Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Truncate the subspace based on eigenvalue energy
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  truncation_tolerance  Specify the maximum percentage (as a decimal) of the eigenvalue energy not captured by the active subspace representation. 
Uses a criterion based on the derivative matrix eigenvalue energy.
Usage Tips
This subspace truncation method may work best when working with nonnormally distributed uncertain variables. If this automated diagnostic does not yield desirable results, consider using the explicit dimension truncation option or one of the other truncation methods.
Using the eigenvalue energy truncation metric, the subspace size is determined using the following equation:
where is the truncation_tolerance, is the estimated subspace size, is the size of the full space, and are the eigenvalues of the derivative matrix.