xref: /petsc/src/ksp/ksp/impls/cg/pipelcg/pipelcg.c (revision 834855d6effb0d027771461c8e947ee1ce5a1e17)
1 #include <petsc/private/kspimpl.h>
2 #include <petsc/private/vecimpl.h>
3 
4 #define offset(j)       PetscMax(((j) - (2 * l)), 0)
5 #define shift(i, j)     ((i) - offset(j))
6 #define G(i, j)         (plcg->G[((j) * (2 * l + 1)) + (shift((i), (j)))])
7 #define G_noshift(i, j) (plcg->G[((j) * (2 * l + 1)) + (i)])
8 #define alpha(i)        (plcg->alpha[i])
9 #define gamma(i)        (plcg->gamma[i])
10 #define delta(i)        (plcg->delta[i])
11 #define sigma(i)        (plcg->sigma[i])
12 #define req(i)          (plcg->req[i])
13 
14 typedef struct KSP_CG_PIPE_L_s KSP_CG_PIPE_L;
15 struct KSP_CG_PIPE_L_s {
16   PetscInt     l; /* pipeline depth */
17   Vec         *Z; /* Z vectors (shifted base) */
18   Vec         *U; /* U vectors (unpreconditioned shifted base) */
19   Vec         *V; /* V vectors (original base) */
20   Vec         *Q; /* Q vectors (auxiliary bases) */
21   Vec          p; /* work vector */
22   PetscScalar *G; /* such that Z = VG (band matrix)*/
23   PetscScalar *gamma, *delta, *alpha;
24   PetscReal    lmin, lmax; /* min and max eigen values estimates to compute base shifts */
25   PetscReal   *sigma;      /* base shifts */
26   MPI_Request *req;        /* request array for asynchronous global collective */
27   PetscBool    show_rstrt; /* flag to show restart information in output (default: not shown) */
28 };
29 
30 /*
31   KSPSetUp_PIPELCG - Sets up the workspace needed by the PIPELCG method.
32 
33   This is called once, usually automatically by KSPSolve() or KSPSetUp()
34   but can be called directly by KSPSetUp()
35 */
KSPSetUp_PIPELCG(KSP ksp)36 static PetscErrorCode KSPSetUp_PIPELCG(KSP ksp)
37 {
38   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
39   PetscInt       l = plcg->l, max_it = ksp->max_it;
40   MPI_Comm       comm;
41 
42   PetscFunctionBegin;
43   comm = PetscObjectComm((PetscObject)ksp);
44   PetscCheck(max_it >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "%s: max_it argument must be positive.", ((PetscObject)ksp)->type_name);
45   PetscCheck(l >= 1, comm, PETSC_ERR_ARG_OUTOFRANGE, "%s: pipel argument must be positive.", ((PetscObject)ksp)->type_name);
46   PetscCheck(l <= max_it, comm, PETSC_ERR_ARG_OUTOFRANGE, "%s: pipel argument must be less than max_it.", ((PetscObject)ksp)->type_name);
47 
48   PetscCall(KSPSetWorkVecs(ksp, 1)); /* get work vectors needed by PIPELCG */
49   plcg->p = ksp->work[0];
50 
51   PetscCall(VecDuplicateVecs(plcg->p, PetscMax(3, l + 1), &plcg->Z));
52   PetscCall(VecDuplicateVecs(plcg->p, 3, &plcg->U));
53   PetscCall(VecDuplicateVecs(plcg->p, 3, &plcg->V));
54   PetscCall(VecDuplicateVecs(plcg->p, 3 * (l - 1) + 1, &plcg->Q));
55   PetscCall(PetscCalloc1(2, &plcg->alpha));
56   PetscCall(PetscCalloc1(l, &plcg->sigma));
57   PetscFunctionReturn(PETSC_SUCCESS);
58 }
59 
KSPReset_PIPELCG(KSP ksp)60 static PetscErrorCode KSPReset_PIPELCG(KSP ksp)
61 {
62   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
63   PetscInt       l    = plcg->l;
64 
65   PetscFunctionBegin;
66   PetscCall(PetscFree(plcg->sigma));
67   PetscCall(PetscFree(plcg->alpha));
68   PetscCall(VecDestroyVecs(PetscMax(3, l + 1), &plcg->Z));
69   PetscCall(VecDestroyVecs(3, &plcg->U));
