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionPointLabelBold.bool"/>
+      </Property>
+      <Property name="SelectionPointLabelColor" id="10845.SelectionPointLabelColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10845.SelectionPointLabelColor.range"/>
+      </Property>
+      <Property name="SelectionPointLabelFontFamily" id="10845.SelectionPointLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.SelectionPointLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionPointLabelFontFile" id="10845.SelectionPointLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionPointLabelFontSize" id="10845.SelectionPointLabelFontSize" number_of_elements="1">
+        <Element index="0" value="18"/>
+        <Domain name="range" id="10845.SelectionPointLabelFontSize.range"/>
+      </Property>
+      <Property name="SelectionPointLabelFormat" id="10845.SelectionPointLabelFormat" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionPointLabelItalic" id="10845.SelectionPointLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionPointLabelItalic.bool"/>
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+      <Property name="SelectionPointLabelJustification" id="10845.SelectionPointLabelJustification" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10845.SelectionPointLabelJustification.enum">
+          <Entry value="0" text="Left"/>
+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
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+      </Property>
+      <Property name="SelectionPointLabelOpacity" id="10845.SelectionPointLabelOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10845.SelectionPointLabelOpacity.range"/>
+      </Property>
+      <Property name="SelectionPointLabelShadow" id="10845.SelectionPointLabelShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionPointLabelShadow.bool"/>
+      </Property>
+      <Property name="SelectionPointLabelVisibility" id="10845.SelectionPointLabelVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10845.SelectionPointLabelVisibility.bool"/>
+      </Property>
+      <Property name="SelectionPointSize" id="10845.SelectionPointSize" number_of_elements="1">
+        <Element index="0" value="5"/>
+        <Domain name="range" id="10845.SelectionPointSize.range"/>
+      </Property>
+      <Property name="SelectionRepresentation" id="10845.SelectionRepresentation" number_of_elements="1">
+        <Element index="0" value="1"/>
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+      <Property name="OrientationMode" id="10365.OrientationMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.OrientationMode.enum">
+          <Entry value="0" text="Direction"/>
+          <Entry value="1" text="Rotation"/>
+          <Entry value="2" text="Quaternion"/>
+        </Domain>
+      </Property>
+      <Property name="Origin" id="10365.Origin" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10365.Origin.range"/>
+      </Property>
+      <Property name="Pickable" id="10365.Pickable" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10365.Pickable.bool"/>
+      </Property>
+      <Property name="PointSize" id="10365.PointSize" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="range" id="10365.PointSize.range"/>
+      </Property>
+      <Property name="Position" id="10365.Position" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10365.Position.range"/>
+      </Property>
+      <Property name="RenderLinesAsTubes" id="10365.RenderLinesAsTubes" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.RenderLinesAsTubes.bool"/>
+      </Property>
+      <Property name="RenderPointsAsSpheres" id="10365.RenderPointsAsSpheres" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.RenderPointsAsSpheres.bool"/>
+      </Property>
+      <Property name="SamplingDimensions" id="10365.SamplingDimensions" number_of_elements="3">
+        <Element index="0" value="128"/>
+        <Element index="1" value="128"/>
+        <Element index="2" value="128"/>
+        <Domain name="range" id="10365.SamplingDimensions.range"/>
+      </Property>
+      <Property name="ScalarOpacityFunction" id="10365.ScalarOpacityFunction">
+        <Domain name="groups" id="10365.ScalarOpacityFunction.groups"/>
+      </Property>
+      <Property name="ScalarOpacityUnitDistance" id="10365.ScalarOpacityUnitDistance" number_of_elements="1">
+        <Element index="0" value="1.1782450137772644"/>
+        <Domain name="bounds" id="10365.ScalarOpacityUnitDistance.bounds"/>
+      </Property>
+      <Property name="Scale" id="10365.Scale" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10365.Scale.range"/>
+      </Property>
+      <Property name="ScaleArrayComponent" id="10365.ScaleArrayComponent" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="comps" id="10365.ScaleArrayComponent.comps">
+          <Entry value="0" text=""/>
+        </Domain>
+      </Property>
+      <Property name="ScaleByArray" id="10365.ScaleByArray" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.ScaleByArray.bool"/>
+      </Property>
+      <Property name="ScaleFactor" id="10365.ScaleFactor" number_of_elements="1">
+        <Element index="0" value="10"/>
+        <Domain name="bounds" id="10365.ScaleFactor.bounds"/>
+        <Domain name="scalar_range" id="10365.ScaleFactor.scalar_range"/>
+        <Domain name="vector_range" id="10365.ScaleFactor.vector_range"/>
+      </Property>
+      <Property name="ScaleMode" id="10365.ScaleMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.ScaleMode.enum">
+          <Entry value="0" text="No Data Scaling Off"/>
+          <Entry value="1" text="Magnitude"/>
+          <Entry value="2" text="Vector Components"/>
+        </Domain>
+      </Property>
+      <Property name="ScaleTransferFunction" id="10365.ScaleTransferFunction" number_of_elements="1">
+        <Proxy value="10303"/>
+        <Domain name="proxy_list" id="10365.ScaleTransferFunction.proxy_list">
+          <Proxy value="10303"/>
+        </Domain>
+      </Property>
+      <Property name="Scaling" id="10365.Scaling" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.Scaling.bool"/>
+      </Property>
+      <Property name="SelectMapper" id="10365.SelectMapper" number_of_elements="1">
+        <Element index="0" value="Projected tetra"/>
+        <Domain name="list" id="10365.SelectMapper.list">
+          <String text="Projected tetra"/>
+          <String text="Z sweep"/>
+          <String text="Bunyk ray cast"/>
+          <String text="Resample To Image"/>
+        </Domain>
+      </Property>
+      <Property name="SelectMaskArray" id="10365.SelectMaskArray" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectOrientationVectors" id="10365.SelectOrientationVectors" number_of_elements="1">
+        <Element index="0" value="None"/>
+        <Domain name="array_list" id="10365.SelectOrientationVectors.array_list">
+          <String text="None"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectScaleArray" id="10365.SelectScaleArray" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10365.SelectScaleArray.array_list">
+          <String text="None"/>
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionCellLabelBold" id="10365.SelectionCellLabelBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionCellLabelBold.bool"/>
+      </Property>
+      <Property name="SelectionCellLabelColor" id="10365.SelectionCellLabelColor" number_of_elements="3">
+        <Element index="0" value="0"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10365.SelectionCellLabelColor.range"/>
+      </Property>
+      <Property name="SelectionCellLabelFontFamily" id="10365.SelectionCellLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.SelectionCellLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionCellLabelFontFile" id="10365.SelectionCellLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionCellLabelFontSize" id="10365.SelectionCellLabelFontSize" number_of_elements="1">
+        <Element index="0" value="18"/>
+        <Domain name="range" id="10365.SelectionCellLabelFontSize.range"/>
+      </Property>
+      <Property name="SelectionCellLabelFormat" id="10365.SelectionCellLabelFormat" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionCellLabelItalic" id="10365.SelectionCellLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionCellLabelItalic.bool"/>
+      </Property>
+      <Property name="SelectionCellLabelJustification" id="10365.SelectionCellLabelJustification" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.SelectionCellLabelJustification.enum">
+          <Entry value="0" text="Left"/>
+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionCellLabelOpacity" id="10365.SelectionCellLabelOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10365.SelectionCellLabelOpacity.range"/>
+      </Property>
+      <Property name="SelectionCellLabelShadow" id="10365.SelectionCellLabelShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionCellLabelShadow.bool"/>
+      </Property>
+      <Property name="SelectionCellLabelVisibility" id="10365.SelectionCellLabelVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionCellLabelVisibility.bool"/>
+      </Property>
+      <Property name="SelectionColor" id="10365.SelectionColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="0"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10365.SelectionColor.range"/>
+      </Property>
+      <Property name="SelectionLineWidth" id="10365.SelectionLineWidth" number_of_elements="1">
+        <Element index="0" value="2"/>
+        <Domain name="range" id="10365.SelectionLineWidth.range"/>
+      </Property>
+      <Property name="SelectionMaximumNumberOfLabels" id="10365.SelectionMaximumNumberOfLabels" number_of_elements="1">
+        <Element index="0" value="100"/>
+        <Domain name="range" id="10365.SelectionMaximumNumberOfLabels.range"/>
+      </Property>
+      <Property name="SelectionOpacity" id="10365.SelectionOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10365.SelectionOpacity.range"/>
+      </Property>
+      <Property name="SelectionPointLabelBold" id="10365.SelectionPointLabelBold" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionPointLabelBold.bool"/>
+      </Property>
+      <Property name="SelectionPointLabelColor" id="10365.SelectionPointLabelColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="0"/>
+        <Domain name="range" id="10365.SelectionPointLabelColor.range"/>
+      </Property>
+      <Property name="SelectionPointLabelFontFamily" id="10365.SelectionPointLabelFontFamily" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.SelectionPointLabelFontFamily.enum">
+          <Entry value="0" text="Arial"/>
+          <Entry value="1" text="Courier"/>
+          <Entry value="2" text="Times"/>
+          <Entry value="4" text="File"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionPointLabelFontFile" id="10365.SelectionPointLabelFontFile" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionPointLabelFontSize" id="10365.SelectionPointLabelFontSize" number_of_elements="1">
+        <Element index="0" value="18"/>
+        <Domain name="range" id="10365.SelectionPointLabelFontSize.range"/>
+      </Property>
+      <Property name="SelectionPointLabelFormat" id="10365.SelectionPointLabelFormat" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="SelectionPointLabelItalic" id="10365.SelectionPointLabelItalic" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionPointLabelItalic.bool"/>
+      </Property>
+      <Property name="SelectionPointLabelJustification" id="10365.SelectionPointLabelJustification" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="enum" id="10365.SelectionPointLabelJustification.enum">
+          <Entry value="0" text="Left"/>
+          <Entry value="1" text="Center"/>
+          <Entry value="2" text="Right"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionPointLabelOpacity" id="10365.SelectionPointLabelOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10365.SelectionPointLabelOpacity.range"/>
+      </Property>
+      <Property name="SelectionPointLabelShadow" id="10365.SelectionPointLabelShadow" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionPointLabelShadow.bool"/>
+      </Property>
+      <Property name="SelectionPointLabelVisibility" id="10365.SelectionPointLabelVisibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionPointLabelVisibility.bool"/>
+      </Property>
+      <Property name="SelectionPointSize" id="10365.SelectionPointSize" number_of_elements="1">
+        <Element index="0" value="5"/>
+        <Domain name="range" id="10365.SelectionPointSize.range"/>
+      </Property>
+      <Property name="SelectionRepresentation" id="10365.SelectionRepresentation" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="enum" id="10365.SelectionRepresentation.enum">
+          <Entry value="0" text="Points"/>
+          <Entry value="1" text="Wireframe"/>
+          <Entry value="2" text="Surface"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionUseOutline" id="10365.SelectionUseOutline" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SelectionUseOutline.bool"/>
+      </Property>
+      <Property name="SetScaleArray" id="10365.SetScaleArray" number_of_elements="5">
+        <Element index="0" value=""/>
+        <Element index="1" value=""/>
+        <Element index="2" value=""/>
+        <Element index="3" value="0"/>
+        <Element index="4" value="type"/>
+        <Domain name="array_list" id="10365.SetScaleArray.array_list">
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="ShaderPreset" id="10365.ShaderPreset" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="enum" id="10365.ShaderPreset.enum">
+          <Entry value="0" text="Gaussian Blur"/>
+          <Entry value="1" text="Sphere"/>
+          <Entry value="2" text="Black-edged circle"/>
+          <Entry value="3" text="Plain circle"/>
+          <Entry value="4" text="Triangle"/>
+          <Entry value="5" text="Square Outline"/>
+          <Entry value="6" text="Custom"/>
+        </Domain>
+      </Property>
+      <Property name="ShaderReplacements" id="10365.ShaderReplacements" number_of_elements="1">
+        <Element index="0" value=""/>
+      </Property>
+      <Property name="Specular" id="10365.Specular" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="10365.Specular.range"/>
+      </Property>
+      <Property name="SpecularColor" id="10365.SpecularColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10365.SpecularColor.range"/>
+      </Property>
+      <Property name="SpecularPower" id="10365.SpecularPower" number_of_elements="1">
+        <Element index="0" value="100"/>
+        <Domain name="range" id="10365.SpecularPower.range"/>
+      </Property>
+      <Property name="StaticMode" id="10365.StaticMode" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.StaticMode.bool"/>
+      </Property>
+      <Property name="SuppressLOD" id="10365.SuppressLOD" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.SuppressLOD.bool"/>
+      </Property>
+      <Property name="Texture" id="10365.Texture">
+        <Domain name="groups" id="10365.Texture.groups"/>
+      </Property>
+      <Property name="Triangulate" id="10365.Triangulate" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.Triangulate.bool"/>
+      </Property>
+      <Property name="UseCompositeGlyphTable" id="10365.UseCompositeGlyphTable" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseCompositeGlyphTable.bool"/>
+      </Property>
+      <Property name="UseDataPartitions" id="10365.UseDataPartitions" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseDataPartitions.bool"/>
+      </Property>
+      <Property name="UseGlyphCullingAndLOD" id="10365.UseGlyphCullingAndLOD" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseGlyphCullingAndLOD.bool"/>
+      </Property>
+      <Property name="UseGlyphTable" id="10365.UseGlyphTable" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseGlyphTable.bool"/>
+      </Property>
+      <Property name="UseScaleFunction" id="10365.UseScaleFunction" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10365.UseScaleFunction.bool"/>
+      </Property>
+      <Property name="UseSeparateColorMap" id="10365.UseSeparateColorMap" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseSeparateColorMap.bool"/>
+      </Property>
+      <Property name="UseShaderReplacements" id="10365.UseShaderReplacements" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10365.UseShaderReplacements.bool"/>
+      </Property>
+      <Property name="UserTransform" id="10365.UserTransform" number_of_elements="16">
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+        <Element index="1" value="0"/>
+        <Element index="2" value="0"/>
+        <Element index="3" value="0"/>
+        <Element index="4" value="0"/>
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+        <Element index="7" value="0"/>
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+        <Element index="12" value="0"/>
+        <Element index="13" value="0"/>
+        <Element index="14" value="0"/>
+        <Element index="15" value="1"/>
+      </Property>
+    </Proxy>
+    <Proxy group="representations" type="StructuredGridRepresentation" id="10611" servers="21">
+      <Property name="DataAxesGrid" id="10611.DataAxesGrid" number_of_elements="1">
+        <Proxy value="10401"/>
+        <Domain name="proxy_list" id="10611.DataAxesGrid.proxy_list">
+          <Proxy value="10401"/>
+        </Domain>
+      </Property>
+      <Property name="Input" id="10611.Input" number_of_elements="1">
+        <Proxy value="10377" output_port="0"/>
+        <Domain name="input_array_point" id="10611.Input.input_array_point"/>
+        <Domain name="input_type" id="10611.Input.input_type"/>
+      </Property>
+      <Property name="PolarAxes" id="10611.PolarAxes" number_of_elements="1">
+        <Proxy value="10416"/>
+        <Domain name="proxy_list" id="10611.PolarAxes.proxy_list">
+          <Proxy value="10416"/>
+        </Domain>
+      </Property>
+      <Property name="Representation" id="10611.Representation" number_of_elements="1">
+        <Element index="0" value="Outline"/>
+        <Domain name="list" id="10611.Representation.list">
+          <String text="3D Glyphs"/>
+          <String text="Feature Edges"/>
+          <String text="Outline"/>
+          <String text="Point Gaussian"/>
+          <String text="Points"/>
+          <String text="Surface"/>
+          <String text="Surface With Edges"/>
+          <String text="Volume"/>
+          <String text="Wireframe"/>
+        </Domain>
+      </Property>
+      <Property name="RepresentationTypesInfo" id="10611.RepresentationTypesInfo" number_of_elements="9">
+        <Element index="0" value="3D Glyphs"/>
+        <Element index="1" value="Feature Edges"/>
+        <Element index="2" value="Outline"/>
+        <Element index="3" value="Point Gaussian"/>
+        <Element index="4" value="Points"/>
+        <Element index="5" value="Surface"/>
+        <Element index="6" value="Surface With Edges"/>
+        <Element index="7" value="Volume"/>
+        <Element index="8" value="Wireframe"/>
+      </Property>
+      <Property name="SelectionCellFieldDataArrayName" id="10611.SelectionCellFieldDataArrayName" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10611.SelectionCellFieldDataArrayName.array_list">
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionPointFieldDataArrayName" id="10611.SelectionPointFieldDataArrayName" number_of_elements="1">
+        <Element index="0" value="type"/>
+        <Domain name="array_list" id="10611.SelectionPointFieldDataArrayName.array_list">
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="SelectionVisibility" id="10611.SelectionVisibility" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="bool" id="10611.SelectionVisibility.bool"/>
+      </Property>
+      <Property name="Visibility" id="10611.Visibility" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10611.Visibility.bool"/>
+      </Property>
+      <Property name="Ambient" id="10611.Ambient" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="range" id="10611.Ambient.range"/>
+      </Property>
+      <Property name="AmbientColor" id="10611.AmbientColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10611.AmbientColor.range"/>
+      </Property>
+      <Property name="BackfaceAmbientColor" id="10611.BackfaceAmbientColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10611.BackfaceAmbientColor.range"/>
+      </Property>
+      <Property name="BackfaceDiffuseColor" id="10611.BackfaceDiffuseColor" number_of_elements="3">
+        <Element index="0" value="1"/>
+        <Element index="1" value="1"/>
+        <Element index="2" value="1"/>
+        <Domain name="range" id="10611.BackfaceDiffuseColor.range"/>
+      </Property>
+      <Property name="BackfaceOpacity" id="10611.BackfaceOpacity" number_of_elements="1">
+        <Element index="0" value="1"/>
+        <Domain name="range" id="10611.BackfaceOpacity.range"/>
+      </Property>
+      <Property name="BackfaceRepresentation" id="10611.BackfaceRepresentation" number_of_elements="1">
+        <Element index="0" value="400"/>
+        <Domain name="enum" id="10611.BackfaceRepresentation.enum">
+          <Entry value="400" text="Follow Frontface"/>
+          <Entry value="401" text="Cull Backface"/>
+          <Entry value="402" text="Cull Frontface"/>
+          <Entry value="0" text="Points"/>
+          <Entry value="1" text="Wireframe"/>
+          <Entry value="2" text="Surface"/>
+          <Entry value="3" text="Surface With Edges"/>
+        </Domain>
+      </Property>
+      <Property name="BlockColor" id="10611.BlockColor"/>
+      <Property name="BlockColorsDistinctValues" id="10611.BlockColorsDistinctValues" number_of_elements="1">
+        <Element index="0" value="12"/>
+        <Domain name="range" id="10611.BlockColorsDistinctValues.range"/>
+      </Property>
+      <Property name="BlockOpacity" id="10611.BlockOpacity"/>
+      <Property name="BlockVisibility" id="10611.BlockVisibility"/>
+      <Property name="ColorArrayName" id="10611.ColorArrayName" number_of_elements="5">
+        <Element index="0" value=""/>
+        <Element index="1" value=""/>
+        <Element index="2" value=""/>
+        <Element index="3" value="0"/>
+        <Element index="4" value="type"/>
+        <Domain name="array_list" id="10611.ColorArrayName.array_list">
+          <String text="type"/>
+        </Domain>
+      </Property>
+      <Property name="ColorByLODIndex" id="10611.ColorByLODIndex" number_of_elements="1">
+        <Element index="0" value="0"/>
+        <Domain name="bool" id="10611.ColorByLODIndex.bool"/>
+      </Property>
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+          <Entry value="3" text="Plain circle"/>
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diff --git a/Matlab-Programs/PhaseDiagramType.vtk b/Matlab-Programs/PhaseDiagramType.vtk
new file mode 100644
index 0000000000000000000000000000000000000000..68fdea32ba2b55ed897ecafd86b1c31d6e09480e
--- /dev/null
+++ b/Matlab-Programs/PhaseDiagramType.vtk
@@ -0,0 +1,11 @@
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+VTK from Matlab
+ASCII
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\ No newline at end of file
diff --git a/Matlab-Programs/PhaseDiagramType2D.vtk b/Matlab-Programs/PhaseDiagramType2D.vtk
new file mode 100644
index 0000000000000000000000000000000000000000..c75ba62a4e2278a4972d138286ade7d1138db713
--- /dev/null
+++ b/Matlab-Programs/PhaseDiagramType2D.vtk
@@ -0,0 +1,11 @@
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+VTK from Matlab
+ASCII
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1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 3.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2.00 2.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
\ No newline at end of file
diff --git a/Matlab-Programs/PhaseDiagrams.mlx b/Matlab-Programs/PhaseDiagrams.mlx
index 7e27b8bfff5acf86e08c65c356092134a349980f..fcc7b1ac70b8eafa1733a46e16d2be5be62a6ae0 100644
Binary files a/Matlab-Programs/PhaseDiagrams.mlx and b/Matlab-Programs/PhaseDiagrams.mlx differ
diff --git a/Matlab-Programs/PythonMatlabTest.py b/Matlab-Programs/PythonMatlabTest.py
new file mode 100644
index 0000000000000000000000000000000000000000..702ac01ba0a4f9d2c5059f92df24165f776a9c58
--- /dev/null
+++ b/Matlab-Programs/PythonMatlabTest.py
@@ -0,0 +1,20 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+#import sys
+import matlab.engine
+
+eng = matlab.engine.start_matlab()
+# tf = eng.findParabolic
+# print(tf)
+# eng.findParabolic(nargout=0)
+eng.Minimization_Script(nargout=0)
+
+
+
+print('Running Python Code')
diff --git a/Matlab-Programs/QMatrix.txt b/Matlab-Programs/QMatrix.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69e0c1d3a06f78a890b8eb120f1ebdadd709d1b2
--- /dev/null
+++ b/Matlab-Programs/QMatrix.txt
@@ -0,0 +1,9 @@
+1 1 2.07819448498850168
+1 2 -9.59442219281886493e-22
+1 3 9.20995372360501347e-07
+2 1 -9.87702818837798838e-20
+2 2 2.08333333333341164
+2 3 -9.79796825055082683e-21
+3 1 6.10325081515254299e-05
+3 2 -1.77052129286940134e-20
+3 3 2.08273199371863926
diff --git a/Matlab-Programs/RedPurpleBlue.json b/Matlab-Programs/RedPurpleBlue.json
new file mode 100644
index 0000000000000000000000000000000000000000..f58bda153f46144a3b18dd32a79db93834bcadbf
--- /dev/null
+++ b/Matlab-Programs/RedPurpleBlue.json
@@ -0,0 +1,73 @@
+[
+	{
+		"ColorSpace" : "Diverging",
+		"Name" : "Preset",
+		"Points" : 
+		[
+			1.0,
+			1.0,
+			0.5,
+			0.0,
+			1.2830188274383545,
+			1.0,
+			0.5,
+			0.0,
+			1.4654088020324707,
+			1.0,
+			0.5,
+			0.0,
+			1.6289308071136475,
+			1.0,
+			0.5,
+			0.0,
+			1.7987420558929443,
+			0.99264705181121826,
+			0.5,
+			0.0,
+			2.0,
+			1.0,
+			0.5,
+			0.0
+		],
+		"RGBPoints" : 
+		[
+			1.0,
+			0.0,
+			0.0,
+			1.0,
+			1.0,
+			0.17254901960784313,
+			0.043137254901960784,
+			0.92156862745098034,
+			1.0,
+			0.78592899999999999,
+			0.247056,
+			0.29547699999999999,
+			1.0,
+			0.17254901960784313,
+			0.043137254901960784,
+			0.92156862745098034,
+			1.1698113679885864,
+			0.41568627450980394,
+			0.0039215686274509803,
+			0.96862745098039216,
+			1.2672955989837646,
+			0.48627450980392156,
+			0.0,
+			0.97254901960784312,
+			1.4937106370925903,
+			1.0,
+			0.058823529411764705,
+			0.98431372549019602,
+			1.7672955989837646,
+			1.0,
+			0.043137254901960784,
+			0.55294117647058827,
+			2.0,
+			1.0,
+			0.0,
+			0.015686274509803921
+		]
+	}
+]
+
diff --git a/Matlab-Programs/SaveSatePythonTest.py b/Matlab-Programs/SaveSatePythonTest.py
new file mode 100644
index 0000000000000000000000000000000000000000..988d78a724431d601c45f18b094c22ce9db5c69f
--- /dev/null
+++ b/Matlab-Programs/SaveSatePythonTest.py
@@ -0,0 +1,124 @@
+# state file generated using paraview version 5.7.0
+
+# ----------------------------------------------------------------
+# setup views used in the visualization
+# ----------------------------------------------------------------
+
+# trace generated using paraview version 5.7.0
+#
+# To ensure correct image size when batch processing, please search 
+# for and uncomment the line `# renderView*.ViewSize = [*,*]`
+
+#### import the simple module from the paraview
+from paraview.simple import *
+#### disable automatic camera reset on 'Show'
+paraview.simple._DisableFirstRenderCameraReset()
+
+# Create a new 'Render View'
+renderView1 = CreateView('RenderView')
+renderView1.ViewSize = [964, 795]
+renderView1.AxesGrid = 'GridAxes3DActor'
+renderView1.CenterOfRotation = [5.5, 5.5, 5.5]
+renderView1.StereoType = 'Crystal Eyes'
+renderView1.CameraPosition = [-1.9013843868480158, -13.320979633549339, 35.98066109404487]
+renderView1.CameraFocalPoint = [1.538094468601466, -4.574729188366619, 21.81606919426716]
+renderView1.CameraViewUp = [0.05745797827794325, -0.8556355497369458, -0.5143796134748793]
+renderView1.CameraFocalDisk = 1.0
+renderView1.CameraParallelScale = 7.794228634059948
+renderView1.Background = [0.32, 0.34, 0.43]
+
+SetActiveView(None)
+
+# ----------------------------------------------------------------
+# setup view layouts
+# ----------------------------------------------------------------
+
+# create new layout object 'Layout #1'
+layout1 = CreateLayout(name='Layout #1')
+layout1.AssignView(0, renderView1)
+
+# ----------------------------------------------------------------
+# restore active view
+SetActiveView(renderView1)
+# ----------------------------------------------------------------
+
+# ----------------------------------------------------------------
+# setup the data processing pipelines
+# ----------------------------------------------------------------
+
+# create a new 'Legacy VTK Reader'
+windvtk = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/wind.vtk'])
+
+# ----------------------------------------------------------------
+# setup the visualization in view 'renderView1'
+# ----------------------------------------------------------------
+
+# show data from windvtk
+windvtkDisplay = Show(windvtk, renderView1)
+
+# get color transfer function/color map for 'type'
+typeLUT = GetColorTransferFunction('type')
+typeLUT.RGBPoints = [1.0, 0.0, 0.0, 1.0, 1.0, 0.17254901960784313, 0.043137254901960784, 0.9215686274509803, 1.0, 0.785929, 0.247056, 0.295477, 1.0, 0.17254901960784313, 0.043137254901960784, 0.9215686274509803, 1.1698113679885864, 0.41568627450980394, 0.00392156862745098, 0.9686274509803922, 1.2672955989837646, 0.48627450980392156, 0.0, 0.9725490196078431, 1.4937106370925903, 1.0, 0.058823529411764705, 0.984313725490196, 1.7672955989837646, 1.0, 0.043137254901960784, 0.5529411764705883, 2.0, 1.0, 0.0, 0.01568627450980392]
+typeLUT.NanColor = [0.0, 1.0, 0.0]
+typeLUT.NumberOfTableValues = 593
+typeLUT.ScalarRangeInitialized = 1.0
+
+# get opacity transfer function/opacity map for 'type'
+typePWF = GetOpacityTransferFunction('type')
+typePWF.Points = [1.0, 1.0, 0.5, 0.0, 1.2830188274383545, 1.0, 0.5, 0.0, 1.4654088020324707, 1.0, 0.5, 0.0, 1.6289308071136475, 1.0, 0.5, 0.0, 1.7987420558929443, 0.9926470518112183, 0.5, 0.0, 2.0, 1.0, 0.5, 0.0]
+typePWF.ScalarRangeInitialized = 1
+
+# trace defaults for the display properties.
+windvtkDisplay.Representation = 'Points'
+windvtkDisplay.ColorArrayName = ['POINTS', 'type']
+windvtkDisplay.LookupTable = typeLUT
+windvtkDisplay.PointSize = 3.0
+windvtkDisplay.OSPRayScaleArray = 'type'
+windvtkDisplay.OSPRayScaleFunction = 'PiecewiseFunction'
+windvtkDisplay.SelectOrientationVectors = 'None'
+windvtkDisplay.ScaleFactor = 0.9
+windvtkDisplay.SelectScaleArray = 'type'
+windvtkDisplay.GlyphType = 'Arrow'
+windvtkDisplay.GlyphTableIndexArray = 'type'
+windvtkDisplay.GaussianRadius = 0.045
+windvtkDisplay.SetScaleArray = ['POINTS', 'type']
+windvtkDisplay.ScaleTransferFunction = 'PiecewiseFunction'
+windvtkDisplay.OpacityArray = ['POINTS', 'type']
+windvtkDisplay.OpacityTransferFunction = 'PiecewiseFunction'
+windvtkDisplay.DataAxesGrid = 'GridAxesRepresentation'
+windvtkDisplay.PolarAxes = 'PolarAxesRepresentation'
+windvtkDisplay.ScalarOpacityFunction = typePWF
+windvtkDisplay.ScalarOpacityUnitDistance = 0.08660254037844385
+
+# init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+windvtkDisplay.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+windvtkDisplay.ScaleTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+windvtkDisplay.OpacityTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+# setup the color legend parameters for each legend in this view
+
+# get color legend/bar for typeLUT in view renderView1
+typeLUTColorBar = GetScalarBar(typeLUT, renderView1)
+typeLUTColorBar.Position = [0.8796680497925311, 0.01509433962264151]
+typeLUTColorBar.Title = 'type'
+typeLUTColorBar.ComponentTitle = ''
+
+# set color bar visibility
+typeLUTColorBar.Visibility = 1
+
+# show color legend
+windvtkDisplay.SetScalarBarVisibility(renderView1, True)
+
+# ----------------------------------------------------------------
+# setup color maps and opacity mapes used in the visualization
+# note: the Get..() functions create a new object, if needed
+# ----------------------------------------------------------------
+
+# ----------------------------------------------------------------
+# finally, restore active source
+SetActiveSource(windvtk)
+# ----------------------------------------------------------------
\ No newline at end of file
diff --git a/Matlab-Programs/T.py b/Matlab-Programs/T.py
new file mode 100644
index 0000000000000000000000000000000000000000..f11e8a74f1a62a95609d2d7bde392153dc38e291
--- /dev/null
+++ b/Matlab-Programs/T.py
@@ -0,0 +1,139 @@
+# state file generated using paraview version 5.7.0
+
+# ----------------------------------------------------------------
+# setup views used in the visualization
+# ----------------------------------------------------------------
+
+# trace generated using paraview version 5.7.0
+#
+# To ensure correct image size when batch processing, please search 
+# for and uncomment the line `# renderView*.ViewSize = [*,*]`
+
+#### import the simple module from the paraview
+from paraview.simple import *
+#### disable automatic camera reset on 'Show'
+paraview.simple._DisableFirstRenderCameraReset()
+
+# Create a new 'Render View'
+renderView1 = CreateView('RenderView')
+renderView1.ViewSize = [901, 795]
+renderView1.AxesGrid = 'GridAxes3DActor'
+renderView1.CenterOfRotation = [0.22986745834350586, 0.03941011428833008, 0.17028677463531494]
+renderView1.StereoType = 'Crystal Eyes'
+renderView1.CameraPosition = [53.44770716226582, -21.61022632014142, -4.102774671003825]
+renderView1.CameraFocalPoint = [0.22986745834350583, 0.039410114288330106, 0.17028677463531497]
+renderView1.CameraViewUp = [-0.28235039193869665, -0.7988816556360265, 0.531099196441028]
+renderView1.CameraFocalDisk = 1.0
+renderView1.CameraParallelScale = 5.748834779828519
+renderView1.Background = [0.32, 0.34, 0.43]
+
+SetActiveView(None)
+
+# ----------------------------------------------------------------
+# setup view layouts
+# ----------------------------------------------------------------
+
+# create new layout object 'Layout #1'
+layout1 = CreateLayout(name='Layout #1')
+layout1.AssignView(0, renderView1)
+
+# ----------------------------------------------------------------
+# restore active view
+SetActiveView(renderView1)
+# ----------------------------------------------------------------
+
+# ----------------------------------------------------------------
+# setup the data processing pipelines
+# ----------------------------------------------------------------
+
+# create a new 'Legacy VTK Reader'
+matlab_exportvtk = LegacyVTKReader(FileNames=['/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/matlab_export.vtk'])
+
+# create a new 'Legacy VTK Reader'
+pointSetvtk = LegacyVTKReader(FileNames=['/home/klaus/Desktop/Paraview-Data/ParaView-v5.9.0/Testing/Data/pointSet.vtk'])
+
+# ----------------------------------------------------------------
+# setup the visualization in view 'renderView1'
+# ----------------------------------------------------------------
+
+# show data from pointSetvtk
+pointSetvtkDisplay = Show(pointSetvtk, renderView1)
+
+# get color transfer function/color map for 'RandomPointScalars'
+randomPointScalarsLUT = GetColorTransferFunction('RandomPointScalars')
+randomPointScalarsLUT.RGBPoints = [2.0, 0.231373, 0.298039, 0.752941, 5.5, 0.865003, 0.865003, 0.865003, 9.0, 0.705882, 0.0156863, 0.14902]
+randomPointScalarsLUT.ScalarRangeInitialized = 1.0
+
+# trace defaults for the display properties.
+pointSetvtkDisplay.Representation = 'Points'
+pointSetvtkDisplay.ColorArrayName = ['POINTS', 'RandomPointScalars']
+pointSetvtkDisplay.LookupTable = randomPointScalarsLUT
+pointSetvtkDisplay.RenderPointsAsSpheres = 1
+pointSetvtkDisplay.OSPRayScaleArray = 'RandomPointScalars'
+pointSetvtkDisplay.OSPRayScaleFunction = 'PiecewiseFunction'
+pointSetvtkDisplay.SelectOrientationVectors = 'RandomCellVectors'
+pointSetvtkDisplay.ScaleFactor = 0.7009325742721558
+pointSetvtkDisplay.SelectScaleArray = 'RandomPointScalars'
+pointSetvtkDisplay.GlyphType = 'Arrow'
+pointSetvtkDisplay.GlyphTableIndexArray = 'RandomPointScalars'
+pointSetvtkDisplay.GaussianRadius = 0.03504662871360779
+pointSetvtkDisplay.SetScaleArray = ['POINTS', 'RandomPointScalars']
+pointSetvtkDisplay.ScaleTransferFunction = 'PiecewiseFunction'
+pointSetvtkDisplay.OpacityArray = ['POINTS', 'RandomPointScalars']
+pointSetvtkDisplay.OpacityTransferFunction = 'PiecewiseFunction'
+pointSetvtkDisplay.DataAxesGrid = 'GridAxesRepresentation'
+pointSetvtkDisplay.PolarAxes = 'PolarAxesRepresentation'
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+pointSetvtkDisplay.ScaleTransferFunction.Points = [2.0, 0.0, 0.5, 0.0, 9.0, 1.0, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+pointSetvtkDisplay.OpacityTransferFunction.Points = [2.0, 0.0, 0.5, 0.0, 9.0, 1.0, 0.5, 0.0]
+
+# show data from matlab_exportvtk
+matlab_exportvtkDisplay = Show(matlab_exportvtk, renderView1)
+
+# trace defaults for the display properties.
+matlab_exportvtkDisplay.Representation = 'Surface With Edges'
+matlab_exportvtkDisplay.ColorArrayName = [None, '']
+matlab_exportvtkDisplay.OSPRayScaleFunction = 'PiecewiseFunction'
