xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision ef95980055a40b479076201faeccb9e6afe7dc9a)
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   #include <thrust/async/for_each.h>
19 #endif
20 #include <thrust/iterator/constant_iterator.h>
21 #include <thrust/remove.h>
22 #include <thrust/sort.h>
23 #include <thrust/unique.h>
24 
25 const char *const MatCUSPARSEStorageFormats[] = {"CSR", "ELL", "HYB", "MatCUSPARSEStorageFormat", "MAT_CUSPARSE_", 0};
26 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
27 /* The following are copied from cusparse.h in CUDA-11.0. In MatCUSPARSESpMVAlgorithms[] etc, we copy them in
28     0-based integer value order, since we want to use PetscOptionsEnum() to parse user command line options for them.
29 
30   typedef enum {
31       CUSPARSE_MV_ALG_DEFAULT = 0,
32       CUSPARSE_COOMV_ALG      = 1,
33       CUSPARSE_CSRMV_ALG1     = 2,
34       CUSPARSE_CSRMV_ALG2     = 3
35   } cusparseSpMVAlg_t;
36 
37   typedef enum {
38       CUSPARSE_MM_ALG_DEFAULT     CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_ALG_DEFAULT) = 0,
39       CUSPARSE_COOMM_ALG1         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG1)    = 1,
40       CUSPARSE_COOMM_ALG2         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG2)    = 2,
41       CUSPARSE_COOMM_ALG3         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG3)    = 3,
42       CUSPARSE_CSRMM_ALG1         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_CSR_ALG1)    = 4,
43       CUSPARSE_SPMM_ALG_DEFAULT = 0,
44       CUSPARSE_SPMM_COO_ALG1    = 1,
45       CUSPARSE_SPMM_COO_ALG2    = 2,
46       CUSPARSE_SPMM_COO_ALG3    = 3,
47       CUSPARSE_SPMM_COO_ALG4    = 5,
48       CUSPARSE_SPMM_CSR_ALG1    = 4,
49       CUSPARSE_SPMM_CSR_ALG2    = 6,
50   } cusparseSpMMAlg_t;
51 
52   typedef enum {
53       CUSPARSE_CSR2CSC_ALG1 = 1, // faster than V2 (in general), deterministic
54       CUSPARSE_CSR2CSC_ALG2 = 2  // low memory requirement, non-deterministic
55   } cusparseCsr2CscAlg_t;
56   */
57 const char *const MatCUSPARSESpMVAlgorithms[]    = {"MV_ALG_DEFAULT", "COOMV_ALG", "CSRMV_ALG1", "CSRMV_ALG2", "cusparseSpMVAlg_t", "CUSPARSE_", 0};
58 const char *const MatCUSPARSESpMMAlgorithms[]    = {"ALG_DEFAULT", "COO_ALG1", "COO_ALG2", "COO_ALG3", "CSR_ALG1", "COO_ALG4", "CSR_ALG2", "cusparseSpMMAlg_t", "CUSPARSE_SPMM_", 0};
59 const char *const MatCUSPARSECsr2CscAlgorithms[] = {"INVALID" /*cusparse does not have enum 0! We created one*/, "ALG1", "ALG2", "cusparseCsr2CscAlg_t", "CUSPARSE_CSR2CSC_", 0};
60 #endif
61 
62 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, const MatFactorInfo *);
63 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, const MatFactorInfo *);
64 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat, Mat, const MatFactorInfo *);
65 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat, Mat, IS, IS, const MatFactorInfo *);
66 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
67 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat, Vec, Vec);
68 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
69 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
70 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
71 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **);
72 #endif
73 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(Mat, PetscOptionItems *PetscOptionsObject);
74 static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat, PetscScalar, Mat, MatStructure);
75 static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat, PetscScalar);
76 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat, Vec, Vec);
77 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
78 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
79 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
80 static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
81 static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec);
82 static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat, Vec, Vec, Vec, PetscBool, PetscBool);
83 
84 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **);
85 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **, MatCUSPARSEStorageFormat);
86 static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **);
87 static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat);
88 
89 static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat);
90 static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat, PetscBool);
91 
92 static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat, PetscInt, const PetscInt[], PetscScalar[]);
93 static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat, PetscCount, PetscInt[], PetscInt[]);
94 static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat, const PetscScalar[], InsertMode);
95 
96 PETSC_INTERN PetscErrorCode MatCUSPARSESetFormat_SeqAIJCUSPARSE(Mat A, MatCUSPARSEFormatOperation op, MatCUSPARSEStorageFormat format)
97 {
98   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
99 
100   PetscFunctionBegin;
101   switch (op) {
102   case MAT_CUSPARSE_MULT:
103     cusparsestruct->format = format;
104     break;
105   case MAT_CUSPARSE_ALL:
106     cusparsestruct->format = format;
107     break;
108   default:
109     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unsupported operation %d for MatCUSPARSEFormatOperation. MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL are currently supported.", op);
110   }
111   PetscFunctionReturn(PETSC_SUCCESS);
112 }
113 
114 /*@
115   MatCUSPARSESetFormat - Sets the storage format of `MATSEQCUSPARSE` matrices for a particular
116   operation. Only the `MatMult()` operation can use different GPU storage formats
117 
118   Not Collective
119 
120   Input Parameters:
121 + A      - Matrix of type `MATSEQAIJCUSPARSE`
122 . op     - `MatCUSPARSEFormatOperation`. `MATSEQAIJCUSPARSE` matrices support `MAT_CUSPARSE_MULT` and `MAT_CUSPARSE_ALL`.
123         `MATMPIAIJCUSPARSE` matrices support `MAT_CUSPARSE_MULT_DIAG`,`MAT_CUSPARSE_MULT_OFFDIAG`, and `MAT_CUSPARSE_ALL`.
124 - format - `MatCUSPARSEStorageFormat` (one of `MAT_CUSPARSE_CSR`, `MAT_CUSPARSE_ELL`, `MAT_CUSPARSE_HYB`.)
