xref: /petsc/src/ksp/pc/impls/bjacobi/bjkokkos/bjkokkos.kokkos.cxx (revision 2d30e087755efd99e28fdfe792ffbeb2ee1ea928)
1 #include <petscvec_kokkos.hpp>
2 #include <petsc/private/deviceimpl.h>
3 #include <petsc/private/pcimpl.h>
4 #include <petsc/private/kspimpl.h>
5 #include <petscksp.h> /*I "petscksp.h" I*/
6 #include "petscsection.h"
7 #include <petscdmcomposite.h>
8 #include "Kokkos_Core.hpp"
9 
10 #include <../src/mat/impls/aij/seq/aij.h>
11 #include <../src/mat/impls/aij/seq/kokkos/aijkok.hpp>
12 
13 #if defined(PETSC_HAVE_CUDA)
14 #include <nvToolsExt.h>
15 #endif
16 
17 #define PCBJKOKKOS_SHARED_LEVEL 0 // 0 is shared, 1 is global
18 #define PCBJKOKKOS_VEC_SIZE     16
19 #define PCBJKOKKOS_TEAM_SIZE    16
20 
21 #define PCBJKOKKOS_VERBOSE_LEVEL 2
22 
23 typedef Kokkos::DefaultExecutionSpace exec_space;
24 using layout           = Kokkos::LayoutRight;
25 using IntView          = Kokkos::View<PetscInt **, layout, exec_space>;
26 using AMatrixValueView = const Kokkos::View<PetscScalar **, layout, exec_space>;
27 using XYType           = const Kokkos::View<PetscScalar **, layout, exec_space>;
28 
29 typedef enum {
30   BATCH_KSP_BICG_IDX,
31   BATCH_KSP_TFQMR_IDX,
32   BATCH_KSP_GMRES_IDX,
33   NUM_BATCH_TYPES
34 } KSPIndex;
35 typedef struct {
36   Vec                                               vec_diag;
37   PetscInt                                          nBlocks; /* total number of blocks */
38   PetscInt                                          n;       // cache host version of d_bid_eqOffset_k[nBlocks]
39   KSP                                               ksp;     // Used just for options. Should have one for each block
40   Kokkos::View<PetscInt *, Kokkos::LayoutRight>    *d_bid_eqOffset_k;
41   Kokkos::View<PetscScalar *, Kokkos::LayoutRight> *d_idiag_k;
42   Kokkos::View<PetscInt *>                         *d_isrow_k;
43   Kokkos::View<PetscInt *>                         *d_isicol_k;
44   KSPIndex                                          ksp_type_idx;
45   PetscInt                                          nwork;
46   PetscInt                                          const_block_size; // used to decide to use shared memory for work vectors
47   PetscInt                                         *dm_Nf;            // Number of fields in each DM
48   PetscInt                                          num_dms;
49   // diagnostics
50   PetscBool                                         reason;
51   PetscBool                                         monitor;
52   PetscInt                                          batch_target;
53   PetscInt                                          nsolves_team;
54   PetscInt                                          max_nits;
55   // caches
56   IntView                                          *rowOffsets;
57   IntView                                          *colIndices;
58   XYType                                           *batch_b;
59   XYType                                           *batch_x;
60   AMatrixValueView                                 *batch_values;
61 } PC_PCBJKOKKOS;
62 
63 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
64 #include <fstream>
65 
66 #include "Kokkos_Timer.hpp"
67 #include "Kokkos_Random.hpp"
68 #include "Kokkos_UnorderedMap.hpp"
69 #include "Kokkos_Sort.hpp"
70 
71 /// KokkosKernels headers
72 #include "KokkosBatched_Util.hpp"
73 #include "KokkosBatched_Vector.hpp"
74 
75 #include <Kokkos_ArithTraits.hpp>
76 #include <KokkosBatched_Util.hpp>
77 #include <KokkosBatched_Vector.hpp>
78 #include <KokkosBatched_Copy_Decl.hpp>
79 #include <KokkosBatched_Copy_Impl.hpp>
80 #include <KokkosBatched_AddRadial_Decl.hpp>
81 #include <KokkosBatched_AddRadial_Impl.hpp>
82 #include <KokkosBatched_Gemm_Decl.hpp>
83 #include <KokkosBatched_Gemm_Serial_Impl.hpp>
84 #include <KokkosBatched_Gemm_Team_Impl.hpp>
85 #include <KokkosBatched_Gemv_Decl.hpp>
86 #include <KokkosBatched_Gemv_Serial_Impl.hpp>
87 #include <KokkosBatched_Gemv_Team_Impl.hpp>
88 #include <KokkosBatched_Trsm_Decl.hpp>
89 #include <KokkosBatched_Trsm_Serial_Impl.hpp>
90 #include <KokkosBatched_Trsm_Team_Impl.hpp>
91 #include <KokkosBatched_Trsv_Decl.hpp>
92 #include <KokkosBatched_Trsv_Serial_Impl.hpp>
93 #include <KokkosBatched_Trsv_Team_Impl.hpp>
94 #include <KokkosBatched_LU_Decl.hpp>
95 #include <KokkosBatched_LU_Serial_Impl.hpp>
96 #include <KokkosBatched_LU_Team_Impl.hpp>
97 #include <KokkosSparse_CrsMatrix.hpp>
98 #include "KokkosBatched_Spmv.hpp"
99 #include "KokkosBatched_CrsMatrix.hpp"
100 #include "KokkosBatched_Krylov_Handle.hpp"
101 #include "KokkosBatched_GMRES.hpp"
102 #include "KokkosBatched_JacobiPrec.hpp"
103 
104 template <typename DeviceType, typename ValuesViewType, typename IntView, typename VectorViewType, typename KrylovHandleType>
105 struct Functor_TestBatchedTeamVectorGMRES {
106   const ValuesViewType _D;
107   const ValuesViewType _diag;
108   const IntView        _r;
109   const IntView        _c;
110   const VectorViewType _X;
111   const VectorViewType _B;
112   const int            _N_team, _team_size, _vector_length;
113   const int            _N_iteration;
114   const double         _tol;
115   const int            _ortho_strategy;
116   const int            _scratch_pad_level;
117   KrylovHandleType     _handle;
118 
119   KOKKOS_INLINE_FUNCTION
120   Functor_TestBatchedTeamVectorGMRES(const ValuesViewType &D, const IntView &r, const IntView &c, const VectorViewType &X, const VectorViewType &B, const int N_team, const int team_size, const int vector_length, const int N_iteration, const double tol, const int ortho_strategy, const int scratch_pad_level, KrylovHandleType &handle) :
121     _D(D), _r(r), _c(c), _X(X), _B(B), _N_team(N_team), _team_size(team_size), _vector_length(vector_length), _N_iteration(N_iteration), _tol(tol), _ortho_strategy(ortho_strategy), _scratch_pad_level(scratch_pad_level), _handle(handle) { }
122 
123   KOKKOS_INLINE_FUNCTION
124   Functor_TestBatchedTeamVectorGMRES(const ValuesViewType &D, const ValuesViewType &diag, const IntView &r, const IntView &c, const VectorViewType &X, const VectorViewType &B, const int N_team, const int team_size, const int vector_length, const int N_iteration, const double tol, int ortho_strategy, const int scratch_pad_level, KrylovHandleType &handle) :
125     _D(D), _diag(diag), _r(r), _c(c), _X(X), _B(B), _N_team(N_team), _team_size(team_size), _vector_length(vector_length), _N_iteration(N_iteration), _tol(tol), _ortho_strategy(ortho_strategy), _scratch_pad_level(scratch_pad_level), _handle(handle) { }
126 
127   template <typename MemberType>
128   KOKKOS_INLINE_FUNCTION void operator()(const MemberType &member) const {
129     const int first_matrix = static_cast<int>(member.league_rank()) * _N_team;
130     const int N            = _D.extent(0);