+matlab_exportvtkDisplay.SelectOrientationVectors = 'None'
+matlab_exportvtkDisplay.ScaleFactor = 9.9
+matlab_exportvtkDisplay.SelectScaleArray = 'None'
+matlab_exportvtkDisplay.GlyphType = 'Arrow'
+matlab_exportvtkDisplay.GlyphTableIndexArray = 'None'
+matlab_exportvtkDisplay.GaussianRadius = 0.495
+matlab_exportvtkDisplay.SetScaleArray = [None, '']
+matlab_exportvtkDisplay.ScaleTransferFunction = 'PiecewiseFunction'
+matlab_exportvtkDisplay.OpacityArray = [None, '']
+matlab_exportvtkDisplay.OpacityTransferFunction = 'PiecewiseFunction'
+matlab_exportvtkDisplay.DataAxesGrid = 'GridAxesRepresentation'
+matlab_exportvtkDisplay.PolarAxes = 'PolarAxesRepresentation'
+
+# setup the color legend parameters for each legend in this view
+
+# get color legend/bar for randomPointScalarsLUT in view renderView1
+randomPointScalarsLUTColorBar = GetScalarBar(randomPointScalarsLUT, renderView1)
+randomPointScalarsLUTColorBar.Title = 'RandomPointScalars'
+randomPointScalarsLUTColorBar.ComponentTitle = ''
+
+# set color bar visibility
+randomPointScalarsLUTColorBar.Visibility = 1
+
+# show color legend
+pointSetvtkDisplay.SetScalarBarVisibility(renderView1, True)
+
+# ----------------------------------------------------------------
+# setup color maps and opacity mapes used in the visualization
+# note: the Get..() functions create a new object, if needed
+# ----------------------------------------------------------------
+
+# get opacity transfer function/opacity map for 'RandomPointScalars'
+randomPointScalarsPWF = GetOpacityTransferFunction('RandomPointScalars')
+randomPointScalarsPWF.Points = [2.0, 0.0, 0.5, 0.0, 9.0, 1.0, 0.5, 0.0]
+randomPointScalarsPWF.ScalarRangeInitialized = 1
+
+# ----------------------------------------------------------------
+# finally, restore active source
+SetActiveSource(matlab_exportvtk)
+# ----------------------------------------------------------------
\ No newline at end of file
diff --git a/Matlab-Programs/TestWriteVTK.m b/Matlab-Programs/TestWriteVTK.m
new file mode 100644
index 0000000000000000000000000000000000000000..acc61eee7a7b8af28c7499faa3ce8f1e23db6efc
--- /dev/null
+++ b/Matlab-Programs/TestWriteVTK.m
@@ -0,0 +1,87 @@
+
+
+x = 1:0.05:10;
+y = 1:0.05:10;
+z = 1:0.05:10;
+
+
+
+[X,Y,Z] = meshgrid(x,y,z);
+
+
+s = size(X,1);
+
+
+% A1 = repmat(1,size,3);
+% A2 = repmat(2,size,3);
+% A3 = rand(size,4)+ones(size,4);
+% % A3 = repmat(2,10,4);
+
+
+A1 = repmat(1,s,50);
+A2 = repmat(2,s,50);
+A3 = rand(s,81)+ones(s,81);
+% A3 = repmat(2,10,4);
+
+
+A  = [A1 A3 A2];
+B  = repmat(A,1,1,s);
+
+
+vtkwrite('wind.vtk', 'structured_grid', X,Y,Z, 'scalars', 'type', B);
+
+
+
+% INPUT Parameters
+mu_1 = 1;
+rho_1 = 1;
+theta = 0.05; 
+alpha = 25; 
+beta= 20;
+
+set_mu_gamma = 'q1';
+% set_mu_gamma = 'q2';
+print_output= false;
+
+x = linspace(0,10,30);     %~alpha   % most interesting area for alpha >= 0 
+% y = linspace(0.05,100,121);     %~beta
+y = linspace(2,10,10);     %~beta %TEST
+y = 2;   % 2D Phase Diagram
+z = linspace(0.01,0.99,30);  %~theta              %theta = 0 , 1  -> parabolic case
+[X,Y,Z] = meshgrid(x,y,z);
+
+
+[A,angle_3D,V_3D,~] = arrayfun(@(a,b,theta)classifyMIN(mu_1,rho_1,a,b,theta,set_mu_gamma,print_output),X,Y,Z,'UniformOutput', false);
+
+
+angle_3D = cell2mat(angle_3D);
+V_3D = cell2mat(V_3D);
+
+vtkwrite('PhaseDiagram.vtk', 'structured_grid', X,Y,Z, 'scalars', 'type',angle_3D);
+
+vtkwrite('PhaseDiagramType.vtk', 'structured_grid', X,Y,Z, 'scalars', 'type',V_3D);
+
+
+
+% 2D Phase Diagram:
+% fix parameter (beta here) 
+% beta= 5;
+% 
+% x = linspace(-50,50,121);     %~alpha
+% z = linspace(0.01,0.99,121);  %~theta              %theta = 0 , 1  -> parabolic case
+% [X,Z] = meshgrid(x,z);
+% 
+% [A,angle_2D,V_2D,~] = arrayfun(@(a,theta)classifyMIN(mu_1,rho_1,a,beta,theta,set_mu_gamma,print_output),X,Z,'UniformOutput', false);
+% 
+% angle_2D = cell2mat(angle_2D);
+% V_2D = cell2mat(V_2D);
+% 
+
+% Y = ones(size(X))*beta;
+% vtkwrite('PhaseDiagram2D.vtk', 'structured_grid', X,Y,Z, 'scalars', 'type',angle_2D);
+% 
+% vtkwrite('PhaseDiagramType2D.vtk', 'structured_grid', X,Y,Z, 'scalars', 'type',V_2D);
+
+
+
+
diff --git a/Matlab-Programs/compute_r.m b/Matlab-Programs/compute_r.m
new file mode 100644
index 0000000000000000000000000000000000000000..223b470b2242cfd42c9364c269ebf20d5033d5d9
--- /dev/null
+++ b/Matlab-Programs/compute_r.m
@@ -0,0 +1,25 @@
+function r = compute_r(alpha,B,q1,q2,q3)
+
+% r = compute_r(alpha,B,q1,q2,q3);
+
+v = [cos(alpha);sin(alpha)];
+
+b1 = B(1,1);
+b2 = B(2,2);
+b3 = B(1,2);
+
+%compute Q(v_alpha x v_alpha)
+Q = q1.*v(1).^4 + q2.*v(2).^4 + 2.*q3.*v(1).^2.*v(2).^2;
+
+
+tmp1 = q1.*(v(1).^2+b1).^2 + q2.*(v(2).^2+b2).^2 + q3.*(sqrt(2)*v(1)*v(2)+b3).^2;
+tmp2 = q1.*b1.^2 + q2.*b2.^2+ q3.*b3.^2;
+L = 0.5*(tmp1-Q-tmp2) ;       %Polarization identity 
+
+r = L./Q;
+
+
+
+
+end
+
diff --git a/Matlab-Programs/findParabolic.m b/Matlab-Programs/findParabolic.m
new file mode 100644
index 0000000000000000000000000000000000000000..950130c1e4f0eac3c33ff388abd7b943ea2218bb
--- /dev/null
+++ b/Matlab-Programs/findParabolic.m
@@ -0,0 +1,95 @@
+
+
+syms f(alpha,beta,theta)
+syms b1(alpha,beta,theta)
+syms b2(alpha,beta,theta)
+syms q1(beta,theta)
+syms q2(beta,theta)
+
+mu_1 = sym(1);
+rho_1 = sym(1);
+
+%TEST (new)
+b1(alpha,beta,theta) = (3*rho_1/2).*beta.*(1-theta.*(1+alpha));
+b2(alpha,beta,theta) = (3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha));
+
+q1(beta,theta) = mu_1.*(beta./(theta+(1-theta).*beta)) ;
+q2(beta,theta) = mu_1.*((1-theta)+theta.*beta); 
+
+
+
+fprintf('Functions to be minimized')
+% f(beta,theta,alpha) = (mu_1.*(beta./(theta+(1-theta).*beta))).*((3*rho_1/2).*beta.*(1-theta.*(1+alpha))).^2 - (mu_1.*((1-theta)+theta.*beta)).*(3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha)).^2;
+f(beta,theta,alpha) = q1(beta,theta).*b1(alpha,beta,theta).^2 - (q2(beta,theta).*b2(alpha,beta,theta).^2) ;
+
+% Fix Theta ... 
+thetav = sym(1/2);
+f = subs(f,theta,thetav);
+b1 = subs(b1,theta,thetav);
+b2 = subs(b2,theta,thetav);
+q1 = subs(q1,theta,thetav);
+q2 = subs(q2,theta,thetav);
+
+
+
+% f = subs(f,theta,0.25);
+% b1 = subs(b1,theta,0.25);
+% b2 = subs(b2,theta,0.25);
+% q1 = subs(q1,theta,0.25);
+% q2 = subs(q2,theta,0.25);
+
+
+
+% f = subs(f,alpha,3);
+
+
+eq = f == 0;
+
+
+S = solve(eq,alpha, beta,'MaxDegree' , 5)
+% S = solve(eq,alpha, beta,theta,'MaxDegree' , 5)
+
+S.alpha
+S.beta
+
+
+% CHECK
+b1 = subs(b1,alpha,S.alpha(1));
+b1 = subs(b1,beta,S.beta(1));
+b2 = subs(b2,alpha,S.alpha(1));
+b2 = subs(b2,beta,S.beta(1));
+
+q1 = subs(q1,beta,S.beta(1));
+q2 = subs(q2,beta,S.beta(1));
+
+b1 = double(b1)
+b2 = double(b2)
+q1 = double(q1)
+q2 = double(q2)
+
+
+b1.*((q1).^2)- ( b2.*(q2.^2)) 
+
+
+
+f = subs(f,alpha,S.alpha(1));
+f = subs(f,beta,S.beta(1))
+simplify(f)
+
+
+% 
+% 
+% mu_h = @(beta,theta) mu_1.*(beta./(theta+(1-theta).*beta));  % harmonic mean
+% mu_bar = @(b,t) mu_1.*((1-theta)+theta.*beta);     % mu_bar
+% 
+% 
+% 
+% %  q1 q2 q3..
+% q1 = mu_h(beta,theta);
+% q2 = mu_bar(beta,theta); 
+
+
+
+fprintf('--------------------')
+
+
diff --git a/Matlab-Programs/findParameters.m b/Matlab-Programs/findParameters.m
new file mode 100644
index 0000000000000000000000000000000000000000..b024d927699fc6c3e4de7967b582e32feaad7ecc
--- /dev/null
+++ b/Matlab-Programs/findParameters.m
@@ -0,0 +1,156 @@
+
+
+
+syms alpha beta theta rho_1 mu_1 
+assume(beta,'positive')
+assume(theta,'positive')
+assume(mu_1,'positive')
+assume(rho_1,'positive')
+
+% syms f(alpha,beta,theta)
+% syms b1(alpha,beta,theta)
+% syms b2(alpha,beta,theta)
+% syms q1(beta,theta)
+% syms q2(beta,theta)
+
+% mu_1 = sym(1);
+% rho_1 = sym(1);
+
+%TEST (new)
+b1(alpha,beta,theta,rho_1) = (3*rho_1/2).*beta.*(1-theta.*(1+alpha));
+b2(alpha,beta,theta,rho_1) = (3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha));
+
+
+
+
+q1(beta,theta,mu_1) = mu_1.*(beta./(theta+(1-theta).*beta)) ;
+q2(beta,theta,mu_1) = mu_1.*((1-theta)+theta.*beta); 
+q3_star(beta,theta,mu_1) = (q1(beta,theta,mu_1)*q2(beta,theta,mu_1))^(1/2)
+
+% 
+% fprintf('Functions to be minimized')
+% % f(beta,theta,alpha) = (mu_1.*(beta./(theta+(1-theta).*beta))).*((3*rho_1/2).*beta.*(1-theta.*(1+alpha))).^2 - (mu_1.*((1-theta)+theta.*beta)).*(3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha)).^2;
+% f(beta,theta,alpha) = q1(beta,theta).*b1(alpha,beta,theta).^2 - (q2(beta,theta).*b2(alpha,beta,theta).^2) ;
+
+% Fix Theta ... 
+% thetav = sym(1/4);
+% q3_star = subs(q3_star,theta,thetav);
+% b1 = subs(b1,theta,thetav);
+% b2 = subs(b2,theta,thetav);
+% q1 = subs(q1,theta,thetav);
+% q2 = subs(q2,theta,thetav);
+
+
+% theta = thetav
+eq1 = (3*rho_1/2).*beta.*(1-theta.*(1+alpha)) == (q1(beta,theta,mu_1)*q2(beta,theta,mu_1))^(1/2)
+
+eq2 = (3*rho_1/(4*((1-theta)+theta.*beta))).*(1-theta.*(1+beta.*alpha)) == mu_1.*(beta./(theta+(1-theta).*beta)) 
+
+eqns = [eq1, eq2] 
+
+% eqns = subs(eqns,{theta,alpha,rho_1},{1/20,2,1} ) % works! 
+% eqns = subs(eqns,{rho_1,alpha,theta},{1,2,1/4} )
+eqns = subs(eqns,{theta},{1/4} )                        % fix only theta...
+% eqns = subs(eqns,{theta,mu_1,rho_1},{1/4,10,1} )
+
+
+% eqns = subs(eqns,{mu_1,beta},{387/1250,7741/10000} )
+% simplify(eqns)
+
+% eqns = subs(eqns,{theta,mu_1,rho_1},{1/4,10,5} )
+% eqns = subs(eqns,beta,2.0)
+
+% S = solve(eqns,mu_1,beta,'MaxDegree' , 5)
+% S = solve(eqns,theta,beta,'MaxDegree' , 5)
+% S = solve(eqns,theta,mu_1,'MaxDegree' , 5)
+
+
+%interesting:
+% eqns = subs(eqns,{theta,alpha,rho_1},{1/20,2,1} )
+% S = solve(eqns,mu_1,beta,'MaxDegree' , 5)
+
+
+% S.mu_1
+% S.beta
+% double(S.mu_1)
+% double(S.beta)
+% 
+% 
+% eqns = subs(eqns,{mu_1,beta},{0.3096,0.7741} )
+% simplify(eqns)
+
+
+S = solve(eqns, alpha,beta, rho_1,mu_1, 'MaxDegree' , 5)
+% S = solve(eqns, mu_1,beta, 'MaxDegree' , 5)
+
+% S = solve(eqns, alpha, beta, 'MaxDegree' , 5)
+
+S.alpha
+S.beta
+double(S.alpha)
+double(S.beta)
+
+eqns = subs(eqns,{alpha,beta},{95.2970,0.1577} )
+% simplify(eqns)
+
+
+% f = subs(f,theta,0.25);
+% b1 = subs(b1,theta,0.25);
+% b2 = subs(b2,theta,0.25);
+% q1 = subs(q1,theta,0.25);
+% q2 = subs(q2,theta,0.25);
+
+
+
+% f = subs(f,alpha,3);
+
+
+
+
+% S = solve(eq,alpha, beta,'MaxDegree' , 5)
+% S = solve(eq,alpha, beta,theta,'MaxDegree' , 5)
+
+% % S.alpha
+% S.beta
+% % 
+% 
+% % CHECK
+% b1 = subs(b1,alpha,S.alpha(1));
+% b1 = subs(b1,beta,S.beta(1));
+% b2 = subs(b2,alpha,S.alpha(1));
+% b2 = subs(b2,beta,S.beta(1));
+% 
+% q1 = subs(q1,beta,S.beta(1));
+% q2 = subs(q2,beta,S.beta(1));
+% 
+% b1 = double(b1)
+% b2 = double(b2)
+% q1 = double(q1)
+% q2 = double(q2)
+% 
+% 
+% b1.*((q1).^2)- ( b2.*(q2.^2)) 
+% 
+% 
+% 
+% f = subs(f,alpha,S.alpha(1));
+% f = subs(f,beta,S.beta(1))
+% simplify(f)
+
+
+% 
+% 
+% mu_h = @(beta,theta) mu_1.*(beta./(theta+(1-theta).*beta));  % harmonic mean
+% mu_bar = @(b,t) mu_1.*((1-theta)+theta.*beta);     % mu_bar
+% 
+% 
+% 
+% %  q1 q2 q3..
+% q1 = mu_h(beta,theta);
+% q2 = mu_bar(beta,theta); 
+
+
+
+fprintf('--------------------')
+
+
diff --git a/Matlab-Programs/matlab.txt b/Matlab-Programs/matlab.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2754956c3a6d5adcaf347773a5de4fb188b739d1
--- /dev/null
+++ b/Matlab-Programs/matlab.txt
@@ -0,0 +1,9 @@
+1 1 1.906127239467446
+1 2 -2.84445771411170261e-27
+1 3 1.36674531873130088e-11
+2 1 -1.70707845907209275e-26
+2 2 2.0833333333333246
+2 3 6.44949347783633458e-19
+3 1 2.21186925202339457e-10
+3 2 6.4495181619832732e-19
+3 3 1.92304720901783655
diff --git a/Matlab-Programs/matlab_export.vtk b/Matlab-Programs/matlab_export.vtk
new file mode 100644
index 0000000000000000000000000000000000000000..143166e316abee800986317bf099bc008d11c7ef
--- /dev/null
+++ b/Matlab-Programs/matlab_export.vtk
@@ -0,0 +1,239 @@
+# vtk DataFile Version 2.0
+VTK from Matlab
+ASCII
+DATASET POLYDATA
+POINTS 102 float
+1.00 0.84 1.00 2.00 0.91 1.41 3.00 0.14 1.73 
+4.00 -0.76 2.00 5.00 -0.96 2.24 6.00 -0.28 2.45 
+7.00 0.66 2.65 8.00 0.99 2.83 9.00 0.41 3.00 
+10.00 -0.54 3.16 11.00 -1.00 3.32 12.00 -0.54 3.46 
+13.00 0.42 3.61 14.00 0.99 3.74 15.00 0.65 3.87 
+16.00 -0.29 4.00 17.00 -0.96 4.12 18.00 -0.75 4.24 
+19.00 0.15 4.36 20.00 0.91 4.47 21.00 0.84 4.58 
+22.00 -0.01 4.69 23.00 -0.85 4.80 24.00 -0.91 4.90 
+25.00 -0.13 5.00 26.00 0.76 5.10 27.00 0.96 5.20 
+28.00 0.27 5.29 29.00 -0.66 5.39 30.00 -0.99 5.48 
+31.00 -0.40 5.57 32.00 0.55 5.66 33.00 1.00 5.74 
+34.00 0.53 5.83 35.00 -0.43 5.92 36.00 -0.99 6.00 
+37.00 -0.64 6.08 38.00 0.30 6.16 39.00 0.96 6.24 
+40.00 0.75 6.32 41.00 -0.16 6.40 42.00 -0.92 6.48 
+43.00 -0.83 6.56 44.00 0.02 6.63 45.00 0.85 6.71 
+46.00 0.90 6.78 47.00 0.12 6.86 48.00 -0.77 6.93 
+49.00 -0.95 7.00 50.00 -0.26 7.07 51.00 0.67 7.14 
+52.00 0.99 7.21 53.00 0.40 7.28 54.00 -0.56 7.35 
+55.00 -1.00 7.42 56.00 -0.52 7.48 57.00 0.44 7.55 
+58.00 0.99 7.62 59.00 0.64 7.68 60.00 -0.30 7.75 
+61.00 -0.97 7.81 62.00 -0.74 7.87 63.00 0.17 7.94 
+64.00 0.92 8.00 65.00 0.83 8.06 66.00 -0.03 8.12 
+67.00 -0.86 8.19 68.00 -0.90 8.25 69.00 -0.11 8.31 
+70.00 0.77 8.37 71.00 0.95 8.43 72.00 0.25 8.49 
+73.00 -0.68 8.54 74.00 -0.99 8.60 75.00 -0.39 8.66 
+76.00 0.57 8.72 77.00 1.00 8.77 78.00 0.51 8.83 
+79.00 -0.44 8.89 80.00 -0.99 8.94 81.00 -0.63 9.00 
+82.00 0.31 9.06 83.00 0.97 9.11 84.00 0.73 9.17 
+85.00 -0.18 9.22 86.00 -0.92 9.27 87.00 -0.82 9.33 
+88.00 0.04 9.38 89.00 0.86 9.43 90.00 0.89 9.49 
+91.00 0.11 9.54 92.00 -0.78 9.59 93.00 -0.95 9.64 
+94.00 -0.25 9.70 95.00 0.68 9.75 96.00 0.98 9.80 
+97.00 0.38 9.85 98.00 -0.57 9.90 99.00 -1.00 9.95 
+100.00 -0.51 10.00 0.00 0.00 0.00 0.00 0.00 0.00 
+
+LINES 198 594
+2 0 1
+2 1 2
+2 2 3
+2 3 4
+2 4 5
+2 5 6
+2 6 7
+2 7 8
+2 8 9
+2 9 10
+2 10 11
+2 11 12
+2 12 13
+2 13 14
+2 14 15
+2 15 16
+2 16 17
+2 17 18
+2 18 19
+2 19 20
+2 20 21
+2 21 22
+2 22 23
+2 23 24
+2 24 25
+2 25 26
+2 26 27
+2 27 28
+2 28 29
+2 29 30
+2 30 31
+2 31 32
+2 32 33
+2 33 34
+2 34 35
+2 35 36
+2 36 37
+2 37 38
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+2 39 40
+2 40 41
+2 41 42
+2 42 43
+2 43 44
+2 44 45
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+2 48 49
+2 49 50
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+2 52 53
+2 53 54
+2 54 55
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+2 72 73
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+2 95 96
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+2 98 99
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+2 2 1
+2 3 2
+2 4 3
+2 5 4
+2 6 5
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+2 20 19
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+2 22 21
+2 23 22
+2 24 23
+2 25 24
+2 26 25
+2 27 26
+2 28 27
+2 29 28
+2 30 29
+2 31 30
+2 32 31
+2 33 32
+2 34 33
+2 35 34
+2 36 35
+2 37 36
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+2 39 38
+2 40 39
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+2 43 42
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diff --git a/Matlab-Programs/pathdef.m b/Matlab-Programs/pathdef.m
new file mode 100644
index 0000000000000000000000000000000000000000..e7d1fb7b5bc2951df872c4755608cb7d983653ae
--- /dev/null
+++ b/Matlab-Programs/pathdef.m
@@ -0,0 +1,385 @@
+function p = pathdef
+%PATHDEF Search path defaults.
+%   PATHDEF returns a string that can be used as input to MATLABPATH
+%   in order to set the path.
+
+  
+%   Copyright 1984-2016 The MathWorks, Inc.
+
+
+% DO NOT MODIFY THIS FILE.  IT IS AN AUTOGENERATED FILE.  
+% EDITING MAY CAUSE THE FILE TO BECOME UNREADABLE TO 
+% THE PATHTOOL AND THE INSTALLER.
+
+p = [...
+%%% BEGIN ENTRIES %%%
+     '/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs:', ...
+     '/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/Testfold:', ...
+     '/home/klaus/Desktop/DUNE/dune-microstructure/Matlab-Programs/mynew:', ...
+     matlabroot,'/toolbox/matlab/matfun:', ...
+     matlabroot,'/toolbox/matlab/funfun:', ...
+     matlabroot,'/toolbox/matlab/ops:', ...
+     matlabroot,'/toolbox/matlab/lang:', ...
+     matlabroot,'/toolbox/matlab/datafun:', ...
+     matlabroot,'/toolbox/matlab/capabilities:', ...
+     matlabroot,'/toolbox/matlab/elmat:', ...
+     matlabroot,'/toolbox/matlab/datatypes:', ...
+     matlabroot,'/toolbox/matlab/timefun:', ...
+     matlabroot,'/toolbox/matlab/iofun:', ...
+     matlabroot,'/toolbox/matlab/validators:', ...
+     matlabroot,'/toolbox/matlab/randfun:', ...
+     matlabroot,'/toolbox/matlab/general:', ...
+     matlabroot,'/toolbox/matlab/strfun:', ...
+     matlabroot,'/toolbox/matlab/strfun/validators:', ...
+     matlabroot,'/toolbox/matlab/specfun:', ...
+     matlabroot,'/toolbox/matlab/polyfun:', ...
+     matlabroot,'/toolbox/matlab/sparfun:', ...
+     matlabroot,'/toolbox/matlab/mvm:', ...
+     matlabroot,'/toolbox/matlab/elfun:', ...
+     matlabroot,'/toolbox/matlab/graphics/math:', ...
+     matlabroot,'/toolbox/matlab/strfun/pattern:', ...
+     matlabroot,'/toolbox/matlab/helptools:', ...
+     matlabroot,'/toolbox/matlab/codetools:', ...
+     matlabroot,'/toolbox/matlab/codetools/embeddedoutputs:', ...
+     matlabroot,'/toolbox/matlab/codetools/embeddedoutputs/DataToolsRegistration:', ...
+     matlabroot,'/toolbox/matlab/codetools/liveapps:', ...
+     matlabroot,'/toolbox/matlab/datatools/desktop_workspacebrowser/matlab:', ...
+     matlabroot,'/toolbox/matlab/datatypes/datetime:', ...
+     matlabroot,'/toolbox/matlab/datamanager:', ...
+     matlabroot,'/toolbox/matlab/datatypes/duration:', ...
+     matlabroot,'/toolbox/matlab/testframework/uiautomation:', ...
+     matlabroot,'/toolbox/matlab/parquetio:', ...
+     matlabroot,'/toolbox/matlab/datatypes/codegen/datetime:', ...
+     matlabroot,'/toolbox/matlab/verctrl:', ...
+     matlabroot,'/toolbox/matlab/testframework/performance/core:', ...
+     matlabroot,'/toolbox/matlab/mapreduceio:', ...
+     matlabroot,'/toolbox/matlab/iot/connectivity:', ...
+     matlabroot,'/toolbox/matlab/testframework/ui/toolstrip:', ...
+     matlabroot,'/toolbox/matlab/demos:', ...
+     matlabroot,'/toolbox/matlab/datastoreio:', ...
+     matlabroot,'/toolbox/matlab/datatypes/shared/matlab_datatypes:', ...
+     matlabroot,'/toolbox/matlab/testframework/mock/core:', ...
+     matlabroot,'/toolbox/matlab/bigdata:', ...
+     matlabroot,'/toolbox/matlab/testframework/unittest/ext:', ...
+     matlabroot,'/toolbox/matlab/datatypes/datetime_nonlibmatlab:', ...
+     matlabroot,'/toolbox/matlab/datatypes/codegen/categorical:', ...
+     matlabroot,'/toolbox/matlab/parquetds:', ...
+     matlabroot,'/toolbox/matlab/graph2d:', ...
+     matlabroot,'/toolbox/matlab/graph3d:', ...
+     matlabroot,'/toolbox/matlab/graphics:', ...
+     matlabroot,'/toolbox/matlab/graphics/annotation:', ...
+     matlabroot,'/toolbox/matlab/graphics/axis:', ...
+     matlabroot,'/toolbox/matlab/graphics/chart:', ...
+     matlabroot,'/toolbox/matlab/graphics/color:', ...
+     matlabroot,'/toolbox/matlab/graphics/function:', ...
+     matlabroot,'/toolbox/matlab/graphics/illustration:', ...
+     matlabroot,'/toolbox/matlab/graphics/legacy:', ...
+     matlabroot,'/toolbox/matlab/graphics/obsolete:', ...
+     matlabroot,'/toolbox/matlab/graphics/printing:', ...
+     matlabroot,'/toolbox/matlab/graphics/objectsystem:', ...
+     matlabroot,'/toolbox/matlab/graphics/primitive:', ...
+     matlabroot,'/toolbox/matlab/plottools:', ...
+     matlabroot,'/toolbox/matlab/scribe:', ...
+     matlabroot,'/toolbox/matlab/scribe/obsolete:', ...
+     matlabroot,'/toolbox/matlab/specgraph:', ...
+     matlabroot,'/toolbox/matlab/uitools:', ...
+     matlabroot,'/toolbox/matlab/uitools/obsolete:', ...
+     matlabroot,'/toolbox/matlab/maps:', ...
+     matlabroot,'/toolbox/matlab/graphics/maps:', ...
+     matlabroot,'/toolbox/matlab/network:', ...
+     matlabroot,'/toolbox/matlab/io/functions:', ...
+     matlabroot,'/toolbox/matlab/guide:', ...
+     matlabroot,'/toolbox/matlab/testframework/measurement/ext:', ...
+     matlabroot,'/toolbox/matlab/matlab_preferences/matlab:', ...
+     matlabroot,'/toolbox/matlab/graphfun:', ...
+     matlabroot,'/toolbox/local:', ...
+     matlabroot,'/toolbox/matlab/io/spreadsheet:', ...
+     matlabroot,'/toolbox/matlab/datatools/desktop_variableeditor/matlab:', ...
+     matlabroot,'/toolbox/matlab/io/ftp:', ...
+     matlabroot,'/toolbox/matlab/datatypes/tabular:', ...
+     matlabroot,'/toolbox/matlab/testframework/unittest/core:', ...
+     matlabroot,'/toolbox/matlab/testframework/obsolete:', ...
+     matlabroot,'/toolbox/matlab/images:', ...
+     matlabroot,'/toolbox/matlab/dataui:', ...
+     matlabroot,'/toolbox/matlab/io/datastore/array:', ...
+     matlabroot,'/toolbox/matlab/urlmanager:', ...
+     matlabroot,'/toolbox/matlab/datatypes/shared/codegen:', ...
+     matlabroot,'/toolbox/matlab/datatypes/codegen/duration:', ...
+     matlabroot,'/toolbox/matlab/plottools/inspector:', ...
+     matlabroot,'/toolbox/matlab/datatypes/categorical:', ...
+     matlabroot,'/toolbox/matlab/datatypes/codegen/tabular:', ...
+     matlabroot,'/toolbox/matlab/io/archive:', ...
+     matlabroot,'/toolbox/matlab/icons:', ...
+     matlabroot,'/toolbox/matlab/testframework/measurement/core:', ...
+     matlabroot,'/toolbox/matlab/datatypes/calendarDuration:', ...
+     matlabroot,'/toolbox/matlab/winfun:', ...
+     matlabroot,'/toolbox/matlab/winfun/NET:', ...
+     matlabroot,'/toolbox/matlab/optimfun:', ...
+     matlabroot,'/toolbox/matlab/iot:', ...
+     matlabroot,'/toolbox/matlab/io/xml:', ...
+     matlabroot,'/toolbox/matlab/parallel:', ...
+     matlabroot,'/toolbox/matlab/testframework/uitest:', ...
+     matlabroot,'/toolbox/matlab/testframework/performance/ext:', ...
+     matlabroot,'/toolbox/matlab/depfun:', ...
+     matlabroot,'/toolbox/matlab/graphics/hg:', ...
+     matlabroot,'/toolbox/matlab/hardware/stubs:', ...
+     matlabroot,'/toolbox/matlab/codeanalysis/reports/analysis:', ...
+     matlabroot,'/toolbox/matlab/io/text:', ...
+     matlabroot,'/toolbox/shared/stateflow:', ...
+     matlabroot,'/toolbox/optim/problemdef:', ...
+     matlabroot,'/toolbox/matlab/pathtool:', ...
+     matlabroot,'/toolbox/shared/pdelib:', ...
+     matlabroot,'/toolbox/matlab/registration_framework/matlab:', ...
+     matlabroot,'/toolbox/shared/multimedia:', ...
+     matlabroot,'/toolbox/shared/simulink:', ...
+     matlabroot,'/toolbox/matlab/serialport:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_java_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/embeddedoutputs/figureoutputs:', ...
+     matlabroot,'/toolbox/shared/imageio:', ...
+     matlabroot,'/toolbox/matlab/toolboxmanagement/matlab_api:', ...
+     matlabroot,'/toolbox/shared/controllib/general:', ...
+     matlabroot,'/toolbox/matlab/imagesci:', ...
+     matlabroot,'/toolbox/matlab/addons_product:', ...
+     matlabroot,'/toolbox/pde:', ...
+     matlabroot,'/toolbox/pde/pdedata:', ...
+     matlabroot,'/toolbox/shared/testmeaslib/general:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/fop:', ...
+     matlabroot,'/toolbox/matlab/storage/matlabdrive:', ...
+     matlabroot,'/toolbox/matlab/profileviewer:', ...
+     matlabroot,'/examples/globaloptim/data:', ...
+     matlabroot,'/toolbox/shared/hwmanager/logger:', ...
+     matlabroot,'/toolbox/matlab/datatools/workspacebrowser/matlab:', ...
+     matlabroot,'/ui/mw-webwindow/mw-webwindow-m:', ...
+     matlabroot,'/toolbox/shared/datacreation:', ...
+     matlabroot,'/toolbox/shared/datacreation/task:', ...
+     matlabroot,'/toolbox/shared/datacreation/task/codegenerator:', ...
+     matlabroot,'/toolbox/shared/datacreation/task/interface:', ...
+     matlabroot,'/toolbox/shared/datacreation/task/ui:', ...
+     matlabroot,'/toolbox/shared/datacreation/uicomponent:', ...
+     matlabroot,'/toolbox/shared/datacreation/datagenerator:', ...
+     matlabroot,'/toolbox/matlab/timeseries:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/dom:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/dom/dom:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/dom/dom/help:', ...
+     matlabroot,'/toolbox/shared/cmlink/matlab:', ...
+     matlabroot,'/toolbox/matlab/datatools/importtool/matlab/peer:', ...
+     matlabroot,'/toolbox/shared/blelib:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/utils:', ...
+     matlabroot,'/toolbox/matlab/appdesigner/appdesigner/runtime:', ...
+     matlabroot,'/toolbox/hdlcoder/hdllib/ml_lib:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/webservices/wsdl:', ...
+     matlabroot,'/toolbox/matlab/reports:', ...
+     matlabroot,'/toolbox/matlab/datatools/datatoolsservices/matlab:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/xml_xpath/xml_xpath/help:', ...
+     matlabroot,'/toolbox/shared/testmeaslib/graphics:', ...
+     matlabroot,'/toolbox/shared/controllib/graphics:', ...
+     matlabroot,'/toolbox/shared/controllib/graphics/utils:', ...
+     matlabroot,'/toolbox/shared/controllib/graphics/plotoptions:', ...
+     matlabroot,'/toolbox/matlab/datatools/peermodel_mcos/matlab:', ...
+     matlabroot,'/toolbox/coder/coderapp/utils/ml:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_vhdl_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/project/views/util:', ...
+     matlabroot,'/toolbox/shared/advisor:', ...
+     matlabroot,'/toolbox/matlab/connector2/logger:', ...
+     matlabroot,'/toolbox/shared/coder/coder:', ...
+     matlabroot,'/toolbox/shared/coder/coder/gpucoder:', ...
+     matlabroot,'/toolbox/shared/coder/reportinfo:', ...
+     matlabroot,'/toolbox/shared/coder/coder/lib:', ...
+     matlabroot,'/toolbox/matlab/connector2/interpreter:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents/plugin/appdesigner:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_tlc_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/datatools/inspector/matlab:', ...
+     matlabroot,'/toolbox/matlab/datatools/inspector/registration:', ...
+     matlabroot,'/toolbox/shared/instrument:', ...
+     matlabroot,'/toolbox/diagram/layout/treelayout:', ...
+     matlabroot,'/toolbox/matlab/helptools_js/matlab_colon_docservice/m:', ...
+     matlabroot,'/toolbox/shared/asynciolib:', ...
+     matlabroot,'/toolbox/matlab/dependency/widget/window:', ...
+     matlabroot,'/toolbox/shared/diagnostic:', ...
+     matlabroot,'/toolbox/matlab/appdesigner/matlab_integration/cfb/cfb:', ...
+     matlabroot,'/toolbox/shared/codergui/codergui:', ...
+     matlabroot,'/toolbox/shared/cxxfe/parser_mi/parser_mi:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents/graphics:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents/style:', ...
+     matlabroot,'/examples/graphics/data:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwconnection:', ...
+     matlabroot,'/toolbox/matlab/system/editor:', ...
+     matlabroot,'/toolbox/globaloptim/globaloptimdemos:', ...
+     matlabroot,'/examples/symbolic/data:', ...
+     matlabroot,'/toolbox/matlab/embeddedoutputs/outpututilities:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_xml_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/connector2/mgg:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/devicedetection:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/devices:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/providers:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/plugins:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/hwsetup:', ...
+     matlabroot,'/toolbox/shared/spreadsheet:', ...
+     matlabroot,'/toolbox/matlab/addons_registry/matlab:', ...
+     matlabroot,'/toolbox/matlab/toolstrip:', ...
+     matlabroot,'/toolbox/matlab/addon_enable_disable_management/matlab:', ...
+     matlabroot,'/toolbox/coder/coderapp/common/ml:', ...
+     matlabroot,'/toolbox/shared/comparisons:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/webservices/restful:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/webservices:', ...
+     matlabroot,'/toolbox/matlab/appdesigner/appdesigner/interface:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/widgets/equation/matlab:', ...
+     matlabroot,'/toolbox/matlab/addons:', ...
+     matlabroot,'/toolbox/matlab/addons/cef:', ...
+     matlabroot,'/toolbox/matlab/addons/fileexchange:', ...
+     matlabroot,'/toolbox/matlab/addons/supportpackages:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwmanagerapp/devicedata:', ...
+     matlabroot,'/toolbox/matlab/connector2/editor:', ...
+     matlabroot,'/toolbox/shared/io/general:', ...
+     matlabroot,'/toolbox/matlab/external/engines/engine_api:', ...
+     matlabroot,'/toolbox/pde/pdedemos:', ...
+     matlabroot,'/toolbox/symbolic/symbolic:', ...
+     matlabroot,'/toolbox/symbolic/graphics:', ...
+     matlabroot,'/toolbox/symbolic/validators:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/python:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/cpp:', ...
+     matlabroot,'/toolbox/matlab/ddux:', ...
+     matlabroot,'/toolbox/symbolic/symbolicdemos:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_js_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/connector2/messageservice:', ...
+     matlabroot,'/examples/antenna/data:', ...
+     matlabroot,'/toolbox/matlab/external/mex:', ...
+     matlabroot,'/toolbox/globaloptim:', ...
+     matlabroot,'/toolbox/globaloptim/globaloptim:', ...
+     matlabroot,'/toolbox/matlab/filebrowser_actions/default_actions/matlab:', ...
+     matlabroot,'/toolbox/matlab/filebrowser_actions/layout_actions/matlab:', ...
+     matlabroot,'/toolbox/matlab/filebrowser_actions/sharing_actions/matlab:', ...
+     matlabroot,'/toolbox/matlab/connector2/nativebridge:', ...
+     matlabroot,'/toolbox/matlab/cefclient:', ...
+     matlabroot,'/toolbox/matlab/addressbar_plugins/browse_for_folder_button/matlab:', ...
+     matlabroot,'/toolbox/matlab/addressbar_plugins/cd_up_one_dir_button/matlab:', ...
+     matlabroot,'/examples/matlabmobile/data:', ...
+     matlabroot,'/toolbox/matlab/connector2/shadowfiles:', ...
+     matlabroot,'/toolbox/shared/supportpkgservices/legacysupportpkginfo:', ...
+     matlabroot,'/toolbox/shared/supportpkgservices/installservices:', ...
+     matlabroot,'/toolbox/shared/supportpkgservices/supportpackageroot:', ...
+     matlabroot,'/toolbox/shared/supportpkgservices/installedapi:', ...
+     matlabroot,'/toolbox/shared/surrogatelib:', ...
+     matlabroot,'/toolbox/shared/deviceplugindetection:', ...
+     matlabroot,'/examples/optim/data:', ...
+     matlabroot,'/toolbox/matlab/addon_updates/matlab:', ...
+     matlabroot,'/toolbox/shared/template_core:', ...
+     matlabroot,'/toolbox/shared/hwconnectinstaller/common:', ...
+     matlabroot,'/toolbox/matlab/dependency/refactoring:', ...
+     matlabroot,'/examples/matlab/data:', ...
+     matlabroot,'/toolbox/matlab/system:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/xml_transform/xml_transform/help:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwservices/hwinfo:', ...
+     matlabroot,'/toolbox/matlab/networklib:', ...
+     matlabroot,'/toolbox/matlab/project/dependency:', ...
+     matlabroot,'/toolbox/shared/polyspace:', ...
+     matlabroot,'/toolbox/matlab/updateinstaller:', ...
+     matlabroot,'/toolbox/comparisons/view/edits:', ...
+     matlabroot,'/toolbox/matlab/datatools/editorconverters/matlab:', ...
+     matlabroot,'/toolbox/matlab/supportpackagemanagement:', ...
+     matlabroot,'/toolbox/matlab/connector2/connector:', ...
+     matlabroot,'/toolbox/shared/mldatx:', ...
+     matlabroot,'/toolbox/matlab/project/views/action_web/project-action-ui/matlab:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/json:', ...
+     matlabroot,'/toolbox/matlab/toolbox_packaging:', ...
+     matlabroot,'/toolbox/matlab/connector2/restmatlab:', ...
+     matlabroot,'/toolbox/shared/hotpluglib:', ...
+     matlabroot,'/toolbox/matlab/filebrowser:', ...
+     matlabroot,'/toolbox/matlab/datatools/variableeditor/matlab:', ...
+     matlabroot,'/toolbox/matlab/debugger:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/ppt:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/ppt/ppt:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/ppt/ppt/help:', ...
+     matlabroot,'/toolbox/rptgen/xmlcomp:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/xml/xml/help:', ...
+     matlabroot,'/toolbox/matlab/audiovideo:', ...
+     matlabroot,'/toolbox/coder/coderapp/form/ml:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents/uicontrol:', ...
+     matlabroot,'/toolbox/matlab/uitools/uicomponents/components:', ...
+     matlabroot,'/toolbox/matlab/connector2/common:', ...
+     matlabroot,'/toolbox/shared/optimlib:', ...
+     matlabroot,'/toolbox/matlab/dependency/app:', ...
+     matlabroot,'/toolbox/matlab/connector2/worker:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/rpt:', ...
+     matlabroot,'/toolbox/shared/mlreportgen/rpt/rpt:', ...
+     matlabroot,'/toolbox/symbolic/tasks:', ...
+     matlabroot,'/toolbox/matlab/appdesigner/appdesigner:', ...
+     matlabroot,'/toolbox/shared/mlarrow:', ...
+     matlabroot,'/toolbox/matlab/preferences/variablesprefpanel/variablesprefpanel-ui:', ...
+     matlabroot,'/toolbox/matlab/resources_folder:', ...
+     matlabroot,'/toolbox/shared/virtualfileio:', ...
+     matlabroot,'/toolbox/matlab/project/unsavedchanges:', ...
+     matlabroot,'/toolbox/matlab/dependency/report:', ...
+     matlabroot,'/toolbox/shared/transportlib:', ...
+     matlabroot,'/toolbox/matlab/configtools:', ...
+     matlabroot,'/toolbox/matlab/storage/mldrivedesktop:', ...
+     matlabroot,'/toolbox/matlab/preferences/workspaceprefpanel/workspaceprefpanel-ui:', ...
+     matlabroot,'/toolbox/matlab/connector2/configuration:', ...
+     matlabroot,'/toolbox/matlab/dependency/analysis:', ...
+     matlabroot,'/toolbox/physmod/simscape/language_editor/m:', ...
+     matlabroot,'/toolbox/optim/optimdemos:', ...
+     matlabroot,'/toolbox/matlab/connector2/session:', ...
+     matlabroot,'/toolbox/matlab/richcontent_preview/matlab:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_verilog_language_support/matlab:', ...
+     matlabroot,'/toolbox/shared/viewmodel/viewmodel:', ...
+     matlabroot,'/toolbox/matlab/rtc_addons/rtclanguagesupport/rtc_clike_language_support/matlab:', ...
+     matlabroot,'/toolbox/matlab/findfiles/m:', ...
+     matlabroot,'/toolbox/classdiagram/app/mcos:', ...
+     matlabroot,'/toolbox/matlab/uicomponents/uicomponents/databrowser:', ...
+     matlabroot,'/toolbox/shared/images_datatypes:', ...
+     matlabroot,'/toolbox/matlab/datatools/plotstab/matlab:', ...
+     matlabroot,'/toolbox/matlab/appcontainer/appcontainer:', ...
+     matlabroot,'/toolbox/shared/hadoopserializer:', ...
+     matlabroot,'/toolbox/matlab/bluetooth:', ...
+     matlabroot,'/toolbox/coder/coderapp/config/ml:', ...
+     matlabroot,'/toolbox/matlab/addons_common/matlab:', ...
+     matlabroot,'/toolbox/matlab/apps:', ...
+     matlabroot,'/toolbox/shared/networklib:', ...
+     matlabroot,'/toolbox/matlab/helptools/reference:', ...
+     matlabroot,'/toolbox/matlab/mex:', ...
+     matlabroot,'/toolbox/matlab/embeddedoutputs/variableoutputs:', ...
+     matlabroot,'/toolbox/matlab/webcam:', ...
+     matlabroot,'/toolbox/diagram/editor/web/m:', ...
+     matlabroot,'/toolbox/shared/appdes/services:', ...
+     matlabroot,'/toolbox/classdiagram/app/core:', ...
+     matlabroot,'/toolbox/matlab/dependency/attribute:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/java/jmi:', ...
+     matlabroot,'/toolbox/matlab/datatools/importtool/matlab/server:', ...
+     matlabroot,'/toolbox/matlab/serial:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwsetup:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwsetup/hwwidgets:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwsetup/hwtemplates:', ...
+     matlabroot,'/toolbox/shared/hwmanager/hwsetup/launch:', ...
+     matlabroot,'/toolbox/shared/seriallib:', ...
+     matlabroot,'/toolbox/shared/supportsoftware/launcher:', ...
+     matlabroot,'/toolbox/shared/supportsoftware/services:', ...
+     matlabroot,'/toolbox/shared/supportsoftware/upgrade:', ...
+     matlabroot,'/toolbox/matlab/embeddedoutputs/outputs:', ...
+     matlabroot,'/toolbox/matlab/datatools/media_widgets/matlab:', ...
+     matlabroot,'/toolbox/optim/optim:', ...
+     matlabroot,'/toolbox/optim:', ...
+     matlabroot,'/examples/pde/data:', ...
+     matlabroot,'/toolbox/matlab/connector2/http:', ...
+     matlabroot,'/toolbox/shared/transportclients:', ...
+     matlabroot,'/toolbox/matlab/project:', ...
+     matlabroot,'/toolbox/matlab/project/example:', ...
+     matlabroot,'/toolbox/matlab/project/toolstrip:', ...
+     matlabroot,'/toolbox/simulink/simulink/slproject:', ...
+     matlabroot,'/toolbox/simulink/simulink/slproject/menu:', ...
+     matlabroot,'/toolbox/shared/rptgen:', ...
+     matlabroot,'/toolbox/matlab/external/interfaces/webservices/http:', ...
+     matlabroot,'/toolbox/matlab/connector2/figures:', ...
+     matlabroot,'/toolbox/matlab/appdesigner/comparison:', ...
+%%% END ENTRIES %%%
+     ...
+];
+
+if startsWith(computer, 'PC') % ispc and pathsep not available
+    separator = ';';
+else
+    separator = ':';
+end
+
+p = [userpath separator getenv('MATLABPATH') separator p];
diff --git a/Matlab-Programs/symMinimization.m b/Matlab-Programs/symMinimization.m
index f714a3203b0aa45b5f71fee8b565afcb66cd56ec..04f3b0571def17f93cfd2182dde116a1a0705003 100644
--- a/Matlab-Programs/symMinimization.m
+++ b/Matlab-Programs/symMinimization.m
@@ -153,7 +153,7 @@ B_minus = tmp2;
 SP_minus = [A_minus,B_minus];
 