125 
126   Level: intermediate
127 
128 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
129 @*/
130 PetscErrorCode MatCUSPARSESetFormat(Mat A, MatCUSPARSEFormatOperation op, MatCUSPARSEStorageFormat format)
131 {
132   PetscFunctionBegin;
133   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
134   PetscTryMethod(A, "MatCUSPARSESetFormat_C", (Mat, MatCUSPARSEFormatOperation, MatCUSPARSEStorageFormat), (A, op, format));
135   PetscFunctionReturn(PETSC_SUCCESS);
136 }
137 
138 PETSC_INTERN PetscErrorCode MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE(Mat A, PetscBool use_cpu)
139 {
140   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
141 
142   PetscFunctionBegin;
143   cusparsestruct->use_cpu_solve = use_cpu;
144   PetscFunctionReturn(PETSC_SUCCESS);
145 }
146 
147 /*@
148   MatCUSPARSESetUseCPUSolve - Sets to use CPU `MatSolve()`.
149 
150   Input Parameters:
151 + A       - Matrix of type `MATSEQAIJCUSPARSE`
152 - use_cpu - set flag for using the built-in CPU `MatSolve()`
153 
154   Level: intermediate
155 
156   Note:
157   The cuSparse LU solver currently computes the factors with the built-in CPU method
158   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.
159   This method to specify if the solve is done on the CPU or GPU (GPU is the default).
160 
161 .seealso: [](ch_matrices), `Mat`, `MatSolve()`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
162 @*/
163 PetscErrorCode MatCUSPARSESetUseCPUSolve(Mat A, PetscBool use_cpu)
164 {
165   PetscFunctionBegin;
166   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
167   PetscTryMethod(A, "MatCUSPARSESetUseCPUSolve_C", (Mat, PetscBool), (A, use_cpu));
168   PetscFunctionReturn(PETSC_SUCCESS);
169 }
170 
171 static PetscErrorCode MatSetOption_SeqAIJCUSPARSE(Mat A, MatOption op, PetscBool flg)
172 {
173   PetscFunctionBegin;
174   switch (op) {
175   case MAT_FORM_EXPLICIT_TRANSPOSE:
176     /* need to destroy the transpose matrix if present to prevent from logic errors if flg is set to true later */
177     if (A->form_explicit_transpose && !flg) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
178     A->form_explicit_transpose = flg;
179     break;
180   default:
181     PetscCall(MatSetOption_SeqAIJ(A, op, flg));
182     break;
183   }
184   PetscFunctionReturn(PETSC_SUCCESS);
185 }
186 
187 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(Mat A, PetscOptionItems *PetscOptionsObject)
188 {
189   MatCUSPARSEStorageFormat format;
190   PetscBool                flg;
191   Mat_SeqAIJCUSPARSE      *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
192 
193   PetscFunctionBegin;
194   PetscOptionsHeadBegin(PetscOptionsObject, "SeqAIJCUSPARSE options");
195   if (A->factortype == MAT_FACTOR_NONE) {
196     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));
197     if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_MULT, format));
198 
199     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));
200     if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_ALL, format));
201     PetscCall(PetscOptionsBool("-mat_cusparse_use_cpu_solve", "Use CPU (I)LU solve", "MatCUSPARSESetUseCPUSolve", cusparsestruct->use_cpu_solve, &cusparsestruct->use_cpu_solve, &flg));
202     if (flg) PetscCall(MatCUSPARSESetUseCPUSolve(A, cusparsestruct->use_cpu_solve));
203 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
204     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));
205     /* If user did use this option, check its consistency with cuSPARSE, since PetscOptionsEnum() sets enum values based on their position in MatCUSPARSESpMVAlgorithms[] */
206   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
207     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");
208   #else
209     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");
210   #endif
211     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));
212     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");
213 
214     PetscCall(
215       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));
216     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");
217 #endif
218   }
219   PetscOptionsHeadEnd();
220   PetscFunctionReturn(PETSC_SUCCESS);
221 }
222 
223 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
224 static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(Mat A)
225 {
226   Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
227   PetscInt                      m  = A->rmap->n;
228   Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
229   const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
230   const MatScalar              *Aa = a->a;
231   PetscInt                     *Mi, *Mj, Mnz;
232   PetscScalar                  *Ma;
233 
234   PetscFunctionBegin;
235   if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
236     if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even when m=0
237       // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host
238       Mnz = (Ai[m] - Ai[0]) + (Adiag[0] - Adiag[m]); // Lnz (without the unit diagonal) + Unz (with the non-unit diagonal)
239       PetscCall(PetscMalloc1(m + 1, &Mi));
240       PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj is temp
241       PetscCall(PetscMalloc1(Mnz, &Ma));
242       Mi[0] = 0;
243       for (PetscInt i = 0; i < m; i++) {
244         PetscInt llen = Ai[i + 1] - Ai[i];
245         PetscInt ulen = Adiag[i] - Adiag[i + 1];
246         PetscCall(PetscArraycpy(Mj + Mi[i], Aj + Ai[i], llen));                           // entries of L
247         Mj[Mi[i] + llen] = i;                                                             // diagonal entry
248         PetscCall(PetscArraycpy(Mj + Mi[i] + llen + 1, Aj + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
249         Mi[i + 1] = Mi[i] + llen + ulen;
250       }
251       // Copy M (L,U) from host to device
252       PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
253       PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
254       PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
255       PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Mi, sizeof(*fs->csrRowPtr) * (m + 1), cudaMemcpyHostToDevice));
256       PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*fs->csrColIdx) * Mnz, cudaMemcpyHostToDevice));
257 
258       // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
259       // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
260       // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
261       // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
262       // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
263       cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_LOWER;
264       cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT;
265       const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;
266 
267       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
268       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
269       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
270 
271       fillMode = CUSPARSE_FILL_MODE_UPPER;
272       diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
273       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
274       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
275       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
276 
277       // Allocate work vectors in SpSv
278       PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
279       PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));
280 
281       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
282       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
283 
284       // Query buffer sizes for SpSV and then allocate buffers, temporarily assuming opA = CUSPARSE_OPERATION_NON_TRANSPOSE
285       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
286       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));
287       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