70   PetscCall(VecDestroyVecs(3, &plcg->V));
71   PetscCall(VecDestroyVecs(3 * (l - 1) + 1, &plcg->Q));
72   PetscFunctionReturn(PETSC_SUCCESS);
73 }
74 
KSPDestroy_PIPELCG(KSP ksp)75 static PetscErrorCode KSPDestroy_PIPELCG(KSP ksp)
76 {
77   PetscFunctionBegin;
78   PetscCall(KSPReset_PIPELCG(ksp));
79   PetscCall(KSPDestroyDefault(ksp));
80   PetscFunctionReturn(PETSC_SUCCESS);
81 }
82 
KSPSetFromOptions_PIPELCG(KSP ksp,PetscOptionItems PetscOptionsObject)83 static PetscErrorCode KSPSetFromOptions_PIPELCG(KSP ksp, PetscOptionItems PetscOptionsObject)
84 {
85   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
86   PetscBool      flag = PETSC_FALSE;
87 
88   PetscFunctionBegin;
89   PetscOptionsHeadBegin(PetscOptionsObject, "KSP PIPELCG options");
90   PetscCall(PetscOptionsInt("-ksp_pipelcg_pipel", "Pipeline length", "", plcg->l, &plcg->l, &flag));
91   if (!flag) plcg->l = 1;
92   PetscCall(PetscOptionsReal("-ksp_pipelcg_lmin", "Estimate for smallest eigenvalue", "", plcg->lmin, &plcg->lmin, &flag));
93   if (!flag) plcg->lmin = 0.0;
94   PetscCall(PetscOptionsReal("-ksp_pipelcg_lmax", "Estimate for largest eigenvalue", "", plcg->lmax, &plcg->lmax, &flag));
95   if (!flag) plcg->lmax = 0.0;
96   PetscCall(PetscOptionsBool("-ksp_pipelcg_monitor", "Output information on restarts when they occur? (default: 0)", "", plcg->show_rstrt, &plcg->show_rstrt, &flag));
97   if (!flag) plcg->show_rstrt = PETSC_FALSE;
98   PetscOptionsHeadEnd();
99   PetscFunctionReturn(PETSC_SUCCESS);
100 }
101 
MPIU_Iallreduce(void * sendbuf,void * recvbuf,PetscMPIInt count,MPI_Datatype datatype,MPI_Op op,MPI_Comm comm,MPI_Request * request)102 static PetscMPIInt MPIU_Iallreduce(void *sendbuf, void *recvbuf, PetscMPIInt count, MPI_Datatype datatype, MPI_Op op, MPI_Comm comm, MPI_Request *request)
103 {
104   PetscMPIInt err;
105 #if defined(PETSC_HAVE_MPI_NONBLOCKING_COLLECTIVES)
106   err = MPI_Iallreduce(sendbuf, recvbuf, count, datatype, op, comm, request);
107 #else
108   err      = MPI_Allreduce(sendbuf, recvbuf, count, datatype, op, comm);
109   *request = MPI_REQUEST_NULL;
110 #endif
111   return err;
112 }
113 
KSPView_PIPELCG(KSP ksp,PetscViewer viewer)114 static PetscErrorCode KSPView_PIPELCG(KSP ksp, PetscViewer viewer)
115 {
116   KSP_CG_PIPE_L *plcg    = (KSP_CG_PIPE_L *)ksp->data;
117   PetscBool      isascii = PETSC_FALSE, isstring = PETSC_FALSE;
118 
119   PetscFunctionBegin;
120   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
121   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
122   if (isascii) {
123     PetscCall(PetscViewerASCIIPrintf(viewer, "  Pipeline depth: %" PetscInt_FMT "\n", plcg->l));
124     PetscCall(PetscViewerASCIIPrintf(viewer, "  Minimal eigenvalue estimate %g\n", (double)plcg->lmin));
125     PetscCall(PetscViewerASCIIPrintf(viewer, "  Maximal eigenvalue estimate %g\n", (double)plcg->lmax));
126   } else if (isstring) {
127     PetscCall(PetscViewerStringSPrintf(viewer, "  Pipeline depth: %" PetscInt_FMT "\n", plcg->l));
128     PetscCall(PetscViewerStringSPrintf(viewer, "  Minimal eigenvalue estimate %g\n", (double)plcg->lmin));
129     PetscCall(PetscViewerStringSPrintf(viewer, "  Maximal eigenvalue estimate %g\n", (double)plcg->lmax));
130   }
131   PetscFunctionReturn(PETSC_SUCCESS);
132 }
133 
