xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision 2ff79c18c26c94ed8cb599682f680f231dca6444)
1 /*
2   Defines the basic matrix operations for the AIJ (compressed row)
3   matrix storage format using the CUSPARSE library,
4 */
5 #define PETSC_SKIP_IMMINTRIN_H_CUDAWORKAROUND 1
6 
7 #include <petscconf.h>
8 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
9 #include <../src/mat/impls/sbaij/seq/sbaij.h>
10 #include <../src/vec/vec/impls/dvecimpl.h>
11 #include <petsc/private/vecimpl.h>
12 #undef VecType
13 #include <../src/mat/impls/aij/seq/seqcusparse/cusparsematimpl.h>
14 #include <thrust/adjacent_difference.h>
15 #if PETSC_CPP_VERSION >= 14
16   #define PETSC_HAVE_THRUST_ASYNC 1
17 // thrust::for_each(thrust::cuda::par.on()) requires C++14
18 #endif
19 #include <thrust/iterator/constant_iterator.h>
20 #include <thrust/remove.h>
21 #include <thrust/sort.h>
22 #include <thrust/unique.h>
23 #if PETSC_PKG_CUDA_VERSION_GE(12, 9, 0) && !PetscDefined(HAVE_THRUST)
24   #include <cuda/std/functional>
25 #endif
26 
27 const char *const MatCUSPARSEStorageFormats[] = {"CSR", "ELL", "HYB", "MatCUSPARSEStorageFormat", "MAT_CUSPARSE_", 0};
28 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
29 /*
30   The following are copied from cusparse.h in CUDA-11.0. In MatCUSPARSESpMVAlgorithms[] etc, we copy them in
31   0-based integer value order, since we want to use PetscOptionsEnum() to parse user command line options for them.
32 */
33 const char *const MatCUSPARSESpMVAlgorithms[]    = {"MV_ALG_DEFAULT", "COOMV_ALG", "CSRMV_ALG1", "CSRMV_ALG2", "cusparseSpMVAlg_t", "CUSPARSE_", 0};
34 const char *const MatCUSPARSESpMMAlgorithms[]    = {"ALG_DEFAULT", "COO_ALG1", "COO_ALG2", "COO_ALG3", "CSR_ALG1", "COO_ALG4", "CSR_ALG2", "cusparseSpMMAlg_t", "CUSPARSE_SPMM_", 0};
35 const char *const MatCUSPARSECsr2CscAlgorithms[] = {"INVALID" /*cusparse does not have enum 0! We created one*/, "ALG1", "ALG2", "cusparseCsr2CscAlg_t", "CUSPARSE_CSR2CSC_", 0};
36 #endif
37 
38 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, const MatFactorInfo *);
39 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, const MatFactorInfo *);
40 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat, Mat, const MatFactorInfo *);
41 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, IS, const MatFactorInfo *);
42 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
43 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat, Vec, Vec);
44 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
45 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
46 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
47 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **);
48 #endif
49 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(Mat, PetscOptionItems PetscOptionsObject);
50 static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat, PetscScalar, Mat, MatStructure);
51 static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat, PetscScalar);
52 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat, Vec, Vec);
53 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
54 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
55 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
56 static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
57 static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
58 static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec, PetscBool, PetscBool);
59 
60 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **);
61 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **, MatCUSPARSEStorageFormat);
62 static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **);
63 static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat);
64 
65 static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat);
66 static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat, PetscBool);
67 
68 static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat, PetscInt, const PetscInt[], PetscScalar[]);
69 static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat, PetscCount, PetscInt[], PetscInt[]);
70 static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat, const PetscScalar[], InsertMode);
71 
72 PETSC_INTERN PetscErrorCode MatCUSPARSESetFormat_SeqAIJCUSPARSE(Mat A, MatCUSPARSEFormatOperation op, MatCUSPARSEStorageFormat format)
73 {
74   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
75 
76   PetscFunctionBegin;
77   switch (op) {
78   case MAT_CUSPARSE_MULT:
79     cusparsestruct->format = format;
80     break;
81   case MAT_CUSPARSE_ALL:
82     cusparsestruct->format = format;
83     break;
84   default:
85     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unsupported operation %d for MatCUSPARSEFormatOperation. MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL are currently supported.", op);
86   }
87   PetscFunctionReturn(PETSC_SUCCESS);
88 }
89 
90 /*@
91   MatCUSPARSESetFormat - Sets the storage format of `MATSEQCUSPARSE` matrices for a particular
92   operation. Only the `MatMult()` operation can use different GPU storage formats
93 
94   Not Collective
95 
96   Input Parameters:
97 + A      - Matrix of type `MATSEQAIJCUSPARSE`
98 . op     - `MatCUSPARSEFormatOperation`. `MATSEQAIJCUSPARSE` matrices support `MAT_CUSPARSE_MULT` and `MAT_CUSPARSE_ALL`.
99         `MATMPIAIJCUSPARSE` matrices support `MAT_CUSPARSE_MULT_DIAG`,`MAT_CUSPARSE_MULT_OFFDIAG`, and `MAT_CUSPARSE_ALL`.
100 - format - `MatCUSPARSEStorageFormat` (one of `MAT_CUSPARSE_CSR`, `MAT_CUSPARSE_ELL`, `MAT_CUSPARSE_HYB`.)
101 
102   Level: intermediate
103 
104 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
105 @*/
106 PetscErrorCode MatCUSPARSESetFormat(Mat A, MatCUSPARSEFormatOperation op, MatCUSPARSEStorageFormat format)
107 {
108   PetscFunctionBegin;
109   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
110   PetscTryMethod(A, "MatCUSPARSESetFormat_C", (Mat, MatCUSPARSEFormatOperation, MatCUSPARSEStorageFormat), (A, op, format));
111   PetscFunctionReturn(PETSC_SUCCESS);
112 }
113 
114 PETSC_INTERN PetscErrorCode MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE(Mat A, PetscBool use_cpu)
115 {
116   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
117 
118   PetscFunctionBegin;
119   cusparsestruct->use_cpu_solve = use_cpu;
120   PetscFunctionReturn(PETSC_SUCCESS);
121 }
122 
123 /*@
124   MatCUSPARSESetUseCPUSolve - Sets to use CPU `MatSolve()`.
125 
126   Input Parameters:
127 + A       - Matrix of type `MATSEQAIJCUSPARSE`
128 - use_cpu - set flag for using the built-in CPU `MatSolve()`
129 
130   Level: intermediate
131 
132   Note:
133   The cuSparse LU solver currently computes the factors with the built-in CPU method
134   and moves the factors to the GPU for the solve. We have observed better performance keeping the data on the CPU and computing the solve there.
135   This method to specify if the solve is done on the CPU or GPU (GPU is the default).
136 
137 .seealso: [](ch_matrices), `Mat`, `MatSolve()`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
138 @*/
139 PetscErrorCode MatCUSPARSESetUseCPUSolve(Mat A, PetscBool use_cpu)
140 {
141   PetscFunctionBegin;
142   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
143   PetscTryMethod(A, "MatCUSPARSESetUseCPUSolve_C", (Mat, PetscBool), (A, use_cpu));
144   PetscFunctionReturn(PETSC_SUCCESS);
145 }
146 
147 static PetscErrorCode MatSetOption_SeqAIJCUSPARSE(Mat A, MatOption op, PetscBool flg)
148 {
149   PetscFunctionBegin;
150   switch (op) {
151   case MAT_FORM_EXPLICIT_TRANSPOSE:
152     /* need to destroy the transpose matrix if present to prevent from logic errors if flg is set to true later */
153     if (A->form_explicit_transpose && !flg) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
154     A->form_explicit_transpose = flg;
155     break;
156   default:
157     PetscCall(MatSetOption_SeqAIJ(A, op, flg));
158     break;
159   }
160   PetscFunctionReturn(PETSC_SUCCESS);
161 }
162 
163 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(Mat A, PetscOptionItems PetscOptionsObject)
164 {
165   MatCUSPARSEStorageFormat format;
166   PetscBool                flg;
167   Mat_SeqAIJCUSPARSE      *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
168 
169   PetscFunctionBegin;
170   PetscOptionsHeadBegin(PetscOptionsObject, "SeqAIJCUSPARSE options");
171   if (A->factortype == MAT_FACTOR_NONE) {
172     PetscCall(PetscOptionsEnum("-mat_cusparse_mult_storage_format", "sets storage format of (seq)aijcusparse gpu matrices for SpMV", "MatCUSPARSESetFormat", MatCUSPARSEStorageFormats, (PetscEnum)cusparsestruct->format, (PetscEnum *)&format, &flg));
173     if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_MULT, format));
174 
175     PetscCall(PetscOptionsEnum("-mat_cusparse_storage_format", "sets storage format of (seq)aijcusparse gpu matrices for SpMV and TriSolve", "MatCUSPARSESetFormat", MatCUSPARSEStorageFormats, (PetscEnum)cusparsestruct->format, (PetscEnum *)&format, &flg));
176     if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_ALL, format));
177     PetscCall(PetscOptionsBool("-mat_cusparse_use_cpu_solve", "Use CPU (I)LU solve", "MatCUSPARSESetUseCPUSolve", cusparsestruct->use_cpu_solve, &cusparsestruct->use_cpu_solve, &flg));
178     if (flg) PetscCall(MatCUSPARSESetUseCPUSolve(A, cusparsestruct->use_cpu_solve));
179 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
180     PetscCall(PetscOptionsEnum("-mat_cusparse_spmv_alg", "sets cuSPARSE algorithm used in sparse-mat dense-vector multiplication (SpMV)", "cusparseSpMVAlg_t", MatCUSPARSESpMVAlgorithms, (PetscEnum)cusparsestruct->spmvAlg, (PetscEnum *)&cusparsestruct->spmvAlg, &flg));
181     /* If user did use this option, check its consistency with cuSPARSE, since PetscOptionsEnum() sets enum values based on their position in MatCUSPARSESpMVAlgorithms[] */
182   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
183     PetscCheck(!flg || CUSPARSE_SPMV_CSR_ALG1 == 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMVAlg_t has been changed but PETSc has not been updated accordingly");
184   #else
185     PetscCheck(!flg || CUSPARSE_CSRMV_ALG1 == 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMVAlg_t has been changed but PETSc has not been updated accordingly");
186   #endif
187     PetscCall(PetscOptionsEnum("-mat_cusparse_spmm_alg", "sets cuSPARSE algorithm used in sparse-mat dense-mat multiplication (SpMM)", "cusparseSpMMAlg_t", MatCUSPARSESpMMAlgorithms, (PetscEnum)cusparsestruct->spmmAlg, (PetscEnum *)&cusparsestruct->spmmAlg, &flg));
188     PetscCheck(!flg || CUSPARSE_SPMM_CSR_ALG1 == 4, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMMAlg_t has been changed but PETSc has not been updated accordingly");
189 
190     PetscCall(
191       PetscOptionsEnum("-mat_cusparse_csr2csc_alg", "sets cuSPARSE algorithm used in converting CSR matrices to CSC matrices", "cusparseCsr2CscAlg_t", MatCUSPARSECsr2CscAlgorithms, (PetscEnum)cusparsestruct->csr2cscAlg, (PetscEnum *)&cusparsestruct->csr2cscAlg, &flg));
192     PetscCheck(!flg || CUSPARSE_CSR2CSC_ALG1 == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseCsr2CscAlg_t has been changed but PETSc has not been updated accordingly");
193 #endif
194   }
195   PetscOptionsHeadEnd();
196   PetscFunctionReturn(PETSC_SUCCESS);
197 }
198 
199 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
200 static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(Mat A)
201 {
202   Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
203   PetscInt                      m  = A->rmap->n;
204   Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
205   const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
206   const MatScalar              *Aa = a->a;
207   PetscInt                     *Mi, *Mj, Mnz;
208   PetscScalar                  *Ma;
209 
210   PetscFunctionBegin;
211   if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
212     if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even when m=0
213       // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host
214       Mnz = (Ai[m] - Ai[0]) + (Adiag[0] - Adiag[m]); // Lnz (without the unit diagonal) + Unz (with the non-unit diagonal)
215       PetscCall(PetscMalloc1(m + 1, &Mi));
216       PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj is temp
217       PetscCall(PetscMalloc1(Mnz, &Ma));
218       Mi[0] = 0;
219       for (PetscInt i = 0; i < m; i++) {
220         PetscInt llen = Ai[i + 1] - Ai[i];
221         PetscInt ulen = Adiag[i] - Adiag[i + 1];
222         PetscCall(PetscArraycpy(Mj + Mi[i], Aj + Ai[i], llen));                           // entries of L
223         Mj[Mi[i] + llen] = i;                                                             // diagonal entry
224         PetscCall(PetscArraycpy(Mj + Mi[i] + llen + 1, Aj + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
225         Mi[i + 1] = Mi[i] + llen + ulen;
226       }
227       // Copy M (L,U) from host to device
228       PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
229       PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
230       PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
231       PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Mi, sizeof(*fs->csrRowPtr) * (m + 1), cudaMemcpyHostToDevice));
232       PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*fs->csrColIdx) * Mnz, cudaMemcpyHostToDevice));
233 
234       // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
235       // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
236       // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
237       // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
238       // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
239       cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_LOWER;
240       cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT;
241       const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;
242 
243       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
244       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
245       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
246 
247       fillMode = CUSPARSE_FILL_MODE_UPPER;
248       diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
249       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
250       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
251       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
252 
253       // Allocate work vectors in SpSv
254       PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
255       PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));
256 
257       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
258       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
259 
260       // Query buffer sizes for SpSV and then allocate buffers, temporarily assuming opA = CUSPARSE_OPERATION_NON_TRANSPOSE
261       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
262       PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));
263       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
264       PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));
265       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
266       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
267 
268       // Record for reuse
269       fs->csrRowPtr_h = Mi;
270       fs->csrVal_h    = Ma;
271       PetscCall(PetscFree(Mj));
272     }
273     // Copy the value
274     Mi  = fs->csrRowPtr_h;
275     Ma  = fs->csrVal_h;
276     Mnz = Mi[m];
277     for (PetscInt i = 0; i < m; i++) {
278       PetscInt llen = Ai[i + 1] - Ai[i];
279       PetscInt ulen = Adiag[i] - Adiag[i + 1];
280       PetscCall(PetscArraycpy(Ma + Mi[i], Aa + Ai[i], llen));                           // entries of L
281       Ma[Mi[i] + llen] = (MatScalar)1.0 / Aa[Adiag[i]];                                 // recover the diagonal entry
282       PetscCall(PetscArraycpy(Ma + Mi[i] + llen + 1, Aa + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
283     }
284     PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));
285 
286   #if PETSC_PKG_CUDA_VERSION_GE(12, 1, 1)
287     if (fs->updatedSpSVAnalysis) { // have done cusparseSpSV_analysis before, and only matrix values changed?
288       // Otherwise cusparse would error out: "On entry to cusparseSpSV_updateMatrix() parameter number 3 (newValues) had an illegal value: NULL pointer"
289       if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_L, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
290       if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_U, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
291     } else
292   #endif
293     {
294       // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
295       PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));
296 
297       PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));
298       fs->updatedSpSVAnalysis          = PETSC_TRUE;
299       fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
300     }
301   }
302   PetscFunctionReturn(PETSC_SUCCESS);
303 }
304 #else
305 static PetscErrorCode MatSeqAIJCUSPARSEBuildILULowerTriMatrix(Mat A)
306 {
307   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
308   PetscInt                           n                  = A->rmap->n;
309   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
310   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
311   const PetscInt                    *ai = a->i, *aj = a->j, *vi;
312   const MatScalar                   *aa = a->a, *v;
313   PetscInt                          *AiLo, *AjLo;
314   PetscInt                           i, nz, nzLower, offset, rowOffset;
315 
316   PetscFunctionBegin;
317   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
318   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
319     try {
320       /* first figure out the number of nonzeros in the lower triangular matrix including 1's on the diagonal. */
321       nzLower = n + ai[n] - ai[1];
322       if (!loTriFactor) {
323         PetscScalar *AALo;
324 
325         PetscCallCUDA(cudaMallocHost((void **)&AALo, nzLower * sizeof(PetscScalar)));
326 
327         /* Allocate Space for the lower triangular matrix */
328         PetscCallCUDA(cudaMallocHost((void **)&AiLo, (n + 1) * sizeof(PetscInt)));
329         PetscCallCUDA(cudaMallocHost((void **)&AjLo, nzLower * sizeof(PetscInt)));
330 
331         /* Fill the lower triangular matrix */
332         AiLo[0]   = (PetscInt)0;
333         AiLo[n]   = nzLower;
334         AjLo[0]   = (PetscInt)0;
335         AALo[0]   = (MatScalar)1.0;
336         v         = aa;
337         vi        = aj;
338         offset    = 1;
339         rowOffset = 1;
340         for (i = 1; i < n; i++) {
341           nz = ai[i + 1] - ai[i];
342           /* additional 1 for the term on the diagonal */
343           AiLo[i] = rowOffset;
344           rowOffset += nz + 1;
345 
346           PetscCall(PetscArraycpy(&AjLo[offset], vi, nz));
347           PetscCall(PetscArraycpy(&AALo[offset], v, nz));
348 
349           offset += nz;
350           AjLo[offset] = (PetscInt)i;
351           AALo[offset] = (MatScalar)1.0;
352           offset += 1;
353 
354           v += nz;
355           vi += nz;
356         }
357 
358         /* allocate space for the triangular factor information */
359         PetscCall(PetscNew(&loTriFactor));
360         loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
361         /* Create the matrix description */
362         PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
363         PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
364   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
365         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
366   #else
367         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
368   #endif
369         PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_LOWER));
370         PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));
371 
372         /* set the operation */
373         loTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
374 
375         /* set the matrix */
376         loTriFactor->csrMat              = new CsrMatrix;
377         loTriFactor->csrMat->num_rows    = n;
378         loTriFactor->csrMat->num_cols    = n;
379         loTriFactor->csrMat->num_entries = nzLower;
380 
381         loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n + 1);
382         loTriFactor->csrMat->row_offsets->assign(AiLo, AiLo + n + 1);
383 
384         loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzLower);
385         loTriFactor->csrMat->column_indices->assign(AjLo, AjLo + nzLower);
386 
387         loTriFactor->csrMat->values = new THRUSTARRAY(nzLower);
388         loTriFactor->csrMat->values->assign(AALo, AALo + nzLower);
389 
390         /* Create the solve analysis information */
391         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
392         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
393   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
394         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
395                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, &loTriFactor->solveBufferSize));
396         PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
397   #endif
398 
399         /* perform the solve analysis */
400         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
401                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
402         PetscCallCUDA(WaitForCUDA());
403         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
404 
405         /* assign the pointer */
406         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;
407         loTriFactor->AA_h                                          = AALo;
408         PetscCallCUDA(cudaFreeHost(AiLo));
409         PetscCallCUDA(cudaFreeHost(AjLo));
410         PetscCall(PetscLogCpuToGpu((n + 1 + nzLower) * sizeof(int) + nzLower * sizeof(PetscScalar)));
411       } else { /* update values only */
412         if (!loTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&loTriFactor->AA_h, nzLower * sizeof(PetscScalar)));
413         /* Fill the lower triangular matrix */
414         loTriFactor->AA_h[0] = 1.0;
415         v                    = aa;
416         vi                   = aj;
417         offset               = 1;
418         for (i = 1; i < n; i++) {
419           nz = ai[i + 1] - ai[i];
420           PetscCall(PetscArraycpy(&loTriFactor->AA_h[offset], v, nz));
421           offset += nz;
422           loTriFactor->AA_h[offset] = 1.0;
423           offset += 1;
424           v += nz;
425         }
426         loTriFactor->csrMat->values->assign(loTriFactor->AA_h, loTriFactor->AA_h + nzLower);
427         PetscCall(PetscLogCpuToGpu(nzLower * sizeof(PetscScalar)));
428       }
429     } catch (char *ex) {
430       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
431     }
432   }
433   PetscFunctionReturn(PETSC_SUCCESS);
434 }
435 
436 static PetscErrorCode MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(Mat A)
437 {
438   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
439   PetscInt                           n                  = A->rmap->n;
440   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
441   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
442   const PetscInt                    *aj = a->j, *adiag = a->diag, *vi;
443   const MatScalar                   *aa = a->a, *v;
444   PetscInt                          *AiUp, *AjUp;
445   PetscInt                           i, nz, nzUpper, offset;
446 
447   PetscFunctionBegin;
448   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
449   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
450     try {
451       /* next, figure out the number of nonzeros in the upper triangular matrix. */
452       nzUpper = adiag[0] - adiag[n];
453       if (!upTriFactor) {
454         PetscScalar *AAUp;
455 
456         PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));
457 
458         /* Allocate Space for the upper triangular matrix */
459         PetscCallCUDA(cudaMallocHost((void **)&AiUp, (n + 1) * sizeof(PetscInt)));
460         PetscCallCUDA(cudaMallocHost((void **)&AjUp, nzUpper * sizeof(PetscInt)));
461 
462         /* Fill the upper triangular matrix */
463         AiUp[0] = (PetscInt)0;
464         AiUp[n] = nzUpper;
465         offset  = nzUpper;
466         for (i = n - 1; i >= 0; i--) {
467           v  = aa + adiag[i + 1] + 1;
468           vi = aj + adiag[i + 1] + 1;
469 
470           /* number of elements NOT on the diagonal */
471           nz = adiag[i] - adiag[i + 1] - 1;
472 
473           /* decrement the offset */
474           offset -= (nz + 1);
475 
476           /* first, set the diagonal elements */
477           AjUp[offset] = (PetscInt)i;
478           AAUp[offset] = (MatScalar)1. / v[nz];
479           AiUp[i]      = AiUp[i + 1] - (nz + 1);
480 
481           PetscCall(PetscArraycpy(&AjUp[offset + 1], vi, nz));
482           PetscCall(PetscArraycpy(&AAUp[offset + 1], v, nz));
483         }
484 
485         /* allocate space for the triangular factor information */
486         PetscCall(PetscNew(&upTriFactor));
487         upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
488 
489         /* Create the matrix description */
490         PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
491         PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
492   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
493         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
494   #else
495         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
496   #endif
497         PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
498         PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));
499 
500         /* set the operation */
501         upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
502 
503         /* set the matrix */
504         upTriFactor->csrMat              = new CsrMatrix;
505         upTriFactor->csrMat->num_rows    = n;
506         upTriFactor->csrMat->num_cols    = n;
507         upTriFactor->csrMat->num_entries = nzUpper;
508 
509         upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n + 1);
510         upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + n + 1);
511 
512         upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzUpper);
513         upTriFactor->csrMat->column_indices->assign(AjUp, AjUp + nzUpper);
514 
515         upTriFactor->csrMat->values = new THRUSTARRAY(nzUpper);
516         upTriFactor->csrMat->values->assign(AAUp, AAUp + nzUpper);
517 
518         /* Create the solve analysis information */
519         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
520         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
521   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
522         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
523                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, &upTriFactor->solveBufferSize));
524         PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
525   #endif
526 
527         /* perform the solve analysis */
528         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
529                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
530 
531         PetscCallCUDA(WaitForCUDA());
532         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
533 
534         /* assign the pointer */
535         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;
536         upTriFactor->AA_h                                          = AAUp;
537         PetscCallCUDA(cudaFreeHost(AiUp));
538         PetscCallCUDA(cudaFreeHost(AjUp));
539         PetscCall(PetscLogCpuToGpu((n + 1 + nzUpper) * sizeof(int) + nzUpper * sizeof(PetscScalar)));
540       } else {
541         if (!upTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&upTriFactor->AA_h, nzUpper * sizeof(PetscScalar)));
542         /* Fill the upper triangular matrix */
543         offset = nzUpper;
544         for (i = n - 1; i >= 0; i--) {
545           v = aa + adiag[i + 1] + 1;
546 
547           /* number of elements NOT on the diagonal */
548           nz = adiag[i] - adiag[i + 1] - 1;
549 
550           /* decrement the offset */
551           offset -= (nz + 1);
552 
553           /* first, set the diagonal elements */
554           upTriFactor->AA_h[offset] = 1. / v[nz];
555           PetscCall(PetscArraycpy(&upTriFactor->AA_h[offset + 1], v, nz));
556         }
557         upTriFactor->csrMat->values->assign(upTriFactor->AA_h, upTriFactor->AA_h + nzUpper);
558         PetscCall(PetscLogCpuToGpu(nzUpper * sizeof(PetscScalar)));
559       }
560     } catch (char *ex) {
561       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
562     }
563   }
564   PetscFunctionReturn(PETSC_SUCCESS);
565 }
566 #endif
567 
568 static PetscErrorCode MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(Mat A)
569 {
570   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ *)A->data;
571   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
572   IS                            isrow = a->row, isicol = a->icol;
573   PetscBool                     row_identity, col_identity;
574   PetscInt                      n = A->rmap->n;
575 
576   PetscFunctionBegin;
577   PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
578 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
579   PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(A));
580 #else
581   PetscCall(MatSeqAIJCUSPARSEBuildILULowerTriMatrix(A));
582   PetscCall(MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(A));
583   if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
584 #endif
585 
586   cusparseTriFactors->nnz = a->nz;
587 
588   A->offloadmask = PETSC_OFFLOAD_BOTH; // factored matrix is sync'ed to GPU
589   /* lower triangular indices */
590   PetscCall(ISIdentity(isrow, &row_identity));
591   if (!row_identity && !cusparseTriFactors->rpermIndices) {
592     const PetscInt *r;
593 
594     PetscCall(ISGetIndices(isrow, &r));
595     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
596     cusparseTriFactors->rpermIndices->assign(r, r + n);
597     PetscCall(ISRestoreIndices(isrow, &r));
598     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
599   }
600 
601   /* upper triangular indices */
602   PetscCall(ISIdentity(isicol, &col_identity));
603   if (!col_identity && !cusparseTriFactors->cpermIndices) {
604     const PetscInt *c;
605 
606     PetscCall(ISGetIndices(isicol, &c));
607     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
608     cusparseTriFactors->cpermIndices->assign(c, c + n);
609     PetscCall(ISRestoreIndices(isicol, &c));
610     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
611   }
612   PetscFunctionReturn(PETSC_SUCCESS);
613 }
614 
615 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
616 static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(Mat A)
617 {
618   Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
619   PetscInt                      m  = A->rmap->n;
620   Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
621   const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
622   const MatScalar              *Aa = a->a;
623   PetscInt                     *Mj, Mnz;
624   PetscScalar                  *Ma, *D;
625 
626   PetscFunctionBegin;
627   if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
628     if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even m=0
629       // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host.
630       // See comments at MatICCFactorSymbolic_SeqAIJ() on the layout of the factored matrix (U) on host.