288       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));
289       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
290       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
291 
292       // Record for reuse
293       fs->csrRowPtr_h = Mi;
294       fs->csrVal_h    = Ma;
295       PetscCall(PetscFree(Mj));
296     }
297     // Copy the value
298     Mi  = fs->csrRowPtr_h;
299     Ma  = fs->csrVal_h;
300     Mnz = Mi[m];
301     for (PetscInt i = 0; i < m; i++) {
302       PetscInt llen = Ai[i + 1] - Ai[i];
303       PetscInt ulen = Adiag[i] - Adiag[i + 1];
304       PetscCall(PetscArraycpy(Ma + Mi[i], Aa + Ai[i], llen));                           // entries of L
305       Ma[Mi[i] + llen] = (MatScalar)1.0 / Aa[Adiag[i]];                                 // recover the diagonal entry
306       PetscCall(PetscArraycpy(Ma + Mi[i] + llen + 1, Aa + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
307     }
308     PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));
309 
310     // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
311     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));
312 
313     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));
314 
315     // L, U values have changed, reset the flag to indicate we need to redo cusparseSpSV_analysis() for transpose solve
316     fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
317   }
318   PetscFunctionReturn(PETSC_SUCCESS);
319 }
320 #else
321 static PetscErrorCode MatSeqAIJCUSPARSEBuildILULowerTriMatrix(Mat A)
322 {
323   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
324   PetscInt                           n                  = A->rmap->n;
325   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
326   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
327   const PetscInt                    *ai = a->i, *aj = a->j, *vi;
328   const MatScalar                   *aa = a->a, *v;
329   PetscInt                          *AiLo, *AjLo;
330   PetscInt                           i, nz, nzLower, offset, rowOffset;
331 
332   PetscFunctionBegin;
333   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
334   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
335     try {
336       /* first figure out the number of nonzeros in the lower triangular matrix including 1's on the diagonal. */
337       nzLower = n + ai[n] - ai[1];
338       if (!loTriFactor) {
339         PetscScalar *AALo;
340 
341         PetscCallCUDA(cudaMallocHost((void **)&AALo, nzLower * sizeof(PetscScalar)));
342 
343         /* Allocate Space for the lower triangular matrix */
344         PetscCallCUDA(cudaMallocHost((void **)&AiLo, (n + 1) * sizeof(PetscInt)));
345         PetscCallCUDA(cudaMallocHost((void **)&AjLo, nzLower * sizeof(PetscInt)));
346 
347         /* Fill the lower triangular matrix */
348         AiLo[0]   = (PetscInt)0;
349         AiLo[n]   = nzLower;
350         AjLo[0]   = (PetscInt)0;
351         AALo[0]   = (MatScalar)1.0;
352         v         = aa;
353         vi        = aj;
354         offset    = 1;
355         rowOffset = 1;
356         for (i = 1; i < n; i++) {
357           nz = ai[i + 1] - ai[i];
358           /* additional 1 for the term on the diagonal */
359           AiLo[i] = rowOffset;
360           rowOffset += nz + 1;
361 
362           PetscCall(PetscArraycpy(&AjLo[offset], vi, nz));
363           PetscCall(PetscArraycpy(&AALo[offset], v, nz));
364 
365           offset += nz;
366           AjLo[offset] = (PetscInt)i;
367           AALo[offset] = (MatScalar)1.0;
368           offset += 1;
369 
370           v += nz;
371           vi += nz;
372         }
373 
374         /* allocate space for the triangular factor information */
375         PetscCall(PetscNew(&loTriFactor));
376         loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
377         /* Create the matrix description */
378         PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
379         PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
380   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
381         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
382   #else
383         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
384   #endif
385         PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_LOWER));
386         PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));
387 
388         /* set the operation */
389         loTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
390 
391         /* set the matrix */
392         loTriFactor->csrMat              = new CsrMatrix;
393         loTriFactor->csrMat->num_rows    = n;
394         loTriFactor->csrMat->num_cols    = n;
395         loTriFactor->csrMat->num_entries = nzLower;
396 
397         loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n + 1);
398         loTriFactor->csrMat->row_offsets->assign(AiLo, AiLo + n + 1);
399 
400         loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzLower);
401         loTriFactor->csrMat->column_indices->assign(AjLo, AjLo + nzLower);
402 
403         loTriFactor->csrMat->values = new THRUSTARRAY(nzLower);
404         loTriFactor->csrMat->values->assign(AALo, AALo + nzLower);
405 
406         /* Create the solve analysis information */
407         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
408         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
409   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
410         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
411                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, &loTriFactor->solveBufferSize));
412         PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
413   #endif
414 
415         /* perform the solve analysis */
416         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
417                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
418         PetscCallCUDA(WaitForCUDA());
419         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
420 
421         /* assign the pointer */
422         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;
423         loTriFactor->AA_h                                          = AALo;
424         PetscCallCUDA(cudaFreeHost(AiLo));
425         PetscCallCUDA(cudaFreeHost(AjLo));
426         PetscCall(PetscLogCpuToGpu((n + 1 + nzLower) * sizeof(int) + nzLower * sizeof(PetscScalar)));
427       } else { /* update values only */
428         if (!loTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&loTriFactor->AA_h, nzLower * sizeof(PetscScalar)));
429         /* Fill the lower triangular matrix */
430         loTriFactor->AA_h[0] = 1.0;
431         v                    = aa;
432         vi                   = aj;
433         offset               = 1;
434         for (i = 1; i < n; i++) {
435           nz = ai[i + 1] - ai[i];
436           PetscCall(PetscArraycpy(&loTriFactor->AA_h[offset], v, nz));
437           offset += nz;
438           loTriFactor->AA_h[offset] = 1.0;
439           offset += 1;
440           v += nz;
441         }
442         loTriFactor->csrMat->values->assign(loTriFactor->AA_h, loTriFactor->AA_h + nzLower);
443         PetscCall(PetscLogCpuToGpu(nzLower * sizeof(PetscScalar)));
444       }
445     } catch (char *ex) {
446       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
447     }
448   }
449   PetscFunctionReturn(PETSC_SUCCESS);
450 }
451 
452 static PetscErrorCode MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(Mat A)
453 {
454   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
455   PetscInt                           n                  = A->rmap->n;
456   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
457   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
458   const PetscInt                    *aj = a->j, *adiag = a->diag, *vi;
459   const MatScalar                   *aa = a->a, *v;
460   PetscInt                          *AiUp, *AjUp;
461   PetscInt                           i, nz, nzUpper, offset;
462 
463   PetscFunctionBegin;
