Singular Value Decomposition Pane

The Singular Value Decomposition pane is on the PEST Properties dialog box.

Singular Value Decomposition and LQSR can not both be used together so activating one deactivates the other. If both are deactivated, PEST’s default solver is used.

The variables specified on the Singular Value Decomposition pane are described in the PEST User Manual, Part I, Section 4.4. More extensive descriptions of these variables are in the PEST user manual. The variables specified on this pane appear in the Singular Value Decomposition section of the PEST control file. The Singular Value Decomposition section is automatically deactivated if the PESTMODE is predictive analysis.

SVDMODE controls whether Singular Value Decomposition is used and how the parameter upgrade vector is computed if it is used. The options are to deactivate Singular Value Decomposition, use the normal method of Singular Value Decomposition, or used a damped version of Singular Value Decomposition. The damped method is preferred for cases involving many observations because it is faster.

MAXSING is the number of singular values before truncation. Ideally this should be equal to the optimal dimensionality of the solution space. This is difficult to determine (though the SUPCALC utility described in part II of the PEST User Manual may provide some help in this regard). Furthermore, normally the role of singular value decomposition is to achieve numerical stability of the inversion process rather than to provide regularization. (Tikhonov constraints normally serve the latter purpose). Hence the EIGTHRESH variable should be used to set the point of singular value truncation. To achieve this, set MAXSING to a number equal to or greater than the maximum number of estimable parameters. This is the best setting to use in the vast majority of cases.

EIGTHRESH is the ratio of lowest to highest eigenvalue of the (JtQJ + λI) matrix at which singular value truncation occurs. In the vast majority of cases a setting of 5E-7 is suitable for EIGTHRESH. Where numerical malperformance of a model adds considerable numerical noise to finite-difference derivatives, EIGTHRESH may need to be set higher than this – possibly as high as 1E-4.

EIGWRITE controls whether eigenvectors are saved by PEST to the .svd file. Sometimes an inspection of singular values can assist in understanding the degree to which an inverse problem is ill-posed. By saving only singular values and not eigenvectors, the size of the .svd file can be considerably reduced.