 % TODO one should use f_plus.subs(A_plus..) to compute function value symbolically?
-% in the end only the stationaryPoints are used.. Ok to compare function values numerically
+% in the end only the stationaryPoints are used.. should be ok to compare function values numerically
 
 % Determine global Minimizer from stationary points:
 % fprintf('function values at stationary points (f_plus):')
diff --git a/Matlab-Programs/symSolveSystem.m b/Matlab-Programs/symSolveSystem.m
new file mode 100644
index 0000000000000000000000000000000000000000..6424b5e7c54d397b89830c0f9306486483c75a4c
--- /dev/null
+++ b/Matlab-Programs/symSolveSystem.m
@@ -0,0 +1,16 @@
+
+
+syms q1 q2 q3 q12 b1 b2  a1 a2 
+
+eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == -2*q1*b1 - q12*b2
+
+eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == -2*q2*b2 - q12*b1
+
+[A,B] = equationsToMatrix([eqn1, eqn2], [a1,a2])
+
+X = linsolve(A,B)
+
+
+% check special case
+fprintf('special case q12 = 0 ') 
+subs(X,q12,0)
\ No newline at end of file
diff --git a/Matlab-Programs/txt.txt b/Matlab-Programs/txt.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/cmake/modules/CMakeLists.txt b/cmake/modules/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4f880839027b026b644bcffe1fec3e251aa4f5ee
--- /dev/null
+++ b/cmake/modules/CMakeLists.txt
@@ -0,0 +1,3 @@
+set(modules "DuneMicrostructureMacros.cmake")
+
+install(FILES ${modules} DESTINATION ${DUNE_INSTALL_MODULEDIR})
diff --git a/cmake/modules/DuneMicrostructureMacros.cmake b/cmake/modules/DuneMicrostructureMacros.cmake
new file mode 100644
index 0000000000000000000000000000000000000000..613dfb664b75999b008f0003a4d7c409cbf409ad
--- /dev/null
+++ b/cmake/modules/DuneMicrostructureMacros.cmake
@@ -0,0 +1 @@
+# File for module specific CMake tests.
diff --git a/inputs/cellsolver.parset b/inputs/cellsolver.parset
index d18133722a982be657dbec630e5a83eeea87f573..7b723865c77fb2277d1226c73780c3470b448996 100644
--- a/inputs/cellsolver.parset
+++ b/inputs/cellsolver.parset
@@ -29,7 +29,7 @@
 