464   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
465   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
466     try {
467       /* next, figure out the number of nonzeros in the upper triangular matrix. */
468       nzUpper = adiag[0] - adiag[n];
469       if (!upTriFactor) {
470         PetscScalar *AAUp;
471 
472         PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));
473 
474         /* Allocate Space for the upper triangular matrix */
475         PetscCallCUDA(cudaMallocHost((void **)&AiUp, (n + 1) * sizeof(PetscInt)));
476         PetscCallCUDA(cudaMallocHost((void **)&AjUp, nzUpper * sizeof(PetscInt)));
477 
478         /* Fill the upper triangular matrix */
479         AiUp[0] = (PetscInt)0;
480         AiUp[n] = nzUpper;
481         offset  = nzUpper;
482         for (i = n - 1; i >= 0; i--) {
483           v  = aa + adiag[i + 1] + 1;
484           vi = aj + adiag[i + 1] + 1;
485 
486           /* number of elements NOT on the diagonal */
487           nz = adiag[i] - adiag[i + 1] - 1;
488 
489           /* decrement the offset */
490           offset -= (nz + 1);
491 
492           /* first, set the diagonal elements */
493           AjUp[offset] = (PetscInt)i;
494           AAUp[offset] = (MatScalar)1. / v[nz];
495           AiUp[i]      = AiUp[i + 1] - (nz + 1);
496 
497           PetscCall(PetscArraycpy(&AjUp[offset + 1], vi, nz));
498           PetscCall(PetscArraycpy(&AAUp[offset + 1], v, nz));
499         }
500 
501         /* allocate space for the triangular factor information */
502         PetscCall(PetscNew(&upTriFactor));
503         upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
504 
505         /* Create the matrix description */
506         PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
507         PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
508   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
509         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
510   #else
511         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
512   #endif
513         PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
514         PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));
515 
516         /* set the operation */
517         upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
518 
519         /* set the matrix */
520         upTriFactor->csrMat              = new CsrMatrix;
521         upTriFactor->csrMat->num_rows    = n;
522         upTriFactor->csrMat->num_cols    = n;
523         upTriFactor->csrMat->num_entries = nzUpper;
524 
525         upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n + 1);
526         upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + n + 1);
527 
528         upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzUpper);
529         upTriFactor->csrMat->column_indices->assign(AjUp, AjUp + nzUpper);
530 
531         upTriFactor->csrMat->values = new THRUSTARRAY(nzUpper);
532         upTriFactor->csrMat->values->assign(AAUp, AAUp + nzUpper);
533 
534         /* Create the solve analysis information */
535         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
536         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
537   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
538         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
539                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, &upTriFactor->solveBufferSize));
540         PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
541   #endif
542 
543         /* perform the solve analysis */
544         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
545                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
546 
547         PetscCallCUDA(WaitForCUDA());
548         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
549 
550         /* assign the pointer */
551         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;
552         upTriFactor->AA_h                                          = AAUp;
553         PetscCallCUDA(cudaFreeHost(AiUp));
554         PetscCallCUDA(cudaFreeHost(AjUp));
555         PetscCall(PetscLogCpuToGpu((n + 1 + nzUpper) * sizeof(int) + nzUpper * sizeof(PetscScalar)));
556       } else {
557         if (!upTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&upTriFactor->AA_h, nzUpper * sizeof(PetscScalar)));
558         /* Fill the upper triangular matrix */
559         offset = nzUpper;
560         for (i = n - 1; i >= 0; i--) {
561           v = aa + adiag[i + 1] + 1;
562 
563           /* number of elements NOT on the diagonal */
564           nz = adiag[i] - adiag[i + 1] - 1;
565 
566           /* decrement the offset */
567           offset -= (nz + 1);
568 
569           /* first, set the diagonal elements */
570           upTriFactor->AA_h[offset] = 1. / v[nz];
571           PetscCall(PetscArraycpy(&upTriFactor->AA_h[offset + 1], v, nz));
572         }
573         upTriFactor->csrMat->values->assign(upTriFactor->AA_h, upTriFactor->AA_h + nzUpper);
574         PetscCall(PetscLogCpuToGpu(nzUpper * sizeof(PetscScalar)));
575       }
576     } catch (char *ex) {
577       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
578     }
579   }
580   PetscFunctionReturn(PETSC_SUCCESS);
581 }
582 #endif
583 
584 static PetscErrorCode MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(Mat A)
585 {
586   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ *)A->data;
587   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
588   IS                            isrow = a->row, iscol = a->icol;
589   PetscBool                     row_identity, col_identity;
590   PetscInt                      n = A->rmap->n;
591 
592   PetscFunctionBegin;
593   PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
594 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
595   PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(A));
596 #else
597   PetscCall(MatSeqAIJCUSPARSEBuildILULowerTriMatrix(A));
598   PetscCall(MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(A));
599   if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
600 #endif
601 
602   cusparseTriFactors->nnz = a->nz;
603 
604   A->offloadmask = PETSC_OFFLOAD_BOTH; // factored matrix is sync'ed to GPU
605   /* lower triangular indices */
606   PetscCall(ISIdentity(isrow, &row_identity));
607   if (!row_identity && !cusparseTriFactors->rpermIndices) {
608     const PetscInt *r;
609 
610     PetscCall(ISGetIndices(isrow, &r));
611     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
612     cusparseTriFactors->rpermIndices->assign(r, r + n);
613     PetscCall(ISRestoreIndices(isrow, &r));
614     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
615   }
616 
617   /* upper triangular indices */
618   PetscCall(ISIdentity(iscol, &col_identity));
619   if (!col_identity && !cusparseTriFactors->cpermIndices) {
620     const PetscInt *c;
621 
622     PetscCall(ISGetIndices(iscol, &c));
623     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
624     cusparseTriFactors->cpermIndices->assign(c, c + n);
625     PetscCall(ISRestoreIndices(iscol, &c));
626     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
627   }
628   PetscFunctionReturn(PETSC_SUCCESS);
629 }
630 
631 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
632 static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(Mat A)
633 {
634   Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
635   PetscInt                      m  = A->rmap->n;
636   Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
637   const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
638   const MatScalar              *Aa = a->a;
639   PetscInt                     *Mj, Mnz;
640   PetscScalar                  *Ma, *D;
641 
642   PetscFunctionBegin;
643   if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
644     if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even m=0
645       // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host.
