Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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truncation_tolerance


Specify the maximum percentage (as a decimal) of the eigenvalue energy not captured by the active subspace representation.

Specification

Alias: none

Argument(s): REAL

Description

The truncation_tolerance is used in the energy truncation method to identify an active subspace. The truncation tolerance is used in the following equation to determine the subspace size:

\[n = \inf \left\lbrace d \in \mathbf{Z} \quad\middle|\quad 1 \le d \le N \quad \wedge\quad 1 - \frac{\sum_{i = 1}^{d} \lambda_i}{\sum_{i = 1}^{N} \lambda_i} \,<\, \epsilon \right\rbrace \]

where $\epsilon$ is the truncation_tolerance, $n$ is the estimated subspace size, $N$ is the size of the full space, and $\lambda_i$ are the eigenvalues of the derivative matrix.

The default value for truncation_tolerance is $1\times 10^{-6}$.