631       Mnz = Ai[m]; // Unz (with the unit diagonal)
632       PetscCall(PetscMalloc1(Mnz, &Ma));
633       PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj[] is temp
634       PetscCall(PetscMalloc1(m, &D));    // the diagonal
635       for (PetscInt i = 0; i < m; i++) {
636         PetscInt ulen = Ai[i + 1] - Ai[i];
637         Mj[Ai[i]]     = i;                                              // diagonal entry
638         PetscCall(PetscArraycpy(Mj + Ai[i] + 1, Aj + Ai[i], ulen - 1)); // entries of U on the right of the diagonal
639       }
640       // Copy M (U) from host to device
641       PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
642       PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
643       PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
644       PetscCallCUDA(cudaMalloc(&fs->diag, sizeof(*fs->diag) * m));
645       PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyHostToDevice));
646       PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*Mj) * Mnz, cudaMemcpyHostToDevice));
647 
648       // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
649       // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
650       // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
651       // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
652       // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
653       cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_UPPER;
654       cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT; // U is unit diagonal
655       const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;
656 
657       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
658       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
659       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
660 
661       // Allocate work vectors in SpSv
662       PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
663       PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));
664 
665       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
666       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
667 
668       // Query buffer sizes for SpSV and then allocate buffers
669       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
670       PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));
671       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
672 
673       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut)); // Ut solve uses the same matrix (spMatDescr_U), but different descr and buffer
674       PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Ut, &fs->spsvBufferSize_Ut));
675       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));
676 
677       // Record for reuse
678       fs->csrVal_h = Ma;
679       fs->diag_h   = D;
680       PetscCall(PetscFree(Mj));
681     }
682     // Copy the value
683     Ma  = fs->csrVal_h;
684     D   = fs->diag_h;
685     Mnz = Ai[m];
686     for (PetscInt i = 0; i < m; i++) {
687       D[i]      = Aa[Adiag[i]];   // actually Aa[Adiag[i]] is the inverse of the diagonal
688       Ma[Ai[i]] = (MatScalar)1.0; // set the unit diagonal, which is cosmetic since cusparse does not really read it given CUSPARSE_DIAG_TYPE_UNIT
689       for (PetscInt k = 0; k < Ai[i + 1] - Ai[i] - 1; k++) Ma[Ai[i] + 1 + k] = -Aa[Ai[i] + k];
690     }
691     PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));
692     PetscCallCUDA(cudaMemcpy(fs->diag, D, sizeof(*D) * m, cudaMemcpyHostToDevice));
693 
694   #if PETSC_PKG_CUDA_VERSION_GE(12, 1, 1)
695     if (fs->updatedSpSVAnalysis) {
696       if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_U, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
697       if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_Ut, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
698     } else
699   #endif
700     {
701       // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
702       PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));
703       PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Ut, fs->spsvBuffer_Ut));
704       fs->updatedSpSVAnalysis = PETSC_TRUE;
705     }
706   }
707   PetscFunctionReturn(PETSC_SUCCESS);
708 }
709 
710 // Solve Ut D U x = b
711 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_Cholesky(Mat A, Vec b, Vec x)
712 {
713   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
714   Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
715   const PetscScalar                    *barray;
716   PetscScalar                          *xarray;
717   thrust::device_ptr<const PetscScalar> bGPU;
718   thrust::device_ptr<PetscScalar>       xGPU;
719   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
720   PetscInt                              m   = A->rmap->n;
721 
722   PetscFunctionBegin;
723   PetscCall(PetscLogGpuTimeBegin());
724   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
725   PetscCall(VecCUDAGetArrayRead(b, &barray));
726   xGPU = thrust::device_pointer_cast(xarray);
727   bGPU = thrust::device_pointer_cast(barray);
728 
729   // Reorder b with the row permutation if needed, and wrap the result in fs->X
730   if (fs->rpermIndices) {
731     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
732     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
733   } else {
734     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
735   }
736 
737   // Solve Ut Y = X
738   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
739   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut));
740 
741   // Solve diag(D) Z = Y. Actually just do Y = Y*D since D is already inverted in MatCholeskyFactorNumeric_SeqAIJ().
742   // It is basically a vector element-wise multiplication, but cublas does not have it!
743   PetscCallThrust(thrust::transform(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::device_pointer_cast(fs->Y), thrust::device_pointer_cast(fs->Y + m), thrust::device_pointer_cast(fs->diag), thrust::device_pointer_cast(fs->Y), thrust::multiplies<PetscScalar>()));
744 
745   // Solve U X = Y
746   if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
747     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
748   } else {
749     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
750   }
751   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_U));
752 
753   // Reorder X with the column permutation if needed, and put the result back to x
754   if (fs->cpermIndices) {
755     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
756                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
757   }
758 
759   PetscCall(VecCUDARestoreArrayRead(b, &barray));
760   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
761   PetscCall(PetscLogGpuTimeEnd());
762   PetscCall(PetscLogGpuFlops(4.0 * aij->nz - A->rmap->n));
763   PetscFunctionReturn(PETSC_SUCCESS);
764 }
765 #else
766 static PetscErrorCode MatSeqAIJCUSPARSEBuildICCTriMatrices(Mat A)
767 {
768   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
769   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
770   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
771   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
772   PetscInt                          *AiUp, *AjUp;
773   PetscScalar                       *AAUp;
774   PetscScalar                       *AALo;
775   PetscInt                           nzUpper = a->nz, n = A->rmap->n, i, offset, nz, j;
776   Mat_SeqSBAIJ                      *b  = (Mat_SeqSBAIJ *)A->data;
777   const PetscInt                    *ai = b->i, *aj = b->j, *vj;
778   const MatScalar                   *aa = b->a, *v;
779 
780   PetscFunctionBegin;
781   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
782   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
783     try {
784       PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));
785       PetscCallCUDA(cudaMallocHost((void **)&AALo, nzUpper * sizeof(PetscScalar)));
786       if (!upTriFactor && !loTriFactor) {
787         /* Allocate Space for the upper triangular matrix */
788         PetscCallCUDA(cudaMallocHost((void **)&AiUp, (n + 1) * sizeof(PetscInt)));
789         PetscCallCUDA(cudaMallocHost((void **)&AjUp, nzUpper * sizeof(PetscInt)));
790 
791         /* Fill the upper triangular matrix */
792         AiUp[0] = (PetscInt)0;
793         AiUp[n] = nzUpper;
794         offset  = 0;
795         for (i = 0; i < n; i++) {
796           /* set the pointers */
797           v  = aa + ai[i];
798           vj = aj + ai[i];
799           nz = ai[i + 1] - ai[i] - 1; /* exclude diag[i] */
800 
801           /* first, set the diagonal elements */
802           AjUp[offset] = (PetscInt)i;
803           AAUp[offset] = (MatScalar)1.0 / v[nz];
804           AiUp[i]      = offset;
805           AALo[offset] = (MatScalar)1.0 / v[nz];
806 
807           offset += 1;
808           if (nz > 0) {
809             PetscCall(PetscArraycpy(&AjUp[offset], vj, nz));
810             PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
811             for (j = offset; j < offset + nz; j++) {
812               AAUp[j] = -AAUp[j];
813               AALo[j] = AAUp[j] / v[nz];
814             }
815             offset += nz;
816           }
817         }
818 
819         /* allocate space for the triangular factor information */
820         PetscCall(PetscNew(&upTriFactor));
821         upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
822 
823         /* Create the matrix description */
824         PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
825         PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
826   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
827         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
828   #else
829         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
830   #endif
831         PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
832         PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));
833 
834         /* set the matrix */
835         upTriFactor->csrMat              = new CsrMatrix;
836         upTriFactor->csrMat->num_rows    = A->rmap->n;
837         upTriFactor->csrMat->num_cols    = A->cmap->n;
838         upTriFactor->csrMat->num_entries = a->nz;
839 
840         upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n + 1);
841         upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + A->rmap->n + 1);
842 
843         upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
844         upTriFactor->csrMat->column_indices->assign(AjUp, AjUp + a->nz);
845 
846         upTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
847         upTriFactor->csrMat->values->assign(AAUp, AAUp + a->nz);
848 
849         /* set the operation */
850         upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
851 
852         /* Create the solve analysis information */
853         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
854         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
855   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
856         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
857                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, &upTriFactor->solveBufferSize));
858         PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
859   #endif
860 
861         /* perform the solve analysis */
862         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
863                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
864 
865         PetscCallCUDA(WaitForCUDA());
866         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
867 
868         /* assign the pointer */
869         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;
870 
871         /* allocate space for the triangular factor information */
872         PetscCall(PetscNew(&loTriFactor));
873         loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
874 
875         /* Create the matrix description */
876         PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
877         PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
878   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
879         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
880   #else
881         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
882   #endif
883         PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
884         PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));
885 
886         /* set the operation */
887         loTriFactor->solveOp = CUSPARSE_OPERATION_TRANSPOSE;
888 
889         /* set the matrix */
890         loTriFactor->csrMat              = new CsrMatrix;
891         loTriFactor->csrMat->num_rows    = A->rmap->n;
892         loTriFactor->csrMat->num_cols    = A->cmap->n;
893         loTriFactor->csrMat->num_entries = a->nz;
894 
895         loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n + 1);
896         loTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + A->rmap->n + 1);
897 
898         loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
899         loTriFactor->csrMat->column_indices->assign(AjUp, AjUp + a->nz);
900 
901         loTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
902         loTriFactor->csrMat->values->assign(AALo, AALo + a->nz);
903 
904         /* Create the solve analysis information */
905         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
906         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
907   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
908         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
909                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, &loTriFactor->solveBufferSize));
910         PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
911   #endif
912 
913         /* perform the solve analysis */
914         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
915                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
916 
917         PetscCallCUDA(WaitForCUDA());
918         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
919 
920         /* assign the pointer */
921         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;
922 
923         PetscCall(PetscLogCpuToGpu(2 * (((A->rmap->n + 1) + (a->nz)) * sizeof(int) + (a->nz) * sizeof(PetscScalar))));
924         PetscCallCUDA(cudaFreeHost(AiUp));
925         PetscCallCUDA(cudaFreeHost(AjUp));
926       } else {
927         /* Fill the upper triangular matrix */
928         offset = 0;
929         for (i = 0; i < n; i++) {
930           /* set the pointers */
931           v  = aa + ai[i];
932           nz = ai[i + 1] - ai[i] - 1; /* exclude diag[i] */
933 
934           /* first, set the diagonal elements */
935           AAUp[offset] = 1.0 / v[nz];
936           AALo[offset] = 1.0 / v[nz];
937 
938           offset += 1;
939           if (nz > 0) {
940             PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
941             for (j = offset; j < offset + nz; j++) {
942               AAUp[j] = -AAUp[j];
943               AALo[j] = AAUp[j] / v[nz];
944             }
945             offset += nz;
946           }
947         }
948         PetscCheck(upTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
949         PetscCheck(loTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
950         upTriFactor->csrMat->values->assign(AAUp, AAUp + a->nz);
951         loTriFactor->csrMat->values->assign(AALo, AALo + a->nz);
952         PetscCall(PetscLogCpuToGpu(2 * (a->nz) * sizeof(PetscScalar)));
953       }
954       PetscCallCUDA(cudaFreeHost(AAUp));
955       PetscCallCUDA(cudaFreeHost(AALo));
956     } catch (char *ex) {
957       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
958     }
959   }
960   PetscFunctionReturn(PETSC_SUCCESS);
961 }
962 #endif
963 
964 static PetscErrorCode MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(Mat A)
965 {
966   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ *)A->data;
967   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
968   IS                            ip                 = a->row;
969   PetscBool                     perm_identity;
970   PetscInt                      n = A->rmap->n;
971 
972   PetscFunctionBegin;
973   PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
974 
975 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
976   PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(A));
977 #else
978   PetscCall(MatSeqAIJCUSPARSEBuildICCTriMatrices(A));
979   if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
980 #endif
981   cusparseTriFactors->nnz = (a->nz - n) * 2 + n;
982 
983   A->offloadmask = PETSC_OFFLOAD_BOTH;
984 
985   /* lower triangular indices */
986   PetscCall(ISIdentity(ip, &perm_identity));
987   if (!perm_identity) {
988     IS              iip;
989     const PetscInt *irip, *rip;
990 
991     PetscCall(ISInvertPermutation(ip, PETSC_DECIDE, &iip));
992     PetscCall(ISGetIndices(iip, &irip));
993     PetscCall(ISGetIndices(ip, &rip));
994     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
995     cusparseTriFactors->rpermIndices->assign(rip, rip + n);
996     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
997     cusparseTriFactors->cpermIndices->assign(irip, irip + n);
998     PetscCall(ISRestoreIndices(iip, &irip));
999     PetscCall(ISDestroy(&iip));
1000     PetscCall(ISRestoreIndices(ip, &rip));
1001     PetscCall(PetscLogCpuToGpu(2. * n * sizeof(PetscInt)));
1002   }
1003   PetscFunctionReturn(PETSC_SUCCESS);
1004 }
1005 
1006 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
1007 {
1008   PetscFunctionBegin;
1009   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
1010   PetscCall(MatCholeskyFactorNumeric_SeqAIJ(B, A, info));
1011   B->offloadmask = PETSC_OFFLOAD_CPU;
1012 
1013 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1014   B->ops->solve          = MatSolve_SeqAIJCUSPARSE_Cholesky;
1015   B->ops->solvetranspose = MatSolve_SeqAIJCUSPARSE_Cholesky;
1016 #else
1017   /* determine which version of MatSolve needs to be used. */
1018   Mat_SeqAIJ *b  = (Mat_SeqAIJ *)B->data;
1019   IS          ip = b->row;
1020   PetscBool   perm_identity;
1021 
1022   PetscCall(ISIdentity(ip, &perm_identity));
1023   if (perm_identity) {
1024     B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
1025     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
1026   } else {
1027     B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
1028     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
1029   }
1030 #endif
1031   B->ops->matsolve          = NULL;
1032   B->ops->matsolvetranspose = NULL;
1033 
1034   /* get the triangular factors */
1035   PetscCall(MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(B));
1036   PetscFunctionReturn(PETSC_SUCCESS);
1037 }
1038 
1039 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
1040 static PetscErrorCode MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(Mat A)
1041 {
1042   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1043   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1044   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1045   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT;
1046   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT;
1047   cusparseIndexBase_t                indexBase;
1048   cusparseMatrixType_t               matrixType;
1049   cusparseFillMode_t                 fillMode;
1050   cusparseDiagType_t                 diagType;
1051 
1052   PetscFunctionBegin;
1053   /* allocate space for the transpose of the lower triangular factor */
1054   PetscCall(PetscNew(&loTriFactorT));
1055   loTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1056 
1057   /* set the matrix descriptors of the lower triangular factor */
1058   matrixType = cusparseGetMatType(loTriFactor->descr);
1059   indexBase  = cusparseGetMatIndexBase(loTriFactor->descr);
1060   fillMode   = cusparseGetMatFillMode(loTriFactor->descr) == CUSPARSE_FILL_MODE_UPPER ? CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
1061   diagType   = cusparseGetMatDiagType(loTriFactor->descr);
1062 
1063   /* Create the matrix description */
1064   PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactorT->descr));
1065   PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactorT->descr, indexBase));
1066   PetscCallCUSPARSE(cusparseSetMatType(loTriFactorT->descr, matrixType));
1067   PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactorT->descr, fillMode));
1068   PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactorT->descr, diagType));
1069 
1070   /* set the operation */
1071   loTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
1072 
1073   /* allocate GPU space for the CSC of the lower triangular factor*/
1074   loTriFactorT->csrMat                 = new CsrMatrix;
1075   loTriFactorT->csrMat->num_rows       = loTriFactor->csrMat->num_cols;
1076   loTriFactorT->csrMat->num_cols       = loTriFactor->csrMat->num_rows;
1077   loTriFactorT->csrMat->num_entries    = loTriFactor->csrMat->num_entries;
1078   loTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_rows + 1);
1079   loTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_entries);
1080   loTriFactorT->csrMat->values         = new THRUSTARRAY(loTriFactorT->csrMat->num_entries);
1081 
1082   /* compute the transpose of the lower triangular factor, i.e. the CSC */
1083   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1084   PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(cusparseTriFactors->handle, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_cols, loTriFactor->csrMat->num_entries, loTriFactor->csrMat->values->data().get(),
1085                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactorT->csrMat->values->data().get(), loTriFactorT->csrMat->row_offsets->data().get(),
1086                                                   loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &loTriFactor->csr2cscBufferSize));
1087   PetscCallCUDA(cudaMalloc(&loTriFactor->csr2cscBuffer, loTriFactor->csr2cscBufferSize));
1088   #endif
1089 
1090   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1091   {
1092     // there is no clean way to have PetscCallCUSPARSE wrapping this function...
1093     auto stat = cusparse_csr2csc(cusparseTriFactors->handle, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_cols, loTriFactor->csrMat->num_entries, loTriFactor->csrMat->values->data().get(), loTriFactor->csrMat->row_offsets->data().get(),
1094                                  loTriFactor->csrMat->column_indices->data().get(), loTriFactorT->csrMat->values->data().get(),
1095   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1096                                  loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, loTriFactor->csr2cscBuffer);
1097   #else
1098                                  loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1099   #endif
1100     PetscCallCUSPARSE(stat);
1101   }
1102 
1103   PetscCallCUDA(WaitForCUDA());
1104   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1105 
1106   /* Create the solve analysis information */
1107   PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1108   PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactorT->solveInfo));
1109   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
1110   PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1111                                             loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, &loTriFactorT->solveBufferSize));
1112   PetscCallCUDA(cudaMalloc(&loTriFactorT->solveBuffer, loTriFactorT->solveBufferSize));
1113   #endif
1114 
1115   /* perform the solve analysis */
1116   PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1117                                             loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1118 
1119   PetscCallCUDA(WaitForCUDA());
1120   PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1121 
1122   /* assign the pointer */
1123   ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtrTranspose = loTriFactorT;
1124 
1125   /*********************************************/
1126   /* Now the Transpose of the Upper Tri Factor */
1127   /*********************************************/
1128 
1129   /* allocate space for the transpose of the upper triangular factor */
1130   PetscCall(PetscNew(&upTriFactorT));
1131   upTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1132 
1133   /* set the matrix descriptors of the upper triangular factor */
1134   matrixType = cusparseGetMatType(upTriFactor->descr);
1135   indexBase  = cusparseGetMatIndexBase(upTriFactor->descr);
1136   fillMode   = cusparseGetMatFillMode(upTriFactor->descr) == CUSPARSE_FILL_MODE_UPPER ? CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
1137   diagType   = cusparseGetMatDiagType(upTriFactor->descr);
1138 
1139   /* Create the matrix description */
1140   PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactorT->descr));
1141   PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactorT->descr, indexBase));
1142   PetscCallCUSPARSE(cusparseSetMatType(upTriFactorT->descr, matrixType));
1143   PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactorT->descr, fillMode));
1144   PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactorT->descr, diagType));
1145 
1146   /* set the operation */
1147   upTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
1148 
1149   /* allocate GPU space for the CSC of the upper triangular factor*/
1150   upTriFactorT->csrMat                 = new CsrMatrix;
1151   upTriFactorT->csrMat->num_rows       = upTriFactor->csrMat->num_cols;
1152   upTriFactorT->csrMat->num_cols       = upTriFactor->csrMat->num_rows;
1153   upTriFactorT->csrMat->num_entries    = upTriFactor->csrMat->num_entries;
1154   upTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_rows + 1);
1155   upTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_entries);
1156   upTriFactorT->csrMat->values         = new THRUSTARRAY(upTriFactorT->csrMat->num_entries);
1157 
1158   /* compute the transpose of the upper triangular factor, i.e. the CSC */
1159   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1160   PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(cusparseTriFactors->handle, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_cols, upTriFactor->csrMat->num_entries, upTriFactor->csrMat->values->data().get(),
1161                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactorT->csrMat->values->data().get(), upTriFactorT->csrMat->row_offsets->data().get(),
1162                                                   upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &upTriFactor->csr2cscBufferSize));
1163   PetscCallCUDA(cudaMalloc(&upTriFactor->csr2cscBuffer, upTriFactor->csr2cscBufferSize));
1164   #endif
1165 
1166   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1167   {
1168     // there is no clean way to have PetscCallCUSPARSE wrapping this function...
1169     auto stat = cusparse_csr2csc(cusparseTriFactors->handle, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_cols, upTriFactor->csrMat->num_entries, upTriFactor->csrMat->values->data().get(), upTriFactor->csrMat->row_offsets->data().get(),
1170                                  upTriFactor->csrMat->column_indices->data().get(), upTriFactorT->csrMat->values->data().get(),
1171   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1172                                  upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, upTriFactor->csr2cscBuffer);
1173   #else
1174                                  upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1175   #endif
1176     PetscCallCUSPARSE(stat);
1177   }
1178 
1179   PetscCallCUDA(WaitForCUDA());
1180   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1181 
1182   /* Create the solve analysis information */
1183   PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1184   PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactorT->solveInfo));
1185   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
1186   PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
1187                                             upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, &upTriFactorT->solveBufferSize));
1188   PetscCallCUDA(cudaMalloc(&upTriFactorT->solveBuffer, upTriFactorT->solveBufferSize));
1189   #endif
1190 
1191   /* perform the solve analysis */
1192   /* christ, would it have killed you to put this stuff in a function????????? */
1193   PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
1194                                             upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1195 
1196   PetscCallCUDA(WaitForCUDA());
1197   PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1198 
1199   /* assign the pointer */
1200   ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtrTranspose = upTriFactorT;
1201   PetscFunctionReturn(PETSC_SUCCESS);
1202 }
1203 #endif
1204 
1205 struct PetscScalarToPetscInt {
1206   __host__ __device__ PetscInt operator()(PetscScalar s) { return (PetscInt)PetscRealPart(s); }
1207 };
1208 
1209 static PetscErrorCode MatSeqAIJCUSPARSEFormExplicitTranspose(Mat A)
1210 {
1211   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
1212   Mat_SeqAIJCUSPARSEMultStruct *matstruct, *matstructT;
1213   Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data;
1214   cusparseStatus_t              stat;
1215   cusparseIndexBase_t           indexBase;
1216 
1217   PetscFunctionBegin;
1218   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1219   matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
1220   PetscCheck(matstruct, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing mat struct");
1221   matstructT = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
1222   PetscCheck(!A->transupdated || matstructT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing matTranspose struct");
1223   if (A->transupdated) PetscFunctionReturn(PETSC_SUCCESS);
1224   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1225   PetscCall(PetscLogGpuTimeBegin());
1226   if (cusparsestruct->format != MAT_CUSPARSE_CSR) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
1227   if (!cusparsestruct->matTranspose) { /* create cusparse matrix */
1228     matstructT = new Mat_SeqAIJCUSPARSEMultStruct;
1229     PetscCallCUSPARSE(cusparseCreateMatDescr(&matstructT->descr));
1230     indexBase = cusparseGetMatIndexBase(matstruct->descr);
1231     PetscCallCUSPARSE(cusparseSetMatIndexBase(matstructT->descr, indexBase));
1232     PetscCallCUSPARSE(cusparseSetMatType(matstructT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
1233 
1234     /* set alpha and beta */
1235     PetscCallCUDA(cudaMalloc((void **)&matstructT->alpha_one, sizeof(PetscScalar)));
1236     PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_zero, sizeof(PetscScalar)));
1237     PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_one, sizeof(PetscScalar)));
1238     PetscCallCUDA(cudaMemcpy(matstructT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1239     PetscCallCUDA(cudaMemcpy(matstructT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1240     PetscCallCUDA(cudaMemcpy(matstructT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1241 
1242     if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
1243       CsrMatrix *matrixT      = new CsrMatrix;
1244       matstructT->mat         = matrixT;
1245       matrixT->num_rows       = A->cmap->n;
1246       matrixT->num_cols       = A->rmap->n;
1247       matrixT->num_entries    = a->nz;
1248       matrixT->row_offsets    = new THRUSTINTARRAY32(matrixT->num_rows + 1);
1249       matrixT->column_indices = new THRUSTINTARRAY32(a->nz);
1250       matrixT->values         = new THRUSTARRAY(a->nz);
1251 
1252       if (!cusparsestruct->rowoffsets_gpu) cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
1253       cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
1254 
1255 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1256   #if PETSC_PKG_CUDA_VERSION_GE(11, 2, 1)
1257       stat = cusparseCreateCsr(&matstructT->matDescr, matrixT->num_rows, matrixT->num_cols, matrixT->num_entries, matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), matrixT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx type due to THRUSTINTARRAY32 */
1258                                indexBase, cusparse_scalartype);
1259       PetscCallCUSPARSE(stat);
1260   #else
1261       /* cusparse-11.x returns errors with zero-sized matrices until 11.2.1,
1262            see https://docs.nvidia.com/cuda/cuda-toolkit-release-notes/index.html#cusparse-11.2.1
1263 
1264            I don't know what a proper value should be for matstructT->matDescr with empty matrices, so I just set
1265            it to NULL to blow it up if one relies on it. Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2,
1266            when nnz = 0, matrixT->row_offsets[] should be filled with indexBase. So I also set it accordingly.
