xref: /petsc/src/ksp/pc/impls/bjacobi/bjkokkos/bjkokkos.kokkos.cxx (revision d2522c19e8fa9bca20aaca277941d9a63e71db6a)
1 #include <petscvec_kokkos.hpp>
2 #include <petsc/private/pcimpl.h>
3 #include <petsc/private/kspimpl.h>
4 #include <petscksp.h> /*I "petscksp.h" I*/
5 #include "petscsection.h"
6 #include <petscdmcomposite.h>
7 #include "Kokkos_Core.hpp"
8 
9 #include <../src/mat/impls/aij/seq/aij.h>
10 #include <../src/mat/impls/aij/seq/kokkos/aijkok.hpp>
11 
12 #if defined(PETSC_HAVE_CUDA_NVTX)
13 #include <nvToolsExt.h>
14 #endif
15 
16 #define PCBJKOKKOS_SHARED_LEVEL 0 // 0 is shared, 1 is global
17 #define PCBJKOKKOS_VEC_SIZE     16
18 #define PCBJKOKKOS_TEAM_SIZE    16
19 
20 #define PCBJKOKKOS_VERBOSE_LEVEL 2
21 
22 typedef Kokkos::DefaultExecutionSpace exec_space;
23 using layout           = Kokkos::LayoutRight;
24 using IntView          = Kokkos::View<PetscInt **, layout, exec_space>;
25 using AMatrixValueView = const Kokkos::View<PetscScalar **, layout, exec_space>;
26 using XYType           = const Kokkos::View<PetscScalar **, layout, exec_space>;
27 
28 typedef enum {
29   BATCH_KSP_BICG_IDX,
30   BATCH_KSP_TFQMR_IDX,
31   BATCH_KSP_GMRES_IDX,
32   NUM_BATCH_TYPES
33 } KSPIndex;
34 typedef struct {
35   Vec                                               vec_diag;
36   PetscInt                                          nBlocks; /* total number of blocks */
37   PetscInt                                          n;       // cache host version of d_bid_eqOffset_k[nBlocks]
38   KSP                                               ksp;     // Used just for options. Should have one for each block
39   Kokkos::View<PetscInt *, Kokkos::LayoutRight>    *d_bid_eqOffset_k;
40   Kokkos::View<PetscScalar *, Kokkos::LayoutRight> *d_idiag_k;
41   Kokkos::View<PetscInt *>                         *d_isrow_k;
42   Kokkos::View<PetscInt *>                         *d_isicol_k;
43   KSPIndex                                          ksp_type_idx;
44   PetscInt                                          nwork;
45   PetscInt                                          const_block_size; // used to decide to use shared memory for work vectors
46   PetscInt                                         *dm_Nf;            // Number of fields in each DM
47   PetscInt                                          num_dms;
48   // diagnostics
49   PetscBool                                         reason;
50   PetscBool                                         monitor;
51   PetscInt                                          batch_target;
52   PetscInt                                          nsolves_team;
53   PetscInt                                          max_nits;
54   // caches
55   IntView                                          *rowOffsets;
56   IntView                                          *colIndices;
57   XYType                                           *batch_b;
58   XYType                                           *batch_x;
59   AMatrixValueView                                 *batch_values;
60 } PC_PCBJKOKKOS;
61 
62 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
63 #include <fstream>
64 
65 #include "Kokkos_Timer.hpp"
66 #include "Kokkos_Random.hpp"
67 #include "Kokkos_UnorderedMap.hpp"
68 #include "Kokkos_Sort.hpp"
69 
70 /// KokkosKernels headers
71 #include "KokkosBatched_Util.hpp"
72 #include "KokkosBatched_Vector.hpp"
73 
74 #include <Kokkos_ArithTraits.hpp>
75 #include <KokkosBatched_Util.hpp>
76 #include <KokkosBatched_Vector.hpp>
77 #include <KokkosBatched_Copy_Decl.hpp>
78 #include <KokkosBatched_Copy_Impl.hpp>
79 #include <KokkosBatched_AddRadial_Decl.hpp>
80 #include <KokkosBatched_AddRadial_Impl.hpp>
81 #include <KokkosBatched_Gemm_Decl.hpp>
82 #include <KokkosBatched_Gemm_Serial_Impl.hpp>
83 #include <KokkosBatched_Gemm_Team_Impl.hpp>
84 #include <KokkosBatched_Gemv_Decl.hpp>
85 #include <KokkosBatched_Gemv_Serial_Impl.hpp>
86 #include <KokkosBatched_Gemv_Team_Impl.hpp>
87 #include <KokkosBatched_Trsm_Decl.hpp>
88 #include <KokkosBatched_Trsm_Serial_Impl.hpp>
89 #include <KokkosBatched_Trsm_Team_Impl.hpp>
90 #include <KokkosBatched_Trsv_Decl.hpp>
91 #include <KokkosBatched_Trsv_Serial_Impl.hpp>
92 #include <KokkosBatched_Trsv_Team_Impl.hpp>
93 #include <KokkosBatched_LU_Decl.hpp>
94 #include <KokkosBatched_LU_Serial_Impl.hpp>
95 #include <KokkosBatched_LU_Team_Impl.hpp>
96 #include <KokkosSparse_CrsMatrix.hpp>
97 #include "KokkosBatched_Spmv.hpp"
98 #include "KokkosBatched_CrsMatrix.hpp"
99 #include "KokkosBatched_Krylov_Handle.hpp"
100 #include "KokkosBatched_GMRES.hpp"
101 #include "KokkosBatched_JacobiPrec.hpp"
102 
103 template <typename DeviceType, typename ValuesViewType, typename IntView, typename VectorViewType, typename KrylovHandleType>
104 struct Functor_TestBatchedTeamVectorGMRES {
105   const ValuesViewType _D;
106   const ValuesViewType _diag;
107   const IntView        _r;
108   const IntView        _c;
109   const VectorViewType _X;
110   const VectorViewType _B;
111   const int            _N_team, _team_size, _vector_length;
112   const int            _N_iteration;
113   const double         _tol;
114   const int            _ortho_strategy;
115   const int            _scratch_pad_level;
116   KrylovHandleType     _handle;
117 
118   KOKKOS_INLINE_FUNCTION
119   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) :
120     _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) { }
121 
122   KOKKOS_INLINE_FUNCTION
123   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) :
124     _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) { }
125 
126   template <typename MemberType>
127   KOKKOS_INLINE_FUNCTION void operator()(const MemberType &member) const {
128     const int first_matrix = static_cast<int>(member.league_rank()) * _N_team;
129     const int N            = _D.extent(0);
130     const int last_matrix  = (static_cast<int>(member.league_rank() + 1) * _N_team < N ? static_cast<int>(member.league_rank() + 1) * _N_team : N);
131     const int graphID      = static_cast<int>(member.league_rank());
132     using TeamVectorCopy1D = KokkosBatched::TeamVectorCopy<MemberType, KokkosBatched::Trans::NoTranspose, 1>;
133 
134     auto d                         = Kokkos::subview(_D, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
135     auto x                         = Kokkos::subview(_X, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
136     auto b                         = Kokkos::subview(_B, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
137     using ScratchPadIntViewType    = Kokkos::View<typename IntView::non_const_value_type *, typename IntView::array_layout, typename IntView::execution_space::scratch_memory_space>;
138     using ScratchPadValuesViewType = Kokkos::View<typename ValuesViewType::non_const_value_type **, typename ValuesViewType::array_layout, typename ValuesViewType::execution_space::scratch_memory_space>;
139 
140     using Operator = KokkosBatched::CrsMatrix<ValuesViewType, ScratchPadIntViewType>;
141     ScratchPadIntViewType r(member.team_scratch(1), _r.extent(1));
142     ScratchPadIntViewType c(member.team_scratch(1), _c.extent(1));
143 
144     TeamVectorCopy1D::invoke(member, Kokkos::subview(_r, graphID, Kokkos::ALL), r);
145     TeamVectorCopy1D::invoke(member, Kokkos::subview(_c, graphID, Kokkos::ALL), c);
146     Operator A(d, r, c);
147 
148     ScratchPadValuesViewType diag(member.team_scratch(1), last_matrix - first_matrix, _diag.extent(1));
149     using PrecOperator = KokkosBatched::JacobiPrec<ScratchPadValuesViewType>;
150 
151     KokkosBatched::TeamVectorCopy<MemberType>::invoke(member, Kokkos::subview(_diag, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL), diag);
152     PrecOperator P(diag);
153     P.setComputedInverse();
154 