KSPSolve_InnerLoop_PIPELCG(KSP ksp)134 static PetscErrorCode KSPSolve_InnerLoop_PIPELCG(KSP ksp)
135 {
136   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
137   Mat            A = NULL, Pmat = NULL;
138   PetscInt       it = 0, max_it = ksp->max_it, l = plcg->l, i = 0, j = 0, k = 0;
139   PetscInt       start = 0, middle = 0, end = 0;
140   Vec           *Z = plcg->Z, *U = plcg->U, *V = plcg->V, *Q = plcg->Q;
141   Vec            x = NULL, p = NULL, temp = NULL;
142   PetscScalar    sum_dummy = 0.0, eta = 0.0, zeta = 0.0, lambda = 0.0;
143   PetscReal      dp = 0.0, tmp = 0.0, beta = 0.0, invbeta2 = 0.0;
144   MPI_Comm       comm;
145   PetscMPIInt    mpin;
146 
147   PetscFunctionBegin;
148   x = ksp->vec_sol;
149   p = plcg->p;
150 
151   comm = PetscObjectComm((PetscObject)ksp);
152   PetscCall(PCGetOperators(ksp->pc, &A, &Pmat));
153 
154   for (it = 0; it < max_it + l; ++it) {
155     /* Multiplication  z_{it+1} =  Az_{it} */
156     /* Shift the U vector pointers */
157     temp = U[2];
158     for (i = 2; i > 0; i--) U[i] = U[i - 1];
159     U[0] = temp;
160     if (it < l) {
161       /* SpMV and Sigma-shift and Prec */
162       PetscCall(MatMult(A, Z[l - it], U[0]));
163       PetscCall(VecAXPY(U[0], -sigma(it), U[1]));
164       PetscCall(KSP_PCApply(ksp, U[0], Z[l - it - 1]));
165       if (it < l - 1) PetscCall(VecCopy(Z[l - it - 1], Q[3 * it]));
166     } else {
167       /* Shift the Z vector pointers */
168       temp = Z[PetscMax(l, 2)];
169       for (i = PetscMax(l, 2); i > 0; --i) Z[i] = Z[i - 1];
170       Z[0] = temp;
171       /* SpMV and Prec */
172       PetscCall(MatMult(A, Z[1], U[0]));
173       PetscCall(KSP_PCApply(ksp, U[0], Z[0]));
174     }
175 
176     /* Adjust the G matrix */
177     if (it >= l) {
178       if (it == l) {
179         /* MPI_Wait for G(0,0),scale V0 and Z and U and Q vectors with 1/beta */
180         PetscCallMPI(MPI_Wait(&req(0), MPI_STATUS_IGNORE));
181         beta    = PetscSqrtReal(PetscRealPart(G(0, 0)));
182         G(0, 0) = 1.0;
183         PetscCall(VecAXPY(V[0], 1.0 / beta, p)); /* this assumes V[0] to be zero initially */
184         for (j = 0; j <= PetscMax(l, 2); ++j) PetscCall(VecScale(Z[j], 1.0 / beta));
185         for (j = 0; j <= 2; ++j) PetscCall(VecScale(U[j], 1.0 / beta));
186         for (j = 0; j < l - 1; ++j) PetscCall(VecScale(Q[3 * j], 1.0 / beta));
187       }
188 
189       /* MPI_Wait until the dot products,started l iterations ago,are completed */
190       PetscCallMPI(MPI_Wait(&req(it - l + 1), MPI_STATUS_IGNORE));
191       if (it >= 2 * l) {
192         for (j = PetscMax(0, it - 3 * l + 1); j <= it - 2 * l; j++) G(j, it - l + 1) = G(it - 2 * l + 1, j + l); /* exploit symmetry in G matrix */
193       }
194 
195       if (it <= 2 * l - 1) {
196         invbeta2 = 1.0 / (beta * beta);
197         /* Scale columns 1 up to l of G with 1/beta^2 */
198         for (j = PetscMax(it - 3 * l + 1, 0); j <= it - l + 1; ++j) G(j, it - l + 1) *= invbeta2;
199       }
200 
201       for (j = PetscMax(it - 2 * l + 2, 0); j <= it - l; ++j) {
202         sum_dummy = 0.0;
203         for (k = PetscMax(it - 3 * l + 1, 0); k <= j - 1; ++k) sum_dummy = sum_dummy + G(k, j) * G(k, it - l + 1);
204         G(j, it - l + 1) = (G(j, it - l + 1) - sum_dummy) / G(j, j);
205       }
206 
207       sum_dummy = 0.0;