131     const int last_matrix  = (static_cast<int>(member.league_rank() + 1) * _N_team < N ? static_cast<int>(member.league_rank() + 1) * _N_team : N);
132     const int graphID      = static_cast<int>(member.league_rank());
133     using TeamVectorCopy1D = KokkosBatched::TeamVectorCopy<MemberType, KokkosBatched::Trans::NoTranspose, 1>;
134 
135     auto d                         = Kokkos::subview(_D, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
136     auto x                         = Kokkos::subview(_X, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
137     auto b                         = Kokkos::subview(_B, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
138     using ScratchPadIntViewType    = Kokkos::View<typename IntView::non_const_value_type *, typename IntView::array_layout, typename IntView::execution_space::scratch_memory_space>;
139     using ScratchPadValuesViewType = Kokkos::View<typename ValuesViewType::non_const_value_type **, typename ValuesViewType::array_layout, typename ValuesViewType::execution_space::scratch_memory_space>;
140 
141     using Operator = KokkosBatched::CrsMatrix<ValuesViewType, ScratchPadIntViewType>;
142     ScratchPadIntViewType r(member.team_scratch(1), _r.extent(1));
143     ScratchPadIntViewType c(member.team_scratch(1), _c.extent(1));
144 
145     TeamVectorCopy1D::invoke(member, Kokkos::subview(_r, graphID, Kokkos::ALL), r);
146     TeamVectorCopy1D::invoke(member, Kokkos::subview(_c, graphID, Kokkos::ALL), c);
147     Operator A(d, r, c);
148 
149     ScratchPadValuesViewType diag(member.team_scratch(1), last_matrix - first_matrix, _diag.extent(1));
150     using PrecOperator = KokkosBatched::JacobiPrec<ScratchPadValuesViewType>;
151 
152     KokkosBatched::TeamVectorCopy<MemberType>::invoke(member, Kokkos::subview(_diag, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL), diag);
153     PrecOperator P(diag);
154     P.setComputedInverse();
155 
156     KokkosBatched::TeamVectorGMRES<MemberType>::template invoke<Operator, VectorViewType, PrecOperator, KrylovHandleType>(member, A, b, x, P, _handle);
157   }
158   inline double run(PC pc) {
159     typedef typename ValuesViewType::value_type value_type;
160     std::string                                 name("KokkosBatched::Test::TeamVectorGMRES");
161     Kokkos::Timer                               timer;
162     Kokkos::Profiling::pushRegion(name.c_str());
163 
164     Kokkos::TeamPolicy<DeviceType> auto_policy(ceil(1. * _D.extent(0) / _N_team), Kokkos::AUTO(), Kokkos::AUTO());
165     Kokkos::TeamPolicy<DeviceType> tuned_policy(ceil(1. * _D.extent(0) / _N_team), _team_size, _vector_length);
166     Kokkos::TeamPolicy<DeviceType> policy;
167 
168     if (_team_size < 1) policy = auto_policy;
169     else policy = tuned_policy;
170 
171     _handle.set_max_iteration(_N_iteration);
172     _handle.set_tolerance(_tol);
173     _handle.set_ortho_strategy(_ortho_strategy);
174     _handle.set_scratch_pad_level(_scratch_pad_level);
175     _handle.set_compute_last_residual(true);
176 
177     int maximum_iteration = _handle.get_max_iteration();
178 
179     using ScalarType = typename ValuesViewType::non_const_value_type;
180     using Layout     = typename ValuesViewType::array_layout;
181     using EXSP       = typename ValuesViewType::execution_space;
182 
183     using MagnitudeType = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
184 
185     using ViewType1D    = Kokkos::View<MagnitudeType *, Layout, EXSP>;
186     using ViewType2D    = Kokkos::View<ScalarType **, Layout, EXSP>;
187     using ViewType3D    = Kokkos::View<ScalarType ***, Layout, EXSP>;
188     using IntViewType1D = Kokkos::View<PetscInt *, Layout, EXSP>;
189 
190     size_t bytes_1D      = ViewType2D::shmem_size(_N_team, 1);
191     size_t bytes_row_ptr = IntViewType1D::shmem_size(_r.extent(1));
192     size_t bytes_col_idc = IntViewType1D::shmem_size(_c.extent(1));
193     size_t bytes_2D_1    = ViewType2D::shmem_size(_N_team, _X.extent(1));
194     size_t bytes_2D_2    = ViewType2D::shmem_size(_N_team, maximum_iteration + 1);
195 
196     size_t bytes_diag = bytes_2D_1;
197     size_t bytes_tmp  = 2 * bytes_2D_1 + 2 * bytes_1D + bytes_2D_2;
198 
199     policy.set_scratch_size(0, Kokkos::PerTeam(bytes_tmp));
200     policy.set_scratch_size(1, Kokkos::PerTeam(bytes_col_idc + bytes_row_ptr + bytes_diag));
201     PetscInfo(pc, "%d scratch memory(0) = %d + %d + %d bytes_diag=%d; %d scratch memory(1); %d maximum_iterations\n", (int)(bytes_tmp), 2 * (int)bytes_2D_1, 2 * (int)bytes_1D, (int)bytes_2D_2, (int)bytes_diag, (int)(bytes_row_ptr + bytes_col_idc + bytes_diag), (int)maximum_iteration);
202     exec_space().fence();
203     timer.reset();
204     Kokkos::parallel_for(name.c_str(), policy, *this);
205     exec_space().fence();
206     double sec = timer.seconds();
207 
208     return sec;
209   }
210 };
211 #endif // KK GMRES
212 
213 typedef Kokkos::TeamPolicy<>::member_type team_member;
214 
215 static PetscErrorCode PCBJKOKKOSCreateKSP_BJKOKKOS(PC pc) {
216   const char    *prefix;
217   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
218   DM             dm;
219 
220   PetscFunctionBegin;
221   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->ksp));
222   PetscCall(KSPSetErrorIfNotConverged(jac->ksp, pc->erroriffailure));
223   PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->ksp, (PetscObject)pc, 1));
224   PetscCall(PCGetOptionsPrefix(pc, &prefix));
225   PetscCall(KSPSetOptionsPrefix(jac->ksp, prefix));
226   PetscCall(KSPAppendOptionsPrefix(jac->ksp, "pc_bjkokkos_"));
227   PetscCall(PCGetDM(pc, &dm));
228   if (dm) {
229     PetscCall(KSPSetDM(jac->ksp, dm));
230     PetscCall(KSPSetDMActive(jac->ksp, PETSC_FALSE));
231   }
232   jac->reason       = PETSC_FALSE;
233   jac->monitor      = PETSC_FALSE;
234   jac->batch_target = -1;
235   jac->nsolves_team = 1;
236   jac->ksp->max_it  = 50; // this is realy for GMRES w/o restarts
237   PetscFunctionReturn(0);
238 }
239 
240 // y <-- Ax
241 KOKKOS_INLINE_FUNCTION PetscErrorCode MatMult(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, const PetscInt start, const PetscInt end, const PetscScalar *x_loc, PetscScalar *y_loc) {
242   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
243     int                rowa = ic[rowb];
244     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
245     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
246     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
247     PetscScalar        sum;
248     Kokkos::parallel_reduce(
249       Kokkos::ThreadVectorRange(team, n), [=](const int i, PetscScalar &lsum) { lsum += aa[i] * x_loc[r[aj[i]] - start]; }, sum);
250     Kokkos::single(Kokkos::PerThread(team), [=]() { y_loc[rowb - start] = sum; });
251   });
252   team.team_barrier();
253   return 0;
254 }
255 
256 // temp buffer per thread with reduction at end?