155     KokkosBatched::TeamVectorGMRES<MemberType>::template invoke<Operator, VectorViewType, PrecOperator, KrylovHandleType>(member, A, b, x, P, _handle);
156   }
157   inline double run(PC pc) {
158     typedef typename ValuesViewType::value_type value_type;
159     std::string                                 name("KokkosBatched::Test::TeamVectorGMRES");
160     Kokkos::Timer                               timer;
161     Kokkos::Profiling::pushRegion(name.c_str());
162 
163     Kokkos::TeamPolicy<DeviceType> auto_policy(ceil(1. * _D.extent(0) / _N_team), Kokkos::AUTO(), Kokkos::AUTO());
164     Kokkos::TeamPolicy<DeviceType> tuned_policy(ceil(1. * _D.extent(0) / _N_team), _team_size, _vector_length);
165     Kokkos::TeamPolicy<DeviceType> policy;
166 
167     if (_team_size < 1) policy = auto_policy;
168     else policy = tuned_policy;
169 
170     _handle.set_max_iteration(_N_iteration);
171     _handle.set_tolerance(_tol);
172     _handle.set_ortho_strategy(_ortho_strategy);
173     _handle.set_scratch_pad_level(_scratch_pad_level);
174     _handle.set_compute_last_residual(true);
175 
176     int maximum_iteration = _handle.get_max_iteration();
177 
178     using ScalarType = typename ValuesViewType::non_const_value_type;
179     using Layout     = typename ValuesViewType::array_layout;
180     using EXSP       = typename ValuesViewType::execution_space;
181 
182     using MagnitudeType = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
183 
184     using ViewType1D    = Kokkos::View<MagnitudeType *, Layout, EXSP>;
185     using ViewType2D    = Kokkos::View<ScalarType **, Layout, EXSP>;
186     using ViewType3D    = Kokkos::View<ScalarType ***, Layout, EXSP>;
187     using IntViewType1D = Kokkos::View<PetscInt *, Layout, EXSP>;
188 
189     size_t bytes_1D      = ViewType2D::shmem_size(_N_team, 1);
190     size_t bytes_row_ptr = IntViewType1D::shmem_size(_r.extent(1));
191     size_t bytes_col_idc = IntViewType1D::shmem_size(_c.extent(1));
192     size_t bytes_2D_1    = ViewType2D::shmem_size(_N_team, _X.extent(1));
193     size_t bytes_2D_2    = ViewType2D::shmem_size(_N_team, maximum_iteration + 1);
194 
195     size_t bytes_diag = bytes_2D_1;
196     size_t bytes_tmp  = 2 * bytes_2D_1 + 2 * bytes_1D + bytes_2D_2;
197 
198     policy.set_scratch_size(0, Kokkos::PerTeam(bytes_tmp));
199     policy.set_scratch_size(1, Kokkos::PerTeam(bytes_col_idc + bytes_row_ptr + bytes_diag));
200     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);
201     exec_space().fence();
202     timer.reset();
203     Kokkos::parallel_for(name.c_str(), policy, *this);
204     exec_space().fence();
205     double sec = timer.seconds();
206 
207     return sec;
208   }
209 };
210 #endif // KK GMRES
211 
212 typedef Kokkos::TeamPolicy<>::member_type team_member;
213 
214 static PetscErrorCode PCBJKOKKOSCreateKSP_BJKOKKOS(PC pc) {
215   const char    *prefix;
216   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
217   DM             dm;
218 
219   PetscFunctionBegin;
220   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->ksp));
221   PetscCall(KSPSetErrorIfNotConverged(jac->ksp, pc->erroriffailure));
222   PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->ksp, (PetscObject)pc, 1));
223   PetscCall(PCGetOptionsPrefix(pc, &prefix));
224   PetscCall(KSPSetOptionsPrefix(jac->ksp, prefix));
225   PetscCall(KSPAppendOptionsPrefix(jac->ksp, "pc_bjkokkos_"));
226   PetscCall(PCGetDM(pc, &dm));
227   if (dm) {
228     PetscCall(KSPSetDM(jac->ksp, dm));
229     PetscCall(KSPSetDMActive(jac->ksp, PETSC_FALSE));
230   }
231   jac->reason       = PETSC_FALSE;
232   jac->monitor      = PETSC_FALSE;
233   jac->batch_target = -1;
234   jac->nsolves_team = 1;
235   jac->ksp->max_it  = 50; // this is realy for GMRES w/o restarts
236   PetscFunctionReturn(0);
237 }
238 
239 // y <-- Ax
240 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) {
241   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
242     int                rowa = ic[rowb];
243     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
244     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
245     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
246     PetscScalar        sum;
247     Kokkos::parallel_reduce(
248       Kokkos::ThreadVectorRange(team, n), [=](const int i, PetscScalar &lsum) { lsum += aa[i] * x_loc[r[aj[i]] - start]; }, sum);
249     Kokkos::single(Kokkos::PerThread(team), [=]() { y_loc[rowb - start] = sum; });
250   });
251   team.team_barrier();
252   return 0;
253 }
254 
255 // temp buffer per thread with reduction at end?
256 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) {
257   Kokkos::parallel_for(Kokkos::TeamVectorRange(team, end - start), [=](int i) { y_loc[i] = 0; });
258   team.team_barrier();
259   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
260     int                rowa = ic[rowb];
261     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
262     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
263     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
264     const PetscScalar  xx   = x_loc[rowb - start]; // rowb = ic[rowa] = ic[r[rowb]]
265     Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
266       PetscScalar val = aa[i] * xx;
267       Kokkos::atomic_fetch_add(&y_loc[r[aj[i]] - start], val);
268     });
269   });
270   team.team_barrier();
271   return 0;
272 }
273 
274 typedef struct Batch_MetaData_TAG {
275   PetscInt           flops;
276   PetscInt           its;
277   KSPConvergedReason reason;
278 } Batch_MetaData;
279 
280 // Solve A(BB^-1)x = y with TFQMR. Right preconditioned to get un-preconditioned residual
281 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) {
282   using Kokkos::parallel_for;
283   using Kokkos::parallel_reduce;
284   int                Nblk = end - start, i, m, stride = stride_shared, idx = 0;
285   PetscReal          dp, dpold, w, dpest, tau, psi, cm, r0;
286   const PetscScalar *Diag = &glb_idiag[start];
287   PetscScalar       *ptr  = work_space_shared, rho, rhoold, a, s, b, eta, etaold, psiold, cf, dpi;
288 
289   if (idx++ == nShareVec) {
290     ptr    = work_space_global;
291     stride = stride_global;
292   }
293   PetscScalar *XX = ptr;
294   ptr += stride;
295   if (idx++ == nShareVec) {
296     ptr    = work_space_global;
297     stride = stride_global;
298   }
299   PetscScalar *R = ptr;
300   ptr += stride;
301   if (idx++ == nShareVec) {
302     ptr    = work_space_global;
303     stride = stride_global;
304   }
305   PetscScalar *RP = ptr;
306   ptr += stride;
307   if (idx++ == nShareVec) {
308     ptr    = work_space_global;
309     stride = stride_global;
310   }
311   PetscScalar *V = ptr;
312   ptr += stride;
313   if (idx++ == nShareVec) {
314     ptr    = work_space_global;
315     stride = stride_global;
316   }
317   PetscScalar *T = ptr;
318   ptr += stride;
319   if (idx++ == nShareVec) {
320     ptr    = work_space_global;
321     stride = stride_global;
322   }
323   PetscScalar *Q = ptr;
324   ptr += stride;
325   if (idx++ == nShareVec) {
326     ptr    = work_space_global;
327     stride = stride_global;
328   }
329   PetscScalar *P = ptr;
330   ptr += stride;
331   if (idx++ == nShareVec) {
332     ptr    = work_space_global;
333     stride = stride_global;
334   }
335   PetscScalar *U = ptr;
336   ptr += stride;
337   if (idx++ == nShareVec) {
338     ptr    = work_space_global;
339     stride = stride_global;
340   }
341   PetscScalar *D = ptr;
342   ptr += stride;
343   if (idx++ == nShareVec) {
344     ptr    = work_space_global;
345     stride = stride_global;
346   }
347   PetscScalar *AUQ = V;
348 
349   // init: get b, zero x
350   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
351     int rowa         = ic[rowb];