1267         */
1268       if (matrixT->num_entries) {
1269         stat = cusparseCreateCsr(&matstructT->matDescr, matrixT->num_rows, matrixT->num_cols, matrixT->num_entries, matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), matrixT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, indexBase, cusparse_scalartype);
1270         PetscCallCUSPARSE(stat);
1271 
1272       } else {
1273         matstructT->matDescr = NULL;
1274         matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
1275       }
1276   #endif
1277 #endif
1278     } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
1279 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1280       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
1281 #else
1282       CsrMatrix *temp  = new CsrMatrix;
1283       CsrMatrix *tempT = new CsrMatrix;
1284       /* First convert HYB to CSR */
1285       temp->num_rows       = A->rmap->n;
1286       temp->num_cols       = A->cmap->n;
1287       temp->num_entries    = a->nz;
1288       temp->row_offsets    = new THRUSTINTARRAY32(A->rmap->n + 1);
1289       temp->column_indices = new THRUSTINTARRAY32(a->nz);
1290       temp->values         = new THRUSTARRAY(a->nz);
1291 
1292       stat = cusparse_hyb2csr(cusparsestruct->handle, matstruct->descr, (cusparseHybMat_t)matstruct->mat, temp->values->data().get(), temp->row_offsets->data().get(), temp->column_indices->data().get());
1293       PetscCallCUSPARSE(stat);
1294 
1295       /* Next, convert CSR to CSC (i.e. the matrix transpose) */
1296       tempT->num_rows       = A->rmap->n;
1297       tempT->num_cols       = A->cmap->n;
1298       tempT->num_entries    = a->nz;
1299       tempT->row_offsets    = new THRUSTINTARRAY32(A->rmap->n + 1);
1300       tempT->column_indices = new THRUSTINTARRAY32(a->nz);
1301       tempT->values         = new THRUSTARRAY(a->nz);
1302 
1303       stat = cusparse_csr2csc(cusparsestruct->handle, temp->num_rows, temp->num_cols, temp->num_entries, temp->values->data().get(), temp->row_offsets->data().get(), temp->column_indices->data().get(), tempT->values->data().get(),
1304                               tempT->column_indices->data().get(), tempT->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1305       PetscCallCUSPARSE(stat);
1306 
1307       /* Last, convert CSC to HYB */
1308       cusparseHybMat_t hybMat;
1309       PetscCallCUSPARSE(cusparseCreateHybMat(&hybMat));
1310       cusparseHybPartition_t partition = cusparsestruct->format == MAT_CUSPARSE_ELL ? CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
1311       stat                             = cusparse_csr2hyb(cusparsestruct->handle, A->rmap->n, A->cmap->n, matstructT->descr, tempT->values->data().get(), tempT->row_offsets->data().get(), tempT->column_indices->data().get(), hybMat, 0, partition);
1312       PetscCallCUSPARSE(stat);
1313 
1314       /* assign the pointer */
1315       matstructT->mat = hybMat;
1316       A->transupdated = PETSC_TRUE;
1317       /* delete temporaries */
1318       if (tempT) {
1319         if (tempT->values) delete (THRUSTARRAY *)tempT->values;
1320         if (tempT->column_indices) delete (THRUSTINTARRAY32 *)tempT->column_indices;
1321         if (tempT->row_offsets) delete (THRUSTINTARRAY32 *)tempT->row_offsets;
1322         delete (CsrMatrix *)tempT;
1323       }
1324       if (temp) {
1325         if (temp->values) delete (THRUSTARRAY *)temp->values;
1326         if (temp->column_indices) delete (THRUSTINTARRAY32 *)temp->column_indices;
1327         if (temp->row_offsets) delete (THRUSTINTARRAY32 *)temp->row_offsets;
1328         delete (CsrMatrix *)temp;
1329       }
1330 #endif
1331     }
1332   }
1333   if (cusparsestruct->format == MAT_CUSPARSE_CSR) { /* transpose mat struct may be already present, update data */
1334     CsrMatrix *matrix  = (CsrMatrix *)matstruct->mat;
1335     CsrMatrix *matrixT = (CsrMatrix *)matstructT->mat;
1336     PetscCheck(matrix, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix");
1337     PetscCheck(matrix->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix rows");
1338     PetscCheck(matrix->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix cols");
1339     PetscCheck(matrix->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix values");
1340     PetscCheck(matrixT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT");
1341     PetscCheck(matrixT->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT rows");
1342     PetscCheck(matrixT->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT cols");
1343     PetscCheck(matrixT->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT values");
1344     if (!cusparsestruct->rowoffsets_gpu) { /* this may be absent when we did not construct the transpose with csr2csc */
1345       cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
1346       cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
1347       PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
1348     }
1349     if (!cusparsestruct->csr2csc_i) {
1350       THRUSTARRAY csr2csc_a(matrix->num_entries);
1351       PetscCallThrust(thrust::sequence(thrust::device, csr2csc_a.begin(), csr2csc_a.end(), 0.0));
1352 
1353       indexBase = cusparseGetMatIndexBase(matstruct->descr);
1354 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1355       void  *csr2cscBuffer;
1356       size_t csr2cscBufferSize;
1357       stat = cusparseCsr2cscEx2_bufferSize(cusparsestruct->handle, A->rmap->n, A->cmap->n, matrix->num_entries, matrix->values->data().get(), cusparsestruct->rowoffsets_gpu->data().get(), matrix->column_indices->data().get(), matrixT->values->data().get(),
1358                                            matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, &csr2cscBufferSize);
1359       PetscCallCUSPARSE(stat);
1360       PetscCallCUDA(cudaMalloc(&csr2cscBuffer, csr2cscBufferSize));
1361 #endif
1362 
1363       if (matrix->num_entries) {
1364         /* When there are no nonzeros, this routine mistakenly returns CUSPARSE_STATUS_INVALID_VALUE in
1365            mat_tests-ex62_15_mpiaijcusparse on ranks 0 and 2 with CUDA-11. But CUDA-10 is OK.
1366            I checked every parameters and they were just fine. I have no clue why cusparse complains.
1367 
1368            Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2, when nnz = 0, matrixT->row_offsets[]
1369            should be filled with indexBase. So I just take a shortcut here.
1370         */
1371         stat = cusparse_csr2csc(cusparsestruct->handle, A->rmap->n, A->cmap->n, matrix->num_entries, csr2csc_a.data().get(), cusparsestruct->rowoffsets_gpu->data().get(), matrix->column_indices->data().get(), matrixT->values->data().get(),
1372 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1373                                 matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, csr2cscBuffer);
1374         PetscCallCUSPARSE(stat);
1375 #else
1376                                 matrixT->column_indices->data().get(), matrixT->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1377         PetscCallCUSPARSE(stat);
1378 #endif
1379       } else {
1380         matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
1381       }
1382 
1383       cusparsestruct->csr2csc_i = new THRUSTINTARRAY(matrix->num_entries);
1384       PetscCallThrust(thrust::transform(thrust::device, matrixT->values->begin(), matrixT->values->end(), cusparsestruct->csr2csc_i->begin(), PetscScalarToPetscInt()));
1385 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1386       PetscCallCUDA(cudaFree(csr2cscBuffer));
1387 #endif
1388     }
1389     PetscCallThrust(
1390       thrust::copy(thrust::device, thrust::make_permutation_iterator(matrix->values->begin(), cusparsestruct->csr2csc_i->begin()), thrust::make_permutation_iterator(matrix->values->begin(), cusparsestruct->csr2csc_i->end()), matrixT->values->begin()));
1391   }
1392   PetscCall(PetscLogGpuTimeEnd());
1393   PetscCall(PetscLogEventEnd(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1394   /* the compressed row indices is not used for matTranspose */
1395   matstructT->cprowIndices = NULL;
1396   /* assign the pointer */
1397   ((Mat_SeqAIJCUSPARSE *)A->spptr)->matTranspose = matstructT;
1398   A->transupdated                                = PETSC_TRUE;
1399   PetscFunctionReturn(PETSC_SUCCESS);
1400 }
1401 
1402 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1403 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
1404 {
1405   const PetscScalar                    *barray;
1406   PetscScalar                          *xarray;
1407   thrust::device_ptr<const PetscScalar> bGPU;
1408   thrust::device_ptr<PetscScalar>       xGPU;
1409   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
1410   const Mat_SeqAIJ                     *aij = static_cast<Mat_SeqAIJ *>(A->data);
1411   const cusparseOperation_t             op  = CUSPARSE_OPERATION_NON_TRANSPOSE;
1412   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
1413   PetscInt                              m   = A->rmap->n;
1414 
1415   PetscFunctionBegin;
1416   PetscCall(PetscLogGpuTimeBegin());
1417   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1418   PetscCall(VecCUDAGetArrayRead(b, &barray));
1419   xGPU = thrust::device_pointer_cast(xarray);
1420   bGPU = thrust::device_pointer_cast(barray);
1421 
1422   // Reorder b with the row permutation if needed, and wrap the result in fs->X
1423   if (fs->rpermIndices) {
1424     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
1425     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1426   } else {
1427     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1428   }
1429 
1430   // Solve L Y = X
1431   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1432   // Note that cusparseSpSV_solve() secretly uses the external buffer used in cusparseSpSV_analysis()!
1433   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_L));
1434 
1435   // Solve U X = Y
1436   if (fs->cpermIndices) {
1437     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1438   } else {
1439     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1440   }
1441   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_U));
1442 
1443   // Reorder X with the column permutation if needed, and put the result back to x
1444   if (fs->cpermIndices) {
1445     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
1446                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
1447   }
1448   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1449   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1450   PetscCall(PetscLogGpuTimeEnd());
1451   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - m));
1452   PetscFunctionReturn(PETSC_SUCCESS);
1453 }
1454 
1455 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
1456 {
1457   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
1458   Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
1459   const PetscScalar                    *barray;
1460   PetscScalar                          *xarray;
1461   thrust::device_ptr<const PetscScalar> bGPU;
1462   thrust::device_ptr<PetscScalar>       xGPU;
1463   const cusparseOperation_t             opA = CUSPARSE_OPERATION_TRANSPOSE;
1464   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
1465   PetscInt                              m   = A->rmap->n;
1466 
1467   PetscFunctionBegin;
1468   PetscCall(PetscLogGpuTimeBegin());
1469   if (!fs->createdTransposeSpSVDescr) { // Call MatSolveTranspose() for the first time
1470     PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
1471     PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* The matrix is still L. We only do transpose solve with it */
1472                                               fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Lt, &fs->spsvBufferSize_Lt));
1473 
1474     PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut));
1475     PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut, &fs->spsvBufferSize_Ut));
1476     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
1477     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));
1478     fs->createdTransposeSpSVDescr = PETSC_TRUE;
1479   }
1480 
1481   if (!fs->updatedTransposeSpSVAnalysis) {
1482     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Lt, fs->spsvBuffer_Lt));
1483 
1484     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut, fs->spsvBuffer_Ut));
1485     fs->updatedTransposeSpSVAnalysis = PETSC_TRUE;
1486   }
1487 
1488   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1489   PetscCall(VecCUDAGetArrayRead(b, &barray));
1490   xGPU = thrust::device_pointer_cast(xarray);
1491   bGPU = thrust::device_pointer_cast(barray);
1492 
1493   // Reorder b with the row permutation if needed, and wrap the result in fs->X
1494   if (fs->rpermIndices) {
1495     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
1496     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1497   } else {
1498     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1499   }
1500 
1501   // Solve Ut Y = X
1502   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1503   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut));
1504 
1505   // Solve Lt X = Y
1506   if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
1507     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1508   } else {
1509     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1510   }
1511   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_Lt));
1512 
1513   // Reorder X with the column permutation if needed, and put the result back to x
1514   if (fs->cpermIndices) {
1515     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
1516                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
1517   }
1518 
1519   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1520   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1521   PetscCall(PetscLogGpuTimeEnd());
1522   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - A->rmap->n));
1523   PetscFunctionReturn(PETSC_SUCCESS);
1524 }
1525 #else
1526 /* Why do we need to analyze the transposed matrix again? Can't we just use op(A) = CUSPARSE_OPERATION_TRANSPOSE in MatSolve_SeqAIJCUSPARSE? */
1527 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat A, Vec bb, Vec xx)
1528 {
1529   PetscInt                              n = xx->map->n;
1530   const PetscScalar                    *barray;
1531   PetscScalar                          *xarray;
1532   thrust::device_ptr<const PetscScalar> bGPU;
1533   thrust::device_ptr<PetscScalar>       xGPU;
1534   Mat_SeqAIJCUSPARSETriFactors         *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1535   Mat_SeqAIJCUSPARSETriFactorStruct    *loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1536   Mat_SeqAIJCUSPARSETriFactorStruct    *upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1537   THRUSTARRAY                          *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1538 
1539   PetscFunctionBegin;
1540   /* Analyze the matrix and create the transpose ... on the fly */
1541   if (!loTriFactorT && !upTriFactorT) {
1542     PetscCall(MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A));
1543     loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1544     upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1545   }
1546 
1547   /* Get the GPU pointers */
1548   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1549   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1550   xGPU = thrust::device_pointer_cast(xarray);
1551   bGPU = thrust::device_pointer_cast(barray);
1552 
1553   PetscCall(PetscLogGpuTimeBegin());
1554   /* First, reorder with the row permutation */
1555   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU + n, cusparseTriFactors->rpermIndices->end()), xGPU);
1556 
1557   /* First, solve U */
1558   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, &PETSC_CUSPARSE_ONE, upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
1559                                          upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, xarray, tempGPU->data().get(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1560 
1561   /* Then, solve L */
1562   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, &PETSC_CUSPARSE_ONE, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1563                                          loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, tempGPU->data().get(), xarray, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1564 
1565   /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
1566   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(xGPU, cusparseTriFactors->cpermIndices->begin()), thrust::make_permutation_iterator(xGPU + n, cusparseTriFactors->cpermIndices->end()), tempGPU->begin());
1567 
1568   /* Copy the temporary to the full solution. */
1569   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), tempGPU->begin(), tempGPU->end(), xGPU);
1570 
1571   /* restore */
1572   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1573   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1574   PetscCall(PetscLogGpuTimeEnd());
1575   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1576   PetscFunctionReturn(PETSC_SUCCESS);
1577 }
1578 
1579 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
1580 {
1581   const PetscScalar                 *barray;
1582   PetscScalar                       *xarray;
1583   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1584   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1585   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1586   THRUSTARRAY                       *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1587 
1588   PetscFunctionBegin;
1589   /* Analyze the matrix and create the transpose ... on the fly */
1590   if (!loTriFactorT && !upTriFactorT) {
1591     PetscCall(MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A));
1592     loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1593     upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1594   }
1595 
1596   /* Get the GPU pointers */
1597   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1598   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1599 
1600   PetscCall(PetscLogGpuTimeBegin());
1601   /* First, solve U */
1602   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, &PETSC_CUSPARSE_ONE, upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
1603                                          upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, barray, tempGPU->data().get(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1604 
1605   /* Then, solve L */
1606   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, &PETSC_CUSPARSE_ONE, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1607                                          loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, tempGPU->data().get(), xarray, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1608 
1609   /* restore */
1610   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1611   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1612   PetscCall(PetscLogGpuTimeEnd());
1613   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1614   PetscFunctionReturn(PETSC_SUCCESS);
1615 }
1616 
1617 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat A, Vec bb, Vec xx)
1618 {
1619   const PetscScalar                    *barray;
1620   PetscScalar                          *xarray;
1621   thrust::device_ptr<const PetscScalar> bGPU;
1622   thrust::device_ptr<PetscScalar>       xGPU;
1623   Mat_SeqAIJCUSPARSETriFactors         *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1624   Mat_SeqAIJCUSPARSETriFactorStruct    *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1625   Mat_SeqAIJCUSPARSETriFactorStruct    *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1626   THRUSTARRAY                          *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1627 
1628   PetscFunctionBegin;
1629   /* Get the GPU pointers */
1630   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1631   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1632   xGPU = thrust::device_pointer_cast(xarray);
1633   bGPU = thrust::device_pointer_cast(barray);
1634 
1635   PetscCall(PetscLogGpuTimeBegin());
1636   /* First, reorder with the row permutation */
1637   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->end()), tempGPU->begin());
1638 
1639   /* Next, solve L */
1640   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, &PETSC_CUSPARSE_ONE, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
1641                                          loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, tempGPU->data().get(), xarray, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
1642 
1643   /* Then, solve U */
1644   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, &PETSC_CUSPARSE_ONE, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
1645                                          upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, xarray, tempGPU->data().get(), upTriFactor->solvePolicy, upTriFactor->solveBuffer));
1646 
1647   /* Last, reorder with the column permutation */
1648   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(tempGPU->begin(), cusparseTriFactors->cpermIndices->begin()), thrust::make_permutation_iterator(tempGPU->begin(), cusparseTriFactors->cpermIndices->end()), xGPU);
1649 
1650   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1651   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1652   PetscCall(PetscLogGpuTimeEnd());
1653   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1654   PetscFunctionReturn(PETSC_SUCCESS);
1655 }
1656 
1657 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
1658 {
1659   const PetscScalar                 *barray;
1660   PetscScalar                       *xarray;
1661   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1662   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1663   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1664   THRUSTARRAY                       *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1665 
1666   PetscFunctionBegin;
1667   /* Get the GPU pointers */
1668   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1669   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1670 
1671   PetscCall(PetscLogGpuTimeBegin());
1672   /* First, solve L */
1673   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, &PETSC_CUSPARSE_ONE, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
1674                                          loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, barray, tempGPU->data().get(), loTriFactor->solvePolicy, loTriFactor->solveBuffer));
1675 
1676   /* Next, solve U */
1677   PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, &PETSC_CUSPARSE_ONE, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
1678                                          upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, tempGPU->data().get(), xarray, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
1679 
1680   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1681   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1682   PetscCall(PetscLogGpuTimeEnd());
1683   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1684   PetscFunctionReturn(PETSC_SUCCESS);
1685 }
1686 #endif
1687 
1688 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1689 static PetscErrorCode MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, const MatFactorInfo *)
1690 {
1691   Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1692   Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
1693   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
1694   CsrMatrix                    *Acsr;
1695   PetscInt                      m, nz;
1696   PetscBool                     flg;
1697 
1698   PetscFunctionBegin;
1699   if (PetscDefined(USE_DEBUG)) {
1700     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1701     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1702   }
1703 
1704   /* Copy A's value to fact */
1705   m  = fact->rmap->n;
1706   nz = aij->nz;
1707   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1708   Acsr = (CsrMatrix *)Acusp->mat->mat;
1709   PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1710 
1711   PetscCall(PetscLogGpuTimeBegin());
1712   /* Factorize fact inplace */
1713   if (m)
1714     PetscCallCUSPARSE(cusparseXcsrilu02(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1715                                         fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
1716   if (PetscDefined(USE_DEBUG)) {
1717     int              numerical_zero;
1718     cusparseStatus_t status;
1719     status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &numerical_zero);
1720     PetscAssert(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Numerical zero pivot detected in csrilu02: A(%d,%d) is zero", numerical_zero, numerical_zero);
1721   }
1722 
1723   #if PETSC_PKG_CUDA_VERSION_GE(12, 1, 1)
1724   if (fs->updatedSpSVAnalysis) {
1725     if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_L, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
1726     if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_U, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
1727   } else
1728   #endif
1729   {
1730     /* cusparseSpSV_analysis() is numeric, i.e., it requires valid matrix values, therefore, we do it after cusparseXcsrilu02()
1731      See discussion at https://github.com/NVIDIA/CUDALibrarySamples/issues/78
1732     */
1733     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));
1734 
1735     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));
1736 
1737     fs->updatedSpSVAnalysis = PETSC_TRUE;
1738     /* L, U values have changed, reset the flag to indicate we need to redo cusparseSpSV_analysis() for transpose solve */
1739     fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
1740   }
1741 
1742   fact->offloadmask            = PETSC_OFFLOAD_GPU;
1743   fact->ops->solve             = MatSolve_SeqAIJCUSPARSE_LU; // spMatDescr_L/U uses 32-bit indices, but cusparseSpSV_solve() supports both 32 and 64. The info is encoded in cusparseSpMatDescr_t.
1744   fact->ops->solvetranspose    = MatSolveTranspose_SeqAIJCUSPARSE_LU;
1745   fact->ops->matsolve          = NULL;
1746   fact->ops->matsolvetranspose = NULL;
1747   PetscCall(PetscLogGpuTimeEnd());
1748   PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
1749   PetscFunctionReturn(PETSC_SUCCESS);
1750 }
1751 
1752 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, IS, IS, const MatFactorInfo *info)
1753 {
1754   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1755   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
1756   PetscInt                      m, nz;
1757 
1758   PetscFunctionBegin;
1759   if (PetscDefined(USE_DEBUG)) {
1760     PetscInt  i;
1761     PetscBool flg, missing;
1762 
1763     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1764     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1765     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Must be square matrix, rows %" PetscInt_FMT " columns %" PetscInt_FMT, A->rmap->n, A->cmap->n);
1766     PetscCall(MatMissingDiagonal(A, &missing, &i));
1767     PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
1768   }
1769 
1770   /* Free the old stale stuff */
1771   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));
1772 
1773   /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
1774      but they will not be used. Allocate them just for easy debugging.
1775    */
1776   PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));
1777 
1778   fact->offloadmask            = PETSC_OFFLOAD_BOTH;
1779   fact->factortype             = MAT_FACTOR_ILU;
1780   fact->info.factor_mallocs    = 0;
1781   fact->info.fill_ratio_given  = info->fill;
1782   fact->info.fill_ratio_needed = 1.0;
1783 
1784   aij->row = NULL;
1785   aij->col = NULL;
1786 
1787   /* ====================================================================== */
1788   /* Copy A's i, j to fact and also allocate the value array of fact.       */
1789   /* We'll do in-place factorization on fact                                */
1790   /* ====================================================================== */
1791   const int *Ai, *Aj;
1792 
1793   m  = fact->rmap->n;
1794   nz = aij->nz;
1795 
1796   PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
1797   PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
1798   PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(*fs->csrVal) * nz));
1799   PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai.  The returned Ai, Aj are 32-bit */
1800   PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1801   PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1802 
1803   /* ====================================================================== */
1804   /* Create descriptors for M, L, U                                         */
1805   /* ====================================================================== */
1806   cusparseFillMode_t fillMode;
1807   cusparseDiagType_t diagType;
1808 
1809   PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
1810   PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
1811   PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));
1812 
1813   /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
1814     cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
1815     assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
1816     all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
1817     assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
1818   */
1819   fillMode = CUSPARSE_FILL_MODE_LOWER;
1820   diagType = CUSPARSE_DIAG_TYPE_UNIT;
1821   PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
1822   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
1823   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
1824 
1825   fillMode = CUSPARSE_FILL_MODE_UPPER;
1826   diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
1827   PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
1828   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
1829   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
1830 
1831   /* ========================================================================= */
1832   /* Query buffer sizes for csrilu0, SpSV and allocate buffers                 */
1833   /* ========================================================================= */
1834   PetscCallCUSPARSE(cusparseCreateCsrilu02Info(&fs->ilu0Info_M));
1835   if (m)
1836     PetscCallCUSPARSE(cusparseXcsrilu02_bufferSize(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1837                                                    fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, &fs->factBufferSize_M));
1838 
1839   PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
1840   PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));
1841 
1842   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
1843   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
1844 
1845   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
1846   PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));
1847 
1848   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
1849   PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));
1850 
1851   /* From my experiment with the example at https://github.com/NVIDIA/CUDALibrarySamples/tree/master/cuSPARSE/bicgstab,
1852      and discussion at https://github.com/NVIDIA/CUDALibrarySamples/issues/77,
1853      spsvBuffer_L/U can not be shared (i.e., the same) for our case, but factBuffer_M can share with either of spsvBuffer_L/U.
1854      To save memory, we make factBuffer_M share with the bigger of spsvBuffer_L/U.
1855    */
1856   if (fs->spsvBufferSize_L > fs->spsvBufferSize_U) {
1857     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
1858     fs->spsvBuffer_L = fs->factBuffer_M;
1859     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
1860   } else {
1861     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_U, (size_t)fs->factBufferSize_M)));
1862     fs->spsvBuffer_U = fs->factBuffer_M;
1863     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
1864   }
1865 
1866   /* ========================================================================== */
1867   /* Perform analysis of ilu0 on M, SpSv on L and U                             */
1868   /* The lower(upper) triangular part of M has the same sparsity pattern as L(U)*/
1869   /* ========================================================================== */
1870   int              structural_zero;
1871   cusparseStatus_t status;
1872 
1873   fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1874   if (m)
1875     PetscCallCUSPARSE(cusparseXcsrilu02_analysis(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1876                                                  fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
1877   if (PetscDefined(USE_DEBUG)) {
1878     /* cusparseXcsrilu02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
1879     status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &structural_zero);
1880     PetscCheck(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Structural zero pivot detected in csrilu02: A(%d,%d) is missing", structural_zero, structural_zero);
1881   }
1882 
1883   /* Estimate FLOPs of the numeric factorization */
1884   {
1885     Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
1886     PetscInt      *Ai, *Adiag, nzRow, nzLeft;
1887     PetscLogDouble flops = 0.0;
1888 
1889     PetscCall(MatMarkDiagonal_SeqAIJ(A));
1890     Ai    = Aseq->i;
1891     Adiag = Aseq->diag;
1892     for (PetscInt i = 0; i < m; i++) {
1893       if (Ai[i] < Adiag[i] && Adiag[i] < Ai[i + 1]) { /* There are nonzeros left to the diagonal of row i */
1894         nzRow  = Ai[i + 1] - Ai[i];
1895         nzLeft = Adiag[i] - Ai[i];
1896         /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
1897           and include the eliminated one will be updated, which incurs a multiplication and an addition.
1898         */
1899         nzLeft = (nzRow - 1) / 2;
1900         flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
1901       }
1902     }
1903     fs->numericFactFlops = flops;
1904   }
1905   fact->ops->lufactornumeric = MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0;
1906   PetscFunctionReturn(PETSC_SUCCESS);
1907 }
1908 
1909 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_ICC0(Mat fact, Vec b, Vec x)
1910 {
1911   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1912   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
1913   const PetscScalar            *barray;
1914   PetscScalar                  *xarray;
1915 
1916   PetscFunctionBegin;
1917   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1918   PetscCall(VecCUDAGetArrayRead(b, &barray));
1919   PetscCall(PetscLogGpuTimeBegin());
1920 
1921   /* Solve L*y = b */
1922   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1923   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1924   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* L Y = X */
1925                                        fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L));
1926 
1927   /* Solve Lt*x = y */
1928   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1929   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* Lt X = Y */
1930                                        fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt));
1931 
1932   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1933   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1934 
1935   PetscCall(PetscLogGpuTimeEnd());
1936   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - fact->rmap->n));
1937   PetscFunctionReturn(PETSC_SUCCESS);
1938 }
1939 
1940 static PetscErrorCode MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, const MatFactorInfo *)
1941 {
1942   Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1943   Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
1944   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
1945   CsrMatrix                    *Acsr;
1946   PetscInt                      m, nz;
1947   PetscBool                     flg;
1948 
1949   PetscFunctionBegin;
1950   if (PetscDefined(USE_DEBUG)) {
1951     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1952     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1953   }
1954 
1955   /* Copy A's value to fact */
1956   m  = fact->rmap->n;
1957   nz = aij->nz;
1958   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1959   Acsr = (CsrMatrix *)Acusp->mat->mat;
1960   PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1961 
1962   /* Factorize fact inplace */
1963   /* https://docs.nvidia.com/cuda/cusparse/index.html#csric02_solve
1964      csric02() only takes the lower triangular part of matrix A to perform factorization.
1965      The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, the fill mode and diagonal type are ignored,
1966      and the strictly upper triangular part is ignored and never touched. It does not matter if A is Hermitian or not.
1967      In other words, from the point of view of csric02() A is Hermitian and only the lower triangular part is provided.