646       // See comments at MatICCFactorSymbolic_SeqAIJ() on the layout of the factored matrix (U) on host.
647       Mnz = Ai[m]; // Unz (with the unit diagonal)
648       PetscCall(PetscMalloc1(Mnz, &Ma));
649       PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj[] is temp
650       PetscCall(PetscMalloc1(m, &D));    // the diagonal
651       for (PetscInt i = 0; i < m; i++) {
652         PetscInt ulen = Ai[i + 1] - Ai[i];
653         Mj[Ai[i]]     = i;                                              // diagonal entry
654         PetscCall(PetscArraycpy(Mj + Ai[i] + 1, Aj + Ai[i], ulen - 1)); // entries of U on the right of the diagonal
655       }
656       // Copy M (U) from host to device
657       PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
658       PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
659       PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
660       PetscCallCUDA(cudaMalloc(&fs->diag, sizeof(*fs->diag) * m));
661       PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyHostToDevice));
662       PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*Mj) * Mnz, cudaMemcpyHostToDevice));
663 
664       // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
665       // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
666       // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
667       // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
668       // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
669       cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_UPPER;
670       cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT; // U is unit diagonal
671       const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;
672 
673       PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
674       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
675       PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
676 
677       // Allocate work vectors in SpSv
678       PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
679       PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));
680 
681       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
682       PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
683 
684       // Query buffer sizes for SpSV and then allocate buffers
685       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
686       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));
687       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
688 
689       PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut)); // Ut solve uses the same matrix (spMatDescr_U), but different descr and buffer
690       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));
691       PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));
692 
693       // Record for reuse
694       fs->csrVal_h = Ma;
695       fs->diag_h   = D;
696       PetscCall(PetscFree(Mj));
697     }
698     // Copy the value
699     Ma  = fs->csrVal_h;
700     D   = fs->diag_h;
701     Mnz = Ai[m];
702     for (PetscInt i = 0; i < m; i++) {
703       D[i]      = Aa[Adiag[i]];   // actually Aa[Adiag[i]] is the inverse of the diagonal
704       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
705       for (PetscInt k = 0; k < Ai[i + 1] - Ai[i] - 1; k++) Ma[Ai[i] + 1 + k] = -Aa[Ai[i] + k];
706     }
707     PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));
708     PetscCallCUDA(cudaMemcpy(fs->diag, D, sizeof(*D) * m, cudaMemcpyHostToDevice));
709 
710     // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
711     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));
712     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));
713   }
714   PetscFunctionReturn(PETSC_SUCCESS);
715 }
716 
717 // Solve Ut D U x = b
718 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_Cholesky(Mat A, Vec b, Vec x)
719 {
720   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
721   Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
722   const PetscScalar                    *barray;
723   PetscScalar                          *xarray;
724   thrust::device_ptr<const PetscScalar> bGPU;
725   thrust::device_ptr<PetscScalar>       xGPU;
726   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
727   PetscInt                              m   = A->rmap->n;
728 
729   PetscFunctionBegin;
730   PetscCall(PetscLogGpuTimeBegin());
731   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
732   PetscCall(VecCUDAGetArrayRead(b, &barray));
733   xGPU = thrust::device_pointer_cast(xarray);
734   bGPU = thrust::device_pointer_cast(barray);
735 
736   // Reorder b with the row permutation if needed, and wrap the result in fs->X
737   if (fs->rpermIndices) {
738     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)));
739     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
740   } else {
741     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
742   }
743 
744   // Solve Ut Y = X
745   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
746   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));
747 
748   // Solve diag(D) Z = Y. Actually just do Y = Y*D since D is already inverted in MatCholeskyFactorNumeric_SeqAIJ().
749   // It is basically a vector element-wise multiplication, but cublas does not have it!