352     R[rowb - start]  = glb_b[rowa];
353     XX[rowb - start] = 0;
354   });
355   team.team_barrier();
356   parallel_reduce(
357     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
358   team.team_barrier();
359   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
360   // diagnostics
361 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
362   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
363 #endif
364   if (dp < atol) {
365     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
366     return 0;
367   }
368   if (0 == maxit) {
369     metad->reason = KSP_DIVERGED_ITS;
370     return 0;
371   }
372 
373   /* Make the initial Rp = R */
374   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { RP[idx] = R[idx]; });
375   team.team_barrier();
376   /* Set the initial conditions */
377   etaold = 0.0;
378   psiold = 0.0;
379   tau    = dp;
380   dpold  = dp;
381 
382   /* rhoold = (r,rp)     */
383   parallel_reduce(
384     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rhoold);
385   team.team_barrier();
386   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
387     U[idx] = R[idx];
388     P[idx] = R[idx];
389     T[idx] = Diag[idx] * P[idx];
390     D[idx] = 0;
391   });
392   team.team_barrier();
393   MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V);
394 
395   i = 0;
396   do {
397     /* s <- (v,rp)          */
398     parallel_reduce(
399       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += V[idx] * PetscConj(RP[idx]); }, s);
400     team.team_barrier();
401     a = rhoold / s; /* a <- rho / s         */
402     /* q <- u - a v    VecWAXPY(w,alpha,x,y): w = alpha x + y.     */
403     /* t <- u + q           */
404     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
405       Q[idx] = U[idx] - a * V[idx];
406       T[idx] = U[idx] + Q[idx];
407     });
408     team.team_barrier();
409     // KSP_PCApplyBAorAB
410     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * T[idx]; });
411     team.team_barrier();
412     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, AUQ);
413     /* r <- r - a K (u + q) */
414     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { R[idx] = R[idx] - a * AUQ[idx]; });
415     team.team_barrier();
416     parallel_reduce(
417       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
418     team.team_barrier();
419     dp = PetscSqrtReal(PetscRealPart(dpi));
420     for (m = 0; m < 2; m++) {
421       if (!m) w = PetscSqrtReal(dp * dpold);
422       else w = dp;
423       psi = w / tau;
424       cm  = 1.0 / PetscSqrtReal(1.0 + psi * psi);
425       tau = tau * psi * cm;
426       eta = cm * cm * a;
427       cf  = psiold * psiold * etaold / a;
428       if (!m) {
429         /* D = U + cf D */
430         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = U[idx] + cf * D[idx]; });
431       } else {
432         /* D = Q + cf D */
433         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = Q[idx] + cf * D[idx]; });
434       }
435       team.team_barrier();
436       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = XX[idx] + eta * D[idx]; });
437       team.team_barrier();
438       dpest = PetscSqrtReal(2 * i + m + 2.0) * tau;
439 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
440       if (monitor && m == 1) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dpest); });
441 #endif
442       if (dpest < atol) {
443         metad->reason = KSP_CONVERGED_ATOL_NORMAL;
444         goto done;
445       }
446       if (dpest / r0 < rtol) {
447         metad->reason = KSP_CONVERGED_RTOL_NORMAL;
448         goto done;
449       }
450 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
451       if (dpest / r0 > dtol) {
452         metad->reason = KSP_DIVERGED_DTOL;
453         Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dpest, r0); });
454         goto done;
455       }
456 #else
457       if (dpest / r0 > dtol) {
458         metad->reason = KSP_DIVERGED_DTOL;
459         goto done;
460       }
461 #endif
462       if (i + 1 == maxit) {
463         metad->reason = KSP_DIVERGED_ITS;
464         goto done;
465       }
466 
467       etaold = eta;
468       psiold = psi;
469     }
470 
471     /* rho <- (r,rp)       */
472     parallel_reduce(
473       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rho);
474     team.team_barrier();
475     b = rho / rhoold; /* b <- rho / rhoold   */
476     /* u <- r + b q        */
477     /* p <- u + b(q + b p) */
478     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
479       U[idx] = R[idx] + b * Q[idx];
480       Q[idx] = Q[idx] + b * P[idx];
481       P[idx] = U[idx] + b * Q[idx];
482     });
483     /* v <- K p  */
484     team.team_barrier();
485     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * P[idx]; });
486     team.team_barrier();
487     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V);
488 
489     rhoold = rho;
490     dpold  = dp;
491 
492     i++;
493   } while (i < maxit);
494 done:
495   // KSPUnwindPreconditioner
496   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = Diag[idx] * XX[idx]; });
497   team.team_barrier();
498   // put x into Plex order
499   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
500     int rowa    = ic[rowb];
501     glb_x[rowa] = XX[rowb - start];
502   });
503   metad->its = i + 1;
504   if (1) {
505     int nnz;
506     parallel_reduce(
507       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
508     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
509   } else {
510     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
511   }
512   return 0;
513 }
514 
515 // Solve Ax = y with biCG
516 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) {
517   using Kokkos::parallel_for;
518   using Kokkos::parallel_reduce;
519   int                Nblk = end - start, i, stride = stride_shared, idx = 0; // start in shared mem
520   PetscReal          dp, r0;
521   const PetscScalar *Di  = &glb_idiag[start];
522   PetscScalar       *ptr = work_space_shared, dpi, a = 1.0, beta, betaold = 1.0, b, b2, ma, mac;
523 
524   if (idx++ == nShareVec) {
525     ptr    = work_space_global;
526     stride = stride_global;
527   }
528   PetscScalar *XX = ptr;
529   ptr += stride;
530   if (idx++ == nShareVec) {
531     ptr    = work_space_global;
532     stride = stride_global;
533   }
534   PetscScalar *Rl = ptr;
535   ptr += stride;
536   if (idx++ == nShareVec) {
537     ptr    = work_space_global;
538     stride = stride_global;
539   }
540   PetscScalar *Zl = ptr;
541   ptr += stride;
542   if (idx++ == nShareVec) {
543     ptr    = work_space_global;
544     stride = stride_global;
545   }
546   PetscScalar *Pl = ptr;
547   ptr += stride;
548   if (idx++ == nShareVec) {
549     ptr    = work_space_global;
550     stride = stride_global;
551   }
552   PetscScalar *Rr = ptr;
553   ptr += stride;
554   if (idx++ == nShareVec) {
555     ptr    = work_space_global;
556     stride = stride_global;
557   }
558   PetscScalar *Zr = ptr;
559   ptr += stride;
560   if (idx++ == nShareVec) {
561     ptr    = work_space_global;
562     stride = stride_global;
563   }
564   PetscScalar *Pr = ptr;
565   ptr += stride;
566 
567   /*     r <- b (x is 0) */
568   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
569     int rowa         = ic[rowb];
570     //PetscCall(VecCopy(Rr,Rl));
571     Rl[rowb - start] = Rr[rowb - start] = glb_b[rowa];
572     XX[rowb - start]                    = 0;
573   });
574   team.team_barrier();
575   /*     z <- Br         */
576   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
577     Zr[idx] = Di[idx] * Rr[idx];
578     Zl[idx] = Di[idx] * Rl[idx];
579   });
580   team.team_barrier();
581   /*    dp <- r'*r       */
582   parallel_reduce(