1968    */
1969   if (m) PetscCallCUSPARSE(cusparseXcsric02(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, fs->policy_M, fs->factBuffer_M));
1970   if (PetscDefined(USE_DEBUG)) {
1971     int              numerical_zero;
1972     cusparseStatus_t status;
1973     status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &numerical_zero);
1974     PetscAssert(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Numerical zero pivot detected in csric02: A(%d,%d) is zero", numerical_zero, numerical_zero);
1975   }
1976 
1977   #if PETSC_PKG_CUDA_VERSION_GE(12, 1, 1)
1978   if (fs->updatedSpSVAnalysis) {
1979     if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_L, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
1980     if (fs->csrVal) PetscCallCUSPARSE(cusparseSpSV_updateMatrix(fs->handle, fs->spsvDescr_Lt, fs->csrVal, CUSPARSE_SPSV_UPDATE_GENERAL));
1981   } else
1982   #endif
1983   {
1984     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));
1985 
1986     /* Note that cusparse reports this error if we use double and CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE
1987     ** On entry to cusparseSpSV_analysis(): conjugate transpose (opA) is not supported for matA data type, current -> CUDA_R_64F
1988   */
1989     PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt, fs->spsvBuffer_Lt));
1990     fs->updatedSpSVAnalysis = PETSC_TRUE;
1991   }
1992 
1993   fact->offloadmask            = PETSC_OFFLOAD_GPU;
1994   fact->ops->solve             = MatSolve_SeqAIJCUSPARSE_ICC0;
1995   fact->ops->solvetranspose    = MatSolve_SeqAIJCUSPARSE_ICC0;
1996   fact->ops->matsolve          = NULL;
1997   fact->ops->matsolvetranspose = NULL;
1998   PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
1999   PetscFunctionReturn(PETSC_SUCCESS);
2000 }
2001 
2002 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, IS, const MatFactorInfo *info)
2003 {
2004   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
2005   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
2006   PetscInt                      m, nz;
2007 
2008   PetscFunctionBegin;
2009   if (PetscDefined(USE_DEBUG)) {
2010     PetscInt  i;
2011     PetscBool flg, missing;
2012 
2013     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2014     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
2015     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Must be square matrix, rows %" PetscInt_FMT " columns %" PetscInt_FMT, A->rmap->n, A->cmap->n);
2016     PetscCall(MatMissingDiagonal(A, &missing, &i));
2017     PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
2018   }
2019 
2020   /* Free the old stale stuff */
2021   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));
2022 
2023   /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
2024      but they will not be used. Allocate them just for easy debugging.
2025    */
2026   PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));
2027 
2028   fact->offloadmask            = PETSC_OFFLOAD_BOTH;
2029   fact->factortype             = MAT_FACTOR_ICC;
2030   fact->info.factor_mallocs    = 0;
2031   fact->info.fill_ratio_given  = info->fill;
2032   fact->info.fill_ratio_needed = 1.0;
2033 
2034   aij->row = NULL;
2035   aij->col = NULL;
2036 
2037   /* ====================================================================== */
2038   /* Copy A's i, j to fact and also allocate the value array of fact.       */
2039   /* We'll do in-place factorization on fact                                */
2040   /* ====================================================================== */
2041   const int *Ai, *Aj;
2042 
2043   m  = fact->rmap->n;
2044   nz = aij->nz;
2045 
2046   PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
2047   PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
2048   PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(PetscScalar) * nz));
2049   PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai */
2050   PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
2051   PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
2052 
2053   /* ====================================================================== */
2054   /* Create mat descriptors for M, L                                        */
2055   /* ====================================================================== */
2056   cusparseFillMode_t fillMode;
2057   cusparseDiagType_t diagType;
2058 
2059   PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
2060   PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
2061   PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));
2062 
2063   /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
2064     cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
2065     assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
2066     all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
2067     assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
2068   */
2069   fillMode = CUSPARSE_FILL_MODE_LOWER;
2070   diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
2071   PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
2072   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
2073   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
2074 
2075   /* ========================================================================= */
2076   /* Query buffer sizes for csric0, SpSV of L and Lt, and allocate buffers     */
2077   /* ========================================================================= */
2078   PetscCallCUSPARSE(cusparseCreateCsric02Info(&fs->ic0Info_M));
2079   if (m) PetscCallCUSPARSE(cusparseXcsric02_bufferSize(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, &fs->factBufferSize_M));
2080 
2081   PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
2082   PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));
2083 
2084   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
2085   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
2086 
2087   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
2088   PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));
2089 
2090   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
2091   PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt, &fs->spsvBufferSize_Lt));
2092 
2093   /* To save device memory, we make the factorization buffer share with one of the solver buffer.
2094      See also comments in MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0().
2095    */
2096   if (fs->spsvBufferSize_L > fs->spsvBufferSize_Lt) {
2097     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
2098     fs->spsvBuffer_L = fs->factBuffer_M;
2099     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
2100   } else {
2101     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_Lt, (size_t)fs->factBufferSize_M)));
2102     fs->spsvBuffer_Lt = fs->factBuffer_M;
2103     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
2104   }
2105 
2106   /* ========================================================================== */
2107   /* Perform analysis of ic0 on M                                               */
2108   /* The lower triangular part of M has the same sparsity pattern as L          */
2109   /* ========================================================================== */
2110   int              structural_zero;
2111   cusparseStatus_t status;
2112 
2113   fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
2114   if (m) PetscCallCUSPARSE(cusparseXcsric02_analysis(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, fs->policy_M, fs->factBuffer_M));
2115   if (PetscDefined(USE_DEBUG)) {
2116     /* cusparseXcsric02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
2117     status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &structural_zero);
2118     PetscCheck(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Structural zero pivot detected in csric02: A(%d,%d) is missing", structural_zero, structural_zero);
2119   }
2120 
2121   /* Estimate FLOPs of the numeric factorization */
2122   {
2123     Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
2124     PetscInt      *Ai, nzRow, nzLeft;
2125     PetscLogDouble flops = 0.0;
2126 
2127     Ai = Aseq->i;
2128     for (PetscInt i = 0; i < m; i++) {
2129       nzRow = Ai[i + 1] - Ai[i];
2130       if (nzRow > 1) {
2131         /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
2132           and include the eliminated one will be updated, which incurs a multiplication and an addition.
2133         */
2134         nzLeft = (nzRow - 1) / 2;
2135         flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
2136       }
2137     }
2138     fs->numericFactFlops = flops;
2139   }
2140   fact->ops->choleskyfactornumeric = MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0;
2141   PetscFunctionReturn(PETSC_SUCCESS);
2142 }
2143 #endif
2144 
2145 static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
2146 {
2147   // use_cpu_solve is a field in Mat_SeqAIJCUSPARSE. B, a factored matrix, uses Mat_SeqAIJCUSPARSETriFactors.
2148   Mat_SeqAIJCUSPARSE *cusparsestruct = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);
2149 
2150   PetscFunctionBegin;
2151   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2152   PetscCall(MatLUFactorNumeric_SeqAIJ(B, A, info));
2153   B->offloadmask = PETSC_OFFLOAD_CPU;
2154 
2155   if (!cusparsestruct->use_cpu_solve) {
2156 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2157     B->ops->solve          = MatSolve_SeqAIJCUSPARSE_LU;
2158     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_LU;
2159 #else
2160     /* determine which version of MatSolve needs to be used. */
2161     Mat_SeqAIJ *b     = (Mat_SeqAIJ *)B->data;
2162     IS          isrow = b->row, iscol = b->col;
2163     PetscBool   row_identity, col_identity;
2164 
2165     PetscCall(ISIdentity(isrow, &row_identity));
2166     PetscCall(ISIdentity(iscol, &col_identity));
2167     if (row_identity && col_identity) {
2168       B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
2169       B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
2170     } else {
2171       B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
2172       B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
2173     }
2174 #endif
2175   }
2176   B->ops->matsolve          = NULL;
2177   B->ops->matsolvetranspose = NULL;
2178 
2179   /* get the triangular factors */
2180   if (!cusparsestruct->use_cpu_solve) PetscCall(MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(B));
2181   PetscFunctionReturn(PETSC_SUCCESS);
2182 }
2183 
2184 static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2185 {
2186   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(B->spptr);
2187 
2188   PetscFunctionBegin;
2189   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2190   PetscCall(MatLUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
2191   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
2192   PetscFunctionReturn(PETSC_SUCCESS);
2193 }
2194 
2195 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2196 {
2197   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2198 
2199   PetscFunctionBegin;
2200 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2201   PetscBool row_identity = PETSC_FALSE, col_identity = PETSC_FALSE;
2202   if (!info->factoronhost) {
2203     PetscCall(ISIdentity(isrow, &row_identity));
2204     PetscCall(ISIdentity(iscol, &col_identity));
2205   }
2206   if (!info->levels && row_identity && col_identity) {
2207     PetscCall(MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(B, A, isrow, iscol, info));
2208   } else
2209 #endif
2210   {
2211     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2212     PetscCall(MatILUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
2213     B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
2214   }
2215   PetscFunctionReturn(PETSC_SUCCESS);
2216 }
2217 
2218 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
2219 {
2220   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2221 
2222   PetscFunctionBegin;
2223 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2224   PetscBool perm_identity = PETSC_FALSE;
2225   if (!info->factoronhost) PetscCall(ISIdentity(perm, &perm_identity));
2226   if (!info->levels && perm_identity) {
2227     PetscCall(MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(B, A, perm, info));
2228   } else
2229 #endif
2230   {
2231     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2232     PetscCall(MatICCFactorSymbolic_SeqAIJ(B, A, perm, info));
2233     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
2234   }
2235   PetscFunctionReturn(PETSC_SUCCESS);
2236 }
2237 
2238 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
2239 {
2240   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2241 
2242   PetscFunctionBegin;
2243   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2244   PetscCall(MatCholeskyFactorSymbolic_SeqAIJ(B, A, perm, info));
2245   B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
2246   PetscFunctionReturn(PETSC_SUCCESS);
2247 }
2248 
2249 static PetscErrorCode MatFactorGetSolverType_seqaij_cusparse(Mat, MatSolverType *type)
2250 {
2251   PetscFunctionBegin;
2252   *type = MATSOLVERCUSPARSE;
2253   PetscFunctionReturn(PETSC_SUCCESS);
2254 }
2255 
2256 /*MC
2257   MATSOLVERCUSPARSE = "cusparse" - A matrix type providing triangular solvers for seq matrices
2258   on a single GPU of type, `MATSEQAIJCUSPARSE`. Currently supported
2259   algorithms are ILU(k) and ICC(k). Typically, deeper factorizations (larger k) results in poorer
2260   performance in the triangular solves. Full LU, and Cholesky decompositions can be solved through the
2261   CuSPARSE triangular solve algorithm. However, the performance can be quite poor and thus these
2262   algorithms are not recommended. This class does NOT support direct solver operations.
2263 
2264   Level: beginner
2265 
2266 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatCreateSeqAIJCUSPARSE()`,
2267           `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
2268 M*/
2269 
2270 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat A, MatFactorType ftype, Mat *B)
2271 {
2272   PetscInt n = A->rmap->n;
2273 
2274   PetscFunctionBegin;
2275   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
2276   PetscCall(MatSetSizes(*B, n, n, n, n));
2277   (*B)->factortype = ftype; // factortype makes MatSetType() allocate spptr of type Mat_SeqAIJCUSPARSETriFactors
2278   PetscCall(MatSetType(*B, MATSEQAIJCUSPARSE));
2279 
2280   if (A->boundtocpu && A->bindingpropagates) PetscCall(MatBindToCPU(*B, PETSC_TRUE));
2281   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
2282     PetscCall(MatSetBlockSizesFromMats(*B, A, A));
2283     if (!A->boundtocpu) {
2284       (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJCUSPARSE;
2285       (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJCUSPARSE;
2286     } else {
2287       (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
2288       (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
2289     }
2290     PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]));
2291     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILU]));
2292     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILUDT]));
2293   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
2294     if (!A->boundtocpu) {
2295       (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJCUSPARSE;
2296       (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJCUSPARSE;
2297     } else {
2298       (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
2299       (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
2300     }
2301     PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_CHOLESKY]));
2302     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ICC]));
2303   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor type not supported for CUSPARSE Matrix Types");
2304 
2305   PetscCall(MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL));
2306   (*B)->canuseordering = PETSC_TRUE;
2307   PetscCall(PetscObjectComposeFunction((PetscObject)*B, "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_cusparse));
2308   PetscFunctionReturn(PETSC_SUCCESS);
2309 }
2310 
2311 static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat A)
2312 {
2313   Mat_SeqAIJ         *a    = (Mat_SeqAIJ *)A->data;
2314   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2315 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2316   Mat_SeqAIJCUSPARSETriFactors *fs = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
2317 #endif
2318 
2319   PetscFunctionBegin;
2320   if (A->offloadmask == PETSC_OFFLOAD_GPU) {
2321     PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
2322     if (A->factortype == MAT_FACTOR_NONE) {
2323       CsrMatrix *matrix = (CsrMatrix *)cusp->mat->mat;
2324       PetscCallCUDA(cudaMemcpy(a->a, matrix->values->data().get(), a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
2325     }
2326 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2327     else if (fs->csrVal) {
2328       /* We have a factorized matrix on device and are able to copy it to host */
2329       PetscCallCUDA(cudaMemcpy(a->a, fs->csrVal, a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
2330     }
2331 #endif
2332     else
2333       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for copying this type of factorized matrix from device to host");
2334     PetscCall(PetscLogGpuToCpu(a->nz * sizeof(PetscScalar)));
2335     PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
2336     A->offloadmask = PETSC_OFFLOAD_BOTH;
2337   }
2338   PetscFunctionReturn(PETSC_SUCCESS);
2339 }
2340 
2341 static PetscErrorCode MatSeqAIJGetArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2342 {
2343   PetscFunctionBegin;
2344   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2345   *array = ((Mat_SeqAIJ *)A->data)->a;
2346   PetscFunctionReturn(PETSC_SUCCESS);
2347 }
2348 
2349 static PetscErrorCode MatSeqAIJRestoreArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2350 {
2351   PetscFunctionBegin;
2352   A->offloadmask = PETSC_OFFLOAD_CPU;
2353   *array         = NULL;
2354   PetscFunctionReturn(PETSC_SUCCESS);
2355 }
2356 
2357 static PetscErrorCode MatSeqAIJGetArrayRead_SeqAIJCUSPARSE(Mat A, const PetscScalar *array[])
2358 {
2359   PetscFunctionBegin;
2360   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2361   *array = ((Mat_SeqAIJ *)A->data)->a;
2362   PetscFunctionReturn(PETSC_SUCCESS);
2363 }
2364 
2365 static PetscErrorCode MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE(Mat, const PetscScalar *array[])
2366 {
2367   PetscFunctionBegin;
2368   *array = NULL;
2369   PetscFunctionReturn(PETSC_SUCCESS);
2370 }
2371 
2372 static PetscErrorCode MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2373 {
2374   PetscFunctionBegin;
2375   *array = ((Mat_SeqAIJ *)A->data)->a;
2376   PetscFunctionReturn(PETSC_SUCCESS);
2377 }
2378 
2379 static PetscErrorCode MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2380 {
2381   PetscFunctionBegin;
2382   A->offloadmask = PETSC_OFFLOAD_CPU;
2383   *array         = NULL;
2384   PetscFunctionReturn(PETSC_SUCCESS);
2385 }
2386 
2387 static PetscErrorCode MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE(Mat A, const PetscInt **i, const PetscInt **j, PetscScalar **a, PetscMemType *mtype)
2388 {
2389   Mat_SeqAIJCUSPARSE *cusp;
2390   CsrMatrix          *matrix;
2391 
2392   PetscFunctionBegin;
2393   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2394   PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2395   cusp = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);
2396   PetscCheck(cusp != NULL, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "cusp is NULL");
2397   matrix = (CsrMatrix *)cusp->mat->mat;
2398 
2399   if (i) {
2400 #if !defined(PETSC_USE_64BIT_INDICES)
2401     *i = matrix->row_offsets->data().get();
2402 #else
2403     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
2404 #endif
2405   }
2406   if (j) {
2407 #if !defined(PETSC_USE_64BIT_INDICES)
2408     *j = matrix->column_indices->data().get();
2409 #else
2410     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
2411 #endif
2412   }
2413   if (a) *a = matrix->values->data().get();
2414   if (mtype) *mtype = PETSC_MEMTYPE_CUDA;
2415   PetscFunctionReturn(PETSC_SUCCESS);
2416 }
2417 
2418 PETSC_INTERN PetscErrorCode MatSeqAIJCUSPARSECopyToGPU(Mat A)
2419 {
2420   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
2421   Mat_SeqAIJCUSPARSEMultStruct *matstruct      = cusparsestruct->mat;
2422   Mat_SeqAIJ                   *a              = (Mat_SeqAIJ *)A->data;
2423   PetscInt                      m              = A->rmap->n, *ii, *ridx, tmp;
2424   cusparseStatus_t              stat;
2425   PetscBool                     both = PETSC_TRUE;
2426 
2427   PetscFunctionBegin;
2428   PetscCheck(!A->boundtocpu, PETSC_COMM_SELF, PETSC_ERR_GPU, "Cannot copy to GPU");
2429   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
2430     if (A->nonzerostate == cusparsestruct->nonzerostate && cusparsestruct->format == MAT_CUSPARSE_CSR) { /* Copy values only */
2431       CsrMatrix *matrix;
2432       matrix = (CsrMatrix *)cusparsestruct->mat->mat;
2433 
2434       PetscCheck(!a->nz || a->a, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR values");
2435       PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2436       matrix->values->assign(a->a, a->a + a->nz);
2437       PetscCallCUDA(WaitForCUDA());
2438       PetscCall(PetscLogCpuToGpu(a->nz * sizeof(PetscScalar)));
2439       PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2440       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
2441     } else {
2442       PetscInt nnz;
2443       PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2444       PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusparsestruct->mat, cusparsestruct->format));
2445       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
2446       delete cusparsestruct->workVector;
2447       delete cusparsestruct->rowoffsets_gpu;
2448       cusparsestruct->workVector     = NULL;
2449       cusparsestruct->rowoffsets_gpu = NULL;
2450       try {
2451         if (a->compressedrow.use) {
2452           m    = a->compressedrow.nrows;
2453           ii   = a->compressedrow.i;
2454           ridx = a->compressedrow.rindex;
2455         } else {
2456           m    = A->rmap->n;
2457           ii   = a->i;
2458           ridx = NULL;
2459         }
2460         PetscCheck(ii, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR row data");
2461         if (!a->a) {
2462           nnz  = ii[m];
2463           both = PETSC_FALSE;
2464         } else nnz = a->nz;
2465         PetscCheck(!nnz || a->j, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR column data");
2466 
2467         /* create cusparse matrix */
2468         cusparsestruct->nrows = m;
2469         matstruct             = new Mat_SeqAIJCUSPARSEMultStruct;
2470         PetscCallCUSPARSE(cusparseCreateMatDescr(&matstruct->descr));
2471         PetscCallCUSPARSE(cusparseSetMatIndexBase(matstruct->descr, CUSPARSE_INDEX_BASE_ZERO));
2472         PetscCallCUSPARSE(cusparseSetMatType(matstruct->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
2473 
2474         PetscCallCUDA(cudaMalloc((void **)&matstruct->alpha_one, sizeof(PetscScalar)));
2475         PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_zero, sizeof(PetscScalar)));
2476         PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_one, sizeof(PetscScalar)));
2477         PetscCallCUDA(cudaMemcpy(matstruct->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2478         PetscCallCUDA(cudaMemcpy(matstruct->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2479         PetscCallCUDA(cudaMemcpy(matstruct->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2480         PetscCallCUSPARSE(cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE));
2481 
2482         /* Build a hybrid/ellpack matrix if this option is chosen for the storage */
2483         if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
2484           /* set the matrix */
2485           CsrMatrix *mat   = new CsrMatrix;
2486           mat->num_rows    = m;
2487           mat->num_cols    = A->cmap->n;
2488           mat->num_entries = nnz;
2489           PetscCallCXX(mat->row_offsets = new THRUSTINTARRAY32(m + 1));
2490           mat->row_offsets->assign(ii, ii + m + 1);
2491 
2492           PetscCallCXX(mat->column_indices = new THRUSTINTARRAY32(nnz));
2493           mat->column_indices->assign(a->j, a->j + nnz);
2494 
2495           PetscCallCXX(mat->values = new THRUSTARRAY(nnz));
2496           if (a->a) mat->values->assign(a->a, a->a + nnz);
2497 
2498           /* assign the pointer */
2499           matstruct->mat = mat;
2500 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2501           if (mat->num_rows) { /* cusparse errors on empty matrices! */
2502             stat = cusparseCreateCsr(&matstruct->matDescr, mat->num_rows, mat->num_cols, mat->num_entries, mat->row_offsets->data().get(), mat->column_indices->data().get(), mat->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx types due to THRUSTINTARRAY32 */
2503                                      CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
2504             PetscCallCUSPARSE(stat);
2505           }
2506 #endif
2507         } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
2508 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2509           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
2510 #else
2511           CsrMatrix *mat   = new CsrMatrix;
2512           mat->num_rows    = m;
2513           mat->num_cols    = A->cmap->n;
2514           mat->num_entries = nnz;
2515           PetscCallCXX(mat->row_offsets = new THRUSTINTARRAY32(m + 1));
2516           mat->row_offsets->assign(ii, ii + m + 1);
2517 
2518           PetscCallCXX(mat->column_indices = new THRUSTINTARRAY32(nnz));
2519           mat->column_indices->assign(a->j, a->j + nnz);
2520 
2521           PetscCallCXX(mat->values = new THRUSTARRAY(nnz));
2522           if (a->a) mat->values->assign(a->a, a->a + nnz);
2523 
2524           cusparseHybMat_t hybMat;
2525           PetscCallCUSPARSE(cusparseCreateHybMat(&hybMat));
2526           cusparseHybPartition_t partition = cusparsestruct->format == MAT_CUSPARSE_ELL ? CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
2527           stat                             = cusparse_csr2hyb(cusparsestruct->handle, mat->num_rows, mat->num_cols, matstruct->descr, mat->values->data().get(), mat->row_offsets->data().get(), mat->column_indices->data().get(), hybMat, 0, partition);
2528           PetscCallCUSPARSE(stat);
2529           /* assign the pointer */
2530           matstruct->mat = hybMat;
2531 
2532           if (mat) {
2533             if (mat->values) delete (THRUSTARRAY *)mat->values;
2534             if (mat->column_indices) delete (THRUSTINTARRAY32 *)mat->column_indices;
2535             if (mat->row_offsets) delete (THRUSTINTARRAY32 *)mat->row_offsets;
2536             delete (CsrMatrix *)mat;
2537           }
2538 #endif
2539         }
2540 
2541         /* assign the compressed row indices */
2542         if (a->compressedrow.use) {
2543           PetscCallCXX(cusparsestruct->workVector = new THRUSTARRAY(m));
2544           PetscCallCXX(matstruct->cprowIndices = new THRUSTINTARRAY(m));
2545           matstruct->cprowIndices->assign(ridx, ridx + m);
2546           tmp = m;
2547         } else {
2548           cusparsestruct->workVector = NULL;
2549           matstruct->cprowIndices    = NULL;
2550           tmp                        = 0;
2551         }
2552         PetscCall(PetscLogCpuToGpu(((m + 1) + (a->nz)) * sizeof(int) + tmp * sizeof(PetscInt) + (3 + (a->nz)) * sizeof(PetscScalar)));
2553 
2554         /* assign the pointer */
2555         cusparsestruct->mat = matstruct;
2556       } catch (char *ex) {
2557         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
2558       }
2559       PetscCallCUDA(WaitForCUDA());
2560       PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2561       cusparsestruct->nonzerostate = A->nonzerostate;
2562     }
2563     if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
2564   }
2565   PetscFunctionReturn(PETSC_SUCCESS);
2566 }
2567 
2568 struct VecCUDAPlusEquals {
2569   template <typename Tuple>
2570   __host__ __device__ void operator()(Tuple t)
2571   {
2572     thrust::get<1>(t) = thrust::get<1>(t) + thrust::get<0>(t);
2573   }
2574 };
2575 
2576 struct VecCUDAEquals {
2577   template <typename Tuple>
2578   __host__ __device__ void operator()(Tuple t)
2579   {
2580     thrust::get<1>(t) = thrust::get<0>(t);
2581   }
2582 };
2583 
2584 struct VecCUDAEqualsReverse {
2585   template <typename Tuple>
2586   __host__ __device__ void operator()(Tuple t)
2587   {
2588     thrust::get<0>(t) = thrust::get<1>(t);
2589   }
2590 };
2591 
2592 struct MatMatCusparse {
2593   PetscBool      cisdense;
2594   PetscScalar   *Bt;
2595   Mat            X;
2596   PetscBool      reusesym; /* Cusparse does not have split symbolic and numeric phases for sparse matmat operations */
2597   PetscLogDouble flops;
2598   CsrMatrix     *Bcsr;
2599 
2600 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2601   cusparseSpMatDescr_t matSpBDescr;
2602   PetscBool            initialized; /* C = alpha op(A) op(B) + beta C */
2603   cusparseDnMatDescr_t matBDescr;
2604   cusparseDnMatDescr_t matCDescr;
