198 static PetscErrorCode PCDeflationSetSpace_Deflation(PC pc, Mat W, PetscBool transpose)  in PCDeflationSetSpace_Deflation()  argument
203   /* possibly allows W' = Wt (which is valid but not tested) */  in PCDeflationSetSpace_Deflation()
204   PetscCall(PetscObjectReference((PetscObject)W));  in PCDeflationSetSpace_Deflation()
207     def->Wt = W;  in PCDeflationSetSpace_Deflation()
209     PetscCall(MatDestroy(&def->W));  in PCDeflationSetSpace_Deflation()
210     def->W = W;  in PCDeflationSetSpace_Deflation()
222 . W         - deflation matrix
223 - transpose - indicates that W is an explicit transpose of the deflation matrix
228   Setting W as a multipliplicative `MATCOMPOSITE` enables use of the multilevel
229   deflation. If W = W0*W1*W2*...*Wn, W0 is taken as the first deflation space and
234   they are merged into a deflation matrix ...*W{n-1}*Wn.
238 PetscErrorCode PCDeflationSetSpace(PC pc, Mat W, PetscBool transpose)  in PCDeflationSetSpace()  argument
242   PetscValidHeaderSpecific(W, MAT_CLASSID, 2);  in PCDeflationSetSpace()
244   PetscTryMethod(pc, "PCDeflationSetSpace_C", (PC, Mat, PetscBool), (pc, W, transpose));  in PCDeflationSetSpace()
260   PCDeflationSetProjectionNullSpaceMat - Set the projection null space matrix (W'*A).
381   x <- x + W*(W'*A*W)^{-1}*W'*r  = x + Q*r
406     PetscCall(MatMult(def->Wt, r, w1)); /*    w1 <- W'*r                */  in PCPreSolve_Deflation()
408     PetscCall(MatMultHermitianTranspose(def->W, r, w1)); /*    w1 <- W'*r                */  in PCPreSolve_Deflation()
410   PetscCall(KSPSolve(def->WtAWinv, w1, w2)); /*    w2 <- (W'*A*W)^{-1}*w1    */  in PCPreSolve_Deflation()
411   PetscCall(MatMult(def->W, w2, r));         /*    r  <- W*w2                */  in PCPreSolve_Deflation()
418     z <- M^{-1}r - W*(W'*A*W)^{-1}*(W'*A*M^{-1}r - l*W'*r) = (P*M^{-1} + l*Q)*r
420     z <- M^{-1}*r - W*(W'*A*W)^{-1}*W'*A*M{-1}*r = P*M^{-1}*r
437     PetscCall(MatMult(def->WtA, z, w1)); /*    w1 <- W'*A*z              */  in PCApply_Deflation()
440         PetscCall(MatMult(def->Wt, r, w2)); /*    w2 <- W'*r                */  in PCApply_Deflation()
442         PetscCall(MatMultHermitianTranspose(def->W, r, w2)); /*    w2 <- W'*r                */  in PCApply_Deflation()
446     PetscCall(KSPSolve(def->WtAWinv, w1, w2)); /*    w2 <- (W'*A*W)^{-1}*w1    */  in PCApply_Deflation()
447     PetscCall(MatMult(def->W, w2, u));         /*    u  <- W*w2                */  in PCApply_Deflation()
475   if (def->W || def->Wt) {  in PCSetUp_Deflation()
482   if (def->W) {  in PCSetUp_Deflation()
483     PetscCall(PetscObjectTypeCompare((PetscObject)def->W, MATCOMPOSITE, &match));  in PCSetUp_Deflation()
485       PetscCall(MatCompositeGetType(def->W, &ctype));  in PCSetUp_Deflation()
486       PetscCall(MatCompositeGetNumberMat(def->W, &size));  in PCSetUp_Deflation()
489     PetscCall(MatCreateHermitianTranspose(def->Wt, &def->W));  in PCSetUp_Deflation()
501         for (i = 0; i < size; i++) PetscCall(MatCompositeGetMat(def->W, i, &mats[i]));  in PCSetUp_Deflation()
503         PetscCall(MatDestroy(&def->W));  in PCSetUp_Deflation()
504         def->W = mats[size];  in PCSetUp_Deflation()
516         /* PetscCall(MatCompositeSetMergeType(def->W,MAT_COMPOSITE_MERGE_LEFT)); */  in PCSetUp_Deflation()
517         PetscCall(MatCompositeMerge(def->W));  in PCSetUp_Deflation()
536         /* PetscCall(MatCompositeSetMergeType(def->W,MAT_COMPOSITE_MERGE_LEFT)); */  in PCSetUp_Deflation()
543     PetscCall(MatDestroy(&def->W));  in PCSetUp_Deflation()
544     PetscCall(MatHermitianTranspose(def->Wt, MAT_INITIAL_MATRIX, &def->W));  in PCSetUp_Deflation()
553       PetscCall(MatHermitianTranspose(def->W, MAT_INITIAL_MATRIX, &def->Wt));  in PCSetUp_Deflation()
556       PetscCall(MatTransposeMatMult(def->W, Amat, MAT_INITIAL_MATRIX, PETSC_CURRENT, &def->WtA));  in PCSetUp_Deflation()
562     PetscCall(MatGetSize(def->W, NULL, &m));  in PCSetUp_Deflation()
564       PetscCall(MatMatMult(def->WtA, def->W, MAT_INITIAL_MATRIX, PETSC_CURRENT, &def->WtAW));  in PCSetUp_Deflation()
569         /* Check columns of W are not in kernel of A */  in PCSetUp_Deflation()
574 …ctComm((PetscObject)def->WtAW), PETSC_ERR_SUP, "Column %" PetscInt_FMT " of W is in kernel of A.",…  in PCSetUp_Deflation()
684   PetscCall(MatDestroy(&def->W));  in PCReset_Deflation()
770 …Given a (complex - transpose is always Hermitian) full rank deflation matrix W, the deflation (int…
771     preconditioner uses projections Q = W*(W'*A*W)^{-1}*W' and P = I - Q*A, where A is pmat.
785 …deflation matrix, and the coarse problem (W'*A*W)^{-1} is solved by `KSPFCG` (if A is `MAT_SPD`) o…
854   def->W             = NULL;  in PCCreate_Deflation()