cobyqa.models.Models.determinants

Models.determinants(x_new, k_new=None)

Compute the normalized determinants of the new interpolation systems.

Parameters:

x_newnumpy.ndarray, shape (n,)

New interpolation point. Its value is interpreted as relative to the origin, not the base point.

k_newint, optional

Index of the updated interpolation point. If k_new is not specified, all the possible determinants are computed.

Returns:

{float, numpy.ndarray, shape (npt,)}

Determinant(s) of the new interpolation system.

Raises:

numpy.linalg.LinAlgError

If the interpolation system is ill-defined.

Notes

The determinants are normalized by the determinant of the current interpolation system. For stability reasons, the calculations are done using the formula (2.12) in [1].

References

[1]

M. J. D. Powell. On updating the inverse of a KKT matrix. Technical Report DAMTP 2004/NA01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2004.