750   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>()));
751 
752   // Solve U X = Y
753   if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
754     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
755   } else {
756     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
757   }
758   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));
759 
760   // Reorder X with the column permutation if needed, and put the result back to x
761   if (fs->cpermIndices) {
762     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
763                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
764   }
765 
766   PetscCall(VecCUDARestoreArrayRead(b, &barray));
767   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
768   PetscCall(PetscLogGpuTimeEnd());
769   PetscCall(PetscLogGpuFlops(4.0 * aij->nz - A->rmap->n));
770   PetscFunctionReturn(PETSC_SUCCESS);
771 }
772 #else
773 static PetscErrorCode MatSeqAIJCUSPARSEBuildICCTriMatrices(Mat A)
774 {
775   Mat_SeqAIJ                        *a                  = (Mat_SeqAIJ *)A->data;
776   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
777   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
778   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
779   PetscInt                          *AiUp, *AjUp;
780   PetscScalar                       *AAUp;
781   PetscScalar                       *AALo;
782   PetscInt                           nzUpper = a->nz, n = A->rmap->n, i, offset, nz, j;
783   Mat_SeqSBAIJ                      *b  = (Mat_SeqSBAIJ *)A->data;
784   const PetscInt                    *ai = b->i, *aj = b->j, *vj;
785   const MatScalar                   *aa = b->a, *v;
786 
787   PetscFunctionBegin;
788   if (!n) PetscFunctionReturn(PETSC_SUCCESS);
789   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
790     try {
791       PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));
792       PetscCallCUDA(cudaMallocHost((void **)&AALo, nzUpper * sizeof(PetscScalar)));
793       if (!upTriFactor && !loTriFactor) {
794         /* Allocate Space for the upper triangular matrix */
795         PetscCallCUDA(cudaMallocHost((void **)&AiUp, (n + 1) * sizeof(PetscInt)));
796         PetscCallCUDA(cudaMallocHost((void **)&AjUp, nzUpper * sizeof(PetscInt)));
797 
798         /* Fill the upper triangular matrix */
799         AiUp[0] = (PetscInt)0;
800         AiUp[n] = nzUpper;
801         offset  = 0;
802         for (i = 0; i < n; i++) {
803           /* set the pointers */
804           v  = aa + ai[i];
805           vj = aj + ai[i];
806           nz = ai[i + 1] - ai[i] - 1; /* exclude diag[i] */
807 
808           /* first, set the diagonal elements */
809           AjUp[offset] = (PetscInt)i;
810           AAUp[offset] = (MatScalar)1.0 / v[nz];
811           AiUp[i]      = offset;
812           AALo[offset] = (MatScalar)1.0 / v[nz];
813 
814           offset += 1;
815           if (nz > 0) {
816             PetscCall(PetscArraycpy(&AjUp[offset], vj, nz));
817             PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
818             for (j = offset; j < offset + nz; j++) {
819               AAUp[j] = -AAUp[j];
820               AALo[j] = AAUp[j] / v[nz];
821             }
822             offset += nz;
823           }
824         }
825 
826         /* allocate space for the triangular factor information */
827         PetscCall(PetscNew(&upTriFactor));
828         upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
829 
830         /* Create the matrix description */
831         PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
832         PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
833   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
834         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
835   #else
836         PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
837   #endif
838         PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
839         PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));
840 
841         /* set the matrix */
842         upTriFactor->csrMat              = new CsrMatrix;
843         upTriFactor->csrMat->num_rows    = A->rmap->n;
844         upTriFactor->csrMat->num_cols    = A->cmap->n;
845         upTriFactor->csrMat->num_entries = a->nz;
846 
847         upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n + 1);
848         upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + A->rmap->n + 1);
849 
850         upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
851         upTriFactor->csrMat->column_indices->assign(AjUp, AjUp + a->nz);
852 
853         upTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
854         upTriFactor->csrMat->values->assign(AAUp, AAUp + a->nz);
855 
856         /* set the operation */
857         upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
858 
859         /* Create the solve analysis information */
860         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
861         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
862   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
863         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
864                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, &upTriFactor->solveBufferSize));
865         PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
866   #endif
867 
868         /* perform the solve analysis */
869         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr, upTriFactor->csrMat->values->data().get(),
870                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
871 
872         PetscCallCUDA(WaitForCUDA());
873         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
874 
875         /* assign the pointer */
876         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;
877 
878         /* allocate space for the triangular factor information */
879         PetscCall(PetscNew(&loTriFactor));
880         loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
881 
882         /* Create the matrix description */
883         PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
884         PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
885   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
886         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
887   #else
888         PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
889   #endif
890         PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
891         PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));
892 
893         /* set the operation */
894         loTriFactor->solveOp = CUSPARSE_OPERATION_TRANSPOSE;
895 
896         /* set the matrix */
897         loTriFactor->csrMat              = new CsrMatrix;
898         loTriFactor->csrMat->num_rows    = A->rmap->n;
899         loTriFactor->csrMat->num_cols    = A->cmap->n;
900         loTriFactor->csrMat->num_entries = a->nz;
901 
902         loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n + 1);
903         loTriFactor->csrMat->row_offsets->assign(AiUp, AiUp + A->rmap->n + 1);
904 
905         loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
906         loTriFactor->csrMat->column_indices->assign(AjUp, AjUp + a->nz);
907 
908         loTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
909         loTriFactor->csrMat->values->assign(AALo, AALo + a->nz);
910 
911         /* Create the solve analysis information */
912         PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
913         PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
914   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
915         PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
916                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, &loTriFactor->solveBufferSize));
917         PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
918   #endif
919 
920         /* perform the solve analysis */
921         PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr, loTriFactor->csrMat->values->data().get(),
922                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
923 
924         PetscCallCUDA(WaitForCUDA());
925         PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