208       for (k = PetscMax(it - 3 * l + 1, 0); k <= it - l; ++k) sum_dummy = sum_dummy + G(k, it - l + 1) * G(k, it - l + 1);
209 
210       tmp = PetscRealPart(G(it - l + 1, it - l + 1) - sum_dummy);
211       /* Breakdown check */
212       if (tmp < 0) {
213         if (plcg->show_rstrt) PetscCall(PetscPrintf(comm, "Sqrt breakdown in iteration %" PetscInt_FMT ": sqrt argument is %e. Iteration was restarted.\n", ksp->its + 1, (double)tmp));
214         /* End hanging dot-products in the pipeline before exiting for-loop */
215         start = it - l + 2;
216         end   = PetscMin(it + 1, max_it + 1); /* !warning! 'it' can actually be greater than 'max_it' */
217         for (i = start; i < end; ++i) PetscCallMPI(MPI_Wait(&req(i), MPI_STATUS_IGNORE));
218         break;
219       }
220       G(it - l + 1, it - l + 1) = PetscSqrtReal(tmp);
221 
222       if (it < 2 * l) {
223         if (it == l) {
224           gamma(it - l) = (G(it - l, it - l + 1) + sigma(it - l) * G(it - l, it - l)) / G(it - l, it - l);
225         } else {
226           gamma(it - l) = (G(it - l, it - l + 1) + sigma(it - l) * G(it - l, it - l) - delta(it - l - 1) * G(it - l - 1, it - l)) / G(it - l, it - l);
227         }
228         delta(it - l) = G(it - l + 1, it - l + 1) / G(it - l, it - l);
229       } else {
230         gamma(it - l) = (G(it - l, it - l) * gamma(it - 2 * l) + G(it - l, it - l + 1) * delta(it - 2 * l) - G(it - l - 1, it - l) * delta(it - l - 1)) / G(it - l, it - l);
231         delta(it - l) = (G(it - l + 1, it - l + 1) * delta(it - 2 * l)) / G(it - l, it - l);
232       }
233 
234       /* Recursively compute the next V, Q, Z and U vectors */
235       /* Shift the V vector pointers */
236       temp = V[2];
237       for (i = 2; i > 0; i--) V[i] = V[i - 1];
238       V[0] = temp;
239 
240       /* Recurrence V vectors */
241       if (l == 1) {
242         PetscCall(VecCopy(Z[1], V[0]));
243       } else {
244         PetscCall(VecCopy(Q[0], V[0]));
245       }
246       if (it == l) {
247         PetscCall(VecAXPY(V[0], sigma(0) - gamma(it - l), V[1]));
248       } else {
249         alpha(0) = sigma(0) - gamma(it - l);
250         alpha(1) = -delta(it - l - 1);
251         PetscCall(VecMAXPY(V[0], 2, &alpha(0), &V[1]));
252       }
253       PetscCall(VecScale(V[0], 1.0 / delta(it - l)));
254 
255       /* Recurrence Q vectors */
256       for (j = 0; j < l - 1; ++j) {
257         /* Shift the Q vector pointers */
258         temp = Q[3 * j + 2];
259         for (i = 2; i > 0; i--) Q[3 * j + i] = Q[3 * j + i - 1];
260         Q[3 * j] = temp;
261 
262         if (j < l - 2) {
263           PetscCall(VecCopy(Q[3 * (j + 1)], Q[3 * j]));
264         } else {
265           PetscCall(VecCopy(Z[1], Q[3 * j]));
266         }
267         if (it == l) {
268           PetscCall(VecAXPY(Q[3 * j], sigma(j + 1) - gamma(it - l), Q[3 * j + 1]));
269         } else {
270           alpha(0) = sigma(j + 1) - gamma(it - l);
271           alpha(1) = -delta(it - l - 1);
272           PetscCall(VecMAXPY(Q[3 * j], 2, &alpha(0), &Q[3 * j + 1]));
273         }
274         PetscCall(VecScale(Q[3 * j], 1.0 / delta(it - l)));
275       }
276 
277       /* Recurrence Z and U vectors */
278       if (it == l) {
279         PetscCall(VecAXPY(Z[0], -gamma(it - l), Z[1]));