583     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
584   team.team_barrier();
585   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
586 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
587   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
588 #endif
589   if (dp < atol) {
590     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
591     return 0;
592   }
593   if (0 == maxit) {
594     metad->reason = KSP_DIVERGED_ITS;
595     return 0;
596   }
597   i = 0;
598   do {
599     /*     beta <- r'z     */
600     parallel_reduce(
601       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += Zr[idx] * PetscConj(Rl[idx]); }, beta);
602     team.team_barrier();
603 #if PCBJKOKKOS_VERBOSE_LEVEL >= 6
604 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
605     Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%7d beta = Z.R = %22.14e \n", i, (double)beta); });
606 #endif
607 #endif
608     if (!i) {
609       if (beta == 0.0) {
610         metad->reason = KSP_DIVERGED_BREAKDOWN_BICG;
611         goto done;
612       }
613       /*     p <- z          */
614       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
615         Pr[idx] = Zr[idx];
616         Pl[idx] = Zl[idx];
617       });
618     } else {
619       b  = beta / betaold;
620       /*     p <- z + b* p   */
621       b2 = PetscConj(b);
622       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
623         Pr[idx] = b * Pr[idx] + Zr[idx];
624         Pl[idx] = b2 * Pl[idx] + Zl[idx];
625       });
626     }
627     team.team_barrier();
628     betaold = beta;
629     /*     z <- Kp         */
630     MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pr, Zr);
631     MatMultTranspose(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pl, Zl);
632     /*     dpi <- z'p      */
633     parallel_reduce(
634       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Zr[idx] * PetscConj(Pl[idx]); }, dpi);
635     team.team_barrier();
636     //
637     a   = beta / dpi; /*     a = beta/p'z    */
638     ma  = -a;
639     mac = PetscConj(ma);
640     /*     x <- x + ap     */
641     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
642       XX[idx] = XX[idx] + a * Pr[idx];
643       Rr[idx] = Rr[idx] + ma * Zr[idx];
644       Rl[idx] = Rl[idx] + mac * Zl[idx];
645     });
646     team.team_barrier();
647     team.team_barrier();
648     /*    dp <- r'*r       */
649     parallel_reduce(
650       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
651     team.team_barrier();
652     dp = PetscSqrtReal(PetscRealPart(dpi));
653 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
654     if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dp); });
655 #endif
656     if (dp < atol) {
657       metad->reason = KSP_CONVERGED_ATOL_NORMAL;
658       goto done;
659     }
660     if (dp / r0 < rtol) {
661       metad->reason = KSP_CONVERGED_RTOL_NORMAL;
662       goto done;
663     }
664 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
665     if (dp / r0 > dtol) {
666       metad->reason = KSP_DIVERGED_DTOL;
667       Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dp, r0); });
668       goto done;
669     }
670 #else
671     if (dp / r0 > dtol) {
672       metad->reason = KSP_DIVERGED_DTOL;
673       goto done;
674     }
675 #endif
676     if (i + 1 == maxit) {
677       metad->reason = KSP_DIVERGED_ITS;
678       goto done;
679     }
680     /* z <- Br  */
681     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
682       Zr[idx] = Di[idx] * Rr[idx];
683       Zl[idx] = Di[idx] * Rl[idx];
684     });
685     i++;
686     team.team_barrier();
687   } while (i < maxit);
688 done:
689   // put x back into Plex order
690   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
691     int rowa    = ic[rowb];
692     glb_x[rowa] = XX[rowb - start];
693   });
694   metad->its = i + 1;
695   if (1) {
696     int nnz;
697     parallel_reduce(
698       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
699     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
700   } else {
701     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
702   }
703   return 0;
704 }
705 
706 // KSP solver solve Ax = b; x is output, bin is input
707 static PetscErrorCode PCApply_BJKOKKOS(PC pc, Vec bin, Vec xout) {
708   PC_PCBJKOKKOS    *jac = (PC_PCBJKOKKOS *)pc->data;
709   Mat               A   = pc->pmat;
710   Mat_SeqAIJKokkos *aijkok;
711 
712   PetscFunctionBegin;
713   PetscCheck(jac->vec_diag && A, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "Not setup???? %p %p", jac->vec_diag, A);
714   aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
715   if (!aijkok) {
716     SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "No aijkok");
717   } else {
718     PetscInt           maxit = jac->ksp->max_it;
719     const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
720     const PetscInt     nwork = jac->nwork, nBlk = jac->nBlocks;
721     PetscScalar       *glb_xdata = NULL;
722     PetscReal          rtol = jac->ksp->rtol, atol = jac->ksp->abstol, dtol = jac->ksp->divtol;
723     const PetscScalar *glb_idiag = jac->d_idiag_k->data(), *glb_bdata = NULL;
724     const PetscInt    *glb_Aai = aijkok->i_device_data(), *glb_Aaj = aijkok->j_device_data(), *d_bid_eqOffset = jac->d_bid_eqOffset_k->data();
725     const PetscScalar *glb_Aaa  = aijkok->a_device_data();
726     const PetscInt    *d_isicol = jac->d_isicol_k->data(), *d_isrow = jac->d_isrow_k->data();
727     PCFailedReason     pcreason;
728     KSPIndex           ksp_type_idx = jac->ksp_type_idx;
729     PetscMemType       mtype;
730     PetscContainer     container;
731     PetscInt           batch_sz;
732     VecScatter         plex_batch = NULL;       // not used
733     Vec                bvec;                    // a copy of b for scatter (just alias to bin now)
734     PetscBool          monitor  = jac->monitor; // captured
735     PetscInt           view_bid = jac->batch_target;
736     MatInfo            info;
737     jac->max_nits = 0;
738     if (view_bid < 0) view_bid = 0;
739     PetscCall(MatGetInfo(A, MAT_LOCAL, &info));
740     // get field major is to map plex IO to/from block/field major
741     PetscCall(PetscObjectQuery((PetscObject)A, "plex_batch_is", (PetscObject *)&container));
742     if (container) {
743       PetscCall(VecDuplicate(bin, &bvec));
744       PetscCall(PetscContainerGetPointer(container, (void **)&plex_batch));
745       PetscCall(VecScatterBegin(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
746       PetscCall(VecScatterEnd(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
747       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No plex_batch_is -- require NO field major ordering for now");
748     } else {
749       bvec = bin;
750     }
751     // get x
752     PetscCall(VecGetArrayAndMemType(xout, &glb_xdata, &mtype));
753 #if defined(PETSC_HAVE_CUDA)
754     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for x %" PetscInt_FMT " != %" PetscInt_FMT, mtype, PETSC_MEMTYPE_DEVICE);
755 #endif
756     PetscCall(VecGetArrayReadAndMemType(bvec, &glb_bdata, &mtype));
757 #if defined(PETSC_HAVE_CUDA)
758     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for b");
759 #endif
760     // get batch size
761     PetscCall(PetscObjectQuery((PetscObject)A, "batch size", (PetscObject *)&container));
762     if (container) {
763       PetscInt *pNf = NULL;
764       PetscCall(PetscContainerGetPointer(container, (void **)&pNf));
765       batch_sz = *pNf;
766     } else batch_sz = 1;
767     PetscCheck(nBlk % batch_sz == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "batch_sz = %" PetscInt_FMT ", nBlk = %" PetscInt_FMT, batch_sz, nBlk);
768     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.)