2605   PetscInt             Blda, Clda; /* Record leading dimensions of B and C here to detect changes*/
2606   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2607   void *dBuffer4;
2608   void *dBuffer5;
2609   #endif
2610   size_t                mmBufferSize;
2611   void                 *mmBuffer;
2612   void                 *mmBuffer2; /* SpGEMM WorkEstimation buffer */
2613   cusparseSpGEMMDescr_t spgemmDesc;
2614 #endif
2615 };
2616 
2617 static PetscErrorCode MatDestroy_MatMatCusparse(void *data)
2618 {
2619   MatMatCusparse *mmdata = (MatMatCusparse *)data;
2620 
2621   PetscFunctionBegin;
2622   PetscCallCUDA(cudaFree(mmdata->Bt));
2623   delete mmdata->Bcsr;
2624 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2625   if (mmdata->matSpBDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mmdata->matSpBDescr));
2626   if (mmdata->matBDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
2627   if (mmdata->matCDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
2628   if (mmdata->spgemmDesc) PetscCallCUSPARSE(cusparseSpGEMM_destroyDescr(mmdata->spgemmDesc));
2629   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2630   if (mmdata->dBuffer4) PetscCallCUDA(cudaFree(mmdata->dBuffer4));
2631   if (mmdata->dBuffer5) PetscCallCUDA(cudaFree(mmdata->dBuffer5));
2632   #endif
2633   if (mmdata->mmBuffer) PetscCallCUDA(cudaFree(mmdata->mmBuffer));
2634   if (mmdata->mmBuffer2) PetscCallCUDA(cudaFree(mmdata->mmBuffer2));
2635 #endif
2636   PetscCall(MatDestroy(&mmdata->X));
2637   PetscCall(PetscFree(data));
2638   PetscFunctionReturn(PETSC_SUCCESS);
2639 }
2640 
2641 #include <../src/mat/impls/dense/seq/dense.h> // MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal()
2642 
2643 static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
2644 {
2645   Mat_Product                  *product = C->product;
2646   Mat                           A, B;
2647   PetscInt                      m, n, blda, clda;
2648   PetscBool                     flg, biscuda;
2649   Mat_SeqAIJCUSPARSE           *cusp;
2650   cusparseStatus_t              stat;
2651   cusparseOperation_t           opA;
2652   const PetscScalar            *barray;
2653   PetscScalar                  *carray;
2654   MatMatCusparse               *mmdata;
2655   Mat_SeqAIJCUSPARSEMultStruct *mat;
2656   CsrMatrix                    *csrmat;
2657 
2658   PetscFunctionBegin;
2659   MatCheckProduct(C, 1);
2660   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
2661   mmdata = (MatMatCusparse *)product->data;
2662   A      = product->A;
2663   B      = product->B;
2664   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2665   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2666   /* currently CopyToGpu does not copy if the matrix is bound to CPU
2667      Instead of silently accepting the wrong answer, I prefer to raise the error */
2668   PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2669   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2670   cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2671   switch (product->type) {
2672   case MATPRODUCT_AB:
2673   case MATPRODUCT_PtAP:
2674     mat = cusp->mat;
2675     opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2676     m   = A->rmap->n;
2677     n   = B->cmap->n;
2678     break;
2679   case MATPRODUCT_AtB:
2680     if (!A->form_explicit_transpose) {
2681       mat = cusp->mat;
2682       opA = CUSPARSE_OPERATION_TRANSPOSE;
2683     } else {
2684       PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
2685       mat = cusp->matTranspose;
2686       opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2687     }
2688     m = A->cmap->n;
2689     n = B->cmap->n;
2690     break;
2691   case MATPRODUCT_ABt:
2692   case MATPRODUCT_RARt:
2693     mat = cusp->mat;
2694     opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2695     m   = A->rmap->n;
2696     n   = B->rmap->n;
2697     break;
2698   default:
2699     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2700   }
2701   PetscCheck(mat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing Mat_SeqAIJCUSPARSEMultStruct");
2702   csrmat = (CsrMatrix *)mat->mat;
2703   /* if the user passed a CPU matrix, copy the data to the GPU */
2704   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSECUDA, &biscuda));
2705   if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSECUDA, MAT_INPLACE_MATRIX, &B));
2706   PetscCall(MatDenseGetArrayReadAndMemType(B, &barray, nullptr));
2707 
2708   PetscCall(MatDenseGetLDA(B, &blda));
2709   if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
2710     PetscCall(MatDenseGetArrayWriteAndMemType(mmdata->X, &carray, nullptr));
2711     PetscCall(MatDenseGetLDA(mmdata->X, &clda));
2712   } else {
2713     PetscCall(MatDenseGetArrayWriteAndMemType(C, &carray, nullptr));
2714     PetscCall(MatDenseGetLDA(C, &clda));
2715   }
2716 
2717   PetscCall(PetscLogGpuTimeBegin());
2718 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2719   cusparseOperation_t opB = (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) ? CUSPARSE_OPERATION_TRANSPOSE : CUSPARSE_OPERATION_NON_TRANSPOSE;
2720   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0)
2721   cusparseSpMatDescr_t &matADescr = mat->matDescr_SpMM[opA];
2722   #else
2723   cusparseSpMatDescr_t &matADescr = mat->matDescr;
2724   #endif
2725 
2726   /* (re)allocate mmBuffer if not initialized or LDAs are different */
2727   if (!mmdata->initialized || mmdata->Blda != blda || mmdata->Clda != clda) {
2728     size_t mmBufferSize;
2729     if (mmdata->initialized && mmdata->Blda != blda) {
2730       PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
2731       mmdata->matBDescr = NULL;
2732     }
2733     if (!mmdata->matBDescr) {
2734       PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matBDescr, B->rmap->n, B->cmap->n, blda, (void *)barray, cusparse_scalartype, CUSPARSE_ORDER_COL));
2735       mmdata->Blda = blda;
2736     }
2737 
2738     if (mmdata->initialized && mmdata->Clda != clda) {
2739       PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
2740       mmdata->matCDescr = NULL;
2741     }
2742     if (!mmdata->matCDescr) { /* matCDescr is for C or mmdata->X */
2743       PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matCDescr, m, n, clda, (void *)carray, cusparse_scalartype, CUSPARSE_ORDER_COL));
2744       mmdata->Clda = clda;
2745     }
2746 
2747   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0) // tested up to 12.6.0
2748     if (matADescr) {
2749       PetscCallCUSPARSE(cusparseDestroySpMat(matADescr)); // Because I find I could not reuse matADescr. It could be a cusparse bug
2750       matADescr = NULL;
2751     }
2752   #endif
2753 
2754     if (!matADescr) {
2755       stat = cusparseCreateCsr(&matADescr, csrmat->num_rows, csrmat->num_cols, csrmat->num_entries, csrmat->row_offsets->data().get(), csrmat->column_indices->data().get(), csrmat->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx types due to THRUSTINTARRAY32 */
2756                                CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
2757       PetscCallCUSPARSE(stat);
2758     }
2759 
2760     PetscCallCUSPARSE(cusparseSpMM_bufferSize(cusp->handle, opA, opB, mat->alpha_one, matADescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, &mmBufferSize));
2761 
2762     if ((mmdata->mmBuffer && mmdata->mmBufferSize < mmBufferSize) || !mmdata->mmBuffer) {
2763       PetscCallCUDA(cudaFree(mmdata->mmBuffer));
2764       PetscCallCUDA(cudaMalloc(&mmdata->mmBuffer, mmBufferSize));
2765       mmdata->mmBufferSize = mmBufferSize;
2766     }
2767 
2768   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0) // the _preprocess was added in 11.2.1, but PETSc worked without it until 12.4.0
2769     PetscCallCUSPARSE(cusparseSpMM_preprocess(cusp->handle, opA, opB, mat->alpha_one, matADescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, mmdata->mmBuffer));
2770   #endif
2771 
2772     mmdata->initialized = PETSC_TRUE;
2773   } else {
2774     /* to be safe, always update pointers of the mats */
2775     PetscCallCUSPARSE(cusparseSpMatSetValues(matADescr, csrmat->values->data().get()));
2776     PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matBDescr, (void *)barray));
2777     PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matCDescr, (void *)carray));
2778   }
2779 
2780   /* do cusparseSpMM, which supports transpose on B */
2781   PetscCallCUSPARSE(cusparseSpMM(cusp->handle, opA, opB, mat->alpha_one, matADescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, mmdata->mmBuffer));
2782 #else
2783   PetscInt k;
2784   /* cusparseXcsrmm does not support transpose on B */
2785   if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) {
2786     cublasHandle_t cublasv2handle;
2787     cublasStatus_t cerr;
2788 
2789     PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
2790     cerr = cublasXgeam(cublasv2handle, CUBLAS_OP_T, CUBLAS_OP_T, B->cmap->n, B->rmap->n, &PETSC_CUSPARSE_ONE, barray, blda, &PETSC_CUSPARSE_ZERO, barray, blda, mmdata->Bt, B->cmap->n);
2791     PetscCallCUBLAS(cerr);
2792     blda = B->cmap->n;
2793     k    = B->cmap->n;
2794   } else {
2795     k = B->rmap->n;
2796   }
2797 
2798   /* perform the MatMat operation, op(A) is m x k, op(B) is k x n */
2799   stat = cusparse_csr_spmm(cusp->handle, opA, m, n, k, csrmat->num_entries, mat->alpha_one, mat->descr, csrmat->values->data().get(), csrmat->row_offsets->data().get(), csrmat->column_indices->data().get(), mmdata->Bt ? mmdata->Bt : barray, blda, mat->beta_zero, carray, clda);
2800   PetscCallCUSPARSE(stat);
2801 #endif
2802   PetscCall(PetscLogGpuTimeEnd());
2803   PetscCall(PetscLogGpuFlops(n * 2.0 * csrmat->num_entries));
2804   PetscCall(MatDenseRestoreArrayReadAndMemType(B, &barray));
2805   if (product->type == MATPRODUCT_RARt) {
2806     PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
2807     PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_FALSE, PETSC_FALSE));
2808   } else if (product->type == MATPRODUCT_PtAP) {
2809     PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
2810     PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_TRUE, PETSC_FALSE));
2811   } else {
2812     PetscCall(MatDenseRestoreArrayWriteAndMemType(C, &carray));
2813   }
2814   if (mmdata->cisdense) PetscCall(MatConvert(C, MATSEQDENSE, MAT_INPLACE_MATRIX, &C));
2815   if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSE, MAT_INPLACE_MATRIX, &B));
2816   PetscFunctionReturn(PETSC_SUCCESS);
2817 }
2818 
2819 static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
2820 {
2821   Mat_Product        *product = C->product;
2822   Mat                 A, B;
2823   PetscInt            m, n;
2824   PetscBool           cisdense, flg;
2825   MatMatCusparse     *mmdata;
2826   Mat_SeqAIJCUSPARSE *cusp;
2827 
2828   PetscFunctionBegin;
2829   MatCheckProduct(C, 1);
2830   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
2831   A = product->A;
2832   B = product->B;
2833   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2834   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2835   cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2836   PetscCheck(cusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2837   switch (product->type) {
2838   case MATPRODUCT_AB:
2839     m = A->rmap->n;
2840     n = B->cmap->n;
2841     PetscCall(MatSetBlockSizesFromMats(C, A, B));
2842     break;
2843   case MATPRODUCT_AtB:
2844     m = A->cmap->n;
2845     n = B->cmap->n;
2846     if (A->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, A->cmap->bs));
2847     if (B->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, B->cmap->bs));
2848     break;
2849   case MATPRODUCT_ABt:
2850     m = A->rmap->n;
2851     n = B->rmap->n;
2852     if (A->rmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, A->rmap->bs));
2853     if (B->rmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, B->rmap->bs));
2854     break;
2855   case MATPRODUCT_PtAP:
2856     m = B->cmap->n;
2857     n = B->cmap->n;
2858     if (B->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, B->cmap->bs));
2859     if (B->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, B->cmap->bs));
2860     break;
2861   case MATPRODUCT_RARt:
2862     m = B->rmap->n;
2863     n = B->rmap->n;
2864     if (B->rmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, B->rmap->bs));
2865     if (B->rmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, B->rmap->bs));
2866     break;
2867   default:
2868     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2869   }
2870   PetscCall(MatSetSizes(C, m, n, m, n));
2871   /* if C is of type MATSEQDENSE (CPU), perform the operation on the GPU and then copy on the CPU */
2872   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &cisdense));
2873   PetscCall(MatSetType(C, MATSEQDENSECUDA));
2874 
2875   /* product data */
2876   PetscCall(PetscNew(&mmdata));
2877   mmdata->cisdense = cisdense;
2878 #if PETSC_PKG_CUDA_VERSION_LT(11, 0, 0)
2879   /* cusparseXcsrmm does not support transpose on B, so we allocate buffer to store B^T */
2880   if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) PetscCallCUDA(cudaMalloc((void **)&mmdata->Bt, (size_t)B->rmap->n * (size_t)B->cmap->n * sizeof(PetscScalar)));
2881 #endif
2882   /* for these products we need intermediate storage */
2883   if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
2884     PetscCall(MatCreate(PetscObjectComm((PetscObject)C), &mmdata->X));
2885     PetscCall(MatSetType(mmdata->X, MATSEQDENSECUDA));
2886     if (product->type == MATPRODUCT_RARt) { /* do not preallocate, since the first call to MatDenseCUDAGetArray will preallocate on the GPU for us */
2887       PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->rmap->n, A->rmap->n, B->rmap->n));
2888     } else {
2889       PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->cmap->n, A->rmap->n, B->cmap->n));
2890     }
2891   }
2892   C->product->data    = mmdata;
2893   C->product->destroy = MatDestroy_MatMatCusparse;
2894 
2895   C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA;
2896   PetscFunctionReturn(PETSC_SUCCESS);
2897 }
2898 
2899 static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
2900 {
2901   Mat_Product                  *product = C->product;
2902   Mat                           A, B;
2903   Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
2904   Mat_SeqAIJ                   *c = (Mat_SeqAIJ *)C->data;
2905   Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
2906   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
2907   PetscBool                     flg;
2908   cusparseStatus_t              stat;
2909   MatProductType                ptype;
2910   MatMatCusparse               *mmdata;
2911 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2912   cusparseSpMatDescr_t BmatSpDescr;
2913 #endif
2914   cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */
2915 
2916   PetscFunctionBegin;
2917   MatCheckProduct(C, 1);
2918   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
2919   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQAIJCUSPARSE, &flg));
2920   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for C of type %s", ((PetscObject)C)->type_name);
2921   mmdata = (MatMatCusparse *)C->product->data;
2922   A      = product->A;
2923   B      = product->B;
2924   if (mmdata->reusesym) { /* this happens when api_user is true, meaning that the matrix values have been already computed in the MatProductSymbolic phase */
2925     mmdata->reusesym = PETSC_FALSE;
2926     Ccusp            = (Mat_SeqAIJCUSPARSE *)C->spptr;
2927     PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2928     Cmat = Ccusp->mat;
2929     PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[C->product->type]);
2930     Ccsr = (CsrMatrix *)Cmat->mat;
2931     PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
2932     goto finalize;
2933   }
2934   if (!c->nz) goto finalize;
2935   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2936   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2937   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
2938   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
2939   PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2940   PetscCheck(!B->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2941   Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2942   Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
2943   Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
2944   PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2945   PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2946   PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2947   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2948   PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
2949 
2950   ptype = product->type;
2951   if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
2952     ptype = MATPRODUCT_AB;
2953     PetscCheck(product->symbolic_used_the_fact_A_is_symmetric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Symbolic should have been built using the fact that A is symmetric");
2954   }
2955   if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
2956     ptype = MATPRODUCT_AB;
2957     PetscCheck(product->symbolic_used_the_fact_B_is_symmetric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Symbolic should have been built using the fact that B is symmetric");
2958   }
2959   switch (ptype) {
2960   case MATPRODUCT_AB:
2961     Amat = Acusp->mat;
2962     Bmat = Bcusp->mat;
2963     break;
2964   case MATPRODUCT_AtB:
2965     Amat = Acusp->matTranspose;
2966     Bmat = Bcusp->mat;
2967     break;
2968   case MATPRODUCT_ABt:
2969     Amat = Acusp->mat;
2970     Bmat = Bcusp->matTranspose;
2971     break;
2972   default:
2973     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2974   }
2975   Cmat = Ccusp->mat;
2976   PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
2977   PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
2978   PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[ptype]);
2979   Acsr = (CsrMatrix *)Amat->mat;
2980   Bcsr = mmdata->Bcsr ? mmdata->Bcsr : (CsrMatrix *)Bmat->mat; /* B may be in compressed row storage */
2981   Ccsr = (CsrMatrix *)Cmat->mat;
2982   PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
2983   PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
2984   PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
2985   PetscCall(PetscLogGpuTimeBegin());
2986 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2987   BmatSpDescr = mmdata->Bcsr ? mmdata->matSpBDescr : Bmat->matDescr; /* B may be in compressed row storage */
2988   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
2989   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2990   stat = cusparseSpGEMMreuse_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
2991   PetscCallCUSPARSE(stat);
2992   #else
2993   stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, mmdata->mmBuffer);
2994   PetscCallCUSPARSE(stat);
2995   stat = cusparseSpGEMM_copy(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
2996   PetscCallCUSPARSE(stat);
2997   #endif
2998 #else
2999   stat = cusparse_csr_spgemm(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->values->data().get(), Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
3000                              Bcsr->values->data().get(), Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->values->data().get(), Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get());
3001   PetscCallCUSPARSE(stat);
3002 #endif
3003   PetscCall(PetscLogGpuFlops(mmdata->flops));
3004   PetscCallCUDA(WaitForCUDA());
3005   PetscCall(PetscLogGpuTimeEnd());
3006   C->offloadmask = PETSC_OFFLOAD_GPU;
3007 finalize:
3008   /* shorter version of MatAssemblyEnd_SeqAIJ */
3009   PetscCall(PetscInfo(C, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; storage space: 0 unneeded,%" PetscInt_FMT " used\n", C->rmap->n, C->cmap->n, c->nz));
3010   PetscCall(PetscInfo(C, "Number of mallocs during MatSetValues() is 0\n"));
3011   PetscCall(PetscInfo(C, "Maximum nonzeros in any row is %" PetscInt_FMT "\n", c->rmax));
3012   c->reallocs = 0;
3013   C->info.mallocs += 0;
3014   C->info.nz_unneeded = 0;
3015   C->assembled = C->was_assembled = PETSC_TRUE;
3016   C->num_ass++;
3017   PetscFunctionReturn(PETSC_SUCCESS);
3018 }
3019 
3020 static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
3021 {
3022   Mat_Product                  *product = C->product;
3023   Mat                           A, B;
3024   Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
3025   Mat_SeqAIJ                   *a, *b, *c;
3026   Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
3027   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
3028   PetscInt                      i, j, m, n, k;
3029   PetscBool                     flg;
3030   cusparseStatus_t              stat;
3031   MatProductType                ptype;
3032   MatMatCusparse               *mmdata;
3033   PetscLogDouble                flops;
3034   PetscBool                     biscompressed, ciscompressed;
3035 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3036   int64_t              C_num_rows1, C_num_cols1, C_nnz1;
3037   cusparseSpMatDescr_t BmatSpDescr;
3038 #else
3039   int cnz;
3040 #endif
3041   cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */
3042 
3043   PetscFunctionBegin;
3044   MatCheckProduct(C, 1);
3045   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
3046   A = product->A;
3047   B = product->B;
3048   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
3049   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
3050   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
3051   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
3052   a = (Mat_SeqAIJ *)A->data;
3053   b = (Mat_SeqAIJ *)B->data;
3054   /* product data */
3055   PetscCall(PetscNew(&mmdata));
3056   C->product->data    = mmdata;
3057   C->product->destroy = MatDestroy_MatMatCusparse;
3058 
3059   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
3060   PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
3061   Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr; /* Access spptr after MatSeqAIJCUSPARSECopyToGPU, not before */
3062   Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
3063   PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
3064   PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
3065 
3066   ptype = product->type;
3067   if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
3068     ptype                                          = MATPRODUCT_AB;
3069     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
3070   }
3071   if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
3072     ptype                                          = MATPRODUCT_AB;
3073     product->symbolic_used_the_fact_B_is_symmetric = PETSC_TRUE;
3074   }
3075   biscompressed = PETSC_FALSE;
3076   ciscompressed = PETSC_FALSE;
3077   switch (ptype) {
3078   case MATPRODUCT_AB:
3079     m    = A->rmap->n;
3080     n    = B->cmap->n;
3081     k    = A->cmap->n;
3082     Amat = Acusp->mat;
3083     Bmat = Bcusp->mat;
3084     if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
3085     if (b->compressedrow.use) biscompressed = PETSC_TRUE;
3086     break;
3087   case MATPRODUCT_AtB:
3088     m = A->cmap->n;
3089     n = B->cmap->n;
3090     k = A->rmap->n;
3091     PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
3092     Amat = Acusp->matTranspose;
3093     Bmat = Bcusp->mat;
3094     if (b->compressedrow.use) biscompressed = PETSC_TRUE;
3095     break;
3096   case MATPRODUCT_ABt:
3097     m = A->rmap->n;
3098     n = B->rmap->n;
3099     k = A->cmap->n;
3100     PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
3101     Amat = Acusp->mat;
3102     Bmat = Bcusp->matTranspose;
3103     if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
3104     break;
3105   default:
3106     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
3107   }
3108 
3109   /* create cusparse matrix */
3110   PetscCall(MatSetSizes(C, m, n, m, n));
3111   PetscCall(MatSetType(C, MATSEQAIJCUSPARSE));
3112   c     = (Mat_SeqAIJ *)C->data;
3113   Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
3114   Cmat  = new Mat_SeqAIJCUSPARSEMultStruct;
3115   Ccsr  = new CsrMatrix;
3116 
3117   c->compressedrow.use = ciscompressed;
3118   if (c->compressedrow.use) { /* if a is in compressed row, than c will be in compressed row format */
3119     c->compressedrow.nrows = a->compressedrow.nrows;
3120     PetscCall(PetscMalloc2(c->compressedrow.nrows + 1, &c->compressedrow.i, c->compressedrow.nrows, &c->compressedrow.rindex));
3121     PetscCall(PetscArraycpy(c->compressedrow.rindex, a->compressedrow.rindex, c->compressedrow.nrows));
3122     Ccusp->workVector  = new THRUSTARRAY(c->compressedrow.nrows);
3123     Cmat->cprowIndices = new THRUSTINTARRAY(c->compressedrow.nrows);
3124     Cmat->cprowIndices->assign(c->compressedrow.rindex, c->compressedrow.rindex + c->compressedrow.nrows);
3125   } else {
3126     c->compressedrow.nrows  = 0;
3127     c->compressedrow.i      = NULL;
3128     c->compressedrow.rindex = NULL;
3129     Ccusp->workVector       = NULL;
3130     Cmat->cprowIndices      = NULL;
3131   }
3132   Ccusp->nrows      = ciscompressed ? c->compressedrow.nrows : m;
3133   Ccusp->mat        = Cmat;
3134   Ccusp->mat->mat   = Ccsr;
3135   Ccsr->num_rows    = Ccusp->nrows;
3136   Ccsr->num_cols    = n;
3137   Ccsr->row_offsets = new THRUSTINTARRAY32(Ccusp->nrows + 1);
3138   PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
3139   PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
3140   PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
3141   PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
3142   PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
3143   PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
3144   PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3145   PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3146   PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3147   if (!Ccsr->num_rows || !Ccsr->num_cols || !a->nz || !b->nz) { /* cusparse raise errors in different calls when matrices have zero rows/columns! */
3148     PetscCallThrust(thrust::fill(thrust::device, Ccsr->row_offsets->begin(), Ccsr->row_offsets->end(), 0));
3149     c->nz                = 0;
3150     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3151     Ccsr->values         = new THRUSTARRAY(c->nz);
3152     goto finalizesym;
3153   }
3154 
3155   PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
3156   PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
3157   Acsr = (CsrMatrix *)Amat->mat;
3158   if (!biscompressed) {
3159     Bcsr = (CsrMatrix *)Bmat->mat;
3160 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3161     BmatSpDescr = Bmat->matDescr;
3162 #endif
3163   } else { /* we need to use row offsets for the full matrix */
3164     CsrMatrix *cBcsr     = (CsrMatrix *)Bmat->mat;
3165     Bcsr                 = new CsrMatrix;
3166     Bcsr->num_rows       = B->rmap->n;
3167     Bcsr->num_cols       = cBcsr->num_cols;
3168     Bcsr->num_entries    = cBcsr->num_entries;
3169     Bcsr->column_indices = cBcsr->column_indices;
3170     Bcsr->values         = cBcsr->values;
3171     if (!Bcusp->rowoffsets_gpu) {
3172       Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
3173       Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
3174       PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
3175     }
3176     Bcsr->row_offsets = Bcusp->rowoffsets_gpu;
3177     mmdata->Bcsr      = Bcsr;
3178 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3179     if (Bcsr->num_rows && Bcsr->num_cols) {
3180       stat = cusparseCreateCsr(&mmdata->matSpBDescr, Bcsr->num_rows, Bcsr->num_cols, Bcsr->num_entries, Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Bcsr->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
3181       PetscCallCUSPARSE(stat);
3182     }
3183     BmatSpDescr = mmdata->matSpBDescr;
3184 #endif
3185   }
3186   PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
3187   PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
3188   /* precompute flops count */
3189   if (ptype == MATPRODUCT_AB) {
3190     for (i = 0, flops = 0; i < A->rmap->n; i++) {
3191       const PetscInt st = a->i[i];
3192       const PetscInt en = a->i[i + 1];
3193       for (j = st; j < en; j++) {
3194         const PetscInt brow = a->j[j];
3195         flops += 2. * (b->i[brow + 1] - b->i[brow]);
3196       }
3197     }
3198   } else if (ptype == MATPRODUCT_AtB) {
3199     for (i = 0, flops = 0; i < A->rmap->n; i++) {
3200       const PetscInt anzi = a->i[i + 1] - a->i[i];
3201       const PetscInt bnzi = b->i[i + 1] - b->i[i];
3202       flops += (2. * anzi) * bnzi;
3203     }
3204   } else { /* TODO */
3205     flops = 0.;
3206   }
3207 
3208   mmdata->flops = flops;
3209   PetscCall(PetscLogGpuTimeBegin());
3210 
3211 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3212   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
3213   // cuda-12.2 requires non-null csrRowOffsets
3214   stat = cusparseCreateCsr(&Cmat->matDescr, Ccsr->num_rows, Ccsr->num_cols, 0, Ccsr->row_offsets->data().get(), NULL, NULL, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
3215   PetscCallCUSPARSE(stat);
3216   PetscCallCUSPARSE(cusparseSpGEMM_createDescr(&mmdata->spgemmDesc));
3217   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
3218   {
3219     /* cusparseSpGEMMreuse has more reasonable APIs than cusparseSpGEMM, so we prefer to use it.