280         PetscCall(VecAXPY(U[0], -gamma(it - l), U[1]));
281       } else {
282         alpha(0) = -gamma(it - l);
283         alpha(1) = -delta(it - l - 1);
284         PetscCall(VecMAXPY(Z[0], 2, &alpha(0), &Z[1]));
285         PetscCall(VecMAXPY(U[0], 2, &alpha(0), &U[1]));
286       }
287       PetscCall(VecScale(Z[0], 1.0 / delta(it - l)));
288       PetscCall(VecScale(U[0], 1.0 / delta(it - l)));
289     }
290 
291     /* Compute and communicate the dot products */
292     if (it < l) {
293       for (j = 0; j < it + 2; ++j) PetscCall((*U[0]->ops->dot_local)(U[0], Z[l - j], &G(j, it + 1))); /* dot-products (U[0],Z[j]) */
294       PetscCall(PetscMPIIntCast(it + 2, &mpin));
295       PetscCallMPI(MPIU_Iallreduce(MPI_IN_PLACE, &G(0, it + 1), mpin, MPIU_SCALAR, MPIU_SUM, comm, &req(it + 1)));
296     } else if ((it >= l) && (it < max_it)) {
297       middle = it - l + 2;
298       end    = it + 2;
299       PetscCall((*U[0]->ops->dot_local)(U[0], V[0], &G(it - l + 1, it + 1)));                                      /* dot-product (U[0],V[0]) */
300       for (j = middle; j < end; ++j) PetscCall((*U[0]->ops->dot_local)(U[0], plcg->Z[it + 1 - j], &G(j, it + 1))); /* dot-products (U[0],Z[j]) */
301       PetscCall(PetscMPIIntCast(l + 1, &mpin));
302       PetscCallMPI(MPIU_Iallreduce(MPI_IN_PLACE, &G(it - l + 1, it + 1), mpin, MPIU_SCALAR, MPIU_SUM, comm, &req(it + 1)));
303     }
304 
305     /* Compute solution vector and residual norm */
306     if (it >= l) {
307       if (it == l) {
308         if (ksp->its != 0) ++ksp->its;
309         eta  = gamma(0);
310         zeta = beta;
311         PetscCall(VecCopy(V[1], p));
312         PetscCall(VecScale(p, 1.0 / eta));
313         PetscCall(VecAXPY(x, zeta, p));
314         dp = beta;
315       } else if (it > l) {
316         k = it - l;
317         ++ksp->its;
318         lambda = delta(k - 1) / eta;
319         eta    = gamma(k) - lambda * delta(k - 1);
320         zeta   = -lambda * zeta;
321         PetscCall(VecScale(p, -delta(k - 1) / eta));
322         PetscCall(VecAXPY(p, 1.0 / eta, V[1]));
323         PetscCall(VecAXPY(x, zeta, p));
324         dp = PetscAbsScalar(zeta);
325       }
326       ksp->rnorm = dp;
327       PetscCall(KSPLogResidualHistory(ksp, dp));
328       PetscCall(KSPMonitor(ksp, ksp->its, dp));
329       PetscCall((*ksp->converged)(ksp, ksp->its, dp, &ksp->reason, ksp->cnvP));
330 
331       if (ksp->its >= max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
332       if (ksp->reason) {
333         /* End hanging dot-products in the pipeline before exiting for-loop */
334         start = it - l + 2;
335         end   = PetscMin(it + 2, max_it + 1); /* !warning! 'it' can actually be greater than 'max_it' */
336         for (i = start; i < end; ++i) PetscCallMPI(MPI_Wait(&req(i), MPI_STATUS_IGNORE));
337         break;
338       }
339     }
340   } /* End inner for loop */
341   PetscFunctionReturn(PETSC_SUCCESS);
342 }
343 
KSPSolve_ReInitData_PIPELCG(KSP ksp)344 static PetscErrorCode KSPSolve_ReInitData_PIPELCG(KSP ksp)
345 {
346   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
347   PetscInt       i = 0, j = 0, l = plcg->l, max_it = ksp->max_it;
348 
349   PetscFunctionBegin;
350   for (i = 0; i < PetscMax(3, l + 1); ++i) PetscCall(VecSet(plcg->Z[i], 0.0));