257 KOKKOS_INLINE_FUNCTION PetscErrorCode MatMultTranspose(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, const PetscInt start, const PetscInt end, const PetscScalar *x_loc, PetscScalar *y_loc) {
258   Kokkos::parallel_for(Kokkos::TeamVectorRange(team, end - start), [=](int i) { y_loc[i] = 0; });
259   team.team_barrier();
260   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
261     int                rowa = ic[rowb];
262     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
263     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
264     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
265     const PetscScalar  xx   = x_loc[rowb - start]; // rowb = ic[rowa] = ic[r[rowb]]
266     Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
267       PetscScalar val = aa[i] * xx;
268       Kokkos::atomic_fetch_add(&y_loc[r[aj[i]] - start], val);
269     });
270   });
271   team.team_barrier();
272   return 0;
273 }
274 
275 typedef struct Batch_MetaData_TAG {
276   PetscInt           flops;
277   PetscInt           its;
278   KSPConvergedReason reason;
279 } Batch_MetaData;
280 
281 // Solve A(BB^-1)x = y with TFQMR. Right preconditioned to get un-preconditioned residual
282 KOKKOS_INLINE_FUNCTION PetscErrorCode BJSolve_TFQMR(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, PetscScalar *work_space_global, const int stride_global, const int nShareVec, PetscScalar *work_space_shared, const int stride_shared, PetscReal rtol, PetscReal atol, PetscReal dtol, PetscInt maxit, Batch_MetaData *metad, const PetscInt start, const PetscInt end, const PetscScalar glb_idiag[], const PetscScalar *glb_b, PetscScalar *glb_x, bool monitor) {
283   using Kokkos::parallel_for;
284   using Kokkos::parallel_reduce;
285   int                Nblk = end - start, i, m, stride = stride_shared, idx = 0;
286   PetscReal          dp, dpold, w, dpest, tau, psi, cm, r0;
287   const PetscScalar *Diag = &glb_idiag[start];
288   PetscScalar       *ptr  = work_space_shared, rho, rhoold, a, s, b, eta, etaold, psiold, cf, dpi;
289 
290   if (idx++ == nShareVec) {
291     ptr    = work_space_global;
292     stride = stride_global;
293   }
294   PetscScalar *XX = ptr;
295   ptr += stride;
296   if (idx++ == nShareVec) {
297     ptr    = work_space_global;
298     stride = stride_global;
299   }
300   PetscScalar *R = ptr;
301   ptr += stride;
302   if (idx++ == nShareVec) {
303     ptr    = work_space_global;
304     stride = stride_global;
305   }
306   PetscScalar *RP = ptr;
307   ptr += stride;
308   if (idx++ == nShareVec) {
309     ptr    = work_space_global;
310     stride = stride_global;
311   }
312   PetscScalar *V = ptr;
313   ptr += stride;
314   if (idx++ == nShareVec) {
315     ptr    = work_space_global;
316     stride = stride_global;
317   }
318   PetscScalar *T = ptr;
319   ptr += stride;
320   if (idx++ == nShareVec) {
321     ptr    = work_space_global;
322     stride = stride_global;
323   }
324   PetscScalar *Q = ptr;
325   ptr += stride;
326   if (idx++ == nShareVec) {
327     ptr    = work_space_global;
328     stride = stride_global;
329   }
330   PetscScalar *P = ptr;
331   ptr += stride;
332   if (idx++ == nShareVec) {
333     ptr    = work_space_global;
334     stride = stride_global;
335   }
336   PetscScalar *U = ptr;
337   ptr += stride;
338   if (idx++ == nShareVec) {
339     ptr    = work_space_global;
340     stride = stride_global;
341   }
342   PetscScalar *D = ptr;
343   ptr += stride;
344   if (idx++ == nShareVec) {
345     ptr    = work_space_global;
346     stride = stride_global;
347   }
348   PetscScalar *AUQ = V;
349 
350   // init: get b, zero x
351   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
352     int rowa         = ic[rowb];
353     R[rowb - start]  = glb_b[rowa];
354     XX[rowb - start] = 0;
355   });
356   team.team_barrier();
357   parallel_reduce(
358     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
359   team.team_barrier();
360   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
361   // diagnostics
362 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
363   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
364 #endif
365   if (dp < atol) {
366     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
367     return 0;
368   }
369   if (0 == maxit) {
370     metad->reason = KSP_DIVERGED_ITS;
371     return 0;
372   }
373 
374   /* Make the initial Rp = R */
375   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { RP[idx] = R[idx]; });
376   team.team_barrier();
377   /* Set the initial conditions */
378   etaold = 0.0;
379   psiold = 0.0;
380   tau    = dp;
381   dpold  = dp;
382 
383   /* rhoold = (r,rp)     */
384   parallel_reduce(
385     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rhoold);
386   team.team_barrier();
387   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
388     U[idx] = R[idx];
389     P[idx] = R[idx];
390     T[idx] = Diag[idx] * P[idx];
391     D[idx] = 0;
392   });
393   team.team_barrier();
394   MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V);
395 
396   i = 0;
397   do {
398     /* s <- (v,rp)          */
399     parallel_reduce(
400       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += V[idx] * PetscConj(RP[idx]); }, s);
401     team.team_barrier();
402     a = rhoold / s; /* a <- rho / s         */
403     /* q <- u - a v    VecWAXPY(w,alpha,x,y): w = alpha x + y.     */
404     /* t <- u + q           */
405     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
406       Q[idx] = U[idx] - a * V[idx];
407       T[idx] = U[idx] + Q[idx];
408     });
409     team.team_barrier();
410     // KSP_PCApplyBAorAB
411     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * T[idx]; });
412     team.team_barrier();
413     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, AUQ);
414     /* r <- r - a K (u + q) */
415     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { R[idx] = R[idx] - a * AUQ[idx]; });
416     team.team_barrier();
417     parallel_reduce(
418       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
419     team.team_barrier();
420     dp = PetscSqrtReal(PetscRealPart(dpi));
421     for (m = 0; m < 2; m++) {
422       if (!m) w = PetscSqrtReal(dp * dpold);
423       else w = dp;
424       psi = w / tau;
425       cm  = 1.0 / PetscSqrtReal(1.0 + psi * psi);
426       tau = tau * psi * cm;
427       eta = cm * cm * a;
428       cf  = psiold * psiold * etaold / a;
429       if (!m) {
430         /* D = U + cf D */
431         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = U[idx] + cf * D[idx]; });
432       } else {
433         /* D = Q + cf D */
434         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = Q[idx] + cf * D[idx]; });
435       }
436       team.team_barrier();
437       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = XX[idx] + eta * D[idx]; });
438       team.team_barrier();
439       dpest = PetscSqrtReal(2 * i + m + 2.0) * tau;
440 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
441       if (monitor && m == 1) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dpest); });
442 #endif
443       if (dpest < atol) {
444         metad->reason = KSP_CONVERGED_ATOL_NORMAL;
445         goto done;
446       }
447       if (dpest / r0 < rtol) {
448         metad->reason = KSP_CONVERGED_RTOL_NORMAL;
449         goto done;
450       }
451 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
452       if (dpest / r0 > dtol) {
453         metad->reason = KSP_DIVERGED_DTOL;
454         Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dpest, r0); });
455         goto done;
456       }
457 #else
458       if (dpest / r0 > dtol) {
459         metad->reason = KSP_DIVERGED_DTOL;
460         goto done;
461       }
462 #endif
463       if (i + 1 == maxit) {
464         metad->reason = KSP_DIVERGED_ITS;
465         goto done;
466       }
467 
468       etaold = eta;
469       psiold = psi;
470     }
471 
472     /* rho <- (r,rp)       */
473     parallel_reduce(
474       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rho);
475     team.team_barrier();
476     b = rho / rhoold; /* b <- rho / rhoold   */
477     /* u <- r + b q        */
478     /* p <- u + b(q + b p) */
479     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
480       U[idx] = R[idx] + b * Q[idx];
481       Q[idx] = Q[idx] + b * P[idx];
482       P[idx] = U[idx] + b * Q[idx];
483     });
484     /* v <- K p  */
485     team.team_barrier();
486     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * P[idx]; });
487     team.team_barrier();
488     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V);
489 
490     rhoold = rho;
491     dpold  = dp;
492 
493     i++;
494   } while (i < maxit);
495 done:
496   // KSPUnwindPreconditioner
497   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = Diag[idx] * XX[idx]; });
498   team.team_barrier();
499   // put x into Plex order
500   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
501     int rowa    = ic[rowb];
502     glb_x[rowa] = XX[rowb - start];
503   });
504   metad->its = i + 1;
505   if (1) {
506     int nnz;
507     parallel_reduce(
508       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
509     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
510   } else {
511     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
512   }
513   return 0;
514 }
515 
516 // Solve Ax = y with biCG
517 KOKKOS_INLINE_FUNCTION PetscErrorCode BJSolve_BICG(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, PetscScalar *work_space_global, const int stride_global, const int nShareVec, PetscScalar *work_space_shared, const int stride_shared, PetscReal rtol, PetscReal atol, PetscReal dtol, PetscInt maxit, Batch_MetaData *metad, const PetscInt start, const PetscInt end, const PetscScalar glb_idiag[], const PetscScalar *glb_b, PetscScalar *glb_x, bool monitor) {
518   using Kokkos::parallel_for;