3220      We follow the sample code at https://github.com/NVIDIA/CUDALibrarySamples/blob/master/cuSPARSE/spgemm_reuse
3221   */
3222     void *dBuffer1 = NULL;
3223     void *dBuffer2 = NULL;
3224     void *dBuffer3 = NULL;
3225     /* dBuffer4, dBuffer5 are needed by cusparseSpGEMMreuse_compute, and therefore are stored in mmdata */
3226     size_t bufferSize1 = 0;
3227     size_t bufferSize2 = 0;
3228     size_t bufferSize3 = 0;
3229     size_t bufferSize4 = 0;
3230     size_t bufferSize5 = 0;
3231 
3232     /* ask bufferSize1 bytes for external memory */
3233     stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, NULL);
3234     PetscCallCUSPARSE(stat);
3235     PetscCallCUDA(cudaMalloc((void **)&dBuffer1, bufferSize1));
3236     /* inspect the matrices A and B to understand the memory requirement for the next step */
3237     stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, dBuffer1);
3238     PetscCallCUSPARSE(stat);
3239 
3240     stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, NULL, &bufferSize3, NULL, &bufferSize4, NULL);
3241     PetscCallCUSPARSE(stat);
3242     PetscCallCUDA(cudaMalloc((void **)&dBuffer2, bufferSize2));
3243     PetscCallCUDA(cudaMalloc((void **)&dBuffer3, bufferSize3));
3244     PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer4, bufferSize4));
3245     stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, dBuffer2, &bufferSize3, dBuffer3, &bufferSize4, mmdata->dBuffer4);
3246     PetscCallCUSPARSE(stat);
3247     PetscCallCUDA(cudaFree(dBuffer1));
3248     PetscCallCUDA(cudaFree(dBuffer2));
3249 
3250     /* get matrix C non-zero entries C_nnz1 */
3251     PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
3252     c->nz = (PetscInt)C_nnz1;
3253     /* allocate matrix C */
3254     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3255     PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3256     Ccsr->values = new THRUSTARRAY(c->nz);
3257     PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3258     /* update matC with the new pointers */
3259     stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
3260     PetscCallCUSPARSE(stat);
3261 
3262     stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, NULL);
3263     PetscCallCUSPARSE(stat);
3264     PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer5, bufferSize5));
3265     stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, mmdata->dBuffer5);
3266     PetscCallCUSPARSE(stat);
3267     PetscCallCUDA(cudaFree(dBuffer3));
3268     stat = cusparseSpGEMMreuse_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
3269     PetscCallCUSPARSE(stat);
3270     PetscCall(PetscInfo(C, "Buffer sizes for type %s, result %" PetscInt_FMT " x %" PetscInt_FMT " (k %" PetscInt_FMT ", nzA %" PetscInt_FMT ", nzB %" PetscInt_FMT ", nzC %" PetscInt_FMT ") are: %ldKB %ldKB\n", MatProductTypes[ptype], m, n, k, a->nz, b->nz, c->nz, bufferSize4 / 1024, bufferSize5 / 1024));
3271   }
3272   #else
3273   size_t bufSize2;
3274   /* ask bufferSize bytes for external memory */
3275   stat = cusparseSpGEMM_workEstimation(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufSize2, NULL);
3276   PetscCallCUSPARSE(stat);
3277   PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer2, bufSize2));
3278   /* inspect the matrices A and B to understand the memory requirement for the next step */
3279   stat = cusparseSpGEMM_workEstimation(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufSize2, mmdata->mmBuffer2);
3280   PetscCallCUSPARSE(stat);
3281   /* ask bufferSize again bytes for external memory */
3282   stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, NULL);
3283   PetscCallCUSPARSE(stat);
3284   /* The CUSPARSE documentation is not clear, nor the API
3285      We need both buffers to perform the operations properly!
3286      mmdata->mmBuffer2 does not appear anywhere in the compute/copy API
3287      it only appears for the workEstimation stuff, but it seems it is needed in compute, so probably the address
3288      is stored in the descriptor! What a messy API... */
3289   PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer, mmdata->mmBufferSize));
3290   /* compute the intermediate product of A * B */
3291   stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, mmdata->mmBuffer);
3292   PetscCallCUSPARSE(stat);
3293   /* get matrix C non-zero entries C_nnz1 */
3294   PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
3295   c->nz = (PetscInt)C_nnz1;
3296   PetscCall(PetscInfo(C, "Buffer sizes for type %s, result %" PetscInt_FMT " x %" PetscInt_FMT " (k %" PetscInt_FMT ", nzA %" PetscInt_FMT ", nzB %" PetscInt_FMT ", nzC %" PetscInt_FMT ") are: %ldKB %ldKB\n", MatProductTypes[ptype], m, n, k, a->nz, b->nz, c->nz, bufSize2 / 1024,
3297                       mmdata->mmBufferSize / 1024));
3298   Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3299   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3300   Ccsr->values = new THRUSTARRAY(c->nz);
3301   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3302   stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
3303   PetscCallCUSPARSE(stat);
3304   stat = cusparseSpGEMM_copy(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
3305   PetscCallCUSPARSE(stat);
3306   #endif // PETSC_PKG_CUDA_VERSION_GE(11,4,0)
3307 #else
3308   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_HOST));
3309   stat = cusparseXcsrgemmNnz(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
3310                              Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->row_offsets->data().get(), &cnz);
3311   PetscCallCUSPARSE(stat);
3312   c->nz                = cnz;
3313   Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3314   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3315   Ccsr->values = new THRUSTARRAY(c->nz);
3316   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3317 
3318   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
3319   /* with the old gemm interface (removed from 11.0 on) we cannot compute the symbolic factorization only.
3320      I have tried using the gemm2 interface (alpha * A * B + beta * D), which allows to do symbolic by passing NULL for values, but it seems quite buggy when
3321      D is NULL, despite the fact that CUSPARSE documentation claims it is supported! */
3322   stat = cusparse_csr_spgemm(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->values->data().get(), Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
3323                              Bcsr->values->data().get(), Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->values->data().get(), Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get());
3324   PetscCallCUSPARSE(stat);
3325 #endif
3326   PetscCall(PetscLogGpuFlops(mmdata->flops));
3327   PetscCall(PetscLogGpuTimeEnd());
3328 finalizesym:
3329   c->free_a = PETSC_TRUE;
3330   PetscCall(PetscShmgetAllocateArray(c->nz, sizeof(PetscInt), (void **)&c->j));
3331   PetscCall(PetscShmgetAllocateArray(m + 1, sizeof(PetscInt), (void **)&c->i));
3332   c->free_ij = PETSC_TRUE;
3333   if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
3334     PetscInt      *d_i = c->i;
3335     THRUSTINTARRAY ii(Ccsr->row_offsets->size());
3336     THRUSTINTARRAY jj(Ccsr->column_indices->size());
3337     ii = *Ccsr->row_offsets;
3338     jj = *Ccsr->column_indices;
3339     if (ciscompressed) d_i = c->compressedrow.i;
3340     PetscCallCUDA(cudaMemcpy(d_i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3341     PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3342   } else {
3343     PetscInt *d_i = c->i;
3344     if (ciscompressed) d_i = c->compressedrow.i;
3345     PetscCallCUDA(cudaMemcpy(d_i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3346     PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3347   }
3348   if (ciscompressed) { /* need to expand host row offsets */
3349     PetscInt r = 0;
3350     c->i[0]    = 0;
3351     for (k = 0; k < c->compressedrow.nrows; k++) {
3352       const PetscInt next = c->compressedrow.rindex[k];
3353       const PetscInt old  = c->compressedrow.i[k];
3354       for (; r < next; r++) c->i[r + 1] = old;
3355     }
3356     for (; r < m; r++) c->i[r + 1] = c->compressedrow.i[c->compressedrow.nrows];
3357   }
3358   PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
3359   PetscCall(PetscMalloc1(m, &c->ilen));
3360   PetscCall(PetscMalloc1(m, &c->imax));
3361   c->maxnz         = c->nz;
3362   c->nonzerorowcnt = 0;
3363   c->rmax          = 0;
3364   for (k = 0; k < m; k++) {
3365     const PetscInt nn = c->i[k + 1] - c->i[k];
3366     c->ilen[k] = c->imax[k] = nn;
3367     c->nonzerorowcnt += (PetscInt)!!nn;
3368     c->rmax = PetscMax(c->rmax, nn);
3369   }
3370   PetscCall(MatMarkDiagonal_SeqAIJ(C));
3371   PetscCall(PetscMalloc1(c->nz, &c->a));
3372   Ccsr->num_entries = c->nz;
3373 
3374   C->nonzerostate++;
3375   PetscCall(PetscLayoutSetUp(C->rmap));
3376   PetscCall(PetscLayoutSetUp(C->cmap));
3377   Ccusp->nonzerostate = C->nonzerostate;
3378   C->offloadmask      = PETSC_OFFLOAD_UNALLOCATED;
3379   C->preallocated     = PETSC_TRUE;
3380   C->assembled        = PETSC_FALSE;
3381   C->was_assembled    = PETSC_FALSE;
3382   if (product->api_user && A->offloadmask == PETSC_OFFLOAD_BOTH && B->offloadmask == PETSC_OFFLOAD_BOTH) { /* flag the matrix C values as computed, so that the numeric phase will only call MatAssembly */
3383     mmdata->reusesym = PETSC_TRUE;
3384     C->offloadmask   = PETSC_OFFLOAD_GPU;
3385   }
3386   C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3387   PetscFunctionReturn(PETSC_SUCCESS);
3388 }
3389 
3390 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat);
3391 
3392 /* handles sparse or dense B */
3393 static PetscErrorCode MatProductSetFromOptions_SeqAIJCUSPARSE(Mat mat)
3394 {
3395   Mat_Product *product = mat->product;
3396   PetscBool    isdense = PETSC_FALSE, Biscusp = PETSC_FALSE, Ciscusp = PETSC_TRUE;
3397 
3398   PetscFunctionBegin;
3399   MatCheckProduct(mat, 1);
3400   PetscCall(PetscObjectBaseTypeCompare((PetscObject)product->B, MATSEQDENSE, &isdense));
3401   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, MATSEQAIJCUSPARSE, &Biscusp));
3402   if (product->type == MATPRODUCT_ABC) {
3403     Ciscusp = PETSC_FALSE;
3404     if (!product->C->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->C, MATSEQAIJCUSPARSE, &Ciscusp));
3405   }
3406   if (Biscusp && Ciscusp) { /* we can always select the CPU backend */
3407     PetscBool usecpu = PETSC_FALSE;
3408     switch (product->type) {
3409     case MATPRODUCT_AB:
3410       if (product->api_user) {
3411         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
3412         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3413         PetscOptionsEnd();
3414       } else {
3415         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
3416         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3417         PetscOptionsEnd();
3418       }
3419       break;
3420     case MATPRODUCT_AtB:
3421       if (product->api_user) {
3422         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
3423         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3424         PetscOptionsEnd();
3425       } else {
3426         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
3427         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3428         PetscOptionsEnd();
3429       }
3430       break;
3431     case MATPRODUCT_PtAP:
3432       if (product->api_user) {
3433         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
3434         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3435         PetscOptionsEnd();
3436       } else {
3437         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
3438         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3439         PetscOptionsEnd();
3440       }
3441       break;
3442     case MATPRODUCT_RARt:
3443       if (product->api_user) {
3444         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatRARt", "Mat");
3445         PetscCall(PetscOptionsBool("-matrart_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3446         PetscOptionsEnd();
3447       } else {
3448         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_RARt", "Mat");
3449         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3450         PetscOptionsEnd();
3451       }
3452       break;
3453     case MATPRODUCT_ABC:
3454       if (product->api_user) {
3455         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMatMult", "Mat");
3456         PetscCall(PetscOptionsBool("-matmatmatmult_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3457         PetscOptionsEnd();
3458       } else {
3459         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_ABC", "Mat");
3460         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3461         PetscOptionsEnd();
3462       }
3463       break;
3464     default:
3465       break;
3466     }
3467     if (usecpu) Biscusp = Ciscusp = PETSC_FALSE;
3468   }
3469   /* dispatch */
3470   if (isdense) {
3471     switch (product->type) {
3472     case MATPRODUCT_AB:
3473     case MATPRODUCT_AtB:
3474     case MATPRODUCT_ABt:
3475     case MATPRODUCT_PtAP:
3476     case MATPRODUCT_RARt:
3477       if (product->A->boundtocpu) {
3478         PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense(mat));
3479       } else {
3480         mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA;
3481       }
3482       break;
3483     case MATPRODUCT_ABC:
3484       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3485       break;
3486     default:
3487       break;
3488     }
3489   } else if (Biscusp && Ciscusp) {
3490     switch (product->type) {
3491     case MATPRODUCT_AB:
3492     case MATPRODUCT_AtB:
3493     case MATPRODUCT_ABt:
3494       mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3495       break;
3496     case MATPRODUCT_PtAP:
3497     case MATPRODUCT_RARt:
3498     case MATPRODUCT_ABC:
3499       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3500       break;
3501     default:
3502       break;
3503     }
3504   } else { /* fallback for AIJ */
3505     PetscCall(MatProductSetFromOptions_SeqAIJ(mat));
3506   }
3507   PetscFunctionReturn(PETSC_SUCCESS);
3508 }
3509 
3510 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3511 {
3512   PetscFunctionBegin;
3513   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_FALSE, PETSC_FALSE));
3514   PetscFunctionReturn(PETSC_SUCCESS);
3515 }
3516 
3517 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3518 {
3519   PetscFunctionBegin;
3520   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_FALSE, PETSC_FALSE));
3521   PetscFunctionReturn(PETSC_SUCCESS);
3522 }
3523 
3524 static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3525 {
3526   PetscFunctionBegin;
3527   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_TRUE));
3528   PetscFunctionReturn(PETSC_SUCCESS);
3529 }
3530 
3531 static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3532 {
3533   PetscFunctionBegin;
3534   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_TRUE));
3535   PetscFunctionReturn(PETSC_SUCCESS);
3536 }
3537 
3538 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3539 {
3540   PetscFunctionBegin;
3541   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_FALSE));
3542   PetscFunctionReturn(PETSC_SUCCESS);
3543 }
3544 
3545 __global__ static void ScatterAdd(PetscInt n, PetscInt *idx, const PetscScalar *x, PetscScalar *y)
3546 {
3547   int i = blockIdx.x * blockDim.x + threadIdx.x;
3548   if (i < n) y[idx[i]] += x[i];
3549 }
3550 
3551 /* z = op(A) x + y. If trans & !herm, op = ^T; if trans & herm, op = ^H; if !trans, op = no-op */
3552 static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz, PetscBool trans, PetscBool herm)
3553 {
3554   Mat_SeqAIJ                   *a              = (Mat_SeqAIJ *)A->data;
3555   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
3556   Mat_SeqAIJCUSPARSEMultStruct *matstruct;
3557   PetscScalar                  *xarray, *zarray, *dptr, *beta, *xptr;
3558   cusparseOperation_t           opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
3559   PetscBool                     compressed;
3560 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3561   PetscInt nx, ny;
3562 #endif
3563 
3564   PetscFunctionBegin;
3565   PetscCheck(!herm || trans, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Hermitian and not transpose not supported");
3566   if (!a->nz) {
3567     if (yy) PetscCall(VecSeq_CUDA::Copy(yy, zz));
3568     else PetscCall(VecSeq_CUDA::Set(zz, 0));
3569     PetscFunctionReturn(PETSC_SUCCESS);
3570   }
3571   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
3572   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
3573   if (!trans) {
3574     matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3575     PetscCheck(matstruct, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "SeqAIJCUSPARSE does not have a 'mat' (need to fix)");
3576   } else {
3577     if (herm || !A->form_explicit_transpose) {
3578       opA       = herm ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE : CUSPARSE_OPERATION_TRANSPOSE;
3579       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3580     } else {
3581       if (!cusparsestruct->matTranspose) PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
3582       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
3583     }
3584   }
3585   /* Does the matrix use compressed rows (i.e., drop zero rows)? */
3586   compressed = matstruct->cprowIndices ? PETSC_TRUE : PETSC_FALSE;
3587 
3588   try {
3589     PetscCall(VecCUDAGetArrayRead(xx, (const PetscScalar **)&xarray));
3590     if (yy == zz) PetscCall(VecCUDAGetArray(zz, &zarray)); /* read & write zz, so need to get up-to-date zarray on GPU */
3591     else PetscCall(VecCUDAGetArrayWrite(zz, &zarray));     /* write zz, so no need to init zarray on GPU */
3592 
3593     PetscCall(PetscLogGpuTimeBegin());
3594     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3595       /* z = A x + beta y.
3596          If A is compressed (with less rows), then Ax is shorter than the full z, so we need a work vector to store Ax.
3597          When A is non-compressed, and z = y, we can set beta=1 to compute y = Ax + y in one call.
3598       */
3599       xptr = xarray;
3600       dptr = compressed ? cusparsestruct->workVector->data().get() : zarray;
3601       beta = (yy == zz && !compressed) ? matstruct->beta_one : matstruct->beta_zero;
3602 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3603       /* Get length of x, y for y=Ax. ny might be shorter than the work vector's allocated length, since the work vector is
3604           allocated to accommodate different uses. So we get the length info directly from mat.
3605        */
3606       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3607         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3608         nx             = mat->num_cols; // since y = Ax
3609         ny             = mat->num_rows;
3610       }
3611 #endif
3612     } else {
3613       /* z = A^T x + beta y
3614          If A is compressed, then we need a work vector as the shorter version of x to compute A^T x.
3615          Note A^Tx is of full length, so we set beta to 1.0 if y exists.
3616        */
3617       xptr = compressed ? cusparsestruct->workVector->data().get() : xarray;
3618       dptr = zarray;
3619       beta = yy ? matstruct->beta_one : matstruct->beta_zero;
3620       if (compressed) { /* Scatter x to work vector */
3621         thrust::device_ptr<PetscScalar> xarr = thrust::device_pointer_cast(xarray);
3622 
3623         thrust::for_each(
3624 #if PetscDefined(HAVE_THRUST_ASYNC)
3625           thrust::cuda::par.on(PetscDefaultCudaStream),
3626 #endif
3627           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))),
3628           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(), VecCUDAEqualsReverse());
3629       }
3630 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3631       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3632         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3633         nx             = mat->num_rows; // since y = A^T x
3634         ny             = mat->num_cols;
3635       }
3636 #endif
3637     }
3638 
3639     /* csr_spmv does y = alpha op(A) x + beta y */
3640     if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3641 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3642   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0)
3643       cusparseSpMatDescr_t &matDescr = matstruct->matDescr_SpMV[opA]; // All opA's should use the same matDescr, but the cusparse issue/bug (#212) after 12.4 forced us to create a new one for each opA.
3644   #else
3645       cusparseSpMatDescr_t &matDescr = matstruct->matDescr;
3646   #endif
3647 
3648       PetscCheck(opA >= 0 && opA <= 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE ABI on cusparseOperation_t has changed and PETSc has not been updated accordingly");
3649   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0)
3650       if (!matDescr) {
3651         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3652         PetscCallCUSPARSE(cusparseCreateCsr(&matDescr, mat->num_rows, mat->num_cols, mat->num_entries, mat->row_offsets->data().get(), mat->column_indices->data().get(), mat->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
3653       }
3654   #endif
3655 
3656       if (!matstruct->cuSpMV[opA].initialized) { /* built on demand */
3657         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecXDescr, nx, xptr, cusparse_scalartype));
3658         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecYDescr, ny, dptr, cusparse_scalartype));
3659         PetscCallCUSPARSE(
3660           cusparseSpMV_bufferSize(cusparsestruct->handle, opA, matstruct->alpha_one, matDescr, matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, &matstruct->cuSpMV[opA].spmvBufferSize));
3661         PetscCallCUDA(cudaMalloc(&matstruct->cuSpMV[opA].spmvBuffer, matstruct->cuSpMV[opA].spmvBufferSize));
3662   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0) // cusparseSpMV_preprocess is added in 12.4
3663         PetscCallCUSPARSE(
3664           cusparseSpMV_preprocess(cusparsestruct->handle, opA, matstruct->alpha_one, matDescr, matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, matstruct->cuSpMV[opA].spmvBuffer));
3665   #endif
3666         matstruct->cuSpMV[opA].initialized = PETSC_TRUE;
3667       } else {
3668         /* x, y's value pointers might change between calls, but their shape is kept, so we just update pointers */
3669         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecXDescr, xptr));
3670         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecYDescr, dptr));
3671       }
3672 
3673       PetscCallCUSPARSE(cusparseSpMV(cusparsestruct->handle, opA, matstruct->alpha_one, matDescr, matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, matstruct->cuSpMV[opA].spmvBuffer));
3674 #else
3675       CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3676       PetscCallCUSPARSE(cusparse_csr_spmv(cusparsestruct->handle, opA, mat->num_rows, mat->num_cols, mat->num_entries, matstruct->alpha_one, matstruct->descr, mat->values->data().get(), mat->row_offsets->data().get(), mat->column_indices->data().get(), xptr, beta, dptr));
3677 #endif
3678     } else {
3679       if (cusparsestruct->nrows) {
3680 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3681         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
3682 #else
3683         cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
3684         PetscCallCUSPARSE(cusparse_hyb_spmv(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->descr, hybMat, xptr, beta, dptr));
3685 #endif
3686       }
3687     }
3688     PetscCall(PetscLogGpuTimeEnd());
3689 
3690     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3691       if (yy) {                                      /* MatMultAdd: zz = A*xx + yy */
3692         if (compressed) {                            /* A is compressed. We first copy yy to zz, then ScatterAdd the work vector to zz */
3693           PetscCall(VecSeq_CUDA::Copy(yy, zz));      /* zz = yy */
3694         } else if (zz != yy) {                       /* A is not compressed. zz already contains A*xx, and we just need to add yy */
3695           PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3696         }
3697       } else if (compressed) { /* MatMult: zz = A*xx. A is compressed, so we zero zz first, then ScatterAdd the work vector to zz */
3698         PetscCall(VecSeq_CUDA::Set(zz, 0));
3699       }
3700 
3701       /* ScatterAdd the result from work vector into the full vector when A is compressed */
3702       if (compressed) {
3703         PetscCall(PetscLogGpuTimeBegin());
3704         PetscInt n = (PetscInt)matstruct->cprowIndices->size();
3705         ScatterAdd<<<(int)((n + 255) / 256), 256, 0, PetscDefaultCudaStream>>>(n, matstruct->cprowIndices->data().get(), cusparsestruct->workVector->data().get(), zarray);
3706         PetscCall(PetscLogGpuTimeEnd());
3707       }
3708     } else {
3709       if (yy && yy != zz) PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3710     }
3711     PetscCall(VecCUDARestoreArrayRead(xx, (const PetscScalar **)&xarray));
3712     if (yy == zz) PetscCall(VecCUDARestoreArray(zz, &zarray));
3713     else PetscCall(VecCUDARestoreArrayWrite(zz, &zarray));
3714   } catch (char *ex) {
3715     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
3716   }
3717   if (yy) {
3718     PetscCall(PetscLogGpuFlops(2.0 * a->nz));
3719   } else {
3720     PetscCall(PetscLogGpuFlops(2.0 * a->nz - a->nonzerorowcnt));
3721   }
3722   PetscFunctionReturn(PETSC_SUCCESS);
3723 }
3724 
3725 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3726 {
3727   PetscFunctionBegin;
3728   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_FALSE));
3729   PetscFunctionReturn(PETSC_SUCCESS);
3730 }
3731 
3732 static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A, MatAssemblyType mode)
3733 {
3734   PetscFunctionBegin;
3735   PetscCall(MatAssemblyEnd_SeqAIJ(A, mode));
3736   PetscFunctionReturn(PETSC_SUCCESS);
3737 }
3738 
3739 /*@
3740   MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in `MATAIJCUSPARSE` (compressed row) format
3741   (the default parallel PETSc format).
3742 
3743   Collective
3744 
3745   Input Parameters:
3746 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3747 . m    - number of rows
3748 . n    - number of columns
3749 . nz   - number of nonzeros per row (same for all rows), ignored if `nnz` is provide
3750 - nnz  - array containing the number of nonzeros in the various rows (possibly different for each row) or `NULL`
3751 
3752   Output Parameter:
3753 . A - the matrix
3754 
3755   Level: intermediate
3756 
3757   Notes:
3758   This matrix will ultimately pushed down to NVIDIA GPUs and use the CuSPARSE library for
3759   calculations. For good matrix assembly performance the user should preallocate the matrix
3760   storage by setting the parameter `nz` (or the array `nnz`).
3761 
3762   It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
3763   MatXXXXSetPreallocation() paradgm instead of this routine directly.
3764   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]
3765 
3766   The AIJ format, also called
3767   compressed row storage, is fully compatible with standard Fortran
3768   storage.  That is, the stored row and column indices can begin at
3769   either one (as in Fortran) or zero.
3770 
3771   Specify the preallocated storage with either nz or nnz (not both).
3772   Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
3773   allocation.