769 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
770       int       Nsolves_team = jac->nsolves_team, fill_idx = 0;
771       int       Nloc    = jac->const_block_size; // same grids
772       const int Nsolves = nBlk;
773       const int nnz     = (int)info.nz_used / Nsolves;      // fix for variable grid size
774       if (Nsolves_team > batch_sz) Nsolves_team = batch_sz; // silently fix this
775       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)");
776       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);
777       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);
778 #if defined(PETSC_HAVE_CUDA_NVTX)
779       nvtxRangePushA("gmres-kk");
780 #endif
781       Kokkos::View<PetscScalar **, layout, exec_space, Kokkos::MemoryTraits<Kokkos::Unmanaged>> inv_diag((PetscScalar *)glb_idiag, Nsolves, Nloc); // in correct order
782       if (!jac->rowOffsets) {
783         jac->rowOffsets   = new IntView("rowOffsets", Nsolves / Nsolves_team, Nloc + 1); // same grids
784         jac->colIndices   = new IntView("colIndices", Nsolves / Nsolves_team, nnz);
785         jac->batch_b      = new XYType("batch rhs", Nsolves, Nloc);
786         jac->batch_x      = new XYType("batch sol", Nsolves, Nloc);
787         jac->batch_values = new AMatrixValueView("batch values", Nsolves, nnz);
788         fill_idx          = 1;
789         PetscInfo(pc, "Setup indices Nloc=%d, nnz=%d\n", Nloc, nnz);
790       }
791       IntView          &rowOffsets   = *jac->rowOffsets;
792       IntView          &colIndices   = *jac->colIndices;
793       XYType           &batch_b      = *jac->batch_b;
794       XYType           &batch_x      = *jac->batch_x;
795       AMatrixValueView &batch_values = *jac->batch_values;
796 
797       Kokkos::deep_copy(batch_x, 0.);
798       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);
799       Kokkos::parallel_for(
800         "rowOffsets+map", Kokkos::TeamPolicy<>(Nsolves, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
801           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
802           if (fill_idx) {
803             if (blkID % Nsolves_team == 0) {                                                        // first matrix on this member
804               Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](const int rowb) { // Nloc
805                 int rowa                                           = d_isicol[rowb];
806                 int n                                              = glb_Aai[rowa + 1] - glb_Aai[rowa];
807                 rowOffsets(blkID / Nsolves_team, rowb + 1 - start) = n; // save sizes
808               });
809             }
810           }
811           // map b into field major space
812           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
813             int rowa                     = d_isicol[rowb];
814             batch_b(blkID, rowb - start) = glb_bdata[rowa];
815           });
816         });
817       Kokkos::fence();
818       if (fill_idx) {
819         Kokkos::parallel_for(
820           "prefix sum", Kokkos::TeamPolicy<>(Nsolves / Nsolves_team, 1, 1), KOKKOS_LAMBDA(const team_member team) {
821             const int graphID      = team.league_rank();
822             rowOffsets(graphID, 0) = 0;
823             for (size_t i = 0; i < Nloc; ++i) rowOffsets(graphID, i + 1) += rowOffsets(graphID, i);
824           });
825         Kokkos::fence();
826       }
827       Kokkos::parallel_for(
828         "copy matrix", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
829           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1], graphID = blkID / Nsolves_team;
830           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
831             int                rowa = d_isicol[rowb]; // global index
832             int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
833             const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa];
834             const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
835             Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
836               PetscScalar val = aa[i];
837               if (fill_idx && blkID % Nsolves_team == 0) colIndices(graphID, rowOffsets(graphID, rowb - start) + i) = d_isrow[aj[i]] - blkID * Nloc; // local" global - block start
838               batch_values(blkID, rowOffsets(graphID, rowb - start) + i) = val;
839             });
840           });
841         });
842       Kokkos::fence();
843       // setup solver
844       using ScalarType                = typename AMatrixValueView::non_const_value_type;
845       using MagnitudeType             = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
846       using NormViewType              = Kokkos::View<MagnitudeType *, layout, exec_space>;
847       using Norm2DViewType            = Kokkos::View<MagnitudeType **, layout, exec_space>;
848       using Scalar3DViewType          = Kokkos::View<ScalarType ***, layout, exec_space>;
849       using IntViewType               = Kokkos::View<int *, layout, exec_space>;
850       using KrylovHandleType          = KokkosBatched::KrylovHandle<Norm2DViewType, IntViewType, Scalar3DViewType>;
851       const int        n_iterations   = maxit;
852       const int        team_size      = -1;
853       const int        vector_length  = -1;
854       const double     tol            = rtol;
855       const int        ortho_strategy = 0;
856       KrylovHandleType handle(Nsolves, Nsolves_team, n_iterations, true);
857       handle.Arnoldi_view = Scalar3DViewType("", Nsolves, n_iterations, Nloc + n_iterations + 3);
858       // solve
859       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)
860                       .run(pc);
861       Kokkos::fence();
862       // get data back
863       Kokkos::parallel_for(
864         "map", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
865           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1]; // 0
866           // map x into Plex/PETSc
867           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
868             int rowa        = d_isicol[rowb];
869             glb_xdata[rowa] = batch_x(blkID, rowb - start);
870           });
871         });
872       // output assume species major - clone from Kokkos solvers
873 #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
874 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
875       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "Iterations\n"));
876 #else
877       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "max iterations per species (gmres) :"));
878 #endif
879       for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
880         for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
881 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
882           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2D:", s));
883           for (int bid = 0; bid < batch_sz; bid++) { PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3D ", handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx]))); }
884           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
885 #else
886           int count = 0, ii;
887           for (int bid = 0; bid < batch_sz; bid++) {
888             if ((ii = handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx])) > count) count = ii;
889           }
890           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3d", count));
891 #endif
892         }
893         head += batch_sz * jac->dm_Nf[dmIdx];
894       }
895 #if PCBJKOKKOS_VERBOSE_LEVEL == 3
896       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
897 #endif
898 #endif
899       // return error code, get max it
900       PetscInt count = 0, mbid = 0;
901       if (handle.is_converged_host()) {
902         pcreason = PC_NOERROR;
903         if (!jac->max_nits) {
904           for (int blkID = 0; blkID < nBlk; blkID++) {
905             if (handle.get_iteration_host(blkID) > jac->max_nits) {
906               jac->max_nits = handle.get_iteration_host(blkID);
907               mbid          = blkID;
908             }
909           }
910         }
911       } else {
912         PetscCall(PetscPrintf(PETSC_COMM_SELF, "There is at least one system that did not converge."));
913         pcreason = PC_SUBPC_ERROR;
914       }
915       // output - assume species major order
916       for (int blkID = 0; blkID < nBlk; blkID++) {
917         if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
918           if (jac->batch_target == blkID) {
919             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));
920           } else if (jac->batch_target == -1 && handle.get_iteration_host(blkID) > count) {
921             jac->max_nits = count = handle.get_iteration_host(blkID);
922             mbid                  = blkID;
923           }
924           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))); }
925         }
926       }
927       if (jac->batch_target == -1 && jac->reason) {
928         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));
929       }
930 #if defined(PETSC_HAVE_CUDA_NVTX)
931       nvtxRangePop();
932 #endif
933 #else
934       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "batch GMRES not supported");
935 #endif
936     } else { // Kokkos Krylov
937       using scr_mem_t    = Kokkos::DefaultExecutionSpace::scratch_memory_space;
938       using vect2D_scr_t = Kokkos::View<PetscScalar **, Kokkos::LayoutLeft, scr_mem_t>;