519   using Kokkos::parallel_reduce;
520   int                Nblk = end - start, i, stride = stride_shared, idx = 0; // start in shared mem
521   PetscReal          dp, r0;
522   const PetscScalar *Di  = &glb_idiag[start];
523   PetscScalar       *ptr = work_space_shared, dpi, a = 1.0, beta, betaold = 1.0, b, b2, ma, mac;
524 
525   if (idx++ == nShareVec) {
526     ptr    = work_space_global;
527     stride = stride_global;
528   }
529   PetscScalar *XX = ptr;
530   ptr += stride;
531   if (idx++ == nShareVec) {
532     ptr    = work_space_global;
533     stride = stride_global;
534   }
535   PetscScalar *Rl = ptr;
536   ptr += stride;
537   if (idx++ == nShareVec) {
538     ptr    = work_space_global;
539     stride = stride_global;
540   }
541   PetscScalar *Zl = ptr;
542   ptr += stride;
543   if (idx++ == nShareVec) {
544     ptr    = work_space_global;
545     stride = stride_global;
546   }
547   PetscScalar *Pl = ptr;
548   ptr += stride;
549   if (idx++ == nShareVec) {
550     ptr    = work_space_global;
551     stride = stride_global;
552   }
553   PetscScalar *Rr = ptr;
554   ptr += stride;
555   if (idx++ == nShareVec) {
556     ptr    = work_space_global;
557     stride = stride_global;
558   }
559   PetscScalar *Zr = ptr;
560   ptr += stride;
561   if (idx++ == nShareVec) {
562     ptr    = work_space_global;
563     stride = stride_global;
564   }
565   PetscScalar *Pr = ptr;
566   ptr += stride;
567 
568   /*     r <- b (x is 0) */
569   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
570     int rowa         = ic[rowb];
571     //PetscCall(VecCopy(Rr,Rl));
572     Rl[rowb - start] = Rr[rowb - start] = glb_b[rowa];
573     XX[rowb - start]                    = 0;
574   });
575   team.team_barrier();
576   /*     z <- Br         */
577   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
578     Zr[idx] = Di[idx] * Rr[idx];
579     Zl[idx] = Di[idx] * Rl[idx];
580   });
581   team.team_barrier();
582   /*    dp <- r'*r       */
583   parallel_reduce(
584     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
585   team.team_barrier();
586   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
587 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
588   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
589 #endif
590   if (dp < atol) {
591     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
592     return 0;
593   }
594   if (0 == maxit) {
595     metad->reason = KSP_DIVERGED_ITS;
596     return 0;
597   }
598   i = 0;
599   do {
600     /*     beta <- r'z     */
601     parallel_reduce(
602       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += Zr[idx] * PetscConj(Rl[idx]); }, beta);
603     team.team_barrier();
604 #if PCBJKOKKOS_VERBOSE_LEVEL >= 6
605 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
606     Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%7d beta = Z.R = %22.14e \n", i, (double)beta); });
607 #endif
608 #endif
609     if (!i) {
610       if (beta == 0.0) {
611         metad->reason = KSP_DIVERGED_BREAKDOWN_BICG;
612         goto done;
613       }
614       /*     p <- z          */
615       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
616         Pr[idx] = Zr[idx];
617         Pl[idx] = Zl[idx];
618       });
619     } else {
620       b  = beta / betaold;
621       /*     p <- z + b* p   */
622       b2 = PetscConj(b);
623       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
624         Pr[idx] = b * Pr[idx] + Zr[idx];
625         Pl[idx] = b2 * Pl[idx] + Zl[idx];
626       });
627     }
628     team.team_barrier();
629     betaold = beta;
630     /*     z <- Kp         */
631     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pr, Zr);
632     MatMultTranspose(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pl, Zl);
633     /*     dpi <- z'p      */
634     parallel_reduce(
635       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Zr[idx] * PetscConj(Pl[idx]); }, dpi);
636     team.team_barrier();
637     //
638     a   = beta / dpi; /*     a = beta/p'z    */
639     ma  = -a;
640     mac = PetscConj(ma);
641     /*     x <- x + ap     */
642     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
643       XX[idx] = XX[idx] + a * Pr[idx];
644       Rr[idx] = Rr[idx] + ma * Zr[idx];
645       Rl[idx] = Rl[idx] + mac * Zl[idx];
646     });
647     team.team_barrier();
648     team.team_barrier();
649     /*    dp <- r'*r       */
650     parallel_reduce(
651       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
652     team.team_barrier();
653     dp = PetscSqrtReal(PetscRealPart(dpi));
654 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
655     if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dp); });
656 #endif
657     if (dp < atol) {
658       metad->reason = KSP_CONVERGED_ATOL_NORMAL;
659       goto done;
660     }
661     if (dp / r0 < rtol) {
662       metad->reason = KSP_CONVERGED_RTOL_NORMAL;
663       goto done;
664     }
665 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
666     if (dp / r0 > dtol) {
667       metad->reason = KSP_DIVERGED_DTOL;
668       Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dp, r0); });
669       goto done;
670     }
671 #else
672     if (dp / r0 > dtol) {
673       metad->reason = KSP_DIVERGED_DTOL;
674       goto done;
675     }
676 #endif
677     if (i + 1 == maxit) {
678       metad->reason = KSP_DIVERGED_ITS;
679       goto done;
680     }
681     /* z <- Br  */
682     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
683       Zr[idx] = Di[idx] * Rr[idx];
684       Zl[idx] = Di[idx] * Rl[idx];
685     });
686     i++;
687     team.team_barrier();
688   } while (i < maxit);
689 done:
690   // put x back into Plex order
691   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
692     int rowa    = ic[rowb];
693     glb_x[rowa] = XX[rowb - start];
694   });
695   metad->its = i + 1;
696   if (1) {
697     int nnz;
698     parallel_reduce(
699       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
700     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
701   } else {
702     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
703   }
704   return 0;
705 }
706 
707 // KSP solver solve Ax = b; x is output, bin is input
708 static PetscErrorCode PCApply_BJKOKKOS(PC pc, Vec bin, Vec xout) {
709   PC_PCBJKOKKOS    *jac = (PC_PCBJKOKKOS *)pc->data;
710   Mat               A   = pc->pmat;
711   Mat_SeqAIJKokkos *aijkok;
712 
713   PetscFunctionBegin;
714   PetscCheck(jac->vec_diag && A, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "Not setup???? %p %p", jac->vec_diag, A);
715   aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
716   if (!aijkok) {
717     SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "No aijkok");
718   } else {
719     PetscInt           maxit = jac->ksp->max_it;
720     const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
721     const PetscInt     nwork = jac->nwork, nBlk = jac->nBlocks;
722     PetscScalar       *glb_xdata = NULL;
723     PetscReal          rtol = jac->ksp->rtol, atol = jac->ksp->abstol, dtol = jac->ksp->divtol;
724     const PetscScalar *glb_idiag = jac->d_idiag_k->data(), *glb_bdata = NULL;
725     const PetscInt    *glb_Aai = aijkok->i_device_data(), *glb_Aaj = aijkok->j_device_data(), *d_bid_eqOffset = jac->d_bid_eqOffset_k->data();
726     const PetscScalar *glb_Aaa  = aijkok->a_device_data();
727     const PetscInt    *d_isicol = jac->d_isicol_k->data(), *d_isrow = jac->d_isrow_k->data();
728     PCFailedReason     pcreason;
729     KSPIndex           ksp_type_idx = jac->ksp_type_idx;
730     PetscMemType       mtype;
731     PetscContainer     container;
732     PetscInt           batch_sz;
733     VecScatter         plex_batch = NULL;       // not used
734     Vec                bvec;                    // a copy of b for scatter (just alias to bin now)
735     PetscBool          monitor  = jac->monitor; // captured
736     PetscInt           view_bid = jac->batch_target;
737     MatInfo            info;
738     jac->max_nits = 0;
739     if (view_bid < 0) view_bid = 0;
740     PetscCall(MatGetInfo(A, MAT_LOCAL, &info));
741     // get field major is to map plex IO to/from block/field major
742     PetscCall(PetscObjectQuery((PetscObject)A, "plex_batch_is", (PetscObject *)&container));
743     if (container) {
744       PetscCall(VecDuplicate(bin, &bvec));
745       PetscCall(PetscContainerGetPointer(container, (void **)&plex_batch));
746       PetscCall(VecScatterBegin(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
747       PetscCall(VecScatterEnd(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
748       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No plex_batch_is -- require NO field major ordering for now");
749     } else {
750       bvec = bin;
751     }
752     // get x
753     PetscCall(VecGetArrayAndMemType(xout, &glb_xdata, &mtype));
754 #if defined(PETSC_HAVE_CUDA)
755     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for x %" PetscInt_FMT " != %" PetscInt_FMT, mtype, PETSC_MEMTYPE_DEVICE);
756 #endif
757     PetscCall(VecGetArrayReadAndMemType(bvec, &glb_bdata, &mtype));
758 #if defined(PETSC_HAVE_CUDA)
759     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for b");
760 #endif
761     // get batch size
762     PetscCall(PetscObjectQuery((PetscObject)A, "batch size", (PetscObject *)&container));
763     if (container) {
764       PetscInt *pNf = NULL;
765       PetscCall(PetscContainerGetPointer(container, (void **)&pNf));
766       batch_sz = *pNf;
767     } else batch_sz = 1;
768     PetscCheck(nBlk % batch_sz == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "batch_sz = %" PetscInt_FMT ", nBlk = %" PetscInt_FMT, batch_sz, nBlk);
769     if (ksp_type_idx == BATCH_KSP_GMRES_IDX) { // KK solver - move PETSc data into Kokkos Views, setup solver, solve, move data out of Kokkos, process metadata (convergence tests, etc.)