 nElements = 32 32
 
-gamma=0.75
+gamma=0.25
 
 
 #############################################
diff --git a/inputs/computeMuGamma.parset b/inputs/computeMuGamma.parset
index defbd13acb87a7a73009c85559a95f9347f66011..6acf41019269f9686a55716591a4c6c2606d09f6 100644
--- a/inputs/computeMuGamma.parset
+++ b/inputs/computeMuGamma.parset
@@ -29,7 +29,7 @@
 
 nElements = 32 32
 
-gamma=0.25
+gamma=0.5
 
 
 #############################################
@@ -63,9 +63,9 @@ write_prestrainFunctions = true  # VTK norm of B ,
 
 
 rho1=1.0
-alpha=9.0
+alpha=9.764705882352942
 
-theta=0.075
+theta=0.15000000000000002
 
 #theta = 0.3    # volume fraction   #default = 1.0/4.0
 #theta = 0.25   # volume fraction
diff --git a/outputs/BMatrix.txt b/outputs/BMatrix.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a80ea6936c0d163da3a74067190369d75f7c6aa
--- /dev/null
+++ b/outputs/BMatrix.txt
@@ -0,0 +1,3 @@
+1 1 -0.324468879874192817
+1 2 -0.598155154475232376
+1 3 2.2946844494900733e-09
diff --git a/outputs/CellProblem-result-level1.vtu b/outputs/CellProblem-result-level1.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..8c2ffb29b02e9e0567cf7c716593a8299a47d763
--- /dev/null
+++ b/outputs/CellProblem-result-level1.vtu
@@ -0,0 +1,63 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <UnstructuredGrid>
+    <Piece NumberOfCells="8" NumberOfPoints="27">
+      <PointData Vectors="Corrector phi_1 level1">
+        <DataArray type="Float32" Name="Corrector phi_1 level1" NumberOfComponents="3" format="ascii">
+          -4.92612e-17 5.12665e-16 -0.00520833 1.4585e-17 -2.06282e-16 -0.00520833 1.52502e-17 -9.02594e-17 -0.00520833 -1.6941e-18 -2.00537e-17 -0.00520833
+          -5.36618e-18 1.25837e-16 0.00520833 6.328e-18 -9.52493e-17 0.00520833 1.70486e-18 3.71619e-17 0.00520833 -1.5501e-18 -7.88106e-17 0.00520833
+          -4.92612e-17 5.12665e-16 -0.00520833 1.52502e-17 -9.02594e-17 -0.00520833 -5.36618e-18 1.25837e-16 0.00520833 1.70486e-18 3.71619e-17 0.00520833
+          -4.92612e-17 5.12665e-16 -0.00520833 1.4585e-17 -2.06282e-16 -0.00520833 -5.36618e-18 1.25837e-16 0.00520833 6.328e-18 -9.52493e-17 0.00520833
+          -4.92612e-17 5.12665e-16 -0.00520833 -5.36618e-18 1.25837e-16 0.00520833 8.50067e-18 3.84459e-17 -0.00520833 2.06099e-17 -1.12811e-16 -0.00520833
+          3.06229e-18 1.79722e-17 -0.00520833 -1.32859e-17 -1.17555e-16 -0.00520833 8.50067e-18 3.84459e-17 -0.00520833 3.06229e-18 1.79722e-17 -0.00520833
+          8.50067e-18 3.84459e-17 -0.00520833 2.06099e-17 -1.12811e-16 -0.00520833 8.50067e-18 3.84459e-17 -0.00520833
+        </DataArray>
+        <DataArray type="Float32" Name="Corrector phi_2 level1" NumberOfComponents="3" format="ascii">
+          -4.50589e-17 5.0976e-16 -0.00520833 1.13853e-17 -2.0196e-16 -0.00520833 1.94525e-17 -8.73542e-17 -0.00520833 -4.89382e-18 -2.43755e-17 -0.00520833
+          -5.01495e-18 1.25709e-16 0.00520833 5.86931e-18 -9.44243e-17 0.00520833 2.05608e-18 3.72899e-17 0.00520833 -2.00879e-18 -7.96356e-17 0.00520833
+          -4.50589e-17 5.0976e-16 -0.00520833 1.94525e-17 -8.73542e-17 -0.00520833 -5.01495e-18 1.25709e-16 0.00520833 2.05608e-18 3.72899e-17 0.00520833
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diff --git a/outputs/CellProblem-result-level2.vtu b/outputs/CellProblem-result-level2.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..2159f2edf2bb048912377811249242a0157f76e0
--- /dev/null
+++ b/outputs/CellProblem-result-level2.vtu
@@ -0,0 +1,210 @@
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diff --git a/outputs/CellProblem-result-level3.vtu b/outputs/CellProblem-result-level3.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..916c51ee664ba1f6751bcd3ade9194fc15ad1673
--- /dev/null
+++ b/outputs/CellProblem-result-level3.vtu
@@ -0,0 +1,1187 @@
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diff --git a/outputs/Compute_MuGamma-Result.vtu b/outputs/Compute_MuGamma-Result.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..95ecfb6da1b1a9b1e7c7adcebf5432c6b1651e2e
--- /dev/null
+++ b/outputs/Compute_MuGamma-Result.vtu
@@ -0,0 +1,901 @@
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diff --git a/outputs/MaterialFunctions-level.vtu b/outputs/MaterialFunctions-level.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..82d15e24dcbd8f951dc72471ef81861c1fddc6d0
--- /dev/null
+++ b/outputs/MaterialFunctions-level.vtu
@@ -0,0 +1,3472 @@
+<?xml version="1.0"?>
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+      </Cells>
+    </Piece>
+  </UnstructuredGrid>
+</VTKFile>
diff --git a/outputs/MaterialFunctions.vtu b/outputs/MaterialFunctions.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..425eb077299b600ba85061666992428affbe7969
--- /dev/null
+++ b/outputs/MaterialFunctions.vtu
@@ -0,0 +1,3472 @@
+<?xml version="1.0"?>
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+          9 9 9 9 9 9 9 9 9 9 9 9
+          9 9 9 9 9 9 9 9 9 9 9 9
+          9 9 9 9 9 9 9 9 9 9 9 9
+          9 9 9 9
+        </DataArray>
+      </Cells>
+    </Piece>
+  </UnstructuredGrid>
+</VTKFile>
diff --git a/outputs/PhaseDiagram2DGamma_0.05.vts b/outputs/PhaseDiagram2DGamma_0.05.vts
new file mode 100644
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diff --git a/outputs/PhaseDiagram3DGamma0.5.vts b/outputs/PhaseDiagram3DGamma0.5.vts
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diff --git a/outputs/QMatrix.txt b/outputs/QMatrix.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c90b556eca4db8f790cd0b5599e276acad84f568
--- /dev/null
+++ b/outputs/QMatrix.txt
@@ -0,0 +1,9 @@
+1 1 2.56734130115762538
+1 2 0.645603935267779705
+1 3 3.11418421488085616e-09
+2 1 0.645603991569954294
+2 2 2.76956101635055951
+2 3 3.98431391489513918e-09
+3 1 2.26345584563976688e-10
+3 2 4.19795476054514084e-10
+3 3 2.00714673351474016
diff --git a/outputs/output.txt b/outputs/output.txt
index 9fb153f078416fb83b087c1ff1c7b9b159f12c34..2f5e34240ed5ee288458bcab6244f444e28e3b5c 100644
--- a/outputs/output.txt
+++ b/outputs/output.txt
@@ -1,69 +1,184 @@
+material_prestrain used: analytical_Example
 ----- Input Parameters -----: 
-alpha: 5
-gamma: 0.01
+alpha: 2
+gamma: 0.25
 theta: 0.25
 beta: 2
 material parameters: 
 mu1: 10
 mu2: 20
-lambda1: 0
-lambda2: 0
+lambda1: 10
+lambda2: 20
 ----------------------------: 
-Number of Elements in each direction: [8,8,8]
-size of FiniteElementBasis: 1728
+Number of Elements in each direction: [2,2,2]
+size of FiniteElementBasis: 36
 Solver-type used:  CG-Solver
 ---------- OUTPUT ----------
  --------------------
 Corrector-Matrix M_1: 
--4.7875e-09 1.11201e-09 0
-1.11201e-09 -1.65324e-21 0
+-9.61284e-16 -1.41525e-28 0
+-1.41525e-28 3.70983e-16 0
 0 0 0
 
  --------------------
 Corrector-Matrix M_2: 
-1.04621e-25 -1.08615e-20 0
--1.08615e-20 -9.4846e-18 0
+3.70983e-16 -1.41525e-28 0
+-1.41525e-28 -9.61284e-16 0
 0 0 0
 
  --------------------
 Corrector-Matrix M_3: 
-1.94872e-09 -9.19575e-10 0
--9.19575e-10 2.93022e-20 0
+2.18395e-35 8.94217e-17 0
+8.94217e-17 2.18395e-35 0
 0 0 0
 
  --------------------
 Effective Matrix Q: 
-2.08099 -5.09371e-24 2.86003e-10
-7.68785e-25 2.08333 -5.64259e-22
--7.27118e-09 -5.65834e-22 2.08306
+2.92824 0.798611 -7.01432e-32
+0.798611 2.92824 -7.01432e-32
+-3.14942e-34 -3.14942e-34 2.12963
+
+--- Prestrain Output --- 
+B_hat: -2.31481 -2.31481 -3.41187e-33
+B_eff: -0.621118 -0.621118 -1.7858e-33 (Effective Prestrain)
+------------------------ 
+q1=2.92824
+q2=2.92824
+q3=2.12963
+q12=0.798611
+b1=-0.621118
+b2=-0.621118
+b3=-1.7858e-33
+b1_hat: -2.31481
+b2_hat: -2.31481
+b3_hat: -3.41187e-33
+mu_gamma=2.12963
+q_onetwo=0.798611
+----- print analytic solutions -----
+b1_hat_ana : -0.714286
+b2_hat_ana : -1.250000
+b3_hat_ana : 0.000000
+b1_eff_ana : -0.375000
+b2_eff_ana : -0.600000
+b3_eff_ana : 0.000000
+q1_ana : 1.904762
+q2_ana : 2.083333
+q3 should be between q1 and q2
+Number of Elements in each direction: [4,4,4]
+size of FiniteElementBasis: 240
+Solver-type used:  CG-Solver
+---------- OUTPUT ----------
+ --------------------
+Corrector-Matrix M_1: 
+-0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Corrector-Matrix M_2: 
+0.000000 0.000000 0.000000
+0.000000 -0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Corrector-Matrix M_3: 
+-0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Effective Matrix Q: 
+2.523499 0.645553 0.000000
+0.645553 2.548864 0.000000
+-0.000000 -0.000000 1.891275
+
+--- Prestrain Output --- 
+B_hat: -1.066335 -1.134114 -0.000000
+B_eff: -0.330126 -0.361338 -0.000000 (Effective Prestrain)
+------------------------ 
+q1=2.523499
+q2=2.548864
+q3=1.891275
+q12=0.645553
+b1=-0.330126
+b2=-0.361338
+b3=-0.000000
+b1_hat: -1.066335
+b2_hat: -1.134114
+b3_hat: -0.000000
+mu_gamma=1.891275
+q_onetwo=0.645553
+----- print analytic solutions -----
+b1_hat_ana : -0.714286
+b2_hat_ana : -1.250000
+b3_hat_ana : 0.000000
+b1_eff_ana : -0.375000
+b2_eff_ana : -0.600000
+b3_eff_ana : 0.000000
+q1_ana : 1.904762
+q2_ana : 2.083333
+q3 should be between q1 and q2
+Number of Elements in each direction: [8,8,8]
+size of FiniteElementBasis: 1728
+Solver-type used:  CG-Solver
+---------- OUTPUT ----------
+ --------------------
+Corrector-Matrix M_1: 
+-0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Corrector-Matrix M_2: 
+-0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Corrector-Matrix M_3: 
+-0.000000 -0.000000 0.000000
+-0.000000 0.000000 0.000000
+0.000000 0.000000 0.000000
+
+ --------------------
+Effective Matrix Q: 
+2.567341 0.645604 0.000000
+0.645604 2.769561 0.000000
+0.000000 0.000000 2.007147
 
 --- Prestrain Output --- 
-B_hat: -1.24298 -1.25 2.78718e-08
-B_eff: -0.597302 -0.6 1.12953e-08 (Effective Prestrain)
+B_hat: -1.219194 -1.866106 0.000000
+B_eff: -0.324469 -0.598155 0.000000 (Effective Prestrain)
 ------------------------ 
-q1: 2.08099
-q2: 2.08333
-q3: 2.08306
-effective b1: -0.597302
-effective b2: -0.6
-effective b3: 1.12953e-08
-b1_hat: -1.24298
-b2_hat: -1.25
-b3_hat: 2.78718e-08
-mu_gamma=2.08306
+q1=2.567341
+q2=2.769561
+q3=2.007147
+q12=0.645604
+b1=-0.324469
+b2=-0.598155
+b3=0.000000
+b1_hat: -1.219194
+b2_hat: -1.866106
+b3_hat: 0.000000
+mu_gamma=2.007147
+q_onetwo=0.645604
 ----- print analytic solutions -----
 b1_hat_ana : -0.714286
-b2_hat_ana : -1.25
-b3_hat_ana : 0
-b1_eff_ana : -0.375
-b2_eff_ana : -0.6
-b3_eff_ana : 0
-q1_ana : 1.90476
-q2_ana : 2.08333
+b2_hat_ana : -1.250000
+b3_hat_ana : 0.000000
+b1_eff_ana : -0.375000
+b2_eff_ana : -0.600000
+b3_eff_ana : 0.000000
+q1_ana : 1.904762
+q2_ana : 2.083333
 q3 should be between q1 and q2
+------------------------------------------------------------------------------------------
    Levels    |  L2SymError  |    Order     |  L2SymNorm   | L2SNorm_ana  |    L2Norm    | 
 ------------------------------------------------------------------------------------------
-     3       & 7.09613e-02  & 0.00000e+00  & 8.19784e-03  & 7.14286e-02  & 5.58336e-03  & 
+     1       &      2       &      3       & ---------------------------------------------------------------------------------------------------------
   Levels     | |q1_ana-q1|  | |q2_ana-q2|  |      q3      | |b1_ana-b1|  | |b2_ana-b2|  | |b3_ana-b3|  | 
 ---------------------------------------------------------------------------------------------------------
-     3       & 1.76231e-01  & 8.88178e-15  & 2.08306e+00  & 2.22302e-01  & 2.44249e-15  & 1.12953e-08  & 
+     1       & 1.02348e+00  & 8.44907e-01  & 2.12963e+00  & 2.46118e-01  & 2.11180e-02  & 1.78580e-33  & 
+     2       & 6.18737e-01  & 4.65531e-01  & 1.89127e+00  & 4.48740e-02  & 2.38662e-01  & 1.10030e-10  & 
+     3       & 6.62579e-01  & 6.86228e-01  & 2.00715e+00  & 5.05311e-02  & 1.84485e-03  & 2.29468e-09  & 
+---------------------------------------------------------------------------------------------------------
diff --git a/outputs/outputMuGamma.txt b/outputs/outputMuGamma.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d55340a10f5814693535857040f62848c75cef2
--- /dev/null
+++ b/outputs/outputMuGamma.txt
@@ -0,0 +1,12 @@
+Number of Elements in each direction: [32,32]
+material_prestrain used: analytical_Example
+----- Input Parameters -----: 
+gamma: 0.5
+theta: 0.148889
+beta: 2
+material parameters: 
+mu1: 10
+mu2: 20
+----- OUTPUT: -----: 
+mu_gamma=1.84137
+q3=1.84137
diff --git a/src/ClassifyMin.py b/src/ClassifyMin.py
index e2d08c74f37047b61c26f367482b9339ddda038d..02ce9e28296c0cb2fe6d662303182c2144b88efb 100644
--- a/src/ClassifyMin.py
+++ b/src/ClassifyMin.py
@@ -25,7 +25,8 @@ import sys
 #
 #
 # Output : MinimizingMatrix, Angle, Type, Curvature
-
+def determinant(q1,q2,q3,q12):                                  # TODO General:Matrix
+    return q1*q2 - (q3**2 + 2*q3*q12 + q12**2)
 
 
 
diff --git a/src/ClassifyMinVec.py b/src/ClassifyMinVec.py
new file mode 100644
index 0000000000000000000000000000000000000000..c66307b46939a13934e94de0bc988327ce1e6c2f
--- /dev/null
+++ b/src/ClassifyMinVec.py
@@ -0,0 +1,375 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+# print(sys.executable)
+# from subprocess import Popen, PIPE
+
+
+# --------------------------------------------------
+# 'classifyMin' classifies Minimizers by utilizing the result of
+# Lemma1.6
+#
+#
+#
+#
+# 'classifyMin_ana': (Special-Case : Lemma1.4)
+# ..additionally assumes Poisson-ratio=0 => q12==0
+#
+#
+#
+# Output : MinimizingMatrix, Angle, Type, Curvature
+def determinant(q1,q2,q3,q12):                                  # TODO General:Matrix
+    return q1*q2 - (q3**2 + 2*q3*q12 + q12**2)
+
+
+
+
+def harmonicMean(mu_1, beta, theta):
+    return mu_1*(beta/(theta+(1-theta)*beta))
+
+
+def arithmeticMean(mu_1, beta, theta):
+    return mu_1*((1-theta)+theta*beta)
+
+
+def prestrain_b1(rho_1, beta, alpha, theta):
+    return (3.0*rho_1/2.0)*beta*(1-(theta*(1+alpha)))
+
+
+def prestrain_b2(rho_1, beta, alpha, theta):
+    return (3.0*rho_1/(4.0*((1.0-theta) + theta*beta)))*(1-theta*(1+beta*alpha))
+
+
+# Define function to be minimized
+def f(a1, a2, q1, q2, q3, q12, b1, b2):
+    A = np.array([[q1, q3 + q12/2.0], [q3 + q12/2.0, q2]])
+    B = np.array([-2.0*q1*b1-q12*b2, -2.0*q2*b2-q12*b1])
+    a = np.array([a1, a2])
+    tmp = np.dot(A, a)
+    tmp2 = np.dot(a, tmp)
+    tmpB = np.dot(B, a)
+    return tmp2 + tmpB + q1*(b1**2) + q2*(b2**2) + q12*b1*b2
+
+# ---- Alternative Version using alpha,beta,theta ,mu_1,rho_1
+def classifyMin_ana(alpha,beta,theta,q3,mu_1,rho_1,print_Cases=False, print_Output=False):
+
+    # Assumption of Classification-Lemma1.6:
+    #  1. [b3 == 0]
+    #  2. Q is orthotropic i.e. q13 = q31 = q23 = q32 == 0
+    # 3. This additionally assumes that Poisson-Ratio = 0 => q12 == 0
+    q12 = 0.0
+
+    q1 = (1.0/6.0)*harmonicMean(mu_1, beta, theta)
+    q2 = (1.0/6.0)*arithmeticMean(mu_1, beta, theta)
+    # print('q1: ', q1)
+    # print('q2: ', q2)
+    b1 = prestrain_b1(rho_1, beta, alpha,theta)
+    b2 = prestrain_b2(rho_1, beta, alpha,theta)
+    return classifyMin(q1, q2, q3, q12,  b1, b2,  print_Cases, print_Output)
+
+
+
+# Matrix Version that just gets matrices Q & B
+def classifyMin_mat(Q,B,print_Cases=False, print_Output=False):
+    q1 = Q[0][0]
+    q2 = Q[1][1]
+    q3 = Q[2][2]
+    q12 = Q[0][1]
+    b1 = B[0]
+    b2 = B[1]
+    b3 = B[2]
+    return classifyMin(q1, q2, q3, q12,  b1, b2,  print_Cases, print_Output)
+
+
+# --------------------------------------------------------------------
+# Classify Type of minimizer  1 = R1 , 2 = R2 , 3 = R3                          # before : destinction between which axis.. (4Types )
+# where
+# R1 : unique local (global) minimizer which is not axial
+# R2 : continuum of local (global) minimizers which are not axial
+# R3 : one or two local (global) minimizers which are axial
+# Partition given by
+# R1 = E1
+# R2 = P1.2
+# R3 = E2 U E3 U P1.1 U P2 U H
+# -------------------------------------------------------------------
+def classifyMin(q1, q2, q3, q12, b1, b2,  print_Cases=False, print_Output=False):   #ClassifyMin_hom?
+    # Assumption of Classification-Lemma1.6:
+    #  1. [b3 == 0]
+    #  2. Q is orthotropic i.e. q13 = q31 = q23 = q32 == 0
+
+    # TODO: check if Q is orthotropic here - assert()
+
+
+    if print_Output: print("Run ClassifyMin...")
+    CaseCount = 0
+    epsilon = sys.float_info.epsilon #Machine epsilon
+
+    B = np.array([-2.0*q1*b1-q12*b2, -2.0*q2*b2-q12*b1])
+    A = np.array([[q1, q3 + q12/2.0], [q3 + q12/2.0, q2]])
+    # print('Matrix A:',  A)
+    # print('Matrix B:', B)
+    # print('Matrix rank of A:', np.linalg.matrix_rank(A))
+    # print('shape of A:', A.shape)
+    # print('shape of B:', B.shape)
+    # print('Matrix [A,B]:', np.c_[A, B])
+    # print('Matrix rank of [A,B]:', np.linalg.matrix_rank(np.c_[A, B]))
+    # print('shape of [A,B]:', C.shape)
+    #
+    # x = np.linalg.solve(A, B)     # works only if A is not singular!!
+    # print("Solution LGS:", x)
+    # # print("sym Matrix", sym.Matrix(([A],[B])))
+    #
+    # # Test
+    # C = np.array([[1, 0], [0, 0]])
+    # d = np.array([5, 0])
+    # y = np.linalg.lstsq(C, d)[0]
+    # print("Solution LGS:", y)
+    # T = np.c_[C, d]
+    # print('T:', T)
+    # Trref = sym.Matrix(T).rref()[0]
+    # Out = np.array(Trref, dtype=float)
+    # print('rref:', Out)
+
+    determinant = q1*q2 - (q3**2 + 2*q3*q12 + q12**2)
+    if print_Cases: print("determinant:", determinant)
+
+    # Define values for axial-Solutions (b1*,0) & (0,b2*)
+    b1_star = (2.0*q1*b1 + b2*q12)/(2*q1)
+    b2_star = (2.0*q2*b2 + b1*q12)/(2*q2)
+
+    # ------------------------------------ Parabolic Case -----------------------------------
+    if abs(determinant) < epsilon:
+        if print_Cases: print('P : parabolic case (determinant equal zero)')
+        # if print_Cases: print('P : parabolic case (determinant equal zero)')
+
+        # check if B is in range of A
+        # check if rank(A) == rank([A,B])
+        # OK this way? (or use Sympy?)
+        if np.linalg.matrix_rank(A) == np.linalg.matrix_rank(np.c_[A, B]):
+            if print_Cases: print('P1 (B is in the range of A)')
+
+            if (q12+q3)/2.0 <= -1.0*epsilon:
+                print('should not happen(not compatible with det = 0)')
+
+            if (abs(B[0]) < epsilon and abs(B[1]) < epsilon) and (q12+q3)/2.0 >= epsilon:
+                if print_Cases: print('P1.1')
+                a1 = 0.0
+                a2 = 0.0
+                type = 3
+                CaseCount += 1
+
+            if (abs(B[0]) >= epsilon or abs(B[1]) >= epsilon) and (q12+q3)/2.0 >= epsilon:
+                # Continuum of minimizers located along a line of negative slope in Lambda
+                if print_Cases: print('P1.2 (Continuum of minimizers located along a line of negative slope in Lambda) ')
+
+                # Just solve Aa* = b (alternatively using SymPy ?)
+                # we know that A is singular (det A = 0 ) here..
+                # & we know that there are either infinitely many solutions or a unique solution ...
+                # ---- determine one via Least Squares
+                # "If A is square and of full rank, then x (but for round-off error)
+                # is the “exact” solution of the equation. Else, x minimizes the
+                # Euclidean 2-norm || b-Ax ||. If there are multiple minimizing solutions,
+                # the one with the smallest 2-norm  is returned. ""
+                a = np.linalg.lstsq(A, B)[0]                            # TODO check is this Ok ?
+                print("Solution LGS: a =", a)
+                a1 = a[0]
+                a2 = a[1]
+
+                type = 2
+                CaseCount += 1
+        else:
+            if print_Cases: print('P2 (B is not in the range of A)')
+            # local Minimizers occur on the boundary of Lambda...
+            # There are at most two local minima and they are either
+            # (b1_star, 0) or (0, b2_star)
+            # could also outsource this to another function..
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) < f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                a1 = b1_star
+                a2 = 0.0
+                type = 3  # 1
+                CaseCount += 1
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) > f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                a1 = 0
+                a2 = b2_star
+                type = 3  # 2
+                CaseCount += 1
+            # TODO Problem: angle depends on how you choose... THE angle is not defined for this case
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) == f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                # Two Minimizers pick one
+                a1 = b1_star
+                a2 = 0.0
+                type = 3  # 4
+                CaseCount += 1
+
+    # ------------------------------------ Elliptic Case -----------------------------------
+    if determinant >= epsilon:
+        if print_Cases: print('E : elliptic case (determinant greater zero)')
+        a1_star = -(2*(b1*(q12**2) + 2*b1*q3*q12 - 4*b1*q1*q2 + 4*b2*q2*q3)) / \
+            (4*(q3**2) + 4*q3*q12 + (q12**2) - 4*q1*q2)
+        a2_star = -(2*(b2*(q12**2) + 2*b2*q3*q12 + 4*b1*q1*q3 - 4*b2*q1*q2)) / \
+            (4*(q3**2) + 4*q3*q12 + (q12**2) - 4*q1*q2)
+        prod = a1_star*a2_star
+
+        if prod >= epsilon:
+            if print_Cases: print('(E1) - inside Lambda ')
+            a1 = a1_star
+            a2 = a2_star
+            type = 1  # non-axial Minimizer
+            CaseCount += 1
+        if abs(prod) < epsilon:   # same as prod = 0 ? or better use <=epsilon ?
+            if print_Cases: print('(E2) - on the boundary of Lambda ')
+            a1 = a1_star
+            a2 = a2_star
+            type = 3  # could check which axis: if a1_star or a2_star close to zero.. ?
+            CaseCount += 1
+
+        if prod <= -1.0*epsilon:
+            if print_Cases: print('(E3) - Outside Lambda ')
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) < f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                a1 = b1_star
+                a2 = 0.0
+                type = 3  # 1
+                CaseCount += 1
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) > f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                a1 = 0
+                a2 = b2_star
+                type = 3  # 2
+                CaseCount += 1
+
+            # TODO Problem: angle depends on how you choose... THE angle is not defined for this case
+            if f(b1_star, 0, q1, q2, q3, q12, b1, b2) == f(0, b2_star, q1, q2, q3, q12, b1, b2):
+                # Two Minimizers pick one
+                a1 = b1_star
+                a2 = 0.0
+                type = 3  # 4
+                CaseCount += 1
+
+    # ------------------------------------ Hyperbolic Case -----------------------------------
+    if determinant <= -1.0*epsilon:
+        if print_Cases: print('H : hyperbolic case (determinant smaller zero)')
+        # One or two minimizers wich are axial
+        type = 3 # (always type 3)
+        if f(b1_star, 0, q1, q2, q3, q12, b1, b2) < f(0, b2_star, q1, q2, q3, q12, b1, b2):
+            a1 = b1_star
+            a2 = 0.0
+            # type = 3  # 1
+            CaseCount += 1
+        if f(b1_star, 0, q1, q2, q3, q12, b1, b2) > f(0, b2_star, q1, q2, q3, q12, b1, b2):
+            a1 = 0
+            a2 = b2_star
+            # type = 3  # 2
+            CaseCount += 1
+        # TODO can add this case to first or second ..
+        if f(b1_star, 0, q1, q2, q3, q12, b1, b2) == f(0, b2_star, q1, q2, q3, q12, b1, b2):
+            # Two Minimizers pick one
+            a1 = b1_star
+            a2 = 0.0
+            # type = 3  # 4
+            CaseCount += 1
+    # ---------------------------------------------------------------------------------------
+
+    if (CaseCount > 1):
+        print('Error: More than one Case happened!')
+
+    # compute a3
+    # a3 = math.sqrt(2.0*a1*a2)   # never needed?
+
+    # compute the angle <(e,e_1) where Minimizer = kappa* (e (x) e)
+    e = [math.sqrt((a1/(a1+a2))), math.sqrt((a2/(a1+a2)))]
+    angle = math.atan2(e[1], e[0])
+
+    # compute kappa
+    kappa = (a1 + a2)
+
+    # Minimizer G
+    Minimizer = np.array([[a1, math.sqrt(a1*a2)], [math.sqrt(a1*a2), a2]],dtype=object)
+
+    MinimizerVec = np.array([a1, a2],dtype=object)
+    # Minimizer = np.array([[a1, math.sqrt(a1*a2)], [math.sqrt(a1*a2), a2]])
+
+    if print_Output:
+        print('--- Output ClassifyMin ---')
+        print("Minimizing Matrix G:")
+        print(Minimizer)
+        print("angle = ", angle)
+        print("type: ", type)
+        print("kappa = ", kappa)
+
+    return MinimizerVec, angle, type, kappa
+# ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+
+# ---------------------------------------------- Main ---------------------
+
+# --- Input Parameters ----
+# mu_1 = 1.0
+# rho_1 = 1.0
+# alpha = 9.0
+# beta = 2.0
+# theta = 1.0/8.0
+
+# # define q1, q2 , mu_gamma, q12
+# # 1. read from Cell-Output
+# # 2. define values from analytic formulas (expect for mu_gamma)
+# q1 = (1.0/6.0)*harmonicMean(mu_1, beta, theta)
+# q2 = (1.0/6.0)*arithmeticMean(mu_1, beta, theta)
+# # TEST
+# q12 = 0.0  # (analytical example)
+# # q12 = 12.0  # (analytical example)
+
+# set mu_gamma  to value or read from Cell-Output
+# mu_gamma = q1   # TODO read from Cell-Output
+# b1 = prestrain_b1(rho_1, beta, alpha, theta)
+# b2 = prestrain_b2(rho_1, beta, alpha, theta)
+
+
+# print('---- Input parameters: -----')
+# print('mu_1: ', mu_1)
+# print('rho_1: ', rho_1)
+# print('alpha: ', alpha)
+# print('beta: ', beta)
+# print('theta: ', theta)
+# print("q1: ", q1)
+# print("q2: ", q2)
+# print("mu_gamma: ", mu_gamma)
+# print("q12: ", q12)
+# print("b1: ", b1)
+# print("b2: ", b2)
+# print('----------------------------')
+# # print("machine epsilon", sys.float_info.epsilon)
+#
+#
+# # ------- Options --------
+# print_Cases = True
+# print_Output = True
+
+# G, angle, type, kappa = classifyMin(q1, q2, mu_gamma, q12,  b1, b2, print_Cases, print_Output)
+#
+# G, angle, type, kappa = classifyMin_ana(alpha, beta, theta, mu_gamma, q12, print_Cases, print_Output)
+#
+# Out = classifyMin_ana(alpha, beta, theta, mu_gamma, q12, print_Cases, print_Output)
+
+# print('TEST:')
+# Out = classifyMin_ana(alpha, beta, theta)
+
+# print('Out[0]', Out[0])
+# print('Out[1]', Out[1])
+# print('Out[2]', Out[2])
+# print('Out[3]', Out[3])
+
+
+# #supress certain Outout..
+# _,_,T,_ = classifyMin_ana(alpha, beta, theta, mu_gamma, q12, print_Cases, print_Output)
+# print('Output only type..:', T)
+
+# Test = f(1,2 ,q1,q2,mu_gamma,q12,b1,b2)
+# print("Test", Test)
+
+# -----------------------------------------------------------------------------------------------------------------------------------------------------------------
diff --git a/src/Compute_MuGamma.cc b/src/Compute_MuGamma.cc
index 17f553785d0eaa573a56212f1bc7dd1c23d5a314..d59db32e028de4796344734f056a71ddec31340a 100644
--- a/src/Compute_MuGamma.cc
+++ b/src/Compute_MuGamma.cc
@@ -877,6 +877,7 @@ int main(int argc, char *argv[])
     std::cout << "mu_gamma:" << mu_gamma << std::endl;
     log << "----- OUTPUT: -----: " << std::endl;
     log << "mu_gamma=" << mu_gamma << std::endl;   
+    log << "q3=" << mu_gamma << std::endl;   
     