3774 
3775 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MATAIJCUSPARSE`
3776 @*/
3777 PetscErrorCode MatCreateSeqAIJCUSPARSE(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
3778 {
3779   PetscFunctionBegin;
3780   PetscCall(MatCreate(comm, A));
3781   PetscCall(MatSetSizes(*A, m, n, m, n));
3782   PetscCall(MatSetType(*A, MATSEQAIJCUSPARSE));
3783   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, (PetscInt *)nnz));
3784   PetscFunctionReturn(PETSC_SUCCESS);
3785 }
3786 
3787 static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
3788 {
3789   PetscFunctionBegin;
3790   if (A->factortype == MAT_FACTOR_NONE) {
3791     PetscCall(MatSeqAIJCUSPARSE_Destroy(A));
3792   } else {
3793     PetscCall(MatSeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors **)&A->spptr));
3794   }
3795   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3796   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetFormat_C", NULL));
3797   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetUseCPUSolve_C", NULL));
3798   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3799   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3800   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3801   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
3802   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3803   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3804   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijcusparse_hypre_C", NULL));
3805   PetscCall(MatDestroy_SeqAIJ(A));
3806   PetscFunctionReturn(PETSC_SUCCESS);
3807 }
3808 
3809 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
3810 static PetscErrorCode       MatBindToCPU_SeqAIJCUSPARSE(Mat, PetscBool);
3811 static PetscErrorCode       MatDuplicate_SeqAIJCUSPARSE(Mat A, MatDuplicateOption cpvalues, Mat *B)
3812 {
3813   PetscFunctionBegin;
3814   PetscCall(MatDuplicate_SeqAIJ(A, cpvalues, B));
3815   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(*B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, B));
3816   PetscFunctionReturn(PETSC_SUCCESS);
3817 }
3818 
3819 static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat Y, PetscScalar a, Mat X, MatStructure str)
3820 {
3821   Mat_SeqAIJ         *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
3822   Mat_SeqAIJCUSPARSE *cy;
3823   Mat_SeqAIJCUSPARSE *cx;
3824   PetscScalar        *ay;
3825   const PetscScalar  *ax;
3826   CsrMatrix          *csry, *csrx;
3827 
3828   PetscFunctionBegin;
3829   cy = (Mat_SeqAIJCUSPARSE *)Y->spptr;
3830   cx = (Mat_SeqAIJCUSPARSE *)X->spptr;
3831   if (X->ops->axpy != Y->ops->axpy) {
3832     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3833     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3834     PetscFunctionReturn(PETSC_SUCCESS);
3835   }
3836   /* if we are here, it means both matrices are bound to GPU */
3837   PetscCall(MatSeqAIJCUSPARSECopyToGPU(Y));
3838   PetscCall(MatSeqAIJCUSPARSECopyToGPU(X));
3839   PetscCheck(cy->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)Y), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3840   PetscCheck(cx->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)X), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3841   csry = (CsrMatrix *)cy->mat->mat;
3842   csrx = (CsrMatrix *)cx->mat->mat;
3843   /* see if we can turn this into a cublas axpy */
3844   if (str != SAME_NONZERO_PATTERN && x->nz == y->nz && !x->compressedrow.use && !y->compressedrow.use) {
3845     bool eq = thrust::equal(thrust::device, csry->row_offsets->begin(), csry->row_offsets->end(), csrx->row_offsets->begin());
3846     if (eq) eq = thrust::equal(thrust::device, csry->column_indices->begin(), csry->column_indices->end(), csrx->column_indices->begin());
3847     if (eq) str = SAME_NONZERO_PATTERN;
3848   }
3849   /* spgeam is buggy with one column */
3850   if (Y->cmap->n == 1 && str != SAME_NONZERO_PATTERN) str = DIFFERENT_NONZERO_PATTERN;
3851 
3852   if (str == SUBSET_NONZERO_PATTERN) {
3853     PetscScalar b = 1.0;
3854 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3855     size_t bufferSize;
3856     void  *buffer;
3857 #endif
3858 
3859     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3860     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3861     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_HOST));
3862 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3863     PetscCallCUSPARSE(cusparse_csr_spgeam_bufferSize(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
3864                                                      csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), &bufferSize));
3865     PetscCallCUDA(cudaMalloc(&buffer, bufferSize));
3866     PetscCall(PetscLogGpuTimeBegin());
3867     PetscCallCUSPARSE(cusparse_csr_spgeam(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
3868                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), buffer));
3869     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3870     PetscCall(PetscLogGpuTimeEnd());
3871     PetscCallCUDA(cudaFree(buffer));
3872 #else
3873     PetscCall(PetscLogGpuTimeBegin());
3874     PetscCallCUSPARSE(cusparse_csr_spgeam(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
3875                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get()));
3876     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3877     PetscCall(PetscLogGpuTimeEnd());
3878 #endif
3879     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_DEVICE));
3880     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3881     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3882     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3883   } else if (str == SAME_NONZERO_PATTERN) {
3884     cublasHandle_t cublasv2handle;
3885     PetscBLASInt   one = 1, bnz = 1;
3886 
3887     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3888     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3889     PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3890     PetscCall(PetscBLASIntCast(x->nz, &bnz));
3891     PetscCall(PetscLogGpuTimeBegin());
3892     PetscCallCUBLAS(cublasXaxpy(cublasv2handle, bnz, &a, ax, one, ay, one));
3893     PetscCall(PetscLogGpuFlops(2.0 * bnz));
3894     PetscCall(PetscLogGpuTimeEnd());
3895     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3896     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3897     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3898   } else {
3899     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3900     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3901   }
3902   PetscFunctionReturn(PETSC_SUCCESS);
3903 }
3904 
3905 static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat Y, PetscScalar a)
3906 {
3907   Mat_SeqAIJ    *y = (Mat_SeqAIJ *)Y->data;
3908   PetscScalar   *ay;
3909   cublasHandle_t cublasv2handle;
3910   PetscBLASInt   one = 1, bnz = 1;
3911 
3912   PetscFunctionBegin;
3913   PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3914   PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3915   PetscCall(PetscBLASIntCast(y->nz, &bnz));
3916   PetscCall(PetscLogGpuTimeBegin());
3917   PetscCallCUBLAS(cublasXscal(cublasv2handle, bnz, &a, ay, one));
3918   PetscCall(PetscLogGpuFlops(bnz));
3919   PetscCall(PetscLogGpuTimeEnd());
3920   PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3921   PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3922   PetscFunctionReturn(PETSC_SUCCESS);
3923 }
3924 
3925 static PetscErrorCode MatZeroEntries_SeqAIJCUSPARSE(Mat A)
3926 {
3927   PetscBool   both = PETSC_FALSE;
3928   Mat_SeqAIJ *a    = (Mat_SeqAIJ *)A->data;
3929 
3930   PetscFunctionBegin;
3931   if (A->factortype == MAT_FACTOR_NONE) {
3932     Mat_SeqAIJCUSPARSE *spptr = (Mat_SeqAIJCUSPARSE *)A->spptr;
3933     if (spptr->mat) {
3934       CsrMatrix *matrix = (CsrMatrix *)spptr->mat->mat;
3935       if (matrix->values) {
3936         both = PETSC_TRUE;
3937         thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3938       }
3939     }
3940     if (spptr->matTranspose) {
3941       CsrMatrix *matrix = (CsrMatrix *)spptr->matTranspose->mat;
3942       if (matrix->values) thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3943     }
3944   }
3945   PetscCall(PetscArrayzero(a->a, a->i[A->rmap->n]));
3946   PetscCall(MatSeqAIJInvalidateDiagonal(A));
3947   if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
3948   else A->offloadmask = PETSC_OFFLOAD_CPU;
3949   PetscFunctionReturn(PETSC_SUCCESS);
3950 }
3951 
3952 static PetscErrorCode MatGetCurrentMemType_SeqAIJCUSPARSE(PETSC_UNUSED Mat A, PetscMemType *m)
3953 {
3954   PetscFunctionBegin;
3955   *m = PETSC_MEMTYPE_CUDA;
3956   PetscFunctionReturn(PETSC_SUCCESS);
3957 }
3958 
3959 static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat A, PetscBool flg)
3960 {
3961   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
3962 
3963   PetscFunctionBegin;
3964   if (A->factortype != MAT_FACTOR_NONE) {
3965     A->boundtocpu = flg;
3966     PetscFunctionReturn(PETSC_SUCCESS);
3967   }
3968   if (flg) {
3969     PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
3970 
3971     A->ops->scale                     = MatScale_SeqAIJ;
3972     A->ops->axpy                      = MatAXPY_SeqAIJ;
3973     A->ops->zeroentries               = MatZeroEntries_SeqAIJ;
3974     A->ops->mult                      = MatMult_SeqAIJ;
3975     A->ops->multadd                   = MatMultAdd_SeqAIJ;
3976     A->ops->multtranspose             = MatMultTranspose_SeqAIJ;
3977     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJ;
3978     A->ops->multhermitiantranspose    = NULL;
3979     A->ops->multhermitiantransposeadd = NULL;
3980     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJ;
3981     A->ops->getcurrentmemtype         = NULL;
3982     PetscCall(PetscMemzero(a->ops, sizeof(Mat_SeqAIJOps)));
3983     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3984     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3985     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3986     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3987     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3988     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3989   } else {
3990     A->ops->scale                     = MatScale_SeqAIJCUSPARSE;
3991     A->ops->axpy                      = MatAXPY_SeqAIJCUSPARSE;
3992     A->ops->zeroentries               = MatZeroEntries_SeqAIJCUSPARSE;
3993     A->ops->mult                      = MatMult_SeqAIJCUSPARSE;
3994     A->ops->multadd                   = MatMultAdd_SeqAIJCUSPARSE;
3995     A->ops->multtranspose             = MatMultTranspose_SeqAIJCUSPARSE;
3996     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJCUSPARSE;
3997     A->ops->multhermitiantranspose    = MatMultHermitianTranspose_SeqAIJCUSPARSE;
3998     A->ops->multhermitiantransposeadd = MatMultHermitianTransposeAdd_SeqAIJCUSPARSE;
3999     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJCUSPARSE;
4000     A->ops->getcurrentmemtype         = MatGetCurrentMemType_SeqAIJCUSPARSE;
4001     a->ops->getarray                  = MatSeqAIJGetArray_SeqAIJCUSPARSE;
4002     a->ops->restorearray              = MatSeqAIJRestoreArray_SeqAIJCUSPARSE;
4003     a->ops->getarrayread              = MatSeqAIJGetArrayRead_SeqAIJCUSPARSE;
4004     a->ops->restorearrayread          = MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE;
4005     a->ops->getarraywrite             = MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE;
4006     a->ops->restorearraywrite         = MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE;
4007     a->ops->getcsrandmemtype          = MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE;
4008 
4009     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", MatSeqAIJCopySubArray_SeqAIJCUSPARSE));
4010     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
4011     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
4012     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJCUSPARSE));
4013     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJCUSPARSE));
4014     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
4015   }
4016   A->boundtocpu = flg;
4017   if (flg && a->inode.size_csr) {
4018     a->inode.use = PETSC_TRUE;
4019   } else {
4020     a->inode.use = PETSC_FALSE;
4021   }
4022   PetscFunctionReturn(PETSC_SUCCESS);
4023 }
4024 
4025 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat A, MatType, MatReuse reuse, Mat *newmat)
4026 {
4027   Mat B;
4028 
4029   PetscFunctionBegin;
4030   PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* first use of CUSPARSE may be via MatConvert */
4031   if (reuse == MAT_INITIAL_MATRIX) {
4032     PetscCall(MatDuplicate(A, MAT_COPY_VALUES, newmat));
4033   } else if (reuse == MAT_REUSE_MATRIX) {
4034     PetscCall(MatCopy(A, *newmat, SAME_NONZERO_PATTERN));
4035   }
4036   B = *newmat;
4037 
4038   PetscCall(PetscFree(B->defaultvectype));
4039   PetscCall(PetscStrallocpy(VECCUDA, &B->defaultvectype));
4040 
4041   if (reuse != MAT_REUSE_MATRIX && !B->spptr) {
4042     if (B->factortype == MAT_FACTOR_NONE) {
4043       Mat_SeqAIJCUSPARSE *spptr;
4044       PetscCall(PetscNew(&spptr));
4045       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4046       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4047       spptr->format = MAT_CUSPARSE_CSR;
4048 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4049   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4050       spptr->spmvAlg = CUSPARSE_SPMV_CSR_ALG1; /* default, since we only support csr */
4051   #else
4052       spptr->spmvAlg = CUSPARSE_CSRMV_ALG1; /* default, since we only support csr */
4053   #endif
4054       spptr->spmmAlg    = CUSPARSE_SPMM_CSR_ALG1; /* default, only support column-major dense matrix B */
4055       spptr->csr2cscAlg = CUSPARSE_CSR2CSC_ALG1;
4056 #endif
4057       B->spptr = spptr;
4058     } else {
4059       Mat_SeqAIJCUSPARSETriFactors *spptr;
4060 
4061       PetscCall(PetscNew(&spptr));
4062       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4063       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4064       B->spptr = spptr;
4065     }
4066     B->offloadmask = PETSC_OFFLOAD_UNALLOCATED;
4067   }
4068   B->ops->assemblyend       = MatAssemblyEnd_SeqAIJCUSPARSE;
4069   B->ops->destroy           = MatDestroy_SeqAIJCUSPARSE;
4070   B->ops->setoption         = MatSetOption_SeqAIJCUSPARSE;
4071   B->ops->setfromoptions    = MatSetFromOptions_SeqAIJCUSPARSE;
4072   B->ops->bindtocpu         = MatBindToCPU_SeqAIJCUSPARSE;
4073   B->ops->duplicate         = MatDuplicate_SeqAIJCUSPARSE;
4074   B->ops->getcurrentmemtype = MatGetCurrentMemType_SeqAIJCUSPARSE;
4075 
4076   PetscCall(MatBindToCPU_SeqAIJCUSPARSE(B, PETSC_FALSE));
4077   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJCUSPARSE));
4078   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetFormat_C", MatCUSPARSESetFormat_SeqAIJCUSPARSE));
4079 #if defined(PETSC_HAVE_HYPRE)
4080   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijcusparse_hypre_C", MatConvert_AIJ_HYPRE));
4081 #endif
4082   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetUseCPUSolve_C", MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE));
4083   PetscFunctionReturn(PETSC_SUCCESS);
4084 }
4085 
4086 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
4087 {
4088   PetscFunctionBegin;
4089   PetscCall(MatCreate_SeqAIJ(B));
4090   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, &B));
4091   PetscFunctionReturn(PETSC_SUCCESS);
4092 }
4093 
4094 /*MC
4095    MATSEQAIJCUSPARSE - MATAIJCUSPARSE = "(seq)aijcusparse" - A matrix type to be used for sparse matrices.
4096 
4097    A matrix type whose data resides on NVIDIA GPUs. These matrices can be in either
4098    CSR, ELL, or Hybrid format.
4099    All matrix calculations are performed on NVIDIA GPUs using the CuSPARSE library.
4100 
4101    Options Database Keys:
4102 +  -mat_type aijcusparse - sets the matrix type to "seqaijcusparse" during a call to `MatSetFromOptions()`
4103 .  -mat_cusparse_storage_format csr - sets the storage format of matrices (for `MatMult()` and factors in `MatSolve()`).
4104                                       Other options include ell (ellpack) or hyb (hybrid).
4105 .  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for `MatMult()`). Other options include ell (ellpack) or hyb (hybrid).
4106 -  -mat_cusparse_use_cpu_solve - Do `MatSolve()` on CPU
4107 
4108   Level: beginner
4109 
4110 .seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJCUSPARSE()`, `MatCUSPARSESetUseCPUSolve()`, `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
4111 M*/
4112 
4113 PETSC_INTERN PetscErrorCode MatSolverTypeRegister_CUSPARSE(void)
4114 {
4115   PetscFunctionBegin;
4116   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_LU, MatGetFactor_seqaijcusparse_cusparse));
4117   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_CHOLESKY, MatGetFactor_seqaijcusparse_cusparse));
4118   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ILU, MatGetFactor_seqaijcusparse_cusparse));
4119   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ICC, MatGetFactor_seqaijcusparse_cusparse));
4120   PetscFunctionReturn(PETSC_SUCCESS);
4121 }
4122 
4123 static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat mat)
4124 {
4125   Mat_SeqAIJCUSPARSE *cusp = static_cast<Mat_SeqAIJCUSPARSE *>(mat->spptr);
4126 
4127   PetscFunctionBegin;
4128   if (cusp) {
4129     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->mat, cusp->format));
4130     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4131     delete cusp->workVector;
4132     delete cusp->rowoffsets_gpu;
4133     delete cusp->csr2csc_i;
4134     delete cusp->coords;
4135     if (cusp->handle) PetscCallCUSPARSE(cusparseDestroy(cusp->handle));
4136     PetscCall(PetscFree(mat->spptr));
4137   }
4138   PetscFunctionReturn(PETSC_SUCCESS);
4139 }
4140 
4141 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **mat)
4142 {
4143   PetscFunctionBegin;
4144   if (*mat) {
4145     delete (*mat)->values;
4146     delete (*mat)->column_indices;
4147     delete (*mat)->row_offsets;
4148     delete *mat;
4149     *mat = 0;
4150   }
4151   PetscFunctionReturn(PETSC_SUCCESS);
4152 }
4153 
4154 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4155 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
4156 {
4157   PetscFunctionBegin;
4158   if (*trifactor) {
4159     if ((*trifactor)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*trifactor)->descr));
4160     if ((*trifactor)->solveInfo) PetscCallCUSPARSE(cusparseDestroyCsrsvInfo((*trifactor)->solveInfo));
4161     PetscCall(CsrMatrix_Destroy(&(*trifactor)->csrMat));
4162     if ((*trifactor)->solveBuffer) PetscCallCUDA(cudaFree((*trifactor)->solveBuffer));
4163     if ((*trifactor)->AA_h) PetscCallCUDA(cudaFreeHost((*trifactor)->AA_h));
4164   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4165     if ((*trifactor)->csr2cscBuffer) PetscCallCUDA(cudaFree((*trifactor)->csr2cscBuffer));
4166   #endif
4167     PetscCall(PetscFree(*trifactor));
4168   }
4169   PetscFunctionReturn(PETSC_SUCCESS);
4170 }
4171 #endif
4172 
4173 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct, MatCUSPARSEStorageFormat format)
4174 {
4175   CsrMatrix *mat;
4176 
4177   PetscFunctionBegin;
4178   if (*matstruct) {
4179     if ((*matstruct)->mat) {
4180       if (format == MAT_CUSPARSE_ELL || format == MAT_CUSPARSE_HYB) {
4181 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4182         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
4183 #else
4184         cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
4185         PetscCallCUSPARSE(cusparseDestroyHybMat(hybMat));
4186 #endif
4187       } else {
4188         mat = (CsrMatrix *)(*matstruct)->mat;
4189         PetscCall(CsrMatrix_Destroy(&mat));
4190       }
4191     }
4192     if ((*matstruct)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*matstruct)->descr));
4193     delete (*matstruct)->cprowIndices;
4194     if ((*matstruct)->alpha_one) PetscCallCUDA(cudaFree((*matstruct)->alpha_one));
4195     if ((*matstruct)->beta_zero) PetscCallCUDA(cudaFree((*matstruct)->beta_zero));
4196     if ((*matstruct)->beta_one) PetscCallCUDA(cudaFree((*matstruct)->beta_one));
4197 
4198 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4199     Mat_SeqAIJCUSPARSEMultStruct *mdata = *matstruct;
4200     if (mdata->matDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr));
4201 
4202     for (int i = 0; i < 3; i++) {
4203       if (mdata->cuSpMV[i].initialized) {
4204         PetscCallCUDA(cudaFree(mdata->cuSpMV[i].spmvBuffer));
4205         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecXDescr));
4206         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecYDescr));
4207   #if PETSC_PKG_CUDA_VERSION_GE(12, 4, 0)
4208         if (mdata->matDescr_SpMV[i]) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr_SpMV[i]));
4209         if (mdata->matDescr_SpMM[i]) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr_SpMM[i]));
4210   #endif
4211       }
4212     }
4213 #endif
4214     delete *matstruct;
4215     *matstruct = NULL;
4216   }
4217   PetscFunctionReturn(PETSC_SUCCESS);
4218 }
4219 
4220 PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors_p *trifactors)
4221 {
4222   Mat_SeqAIJCUSPARSETriFactors *fs = *trifactors;
4223 
4224   PetscFunctionBegin;
4225   if (fs) {
4226 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4227     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtr));
4228     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtr));
4229     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtrTranspose));
4230     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtrTranspose));
4231     delete fs->workVector;
4232     fs->workVector = NULL;
4233 #endif
4234     delete fs->rpermIndices;
4235     delete fs->cpermIndices;
4236     fs->rpermIndices  = NULL;
4237     fs->cpermIndices  = NULL;
4238     fs->init_dev_prop = PETSC_FALSE;
4239 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4240     PetscCallCUDA(cudaFree(fs->csrRowPtr));
4241     PetscCallCUDA(cudaFree(fs->csrColIdx));
4242     PetscCallCUDA(cudaFree(fs->csrRowPtr32));
4243     PetscCallCUDA(cudaFree(fs->csrColIdx32));
4244     PetscCallCUDA(cudaFree(fs->csrVal));
4245     PetscCallCUDA(cudaFree(fs->diag));
4246     PetscCallCUDA(cudaFree(fs->X));
4247     PetscCallCUDA(cudaFree(fs->Y));
4248     // PetscCallCUDA(cudaFree(fs->factBuffer_M)); /* No needed since factBuffer_M shares with one of spsvBuffer_L/U */
4249     PetscCallCUDA(cudaFree(fs->spsvBuffer_L));
4250     PetscCallCUDA(cudaFree(fs->spsvBuffer_U));
4251     PetscCallCUDA(cudaFree(fs->spsvBuffer_Lt));
4252     PetscCallCUDA(cudaFree(fs->spsvBuffer_Ut));
4253     PetscCallCUSPARSE(cusparseDestroyMatDescr(fs->matDescr_M));
4254     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_L));
4255     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_U));
4256     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_L));
4257     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Lt));
4258     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_U));
4259     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Ut));
4260     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_X));
4261     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_Y));
4262     PetscCallCUSPARSE(cusparseDestroyCsrilu02Info(fs->ilu0Info_M));
4263     PetscCallCUSPARSE(cusparseDestroyCsric02Info(fs->ic0Info_M));
4264     PetscCall(PetscFree(fs->csrRowPtr_h));
4265     PetscCall(PetscFree(fs->csrVal_h));
4266     PetscCall(PetscFree(fs->diag_h));
4267     fs->createdTransposeSpSVDescr    = PETSC_FALSE;
4268     fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
4269 #endif
4270   }
4271   PetscFunctionReturn(PETSC_SUCCESS);
4272 }
4273 
4274 static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **trifactors)
4275 {
4276   PetscFunctionBegin;
4277   if (*trifactors) {
4278     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(trifactors));
4279     PetscCallCUSPARSE(cusparseDestroy((*trifactors)->handle));
4280     PetscCall(PetscFree(*trifactors));
4281   }
4282   PetscFunctionReturn(PETSC_SUCCESS);
4283 }
4284 
4285 struct IJCompare {
4286   __host__ __device__ inline bool operator()(const thrust::tuple<PetscInt, PetscInt> &t1, const thrust::tuple<PetscInt, PetscInt> &t2)
4287   {
4288     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4289     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4290     return false;
4291   }
4292 };
4293 
4294 static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat A, PetscBool destroy)
4295 {
4296   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4297 
4298   PetscFunctionBegin;
4299   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4300   if (!cusp) PetscFunctionReturn(PETSC_SUCCESS);
4301   if (destroy) {
4302     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4303     delete cusp->csr2csc_i;
4304     cusp->csr2csc_i = NULL;
4305   }
4306   A->transupdated = PETSC_FALSE;
4307   PetscFunctionReturn(PETSC_SUCCESS);
4308 }
4309 
4310 static PetscErrorCode MatCOOStructDestroy_SeqAIJCUSPARSE(void **data)
4311 {
4312   MatCOOStruct_SeqAIJ *coo = (MatCOOStruct_SeqAIJ *)*data;
4313 
4314   PetscFunctionBegin;
4315   PetscCallCUDA(cudaFree(coo->perm));
4316   PetscCallCUDA(cudaFree(coo->jmap));
4317   PetscCall(PetscFree(coo));
4318   PetscFunctionReturn(PETSC_SUCCESS);
4319 }
4320 
4321 static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
4322 {
4323   PetscBool            dev_ij = PETSC_FALSE;
4324   PetscMemType         mtype  = PETSC_MEMTYPE_HOST;
4325   PetscInt            *i, *j;
4326   PetscContainer       container_h;
4327   MatCOOStruct_SeqAIJ *coo_h, *coo_d;
4328 
4329   PetscFunctionBegin;
4330   PetscCall(PetscGetMemType(coo_i, &mtype));
4331   if (PetscMemTypeDevice(mtype)) {
4332     dev_ij = PETSC_TRUE;
4333     PetscCall(PetscMalloc2(coo_n, &i, coo_n, &j));
4334     PetscCallCUDA(cudaMemcpy(i, coo_i, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4335     PetscCallCUDA(cudaMemcpy(j, coo_j, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4336   } else {
4337     i = coo_i;
4338     j = coo_j;
4339   }
4340 
4341   PetscCall(MatSetPreallocationCOO_SeqAIJ(mat, coo_n, i, j));
4342   if (dev_ij) PetscCall(PetscFree2(i, j));
4343   mat->offloadmask = PETSC_OFFLOAD_CPU;
4344   // Create the GPU memory
4345   PetscCall(MatSeqAIJCUSPARSECopyToGPU(mat));
4346 
4347   // Copy the COO struct to device
4348   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container_h));
4349   PetscCall(PetscContainerGetPointer(container_h, (void **)&coo_h));
4350   PetscCall(PetscMalloc1(1, &coo_d));
4351   *coo_d = *coo_h; // do a shallow copy and then amend some fields that need to be different
4352   PetscCallCUDA(cudaMalloc((void **)&coo_d->jmap, (coo_h->nz + 1) * sizeof(PetscCount)));
4353   PetscCallCUDA(cudaMemcpy(coo_d->jmap, coo_h->jmap, (coo_h->nz + 1) * sizeof(PetscCount), cudaMemcpyHostToDevice));
4354   PetscCallCUDA(cudaMalloc((void **)&coo_d->perm, coo_h->Atot * sizeof(PetscCount)));
4355   PetscCallCUDA(cudaMemcpy(coo_d->perm, coo_h->perm, coo_h->Atot * sizeof(PetscCount), cudaMemcpyHostToDevice));
4356 
4357   // Put the COO struct in a container and then attach that to the matrix
4358   PetscCall(PetscObjectContainerCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Device", coo_d, MatCOOStructDestroy_SeqAIJCUSPARSE));
4359   PetscFunctionReturn(PETSC_SUCCESS);
4360 }
4361 
4362 __global__ static void MatAddCOOValues(const PetscScalar kv[], PetscCount nnz, const PetscCount jmap[], const PetscCount perm[], InsertMode imode, PetscScalar a[])
4363 {
4364   PetscCount       i         = blockIdx.x * blockDim.x + threadIdx.x;
4365   const PetscCount grid_size = gridDim.x * blockDim.x;
4366   for (; i < nnz; i += grid_size) {
4367     PetscScalar sum = 0.0;
4368     for (PetscCount k = jmap[i]; k < jmap[i + 1]; k++) sum += kv[perm[k]];
4369     a[i] = (imode == INSERT_VALUES ? 0.0 : a[i]) + sum;
4370   }
4371 }
4372 
4373 static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat A, const PetscScalar v[], InsertMode imode)
4374 {
4375   Mat_SeqAIJ          *seq  = (Mat_SeqAIJ *)A->data;
4376   Mat_SeqAIJCUSPARSE  *dev  = (Mat_SeqAIJCUSPARSE *)A->spptr;
4377   PetscCount           Annz = seq->nz;
4378   PetscMemType         memtype;
4379   const PetscScalar   *v1 = v;
4380   PetscScalar         *Aa;
4381   PetscContainer       container;
4382   MatCOOStruct_SeqAIJ *coo;
4383 
4384   PetscFunctionBegin;
4385   if (!dev->mat) PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4386 
4387   PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_MatCOOStruct_Device", (PetscObject *)&container));
4388   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
4389 
4390   PetscCall(PetscGetMemType(v, &memtype));
4391   if (PetscMemTypeHost(memtype)) { /* If user gave v[] in host, we might need to copy it to device if any */
4392     PetscCallCUDA(cudaMalloc((void **)&v1, coo->n * sizeof(PetscScalar)));
4393     PetscCallCUDA(cudaMemcpy((void *)v1, v, coo->n * sizeof(PetscScalar), cudaMemcpyHostToDevice));
4394   }
4395 
4396   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSEGetArrayWrite(A, &Aa));
4397   else PetscCall(MatSeqAIJCUSPARSEGetArray(A, &Aa));
4398 
4399   PetscCall(PetscLogGpuTimeBegin());
4400   if (Annz) {
4401     MatAddCOOValues<<<((int)(Annz + 255) / 256), 256>>>(v1, Annz, coo->jmap, coo->perm, imode, Aa);
4402     PetscCallCUDA(cudaPeekAtLastError());
4403   }
4404   PetscCall(PetscLogGpuTimeEnd());
4405 
4406   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSERestoreArrayWrite(A, &Aa));
4407   else PetscCall(MatSeqAIJCUSPARSERestoreArray(A, &Aa));
4408 
4409   if (PetscMemTypeHost(memtype)) PetscCallCUDA(cudaFree((void *)v1));