939       Kokkos::View<Batch_MetaData *, Kokkos::DefaultExecutionSpace> d_metadata("solver meta data", nBlk);
940       int                                                           stride_shared, stride_global, global_buff_words;
941       d_bid_eqOffset            = jac->d_bid_eqOffset_k->data();
942       // solve each block independently
943       int scr_bytes_team_shared = 0, nShareVec = 0, nGlobBVec = 0;
944       if (jac->const_block_size) { // use shared memory for work vectors only if constant block size - todo: test efficiency loss
945         int maximum_shared_mem_size;
946         stride_shared = jac->const_block_size; // captured
947 #if defined(PETSC_HAVE_CUDA)
948         int         device;
949         cudaError_t ier = cudaGetDevice(&device);
950         ier             = cudaDeviceGetAttribute(&maximum_shared_mem_size, cudaDevAttrMaxSharedMemoryPerBlock, device);
951 #elif defined(PETSC_HAVE_HIP)
952         int device;
953         hipGetDevice(&device);
954         hipDeviceGetAttribute(&maximum_shared_mem_size, hipDeviceAttributeMaxSharedMemoryPerBlock, device);
955 #elif defined(PETSC_HAVE_SYCL)
956         maximum_shared_mem_size = 64000;
957 #else
958         maximum_shared_mem_size = 72000;
959 #endif
960         nShareVec = maximum_shared_mem_size / (jac->const_block_size * sizeof(PetscScalar)); // integer floor, number of vectors that fit in shared
961         if (nShareVec > nwork) nShareVec = nwork;
962         else nGlobBVec = nwork - nShareVec;
963         global_buff_words     = jac->n * nGlobBVec;
964         scr_bytes_team_shared = jac->const_block_size * nShareVec * sizeof(PetscScalar);
965         //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));
966       } else {
967         scr_bytes_team_shared = 0;
968         stride_shared         = 0;
969         global_buff_words     = jac->n * nwork;
970         nGlobBVec             = nwork; // not needed == fix
971       }
972       stride_global = jac->n; // captured
973 #if defined(PETSC_HAVE_CUDA_NVTX)
974       nvtxRangePushA("batch-kokkos-solve");
975 #endif
976       Kokkos::View<PetscScalar *, Kokkos::DefaultExecutionSpace> d_work_vecs_k("workvectors", global_buff_words); // global work vectors
977       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);
978       PetscScalar *d_work_vecs = d_work_vecs_k.data();
979       Kokkos::parallel_for(
980         "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) {
981           const int    blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
982           vect2D_scr_t work_vecs_shared(team.team_scratch(PCBJKOKKOS_SHARED_LEVEL), end - start, nShareVec);
983           PetscScalar *work_buff_shared = work_vecs_shared.data();
984           PetscScalar *work_buff_global = &d_work_vecs[start]; // start inc'ed in
985           bool         print            = monitor && (blkID == view_bid);
986           switch (ksp_type_idx) {
987           case BATCH_KSP_BICG_IDX:
988             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);
989             break;
990           case BATCH_KSP_TFQMR_IDX:
991             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);
992             break;
993           case BATCH_KSP_GMRES_IDX:
994             //BJSolve_GMRES();
995             break;
996           default:
997 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
998             printf("Unknown KSP type %d\n", ksp_type_idx);
999 #else
1000             /* void */;
1001 #endif
1002           }
1003         });
1004       Kokkos::fence();
1005 #if defined(PETSC_HAVE_CUDA_NVTX)
1006       nvtxRangePop();
1007       nvtxRangePushA("Post-solve-metadata");
1008 #endif
1009       auto h_metadata = Kokkos::create_mirror(Kokkos::HostSpace::memory_space(), d_metadata);
1010       Kokkos::deep_copy(h_metadata, d_metadata);
1011 #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
1012 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1013       PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Iterations\n"));
1014 #endif
1015       // assume species major
1016 #if PCBJKOKKOS_VERBOSE_LEVEL < 4
1017       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "max iterations per species (%s) :", ksp_type_idx == BATCH_KSP_BICG_IDX ? "bicg" : "tfqmr"));
1018 #endif
1019       for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
1020         for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
1021 #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1022           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2" PetscInt_FMT ":", s));
1023           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)); }
1024           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1025 #else
1026           PetscInt count = 0;
1027           for (int bid = 0; bid < batch_sz; bid++) {
1028             if (h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its > count) count = h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its;
1029           }
1030           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3" PetscInt_FMT " ", count));
1031 #endif
1032         }
1033         head += batch_sz * jac->dm_Nf[dmIdx];
1034       }
1035 #if PCBJKOKKOS_VERBOSE_LEVEL == 3
1036       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1037 #endif
1038 #endif
1039       PetscInt count = 0, mbid = 0;
1040       for (int blkID = 0; blkID < nBlk; blkID++) {
1041         PetscCall(PetscLogGpuFlops((PetscLogDouble)h_metadata[blkID].flops));
1042         if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
1043           if (jac->batch_target == blkID) {
1044             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));
1045           } else if (jac->batch_target == -1 && h_metadata[blkID].its > count) {
1046             jac->max_nits = count = h_metadata[blkID].its;
1047             mbid                  = blkID;
1048           }
1049           if (h_metadata[blkID].reason < 0) {
1050             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));
1051           }
1052         }
1053       }
1054       if (jac->batch_target == -1 && jac->reason) {
1055         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));
1056       }
1057       {
1058         int errsum;
1059         Kokkos::parallel_reduce(
1060           nBlk,
1061           KOKKOS_LAMBDA(const int idx, int &lsum) {
1062             if (d_metadata[idx].reason < 0) ++lsum;
1063           },
1064           errsum);
1065         pcreason = errsum ? PC_SUBPC_ERROR : PC_NOERROR;
1066         if (!errsum && !jac->max_nits) { // set max its to give back to top KSP
1067           for (int blkID = 0; blkID < nBlk; blkID++) {
1068             if (h_metadata[blkID].its > jac->max_nits) jac->max_nits = h_metadata[blkID].its;
1069           }
1070         } else if (errsum) {
1071           PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR Kokkos batch solver did not converge in all solves\n"));
1072         }
1073       }
1074 #if defined(PETSC_HAVE_CUDA_NVTX)
1075       nvtxRangePop();
1076 #endif
1077     } // end of Kokkos (not Kernels) solvers block
1078     PetscCall(VecRestoreArrayAndMemType(xout, &glb_xdata));
1079     PetscCall(VecRestoreArrayReadAndMemType(bvec, &glb_bdata));
1080     PetscCall(PCSetFailedReason(pc, pcreason));
1081     // map back to Plex space - not used
1082     if (plex_batch) {
1083       PetscCall(VecCopy(xout, bvec));
1084       PetscCall(VecScatterBegin(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1085       PetscCall(VecScatterEnd(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1086       PetscCall(VecDestroy(&bvec));
1087     }
1088   } // whole 'have aijkok' block
1089   PetscFunctionReturn(0);
1090 }
1091 
1092 static PetscErrorCode PCSetUp_BJKOKKOS(PC pc) {
1093   PC_PCBJKOKKOS    *jac = (PC_PCBJKOKKOS *)pc->data;
1094   Mat               A   = pc->pmat;
1095   Mat_SeqAIJKokkos *aijkok;
1096   PetscBool         flg;
1097 
1098   PetscFunctionBegin;
1099   PetscCheck(!pc->useAmat, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "No support for using 'use_amat'");
1100   PetscCheck(A, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No matrix - A is used above");
1101   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &flg, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, MATAIJKOKKOS, ""));
1102   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "must use '-dm_mat_type aijkokkos -dm_vec_type kokkos' for -pc_type bjkokkos");
1103   if (!(aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr))) {
1104     SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No aijkok");
1105   } else {
1106     if (!jac->vec_diag) {
1107       Vec           *subX;
1108       DM             pack, *subDM;
1109       PetscInt       nDMs, n;
1110       PetscContainer container;
1111       PetscCall(PetscObjectQuery((PetscObject)A, "plex_batch_is", (PetscObject *)&container));
1112       { // Permute the matrix to get a block diagonal system: d_isrow_k, d_isicol_k
1113         MatOrderingType rtype;
1114         IS              isrow, isicol;
1115         const PetscInt *rowindices, *icolindices;
1116         rtype = MATORDERINGRCM;
1117         // get permutation. Not what I expect so inverted here
1118         PetscCall(MatGetOrdering(A, rtype, &isrow, &isicol));
1119         PetscCall(ISDestroy(&isrow));
1120         PetscCall(ISInvertPermutation(isicol, PETSC_DECIDE, &isrow)); // THIS IS BACKWARD -- isrow is inverse -- FIX!!!!!