 //     std::cout.precision(10);
 //     std::cout << "mu_gamma:" << std::fixed << mu_gamma  << std::endl;
@@ -949,5 +950,7 @@ int main(int argc, char *argv[])
      
      MaterialVtkWriter.write(outputPath + "/MaterialFunctions" );
         std::cout << "wrote data to file:" + outputPath  +  "/MaterialFunctions" << std::endl;  
+        
+    log.close();
      
 }
diff --git a/src/PhaseDiagram (copy).py b/src/PhaseDiagram (copy).py
new file mode 100644
index 0000000000000000000000000000000000000000..3991bdb639c3cf93dd71334a0000175b0a621c67
--- /dev/null
+++ b/src/PhaseDiagram (copy).py	
@@ -0,0 +1,346 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+
+import time
+# print(sys.executable)
+
+# --------------------------------------------------------------------
+# START :
+# INPUT (Parameters):   alpha, beta, theta, gamma, mu1, rho1
+#
+# -Option 1 : (Case lambda = 0 => q12 = 0)
+#   compute q1,q2,b1,b2 from Formula
+#       Option 1.1 :
+#           set mu_gamma = 'q1' or 'q2' (extreme regimes: gamma \in {0,\infty})
+#       Option 1.2 :
+#           compute mu_gamma with 'Compute_MuGamma' (2D problem much faster then Cell-Problem)
+# -Option 2 :
+#   compute Q_hom & B_eff by running 'Cell-Problem'
+#
+# -> CLASSIFY ...
+#
+# OUTPUT: Minimizer G, angle , type, curvature
+# -----------------------------------------------------------------------
+#
+#
+# def GetMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset",
+#                 OutputFilePath = os.path.dirname(os.getcwd()) + "/outputs/outputMuGamma.txt" ):
+#     # ------------------------------------ get mu_gamma ------------------------------
+#     # ---Scenario 1.1: extreme regimes
+#     if gamma == '0':
+#         print('extreme regime: gamma = 0')
+#         mu_gamma = (1.0/6.0)*arithmeticMean(mu1, beta, theta) # = q2
+#         print("mu_gamma:", mu_gamma)
+#     elif gamma == 'infinity':
+#         print('extreme regime: gamma = infinity')
+#         mu_gamma = (1.0/6.0)*harmonicMean(mu1, beta, theta)   # = q1
+#         print("mu_gamma:", mu_gamma)
+#     else:
+#         # --- Scenario 1.2:  compute mu_gamma with 'Compute_MuGamma' (much faster than running full Cell-Problem)
+#         # print("Run computeMuGamma for Gamma = ", gamma)
+#         with open(InputFilePath, 'r') as file:
+#             filedata = file.read()
+#         filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),filedata)
+#         # filedata = re.sub('(?m)^alpha=.*','alpha='+str(alpha),filedata)
+#         filedata = re.sub('(?m)^beta=.*','beta='+str(beta),filedata)
+#         filedata = re.sub('(?m)^theta=.*','theta='+str(theta),filedata)
+#         filedata = re.sub('(?m)^mu1=.*','mu1='+str(mu1),filedata)
+#         filedata = re.sub('(?m)^rho1=.*','rho1='+str(rho1),filedata)
+#         f = open(InputFilePath,'w')
+#         f.write(filedata)
+#         f.close()
+#         # --- Run Cell-Problem
+#
+#         # Check Time
+#         # t = time.time()
+#         # subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
+#         #                                      capture_output=True, text=True)
+#         # --- Run Cell-Problem_muGama   -> faster
+#         # subprocess.run(['./build-cmake/src/Cell-Problem_muGamma', './inputs/cellsolver.parset'],
+#         #                                              capture_output=True, text=True)
+#         # --- Run Compute_muGamma (2D Problem much much faster)
+#
+#         subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
+#                                                              capture_output=True, text=True)
+#         # print('elapsed time:', time.time() - t)
+#
+#         #Extract mu_gamma from Output-File                                           TODO: GENERALIZED THIS FOR QUANTITIES OF INTEREST
+#         with open(OutputFilePath, 'r') as file:
+#             output = file.read()
+#         tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
+#         s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+#         mu_gamma = float(s[0])
+#         # print("mu_gamma:", mu_gammaValue)
+#     # --------------------------------------------------------------------------------------
+#     return mu_gamma
+#
+
+
+
+# ----------- SETUP PATHS
+# InputFile  = "/inputs/cellsolver.parset"
+# OutputFile = "/outputs/output.txt"
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+
+# -------------------------- Input Parameters --------------------
+mu1 = 10.0               # TODO : here must be the same values as in the Parset for computeMuGamma
+rho1 = 1.0
+alpha = 2.0
+beta = 2.0
+# beta = 10.0
+theta = 1.0/4.0
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+# gamma = 'infinity'
+# gamma = 0.5
+# gamma = 0.25
+# gamma = 1.0
+
+# gamma = 5.0
+
+#added
+# lambda1 = 10.0
+lambda1 = 0.0
+
+
+
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+
+
+# gamma_min = 0.5
+# gamma_max = 1.0
+#
+# # gamma_min = 1
+# # gamma_max = 1
+# Gamma_Values = np.linspace(gamma_min, gamma_max, num=3)
+# # #
+# # # Gamma_Values = np.linspace(gamma_min, gamma_max, num=13)    # TODO variable Input Parameters...alpha,beta...
+# print('(Input) Gamma_Values:', Gamma_Values)
+# # #
+# for gamma in Gamma_Values:
+
+
+    # muGamma = GetMuGamma(beta,theta,gamma,mu1,rho1,InputFilePath)
+    # # muGamma = GetMuGamma(beta,theta,gamma,mu1,rho1)
+    # print('Test MuGamma:', muGamma)
+
+    # ------- Options --------
+    # print_Cases = True
+    # print_Output = True
+
+                        #TODO
+# generalCase = True #Read Output from Cell-Problem instead of using Lemma1.4 (special case)
+generalCase = False
+
+# make_3D_plot = True
+# make_3D_PhaseDiagram = True
+make_2D_plot = False
+# make_2D_PhaseDiagram = False
+make_3D_plot = False
+make_3D_PhaseDiagram = False
+# make_2D_plot = True
+make_2D_PhaseDiagram = True
+
+
+# --- Define effective quantities: q1, q2 , q3 = mu_gamma, q12 ---
+# q1 = harmonicMean(mu1, beta, theta)
+# q2 = arithmeticMean(mu1, beta, theta)
+# --- Set q12
+# q12 = 0.0  # (analytical example)              # TEST / TODO read from Cell-Output
+
+
+
+
+
+# b1 = prestrain_b1(rho1, beta, alpha, theta)
+# b2 = prestrain_b2(rho1, beta, alpha, theta)
+#
+# print('---- Input parameters: -----')
+# print('mu1: ', mu1)
+# print('rho1: ', rho1)
+# print('alpha: ', alpha)
+# print('beta: ', beta)
+# print('theta: ', theta)
+# print("q1: ", q1)
+# print("q2: ", q2)
+# print("mu_gamma: ", mu_gamma)
+# print("q12: ", q12)
+# print("b1: ", b1)
+# print("b2: ", b2)
+# print('----------------------------')
+# print("machine epsilon", sys.float_info.epsilon)
+
+# G, angle, type, kappa = classifyMin(q1, q2, mu_gamma, q12,  b1, b2, print_Cases, print_Output)
+# Test = f(1,2 ,q1,q2,mu_gamma,q12,b1,b2)
+# print("Test", Test)
+
+# ---------------------- MAKE PLOT / Write to VTK------------------------------------------------------------------------------
+
+# SamplePoints_3D = 10 # Number of sample points in each direction
+# SamplePoints_2D = 10 # Number of sample points in each direction
+SamplePoints_3D = 300 # Number of sample points in each direction
+SamplePoints_2D = 100 # Number of sample points in each direction
+
+
+
+if make_3D_PhaseDiagram:
+    alphas_ = np.linspace(-20, 20, SamplePoints_3D)
+    betas_  = np.linspace(0.01,40.01,SamplePoints_3D)
+    thetas_ = np.linspace(0.01,0.99,SamplePoints_3D)
+    # print('type of alphas', type(alphas_))
+    # print('Test:', type(np.array([mu_gamma])) )
+    alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')
+    classifyMin_anaVec = np.vectorize(classifyMin_ana)
+
+    # Get MuGamma values ...
+    GetMuGammaVec = np.vectorize(GetMuGamma)
+    muGammas = GetMuGammaVec(betas, thetas, gamma, mu1, rho1)
+    # Classify Minimizers....
+    G, angles, Types, curvature = classifyMin_anaVec(alphas, betas, thetas, muGammas,  mu1, rho1)   # Sets q12 to zero!!!
+    # print('size of G:', G.shape)
+    # print('G:', G)
+    # Out = classifyMin_anaVec(alphas,betas,thetas)
+    # T = Out[2]
+    # --- Write to VTK
+
+    GammaString = str(gamma)
+    VTKOutputName = "outputs/PhaseDiagram3D" + "Gamma" + GammaString
+    gridToVTK(VTKOutputName , alphas, betas, thetas, pointData = {'Type': Types, 'angles': angles, 'curvature': curvature} )
+    print('Written to VTK-File:', VTKOutputName )
+
+if make_2D_PhaseDiagram:
+    # alphas_ = np.linspace(-20, 20, SamplePoints_2D)
+    # thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
+    # alphas_ = np.linspace(-5, 15, SamplePoints_2D)
+    # thetas_ = np.linspace(0.05,0.25,SamplePoints_2D)
+
+
+    # good range:
+    # alphas_ = np.linspace(9, 10, SamplePoints_2D)
+    # thetas_ = np.linspace(0.075,0.14,SamplePoints_2D)
+
+    alphas_ = np.linspace(8, 10, SamplePoints_2D)
+    thetas_ = np.linspace(0.05,0.16,SamplePoints_2D)
+
+        # alphas_ = np.linspace(8, 12, SamplePoints_2D)
+        # thetas_ = np.linspace(0.05,0.2,SamplePoints_2D)
+    # betas_  = np.linspace(0.01,40.01,1)
+    #fix to one value:
+    betas_ = 2.0;
+    alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')
+
+
+    if generalCase:
+        classifyMin_matVec = np.vectorize(classifyMin_mat)
+        GetCellOutputVec = np.vectorize(GetCellOutput, otypes=[np.ndarray, np.ndarray])
+        Q, B = GetCellOutputVec(alphas,betas,thetas,gamma,mu1,rho1,lambda1, InputFilePath ,OutputFilePath )
+
+
+        # print('type of Q:', type(Q))
+        # print('Q:', Q)
+        G, angles, Types, curvature = classifyMin_matVec(Q,B)
+
+    else:
+        classifyMin_anaVec = np.vectorize(classifyMin_ana)
+        GetMuGammaVec = np.vectorize(GetMuGamma)
+        muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+        G, angles, Types, curvature = classifyMin_anaVec(alphas,betas,thetas, muGammas,  mu1, rho1)    # Sets q12 to zero!!!
+        # print('size of G:', G.shape)
+        # print('G:', G)
+        # print('Types:', Types)
+        # Out = classifyMin_anaVec(alphas,betas,thetas)
+        # T = Out[2]
+        # --- Write to VTK
+        # VTKOutputName = + path + "./PhaseDiagram2DNEW"
+
+    GammaString = str(gamma)
+    VTKOutputName = "outputs/PhaseDiagram2D" + "Gamma_" + GammaString
+    gridToVTK(VTKOutputName , alphas, betas, thetas, pointData = {'Type': Types, 'angles': angles, 'curvature': curvature} )
+    print('Written to VTK-File:', VTKOutputName )
+
+
+# --- Make 3D Scatter plot
+if(make_3D_plot or make_2D_plot):
+    fig = plt.figure()
+    ax = fig.add_subplot(111, projection='3d')
+    colors = cm.plasma(Types)
+    # if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=Types.flat)
+    # if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=Types.flat)
+    if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=angles.flat)
+    if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=angles.flat)
+    # cbar=plt.colorbar(pnt3d)
+    # cbar.set_label("Values (units)")
+    plt.axvline(x = 8, color = 'b', linestyle = ':', label='$q_1$')
+    plt.axhline(y = 0.083333333, color = 'b', linestyle = ':', label='$q_1$')
+
+    ax.set_xlabel('alpha')
+    ax.set_ylabel('beta')
+    if make_3D_plot: ax.set_zlabel('theta')
+    plt.show()
+    # plt.savefig('common_labels.png', dpi=300)
+    # print('T:', T)
+    # print('Type 1 occured here:', np.where(T == 1))
+    # print('Type 2 occured here:', np.where(T == 2))
+
+
+    # print(alphas_)
+    # print(betas_)
+
+
+
+
+
+# ALTERNATIVE
+# colors = ("red", "green", "blue")
+# groups = ("Type 1", "Type2", "Type3")
+#
+# # Create plot
+# fig = plt.figure()
+# ax = fig.add_subplot(1, 1, 1)
+#
+# for data, color, group in zip(Types, colors, groups):
+#     # x, y = data
+#     ax.scatter(alphas, thetas, alpha=0.8, c=color, edgecolors='none', label=group)
+#
+# plt.title('Matplot scatter plot')
+# plt.legend(loc=2)
+# plt.show()
diff --git a/src/PhaseDiagram.py b/src/PhaseDiagram.py
index 19d9e9bfd454b6614df2cf883af19711da7ee9c6..a37f282e1be9bfcbee4390dceb08b4101f07a5ea 100644
--- a/src/PhaseDiagram.py
+++ b/src/PhaseDiagram.py
@@ -114,17 +114,24 @@ mu1 = 10.0               # TODO : here must be the same values as in the Parset
 rho1 = 1.0
 alpha = 2.0
 beta = 2.0
-# beta = 10.0
+beta = 10.0
 theta = 1.0/4.0
 #set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
 gamma = '0'
 # gamma = 'infinity'
 # gamma = 0.5
-gamma = 0.25
+# gamma = 0.25
 # gamma = 1.0
 
+# gamma = 5.0
+
 #added
-lambda1 = 10.0
+# lambda1 = 10.0
+lambda1 = 0.0
+
+
+
+
 
 print('---- Input parameters: -----')
 print('mu1: ', mu1)
@@ -138,17 +145,17 @@ print('lambda1: ', lambda1)
 print('----------------------------')
 # ----------------------------------------------------------------
 
-
-# gamma_min = 0.05
-# gamma_max = 2.0
-
-# gamma_min = 1
-# gamma_max = 1
-# Gamma_Values = np.linspace(gamma_min, gamma_max, num=1)
 #
-# # Gamma_Values = np.linspace(gamma_min, gamma_max, num=13)    # TODO variable Input Parameters...alpha,beta...
-# print('(Input) Gamma_Values:', Gamma_Values)
+# gamma_min = 0.5
+# gamma_max = 1.0
 #
+# # gamma_min = 1
+# # gamma_max = 1
+# Gamma_Values = np.linspace(gamma_min, gamma_max, num=3)
+# # #
+# # # Gamma_Values = np.linspace(gamma_min, gamma_max, num=13)    # TODO variable Input Parameters...alpha,beta...
+# print('(Input) Gamma_Values:', Gamma_Values)
+# # #
 # for gamma in Gamma_Values:
 
 
@@ -161,7 +168,8 @@ print('----------------------------')
     # print_Output = True
 
                         #TODO
-generalCase = True #Read Output from Cell-Problem instead of using Lemma1.4 (special case)
+# generalCase = True #Read Output from Cell-Problem instead of using Lemma1.4 (special case)
+generalCase = False
 
 # make_3D_plot = True
 # make_3D_PhaseDiagram = True
@@ -210,7 +218,7 @@ make_2D_PhaseDiagram = True
 # SamplePoints_3D = 10 # Number of sample points in each direction
 # SamplePoints_2D = 10 # Number of sample points in each direction
 SamplePoints_3D = 300 # Number of sample points in each direction
-SamplePoints_2D = 1 # Number of sample points in each direction
+SamplePoints_2D = 300 # Number of sample points in each direction
 
 
 
@@ -240,11 +248,20 @@ if make_3D_PhaseDiagram:
     print('Written to VTK-File:', VTKOutputName )
 
 if make_2D_PhaseDiagram:
-    # alphas_ = np.linspace(-20, 20, SamplePoints_2D)
-    # thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
+    alphas_ = np.linspace(-20, 20, SamplePoints_2D)
+    thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
+    # alphas_ = np.linspace(-5, 15, SamplePoints_2D)
+    # thetas_ = np.linspace(0.05,0.25,SamplePoints_2D)
+
+
+    # good range:
     alphas_ = np.linspace(9, 10, SamplePoints_2D)
     thetas_ = np.linspace(0.075,0.14,SamplePoints_2D)
 
+    # range used:
+    # alphas_ = np.linspace(8, 10, SamplePoints_2D)
+    # thetas_ = np.linspace(0.05,0.16,SamplePoints_2D)
+
         # alphas_ = np.linspace(8, 12, SamplePoints_2D)
         # thetas_ = np.linspace(0.05,0.2,SamplePoints_2D)
     # betas_  = np.linspace(0.01,40.01,1)
@@ -253,10 +270,10 @@ if make_2D_PhaseDiagram:
     alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')
 
 
-    if generalCase:              #TODO
+    if generalCase:
         classifyMin_matVec = np.vectorize(classifyMin_mat)
         GetCellOutputVec = np.vectorize(GetCellOutput, otypes=[np.ndarray, np.ndarray])
-        Q, B = GetCellOutputVec(alphas,betas,thetas,gamma,mu1,rho1,lamba1, InputFilePath ,OutputFilePath )
+        Q, B = GetCellOutputVec(alphas,betas,thetas,gamma,mu1,rho1,lambda1, InputFilePath ,OutputFilePath )
 
 
         # print('type of Q:', type(Q))
@@ -293,6 +310,9 @@ if(make_3D_plot or make_2D_plot):
     if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=angles.flat)
     # cbar=plt.colorbar(pnt3d)
     # cbar.set_label("Values (units)")
+    plt.axvline(x = 8, color = 'b', linestyle = ':', label='$q_1$')
+    plt.axhline(y = 0.083333333, color = 'b', linestyle = ':', label='$q_1$')
+
     ax.set_xlabel('alpha')
     ax.set_ylabel('beta')
     if make_3D_plot: ax.set_zlabel('theta')
@@ -303,8 +323,8 @@ if(make_3D_plot or make_2D_plot):
     # print('Type 2 occured here:', np.where(T == 2))
 
 
-# print(alphas_)
-# print(betas_)
+    # print(alphas_)
+    # print(betas_)
 