770 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
771       int       Nsolves_team = jac->nsolves_team, fill_idx = 0;
772       int       Nloc    = jac->const_block_size; // same grids
773       const int Nsolves = nBlk;
774       const int nnz     = (int)info.nz_used / Nsolves;      // fix for variable grid size
775       if (Nsolves_team > batch_sz) Nsolves_team = batch_sz; // silently fix this
776       PetscCheck(jac->const_block_size, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Kokkos (GMRES) solver requires constant block size (but can be made to work with species ordering or N_team==1)");
777       PetscCheck(Nsolves % Nsolves_team == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Nsolves.mod(Nsolves_team) != 0: Nsolves = %d, Nsolves_team = %d", Nsolves, Nsolves_team);
778       PetscCheck(((int)info.nz_used) % Nsolves == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "info.nz_used.mod(Nsolves) != 0: info.nz_used = %g, Nsolves = %d", info.nz_used, Nsolves);
779 #if defined(PETSC_HAVE_CUDA)
780       nvtxRangePushA("gmres-kk");
781 #endif
782       Kokkos::View<PetscScalar **, layout, exec_space, Kokkos::MemoryTraits<Kokkos::Unmanaged>> inv_diag((PetscScalar *)glb_idiag, Nsolves, Nloc); // in correct order
783       if (!jac->rowOffsets) {
784         jac->rowOffsets   = new IntView("rowOffsets", Nsolves / Nsolves_team, Nloc + 1); // same grids
785         jac->colIndices   = new IntView("colIndices", Nsolves / Nsolves_team, nnz);
786         jac->batch_b      = new XYType("batch rhs", Nsolves, Nloc);
787         jac->batch_x      = new XYType("batch sol", Nsolves, Nloc);
788         jac->batch_values = new AMatrixValueView("batch values", Nsolves, nnz);
789         fill_idx          = 1;
790         PetscInfo(pc, "Setup indices Nloc=%d, nnz=%d\n", Nloc, nnz);
791       }
792       IntView          &rowOffsets   = *jac->rowOffsets;
793       IntView          &colIndices   = *jac->colIndices;
794       XYType           &batch_b      = *jac->batch_b;
795       XYType           &batch_x      = *jac->batch_x;
796       AMatrixValueView &batch_values = *jac->batch_values;
797 
798       Kokkos::deep_copy(batch_x, 0.);
799       PetscInfo(pc, "\tjac->n = %" PetscInt_FMT ", Nloc = %d, Nsolves = %d, nnz = %d, Nsolves_team = %d, league size = %d, maxit = %" PetscInt_FMT "\n", jac->n, Nloc, Nsolves, nnz, Nsolves_team, Nsolves / Nsolves_team, maxit);
800       Kokkos::parallel_for(
801         "rowOffsets+map", Kokkos::TeamPolicy<>(Nsolves, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
802           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
803           if (fill_idx) {
804             if (blkID % Nsolves_team == 0) {                                                        // first matrix on this member
805               Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](const int rowb) { // Nloc
806                 int rowa                                           = d_isicol[rowb];
807                 int n                                              = glb_Aai[rowa + 1] - glb_Aai[rowa];
808                 rowOffsets(blkID / Nsolves_team, rowb + 1 - start) = n; // save sizes
809               });
810             }
811           }
812           // map b into field major space
813           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
814             int rowa                     = d_isicol[rowb];
815             batch_b(blkID, rowb - start) = glb_bdata[rowa];
816           });
817         });
818       Kokkos::fence();
819       if (fill_idx) {
820         Kokkos::parallel_for(
821           "prefix sum", Kokkos::TeamPolicy<>(Nsolves / Nsolves_team, 1, 1), KOKKOS_LAMBDA(const team_member team) {
822             const int graphID      = team.league_rank();
823             rowOffsets(graphID, 0) = 0;
824             for (size_t i = 0; i < Nloc; ++i) rowOffsets(graphID, i + 1) += rowOffsets(graphID, i);
825           });
826         Kokkos::fence();
827       }
828       Kokkos::parallel_for(
829         "copy matrix", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
830           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1], graphID = blkID / Nsolves_team;
831           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
832             int                rowa = d_isicol[rowb]; // global index
833             int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
834             const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
835             const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
836             Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
837               PetscScalar val = aa[i];
838               if (fill_idx && blkID % Nsolves_team == 0) colIndices(graphID, rowOffsets(graphID, rowb - start) + i) = d_isrow[aj[i]] - blkID * Nloc; // local" global - block start
839               batch_values(blkID, rowOffsets(graphID, rowb - start) + i) = val;
840             });
841           });
842         });
843       Kokkos::fence();
844       // setup solver
845       using ScalarType                = typename AMatrixValueView::non_const_value_type;
846       using MagnitudeType             = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
847       using NormViewType              = Kokkos::View<MagnitudeType *, layout, exec_space>;
848       using Norm2DViewType            = Kokkos::View<MagnitudeType **, layout, exec_space>;
849       using Scalar3DViewType          = Kokkos::View<ScalarType ***, layout, exec_space>;
850       using IntViewType               = Kokkos::View<int *, layout, exec_space>;
851       using KrylovHandleType          = KokkosBatched::KrylovHandle<Norm2DViewType, IntViewType, Scalar3DViewType>;
852       const int        n_iterations   = maxit;
853       const int        team_size      = -1;
854       const int        vector_length  = -1;
855       const double     tol            = rtol;
856       const int        ortho_strategy = 0;
857       KrylovHandleType handle(Nsolves, Nsolves_team, n_iterations, true);
858       handle.Arnoldi_view = Scalar3DViewType("", Nsolves, n_iterations, Nloc + n_iterations + 3);
859       // solve
860       double time         = Functor_TestBatchedTeamVectorGMRES<exec_space, AMatrixValueView, IntView, XYType, KrylovHandleType>(batch_values, inv_diag, rowOffsets, colIndices, batch_x, batch_b, Nsolves_team, team_size, vector_length, n_iterations, tol, ortho_strategy, 0, handle)
861                       .run(pc);
862       Kokkos::fence();
863       // get data back
864       Kokkos::parallel_for(
865         "map", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
866           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1]; // 0
867           // map x into Plex/PETSc
868           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
869             int rowa        = d_isicol[rowb];
870             glb_xdata[rowa] = batch_x(blkID, rowb - start);
871           });
872         });
873       // output assume species major - clone from Kokkos solvers
874 #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
875 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
876       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "Iterations\n"));
877 #else
878       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "max iterations per species (gmres) :"));
879 #endif
880       for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
881         for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
882 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
883           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2D:", s));
884           for (int bid = 0; bid < batch_sz; bid++) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3D ", handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx])));
885           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
886 #else
887           int count = 0, ii;
888           for (int bid = 0; bid < batch_sz; bid++) {
889             if ((ii = handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx])) > count) count = ii;
890           }
891           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3d", count));
892 #endif
893         }
894         head += batch_sz * jac->dm_Nf[dmIdx];
895       }
896 #if PCBJKOKKOS_VERBOSE_LEVEL == 3
897       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
898 #endif
899 #endif
900       // return error code, get max it
901       PetscInt count = 0, mbid = 0;
902       if (handle.is_converged_host()) {
903         pcreason = PC_NOERROR;
904         if (!jac->max_nits) {
905           for (int blkID = 0; blkID < nBlk; blkID++) {
906             if (handle.get_iteration_host(blkID) > jac->max_nits) {
907               jac->max_nits = handle.get_iteration_host(blkID);
908               mbid          = blkID;
909             }
910           }
911         }
912       } else {
913         PetscCall(PetscPrintf(PETSC_COMM_SELF, "There is at least one system that did not converge."));
914         pcreason = PC_SUBPC_ERROR;
915       }
916       // output - assume species major order
917       for (int blkID = 0; blkID < nBlk; blkID++) {
918         if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
919           if (jac->batch_target == blkID) {
920             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iterations, batch %" PetscInt_FMT ", species %" PetscInt_FMT "\n", handle.is_converged_host(blkID) ? "converged" : "diverged", handle.get_iteration_host(blkID), blkID % batch_sz, blkID / batch_sz));
921           } else if (jac->batch_target == -1 && handle.get_iteration_host(blkID) > count) {
922             jac->max_nits = count = handle.get_iteration_host(blkID);
923             mbid                  = blkID;
924           }
925           if (!handle.is_converged_host(blkID)) PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR species %d, batch %d did not converge with %d iterations\n", (int)(blkID / batch_sz), (int)blkID % batch_sz, handle.get_iteration_host(blkID)));
926         }
927       }
928       if (jac->batch_target == -1 && jac->reason) {
929         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iteration, batch %" PetscInt_FMT ", specie %" PetscInt_FMT "\n", handle.is_converged_host(mbid) ? "converged" : "diverged", jac->max_nits, mbid % batch_sz, mbid / batch_sz));
930       }
931 #if defined(PETSC_HAVE_CUDA)
932       nvtxRangePop();
933 #endif
934 #else
935       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "batch GMRES not supported");
936 #endif
937     } else { // Kokkos Krylov
938       using scr_mem_t    = Kokkos::DefaultExecutionSpace::scratch_memory_space;
939       using vect2D_scr_t = Kokkos::View<PetscScalar **, Kokkos::LayoutLeft, scr_mem_t>;
940       Kokkos::View<Batch_MetaData *, Kokkos::DefaultExecutionSpace> d_metadata("solver meta data", nBlk);