1121 
1122         Mat mat_block_order;
1123         PetscCall(MatCreateSubMatrix(A, isicol, isicol, MAT_INITIAL_MATRIX, &mat_block_order));
1124         PetscCall(MatViewFromOptions(mat_block_order, NULL, "-ksp_batch_reorder_view"));
1125         PetscCall(MatDestroy(&mat_block_order));
1126 
1127         PetscCall(ISGetIndices(isrow, &rowindices));
1128         PetscCall(ISGetIndices(isicol, &icolindices));
1129         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isrow_k((PetscInt *)rowindices, A->rmap->n);
1130         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isicol_k((PetscInt *)icolindices, A->rmap->n);
1131         jac->d_isrow_k  = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isrow_k));
1132         jac->d_isicol_k = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isicol_k));
1133         Kokkos::deep_copy(*jac->d_isrow_k, h_isrow_k);
1134         Kokkos::deep_copy(*jac->d_isicol_k, h_isicol_k);
1135         PetscCall(ISRestoreIndices(isrow, &rowindices));
1136         PetscCall(ISRestoreIndices(isicol, &icolindices));
1137         PetscCall(ISDestroy(&isrow));
1138         PetscCall(ISDestroy(&isicol));
1139       }
1140       // get block sizes
1141       PetscCall(PCGetDM(pc, &pack));
1142       PetscCheck(pack, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "no DM. Requires a composite DM");
1143       PetscCall(PetscObjectTypeCompare((PetscObject)pack, DMCOMPOSITE, &flg));
1144       PetscCheck(flg, PetscObjectComm((PetscObject)pack), PETSC_ERR_USER, "Not for type %s", ((PetscObject)pack)->type_name);
1145       PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
1146       jac->num_dms = nDMs;
1147       PetscCall(DMCreateGlobalVector(pack, &jac->vec_diag));
1148       PetscCall(VecGetLocalSize(jac->vec_diag, &n));
1149       jac->n         = n;
1150       jac->d_idiag_k = new Kokkos::View<PetscScalar *, Kokkos::LayoutRight>("idiag", n);
1151       // options
1152       PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1153       PetscCall(KSPSetFromOptions(jac->ksp));
1154       PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPBICG, ""));
1155       if (flg) {
1156         jac->ksp_type_idx = BATCH_KSP_BICG_IDX;
1157         jac->nwork        = 7;
1158       } else {
1159         PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPTFQMR, ""));
1160         if (flg) {
1161           jac->ksp_type_idx = BATCH_KSP_TFQMR_IDX;
1162           jac->nwork        = 10;
1163         } else {
1164           PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPGMRES, ""));
1165           if (flg) {
1166             jac->ksp_type_idx = BATCH_KSP_GMRES_IDX;
1167             jac->nwork        = 0;
1168           } else {
1169             SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unsupported batch ksp type");
1170           }
1171         }
1172       }
1173       PetscOptionsBegin(PetscObjectComm((PetscObject)jac->ksp), ((PetscObject)jac->ksp)->prefix, "Options for Kokkos batch solver", "none");
1174       PetscCall(PetscOptionsBool("-ksp_converged_reason", "", "bjkokkos.kokkos.cxx.c", jac->reason, &jac->reason, NULL));
1175       PetscCall(PetscOptionsBool("-ksp_monitor", "", "bjkokkos.kokkos.cxx.c", jac->monitor, &jac->monitor, NULL));
1176       PetscCall(PetscOptionsInt("-ksp_batch_target", "", "bjkokkos.kokkos.cxx.c", jac->batch_target, &jac->batch_target, NULL));
1177       PetscCall(PetscOptionsInt("-ksp_batch_nsolves_team", "", "bjkokkos.kokkos.cxx.c", jac->nsolves_team, &jac->nsolves_team, NULL));
1178       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);
1179       PetscOptionsEnd();
1180       // get blocks - jac->d_bid_eqOffset_k
1181       PetscCall(PetscMalloc(sizeof(*subX) * nDMs, &subX));
1182       PetscCall(PetscMalloc(sizeof(*subDM) * nDMs, &subDM));
1183       PetscCall(PetscMalloc(sizeof(*jac->dm_Nf) * nDMs, &jac->dm_Nf));
1184       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));
1185       PetscCall(DMCompositeGetEntriesArray(pack, subDM));
1186       jac->nBlocks = 0;
1187       for (PetscInt ii = 0; ii < nDMs; ii++) {
1188         PetscSection section;
1189         PetscInt     Nf;
1190         DM           dm = subDM[ii];
1191         PetscCall(DMGetLocalSection(dm, &section));
1192         PetscCall(PetscSectionGetNumFields(section, &Nf));
1193         jac->nBlocks += Nf;
1194 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1195         if (ii == 0) PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1196 #else
1197         PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1198 #endif
1199         jac->dm_Nf[ii] = Nf;
1200       }
1201       { // d_bid_eqOffset_k
1202         Kokkos::View<PetscInt *, Kokkos::LayoutRight, Kokkos::HostSpace> h_block_offsets("block_offsets", jac->nBlocks + 1);
1203         PetscCall(DMCompositeGetAccessArray(pack, jac->vec_diag, nDMs, NULL, subX));
1204         h_block_offsets[0]    = 0;
1205         jac->const_block_size = -1;
1206         for (PetscInt ii = 0, idx = 0; ii < nDMs; ii++) {
1207           PetscInt nloc, nblk;
1208           PetscCall(VecGetSize(subX[ii], &nloc));
1209           nblk = nloc / jac->dm_Nf[ii];
1210           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]);
1211           for (PetscInt jj = 0; jj < jac->dm_Nf[ii]; jj++, idx++) {
1212             h_block_offsets[idx + 1] = h_block_offsets[idx] + nblk;
1213 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1214             if (idx == 0) PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1215 #else
1216             PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1217 #endif
1218             if (jac->const_block_size == -1) jac->const_block_size = nblk;
1219             else if (jac->const_block_size > 0 && jac->const_block_size != nblk) jac->const_block_size = 0;
1220           }
1221         }
1222         PetscCall(DMCompositeRestoreAccessArray(pack, jac->vec_diag, jac->nBlocks, NULL, subX));
1223         PetscCall(PetscFree(subX));
1224         PetscCall(PetscFree(subDM));
1225         jac->d_bid_eqOffset_k = new Kokkos::View<PetscInt *, Kokkos::LayoutRight>(Kokkos::create_mirror(Kokkos::DefaultExecutionSpace::memory_space(), h_block_offsets));
1226         Kokkos::deep_copy(*jac->d_bid_eqOffset_k, h_block_offsets);
1227       }
1228     }
1229     { // get jac->d_idiag_k (PC setup),
1230       const PetscInt    *d_ai = aijkok->i_device_data(), *d_aj = aijkok->j_device_data();
1231       const PetscScalar *d_aa = aijkok->a_device_data();
1232       const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
1233       PetscInt          *d_bid_eqOffset = jac->d_bid_eqOffset_k->data(), *r = jac->d_isrow_k->data(), *ic = jac->d_isicol_k->data();
1234       PetscScalar       *d_idiag = jac->d_idiag_k->data();
1235       Kokkos::parallel_for(
1236         "Diag", Kokkos::TeamPolicy<>(jac->nBlocks, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
1237           const PetscInt blkID = team.league_rank();
1238           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, d_bid_eqOffset[blkID], d_bid_eqOffset[blkID + 1]), [=](const int rowb) {
1239             const PetscInt     rowa = ic[rowb], ai = d_ai[rowa], *aj = d_aj + ai; // grab original data
1240             const PetscScalar *aa   = d_aa + ai;
1241             const PetscInt     nrow = d_ai[rowa + 1] - ai;
1242             int                found;
1243             Kokkos::parallel_reduce(
1244               Kokkos::ThreadVectorRange(team, nrow),
