#include "slepcsvd.h" PetscErrorCode SVDSetThreshold(SVD svd,PetscReal thres,PetscBool rel)Logically Collective
| svd | - the singular value solver context | |
| thres | - the threshold value | |
| rel | - whether the threshold is relative or not |
| -svd_threshold_absolute <thres> | - Sets an absolute threshold | |
| -svd_threshold_relative <thres> | - Sets a relative threshold |
If the solver is configured to compute smallest singular values, then the threshold must be interpreted in the opposite direction, i.e., the computation will stop when one of the computed singular values is above the threshold.
In the case of largest singular values, the threshold can be made relative with respect to the largest singular value (i.e., the matrix norm).
The test against the threshold is done for converged singular values, which implies that the final number of converged singular values will be at least one more than the actual number of values below/above the threshold.
Since the number of computed singular values is not known a priori, the solver will need to reallocate the basis of vectors internally, to have enough room to accommodate all the singular vectors. Hence, this option must be used with caution to avoid out-of-memory problems. The recommendation is to set the value of ncv to be larger than the estimated number of singular values, to minimize the number of reallocations.
This functionality is most useful when computing largest singular values. A typical use case is to compute a low rank approximation of a matrix. Suppose we know that singular values decay abruptly around a certain index k, which is unknown. Then using a small relative threshold such as 0.2 will guarantee that the computed singular vectors capture the numerical rank k. However, if the matrix does not have low rank, i.e., singular values decay progressively, then a value of 0.2 will imply a very high cost, both computationally and in memory.
If a number of wanted singular values has been set with SVDSetDimensions() it is also taken into account and the solver will stop when one of the two conditions (threshold or number of converged values) is met.
Use SVDSetStoppingTest() to return to the usual computation of a fixed number of singular values.