351   for (i = 1; i < 3; ++i) PetscCall(VecSet(plcg->U[i], 0.0));
352   for (i = 0; i < 3; ++i) PetscCall(VecSet(plcg->V[i], 0.0));
353   for (i = 0; i < 3 * (l - 1) + 1; ++i) PetscCall(VecSet(plcg->Q[i], 0.0));
354   for (j = 0; j < (max_it + 1); ++j) {
355     gamma(j) = 0.0;
356     delta(j) = 0.0;
357     for (i = 0; i < (2 * l + 1); ++i) G_noshift(i, j) = 0.0;
358   }
359   PetscFunctionReturn(PETSC_SUCCESS);
360 }
361 
362 /*
363   KSPSolve_PIPELCG - This routine actually applies the pipelined(l) conjugate gradient method
364 */
KSPSolve_PIPELCG(KSP ksp)365 static PetscErrorCode KSPSolve_PIPELCG(KSP ksp)
366 {
367   KSP_CG_PIPE_L *plcg = (KSP_CG_PIPE_L *)ksp->data;
368   Mat            A = NULL, Pmat = NULL;
369   Vec            b = NULL, x = NULL, p = NULL;
370   PetscInt       max_it = ksp->max_it, l = plcg->l;
371   PetscInt       i = 0, outer_it = 0, curr_guess_zero = 0;
372   PetscReal      lmin = plcg->lmin, lmax = plcg->lmax;
373   PetscBool      diagonalscale = PETSC_FALSE;
374   MPI_Comm       comm;
375 
376   PetscFunctionBegin;
377   comm = PetscObjectComm((PetscObject)ksp);
378   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
379   PetscCheck(!diagonalscale, comm, PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);
380 
381   x = ksp->vec_sol;
382   b = ksp->vec_rhs;
383   p = plcg->p;
384 
385   PetscCall(PetscCalloc1((max_it + 1) * (2 * l + 1), &plcg->G));
386   PetscCall(PetscCalloc1(max_it + 1, &plcg->gamma));
387   PetscCall(PetscCalloc1(max_it + 1, &plcg->delta));
388   PetscCall(PetscCalloc1(max_it + 1, &plcg->req));
389 
390   PetscCall(PCGetOperators(ksp->pc, &A, &Pmat));
391 
392   for (i = 0; i < l; ++i) sigma(i) = (0.5 * (lmin + lmax) + (0.5 * (lmax - lmin) * PetscCosReal(PETSC_PI * (2.0 * i + 1.0) / (2.0 * l))));
393 
394   ksp->its        = 0;
395   outer_it        = 0;
396   curr_guess_zero = !!ksp->guess_zero;
397 
398   while (ksp->its < max_it) { /* OUTER LOOP (gmres-like restart to handle breakdowns) */
399     /* RESTART LOOP */
400     if (!curr_guess_zero) {
401       PetscCall(KSP_MatMult(ksp, A, x, plcg->U[0])); /* u <- b - Ax */
402       PetscCall(VecAYPX(plcg->U[0], -1.0, b));
403     } else {
404       PetscCall(VecCopy(b, plcg->U[0])); /* u <- b (x is 0) */
405     }
406     PetscCall(KSP_PCApply(ksp, plcg->U[0], p)); /* p <- Bu */
407 
408     if (outer_it > 0) {
409       /* Re-initialize Z,U,V,Q,gamma,delta,G after restart occurred */
410       PetscCall(KSPSolve_ReInitData_PIPELCG(ksp));
411     }
412 
413     PetscCall((*plcg->U[0]->ops->dot_local)(plcg->U[0], p, &G(0, 0)));
414     PetscCallMPI(MPIU_Iallreduce(MPI_IN_PLACE, &G(0, 0), 1, MPIU_SCALAR, MPIU_SUM, comm, &req(0)));
415     PetscCall(VecCopy(p, plcg->Z[l]));
416 
417     PetscCall(KSPSolve_InnerLoop_PIPELCG(ksp));
418 
419     if (ksp->reason) break; /* convergence or divergence */
420     ++outer_it;
421     curr_guess_zero = 0;
422   }
423 
424   if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
425   PetscCall(PetscFree(plcg->G));
426   PetscCall(PetscFree(plcg->gamma));
427   PetscCall(PetscFree(plcg->delta));
428   PetscCall(PetscFree(plcg->req));
429   PetscFunctionReturn(PETSC_SUCCESS);
430 }
431 
432 /*MC
433     KSPPIPELCG - Deep pipelined (length l) Conjugate Gradient method {cite}`cornelis2018communication` and {cite}`cools2019numerically`.
