Calibration solvers

Two calibration solvers are available in ASKAPsoft. The solver parset parameter defines the type of the calibration solver to use with the choice between SVD, and LSQR. The SVD solver is based on calculation of the singular value decomposition. It generally performs well for small problem sizes, but shows poor performance for large number of anthennas. It does not require setting free parameters. The iterative least-squares LSQR solver is a high performance solver, that is capable of performing calibration on the SKA scales (i.e., very large number of antennas). It scales nearly linearly with the number of data, i.e., quadratically with the number of antennas. It requires setting several free parameters, such as stopping criteria and damping parameters. Due to its general least-square nature, it also allows adding additional constraints into the system of equations (for example, solution smoothness).

Common Parameters

Parameters for all solvers:

Parameter	Type	Default	Description
solver	string	SVD	Selection of solver. Either “SVD” or “LSQR”.

The SVD solver does not require any additional parameters. Additional parameters understood by the LSQR solver are given in the following section.

LSQR Solver Parameters

All parameters given in the next table have solver.LSQR prefix (e.g., Cbpcalibrator.solver.LSQR.niter).

Parameter	Type	Default	Description
rmin	float	1.e-13	Minimum relative residual stopping criterion.
niter	int	100	Maximum number of minor cycles. This stopping criterion is used when minimum relative residual stopping criterion could not be reached within the specified number of solver iterations.
alpha	float	0.01	The damping on the solution perturbation (that is performed at every major cycle). Nonzero damping values help dealing with rank deficient systems.
verbose	bool	false	The value of “true” enables lots of output.
parallelMatrix	bool	false	Enables regime where all frequency channels are solved together, and therefore can be coupled via frequency-dependant constraints (e.g. smoothness). The columns of the (block-diagonal) matrix, and the bandpass solution are split between different ranks. This option is only supported in ccalibrator, and must be accompanied by the following options: Ccalibrator.solver=LSQR, Ccalibrator.solve=bandpass. The data partitioning is then defined via setting Ccalibrator.chanperworker, and Ccalibrator.chunk, in analogous to Channels option in cimager (see cimager for more details).
smoothing	bool	false	Enables smoothing constraints along frequency channels. This allows obtaining smoother gain phase and amplitude. Must be used together with Ccalibrator.solve=bandpass option.
smoothing.MinWeight	float	0.0	Starting smoothing weight (at the first major cycle).
smoothing.MaxWeight	float	3.e+6	Final smoothing weight (after nsteps cycles). Basically, this controls the degree of smoothness.
smoothing.nsteps	int	10	The number of major cycles during which the smoothing weight is increased from MinWeight to MaxWeight, using logarithmic steps.

Examples

LSQR Solver

Cbpcalibrator.solver                            = LSQR
Cbpcalibrator.solver.LSQR.niter                 = 100
Cbpcalibrator.solver.LSQR.rmin                  = 1.e-13
Cbpcalibrator.solver.LSQR.alpha                 = 0.01
Cbpcalibrator.solver.LSQR.verbose               = false