926 
927         /* assign the pointer */
928         ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;
929 
930         PetscCall(PetscLogCpuToGpu(2 * (((A->rmap->n + 1) + (a->nz)) * sizeof(int) + (a->nz) * sizeof(PetscScalar))));
931         PetscCallCUDA(cudaFreeHost(AiUp));
932         PetscCallCUDA(cudaFreeHost(AjUp));
933       } else {
934         /* Fill the upper triangular matrix */
935         offset = 0;
936         for (i = 0; i < n; i++) {
937           /* set the pointers */
938           v  = aa + ai[i];
939           nz = ai[i + 1] - ai[i] - 1; /* exclude diag[i] */
940 
941           /* first, set the diagonal elements */
942           AAUp[offset] = 1.0 / v[nz];
943           AALo[offset] = 1.0 / v[nz];
944 
945           offset += 1;
946           if (nz > 0) {
947             PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
948             for (j = offset; j < offset + nz; j++) {
949               AAUp[j] = -AAUp[j];
950               AALo[j] = AAUp[j] / v[nz];
951             }
952             offset += nz;
953           }
954         }
955         PetscCheck(upTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
956         PetscCheck(loTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
957         upTriFactor->csrMat->values->assign(AAUp, AAUp + a->nz);
958         loTriFactor->csrMat->values->assign(AALo, AALo + a->nz);
959         PetscCall(PetscLogCpuToGpu(2 * (a->nz) * sizeof(PetscScalar)));
960       }
961       PetscCallCUDA(cudaFreeHost(AAUp));
962       PetscCallCUDA(cudaFreeHost(AALo));
963     } catch (char *ex) {
964       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
965     }
966   }
967   PetscFunctionReturn(PETSC_SUCCESS);
968 }
969 #endif
970 
971 static PetscErrorCode MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(Mat A)
972 {
973   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ *)A->data;
974   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
975   IS                            ip                 = a->row;
976   PetscBool                     perm_identity;
977   PetscInt                      n = A->rmap->n;
978 
979   PetscFunctionBegin;
980   PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
981 
982 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
983   PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(A));
984 #else
985   PetscCall(MatSeqAIJCUSPARSEBuildICCTriMatrices(A));
986   if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
987 #endif
988   cusparseTriFactors->nnz = (a->nz - n) * 2 + n;
989 
990   A->offloadmask = PETSC_OFFLOAD_BOTH;
991 
992   /* lower triangular indices */
993   PetscCall(ISIdentity(ip, &perm_identity));
994   if (!perm_identity) {
995     IS              iip;
996     const PetscInt *irip, *rip;
997 
998     PetscCall(ISInvertPermutation(ip, PETSC_DECIDE, &iip));
999     PetscCall(ISGetIndices(iip, &irip));
1000     PetscCall(ISGetIndices(ip, &rip));
1001     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
1002     cusparseTriFactors->rpermIndices->assign(rip, rip + n);
1003     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
1004     cusparseTriFactors->cpermIndices->assign(irip, irip + n);
1005     PetscCall(ISRestoreIndices(iip, &irip));
1006     PetscCall(ISDestroy(&iip));
1007     PetscCall(ISRestoreIndices(ip, &rip));
1008     PetscCall(PetscLogCpuToGpu(2. * n * sizeof(PetscInt)));
1009   }
1010   PetscFunctionReturn(PETSC_SUCCESS);
1011 }
1012 
1013 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
1014 {
1015   PetscFunctionBegin;
1016   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
1017   PetscCall(MatCholeskyFactorNumeric_SeqAIJ(B, A, info));
1018   B->offloadmask = PETSC_OFFLOAD_CPU;
1019 
1020 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1021   B->ops->solve          = MatSolve_SeqAIJCUSPARSE_Cholesky;
1022   B->ops->solvetranspose = MatSolve_SeqAIJCUSPARSE_Cholesky;
1023 #else
1024   /* determine which version of MatSolve needs to be used. */
1025   Mat_SeqAIJ *b  = (Mat_SeqAIJ *)B->data;
1026   IS          ip = b->row;
1027   PetscBool   perm_identity;
1028 
1029   PetscCall(ISIdentity(ip, &perm_identity));
1030   if (perm_identity) {
1031     B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
1032     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
1033   } else {
1034     B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
1035     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
1036   }
1037 #endif
1038   B->ops->matsolve          = NULL;
1039   B->ops->matsolvetranspose = NULL;
1040 
1041   /* get the triangular factors */
1042   PetscCall(MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(B));
1043   PetscFunctionReturn(PETSC_SUCCESS);
1044 }
1045 
1046 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
1047 static PetscErrorCode MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(Mat A)
1048 {
1049   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1050   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1051   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1052   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT;
1053   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT;
1054   cusparseIndexBase_t                indexBase;
1055   cusparseMatrixType_t               matrixType;
1056   cusparseFillMode_t                 fillMode;
1057   cusparseDiagType_t                 diagType;
1058 
1059   PetscFunctionBegin;
1060   /* allocate space for the transpose of the lower triangular factor */
1061   PetscCall(PetscNew(&loTriFactorT));
1062   loTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1063 
1064   /* set the matrix descriptors of the lower triangular factor */
1065   matrixType = cusparseGetMatType(loTriFactor->descr);
1066   indexBase  = cusparseGetMatIndexBase(loTriFactor->descr);
1067   fillMode   = cusparseGetMatFillMode(loTriFactor->descr) == CUSPARSE_FILL_MODE_UPPER ? CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
1068   diagType   = cusparseGetMatDiagType(loTriFactor->descr);
1069 
1070   /* Create the matrix description */
1071   PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactorT->descr));
1072   PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactorT->descr, indexBase));
1073   PetscCallCUSPARSE(cusparseSetMatType(loTriFactorT->descr, matrixType));
1074   PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactorT->descr, fillMode));
1075   PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactorT->descr, diagType));
1076 
1077   /* set the operation */
1078   loTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
1079 
1080   /* allocate GPU space for the CSC of the lower triangular factor*/
1081   loTriFactorT->csrMat                 = new CsrMatrix;
1082   loTriFactorT->csrMat->num_rows       = loTriFactor->csrMat->num_cols;
1083   loTriFactorT->csrMat->num_cols       = loTriFactor->csrMat->num_rows;
1084   loTriFactorT->csrMat->num_entries    = loTriFactor->csrMat->num_entries;
1085   loTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_rows + 1);
1086   loTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_entries);
1087   loTriFactorT->csrMat->values         = new THRUSTARRAY(loTriFactorT->csrMat->num_entries);
1088 
1089   /* compute the transpose of the lower triangular factor, i.e. the CSC */
1090   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1091   PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(cusparseTriFactors->handle, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_cols, loTriFactor->csrMat->num_entries, loTriFactor->csrMat->values->data().get(),
1092                                                   loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactorT->csrMat->values->data().get(), loTriFactorT->csrMat->row_offsets->data().get(),
1093                                                   loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &loTriFactor->csr2cscBufferSize));
1094   PetscCallCUDA(cudaMalloc(&loTriFactor->csr2cscBuffer, loTriFactor->csr2cscBufferSize));
1095   #endif
1096 
1097   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1098   {
1099     // there is no clean way to have PetscCallCUSPARSE wrapping this function...