941       int                                                           stride_shared, stride_global, global_buff_words;
942       d_bid_eqOffset            = jac->d_bid_eqOffset_k->data();
943       // solve each block independently
944       int scr_bytes_team_shared = 0, nShareVec = 0, nGlobBVec = 0;
945       if (jac->const_block_size) { // use shared memory for work vectors only if constant block size - todo: test efficiency loss
946         int maximum_shared_mem_size = 64000;
947 
948         if (PetscDeviceConfiguredFor_Internal(PETSC_DEVICE_DEFAULT)) {
949           // FIXME: remove the configuredfor check once the PETSC_DEVICE_HOST MR is merged in
950           PetscDevice device;
951 
952           PetscCall(PetscDeviceGetDefault_Internal(&device));
953           PetscCall(PetscDeviceGetAttribute(device, PETSC_DEVICE_ATTR_SIZE_T_SHARED_MEM_PER_BLOCK, &maximum_shared_mem_size));
954         }
955         stride_shared = jac->const_block_size;                                                   // captured
956         nShareVec     = maximum_shared_mem_size / (jac->const_block_size * sizeof(PetscScalar)); // integer floor, number of vectors that fit in shared
957         if (nShareVec > nwork) nShareVec = nwork;
958         else nGlobBVec = nwork - nShareVec;
959         global_buff_words     = jac->n * nGlobBVec;
960         scr_bytes_team_shared = jac->const_block_size * nShareVec * sizeof(PetscScalar);
961         //PetscCall(PetscPrintf(PETSC_COMM_WORLD,"maximum_shared_mem_size=%d scr_bytes_shared=%d nShareVec=%d, nGlobBVec=%d vec size=%d jac->const_block_size=%d\n",maximum_shared_mem_size,scr_bytes_team_shared,nShareVec,nGlobBVec,jac->const_block_size*sizeof(PetscScalar),jac->const_block_size));
962       } else {
963         scr_bytes_team_shared = 0;
964         stride_shared         = 0;
965         global_buff_words     = jac->n * nwork;
966         nGlobBVec             = nwork; // not needed == fix
967       }
968       stride_global = jac->n; // captured
969 #if defined(PETSC_HAVE_CUDA)
970       nvtxRangePushA("batch-kokkos-solve");
971 #endif
972       Kokkos::View<PetscScalar *, Kokkos::DefaultExecutionSpace> d_work_vecs_k("workvectors", global_buff_words); // global work vectors
973       PetscInfo(pc, "\tn = %d. %d shared bytes/team, %d global mem bytes, rtol=%e, num blocks %d, team_size=%d, %d vector threads, %d shared vectors, %d global vectors\n", (int)jac->n, scr_bytes_team_shared, global_buff_words, rtol, (int)nBlk, (int)team_size, PCBJKOKKOS_VEC_SIZE, nShareVec, nGlobBVec);
974       PetscScalar *d_work_vecs = d_work_vecs_k.data();
975       Kokkos::parallel_for(
976         "Solve", Kokkos::TeamPolicy<Kokkos::LaunchBounds<256, 4>>(nBlk, team_size, PCBJKOKKOS_VEC_SIZE).set_scratch_size(PCBJKOKKOS_SHARED_LEVEL, Kokkos::PerTeam(scr_bytes_team_shared)), KOKKOS_LAMBDA(const team_member team) {
977           const int    blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
978           vect2D_scr_t work_vecs_shared(team.team_scratch(PCBJKOKKOS_SHARED_LEVEL), end - start, nShareVec);
979           PetscScalar *work_buff_shared = work_vecs_shared.data();
980           PetscScalar *work_buff_global = &d_work_vecs[start]; // start inc'ed in
981           bool         print            = monitor && (blkID == view_bid);
982           switch (ksp_type_idx) {
983           case BATCH_KSP_BICG_IDX:
984             BJSolve_BICG(team, glb_Aai, glb_Aaj, glb_Aaa, d_isrow, d_isicol, work_buff_global, stride_global, nShareVec, work_buff_shared, stride_shared, rtol, atol, dtol, maxit, &d_metadata[blkID], start, end, glb_idiag, glb_bdata, glb_xdata, print);
985             break;
986           case BATCH_KSP_TFQMR_IDX:
987             BJSolve_TFQMR(team, glb_Aai, glb_Aaj, glb_Aaa, d_isrow, d_isicol, work_buff_global, stride_global, nShareVec, work_buff_shared, stride_shared, rtol, atol, dtol, maxit, &d_metadata[blkID], start, end, glb_idiag, glb_bdata, glb_xdata, print);
988             break;
989           case BATCH_KSP_GMRES_IDX:
990             //BJSolve_GMRES();
991             break;
992           default:
993 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
994             printf("Unknown KSP type %d\n", ksp_type_idx);
995 #else
996             /* void */;
997 #endif
998           }
999         });
1000       Kokkos::fence();
1001 #if defined(PETSC_HAVE_CUDA)
1002       nvtxRangePop();
1003       nvtxRangePushA("Post-solve-metadata");
1004 #endif
1005       auto h_metadata = Kokkos::create_mirror(Kokkos::HostSpace::memory_space(), d_metadata);
1006       Kokkos::deep_copy(h_metadata, d_metadata);
1007 #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
1008 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1009       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Iterations\n"));
1010 #endif
1011       // assume species major
1012 #if PCBJKOKKOS_VERBOSE_LEVEL < 4
1013       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "max iterations per species (%s) :", ksp_type_idx == BATCH_KSP_BICG_IDX ? "bicg" : "tfqmr"));
1014 #endif
1015       for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
1016         for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
1017 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1018           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2" PetscInt_FMT ":", s));
1019           for (int bid = 0; bid < batch_sz; bid++) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3" PetscInt_FMT " ", h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its));
1020           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1021 #else
1022           PetscInt count = 0;
1023           for (int bid = 0; bid < batch_sz; bid++) {
1024             if (h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its > count) count = h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its;
1025           }
1026           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3" PetscInt_FMT " ", count));
1027 #endif
1028         }
1029         head += batch_sz * jac->dm_Nf[dmIdx];
1030       }
1031 #if PCBJKOKKOS_VERBOSE_LEVEL == 3
1032       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1033 #endif
1034 #endif
1035       PetscInt count = 0, mbid = 0;
1036       for (int blkID = 0; blkID < nBlk; blkID++) {
1037         PetscCall(PetscLogGpuFlops((PetscLogDouble)h_metadata[blkID].flops));
1038         if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
1039           if (jac->batch_target == blkID) {
1040             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, batch %" PetscInt_FMT ", species %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[blkID].reason], h_metadata[blkID].its, blkID % batch_sz, blkID / batch_sz));
1041           } else if (jac->batch_target == -1 && h_metadata[blkID].its > count) {
1042             jac->max_nits = count = h_metadata[blkID].its;
1043             mbid                  = blkID;
1044           }
1045           if (h_metadata[blkID].reason < 0) {
1046             PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR reason=%s, its=%" PetscInt_FMT ". species %" PetscInt_FMT ", batch %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[blkID].reason], h_metadata[blkID].its, blkID / batch_sz, blkID % batch_sz));
1047           }
1048         }
1049       }
1050       if (jac->batch_target == -1 && jac->reason) {
1051         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, batch %" PetscInt_FMT ", specie %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[mbid].reason], h_metadata[mbid].its, mbid % batch_sz, mbid / batch_sz));
1052       }
1053       {
1054         int errsum;
1055         Kokkos::parallel_reduce(
1056           nBlk,
1057           KOKKOS_LAMBDA(const int idx, int &lsum) {
1058             if (d_metadata[idx].reason < 0) ++lsum;
1059           },
1060           errsum);
1061         pcreason = errsum ? PC_SUBPC_ERROR : PC_NOERROR;
1062         if (!errsum && !jac->max_nits) { // set max its to give back to top KSP
1063           for (int blkID = 0; blkID < nBlk; blkID++) {
1064             if (h_metadata[blkID].its > jac->max_nits) jac->max_nits = h_metadata[blkID].its;
1065           }
1066         } else if (errsum) {
1067           PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR Kokkos batch solver did not converge in all solves\n"));
1068         }
1069       }
1070 #if defined(PETSC_HAVE_CUDA)
1071       nvtxRangePop();
1072 #endif
1073     } // end of Kokkos (not Kernels) solvers block
1074     PetscCall(VecRestoreArrayAndMemType(xout, &glb_xdata));
1075     PetscCall(VecRestoreArrayReadAndMemType(bvec, &glb_bdata));
1076     PetscCall(PCSetFailedReason(pc, pcreason));
1077     // map back to Plex space - not used
1078     if (plex_batch) {
1079       PetscCall(VecCopy(xout, bvec));
1080       PetscCall(VecScatterBegin(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1081       PetscCall(VecScatterEnd(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1082       PetscCall(VecDestroy(&bvec));
1083     }
1084   } // whole 'have aijkok' block
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 static PetscErrorCode PCSetUp_BJKOKKOS(PC pc) {
1089   PC_PCBJKOKKOS    *jac = (PC_PCBJKOKKOS *)pc->data;
1090   Mat               A   = pc->pmat;
1091   Mat_SeqAIJKokkos *aijkok;
1092   PetscBool         flg;
1093 
1094   PetscFunctionBegin;
1095   PetscCheck(!pc->useAmat, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "No support for using 'use_amat'");
1096   PetscCheck(A, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No matrix - A is used above");
1097   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &flg, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, MATAIJKOKKOS, ""));
1098   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for -pc_type bjkokkos");
1099   if (!(aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr))) {
1100     SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No aijkok");
1101   } else {
1102     if (!jac->vec_diag) {
1103       Vec           *subX;
1104       DM             pack, *subDM;
1105       PetscInt       nDMs, n;
1106       PetscContainer container;
1107       PetscCall(PetscObjectQuery((PetscObject)A, "plex_batch_is", (PetscObject *)&container));
1108       { // Permute the matrix to get a block diagonal system: d_isrow_k, d_isicol_k
1109         MatOrderingType rtype;
1110         IS              isrow, isicol;
1111         const PetscInt *rowindices, *icolindices;
1112         rtype = MATORDERINGRCM;
1113         // get permutation. Not what I expect so inverted here
1114         PetscCall(MatGetOrdering(A, rtype, &isrow, &isicol));
1115         PetscCall(ISDestroy(&isrow));
1116         PetscCall(ISInvertPermutation(isicol, PETSC_DECIDE, &isrow)); // THIS IS BACKWARD -- isrow is inverse -- FIX!!!!!