4410   PetscFunctionReturn(PETSC_SUCCESS);
4411 }
4412 
4413 /*@C
4414   MatSeqAIJCUSPARSEGetIJ - returns the device row storage `i` and `j` indices for `MATSEQAIJCUSPARSE` matrices.
4415 
4416   Not Collective
4417 
4418   Input Parameters:
4419 + A          - the matrix
4420 - compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4421 
4422   Output Parameters:
4423 + i - the CSR row pointers
4424 - j - the CSR column indices
4425 
4426   Level: developer
4427 
4428   Note:
4429   When compressed is true, the CSR structure does not contain empty rows
4430 
4431 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSERestoreIJ()`, `MatSeqAIJCUSPARSEGetArrayRead()`
4432 @*/
4433 PetscErrorCode MatSeqAIJCUSPARSEGetIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4434 {
4435   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4436   CsrMatrix          *csr;
4437   Mat_SeqAIJ         *a = (Mat_SeqAIJ *)A->data;
4438 
4439   PetscFunctionBegin;
4440   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4441   if (!i || !j) PetscFunctionReturn(PETSC_SUCCESS);
4442   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4443   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4444   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4445   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4446   csr = (CsrMatrix *)cusp->mat->mat;
4447   if (i) {
4448     if (!compressed && a->compressedrow.use) { /* need full row offset */
4449       if (!cusp->rowoffsets_gpu) {
4450         cusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4451         cusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4452         PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4453       }
4454       *i = cusp->rowoffsets_gpu->data().get();
4455     } else *i = csr->row_offsets->data().get();
4456   }
4457   if (j) *j = csr->column_indices->data().get();
4458   PetscFunctionReturn(PETSC_SUCCESS);
4459 }
4460 
4461 /*@C
4462   MatSeqAIJCUSPARSERestoreIJ - restore the device row storage `i` and `j` indices obtained with `MatSeqAIJCUSPARSEGetIJ()`
4463 
4464   Not Collective
4465 
4466   Input Parameters:
4467 + A          - the matrix
4468 . compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4469 . i          - the CSR row pointers
4470 - j          - the CSR column indices
4471 
4472   Level: developer
4473 
4474 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetIJ()`
4475 @*/
4476 PetscErrorCode MatSeqAIJCUSPARSERestoreIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4477 {
4478   PetscFunctionBegin;
4479   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4480   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4481   if (i) *i = NULL;
4482   if (j) *j = NULL;
4483   (void)compressed;
4484   PetscFunctionReturn(PETSC_SUCCESS);
4485 }
4486 
4487 /*@C
4488   MatSeqAIJCUSPARSEGetArrayRead - gives read-only access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4489 
4490   Not Collective
4491 
4492   Input Parameter:
4493 . A - a `MATSEQAIJCUSPARSE` matrix
4494 
4495   Output Parameter:
4496 . a - pointer to the device data
4497 
4498   Level: developer
4499 
4500   Note:
4501   May trigger host-device copies if up-to-date matrix data is on host
4502 
4503 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArrayRead()`
4504 @*/
4505 PetscErrorCode MatSeqAIJCUSPARSEGetArrayRead(Mat A, const PetscScalar **a)
4506 {
4507   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4508   CsrMatrix          *csr;
4509 
4510   PetscFunctionBegin;
4511   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4512   PetscAssertPointer(a, 2);
4513   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4514   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4515   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4516   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4517   csr = (CsrMatrix *)cusp->mat->mat;
4518   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4519   *a = csr->values->data().get();
4520   PetscFunctionReturn(PETSC_SUCCESS);
4521 }
4522 
4523 /*@C
4524   MatSeqAIJCUSPARSERestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJCUSPARSEGetArrayRead()`
4525 
4526   Not Collective
4527 
4528   Input Parameters:
4529 + A - a `MATSEQAIJCUSPARSE` matrix
4530 - a - pointer to the device data
4531 
4532   Level: developer
4533 
4534 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`
4535 @*/
4536 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayRead(Mat A, const PetscScalar **a)
4537 {
4538   PetscFunctionBegin;
4539   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4540   PetscAssertPointer(a, 2);
4541   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4542   *a = NULL;
4543   PetscFunctionReturn(PETSC_SUCCESS);
4544 }
4545 
4546 /*@C
4547   MatSeqAIJCUSPARSEGetArray - gives read-write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4548 
4549   Not Collective
4550 
4551   Input Parameter:
4552 . A - a `MATSEQAIJCUSPARSE` matrix
4553 
4554   Output Parameter:
4555 . a - pointer to the device data
4556 
4557   Level: developer
4558 
4559   Note:
4560   May trigger host-device copies if up-to-date matrix data is on host
4561 
4562 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArray()`
4563 @*/
4564 PetscErrorCode MatSeqAIJCUSPARSEGetArray(Mat A, PetscScalar **a)
4565 {
4566   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4567   CsrMatrix          *csr;
4568 
4569   PetscFunctionBegin;
4570   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4571   PetscAssertPointer(a, 2);
4572   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4573   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4574   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4575   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4576   csr = (CsrMatrix *)cusp->mat->mat;
4577   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4578   *a             = csr->values->data().get();
4579   A->offloadmask = PETSC_OFFLOAD_GPU;
4580   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4581   PetscFunctionReturn(PETSC_SUCCESS);
4582 }
4583 /*@C
4584   MatSeqAIJCUSPARSERestoreArray - restore the read-write access array obtained from `MatSeqAIJCUSPARSEGetArray()`
4585 
4586   Not Collective
4587 
4588   Input Parameters:
4589 + A - a `MATSEQAIJCUSPARSE` matrix
4590 - a - pointer to the device data
4591 
4592   Level: developer
4593 
4594 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`
4595 @*/
4596 PetscErrorCode MatSeqAIJCUSPARSERestoreArray(Mat A, PetscScalar **a)
4597 {
4598   PetscFunctionBegin;
4599   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4600   PetscAssertPointer(a, 2);
4601   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4602   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4603   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4604   *a = NULL;
4605   PetscFunctionReturn(PETSC_SUCCESS);
4606 }
4607 
4608 /*@C
4609   MatSeqAIJCUSPARSEGetArrayWrite - gives write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4610 
4611   Not Collective
4612 
4613   Input Parameter:
4614 . A - a `MATSEQAIJCUSPARSE` matrix
4615 
4616   Output Parameter:
4617 . a - pointer to the device data
4618 
4619   Level: developer
4620 
4621   Note:
4622   Does not trigger host-device copies and flags data validity on the GPU
4623 
4624 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSERestoreArrayWrite()`
4625 @*/
4626 PetscErrorCode MatSeqAIJCUSPARSEGetArrayWrite(Mat A, PetscScalar **a)
4627 {
4628   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4629   CsrMatrix          *csr;
4630 
4631   PetscFunctionBegin;
4632   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4633   PetscAssertPointer(a, 2);
4634   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4635   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4636   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4637   csr = (CsrMatrix *)cusp->mat->mat;
4638   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4639   *a             = csr->values->data().get();
4640   A->offloadmask = PETSC_OFFLOAD_GPU;
4641   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4642   PetscFunctionReturn(PETSC_SUCCESS);
4643 }
4644 
4645 /*@C
4646   MatSeqAIJCUSPARSERestoreArrayWrite - restore the write-only access array obtained from `MatSeqAIJCUSPARSEGetArrayWrite()`
4647 
4648   Not Collective
4649 
4650   Input Parameters:
4651 + A - a `MATSEQAIJCUSPARSE` matrix
4652 - a - pointer to the device data
4653 
4654   Level: developer
4655 
4656 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayWrite()`
4657 @*/
4658 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayWrite(Mat A, PetscScalar **a)
4659 {
4660   PetscFunctionBegin;
4661   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4662   PetscAssertPointer(a, 2);
4663   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4664   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4665   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4666   *a = NULL;
4667   PetscFunctionReturn(PETSC_SUCCESS);
4668 }
4669 
4670 struct IJCompare4 {
4671   __host__ __device__ inline bool operator()(const thrust::tuple<int, int, PetscScalar, int> &t1, const thrust::tuple<int, int, PetscScalar, int> &t2)
4672   {
4673     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4674     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4675     return false;
4676   }
4677 };
4678 
4679 struct Shift {
4680   int _shift;
4681 
4682   Shift(int shift) : _shift(shift) { }
4683   __host__ __device__ inline int operator()(const int &c) { return c + _shift; }
4684 };
4685 
4686 /* merges two SeqAIJCUSPARSE matrices A, B by concatenating their rows. [A';B']' operation in MATLAB notation */
4687 PetscErrorCode MatSeqAIJCUSPARSEMergeMats(Mat A, Mat B, MatReuse reuse, Mat *C)
4688 {
4689   Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
4690   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr, *Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr, *Ccusp;
4691   Mat_SeqAIJCUSPARSEMultStruct *Cmat;
4692   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
4693   PetscInt                      Annz, Bnnz;
4694   cusparseStatus_t              stat;
4695   PetscInt                      i, m, n, zero = 0;
4696 
4697   PetscFunctionBegin;
4698   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4699   PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
4700   PetscAssertPointer(C, 4);
4701   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4702   PetscCheckTypeName(B, MATSEQAIJCUSPARSE);
4703   PetscCheck(A->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Invalid number or rows %" PetscInt_FMT " != %" PetscInt_FMT, A->rmap->n, B->rmap->n);
4704   PetscCheck(reuse != MAT_INPLACE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_INPLACE_MATRIX not supported");
4705   PetscCheck(Acusp->format != MAT_CUSPARSE_ELL && Acusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4706   PetscCheck(Bcusp->format != MAT_CUSPARSE_ELL && Bcusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4707   if (reuse == MAT_INITIAL_MATRIX) {
4708     m = A->rmap->n;
4709     n = A->cmap->n + B->cmap->n;
4710     PetscCall(MatCreate(PETSC_COMM_SELF, C));
4711     PetscCall(MatSetSizes(*C, m, n, m, n));
4712     PetscCall(MatSetType(*C, MATSEQAIJCUSPARSE));
4713     c                       = (Mat_SeqAIJ *)(*C)->data;
4714     Ccusp                   = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4715     Cmat                    = new Mat_SeqAIJCUSPARSEMultStruct;
4716     Ccsr                    = new CsrMatrix;
4717     Cmat->cprowIndices      = NULL;
4718     c->compressedrow.use    = PETSC_FALSE;
4719     c->compressedrow.nrows  = 0;
4720     c->compressedrow.i      = NULL;
4721     c->compressedrow.rindex = NULL;
4722     Ccusp->workVector       = NULL;
4723     Ccusp->nrows            = m;
4724     Ccusp->mat              = Cmat;
4725     Ccusp->mat->mat         = Ccsr;
4726     Ccsr->num_rows          = m;
4727     Ccsr->num_cols          = n;
4728     PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
4729     PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
4730     PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4731     PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
4732     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
4733     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
4734     PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4735     PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4736     PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4737     PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4738     PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4739     PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4740     PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4741 
4742     Acsr                 = (CsrMatrix *)Acusp->mat->mat;
4743     Bcsr                 = (CsrMatrix *)Bcusp->mat->mat;
4744     Annz                 = (PetscInt)Acsr->column_indices->size();
4745     Bnnz                 = (PetscInt)Bcsr->column_indices->size();
4746     c->nz                = Annz + Bnnz;
4747     Ccsr->row_offsets    = new THRUSTINTARRAY32(m + 1);
4748     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
4749     Ccsr->values         = new THRUSTARRAY(c->nz);
4750     Ccsr->num_entries    = c->nz;
4751     Ccusp->coords        = new THRUSTINTARRAY(c->nz);
4752     if (c->nz) {
4753       auto              Acoo = new THRUSTINTARRAY32(Annz);
4754       auto              Bcoo = new THRUSTINTARRAY32(Bnnz);
4755       auto              Ccoo = new THRUSTINTARRAY32(c->nz);
4756       THRUSTINTARRAY32 *Aroff, *Broff;
4757 
4758       if (a->compressedrow.use) { /* need full row offset */
4759         if (!Acusp->rowoffsets_gpu) {
4760           Acusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4761           Acusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4762           PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4763         }
4764         Aroff = Acusp->rowoffsets_gpu;
4765       } else Aroff = Acsr->row_offsets;
4766       if (b->compressedrow.use) { /* need full row offset */
4767         if (!Bcusp->rowoffsets_gpu) {
4768           Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
4769           Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
4770           PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
4771         }
4772         Broff = Bcusp->rowoffsets_gpu;
4773       } else Broff = Bcsr->row_offsets;
4774       PetscCall(PetscLogGpuTimeBegin());
4775       stat = cusparseXcsr2coo(Acusp->handle, Aroff->data().get(), Annz, m, Acoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4776       PetscCallCUSPARSE(stat);
4777       stat = cusparseXcsr2coo(Bcusp->handle, Broff->data().get(), Bnnz, m, Bcoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4778       PetscCallCUSPARSE(stat);
4779       /* Issues when using bool with large matrices on SUMMIT 10.2.89 */
4780       auto Aperm = thrust::make_constant_iterator(1);
4781       auto Bperm = thrust::make_constant_iterator(0);
4782 #if PETSC_PKG_CUDA_VERSION_GE(10, 0, 0)
4783       auto Bcib = thrust::make_transform_iterator(Bcsr->column_indices->begin(), Shift(A->cmap->n));
4784       auto Bcie = thrust::make_transform_iterator(Bcsr->column_indices->end(), Shift(A->cmap->n));
4785 #else
4786       /* there are issues instantiating the merge operation using a transform iterator for the columns of B */
4787       auto Bcib = Bcsr->column_indices->begin();
4788       auto Bcie = Bcsr->column_indices->end();
4789       thrust::transform(Bcib, Bcie, Bcib, Shift(A->cmap->n));
4790 #endif
4791       auto wPerm = new THRUSTINTARRAY32(Annz + Bnnz);
4792       auto Azb   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->begin(), Acsr->column_indices->begin(), Acsr->values->begin(), Aperm));
4793       auto Aze   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->end(), Acsr->column_indices->end(), Acsr->values->end(), Aperm));
4794       auto Bzb   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->begin(), Bcib, Bcsr->values->begin(), Bperm));
4795       auto Bze   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->end(), Bcie, Bcsr->values->end(), Bperm));
4796       auto Czb   = thrust::make_zip_iterator(thrust::make_tuple(Ccoo->begin(), Ccsr->column_indices->begin(), Ccsr->values->begin(), wPerm->begin()));
4797       auto p1    = Ccusp->coords->begin();
4798       auto p2    = Ccusp->coords->begin();
4799       thrust::advance(p2, Annz);
4800       PetscCallThrust(thrust::merge(thrust::device, Azb, Aze, Bzb, Bze, Czb, IJCompare4()));
4801 #if PETSC_PKG_CUDA_VERSION_LT(10, 0, 0)
4802       thrust::transform(Bcib, Bcie, Bcib, Shift(-A->cmap->n));
4803 #endif
4804       auto cci = thrust::make_counting_iterator(zero);
4805       auto cce = thrust::make_counting_iterator(c->nz);
4806 #if 0 //Errors on SUMMIT cuda 11.1.0
4807       PetscCallThrust(thrust::partition_copy(thrust::device,cci,cce,wPerm->begin(),p1,p2,thrust::identity<int>()));
4808 #else
4809   #if PETSC_PKG_CUDA_VERSION_LT(12, 9, 0) || PetscDefined(HAVE_THRUST)
4810       auto pred = thrust::identity<int>();
4811   #else
4812       auto pred = cuda::std::identity();
4813   #endif
4814       PetscCallThrust(thrust::copy_if(thrust::device, cci, cce, wPerm->begin(), p1, pred));
4815       PetscCallThrust(thrust::remove_copy_if(thrust::device, cci, cce, wPerm->begin(), p2, pred));
4816 #endif
4817       stat = cusparseXcoo2csr(Ccusp->handle, Ccoo->data().get(), c->nz, m, Ccsr->row_offsets->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4818       PetscCallCUSPARSE(stat);
4819       PetscCall(PetscLogGpuTimeEnd());
4820       delete wPerm;
4821       delete Acoo;
4822       delete Bcoo;
4823       delete Ccoo;
4824 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4825       stat = cusparseCreateCsr(&Cmat->matDescr, Ccsr->num_rows, Ccsr->num_cols, Ccsr->num_entries, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
4826       PetscCallCUSPARSE(stat);
4827 #endif
4828       if (A->form_explicit_transpose && B->form_explicit_transpose) { /* if A and B have the transpose, generate C transpose too */
4829         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
4830         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
4831         PetscBool                     AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4832         Mat_SeqAIJCUSPARSEMultStruct *CmatT = new Mat_SeqAIJCUSPARSEMultStruct;
4833         CsrMatrix                    *CcsrT = new CsrMatrix;
4834         CsrMatrix                    *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4835         CsrMatrix                    *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4836 
4837         (*C)->form_explicit_transpose = PETSC_TRUE;
4838         (*C)->transupdated            = PETSC_TRUE;
4839         Ccusp->rowoffsets_gpu         = NULL;
4840         CmatT->cprowIndices           = NULL;
4841         CmatT->mat                    = CcsrT;
4842         CcsrT->num_rows               = n;
4843         CcsrT->num_cols               = m;
4844         CcsrT->num_entries            = c->nz;
4845 
4846         CcsrT->row_offsets    = new THRUSTINTARRAY32(n + 1);
4847         CcsrT->column_indices = new THRUSTINTARRAY32(c->nz);
4848         CcsrT->values         = new THRUSTARRAY(c->nz);
4849 
4850         PetscCall(PetscLogGpuTimeBegin());
4851         auto rT = CcsrT->row_offsets->begin();
4852         if (AT) {
4853           rT = thrust::copy(AcsrT->row_offsets->begin(), AcsrT->row_offsets->end(), rT);
4854           thrust::advance(rT, -1);
4855         }
4856         if (BT) {
4857           auto titb = thrust::make_transform_iterator(BcsrT->row_offsets->begin(), Shift(a->nz));
4858           auto tite = thrust::make_transform_iterator(BcsrT->row_offsets->end(), Shift(a->nz));
4859           thrust::copy(titb, tite, rT);
4860         }
4861         auto cT = CcsrT->column_indices->begin();
4862         if (AT) cT = thrust::copy(AcsrT->column_indices->begin(), AcsrT->column_indices->end(), cT);
4863         if (BT) thrust::copy(BcsrT->column_indices->begin(), BcsrT->column_indices->end(), cT);
4864         auto vT = CcsrT->values->begin();
4865         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4866         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4867         PetscCall(PetscLogGpuTimeEnd());
4868 
4869         PetscCallCUSPARSE(cusparseCreateMatDescr(&CmatT->descr));
4870         PetscCallCUSPARSE(cusparseSetMatIndexBase(CmatT->descr, CUSPARSE_INDEX_BASE_ZERO));
4871         PetscCallCUSPARSE(cusparseSetMatType(CmatT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4872         PetscCallCUDA(cudaMalloc((void **)&CmatT->alpha_one, sizeof(PetscScalar)));
4873         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_zero, sizeof(PetscScalar)));
4874         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_one, sizeof(PetscScalar)));
4875         PetscCallCUDA(cudaMemcpy(CmatT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4876         PetscCallCUDA(cudaMemcpy(CmatT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4877         PetscCallCUDA(cudaMemcpy(CmatT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4878 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4879         stat = cusparseCreateCsr(&CmatT->matDescr, CcsrT->num_rows, CcsrT->num_cols, CcsrT->num_entries, CcsrT->row_offsets->data().get(), CcsrT->column_indices->data().get(), CcsrT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
4880         PetscCallCUSPARSE(stat);
4881 #endif
4882         Ccusp->matTranspose = CmatT;
4883       }
4884     }
4885 
4886     c->free_a = PETSC_TRUE;
4887     PetscCall(PetscShmgetAllocateArray(c->nz, sizeof(PetscInt), (void **)&c->j));
4888     PetscCall(PetscShmgetAllocateArray(m + 1, sizeof(PetscInt), (void **)&c->i));
4889     c->free_ij = PETSC_TRUE;
4890     if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
4891       THRUSTINTARRAY ii(Ccsr->row_offsets->size());
4892       THRUSTINTARRAY jj(Ccsr->column_indices->size());
4893       ii = *Ccsr->row_offsets;
4894       jj = *Ccsr->column_indices;
4895       PetscCallCUDA(cudaMemcpy(c->i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4896       PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4897     } else {
4898       PetscCallCUDA(cudaMemcpy(c->i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4899       PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4900     }
4901     PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
4902     PetscCall(PetscMalloc1(m, &c->ilen));
4903     PetscCall(PetscMalloc1(m, &c->imax));
4904     c->maxnz         = c->nz;
4905     c->nonzerorowcnt = 0;
4906     c->rmax          = 0;
4907     for (i = 0; i < m; i++) {
4908       const PetscInt nn = c->i[i + 1] - c->i[i];
4909       c->ilen[i] = c->imax[i] = nn;
4910       c->nonzerorowcnt += (PetscInt)!!nn;
4911       c->rmax = PetscMax(c->rmax, nn);
4912     }
4913     PetscCall(MatMarkDiagonal_SeqAIJ(*C));
4914     PetscCall(PetscMalloc1(c->nz, &c->a));
4915     (*C)->nonzerostate++;
4916     PetscCall(PetscLayoutSetUp((*C)->rmap));
4917     PetscCall(PetscLayoutSetUp((*C)->cmap));
4918     Ccusp->nonzerostate = (*C)->nonzerostate;
4919     (*C)->preallocated  = PETSC_TRUE;
4920   } else {
4921     PetscCheck((*C)->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Invalid number or rows %" PetscInt_FMT " != %" PetscInt_FMT, (*C)->rmap->n, B->rmap->n);
4922     c = (Mat_SeqAIJ *)(*C)->data;
4923     if (c->nz) {
4924       Ccusp = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4925       PetscCheck(Ccusp->coords, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing coords");
4926       PetscCheck(Ccusp->format != MAT_CUSPARSE_ELL && Ccusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4927       PetscCheck(Ccusp->nonzerostate == (*C)->nonzerostate, PETSC_COMM_SELF, PETSC_ERR_COR, "Wrong nonzerostate");
4928       PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4929       PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4930       PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4931       PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4932       Acsr = (CsrMatrix *)Acusp->mat->mat;
4933       Bcsr = (CsrMatrix *)Bcusp->mat->mat;
4934       Ccsr = (CsrMatrix *)Ccusp->mat->mat;
4935       PetscCheck(Acsr->num_entries == (PetscInt)Acsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "A nnz %" PetscInt_FMT " != %" PetscInt_FMT, Acsr->num_entries, (PetscInt)Acsr->values->size());
4936       PetscCheck(Bcsr->num_entries == (PetscInt)Bcsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "B nnz %" PetscInt_FMT " != %" PetscInt_FMT, Bcsr->num_entries, (PetscInt)Bcsr->values->size());
4937       PetscCheck(Ccsr->num_entries == (PetscInt)Ccsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "C nnz %" PetscInt_FMT " != %" PetscInt_FMT, Ccsr->num_entries, (PetscInt)Ccsr->values->size());
4938       PetscCheck(Ccsr->num_entries == Acsr->num_entries + Bcsr->num_entries, PETSC_COMM_SELF, PETSC_ERR_COR, "C nnz %" PetscInt_FMT " != %" PetscInt_FMT " + %" PetscInt_FMT, Ccsr->num_entries, Acsr->num_entries, Bcsr->num_entries);
4939       PetscCheck(Ccusp->coords->size() == Ccsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "permSize %" PetscInt_FMT " != %" PetscInt_FMT, (PetscInt)Ccusp->coords->size(), (PetscInt)Ccsr->values->size());
4940       auto pmid = Ccusp->coords->begin();
4941       thrust::advance(pmid, Acsr->num_entries);
4942       PetscCall(PetscLogGpuTimeBegin());
4943       auto zibait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->begin())));
4944       auto zieait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4945       thrust::for_each(zibait, zieait, VecCUDAEquals());
4946       auto zibbit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4947       auto ziebit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->end())));
4948       thrust::for_each(zibbit, ziebit, VecCUDAEquals());
4949       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(*C, PETSC_FALSE));
4950       if (A->form_explicit_transpose && B->form_explicit_transpose && (*C)->form_explicit_transpose) {
4951         PetscCheck(Ccusp->matTranspose, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing transpose Mat_SeqAIJCUSPARSEMultStruct");
4952         PetscBool  AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4953         CsrMatrix *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4954         CsrMatrix *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4955         CsrMatrix *CcsrT = (CsrMatrix *)Ccusp->matTranspose->mat;
4956         auto       vT    = CcsrT->values->begin();
4957         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4958         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4959         (*C)->transupdated = PETSC_TRUE;
4960       }
4961       PetscCall(PetscLogGpuTimeEnd());
4962     }
4963   }
4964   PetscCall(PetscObjectStateIncrease((PetscObject)*C));
4965   (*C)->assembled     = PETSC_TRUE;
4966   (*C)->was_assembled = PETSC_FALSE;
4967   (*C)->offloadmask   = PETSC_OFFLOAD_GPU;
4968   PetscFunctionReturn(PETSC_SUCCESS);
4969 }
4970 
4971 static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
4972 {
4973   bool               dmem;
4974   const PetscScalar *av;
4975 
4976   PetscFunctionBegin;
4977   dmem = isCudaMem(v);
4978   PetscCall(MatSeqAIJCUSPARSEGetArrayRead(A, &av));
4979   if (n && idx) {
4980     THRUSTINTARRAY widx(n);
4981     widx.assign(idx, idx + n);
4982     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
4983 
4984     THRUSTARRAY                    *w = NULL;
4985     thrust::device_ptr<PetscScalar> dv;
4986     if (dmem) {
4987       dv = thrust::device_pointer_cast(v);
4988     } else {
4989       w  = new THRUSTARRAY(n);
4990       dv = w->data();
4991     }
4992     thrust::device_ptr<const PetscScalar> dav = thrust::device_pointer_cast(av);
4993 
4994     auto zibit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.begin()), dv));
4995     auto zieit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.end()), dv + n));
4996     thrust::for_each(zibit, zieit, VecCUDAEquals());
4997     if (w) PetscCallCUDA(cudaMemcpy(v, w->data().get(), n * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
4998     delete w;
4999   } else {
5000     PetscCallCUDA(cudaMemcpy(v, av, n * sizeof(PetscScalar), dmem ? cudaMemcpyDeviceToDevice : cudaMemcpyDeviceToHost));
5001   }
5002   if (!dmem) PetscCall(PetscLogCpuToGpu(n * sizeof(PetscScalar)));
5003   PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(A, &av));
5004   PetscFunctionReturn(PETSC_SUCCESS);
5005 }
5006