434     This method has only a single non-blocking global
435     reduction per iteration, compared to 2 blocking reductions for standard `KSPCG`. The reduction is overlapped by the
436     matrix-vector product and preconditioner application of the next l iterations. The pipeline length l is a parameter
437     of the method. [](sec_pipelineksp)
438 
439     Options Database Keys:
440 +   -ksp_pipelcg_pipel - pipelined length
441 .   -ksp_pipelcg_lmin - approximation to the smallest eigenvalue of the preconditioned operator (default: 0.0)
442 .   -ksp_pipelcg_lmax - approximation to the largest eigenvalue of the preconditioned operator (default: 0.0)
443 -   -ksp_pipelcg_monitor - output where/why the method restarts when a sqrt breakdown occurs
444 
445     Example usage:
446 .vb
447     KSP tutorials ex2, no preconditioner, pipel = 2, lmin = 0.0, lmax = 8.0 :
448         $mpiexec -n 14 ./ex2 -m 1000 -n 1000 -ksp_type pipelcg -pc_type none -ksp_norm_type natural
449            -ksp_rtol 1e-10 -ksp_max_it 1000 -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 8.0 -log_view
450     SNES tutorials ex48, bjacobi preconditioner, pipel = 3, lmin = 0.0, lmax = 2.0, show restart information :
451         $mpiexec -n 14 ./ex48 -M 150 -P 100 -ksp_type pipelcg -pc_type bjacobi -ksp_rtol 1e-10 -ksp_pipelcg_pipel 3
452            -ksp_pipelcg_lmin 0.0 -ksp_pipelcg_lmax 2.0 -ksp_pipelcg_monitor -log_view
453 .ve
454 
455     Level: advanced
456 
457     Notes:
458     MPI configuration may be necessary for reductions to make asynchronous progress, which is important for
459     performance of pipelined methods. See [](doc_faq_pipelined)
460 
461     Contributed by:
462     Siegfried Cools, University of Antwerp, Dept. Mathematics and Computer Science,
463     funded by Flemish Research Foundation (FWO) grant number 12H4617N.
464 
465 .seealso: [](ch_ksp), [](sec_pipelineksp), [](doc_faq_pipelined), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSPCG`, `KSPPIPECG`, `KSPPIPECGRR`, `KSPPGMRES`,
466           `KSPPIPEBCGS`, `KSPSetPCSide()`, `KSPGROPPCG`
467 M*/
KSPCreate_PIPELCG(KSP ksp)468 PETSC_EXTERN PetscErrorCode KSPCreate_PIPELCG(KSP ksp)
469 {
470   KSP_CG_PIPE_L *plcg = NULL;
471 
472   PetscFunctionBegin;
473   PetscCall(PetscNew(&plcg));
474   ksp->data = (void *)plcg;
475 
476   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));
477   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));
478 
479   ksp->ops->setup          = KSPSetUp_PIPELCG;
480   ksp->ops->solve          = KSPSolve_PIPELCG;
481   ksp->ops->reset          = KSPReset_PIPELCG;
482   ksp->ops->destroy        = KSPDestroy_PIPELCG;
483   ksp->ops->view           = KSPView_PIPELCG;
484   ksp->ops->setfromoptions = KSPSetFromOptions_PIPELCG;
485   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
486   ksp->ops->buildresidual  = KSPBuildResidualDefault;
487   PetscFunctionReturn(PETSC_SUCCESS);
488 }
489