 
 
diff --git a/src/Plot_Angle_Lemma1.4.py b/src/Plot_Angle_Lemma1.4.py
new file mode 100644
index 0000000000000000000000000000000000000000..e60ba683143816da39cab3f0503f51f2804ad482
--- /dev/null
+++ b/src/Plot_Angle_Lemma1.4.py
@@ -0,0 +1,407 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMin import *
+
+import matplotlib.ticker as ticker
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+# InputFile  = "/inputs/cellsolver.parset"
+# OutputFile = "/outputs/output.txt"
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 5.0
+beta = 10.0
+theta = 1.0/4.0
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+# gamma = '0'
+# gamma = 0.5
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+yName = 'angle'
+# yName = 'curvature'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+
+
+# --- define Interval of x-va1ues:
+xmin = 0.01
+xmax = 0.41
+
+# xmin = 0.18           #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.41           # Materialfunktion muss von Gitter aufgelöst werden
+                      # müssen vielfache von (1/2^i) sein wobei i integer
+
+
+# xmin = 0.18           #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.23
+
+
+
+
+# xmin = 0.01
+# xmax = 3.0
+# numPoints = 200
+numPoints = 101
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+
+
+
+
+
+for theta in X_Values:
+
+    print('Situation of Lemma1.4')
+    q12 = 0.0
+    q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+    q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+    b1 = prestrain_b1(rho1, beta, alpha,theta)
+    b2 = prestrain_b2(rho1, beta, alpha,theta)
+    b3 = 0.0
+    # if gamma == '0':
+    #     q3 = q2
+    # if gamma == 'infinity':
+    #     q3 = q1
+    q3 = GetMuGamma(beta,theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
+
+
+    if yName == 'q1':                   # TODO: Better use dictionary?...
+        print('q1 used')
+        Y_Values.append(q1)
+    elif yName =='q2':
+        print('q2 used')
+        Y_Values.append(q2)
+    elif yName =='q3':
+        print('q3 used')
+        Y_Values.append(q3)
+    elif yName =='q12':
+        print('q12 used')
+        Y_Values.append(q12)
+    elif yName =='b1':
+        print('b1 used')
+        Y_Values.append(b1)
+    elif yName =='b2':
+        print('b2 used')
+        Y_Values.append(b2)
+    elif yName =='b3':
+        print('b3 used')
+        Y_Values.append(b3)
+    elif yName == 'angle' or yName =='type' or yName =='curvature':
+        G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3,  mu1, rho1)
+        if yName =='angle':
+            print('angle used')
+            Y_Values.append(angle)
+        if yName =='type':
+            print('angle used')
+            Y_Values.append(type)
+        if yName =='curvature':
+            print('angle used')
+            Y_Values.append(curvature)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+idx = find_nearestIdx(Y_Values, 0)
+print(' Idx of value  closest to 0', idx)
+ValueClose = Y_Values[idx]
+print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+
+
+
+# Find Indices where the difference between the next one is larger than epsilon...
+jump_idx = []
+jump_xValues = []
+jump_yValues = []
+tmp = X_Values[0]
+for idx, x in enumerate(X_Values):
+    print(idx, x)
+    if idx > 0:
+        if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+            print('jump candidate')
+            jump_idx.append(idx)
+            jump_xValues.append(x)
+            jump_yValues.append(Y_Values[idx])
+
+
+
+
+
+
+
+print("Jump Indices", jump_idx)
+print("Jump X-values:", jump_xValues)
+print("Jump Y-values:", jump_yValues)
+
+y_plotValues = [Y_Values[0]]
+x_plotValues = [X_Values[0]]
+# y_plotValues.extend(jump_yValues)
+for i in jump_idx:
+    y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+    x_plotValues.extend([X_Values[i-1], X_Values[i]])
+
+
+y_plotValues.append(Y_Values[-1])
+# x_plotValues = [X_Values[0]]
+# x_plotValues.extend(jump_xValues)
+x_plotValues.append(X_Values[-1])
+
+
+print("y_plotValues:", y_plotValues)
+print("x_plotValues:", x_plotValues)
+# Y_Values[np.diff(y) >= 0.5] = np.nan
+
+
+#get values bigger than jump position
+# gamma = infty
+# x_rest = X_Values[X_Values>x_plotValues[1]]
+# Y_Values = np.array(Y_Values)  #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[1]]
+#
+#
+# # gamma = 0
+# x_rest = X_Values[X_Values>x_plotValues[3]]
+# Y_Values = np.array(Y_Values)  #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+
+# gamma between
+# Y_Values = np.array(Y_Values)  #convert the np array
+# X_Values = np.array(X_Values)  #convert the np array
+#
+# x_one = X_Values[X_Values>x_plotValues[3]]
+# # ax.scatter(X_Values, Y_Values)
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+# ax.plot(X_Values[X_Values>0.135], Y_Values[X_Values<0.135])
+#
+#
+#
+
+
+# y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+# print('X_Values:', X_Values)
+# print('Y_Values:', Y_Values)
+# print('x_rest:', x_rest)
+# print('y_rest:', y_rest)
+# print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+# ---------------- Create Plot -------------------
+plt.figure()
+
+f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+
+
+
+# Gamma = '0'
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+#
+# ax.plot([x_plotValues[1],x_plotValues[3]], [y_plotValues[2],y_plotValues[3]] , 'b')
+#
+# ax.plot(x_rest, y_rest, 'b')
+
+
+# Gamma between
+
+# x jump values (gamma 0): [0.13606060606060608, 0.21090909090909093]
+
+# ax.plot([[0,jump_xValues[0]], [0, 0]] , 'b')
+# ax.plot([jump_xValues[0],xmin], [y_plotValues[2],y_plotValues[2]] , 'b')
+
+# ax.plot([[0,0.13606060606060608], [0, 0]] , 'b')
+# ax.plot([[0.13606060606060608,xmin], [(math.pi/2),(math.pi/2)]], 'b')
+
+# jump_xValues[0]
+
+Y_Values = np.array(Y_Values)  #convert the np array
+X_Values = np.array(X_Values)  #convert the np array
+
+# leave out jumps:
+# ax.scatter(X_Values, Y_Values)
+# leave out jumps:
+# ax.plot(X_Values[X_Values>jump_xValues[0]], Y_Values[X_Values>jump_xValues[0]] , 'b')
+# ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]], 'b')
+
+
+
+
+
+# ax.plot(X_Values[X_Values>0.136], Y_Values[X_Values>0.136])
+# ax.plot(X_Values[X_Values<0.135], Y_Values[X_Values<0.135])
+ax.scatter(X_Values, Y_Values)
+ax.plot(X_Values, Y_Values)
+
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+plt.xlabel(xName)
+plt.ylabel(yName)
+
+# plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+ax.grid(True)
+ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+
+ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+# Plot every other line.. not the jumps...
+tmp = 1
+# for idx, x in enumerate(x_plotValues):
+#     if idx > 0 and tmp == 1:
+#         # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         tmp = 0
+#     else:
+#         tmp = 1
+
+# plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
+# plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
+# plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
+# plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
+
+
+for x in jump_xValues:
+    plt.axvline(x,ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plot_CurvatureLemma1.4.py b/src/Plot_CurvatureLemma1.4.py
new file mode 100644
index 0000000000000000000000000000000000000000..ea4f16b708ae6a8d89f98dc24d90ce8e57544b46
--- /dev/null
+++ b/src/Plot_CurvatureLemma1.4.py
@@ -0,0 +1,367 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMin import *
+
+import matplotlib.ticker as ticker
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+# mu1 = 10.0
+# # lambda1 = 10.0
+rho1 = 1.0
+# alpha = 5.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+
+mu1 = 10.0
+# lambda1 = 10.0
+# rho1 = 10.0
+alpha = 5.0
+# beta = 2.0
+beta = 10.0
+theta = 1.0/4.0
+
+theta = 1.0/2.0
+# theta = 1.0/12.0
+
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+# gamma = '0'
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+yName = 'angle'
+yName = 'curvature'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+# xName = 'alpha'
+
+
+# --- define Interval of x-values:
+xmin = 0
+xmax = 30
+
+# xmin = 0.245
+# xmax = 0.99
+#
+#
+# xmin = 0.14
+# xmax = 0.19
+
+# xmin = 0.01
+# xmax = 3.0
+
+xmin = 0.01
+xmax = 0.4
+
+
+
+numPoints = 100
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+
+
+
+
+for theta in X_Values:
+# for alpha in X_Values:
+
+    print('Situation of Lemma1.4')
+    q12 = 0.0
+    q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+    q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+    b1 = prestrain_b1(rho1, beta, alpha,theta)
+    b2 = prestrain_b2(rho1, beta, alpha,theta)
+    b3 = 0.0
+    if gamma == '0':
+        q3 = q2
+    if gamma == 'infinity':
+        q3 = q1
+
+    if yName == 'q1':                   # TODO: Better use dictionary?...
+        print('q1 used')
+        Y_Values.append(q1)
+    elif yName =='q2':
+        print('q2 used')
+        Y_Values.append(q2)
+    elif yName =='q3':
+        print('q3 used')
+        Y_Values.append(q3)
+    elif yName =='q12':
+        print('q12 used')
+        Y_Values.append(q12)
+    elif yName =='b1':
+        print('b1 used')
+        Y_Values.append(b1)
+    elif yName =='b2':
+        print('b2 used')
+        Y_Values.append(b2)
+    elif yName =='b3':
+        print('b3 used')
+        Y_Values.append(b3)
+    elif yName == 'angle' or yName =='type' or yName =='curvature':
+        G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3,  mu1, rho1)
+        if yName =='angle':
+            print('angle used')
+            Y_Values.append(angle)
+        if yName =='type':
+            print('angle used')
+            Y_Values.append(type)
+        if yName =='curvature':
+            print('angle used')
+            Y_Values.append(curvature)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+idx = find_nearestIdx(Y_Values, 0)
+print(' Idx of value  closest to 0', idx)
+ValueClose = Y_Values[idx]
+print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+
+
+
+# Find Indices where the difference between the next one is larger than epsilon...
+jump_idx = []
+jump_xValues = []
+jump_yValues = []
+tmp = X_Values[0]
+for idx, x in enumerate(X_Values):
+    print(idx, x)
+    if idx > 0:
+        if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+            print('jump candidate')
+            jump_idx.append(idx)
+            jump_xValues.append(x)
+            jump_yValues.append(Y_Values[idx])
+
+
+
+
+
+
+
+print("Jump Indices", jump_idx)
+print("Jump X-values:", jump_xValues)
+print("Jump Y-values:", jump_yValues)
+
+y_plotValues = [Y_Values[0]]
+x_plotValues = [X_Values[0]]
+# y_plotValues.extend(jump_yValues)
+for i in jump_idx:
+    y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+    x_plotValues.extend([X_Values[i-1], X_Values[i]])
+
+
+y_plotValues.append(Y_Values[-1])
+# x_plotValues = [X_Values[0]]
+# x_plotValues.extend(jump_xValues)
+x_plotValues.append(X_Values[-1])
+
+
+print("y_plotValues:", y_plotValues)
+print("x_plotValues:", x_plotValues)
+# Y_Values[np.diff(y) >= 0.5] = np.nan
+
+
+#get values bigger than jump position
+x_rest = X_Values[X_Values>x_plotValues[1]]
+
+Y_Values = np.array(Y_Values)  #convert the np array
+
+y_rest = Y_Values[X_Values>x_plotValues[1]]
+# y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+print('X_Values:', X_Values)
+print('Y_Values:', Y_Values)
+print('x_rest:', x_rest)
+print('y_rest:', y_rest)
+print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+# ---------------- Create Plot -------------------
+plt.figure()
+
+f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+# ax.plot(x_rest, y_rest, 'b')
+
+
+
+# ax.plot(X_Values, Y_Values)
+ax.scatter(X_Values, Y_Values)
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+plt.xlabel(xName)
+# plt.ylabel(yName)
+
+plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+
+
+
+ax.grid(True)
+
+# # if angle PLOT :
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+#
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+#
+# # Plot every other line.. not the jumps...
+# tmp = 1
+# for idx, x in enumerate(x_plotValues):
+#     if idx > 0 and tmp == 1:
+#         # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] ,'b')
+#         tmp = 0
+#     else:
+#         tmp = 1
+
+# plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
+# plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
+# plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
+# plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
+
+
+for x in jump_xValues:
+    plt.axvline(x,ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plot_Lemma1.4.py b/src/Plot_Lemma1.4.py
new file mode 100644
index 0000000000000000000000000000000000000000..16c12145518e7b4f602337f975d296c681821528
--- /dev/null
+++ b/src/Plot_Lemma1.4.py
@@ -0,0 +1,349 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMin import *
+
+import matplotlib.ticker as ticker
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+# mu1 = 10.0
+# # lambda1 = 10.0
+# rho1 = 1.0
+# alpha = 5.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 5.0
+beta = 2.0
+theta = 1.0/4.0
+# theta = 1.0/12.0
+
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+gamma = '0'
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+yName = 'angle'
+# yName = 'curvature'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+xName = 'alpha'
+
+
+# --- define Interval of x-values:
+xmin = 2
+xmax = 6
+
+# xmin = 0.245
+# xmax = 0.99
+
+# xmin = 0.01
+# xmax = 3.0
+numPoints = 400
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+
+
+
+
+# for theta in X_Values:
+for alpha in X_Values:
+
+    print('Situation of Lemma1.4')
+    q12 = 0.0
+    q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+    q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+    b1 = prestrain_b1(rho1, beta, alpha,theta)
+    b2 = prestrain_b2(rho1, beta, alpha,theta)
+    b3 = 0.0
+    if gamma == '0':
+        q3 = q2
+    if gamma == 'infinity':
+        q3 = q1
+
+    if yName == 'q1':                   # TODO: Better use dictionary?...
+        print('q1 used')
+        Y_Values.append(q1)
+    elif yName =='q2':
+        print('q2 used')
+        Y_Values.append(q2)
+    elif yName =='q3':
+        print('q3 used')
+        Y_Values.append(q3)
+    elif yName =='q12':
+        print('q12 used')
+        Y_Values.append(q12)
+    elif yName =='b1':
+        print('b1 used')
+        Y_Values.append(b1)
+    elif yName =='b2':
+        print('b2 used')
+        Y_Values.append(b2)
+    elif yName =='b3':
+        print('b3 used')
+        Y_Values.append(b3)
+    elif yName == 'angle' or yName =='type' or yName =='curvature':
+        G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3,  mu1, rho1)
+        if yName =='angle':
+            print('angle used')
+            Y_Values.append(angle)
+        if yName =='type':
+            print('angle used')
+            Y_Values.append(type)
+        if yName =='curvature':
+            print('angle used')
+            Y_Values.append(curvature)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+idx = find_nearestIdx(Y_Values, 0)
+print(' Idx of value  closest to 0', idx)
+ValueClose = Y_Values[idx]
+print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+
+
+
+# Find Indices where the difference between the next one is larger than epsilon...
+jump_idx = []
+jump_xValues = []
+jump_yValues = []
+tmp = X_Values[0]
+for idx, x in enumerate(X_Values):
+    print(idx, x)
+    if idx > 0:
+        if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+            print('jump candidate')
+            jump_idx.append(idx)
+            jump_xValues.append(x)
+            jump_yValues.append(Y_Values[idx])
+
+
+
+
+
+
+
+print("Jump Indices", jump_idx)
+print("Jump X-values:", jump_xValues)
+print("Jump Y-values:", jump_yValues)
+
+y_plotValues = [Y_Values[0]]
+x_plotValues = [X_Values[0]]
+# y_plotValues.extend(jump_yValues)
+for i in jump_idx:
+    y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+    x_plotValues.extend([X_Values[i-1], X_Values[i]])
+
+
+y_plotValues.append(Y_Values[-1])
+# x_plotValues = [X_Values[0]]
+# x_plotValues.extend(jump_xValues)
+x_plotValues.append(X_Values[-1])
+
+
+print("y_plotValues:", y_plotValues)
+print("x_plotValues:", x_plotValues)
+# Y_Values[np.diff(y) >= 0.5] = np.nan
+
+
+#get values bigger than jump position
+x_rest = X_Values[X_Values>x_plotValues[1]]
+
+Y_Values = np.array(Y_Values)  #convert the np array
+
+y_rest = Y_Values[X_Values>x_plotValues[1]]
+# y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+print('X_Values:', X_Values)
+print('Y_Values:', Y_Values)
+print('x_rest:', x_rest)
+print('y_rest:', y_rest)
+print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+# ---------------- Create Plot -------------------
+plt.figure()
+
+f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+# ax.plot(x_rest, y_rest, 'b')
+
+
+
+ax.plot(X_Values, Y_Values)
+
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+plt.xlabel(xName)
+plt.ylabel(yName)
+
+# plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+ax.grid(True)
+ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+
+ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+# Plot every other line.. not the jumps...
+tmp = 1
+# for idx, x in enumerate(x_plotValues):
+#     if idx > 0 and tmp == 1:
+#         # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         tmp = 0
+#     else:
+#         tmp = 1
+
+# plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
+# plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
+# plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
+# plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
+
+
+for x in jump_xValues:
+    plt.axvline(x,ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plot_MinVec.py b/src/Plot_MinVec.py
new file mode 100644
index 0000000000000000000000000000000000000000..8a37ee21d00bdabcc1519311f624e44b39067cfb
--- /dev/null
+++ b/src/Plot_MinVec.py
@@ -0,0 +1,548 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMinVec import *
+import matplotlib.cm as cm
+from matplotlib.colors import Normalize
+
+import matplotlib.ticker as ticker
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+# mu1 = 10.0
+# # lambda1 = 10.0
+rho1 = 1.0
+# alpha = 5.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+
+mu1 = 10.0
+# lambda1 = 10.0
+# rho1 = 10.0
+alpha = 5.0
+# beta = 2.0
+beta = 10.0
+theta = 1.0/4.0
+
+theta = 1.0/2.0
+# theta = 1.0/12.0
+
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+# gamma = '0'
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+yName = 'angle'
+yName = 'curvature'
+yName = 'MinVec'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+# xName = 'alpha'
+
+
+# --- define Interval of x-values:
+xmin = 0
+xmax = 30
+
+# xmin = 0.245
+# xmax = 0.99
+#
+#
+# xmin = 0.14
+# xmax = 0.19
+
+# xmin = 0.01
+# xmax = 3.0
+
+xmin = 0.125
+xmax = 0.250
+
+xmin = 0.05
+xmax = 0.3
+
+xmin = 0.15
+xmax = 0.3
+
+xmin = 0.193
+xmax = 0.24
+
+xmin=0.05
+xmax=0.4
+
+numPoints =100
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print('X_values:', X_Values)
+
+
+Y_Values = []
+Angle_Values = []
+
+
+
+
+
+
+for theta in X_Values:
+# for alpha in X_Values:
+
+    print('Situation of Lemma1.4')
+    q12 = 0.0
+    q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+    q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+    b1 = prestrain_b1(rho1, beta, alpha,theta)
+    b2 = prestrain_b2(rho1, beta, alpha,theta)
+    b3 = 0.0
+    if gamma == '0':
+        q3 = q2
+    if gamma == 'infinity':
+        q3 = q1
+
+    if yName == 'q1':                   # TODO: Better use dictionary?...
+        print('q1 used')
+        Y_Values.append(q1)
+    elif yName =='q2':
+        print('q2 used')
+        Y_Values.append(q2)
+    elif yName =='q3':
+        print('q3 used')
+        Y_Values.append(q3)
+    elif yName =='q12':
+        print('q12 used')
+        Y_Values.append(q12)
+    elif yName =='b1':
+        print('b1 used')
+        Y_Values.append(b1)
+    elif yName =='b2':
+        print('b2 used')
+        Y_Values.append(b2)
+    elif yName =='b3':
+        print('b3 used')
+        Y_Values.append(b3)
+    elif yName == 'angle' or yName =='type' or yName =='curvature' or yName =='MinVec':
+        G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3,  mu1, rho1)
+        if yName =='angle':
+            print('angle used')
+            Y_Values.append(angle)
+        if yName =='type':
+            print('angle used')
+            Y_Values.append(type)
+        if yName =='curvature':
+            print('angle used')
+            Y_Values.append(curvature)
+        if yName =='MinVec':
+            print('Minvec used')
+            Y_Values.append(G)
+            Angle_Values.append(angle)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+# idx = find_nearestIdx(Y_Values, 0)
+# print(' Idx of value  closest to 0', idx)
+# ValueClose = Y_Values[idx]
+# print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+#
+#
+#
+# # Find Indices where the difference between the next one is larger than epsilon...
+# jump_idx = []
+# jump_xValues = []
+# jump_yValues = []
+# tmp = X_Values[0]
+# for idx, x in enumerate(X_Values):
+#     print(idx, x)
+#     if idx > 0:
+#         if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+#             print('jump candidate')
+#             jump_idx.append(idx)
+#             jump_xValues.append(x)
+#             jump_yValues.append(Y_Values[idx])
+#
+
+
+
+
+#
+#
+# print("Jump Indices", jump_idx)
+# print("Jump X-values:", jump_xValues)
+# print("Jump Y-values:", jump_yValues)
+#
+# y_plotValues = [Y_Values[0]]
+# x_plotValues = [X_Values[0]]
+# # y_plotValues.extend(jump_yValues)
+# for i in jump_idx:
+#     y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+#     x_plotValues.extend([X_Values[i-1], X_Values[i]])
+#
+#
+# y_plotValues.append(Y_Values[-1])
+# # x_plotValues = [X_Values[0]]
+# # x_plotValues.extend(jump_xValues)
+# x_plotValues.append(X_Values[-1])
+#
+#
+# print("y_plotValues:", y_plotValues)
+# print("x_plotValues:", x_plotValues)
+# # Y_Values[np.diff(y) >= 0.5] = np.nan
+
+#
+# #get values bigger than jump position
+# x_rest = X_Values[X_Values>x_plotValues[1]]
+#
+# Y_Values = np.array(Y_Values)  #convert the np array
+#
+# y_rest = Y_Values[X_Values>x_plotValues[1]]
+# # y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+# print('X_Values:', X_Values)
+# print('Y_Values:', Y_Values)
+# print('x_rest:', x_rest)
+# print('y_rest:', y_rest)
+# print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+# ---------------- Create Plot -------------------
+plt.figure()
+
+f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+# ax.plot(x_rest, y_rest, 'b')
+
+ #Define jump
+JumpVal = 0.19
+X_Values = np.array(X_Values)
+Y_Values = np.array(Y_Values)
+Angle_Values = np.array(Angle_Values)
+X_one = X_Values[X_Values<0.19]
+Y_one = Y_Values[X_Values<0.19]
+Angle_one=Angle_Values[X_Values<0.19]
+X_two = X_Values[X_Values>=0.19]
+Y_two = Y_Values[X_Values>=0.19]
+Angle_two=Angle_Values[X_Values>=0.19]
+
+X_Values = X_two
+Y_Values = Y_two
+Angle_Values = Angle_two
+print('X_one:', X_Values)
+
+
+color=['r','b','g']
+cmap = cm.get_cmap(name='rainbow')
+Y_arr = np.asarray(Y_Values, dtype=float)
+Angle_arr = np.asarray(Angle_Values, dtype=float)
+X_Values = np.asarray(X_Values, dtype=float)
+
+Y_one = np.asarray(Y_one, dtype=float)
+Angle_one = np.asarray(Angle_one, dtype=float)
+X_one = np.asarray(X_one, dtype=float)
+
+
+print('X_Values:', X_Values)
+print('Y_arr:', Y_arr)
+print('Angle_arr:', Angle_arr)
+
+
+
+
+# Or = np.zeros_like(Y_arr)
+Or_tmp = np.ones_like(X_Values)
+
+# Or = np.concatenate(([X_Values],[Or_tmp])  ,axis=1)
+# Or = np.array([X_Values,Or_tmp])
+
+print('np.transpose(X_Values)', np.transpose(X_Values))
+print('X_Values.shape', X_Values.shape[0] )
+print('reshape X_Values', X_Values.reshape(X_Values.shape[0],1).shape)
+
+print('ones.', np.ones((5,1),dtype=float))
+
+
+
+
+
+# Or = np.hstack([np.transpose(X_Values),np.transpose(Or_tmp)])
+# Or = np.hstack((X_Values,np.ones((X_Values.shape[0],1), dtype=X_Values.dtype)))
+X_Values= X_Values.reshape(X_Values.shape[0],1)
+X_one= X_one.reshape(X_one.shape[0],1)
+
+Or_one = np.hstack((X_one,np.zeros((X_one.shape[0],1),dtype=float)))
+Or = np.hstack((X_Values,np.zeros((X_Values.shape[0],1),dtype=float)))
+print('Or:', Or)
+
+# -----------------------------------------------------------------------------
+
+#normalize
+sum_of_rows = Y_arr.sum(axis=1)
+Y_arrN = Y_arr / sum_of_rows[:,np.newaxis]
+# Y_arrN = Y_arr / np.sqrt(np.sum(Y_arr**2))
+print('normalized Y_arrN:', Y_arrN)
+
+plt.grid(b=True, which='major')
+
+
+# plt.quiver([Or[:,0], Or[:,1]] , Y_arrN[:,0], Y_arrN[:,1])
+print(Or[:,1])
+print(Or[:,0])
+print(Y_arrN[:,0])
+
+norm = Normalize()
+norm.autoscale(Angle_arr)
+colormap = cm.RdBu
+
+
+
+
+
+
+
+# Plot only every second one
+skip = (slice(None,None,2))
+skip = (slice(None,None,2))
+
+# Q = ax.quiver(Or[:,0][skip], Or[:,1][skip] , Y_arrN[:,0][skip], Y_arrN[:,1][skip], color = colormap(norm(Angle_arr)), angles='xy', scale=5, units='xy', alpha=0.8,
+# headwidth=2)
+Q_2 = ax.quiver(Or[:,0][skip], Or[:,1][skip] , Y_arrN[:,0][skip], Y_arrN[:,1][skip], color = colormap(norm(Angle_arr)), angles='xy', scale=5, units='xy', alpha=0.8,
+headwidth=2)
+
+Q = ax.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], color = colormap(norm(Angle_arr)), angles='xy', scale=8, units='xy', alpha=0.8,
+headwidth=2)
+
+# f.colorbar(Q,extend='max')
+
+
+
+# ax.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], scale=5, units='xy')
+# ax.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], Angle_arr, angles='xy', scale=5, units='xy')
+# ax.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], color = colormap(norm(Angle_arr)), angles='xy', scale=15, units='xy')
+# ax.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], color = colormap(norm(Angle_arr)), angles='xy', scale=5, units='xy', alpha=0.8,
+# headwidth=2)
+ax.scatter(Or[:,0], Or[:,1], c='black', s=10)
+
+# ax.set_aspect('equal')
+# ax.set_aspect('auto')
+# ax.axis([0.1,0.4 , -0.1, 0.75])
+# plt.quiver(Or[:,0], Or[:,1] , Y_arrN[:,0], Y_arrN[:,1], scale=1)
+
+# ax.set_xlim((0.1, X_Values[:,0].max()))
+# ax.set_ylim((-0.1, Y_arrN[:,1].max()))
+
+
+ax.set_xlim((0.1, X_Values[:,0].max()+0.2))
+ax.set_ylim((-0.1, 0.2 ))
+# ax.tick_params(labelleft = False)
+
+
+plt.show()
+# plt.quiver(Or , Y_arrN[:,0], Y_arrN[:,1])
+
+
+
+
+for i, y in enumerate(Y_Values):
+    maxes = 1.1*np.amax(abs(Y_Values[i]), axis = 0)
+    tmp = Y_Values[i]
+    print('tmp:', tmp)
+
+    tmp_normalized = tmp / np.sqrt(np.sum(tmp**2))
+    print('tmp_normalized:', tmp_normalized)
+    # origin = np.array([[0, 0, 0],[0, 0, 0]]) # origin point
+    origin = np.array([X_Values[i], 1])
+    # origin = np.array([0,0])
+    print('origin:', origin)
+    plt.scatter(origin[0],origin[1])
+    # plt.plot(origin, 'ok')
+    # plt.axis('equal')
+    # plt.axis('auto')
+    plt.xlim([-0.1, 0.4])
+    plt.ylim([0, 4])
+    # plt.xlim([-maxes[0], maxes[0]])
+    # plt.ylim([-maxes[1], maxes[1]])
+# plt.quiver(*origin, tmp[0], tmp[1], headlength=4)
+    # plt.axes().arrow(*origin, tmp[0], tmp[1],head_width=0.05, head_length = 0.1, color = color[1])
+    # plt.arrow(*origin, tmp[0], tmp[1],head_width=0.05, head_length = 0.1, color = color[1])
+    # plt.arrow(*origin, tmp_normalized[0], tmp_normalized[1], color = color[1])
+    # plt.arrow(*origin, tmp_normalized[0], tmp_normalized[1], head_width=0.05, head_length = 0.1, color = color[1])
+    plt.arrow(*origin, tmp_normalized[0], tmp_normalized[1], head_width=0.05, head_length = 0.1, color = cmap(i))
+    plt.grid(b=True, which='major')
+# plt.quiver(*origin, test[0], test[1], color=['r','b','g'], scale=21)
+# plt.quiver(*origin, Y_Values[0][:,0], Y_Values[0][:,1], color=['r','b','g'], scale=21)
+# plt.quiver(*origin, Y_Values[:,0], V[:,1], color=['r','b','g'], scale=21)
+# plt.quiver(*origin, Y_Values[:,0], V[:,1], color=['r','b','g'], scale=21)
+
+
+
+
+
+plt.show()
+# ax.plot(X_Values, Y_Values)
+# ax.scatter(X_Values, Y_Values)
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+plt.xlabel(xName)
+# plt.ylabel(yName)
+
+plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+
+
+
+ax.grid(True)
+
+# # if angle PLOT :
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+#
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+#
+# # Plot every other line.. not the jumps...
+# tmp = 1
+# for idx, x in enumerate(x_plotValues):
+#     if idx > 0 and tmp == 1:
+#         # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+#         ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] ,'b')
+#         tmp = 0
+#     else:
+#         tmp = 1
+
+# plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
+# plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
+# plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
+# plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
+
+#
+# for x in jump_xValues:
+#     plt.axvline(x,ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+# plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plot_Prestrain_Lemma1.4.py b/src/Plot_Prestrain_Lemma1.4.py
new file mode 100644
index 0000000000000000000000000000000000000000..b8e051d2572ef7e1cec341458fb3410bdd2c25c3
--- /dev/null
+++ b/src/Plot_Prestrain_Lemma1.4.py
@@ -0,0 +1,500 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMin import *
+# from mpl_toolkits.mplot3d import axes3d
+from mpl_toolkits import mplot3d
+
+import matplotlib.ticker as ticker
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+# mu1 = 10.0
+# # lambda1 = 10.0
+# rho1 = 1.0
+# alpha = 5.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 5.0
+beta = 2.0
+theta = 1.0/4.0
+# theta = 1.0/12.0
+
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+gamma = '0'
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+yName = 'angle'
+# yName = 'curvature'
+
+
+xName = 'theta'
+xName = 'alpha'
+
+
+# --- define Interval of x-values:
+xmin = 2
+xmax = 6
+
+
+numPoints = 400
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+SamplePoints_2D = 20
+
+prestrain_b1Vec = np.vectorize(prestrain_b1)
+prestrain_b2Vec = np.vectorize(prestrain_b2)
+
+
+alphas_ = np.linspace(-20, 20, SamplePoints_2D)
+thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
+#fix to one value:
+betas_ = 2.0;
+alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')
+
+B1 = prestrain_b1Vec(rho1, betas, alphas, thetas)
+B2 = prestrain_b2Vec(rho1, betas, alphas, thetas)
+print('B1:', B1)
+
+B1 = np.array(B1)  #convert the np array
+B2 = np.array(B2)
+
+
+
+f,ax=plt.subplots(1)
+
+ax.plot(thetas, B1)
+ax.scatter(thetas, B1)
+
+
+plt.xlabel("$q_3$")
+plt.xlabel("$\gamma$")
+plt.ylabel("angle")
+ax.grid(True)
+
+
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 4))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.25))
+
+
+# ax.yaxis.set_major_formatter(ticker.FuncFormatter(
+# lambda val,pos: '{:.0g}$\pi$'.format(2*val/np.pi) if val !=0 else '0'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.5*np.pi))
+
+# ---------------------------- show pi values ------------------------------------
+# ax.axvline(x = q1, color = 'b', linestyle = ':', label='$q_1$')
+# ax.axvline(x = q2, color = 'r', linestyle = 'dashed', label='$q_2$')
+# ax.legend()
+# # ax.set(xlim=(1.750, 1.880), ylim=(0, math.pi/2.0))
+# ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+# # ax.set_yticks([0,  np.pi/4 ,np.pi/2])
+# # labels = ['$0$', r'$\pi/4$', r'$\pi/2$']
+# ax.set_yticks([0, np.pi/8, np.pi/4 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+# ax.set_yticklabels(labels)
+# ---------------------------------------------------------------
+
+ax.legend()
+# ax.set(xlim=(1.750, 1.880), ylim=(0, math.pi/2.0))
+
+# ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+# ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+# ax.set_yticks([0,  np.pi/4 ,np.pi/2])
+# labels = ['$0$', r'$\pi/4$', r'$\pi/2$']
+ax.set_yticks([0, np.pi/8, np.pi/4 ])
+labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+ax.set_yticklabels(labels)
+
+
+# Plot Gamma Value that is closest to q3_star
+ax.axvline(x = gammaClose, color = 'b', linestyle = 'dashed', label='$\gamma^*$')
+ax.axvspan(gamma_min, gammaClose, color='red', alpha=0.5)
+ax.axvspan(gammaClose, gamma_max, color='green', alpha=0.5)
+
+
+
+
+# plt.xlabel("$q_3(\gamma)$")
+plt.xlabel("$\gamma$")
+plt.ylabel("angle")
+plt.legend(loc='upper center')
+
+plt.show()
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+#
+# fig = plt.figure(figsize=(14,6))
+#
+# # `ax` is a 3D-aware axis instance because of the projection='3d' keyword argument to add_subplot
+# ax = fig.add_subplot(1, 2, 1, projection='3d')
+#
+# p = ax.plot_surface(alphas, thetas, B1, rstride=4, cstride=4, linewidth=0)
+#
+# # surface_plot with color grading and color bar
+# ax = fig.add_subplot(1, 2, 2, projection='3d')
+# p = ax.plot_surface(alphas, thetas, B1, rstride=1, cstride=1, cmap=matplotlib.cm.coolwarm, linewidth=0, antialiased=False)
+# cb = fig.colorbar(p, shrink=0.5)
+#
+#
+#
+# fig = plt.figure()
+# ax = plt.axes(projection='3d')
+#
+# # fig = plt.figure(figsize=(6,6))
+# # ax = fig.add_subplot(111, projection='3d')
+# ax = fig.add_subplot(111)
+#
+# # f,ax=plt.subplots(1)
+#
+# # Plot a 3D surface
+# # ax.plot_surface(alphas, thetas, B1,cmap='viridis', edgecolor='none')
+# # ax.plot_surface(alphas, thetas, B1)
+# # ax.plot_surface(alphas, thetas, B1)
+#
+# ax.plot3D(alphas, thetas, B1, 'gray')
+# # ax = fig.add_subplot(211, projection='3d')
+# #
+# #
+# # # Plot a 3D surface
+# # ax.plot_surface(alphas, thetas, B1)
+#
+# plt.show()
+
+# fig = plt.figure()
+# ax = fig.add_subplot(111, projection='3d')
+# colors = cm.plasma(Types)
+# # if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=Types.flat)
+# # if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=Types.flat)
+# if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=angles.flat)
+# if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=angles.flat)
+# # cbar=plt.colorbar(pnt3d)
+# # cbar.set_label("Values (units)")
+# plt.axvline(x = 8, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 0.083333333, color = 'b', linestyle = ':', label='$q_1$')
+#
+# ax.set_xlabel('alpha')
+# ax.set_ylabel('beta')
+# if make_3D_plot: ax.set_zlabel('theta')
+# plt.show()
+
+
+#
+#
+# # for theta in X_Values:
+# for alpha in X_Values:
+#
+#     print('Situation of Lemma1.4')
+#     q12 = 0.0
+#     q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+#     q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+#     b1 = prestrain_b1(rho1, beta, alpha,theta)
+#     b2 = prestrain_b2(rho1, beta, alpha,theta)
+#     b3 = 0.0
+#     if gamma == '0':
+#         q3 = q2
+#     if gamma == 'infinity':
+#         q3 = q1
+#
+#     if yName == 'q1':                   # TODO: Better use dictionary?...
+#         print('q1 used')
+#         Y_Values.append(q1)
+#     elif yName =='q2':
+#         print('q2 used')
+#         Y_Values.append(q2)
+#     elif yName =='q3':
+#         print('q3 used')
+#         Y_Values.append(q3)
+#     elif yName =='q12':
+#         print('q12 used')
+#         Y_Values.append(q12)
+#     elif yName =='b1':
+#         print('b1 used')
+#         Y_Values.append(b1)
+#     elif yName =='b2':
+#         print('b2 used')
+#         Y_Values.append(b2)
+#     elif yName =='b3':
+#         print('b3 used')
+#         Y_Values.append(b3)
+#     elif yName == 'angle' or yName =='type' or yName =='curvature':
+#         G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3,  mu1, rho1)
+#         if yName =='angle':
+#             print('angle used')
+#             Y_Values.append(angle)
+#         if yName =='type':
+#             print('angle used')
+#             Y_Values.append(type)
+#         if yName =='curvature':
+#             print('angle used')
+#             Y_Values.append(curvature)
+#
+#
+# print("(Output) Values of " + yName + ": ", Y_Values)
+#
+#
+# idx = find_nearestIdx(Y_Values, 0)
+# print(' Idx of value  closest to 0', idx)
+# ValueClose = Y_Values[idx]
+# print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+#
+#
+#
+# # Find Indices where the difference between the next one is larger than epsilon...
+# jump_idx = []
+# jump_xValues = []
+# jump_yValues = []
+# tmp = X_Values[0]
+# for idx, x in enumerate(X_Values):
+#     print(idx, x)
+#     if idx > 0:
+#         if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+#             print('jump candidate')
+#             jump_idx.append(idx)
+#             jump_xValues.append(x)
+#             jump_yValues.append(Y_Values[idx])
+#
+#
+#
+#
+#
+#
+#
+# print("Jump Indices", jump_idx)
+# print("Jump X-values:", jump_xValues)
+# print("Jump Y-values:", jump_yValues)
+#
+# y_plotValues = [Y_Values[0]]
+# x_plotValues = [X_Values[0]]
+# # y_plotValues.extend(jump_yValues)
+# for i in jump_idx:
+#     y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+#     x_plotValues.extend([X_Values[i-1], X_Values[i]])
+#
+#
+# y_plotValues.append(Y_Values[-1])
+# # x_plotValues = [X_Values[0]]
+# # x_plotValues.extend(jump_xValues)
+# x_plotValues.append(X_Values[-1])
+#
+#
+# print("y_plotValues:", y_plotValues)
+# print("x_plotValues:", x_plotValues)
+# # Y_Values[np.diff(y) >= 0.5] = np.nan
+#
+#
+# #get values bigger than jump position
+# x_rest = X_Values[X_Values>x_plotValues[1]]
+#
+# Y_Values = np.array(Y_Values)  #convert the np array
+#
+# y_rest = Y_Values[X_Values>x_plotValues[1]]
+# # y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+# print('X_Values:', X_Values)
+# print('Y_Values:', Y_Values)
+# print('x_rest:', x_rest)
+# print('y_rest:', y_rest)
+# print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+#
+#
+# # ---------------- Create Plot -------------------
+# plt.figure()
+#
+# f,ax=plt.subplots(1)
+#
+# # plt.title(r''+ yName + '-Plot')
+# # plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# # plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# # plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+#
+# # plt.plot(X_Values, Y_Values)
+#
+# # ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# # ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+# # ax.plot(x_rest, y_rest, 'b')
+#
+#
+#
+# ax.plot(X_Values, Y_Values)
+#
+# # plt.plot(x_plotValues, y_plotValues,'.')
+# # plt.scatter(X_Values, Y_Values, alpha=0.3)
+# # plt.scatter(X_Values, Y_Values)
+# # plt.plot(X_Values, Y_Values,'.')
+# # plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# # plt.axis([0, 6, 0, 20])
+#
+# plt.xlabel(xName)
+# plt.ylabel(yName)
+#
+# # plt.ylabel('$\kappa$')
+#
+# # ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# # ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+#
+# ax.grid(True)
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+#
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+#
+# # Plot every other line.. not the jumps...
+# tmp = 1
+# # for idx, x in enumerate(x_plotValues):
+# #     if idx > 0 and tmp == 1:
+# #         # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+# #         ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+# #         tmp = 0
+# #     else:
+# #         tmp = 1
+#
+# # plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
+# # plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
+# # plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
+# # plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
+#
+#
+# for x in jump_xValues:
+#     plt.axvline(x,ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+#
+# # plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+#
+# # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# # plt.legend()
+# plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plotq12.py b/src/Plotq12.py
new file mode 100644
index 0000000000000000000000000000000000000000..a2b8fac84af4a535cede6e7f8dde77748e4d1214
--- /dev/null
+++ b/src/Plotq12.py
@@ -0,0 +1,86 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Plotq12.py #########################
+#  Input: Lame-Parameter Lambda
+#  compute q12 entry of Q_hom for each Lambda
+#  create plot:  q12(lambda)
+###########################################################
+
+
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+Lambda_Values = np.linspace(0.0, 10.0, num=10)
+print(Lambda_Values)
+q12 = []
+
+
+# --- Options
+RUN = True
+# RUN = False
+# make_Plot = False
+make_Plot = True      # vll besser : Plot_muGamma
+
+if RUN:
+    for lambda1 in Lambda_Values:
+        print("Run Cell-Problem for Lambda = ", lambda1)
+        # print('gamma='+str(gamma))
+        with open(InputFilePath, 'r') as file:
+            filedata = file.read()
+        filedata = re.sub('(?m)^lambda1=.*','lambda1='+str(lambda1),filedata)
+        f = open(InputFilePath,'w')
+        f.write(filedata)
+        f.close()
+        # Run Cell-Problem
+        subprocess.run(['./build-cmake/src/dune-microstructure', './inputs/cellsolver.parset'],
+                                             capture_output=True, text=True)
+        #Extract mu_gamma from Output-File
+        with open(OutputFilePath, 'r') as file:
+            output = file.read()
+        tmp = re.search(r'(?m)^q_onetwo=.*',output).group()
+        s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+        q12Value = float(s[0])
+        print("q12:", q12Value)
+        q12.append(q12Value)
+    # ------------end of for-loop -----------------
+    print("(Output) Values of q12: ", q12)
+# ----------------end of if-statement -------------
+
+
+# Make Plot
+if make_Plot:
+    plt.figure()
+    plt.title(r'$q_{12}(\lambda)$-Plot')  # USE MATHEMATICAL EXPRESSIONS IN TITLE
+    plt.plot(Lambda_Values, q12)
+    plt.scatter(Lambda_Values, q12)
+    # plt.axis([0, 6, 0, 20])
+    plt.xlabel("$\lambda$")
+    plt.ylabel("$q_{12}$")
+    plt.legend()
+    plt.show()
+
+# #---------------------------------------------------------------
diff --git a/src/Plotq3-Angle.py b/src/Plotq3-Angle.py
index 678b66bd288768b53651c878913e896088c1b067..0d3b277b4e5952946801af50693e1792332581dd 100644
--- a/src/Plotq3-Angle.py
+++ b/src/Plotq3-Angle.py
@@ -16,6 +16,30 @@ import matplotlib.cm as cm
 from vtk.util import numpy_support
 from pyevtk.hl import gridToVTK
 import time
+import matplotlib.ticker as ticker
+
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
 