1117 
1118         Mat mat_block_order;
1119         PetscCall(MatCreateSubMatrix(A, isicol, isicol, MAT_INITIAL_MATRIX, &mat_block_order));
1120         PetscCall(MatViewFromOptions(mat_block_order, NULL, "-ksp_batch_reorder_view"));
1121         PetscCall(MatDestroy(&mat_block_order));
1122 
1123         PetscCall(ISGetIndices(isrow, &rowindices));
1124         PetscCall(ISGetIndices(isicol, &icolindices));
1125         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isrow_k((PetscInt *)rowindices, A->rmap->n);
1126         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isicol_k((PetscInt *)icolindices, A->rmap->n);
1127         jac->d_isrow_k  = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isrow_k));
1128         jac->d_isicol_k = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isicol_k));
1129         Kokkos::deep_copy(*jac->d_isrow_k, h_isrow_k);
1130         Kokkos::deep_copy(*jac->d_isicol_k, h_isicol_k);
1131         PetscCall(ISRestoreIndices(isrow, &rowindices));
1132         PetscCall(ISRestoreIndices(isicol, &icolindices));
1133         PetscCall(ISDestroy(&isrow));
1134         PetscCall(ISDestroy(&isicol));
1135       }
1136       // get block sizes
1137       PetscCall(PCGetDM(pc, &pack));
1138       PetscCheck(pack, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "no DM. Requires a composite DM");
1139       PetscCall(PetscObjectTypeCompare((PetscObject)pack, DMCOMPOSITE, &flg));
1140       PetscCheck(flg, PetscObjectComm((PetscObject)pack), PETSC_ERR_USER, "Not for type %s", ((PetscObject)pack)->type_name);
1141       PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
1142       jac->num_dms = nDMs;
1143       PetscCall(DMCreateGlobalVector(pack, &jac->vec_diag));
1144       PetscCall(VecGetLocalSize(jac->vec_diag, &n));
1145       jac->n         = n;
1146       jac->d_idiag_k = new Kokkos::View<PetscScalar *, Kokkos::LayoutRight>("idiag", n);
1147       // options
1148       PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1149       PetscCall(KSPSetFromOptions(jac->ksp));
1150       PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPBICG, ""));
1151       if (flg) {
1152         jac->ksp_type_idx = BATCH_KSP_BICG_IDX;
1153         jac->nwork        = 7;
1154       } else {
1155         PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPTFQMR, ""));
1156         if (flg) {
1157           jac->ksp_type_idx = BATCH_KSP_TFQMR_IDX;
1158           jac->nwork        = 10;
1159         } else {
1160           PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPGMRES, ""));
1161           if (flg) {
1162             jac->ksp_type_idx = BATCH_KSP_GMRES_IDX;
1163             jac->nwork        = 0;
1164           } else {
1165             SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unsupported batch ksp type");
1166           }
1167         }
1168       }
1169       PetscOptionsBegin(PetscObjectComm((PetscObject)jac->ksp), ((PetscObject)jac->ksp)->prefix, "Options for Kokkos batch solver", "none");
1170       PetscCall(PetscOptionsBool("-ksp_converged_reason", "", "bjkokkos.kokkos.cxx.c", jac->reason, &jac->reason, NULL));
1171       PetscCall(PetscOptionsBool("-ksp_monitor", "", "bjkokkos.kokkos.cxx.c", jac->monitor, &jac->monitor, NULL));
1172       PetscCall(PetscOptionsInt("-ksp_batch_target", "", "bjkokkos.kokkos.cxx.c", jac->batch_target, &jac->batch_target, NULL));
1173       PetscCall(PetscOptionsInt("-ksp_batch_nsolves_team", "", "bjkokkos.kokkos.cxx.c", jac->nsolves_team, &jac->nsolves_team, NULL));
1174       PetscCheck(jac->batch_target < jac->num_dms, PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "-ksp_batch_target (%" PetscInt_FMT ") >= number of DMs (%" PetscInt_FMT ")", jac->batch_target, jac->num_dms);
1175       PetscOptionsEnd();
1176       // get blocks - jac->d_bid_eqOffset_k
1177       PetscCall(PetscMalloc(sizeof(*subX) * nDMs, &subX));
1178       PetscCall(PetscMalloc(sizeof(*subDM) * nDMs, &subDM));
1179       PetscCall(PetscMalloc(sizeof(*jac->dm_Nf) * nDMs, &jac->dm_Nf));
1180       PetscCall(PetscInfo(pc, "Have %" PetscInt_FMT " DMs, n=%" PetscInt_FMT " rtol=%g type = %s\n", nDMs, n, (double)jac->ksp->rtol, ((PetscObject)jac->ksp)->type_name));
1181       PetscCall(DMCompositeGetEntriesArray(pack, subDM));
1182       jac->nBlocks = 0;
1183       for (PetscInt ii = 0; ii < nDMs; ii++) {
1184         PetscSection section;
1185         PetscInt     Nf;
1186         DM           dm = subDM[ii];
1187         PetscCall(DMGetLocalSection(dm, &section));
1188         PetscCall(PetscSectionGetNumFields(section, &Nf));
1189         jac->nBlocks += Nf;
1190 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1191         if (ii == 0) PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1192 #else
1193         PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1194 #endif
1195         jac->dm_Nf[ii] = Nf;
1196       }
1197       { // d_bid_eqOffset_k
1198         Kokkos::View<PetscInt *, Kokkos::LayoutRight, Kokkos::HostSpace> h_block_offsets("block_offsets", jac->nBlocks + 1);
1199         PetscCall(DMCompositeGetAccessArray(pack, jac->vec_diag, nDMs, NULL, subX));
1200         h_block_offsets[0]    = 0;
1201         jac->const_block_size = -1;
1202         for (PetscInt ii = 0, idx = 0; ii < nDMs; ii++) {
1203           PetscInt nloc, nblk;
1204           PetscCall(VecGetSize(subX[ii], &nloc));
1205           nblk = nloc / jac->dm_Nf[ii];
1206           PetscCheck(nloc % jac->dm_Nf[ii] == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "nloc%%jac->dm_Nf[ii] (%" PetscInt_FMT ") != 0 DMs", nloc % jac->dm_Nf[ii]);
1207           for (PetscInt jj = 0; jj < jac->dm_Nf[ii]; jj++, idx++) {
1208             h_block_offsets[idx + 1] = h_block_offsets[idx] + nblk;
1209 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1210             if (idx == 0) PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1211 #else
1212             PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1213 #endif
1214             if (jac->const_block_size == -1) jac->const_block_size = nblk;
1215             else if (jac->const_block_size > 0 && jac->const_block_size != nblk) jac->const_block_size = 0;
1216           }
1217         }
1218         PetscCall(DMCompositeRestoreAccessArray(pack, jac->vec_diag, jac->nBlocks, NULL, subX));
1219         PetscCall(PetscFree(subX));
1220         PetscCall(PetscFree(subDM));
1221         jac->d_bid_eqOffset_k = new Kokkos::View<PetscInt *, Kokkos::LayoutRight>(Kokkos::create_mirror(Kokkos::DefaultExecutionSpace::memory_space(), h_block_offsets));
1222         Kokkos::deep_copy(*jac->d_bid_eqOffset_k, h_block_offsets);
1223       }
1224     }
1225     { // get jac->d_idiag_k (PC setup),
1226       const PetscInt    *d_ai = aijkok->i_device_data(), *d_aj = aijkok->j_device_data();
1227       const PetscScalar *d_aa = aijkok->a_device_data();
1228       const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
1229       PetscInt          *d_bid_eqOffset = jac->d_bid_eqOffset_k->data(), *r = jac->d_isrow_k->data(), *ic = jac->d_isicol_k->data();
1230       PetscScalar       *d_idiag = jac->d_idiag_k->data();
1231       Kokkos::parallel_for(
1232         "Diag", Kokkos::TeamPolicy<>(jac->nBlocks, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
1233           const PetscInt blkID = team.league_rank();
1234           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, d_bid_eqOffset[blkID], d_bid_eqOffset[blkID + 1]), [=](const int rowb) {
1235             const PetscInt     rowa = ic[rowb], ai = d_ai[rowa], *aj = d_aj + ai; // grab original data
1236             const PetscScalar *aa   = d_aa + ai;
1237             const PetscInt     nrow = d_ai[rowa + 1] - ai;
1238             int                found;
