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<h1>
Efficient extraction of eigenvalues from a list of tensors
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<time class="published" datetime="2018-08-22T22:04:00+02:00">
22 août 2018
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<p>When you manipulate FEM results you generally have either a:
<em> scalar field,
</em> vector field,
* tensor field.</p>
<p>With tensorial results, it is often useful to extract the eigenvalues in order to find the principal values.</p>
<p>I have found that it is easier to store the components of the tensors in a 6 column pandas dataframe (because of the symmetric property of stress and strain tensors)</p>
<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="n">node</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1001</span><span class="p">,</span> <span class="mi">1002</span><span class="p">,</span> <span class="mi">1003</span><span class="p">,</span> <span class="mi">1004</span><span class="p">]</span> <span class="c1">#when dealing with FEM results you should remember at which element/node the result is computed (in the example, let&#39;s assume that we look at node from 1001 to 1004)</span>
<span class="n">tensor1</span><span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="c1">#eigen : 1</span>
<span class="n">tensor2</span><span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="c1">#eigen : 5.58443, -1.77931, -0.805118</span>
<span class="n">tensor3</span><span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="c1">#eigen : 8.85036, 4.46542, -1.31577</span>
<span class="n">tensor4</span><span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="c1">#eigen : 1, 2, 3</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">([</span><span class="n">tensor1</span><span class="p">,</span> <span class="n">tensor2</span><span class="p">,</span> <span class="n">tensor3</span><span class="p">,</span> <span class="n">tensor4</span><span class="p">],</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;XX&quot;</span><span class="p">,</span><span class="s2">&quot;YY&quot;</span><span class="p">,</span><span class="s2">&quot;ZZ&quot;</span><span class="p">,</span><span class="s2">&quot;XY&quot;</span><span class="p">,</span><span class="s2">&quot;XZ&quot;</span><span class="p">,</span><span class="s2">&quot;YZ&quot;</span><span class="p">])</span>
<span class="n">df</span><span class="o">.</span><span class="n">index</span> <span class="o">=</span> <span class="n">node</span>
<span class="n">df</span>
</pre></div>
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<th>1001</th>
<td>1</td>
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<td>0</td>
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<td>1</td>
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<td>1</td>
<td>2</td>
<td>3</td>
<td>0</td>
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<p>If you want to extract the eigenvalues of a tensor with numpy you have to pass a n by n ndarray to the eigenvalue function. In order to avoid having to loop over each node, this oneliner is highly optimized and will help you invert a large number of tensors efficiently.</p>
<p>The steps are basically, create a list of n by n values (here n=3) in the right order =&gt; reshape it to a list of tensors =&gt; pass it to the eigenvals function</p>
<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">LA</span>
</pre></div>
<div class="highlight"><pre><span></span><span class="n">eigenvals</span> <span class="o">=</span> <span class="n">LA</span><span class="o">.</span><span class="n">eigvals</span><span class="p">(</span><span class="n">df</span><span class="p">[[</span><span class="s2">&quot;XX&quot;</span><span class="p">,</span><span class="s2">&quot;XY&quot;</span><span class="p">,</span><span class="s2">&quot;XZ&quot;</span><span class="p">,</span><span class="s2">&quot;XY&quot;</span><span class="p">,</span><span class="s2">&quot;YY&quot;</span><span class="p">,</span><span class="s2">&quot;YZ&quot;</span><span class="p">,</span><span class="s2">&quot;XZ&quot;</span><span class="p">,</span><span class="s2">&quot;YZ&quot;</span><span class="p">,</span><span class="s2">&quot;ZZ&quot;</span><span class="p">]]</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">df</span><span class="p">),</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span>
<span class="n">eigenvals</span>
</pre></div>
<div class="highlight"><pre><span></span>array([[ 1. , 1. , 1. ],
[ 5.58442834, -0.80511809, -1.77931025],
[-1.31577211, 8.85035616, 4.46541595],
[ 1. , 2. , 3. ]])
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@ -235,7 +235,7 @@ At line 5 there is a plum which is purple and contains 28 kcal
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python/Moving_average_pandas.html
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python/Opening_SQLite_database.html
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python/Opening_file.html
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@ -193,7 +193,7 @@ If you try to open a non existing file in read mode 'r', a FileNotFoundError wil
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python/Optimized_numpy_random_intel.html
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python/Reading_data_from_a_sql_database_with_pandas.html
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python/Saving_a_matplotlib_figure_with_a_high_resolution.html
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python/Setting_up_the_notebook_for_plotting_with_matplotlib.html
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python/Writing_data_to_a_sql_database_with_pandas.html
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python/dask_distributed_parallelism.html
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python/updating_all_python_package_with_anaconda.html
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search.html
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sql/Sorting_results.html
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sql/WHERE_SQL_keywords.html
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sql/display_table.html
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sql/display_table_filter.html
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tipuesearch_content.json
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