docu

Author: ralfHielscher

_data/sidebars/function_reference_sidebar.yml

@@ -4822,6 +4822,10 @@ entries:
           url: /S2FunHarmonic.acos.html
           output: web
 
+        - title: "adjoint"
+          url: /S2FunHarmonic.adjoint.html
+          output: web
+
         - title: "approximate"
           url: /S2FunHarmonic.approximate.html
           output: web
@@ -4886,6 +4890,10 @@ entries:
           url: /S2FunHarmonic.horzcat.html
           output: web
 
+        - title: "interpolate"
+          url: /S2FunHarmonic.interpolate.html
+          output: web
+
         - title: "isempty"
           url: /S2FunHarmonic.isempty.html
           output: web
@@ -5122,6 +5130,10 @@ entries:
           url: /S2AxisFieldHarmonic.eval.html
           output: web
 
+        - title: "interpolate"
+          url: /S2AxisFieldHarmonic.interpolate.html
+          output: web
+
         - title: "quadrature"
           url: /S2AxisFieldHarmonic.quadrature.html
           output: web
@@ -5232,6 +5244,10 @@ entries:
           url: /S2VectorFieldHarmonic.eval.html
           output: web
 
+        - title: "interpolate"
+          url: /S2VectorFieldHarmonic.interpolate.html
+          output: web
+
         - title: "mean"
           url: /S2VectorFieldHarmonic.mean.html
           output: web
@@ -6449,6 +6465,10 @@ entries:
       url: /plottingOverview.html
       output: web
 
+    - title: "plottingConvention"
+      url: /plottingConvention.html
+      output: web
+
     - title: "mapPlot"
       url: /mapPlot.html
       output: web

pages/documentation_matlab/AxesAlignment.html

@@ -46,7 +46,7 @@
   north      : (0,1,0)
   east       : (1,0,0)
 {% endhighlight %}
-<p>The property <code class="language-plaintext highlighter-rouge">how2plot</code> is a handle class of type @plottingConvention and tells MTEX how to align the corresponding coordinate system on screen.</p>
+<p>The property <code class="language-plaintext highlighter-rouge">how2plot</code> is a handle class of type <code class="language-plaintext highlighter-rouge"><a href="plottingConvention.plottingConvention.html">plottingConvention</a></code> and tells MTEX how to align the corresponding coordinate system on screen.</p>
 {% highlight matlab %}
 plot(v1,'label','v_1','figSize','small')
 annotate([xvector,yvector,zvector],'labeled','backgroundcolor','w')
@@ -69,7 +69,7 @@
 <center>
 {% include inline_image.html file="AxesAlignment_02.png" %}
 </center>
-<p>Note that @plottingConvention is a handle class, i.e. changing <code class="language-plaintext highlighter-rouge">v1.how2plot</code> changes also <code class="language-plaintext highlighter-rouge">v2.how2plot</code>
+<p>Note that <code class="language-plaintext highlighter-rouge"><a href="plottingConvention.plottingConvention.html">plottingConvention</a></code> is a handle class, i.e. changing <code class="language-plaintext highlighter-rouge">v1.how2plot</code> changes also <code class="language-plaintext highlighter-rouge">v2.how2plot</code>
 </p>
 {% highlight matlab %}
 v2.how2plot
@@ -88,7 +88,7 @@
 <center>
 {% include inline_image.html file="AxesAlignment_03.png" %}
 </center>
-<p>In order to have different plotting axes alignments within one MTEX session we have to define a new @plottingConvention by</p>
+<p>In order to have different plotting axes alignments within one MTEX session we have to define a new <code class="language-plaintext highlighter-rouge"><a href="plottingConvention.plottingConvention.html">plottingConvention</a></code> by</p>
 {% highlight matlab %}
 % instantiate a new plotting convention and sets it up
 pC2 = plottingConvention; pC2.north = yvector
@@ -114,7 +114,7 @@
 <center>
 {% include inline_image.html file="AxesAlignment_04.png" %}
 </center>
-<p>When initiating a new <a href="vector3d.vector3d.html">vector3d</a> MTEX uses <code class="language-plaintext highlighter-rouge">plottingConvention.default</code> as default plotting convention. This default plotting convention can be changed by</p>
+<p>When initiating a new <code class="language-plaintext highlighter-rouge"><a href="vector3d.vector3d.html">vector3d</a></code> MTEX uses <code class="language-plaintext highlighter-rouge">plottingConvention.default</code> as default plotting convention. This default plotting convention can be changed by</p>
 {% highlight matlab %}
 plotx2north
 plotzOutOfPlane

