.. _auto_curves_eigen_values:

*COMPUTE EIGEN-VALUES OF A SYMMETRIC 3X3 MATRIX. ONLY 6 COMPONENTS ARE NEEDED.*
===============================================================================

Computes the three eigenvalues of a symmetric 3×3 matrix whose six independent components are supplied as time-history curves. Use this worker whenever you need the principal values of a stress, strain, or inertia tensor at every time step.

When to use
-----------

Classification: **process**.

Tagged: ``3x3``, ``eigen_values``, ``linear_algebra``, ``principal_values``, ``symmetric_matrix``, ``tensor``, ``time_history``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curves
     - curves
     - vector
     - —
     - 
     - Vector of time-history curves representing the six independent components of the symmetric 3×3 matrix (e.g., S11, S22, S33, S12, S13, S23 for a stress tensor); supply exactly 6 component curves in consistent units.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - curves_eigen_values_output_1
     - curves_eigen_values_output_1
     - vector
     - Vector of three time-history curves containing the three eigenvalues (principal values) of the input symmetric 3×3 matrix at each time step, ordered from smallest to largest.

Disciplines
-----------

- data.curve.transform
- data.signal_processing
- engineering.material.characterization
- engineering.structures

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curves_eigen_values <https://www.d3view.com/api/workflow/example?id=curves_eigen_values>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curves_eigen_values</code>. Schema hash: <code>42b498de9234</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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