1239             Kokkos::parallel_reduce(
1240               Kokkos::ThreadVectorRange(team, nrow),
1241               [=](const int &j, int &count) {
1242                 const PetscInt colb = r[aj[j]];
1243                 if (colb == rowb) {
1244                   d_idiag[rowb] = 1. / aa[j];
1245                   count++;
1246                 }
1247               },
1248               found);
1249 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
1250             if (found != 1) Kokkos::single(Kokkos::PerThread(team), [=]() { printf("ERRORrow %d) found = %d\n", rowb, found); });
1251 #endif
1252           });
1253         });
1254     }
1255   }
1256   PetscFunctionReturn(0);
1257 }
1258 
1259 /* Default destroy, if it has never been setup */
1260 static PetscErrorCode PCReset_BJKOKKOS(PC pc) {
1261   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1262 
1263   PetscFunctionBegin;
1264   PetscCall(KSPDestroy(&jac->ksp));
1265   PetscCall(VecDestroy(&jac->vec_diag));
1266   if (jac->d_bid_eqOffset_k) delete jac->d_bid_eqOffset_k;
1267   if (jac->d_idiag_k) delete jac->d_idiag_k;
1268   if (jac->d_isrow_k) delete jac->d_isrow_k;
1269   if (jac->d_isicol_k) delete jac->d_isicol_k;
1270   jac->d_bid_eqOffset_k = NULL;
1271   jac->d_idiag_k        = NULL;
1272   jac->d_isrow_k        = NULL;
1273   jac->d_isicol_k       = NULL;
1274   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", NULL)); // not published now (causes configure errors)
1275   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", NULL));
1276   PetscCall(PetscFree(jac->dm_Nf));
1277   jac->dm_Nf = NULL;
1278   if (jac->rowOffsets) delete jac->rowOffsets;
1279   if (jac->colIndices) delete jac->colIndices;
1280   if (jac->batch_b) delete jac->batch_b;
1281   if (jac->batch_x) delete jac->batch_x;
1282   if (jac->batch_values) delete jac->batch_values;
1283   jac->rowOffsets   = NULL;
1284   jac->colIndices   = NULL;
1285   jac->batch_b      = NULL;
1286   jac->batch_x      = NULL;
1287   jac->batch_values = NULL;
1288 
1289   PetscFunctionReturn(0);
1290 }
1291 
1292 static PetscErrorCode PCDestroy_BJKOKKOS(PC pc) {
1293   PetscFunctionBegin;
1294   PetscCall(PCReset_BJKOKKOS(pc));
1295   PetscCall(PetscFree(pc->data));
1296   PetscFunctionReturn(0);
1297 }
1298 
1299 static PetscErrorCode PCView_BJKOKKOS(PC pc, PetscViewer viewer) {
1300   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1301   PetscBool      iascii;
1302 
1303   PetscFunctionBegin;
1304   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1305   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1306   if (iascii) {
1307     PetscCall(PetscViewerASCIIPrintf(viewer, "  Batched device linear solver: Krylov (KSP) method with Jacobi preconditioning\n"));
1308     PetscCall(PetscViewerASCIIPrintf(viewer, "\t\tnwork = %" PetscInt_FMT ", rel tol = %e, abs tol = %e, div tol = %e, max it =%" PetscInt_FMT ", type = %s\n", jac->nwork, jac->ksp->rtol, jac->ksp->abstol, jac->ksp->divtol, jac->ksp->max_it,
1309                                      ((PetscObject)jac->ksp)->type_name));
1310   }
1311   PetscFunctionReturn(0);
1312 }
1313 
1314 static PetscErrorCode PCSetFromOptions_BJKOKKOS(PC pc, PetscOptionItems *PetscOptionsObject) {
1315   PetscFunctionBegin;
1316   PetscOptionsHeadBegin(PetscOptionsObject, "PC BJKOKKOS options");
1317   PetscOptionsHeadEnd();
1318   PetscFunctionReturn(0);
1319 }
1320 
1321 static PetscErrorCode PCBJKOKKOSSetKSP_BJKOKKOS(PC pc, KSP ksp) {
1322   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1323 
1324   PetscFunctionBegin;
1325   PetscCall(PetscObjectReference((PetscObject)ksp));
1326   PetscCall(KSPDestroy(&jac->ksp));
1327   jac->ksp = ksp;
1328   PetscFunctionReturn(0);
1329 }
1330 
1331 /*@C
1332    PCBJKOKKOSSetKSP - Sets the KSP context for a KSP PC.
1333 
1334    Collective on PC
1335 
1336    Input Parameters:
1337 +  pc - the preconditioner context
1338 -  ksp - the KSP solver
1339 
1340    Notes:
1341    The PC and the KSP must have the same communicator
1342 
1343    Level: advanced
1344 
1345 @*/
1346 PetscErrorCode PCBJKOKKOSSetKSP(PC pc, KSP ksp) {
1347   PetscFunctionBegin;
1348   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1349   PetscValidHeaderSpecific(ksp, KSP_CLASSID, 2);
1350   PetscCheckSameComm(pc, 1, ksp, 2);
1351   PetscTryMethod(pc, "PCBJKOKKOSSetKSP_C", (PC, KSP), (pc, ksp));
1352   PetscFunctionReturn(0);
1353 }
1354 
1355 static PetscErrorCode PCBJKOKKOSGetKSP_BJKOKKOS(PC pc, KSP *ksp) {
1356   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1357 
1358   PetscFunctionBegin;
1359   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1360   *ksp = jac->ksp;
1361   PetscFunctionReturn(0);
1362 }
1363 
1364 /*@C
1365    PCBJKOKKOSGetKSP - Gets the KSP context for a KSP PC.
1366 
1367    Not Collective but KSP returned is parallel if PC was parallel
1368 
1369    Input Parameter:
1370 .  pc - the preconditioner context
1371 
1372    Output Parameters:
1373 .  ksp - the KSP solver
1374 
1375    Notes:
1376    You must call KSPSetUp() before calling PCBJKOKKOSGetKSP().
1377 
1378    If the PC is not a PCBJKOKKOS object it raises an error
1379 
1380    Level: advanced
1381 
1382 @*/
1383 PetscErrorCode PCBJKOKKOSGetKSP(PC pc, KSP *ksp) {
1384   PetscFunctionBegin;
1385   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1386   PetscValidPointer(ksp, 2);
1387   PetscUseMethod(pc, "PCBJKOKKOSGetKSP_C", (PC, KSP *), (pc, ksp));
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 static PetscErrorCode PCPostSolve_BJKOKKOS(PC pc, KSP ksp, Vec b, Vec x) {
1392   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1393 
1394   PetscFunctionBegin;
1395   ksp->its = jac->max_nits;
1396   PetscFunctionReturn(0);
1397 }
1398 
1399 /* ----------------------------------------------------------------------------------*/
1400 
1401 /*MC
1402      PCBJKOKKOS -  Defines a preconditioner that applies a Krylov solver and preconditioner to the blocks in a AIJASeq matrix on the GPU.
1403 
1404    Options Database Key:
1405 .     -pc_bjkokkos_ - options prefix with ksp options
1406 
1407    Level: intermediate
1408 
1409    Notes:
1410     For use with -ksp_type preonly to bypass any CPU work
1411 
1412    Developer Notes:
1413 
1414 .seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`,
1415           `PCSHELL`, `PCCOMPOSITE`, `PCSetUseAmat()`, `PCBJKOKKOSGetKSP()`
1416 
1417 M*/
1418 
1419 PETSC_EXTERN PetscErrorCode PCCreate_BJKOKKOS(PC pc) {
1420   PC_PCBJKOKKOS *jac;
1421 
1422   PetscFunctionBegin;
1423   PetscCall(PetscNewLog(pc, &jac));
1424   pc->data = (void *)jac;
1425 
1426   jac->ksp              = NULL;
1427   jac->vec_diag         = NULL;
1428   jac->d_bid_eqOffset_k = NULL;
1429   jac->d_idiag_k        = NULL;
1430   jac->d_isrow_k        = NULL;
1431   jac->d_isicol_k       = NULL;
1432   jac->nBlocks          = 1;
1433   jac->max_nits         = 0;
1434 
1435   PetscCall(PetscMemzero(pc->ops, sizeof(struct _PCOps)));
1436   pc->ops->apply          = PCApply_BJKOKKOS;
1437   pc->ops->applytranspose = NULL;
1438   pc->ops->setup          = PCSetUp_BJKOKKOS;
1439   pc->ops->reset          = PCReset_BJKOKKOS;
1440   pc->ops->destroy        = PCDestroy_BJKOKKOS;
1441   pc->ops->setfromoptions = PCSetFromOptions_BJKOKKOS;
1442   pc->ops->view           = PCView_BJKOKKOS;
1443   pc->ops->postsolve      = PCPostSolve_BJKOKKOS;
1444 
1445   jac->rowOffsets   = NULL;
1446   jac->colIndices   = NULL;
1447   jac->batch_b      = NULL;
1448   jac->batch_x      = NULL;
1449   jac->batch_values = NULL;
1450 
1451   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", PCBJKOKKOSGetKSP_BJKOKKOS));
1452   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", PCBJKOKKOSSetKSP_BJKOKKOS));
1453   PetscFunctionReturn(0);
1454 }
1455