pages/documentation_matlab/HarmonicApproximationTheory.html

@@ -10,8 +10,8 @@
 <head>
 <META http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <!--
-      This HTML was auto-generated from MATLAB code.
-      To make changes, update the MATLAB code and republish this document.
+This HTML was auto-generated from MATLAB code.
+To make changes, update the MATLAB code and republish this document.
     -->
 <title>Harmonic Approximation from Discrete Data</title>
 <link rel="schema.DC" href="http://purl.org/dc/elements/1.1/">
@@ -62,7 +62,9 @@ <h2 id="5">Harmonic Approximation (without Regularization)</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+SO3F1 = SO3FunHarmonic (1 → xyz)
+  bandwidth: 17
+  weight: 0.99
 {% endhighlight %}
 <center>
 {% include inline_image.html file="HarmonicApproximationTheory_02.png" %}
@@ -73,7 +75,8 @@ <h2 id="5">Harmonic Approximation (without Regularization)</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+ans =
+    0.0779
 {% endhighlight %}
 <p>If we choose the bandwidth to high and try to compute more Fourier coefficients as there are data points given, then we are in the overdetermined case and obtain oversampling.</p>
 {% highlight matlab %}
@@ -82,7 +85,15 @@ <h2 id="5">Harmonic Approximation (without Regularization)</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+Warning: The oversampling factor in the
+approximation process is 0.43553. This could lead to
+a bad approximation. You may should not set the
+regularization parameter to 0 in the approximation
+method. 
+ 
+SO3F2 = SO3FunHarmonic (1 → xyz)
+  bandwidth: 32
+  weight: 0.25
 {% endhighlight %}
 <center>
 {% include inline_image.html file="HarmonicApproximationTheory_03.png" %}
@@ -93,7 +104,8 @@ <h2 id="5">Harmonic Approximation (without Regularization)</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+ans =
+    0.0123
 {% endhighlight %}
 <p>Lets take a look on the Fourier coefficients of this approximations.</p>
 {% highlight matlab %}
@@ -120,7 +132,9 @@ <h2 id="12">Harmonic Approximation with Regularization</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+SO3F3 = SO3FunHarmonic (1 → xyz)
+  bandwidth: 32
+  weight: 0.99
 {% endhighlight %}
 <center>
 {% include inline_image.html file="HarmonicApproximationTheory_05.png" %}
@@ -132,7 +146,8 @@ <h2 id="12">Harmonic Approximation with Regularization</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+ans =
+    0.0824
 {% endhighlight %}
 <p>Note that this Error is not the value of the above energy functional which is minimized by lsqr.</p>
 <p>It is not easy to specify the parameter \(\lambda\), which describes the intensity of regularization. If we choose a value that is too large, we smooth the function too much. If \(\lambda\) is chosen too small, there is almost no regularization and we get oscillations.</p>
@@ -176,7 +191,9 @@ <h2 id="12">Harmonic Approximation with Regularization</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+SO3F5 = SO3FunHarmonic (1 → xyz)
+  bandwidth: 32
+  weight: 0.98
 {% endhighlight %}
 <center>
 {% include inline_image.html file="HarmonicApproximationTheory_08.png" %}
@@ -203,7 +220,13 @@ <h2 id="21">LSQR-Parameters</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
+Elapsed time is 1.691727 seconds.
+Number of iterations = 6
+Value of energy functional = 100.132
 
+Elapsed time is 8.968955 seconds.
+Number of iterations = 36
+Value of energy functional = 100.0924
 {% endhighlight %}
 </div>
 </body>

pages/examples_matlab/ExSeismicPlots.html

@@ -53,7 +53,18 @@ <h2 id="1">Crystal Symmetry and definition of the elastic stiffness tensor</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+C = stiffnessTensor (Olivine)
+  density: 3.355            
+  unit   : GPa              
+  rank   : 4 (3 x 3 x 3 x 3)
+ 
+  tensor in Voigt matrix representation:
+ 320.5  68.2  71.6     0     0     0
+  68.2 196.5  76.8     0     0     0
+  71.6  76.8 233.5     0     0     0
+     0     0     0    64     0     0
+     0     0     0     0    77     0
+     0     0     0     0     0  78.7
 {% endhighlight %}
 <p>Compute seismic velocities as functions on the sphere</p>
 {% highlight matlab %}

pages/examples_matlab/ExSlipSystemAlumina.html

@@ -153,7 +153,10 @@ <h2 id="7">Schmid Factor Analysis</h2>
 {% endhighlight %}
 
 {% highlight plaintext %}
-
+sS = slipSystem (Corundum)
+ 
+   U    V    T    W  | H    K    I    L CRSS
+  -1    2   -1    0    1    0   -1    1    1
 {% endhighlight %}
 <p>Next we determine the Schmid factor for all symmetrically equivalent slip systems.</p>
 {% highlight matlab %}