KSPCGUseSingleReduction#

Merge the two inner products needed in KSPCG into a single MPI_Allreduce() call.

Synopsis#

#include "petscksp.h" 
PetscErrorCode KSPCGUseSingleReduction(KSP ksp, PetscBool flg)

Logically Collective

Input Parameters#

ksp - the iterative context
flg - turn on or off the single reduction

Options Database Key#

-ksp_cg_single_reduction (true|false) - Merge inner products into single MPI_Allreduce()

Notes#

The algorithm used in this case is described as Method 1 in [DAzevedoER93]. V. Eijkhout credits the algorithm initially to Chronopoulos and Gear.

It requires two extra work vectors than the conventional implementation in PETSc.

An active trust-region radius, a preconditioned trust-region norm, a negative objective target, or convergence at negative curvature is unsupported and raises an error during KSPSolve() when this variant is enabled. This variant does not compute the objective returned by KSPCGGetObjFcn() or the solution norm returned by KSPCGGetTRSolutionNorm().

See also KSPPIPECG, KSPPIPECR, and KSPGROPPCG that use non-blocking reductions. Pipelined Krylov Methods,

References#

[DAzevedoER93]

EF D’Azevedo, VL Eijkhout, and CH Romine. Conjugate gradient algorithms with reduced synchronization overhead on distributed memory multiprocessors. Computer Science Technical Report CS-93-185, University of Tennessee, Knoxville, 1993.