1245               [=](const int &j, int &count) {
1246                 const PetscInt colb = r[aj[j]];
1247                 if (colb == rowb) {
1248                   d_idiag[rowb] = 1. / aa[j];
1249                   count++;
1250                 }
1251               },
1252               found);
1253 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
1254             if (found != 1) Kokkos::single(Kokkos::PerThread(team), [=]() { printf("ERRORrow %d) found = %d\n", rowb, found); });
1255 #endif
1256           });
1257         });
1258     }
1259   }
1260   PetscFunctionReturn(0);
1261 }
1262 
1263 /* Default destroy, if it has never been setup */
1264 static PetscErrorCode PCReset_BJKOKKOS(PC pc) {
1265   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1266 
1267   PetscFunctionBegin;
1268   PetscCall(KSPDestroy(&jac->ksp));
1269   PetscCall(VecDestroy(&jac->vec_diag));
1270   if (jac->d_bid_eqOffset_k) delete jac->d_bid_eqOffset_k;
1271   if (jac->d_idiag_k) delete jac->d_idiag_k;
1272   if (jac->d_isrow_k) delete jac->d_isrow_k;
1273   if (jac->d_isicol_k) delete jac->d_isicol_k;
1274   jac->d_bid_eqOffset_k = NULL;
1275   jac->d_idiag_k        = NULL;
1276   jac->d_isrow_k        = NULL;
1277   jac->d_isicol_k       = NULL;
1278   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", NULL)); // not published now (causes configure errors)
1279   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", NULL));
1280   PetscCall(PetscFree(jac->dm_Nf));
1281   jac->dm_Nf = NULL;
1282   if (jac->rowOffsets) delete jac->rowOffsets;
1283   if (jac->colIndices) delete jac->colIndices;
1284   if (jac->batch_b) delete jac->batch_b;
1285   if (jac->batch_x) delete jac->batch_x;
1286   if (jac->batch_values) delete jac->batch_values;
1287   jac->rowOffsets   = NULL;
1288   jac->colIndices   = NULL;
1289   jac->batch_b      = NULL;
1290   jac->batch_x      = NULL;
1291   jac->batch_values = NULL;
1292 
1293   PetscFunctionReturn(0);
1294 }
1295 
1296 static PetscErrorCode PCDestroy_BJKOKKOS(PC pc) {
1297   PetscFunctionBegin;
1298   PetscCall(PCReset_BJKOKKOS(pc));
1299   PetscCall(PetscFree(pc->data));
1300   PetscFunctionReturn(0);
1301 }
1302 
1303 static PetscErrorCode PCView_BJKOKKOS(PC pc, PetscViewer viewer) {
1304   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1305   PetscBool      iascii;
1306 
1307   PetscFunctionBegin;
1308   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1309   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1310   if (iascii) {
1311     PetscCall(PetscViewerASCIIPrintf(viewer, "  Batched device linear solver: Krylov (KSP) method with Jacobi preconditioning\n"));
1312     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,
1313                                      ((PetscObject)jac->ksp)->type_name));
1314   }
1315   PetscFunctionReturn(0);
1316 }
1317 
1318 static PetscErrorCode PCSetFromOptions_BJKOKKOS(PC pc, PetscOptionItems *PetscOptionsObject) {
1319   PetscFunctionBegin;
1320   PetscOptionsHeadBegin(PetscOptionsObject, "PC BJKOKKOS options");
1321   PetscOptionsHeadEnd();
1322   PetscFunctionReturn(0);
1323 }
1324 
1325 static PetscErrorCode PCBJKOKKOSSetKSP_BJKOKKOS(PC pc, KSP ksp) {
1326   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1327 
1328   PetscFunctionBegin;
1329   PetscCall(PetscObjectReference((PetscObject)ksp));
1330   PetscCall(KSPDestroy(&jac->ksp));
1331   jac->ksp = ksp;
1332   PetscFunctionReturn(0);
1333 }
1334 
1335 /*@C
1336    PCBJKOKKOSSetKSP - Sets the KSP context for a KSP PC.
1337 
1338    Collective on PC
1339 
1340    Input Parameters:
1341 +  pc - the preconditioner context
1342 -  ksp - the KSP solver
1343 
1344    Notes:
1345    The PC and the KSP must have the same communicator
1346 
1347    Level: advanced
1348 
1349 @*/
1350 PetscErrorCode PCBJKOKKOSSetKSP(PC pc, KSP ksp) {
1351   PetscFunctionBegin;
1352   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1353   PetscValidHeaderSpecific(ksp, KSP_CLASSID, 2);
1354   PetscCheckSameComm(pc, 1, ksp, 2);
1355   PetscTryMethod(pc, "PCBJKOKKOSSetKSP_C", (PC, KSP), (pc, ksp));
1356   PetscFunctionReturn(0);
1357 }
1358 
1359 static PetscErrorCode PCBJKOKKOSGetKSP_BJKOKKOS(PC pc, KSP *ksp) {
1360   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1361 
1362   PetscFunctionBegin;
1363   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1364   *ksp = jac->ksp;
1365   PetscFunctionReturn(0);
1366 }
1367 
1368 /*@C
1369    PCBJKOKKOSGetKSP - Gets the KSP context for a KSP PC.
1370 
1371    Not Collective but KSP returned is parallel if PC was parallel
1372 
1373    Input Parameter:
1374 .  pc - the preconditioner context
1375 
1376    Output Parameters:
1377 .  ksp - the KSP solver
1378 
1379    Notes:
1380    You must call KSPSetUp() before calling PCBJKOKKOSGetKSP().
1381 
1382    If the PC is not a PCBJKOKKOS object it raises an error
1383 
1384    Level: advanced
1385 
1386 @*/
1387 PetscErrorCode PCBJKOKKOSGetKSP(PC pc, KSP *ksp) {
1388   PetscFunctionBegin;
1389   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1390   PetscValidPointer(ksp, 2);
1391   PetscUseMethod(pc, "PCBJKOKKOSGetKSP_C", (PC, KSP *), (pc, ksp));
1392   PetscFunctionReturn(0);
1393 }
1394 
1395 static PetscErrorCode PCPostSolve_BJKOKKOS(PC pc, KSP ksp, Vec b, Vec x) {
1396   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1397 
1398   PetscFunctionBegin;
1399   ksp->its = jac->max_nits;
1400   PetscFunctionReturn(0);
1401 }
1402 
1403 /* ----------------------------------------------------------------------------------*/
1404 
1405 /*MC
1406      PCBJKOKKOS -  Defines a preconditioner that applies a Krylov solver and preconditioner to the blocks in a AIJASeq matrix on the GPU.
1407 
1408    Options Database Key:
1409 .     -pc_bjkokkos_ - options prefix with ksp options
1410 
1411    Level: intermediate
1412 
1413    Notes:
1414     For use with -ksp_type preonly to bypass any CPU work
1415 
1416    Developer Notes:
1417 
1418 .seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`,
1419           `PCSHELL`, `PCCOMPOSITE`, `PCSetUseAmat()`, `PCBJKOKKOSGetKSP()`
1420 
1421 M*/
1422 
1423 PETSC_EXTERN PetscErrorCode PCCreate_BJKOKKOS(PC pc) {
1424   PC_PCBJKOKKOS *jac;
1425 
1426   PetscFunctionBegin;
1427   PetscCall(PetscNewLog(pc, &jac));
1428   pc->data = (void *)jac;
1429 
1430   jac->ksp              = NULL;
1431   jac->vec_diag         = NULL;
1432   jac->d_bid_eqOffset_k = NULL;
1433   jac->d_idiag_k        = NULL;
1434   jac->d_isrow_k        = NULL;
1435   jac->d_isicol_k       = NULL;
1436   jac->nBlocks          = 1;
1437   jac->max_nits         = 0;
1438 
1439   PetscCall(PetscMemzero(pc->ops, sizeof(struct _PCOps)));
1440   pc->ops->apply          = PCApply_BJKOKKOS;
1441   pc->ops->applytranspose = NULL;
1442   pc->ops->setup          = PCSetUp_BJKOKKOS;
1443   pc->ops->reset          = PCReset_BJKOKKOS;
1444   pc->ops->destroy        = PCDestroy_BJKOKKOS;
1445   pc->ops->setfromoptions = PCSetFromOptions_BJKOKKOS;
1446   pc->ops->view           = PCView_BJKOKKOS;
1447   pc->ops->postsolve      = PCPostSolve_BJKOKKOS;
1448 
1449   jac->rowOffsets   = NULL;
1450   jac->colIndices   = NULL;
1451   jac->batch_b      = NULL;
1452   jac->batch_x      = NULL;
1453   jac->batch_values = NULL;
1454 
1455   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", PCBJKOKKOSGetKSP_BJKOKKOS));
1456   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", PCBJKOKKOSSetKSP_BJKOKKOS));
1457   PetscFunctionReturn(0);
1458 }
1459