 
 def find_nearest(array, value):
@@ -46,18 +70,69 @@ print("Path: ", path)
 print('---- Input parameters: -----')
 # mu1 = 10.0
 # rho1 = 1.0
+# alpha = 2.56140350877193 #2.56140350877193, 4.0852130325814535
+# beta = 2.0  #5.0
+# theta = 1.0/4.0
+# theta = 1.0/8.0  # 0.5
+# theta = 0.075  # 0.5
+# mu1 = 10.0
+# rho1 = 1.0
 # alpha = 10
 # beta = 40.0
 # theta = 0.125
-#
+
 
 
 mu1 = 10.0
 rho1 = 1.0
-# alpha = 10.02021333
 alpha = 10.0
-beta = 2.0
-theta = 0.125
+beta = 2.0  #5.0
+theta = 1.0/8.0
+#
+
+
+# mu1 = 10.0
+# rho1 = 1.0
+# # alpha = 10.02021333
+# alpha = 10.0
+# beta = 2.0
+# theta = 0.125
+
+
+
+# mu1 = 10.0
+# rho1 = 1.0
+# # alpha = 10.02021333
+# alpha = 9.0
+# beta = 2.0
+# theta = 0.075
+
+#
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 4.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+# alpha = 10   #1.05263158
+# beta = 40.0  #5.0
+# # theta = 1.0/4.0
+# theta = 1.0/8.0  # 0.5
+#
+#
+# alpha = 2.0
+# beta = 2.0 #5.0
+# theta = 1/4.0
+# rho1 = 1.0
+# mu1 = 10.0
+
+# InterestingParameterSet :
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 10
+# beta = 40.0
+
+
 # theta = 0.124242
 # gamma = 0.75
 #set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
@@ -78,11 +153,12 @@ print('----------------------------')
 
 
 gamma_min = 0.01
-gamma_max = 1.0
+gamma_max = 3.0
 Gamma_Values = np.linspace(gamma_min, gamma_max, num=100)    # TODO variable Input Parameters...alpha,beta...
 print('(Input) Gamma_Values:', Gamma_Values)
 # mu_gamma = []
 
+# Gamma_Values = '0'
 
 # # --- Options
 # # make_Plot = False
@@ -123,10 +199,13 @@ G, angles, Types, curvature = classifyMin_anaVec(alpha, beta, theta, muGammas,
 
 print('angles:', angles)
 
-idx = find_nearestIdx(muGammas, q3_star)
-print('GammaValue Idx closest to q_3^*', idx)
-gammaClose = Gamma_Values[idx]
-print('GammaValue(Idx) with mu_gamma closest to q_3^*', gammaClose)
+
+
+
+# idx = find_nearestIdx(muGammas, q3_star)
+# print('GammaValue Idx closest to q_3^*', idx)
+# gammaClose = Gamma_Values[idx]
+# print('GammaValue(Idx) with mu_gamma closest to q_3^*', gammaClose)
 
 
 
@@ -135,28 +214,85 @@ print('GammaValue(Idx) with mu_gamma closest to q_3^*', gammaClose)
 
 # Make Plot
 if make_Plot:
-    plt.figure()
-    # plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
-    plt.title(r'angle$-\gamma$-Plot')
-    plt.plot(Gamma_Values, angles)
-    plt.scatter(Gamma_Values, angles)
+    # plt.figure()
+    #
+    #
+    #
+    #
+    # # plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    # # plt.title(r'angle$-\gamma$-Plot')
+    # # plt.plot(Gamma_Values, angles)
+    # # plt.scatter(Gamma_Values, angles)
     # plt.plot(muGammas, angles)
     # plt.scatter(muGammas, angles)
-    # plt.axis([0, 6, 0, 20])
-    # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
-    # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # # plt.axis([0, 6, 0, 20])
+    # # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
     # plt.axvline(x = q1, color = 'b', linestyle = ':', label='$q_1$')
     # plt.axvline(x = q2, color = 'r', linestyle = 'dashed', label='$q_2$')
-    # plt.axvline(x = q3_star, color = 'r', linestyle = 'dashed', label='$\gamma^*$')
+    # # plt.axvline(x = q3_star, color = 'r', linestyle = 'dashed', label='$\gamma^*$')
 
 
-    # Plot Gamma Value that is closest to q3_star
-    plt.axvline(x = gammaClose, color = 'b', linestyle = 'dashed', label='$\gamma^*$')
 
-    plt.axvspan(gamma_min, gammaClose, color='red', alpha=0.5)
-    plt.axvspan(gammaClose, gamma_max, color='green', alpha=0.5)
+    f,ax=plt.subplots(1)
+    ax.plot(muGammas, angles)
+    ax.scatter(muGammas, angles)
+    plt.xlabel("$q_3$")
+    plt.ylabel("angle")
+    ax.grid(True)
+    # ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+    # ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+
+    # ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 4))
+    # ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+    # ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+    # ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+    # ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.25))
 
-    plt.xlabel("$\gamma$")
+
+    # ax.yaxis.set_major_formatter(ticker.FuncFormatter(
+    # lambda val,pos: '{:.0g}$\pi$'.format(2*val/np.pi) if val !=0 else '0'))
+    # ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.5*np.pi))
+
+
+    ax.axvline(x = q1, color = 'b', linestyle = ':', label='$q_1$')
+    ax.axvline(x = q2, color = 'r', linestyle = 'dashed', label='$q_2$')
+    ax.legend()
+    # ax.set(xlim=(1.750, 1.880), ylim=(0, math.pi/2.0))
+    ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+    # ax.set_yticks([0,  np.pi/4 ,np.pi/2])
+    # labels = ['$0$', r'$\pi/4$', r'$\pi/2$']
+    ax.set_yticks([0, np.pi/8, np.pi/4 ])
+    labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+    ax.set_yticklabels(labels)
+
+    # Plot Gamma Value that is closest to q3_star
+    # plt.axvline(x = gammaClose, color = 'b', linestyle = 'dashed', label='$\gamma^*$')
+    # plt.axvspan(gamma_min, gammaClose, color='red', alpha=0.5)
+    # plt.axvspan(gammaClose, gamma_max, color='green', alpha=0.5)
+
+    plt.xlabel("$q_3(\gamma)$")
+    # plt.xlabel("$\gamma$")
     plt.ylabel("angle")
-    plt.legend()
+    plt.legend(loc='upper center')
+
     plt.show()
+
+
+
+
+    # plt.figure()
+    # plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    # plt.plot(muGammas, angles)
+    # plt.scatter(muGammas, angles)
+    # # plt.axis([0, 6, 0, 20])
+    # # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # plt.axvline(x = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # plt.axvline(x = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # plt.xlabel("$\mu_\gamma$")
+    # plt.ylabel("angle")
+    # plt.legend()
+    # plt.show()
+    #
diff --git a/src/Plotq3-Angle2.py b/src/Plotq3-Angle2.py
new file mode 100644
index 0000000000000000000000000000000000000000..9e25264dc1c57aaeb32fc62b624d4e57e0e635c6
--- /dev/null
+++ b/src/Plotq3-Angle2.py
@@ -0,0 +1,339 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    N = int(np.round(2 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/2$"
+    elif N == 2:
+        return r"$\pi$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 2.56140350877193 #2.56140350877193, 4.0852130325814535
+# beta = 2.0  #5.0
+# theta = 1.0/4.0
+# theta = 1.0/8.0  # 0.5
+# theta = 0.075  # 0.5
+# mu1 = 10.0
+# rho1 = 1.0
+alpha = 10
+# beta = 40.0
+# theta = 0.125
+
+mu1 = 10.0
+rho1 = 1.0
+# alpha = 2.0
+beta = 2.0  #5.0
+# theta = 1.0/4.0
+theta = 1.0/8.0
+#
+
+
+
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 10.0
+# beta = 2.0  #5.0
+# theta = 1.0/8.0
+# #
+
+
+# mu1 = 10.0
+# rho1 = 1.0
+# # alpha = 10.02021333
+# alpha = 10.0
+# beta = 2.0
+# theta = 0.125
+
+
+
+# mu1 = 10.0
+# rho1 = 1.0
+# # alpha = 10.02021333
+# alpha = 9.0
+# beta = 2.0
+# theta = 0.075
+
+#
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 4.0
+# beta = 10.0
+# theta = 1.0/4.0
+
+# alpha = 10   #1.05263158
+# beta = 40.0  #5.0
+# # theta = 1.0/4.0
+# theta = 1.0/8.0  # 0.5
+#
+#
+# alpha = 2.0
+# beta = 2.0 #5.0
+# theta = 1/4.0
+# rho1 = 1.0
+# mu1 = 10.0
+
+# InterestingParameterSet :
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 10
+# beta = 40.0
+
+
+# theta = 0.124242
+# gamma = 0.75
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+# gamma = '0'
+# gamma = 'infinity'
+# gamma = 0.5
+# gamma = 0.25
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+# print('gamma:', gamma)
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+gamma_min = 0.01
+gamma_max = 1.0
+Gamma_Values = np.linspace(gamma_min, gamma_max, num=100)    # TODO variable Input Parameters...alpha,beta...
+print('(Input) Gamma_Values:', Gamma_Values)
+# mu_gamma = []
+
+# Gamma_Values = '0'
+
+# # --- Options
+# # make_Plot = False
+make_Plot = True
+
+# Get values for mu_Gamma
+GetMuGammaVec = np.vectorize(GetMuGamma)
+muGammas = GetMuGammaVec(beta,theta,Gamma_Values,mu1,rho1, InputFilePath ,OutputFilePath )
+print('muGammas:', muGammas)
+
+q12 = 0.0
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+print('q1: ', q1)
+print('q2: ', q2)
+b1 = prestrain_b1(rho1, beta, alpha,theta)
+b2 = prestrain_b2(rho1, beta, alpha,theta)
+q3_star = math.sqrt(q1*q2)
+print('q3_star:', q3_star)
+
+# TODO these have to be compatible with input parameters!!!
+# compute certain ParameterValues that this makes sense
+# b1 = q3_star
+# b2 = q1
+print('b1: ', b1)
+print('b2: ', b2)
+
+# return classifyMin(q1, q2, q3, q12,  b1, b2,  print_Cases, print_Output)
+
+
+
+# classifyMin_anaVec = np.vectorize(classifyMin_ana)
+# G, angles, Types, curvature = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+classifyMin_anaVec = np.vectorize(classifyMin_ana)
+G, angles, Types, curvature = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+
+# _,angles,_,_ = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+
+print('angles:', angles)
+
+
+
+
+idx = find_nearestIdx(muGammas, q3_star)
+print('GammaValue Idx closest to q_3^*', idx)
+gammaClose = Gamma_Values[idx]
+print('GammaValue(Idx) with mu_gamma closest to q_3^*', gammaClose)
+
+
+
+determinantVec = np.vectorize(determinant)
+
+detValues = determinantVec(q1,q2,muGammas,q12)
+print('detValues:', detValues)
+
+
+detZeroidx = find_nearestIdx(detValues, 0)
+print('idx where det nearest to zero', idx)
+gammaClose = Gamma_Values[detZeroidx]
+print('gammaClose:', gammaClose)
+
+
+# Make Plot
+if make_Plot:
+    # plt.figure()
+    #
+    #
+    #
+    #
+    # # plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    # # plt.title(r'angle$-\gamma$-Plot')
+    plt.plot(Gamma_Values, angles)
+    plt.scatter(Gamma_Values, angles)
+    # plt.plot(muGammas, angles)
+    # plt.scatter(muGammas, angles)
+    # # plt.axis([0, 6, 0, 20])
+    # # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # plt.axvline(x = q1, color = 'b', linestyle = ':', label='$q_1$')
+    # plt.axvline(x = q2, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # # plt.axvline(x = q3_star, color = 'r', linestyle = 'dashed', label='$\gamma^*$')
+
+
+
+    f,ax=plt.subplots(1)
+    # ax.plot(muGammas, angles)
+    # ax.scatter(muGammas, angles)
+
+    ax.plot(Gamma_Values, angles)
+    ax.scatter(Gamma_Values, angles)
+
+
+    plt.xlabel("$q_3$")
+    plt.xlabel("$\gamma$")
+    plt.ylabel("angle")
+    ax.grid(True)
+
+
+    # ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+    # ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+
+    # ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 4))
+    # ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+    # ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+    # ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+    # ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.25))
+
+
+    # ax.yaxis.set_major_formatter(ticker.FuncFormatter(
+    # lambda val,pos: '{:.0g}$\pi$'.format(2*val/np.pi) if val !=0 else '0'))
+    # ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.5*np.pi))
+
+    # ---------------------------- show pi values ------------------------------------
+    # ax.axvline(x = q1, color = 'b', linestyle = ':', label='$q_1$')
+    # ax.axvline(x = q2, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # ax.legend()
+    # # ax.set(xlim=(1.750, 1.880), ylim=(0, math.pi/2.0))
+    # ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+    # # ax.set_yticks([0,  np.pi/4 ,np.pi/2])
+    # # labels = ['$0$', r'$\pi/4$', r'$\pi/2$']
+    # ax.set_yticks([0, np.pi/8, np.pi/4 ])
+    # labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+    # ax.set_yticklabels(labels)
+    # ---------------------------------------------------------------
+
+    ax.legend()
+    # ax.set(xlim=(1.750, 1.880), ylim=(0, math.pi/2.0))
+
+    # ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+    # ax.set(xlim=(1.760, 1.880), ylim=(-0.1, np.pi/4.0))
+    # ax.set_yticks([0,  np.pi/4 ,np.pi/2])
+    # labels = ['$0$', r'$\pi/4$', r'$\pi/2$']
+    ax.set_yticks([0, np.pi/8, np.pi/4 ])
+    labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+    ax.set_yticklabels(labels)
+
+
+    # Plot Gamma Value that is closest to q3_star
+    ax.axvline(x = gammaClose, color = 'b', linestyle = 'dashed', label='$\gamma^*$')
+    ax.axvspan(gamma_min, gammaClose, color='red', alpha=0.5)
+    ax.axvspan(gammaClose, gamma_max, color='green', alpha=0.5)
+
+
+
+
+    # plt.xlabel("$q_3(\gamma)$")
+    plt.xlabel("$\gamma$")
+    plt.ylabel("angle")
+    plt.legend(loc='upper center')
+
+    plt.show()
+
+
+
+
+    # plt.figure()
+    # plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    # plt.plot(muGammas, angles)
+    # plt.scatter(muGammas, angles)
+    # # plt.axis([0, 6, 0, 20])
+    # # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # plt.axvline(x = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # plt.axvline(x = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    # plt.xlabel("$\mu_\gamma$")
+    # plt.ylabel("angle")
+    # plt.legend()
+    # plt.show()
+    #
diff --git a/src/Plotq3-AngleOld.py b/src/Plotq3-AngleOld.py
new file mode 100644
index 0000000000000000000000000000000000000000..b46195d84a6e58ca37ad83c607e7fa3a03a89671
--- /dev/null
+++ b/src/Plotq3-AngleOld.py
@@ -0,0 +1,246 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+# from subprocess import Popen, PIPE
+#import sys
+
+# unabhängig von alpha...
+def GetMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset"):
+    # ------------------------------------ get mu_gamma ------------------------------
+    # ---Scenario 1.1: extreme regimes
+    if gamma == '0':
+        print('extreme regime: gamma = 0')
+        mu_gamma = (1.0/6.0)*arithmeticMean(mu1, beta, theta) # = q2
+        print("mu_gamma:", mu_gamma)
+    elif gamma == 'infinity':
+        print('extreme regime: gamma = infinity')
+        mu_gamma = (1.0/6.0)*harmonicMean(mu1, beta, theta)   # = q1
+        print("mu_gamma:", mu_gamma)
+    else:
+        # --- Scenario 1.2:  compute mu_gamma with 'Compute_MuGamma' (much faster than running full Cell-Problem)
+        # print("Run computeMuGamma for Gamma = ", gamma)
+        with open(InputFilePath, 'r') as file:
+            filedata = file.read()
+        filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),filedata)
+        # filedata = re.sub('(?m)^alpha=.*','alpha='+str(alpha),filedata)
+        filedata = re.sub('(?m)^beta=.*','beta='+str(beta),filedata)
+        filedata = re.sub('(?m)^theta=.*','theta='+str(theta),filedata)
+        filedata = re.sub('(?m)^mu1=.*','mu1='+str(mu1),filedata)
+        filedata = re.sub('(?m)^rho1=.*','rho1='+str(rho1),filedata)
+        f = open(InputFilePath,'w')
+        f.write(filedata)
+        f.close()
+        # --- Run Cell-Problem
+
+        # Check Time
+        # t = time.time()
+        # subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
+        #                                      capture_output=True, text=True)
+        # --- Run Cell-Problem_muGama   -> faster
+        # subprocess.run(['./build-cmake/src/Cell-Problem_muGamma', './inputs/cellsolver.parset'],
+        #                                              capture_output=True, text=True)
+        # --- Run Compute_muGamma (2D Problem much much faster)
+
+        subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
+                                                             capture_output=True, text=True)
+        # print('elapsed time:', time.time() - t)
+
+        #Extract mu_gamma from Output-File                                           TODO: GENERALIZED THIS FOR QUANTITIES OF INTEREST
+        with open(OutputFilePath, 'r') as file:
+            output = file.read()
+        tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
+        s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+        mu_gamma = float(s[0])
+        # print("mu_gamma:", mu_gammaValue)
+    # --------------------------------------------------------------------------------------
+    return mu_gamma
+
+
+
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+
+#1. Define Inputs Gamma-Array..
+#2. for(i=0; i<length(array)) ..compute Q_hom, B_eff from Cell-Problem
+#3
+
+# matrix = np.loadtxt(path + 'Qmatrix.txt', usecols=range(3))
+# print(matrix)
+
+# Use Shell Commands:
+# subprocess.run('ls', shell=True)
+
+
+#---------------------------------------------------------------
+
+# -------------------------- Input Parameters --------------------
+mu1 = 10.0
+rho1 = 1.0
+alpha = 10   #1.05263158
+beta = 40.0  #5.0
+# theta = 1.0/4.0
+theta = 1.0/8.0  # 0.5
+
+# InterestingParameterSet :
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 10
+# beta = 40.0
+# theta = 1.0/8.0
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+# gamma = '0'
+# gamma = 'infinity'
+# gamma = 0.5
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+# print('gamma:', gamma)
+print('----------------------------')
+# ----------------------------------------------------------------
+
+
+
+
+
+Gamma_Values = np.linspace(0.01, 5, num=20)    # TODO variable Input Parameters...alpha,beta...
+print('(Input) Gamma_Values:', Gamma_Values)
+# mu_gamma = []
+
+
+#
+# # --- Options
+# RUN = True
+# # RUN = False
+# # make_Plot = False
+make_Plot = True      # vll besser : Plot_muGamma
+#
+# if RUN:
+#     for gamma in Gamma_Values:
+#         print("Run Cell-Problem for Gamma = ", gamma)
+#         # print('gamma='+str(gamma))
+#         with open(InputFilePath, 'r') as file:
+#             filedata = file.read()
+#         filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),filedata)
+#         f = open(InputFilePath,'w')
+#         f.write(filedata)
+#         f.close()
+#         # --- Run Cell-Problem
+#         t = time.time()
+#         # subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
+#         #                                      capture_output=True, text=True)
+#         # --- Run Cell-Problem_muGama   -> faster
+#         # subprocess.run(['./build-cmake/src/Cell-Problem_muGamma', './inputs/cellsolver.parset'],
+#         #                                              capture_output=True, text=True)
+#         # --- Run Compute_muGamma (2D Problem much much faster)
+#         subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
+#                                                              capture_output=True, text=True)
+#         print('elapsed time:', time.time() - t)
+#
+#         #Extract mu_gamma from Output-File                                           TODO: GENERALIZED THIS FOR QUANTITIES OF INTEREST
+#         with open(OutputFilePath, 'r') as file:
+#             output = file.read()
+#         tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
+#         s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+#         mu_gammaValue = float(s[0])
+#         print("mu_gamma:", mu_gammaValue)
+#         mu_gamma.append(mu_gammaValue)
+#     # ------------end of for-loop -----------------
+#     print("(Output) Values of mu_gamma: ", mu_gamma)
+# # ----------------end of if-statement -------------
+#
+# # mu_gamma=[2.06099, 1.90567, 1.905]
+# # mu_gamma=[2.08306, 1.905, 1.90482, 1.90479, 1.90478, 1.90477]
+#
+# ##Gamma_Values = np.linspace(0.01, 20, num=12) :
+# #mu_gamma= [2.08306, 1.91108, 1.90648, 1.90554, 1.90521, 1.90505, 1.90496, 1.90491, 1.90487, 1.90485, 1.90483, 1.90482]
+#
+# ##Gamma_Values = np.linspace(0.01, 2.5, num=12)
+# # mu_gamma=[2.08306, 2.01137, 1.96113, 1.93772, 1.92592, 1.91937, 1.91541, 1.91286, 1.91112, 1.90988, 1.90897, 1.90828]
+#
+# # Gamma_Values = np.linspace(0.01, 2.5, num=6)
+# # mu_gamma=[2.08306, 1.95497, 1.92287, 1.91375, 1.9101, 1.90828]
+
+
+GetMuGammaVec = np.vectorize(GetMuGamma)
+muGammas = GetMuGammaVec(beta,theta,Gamma_Values,mu1,rho1)
+
+
+classifyMin_anaVec = np.vectorize(classifyMin_ana)
+
+G, angles, Types, curvature = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+# _,angles,_,_ = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+
+print('angles:', angles)
+
+# Make Plot
+if make_Plot:
+    plt.figure()
+    plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    plt.plot(muGammas, angles)
+    plt.scatter(muGammas, angles)
+    # plt.axis([0, 6, 0, 20])
+    # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    plt.axvline(x = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    plt.axvline(x = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    plt.xlabel("$\mu_\gamma$")
+    plt.ylabel("angle")
+    plt.legend()
+    plt.show()
+
+#
+# # ------------- RUN Matlab symbolic minimization program
+# eng = matlab.engine.start_matlab()
+# # s = eng.genpath(path + '/Matlab-Programs')
+# s = eng.genpath(path)
+# eng.addpath(s, nargout=0)
+# # print('current Matlab folder:', eng.pwd(nargout=1))
+# eng.cd('Matlab-Programs', nargout=0)  #switch to Matlab-Programs folder
+# # print('current Matlab folder:', eng.pwd(nargout=1))
+# Inp = False
+# print('Run symbolic Minimization...')
+# G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp, nargout=4)  #Name of program:symMinimization
+# # G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp,path + "/outputs", nargout=4)  #Optional: add Path
+# G = np.asarray(G) #cast Matlab Outout to numpy array
+#
+# # --- print Output ---
+# print('Minimizer G:')
+# print(G)
+# print('angle:', angle)
+# print('type:', type )
+# print('curvature:', kappa)
diff --git a/src/Plotq3-AngleV1.py b/src/Plotq3-AngleV1.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd07176cba8e3de05b3ec5b41f7748ecc1e946ec
--- /dev/null
+++ b/src/Plotq3-AngleV1.py
@@ -0,0 +1,147 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+
+
+
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+mu1 = 10.0
+rho1 = 1.0
+alpha = 2.8
+beta = 2.0
+theta = 1.0/4.0
+# gamma = 0.75
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+# gamma = '0'
+# gamma = 'infinity'
+# gamma = 0.5
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+# print('gamma:', gamma)
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+Gamma_Values = np.linspace(0.01, 5, num=15)    # TODO variable Input Parameters...alpha,beta...
+print('(Input) Gamma_Values:', Gamma_Values)
+# mu_gamma = []
+
+
+#
+# # --- Options
+# RUN = True
+# # RUN = False
+# # make_Plot = False
+make_Plot = True      # vll besser : Plot_muGamma
+#
+# if RUN:
+#     for gamma in Gamma_Values:
+#         print("Run Cell-Problem for Gamma = ", gamma)
+#         # print('gamma='+str(gamma))
+#         with open(InputFilePath, 'r') as file:
+#             filedata = file.read()
+#         filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),filedata)
+#         f = open(InputFilePath,'w')
+#         f.write(filedata)
+#         f.close()
+#         # --- Run Cell-Problem
+#         t = time.time()
+#         # subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
+#         #                                      capture_output=True, text=True)
+#         # --- Run Cell-Problem_muGama   -> faster
+#         # subprocess.run(['./build-cmake/src/Cell-Problem_muGamma', './inputs/cellsolver.parset'],
+#         #                                              capture_output=True, text=True)
+#         # --- Run Compute_muGamma (2D Problem much much faster)
+#         subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
+#                                                              capture_output=True, text=True)
+#         print('elapsed time:', time.time() - t)
+#
+#         #Extract mu_gamma from Output-File                                           TODO: GENERALIZED THIS FOR QUANTITIES OF INTEREST
+#         with open(OutputFilePath, 'r') as file:
+#             output = file.read()
+#         tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
+#         s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+#         mu_gammaValue = float(s[0])
+#         print("mu_gamma:", mu_gammaValue)
+#         mu_gamma.append(mu_gammaValue)
+#     # ------------end of for-loop -----------------
+#     print("(Output) Values of mu_gamma: ", mu_gamma)
+# # ----------------end of if-statement -------------
+#
+# # mu_gamma=[2.06099, 1.90567, 1.905]
+# # mu_gamma=[2.08306, 1.905, 1.90482, 1.90479, 1.90478, 1.90477]
+#
+# ##Gamma_Values = np.linspace(0.01, 20, num=12) :
+# #mu_gamma= [2.08306, 1.91108, 1.90648, 1.90554, 1.90521, 1.90505, 1.90496, 1.90491, 1.90487, 1.90485, 1.90483, 1.90482]
+#
+# ##Gamma_Values = np.linspace(0.01, 2.5, num=12)
+# # mu_gamma=[2.08306, 2.01137, 1.96113, 1.93772, 1.92592, 1.91937, 1.91541, 1.91286, 1.91112, 1.90988, 1.90897, 1.90828]
+#
+# # Gamma_Values = np.linspace(0.01, 2.5, num=6)
+# # mu_gamma=[2.08306, 1.95497, 1.92287, 1.91375, 1.9101, 1.90828]
+
+
+GetMuGammaVec = np.vectorize(GetMuGamma)
+muGammas = GetMuGammaVec(beta,theta,Gamma_Values,mu1,rho1)
+
+
+classifyMin_anaVec = np.vectorize(classifyMin_ana)
+
+G, angles, Types, curvature = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+# _,angles,_,_ = classifyMin_anaVec(alpha, beta, theta, muGammas,  mu1, rho1)
+
+print('angles:', angles)
+
+# Make Plot
+if make_Plot:
+    plt.figure()
+    plt.title(r'angle$-\mu_\gamma(\gamma)$-Plot')
+    plt.plot(muGammas, angles)
+    plt.scatter(muGammas, angles)
+    # plt.axis([0, 6, 0, 20])
+    # plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    # plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    plt.axvline(x = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+    plt.axvline(x = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+    plt.xlabel("$\mu_\gamma$")
+    plt.ylabel("angle")
+    plt.legend()
+    plt.show()
diff --git a/src/__pycache__/CellScript.cpython-38.pyc b/src/__pycache__/CellScript.cpython-38.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..72b0e979aac3958531dc09f69b37c3cc47b4d46e
Binary files /dev/null and b/src/__pycache__/CellScript.cpython-38.pyc differ
diff --git a/src/__pycache__/ClassifyMin.cpython-38.pyc b/src/__pycache__/ClassifyMin.cpython-38.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..c43e441abd4796ed507f8c6b2fbd5616322adbb7
Binary files /dev/null and b/src/__pycache__/ClassifyMin.cpython-38.pyc differ
diff --git a/src/__pycache__/ClassifyMinVec.cpython-38.pyc b/src/__pycache__/ClassifyMinVec.cpython-38.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..c6f0cf3414d5759d2e5de607cc4ead84668cbf21
Binary files /dev/null and b/src/__pycache__/ClassifyMinVec.cpython-38.pyc differ
diff --git a/src/__pycache__/HelperFunctions.cpython-38.pyc b/src/__pycache__/HelperFunctions.cpython-38.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..58ea41ffbab3ee55b10f621c3d67a4aaf0de778c
Binary files /dev/null and b/src/__pycache__/HelperFunctions.cpython-38.pyc differ
diff --git a/src/makePlot.py b/src/makePlot.py
index d6caac4944125f988ec67dee2776d6a6bfe158d2..a3b23a7283427f503cb846e5a9abeeb2bacb62ca 100644
--- a/src/makePlot.py
+++ b/src/makePlot.py
@@ -8,6 +8,7 @@ import fileinput
 import re
 import matlab.engine
 from HelperFunctions import *
+from ClassifyMin import *
 # from subprocess import Popen, PIPE
 #import sys
 
@@ -48,15 +49,35 @@ print("Path: ", path)
 #---------------------------------------------------------------
 
 print('---- Input parameters: -----')
+# mu1 = 10.0
+# lambda1 = 10.0
+# rho1 = 1.0
+# alpha = 2.8
+# beta = 2.0
+# theta = 1.0/4.0
+
+
 mu1 = 10.0
-lambda1 = 10.0
+# lambda1 = 10.0
+lambda1 = 0.0
 rho1 = 1.0
-alpha = 2.8
+alpha = 2.0
 beta = 2.0
-theta = 1.0/4.0
+theta = 1.0/8.0
 
 
 gamma = 1.0/4.0
+#
+# gamma = 'infinity'
+
+
+
+# Values of the other Plots:
+# mu1 = 10.0
+# rho1 = 1.0
+# alpha = 10.0
+# beta = 2.0  #5.0
+# theta = 1.0/8.0
 
 
 print('mu1: ', mu1)
@@ -64,7 +85,7 @@ print('rho1: ', rho1)
 print('alpha: ', alpha)
 print('beta: ', beta)
 print('theta: ', theta)
-print('gamma:', gamma)
+# print('gamma:', gamma)
 print('----------------------------')
 
 
@@ -81,24 +102,30 @@ print('----------------------------')
 # Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
 # TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
 yName = 'q12'
-# yName = 'b1'
-yName = 'q3'
-yName = 'angle'
+# # yName = 'b1'
+# yName = 'q3'
+# yName = 'angle'
+# yName = 'curvature'
 
 # --- Define Parameter this function/quantity depends on:
 # Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
 # xName = 'theta'
 # xName = 'gamma'
-# xName = 'lambda1'
-xName = 'alpha'
+xName = 'lambda1'
+# xName = 'theta'
 
 
 # --- define Interval of x-values:
-xmin = 0.0
-xmax = 10.0
+xmin = 0.05
+xmax = 2.0
 # xmin = 0.01
 # xmax = 3.0
-numPoints = 5
+numPoints = 10
+
+
+xmin = 0.0
+xmax = 10.0
+
 X_Values = np.linspace(xmin, xmax, num=numPoints)
 print(X_Values)
 
@@ -116,6 +143,60 @@ make_Plot = True
 if RUN:
     for x in X_Values:
 
+        #
+        # if xName != 'gamma' and (gamma=='0' or gamma=='infinity') and lambda1 ==0.0
+        #
+        #     print('Situation of Lemma1.4')
+        #     q12 = 0.0
+        #     q1 = (1.0/6.0)*harmonicMean(mu_1, beta, theta)
+        #     q2 = (1.0/6.0)*arithmeticMean(mu_1, beta, theta)
+        #     b1 = prestrain_b1(rho_1, beta, alpha,theta)
+        #     b2 = prestrain_b2(rho_1, beta, alpha,theta)
+        #     b3 = 0.0
+        #
+        #
+        #
+        #     if yName == 'q1':                   # TODO: Better use dictionary?...
+        #         print('q1 used')
+        #         Y_Values.append(Q[0][0])
+        #     elif yName =='q2':
+        #         print('q2 used')
+        #         Y_Values.append(Q[1][1])
+        #     elif yName =='q3':
+        #         print('q3 used')
+        #         if gamma == '0':
+        #             Y_Values.append(q2)
+        #         if gamma == 'infinity':
+        #             Y_Values.append(q1)
+        #     elif yName =='q12':
+        #         print('q12 used')
+        #         Y_Values.append(q12)
+        #     elif yName =='b1':
+        #         print('b1 used')
+        #         Y_Values.append(b1)
+        #     elif yName =='b2':
+        #         print('b2 used')
+        #         Y_Values.append(b2)
+        #     elif yName =='b3':
+        #         print('b3 used')
+        #         Y_Values.append(b3)
+        #     elif yName == 'angle' or yName =='type' or yName =='curvature':
+        #         G, angle, Type, curvature = classifyMin_anaVec(alphas,betas,thetas, muGammas,  mu1, rho1)
+        #         if yName =='angle':
+        #             print('angle used')
+        #             Y_Values.append(angle)
+        #         if yName =='type':
+        #             print('angle used')
+        #             Y_Values.append(type)
+        #         if yName =='kappa':
+        #             print('angle used')
+        #             Y_Values.append(curvature)
+        #
+        #
+
+
+
+
         if yName =='q3' or yName == 'mu_gamma':   # if only q3 is needed .. compute 2D problem (much faster)
 
             # fist replace old parameters in parset
@@ -191,36 +272,50 @@ if RUN:
                 print('b3 used')
                 Y_Values.append(B[2])
             elif yName == 'angle' or yName =='type' or yName =='curvature':
-                # ------------- Run Matlab symbolic minimization program 'symMinimization'
-                eng = matlab.engine.start_matlab()
-                # s = eng.genpath(path + '/Matlab-Programs')
-                s = eng.genpath(path)
-                eng.addpath(s, nargout=0)
-                # print('current Matlab folder:', eng.pwd(nargout=1))
-                eng.cd('Matlab-Programs', nargout=0)  #switch to Matlab-Programs folder
-                # print('current Matlab folder:', eng.pwd(nargout=1))
-                Inp = False
-                Inp_T = True
-                print('Run symbolic Minimization...')
-                #Arguments: symMinization(print_Input,print_statPoint,print_Output,make_FunctionPlot, InputPath)
-                G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp, nargout=4)  #Name of program:symMinimization
-                # G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp,path + "/outputs", nargout=4)  #Optional: add Path
-                G = np.asarray(G) #cast Matlab Outout to numpy array
+                G, angle, type, curvature = classifyMin_mat(Q,B)
+
+
+
+
+
+
+
+                # ----------------------------------------------------------
+                # # LATER (general) :
+                # # ------------- Run Matlab symbolic minimization program 'symMinimization'
+                # eng = matlab.engine.start_matlab()
+                # # s = eng.genpath(path + '/Matlab-Programs')
+                # s = eng.genpath(path)
+                # eng.addpath(s, nargout=0)
+                # # print('current Matlab folder:', eng.pwd(nargout=1))
+                # eng.cd('Matlab-Programs', nargout=0)  #switch to Matlab-Programs folder
+                # # print('current Matlab folder:', eng.pwd(nargout=1))
+                # Inp = False
+                # Inp_T = True
+                # print('Run symbolic Minimization...')
+                # #Arguments: symMinization(print_Input,print_statPoint,print_Output,make_FunctionPlot, InputPath)
+                # G, angle, type, curvature = eng.symMinimization(Inp,Inp,Inp,Inp, nargout=4)  #Name of program:symMinimization
+                # # G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp,path + "/outputs", nargout=4)  #Optional: add Path
+                # G = np.asarray(G) #cast Matlab Outout to numpy array
+                # ---------------------------------------------------------------
+
+
+
                 # --- print Output ---
                 print('Minimizer G:')
                 print(G)
                 print('angle:', angle)
                 print('type:', type )
-                print('curvature:', kappa)
+                print('curvature:', curvature)
                 if yName =='angle':
                     print('angle used')
                     Y_Values.append(angle)
                 if yName =='type':
-                    print('angle used')
-                    Y_Values.append(angle)
-                if yName =='kappa':
-                    print('angle used')
-                    Y_Values.append(angle)
+                    print('type used')
+                    Y_Values.append(type)
+                if yName =='curvature':
+                    print('curvature used')
+                    Y_Values.append(curvature)
     # ------------end of for-loop -----------------
     print("(Output) Values of " + yName + ": ", Y_Values)
 # ----------------end of if-statement -------------
diff --git a/src/makePlotmuGamma.py b/src/makePlotmuGamma.py
new file mode 100644
index 0000000000000000000000000000000000000000..748a9d29b65b4038ed2dbdd15b0279c95a494e6a
--- /dev/null
+++ b/src/makePlotmuGamma.py
@@ -0,0 +1,307 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+from HelperFunctions import *
+from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+#  Generalized Plot-Script giving the option to define
+#  quantity of interest and the parameter it depends on
+#  to create a plot
+#
+#  Input: Define y & x for "x-y plot" as Strings
+#  - Run the 'Cell-Problem' for the different Parameter-Points
+#  (alternatively run 'Compute_MuGamma' if quantity of interest
+#   is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+InputFile  = "/inputs/cellsolver.parset"
+OutputFile = "/outputs/output.txt"
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+#---------------------------------------------------------------
+
+print('---- Input parameters: -----')
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 2.8
+beta = 2.0
+theta = 1.0/4.0
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity'
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+yName = 'q12'
+# yName = 'b1'
+yName = 'q3'
+yName = 'angle'
+# yName = 'curvature'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+
+
+# --- define Interval of x-values:
+xmin = 0.05
+xmax = 0.2
+# xmin = 0.01
+# xmax = 3.0
+numPoints = 5
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+# --- Options
+RUN = True
+# RUN = False
+# make_Plot = False
+make_Plot = True
+
+if RUN:
+    for x in X_Values:
+
+        #
+        # if xName != 'gamma' and (gamma=='0' or gamma=='infinity') and lambda1 ==0.0
+        #
+        #     print('Situation of Lemma1.4')
+        #     q12 = 0.0
+        #     q1 = (1.0/6.0)*harmonicMean(mu_1, beta, theta)
+        #     q2 = (1.0/6.0)*arithmeticMean(mu_1, beta, theta)
+        #     b1 = prestrain_b1(rho_1, beta, alpha,theta)
+        #     b2 = prestrain_b2(rho_1, beta, alpha,theta)
+        #     b3 = 0.0
+        #
+        #
+        #
+        #     if yName == 'q1':                   # TODO: Better use dictionary?...
+        #         print('q1 used')
+        #         Y_Values.append(Q[0][0])
+        #     elif yName =='q2':
+        #         print('q2 used')
+        #         Y_Values.append(Q[1][1])
+        #     elif yName =='q3':
+        #         print('q3 used')
+        #         if gamma == '0':
+        #             Y_Values.append(q2)
+        #         if gamma == 'infinity':
+        #             Y_Values.append(q1)
+        #     elif yName =='q12':
+        #         print('q12 used')
+        #         Y_Values.append(q12)
+        #     elif yName =='b1':
+        #         print('b1 used')
+        #         Y_Values.append(b1)
+        #     elif yName =='b2':
+        #         print('b2 used')
+        #         Y_Values.append(b2)
+        #     elif yName =='b3':
+        #         print('b3 used')
+        #         Y_Values.append(b3)
+        #     elif yName == 'angle' or yName =='type' or yName =='curvature':
+        #         G, angle, Type, curvature = classifyMin_anaVec(alphas,betas,thetas, muGammas,  mu1, rho1)
+        #         if yName =='angle':
+        #             print('angle used')
+        #             Y_Values.append(angle)
+        #         if yName =='type':
+        #             print('angle used')
+        #             Y_Values.append(type)
+        #         if yName =='kappa':
+        #             print('angle used')
+        #             Y_Values.append(curvature)
+        #
+        #
+
+
+
+
+        if yName =='q3' or yName == 'mu_gamma':   # if only q3 is needed .. compute 2D problem (much faster)
+
+            # fist replace old parameters in parset
+            SetParametersComputeMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath)
+
+            # replace the sought after x value in the parset
+            with open(path+"/inputs/computeMuGamma.parset", 'r') as file:
+                filedata = file.read()
+            filedata = re.sub('(?m)^'+xName+'=.*',xName+'='+str(x),filedata)
+            f = open(path+"/inputs/computeMuGamma.parset",'w')
+            f.write(filedata)
+            f.close()
+            #Run Compute_MuGamma since its much faster
+            print("Run Compute_MuGamma for " + xName + " =" , x)
+            subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
+                                                                 capture_output=True, text=True)
+            #Extract mu_gamma from Output-File
+            with open(path + '/outputs/outputMuGamma.txt', 'r') as file:
+                output = file.read()
+            tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
+            s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
+            Y_Values.append(float(s[0]))
+        else :     # Run full Cell-Problem...
+            # fist replace old parameters in parset
+            SetParametersCellProblem(alpha,beta,theta,gamma,mu1,rho1,lambda1,InputFilePath)
+
+            with open(InputFilePath, 'r') as file:
+                filedata = file.read()
+            filedata = re.sub('(?m)^'+xName+'=.*',xName+'='+str(x),filedata)
+            f = open(InputFilePath,'w')
+            f.write(filedata)
+            f.close()
+            # Run Cell-Problem
+            print("Run Cell-Problem for " + xName + " =" , x)
+            subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
+                                                 capture_output=True, text=True)
+            #Extract quantity from Output-File
+            Q, B = ReadEffectiveQuantities()
+            if yName == 'q1':                   # TODO: Better use dictionary?...
+                print('q1 used')
+                Y_Values.append(Q[0][0])
+            elif yName =='q2':
+                print('q2 used')
+                Y_Values.append(Q[1][1])
+            # elif yName =='q3':
+            #     print('q3 used')
+            #     Y_Values.append(Q[0][0])
+            elif yName =='q12':
+                print('q12 used')
+                Y_Values.append(Q[0][1])
+            elif yName =='q21':
+                print('q21 used')
+                Y_Values.append(Q[1][0])
+            elif yName =='q13':
+                print('q13 used')
+                Y_Values.append(Q[0][2])
+            elif yName =='q31':
+                print('q31 used')
+                Y_Values.append(Q[2][0])
+            elif yName =='q23':
+                print('q23 used')
+                Y_Values.append(Q[1][2])
+            elif yName =='q32':
+                print('q32 used')
+                Y_Values.append(Q[2][1])
+            elif yName =='b1':
+                print('b1 used')
+                Y_Values.append(B[0])
+            elif yName =='b2':
+                print('b2 used')
+                Y_Values.append(B[1])
+            elif yName =='b3':
+                print('b3 used')
+                Y_Values.append(B[2])
+            elif yName == 'angle' or yName =='type' or yName =='curvature':
+                # ------------- Run Matlab symbolic minimization program 'symMinimization'
+                eng = matlab.engine.start_matlab()
+                # s = eng.genpath(path + '/Matlab-Programs')
+                s = eng.genpath(path)
+                eng.addpath(s, nargout=0)
+                # print('current Matlab folder:', eng.pwd(nargout=1))
+                eng.cd('Matlab-Programs', nargout=0)  #switch to Matlab-Programs folder
+                # print('current Matlab folder:', eng.pwd(nargout=1))
+                Inp = False
+                Inp_T = True
+                print('Run symbolic Minimization...')
+                #Arguments: symMinization(print_Input,print_statPoint,print_Output,make_FunctionPlot, InputPath)
+                G, angle, type, curvature = eng.symMinimization(Inp,Inp,Inp,Inp, nargout=4)  #Name of program:symMinimization
+                # G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp,path + "/outputs", nargout=4)  #Optional: add Path
+                G = np.asarray(G) #cast Matlab Outout to numpy array
+                # --- print Output ---
+                print('Minimizer G:')
+                print(G)
+                print('angle:', angle)
+                print('type:', type )
+                print('curvature:', curvature)
+                if yName =='angle':
+                    print('angle used')
+                    Y_Values.append(angle)
+                if yName =='type':
+                    print('type used')
+                    Y_Values.append(type)
+                if yName =='curvature':
+                    print('curvature used')
+                    Y_Values.append(curvature)
+    # ------------end of for-loop -----------------
+    print("(Output) Values of " + yName + ": ", Y_Values)
+# ----------------end of if-statement -------------
+
+
+
+
+
+
+
+
+# ---------------- Create Plot -------------------
+plt.figure()
+# plt.title(r''+ yName + '-Plot')
+plt.plot(X_Values, Y_Values)
+plt.scatter(X_Values, Y_Values)
+# plt.axis([0, 6, 0, 20])
+plt.xlabel(xName)
+plt.ylabel(yName)
+
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+plt.show()
+# #---------------------------------------------------------------
diff --git a/txt.txt b/txt.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb87569bcf7e160256f79160602fa3af9664c3a2
--- /dev/null
+++ b/txt.txt
@@ -0,0 +1 @@
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\ No newline at end of file