1100     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(),
1101                                  loTriFactor->csrMat->column_indices->data().get(), loTriFactorT->csrMat->values->data().get(),
1102   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1103                                  loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, loTriFactor->csr2cscBuffer);
1104   #else
1105                                  loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1106   #endif
1107     PetscCallCUSPARSE(stat);
1108   }
1109 
1110   PetscCallCUDA(WaitForCUDA());
1111   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1112 
1113   /* Create the solve analysis information */
1114   PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1115   PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactorT->solveInfo));
1116   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
1117   PetscCallCUSPARSE(cusparseXcsrsv_buffsize(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1118                                             loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, &loTriFactorT->solveBufferSize));
1119   PetscCallCUDA(cudaMalloc(&loTriFactorT->solveBuffer, loTriFactorT->solveBufferSize));
1120   #endif
1121 
1122   /* perform the solve analysis */
1123   PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
1124                                             loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1125 
1126   PetscCallCUDA(WaitForCUDA());
1127   PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1128 
1129   /* assign the pointer */
1130   ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtrTranspose = loTriFactorT;
1131 
1132   /*********************************************/
1133   /* Now the Transpose of the Upper Tri Factor */
1134   /*********************************************/
1135 
1136   /* allocate space for the transpose of the upper triangular factor */
1137   PetscCall(PetscNew(&upTriFactorT));
1138   upTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1139 
1140   /* set the matrix descriptors of the upper triangular factor */
1141   matrixType = cusparseGetMatType(upTriFactor->descr);
1142   indexBase  = cusparseGetMatIndexBase(upTriFactor->descr);
1143   fillMode   = cusparseGetMatFillMode(upTriFactor->descr) == CUSPARSE_FILL_MODE_UPPER ? CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
1144   diagType   = cusparseGetMatDiagType(upTriFactor->descr);
1145 
1146   /* Create the matrix description */
1147   PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactorT->descr));
1148   PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactorT->descr, indexBase));
1149   PetscCallCUSPARSE(cusparseSetMatType(upTriFactorT->descr, matrixType));
1150   PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactorT->descr, fillMode));
1151   PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactorT->descr, diagType));
1152 
1153   /* set the operation */
1154   upTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
1155 
1156   /* allocate GPU space for the CSC of the upper triangular factor*/
1157   upTriFactorT->csrMat                 = new CsrMatrix;
1158   upTriFactorT->csrMat->num_rows       = upTriFactor->csrMat->num_cols;
1159   upTriFactorT->csrMat->num_cols       = upTriFactor->csrMat->num_rows;
1160   upTriFactorT->csrMat->num_entries    = upTriFactor->csrMat->num_entries;
1161   upTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_rows + 1);
1162   upTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_entries);
1163   upTriFactorT->csrMat->values         = new THRUSTARRAY(upTriFactorT->csrMat->num_entries);
1164 
1165   /* compute the transpose of the upper triangular factor, i.e. the CSC */
1166   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1167   PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(cusparseTriFactors->handle, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_cols, upTriFactor->csrMat->num_entries, upTriFactor->csrMat->values->data().get(),
1168                                                   upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactorT->csrMat->values->data().get(), upTriFactorT->csrMat->row_offsets->data().get(),
1169                                                   upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &upTriFactor->csr2cscBufferSize));
1170   PetscCallCUDA(cudaMalloc(&upTriFactor->csr2cscBuffer, upTriFactor->csr2cscBufferSize));
1171   #endif
1172 
1173   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1174   {
1175     // there is no clean way to have PetscCallCUSPARSE wrapping this function...
1176     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(),
1177                                  upTriFactor->csrMat->column_indices->data().get(), upTriFactorT->csrMat->values->data().get(),
1178   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1179                                  upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, upTriFactor->csr2cscBuffer);
1180   #else
1181                                  upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1182   #endif
1183     PetscCallCUSPARSE(stat);
1184   }
1185 
1186   PetscCallCUDA(WaitForCUDA());
1187   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1188 
1189   /* Create the solve analysis information */
1190   PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1191   PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactorT->solveInfo));
1192   #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
1193   PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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->solveBufferSize));
1195   PetscCallCUDA(cudaMalloc(&upTriFactorT->solveBuffer, upTriFactorT->solveBufferSize));
1196   #endif
1197 
1198   /* perform the solve analysis */
1199   /* christ, would it have killed you to put this stuff in a function????????? */
1200   PetscCallCUSPARSE(cusparseXcsrsv_analysis(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
1201                                             upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1202 
1203   PetscCallCUDA(WaitForCUDA());
1204   PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
1205 
1206   /* assign the pointer */
1207   ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtrTranspose = upTriFactorT;
1208   PetscFunctionReturn(PETSC_SUCCESS);
1209 }
1210 #endif
1211 
1212 struct PetscScalarToPetscInt {
1213   __host__ __device__ PetscInt operator()(PetscScalar s) { return (PetscInt)PetscRealPart(s); }
1214 };
1215 
1216 static PetscErrorCode MatSeqAIJCUSPARSEFormExplicitTranspose(Mat A)
1217 {
1218   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
1219   Mat_SeqAIJCUSPARSEMultStruct *matstruct, *matstructT;
1220   Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data;
1221   cusparseStatus_t              stat;
1222   cusparseIndexBase_t           indexBase;
1223 
1224   PetscFunctionBegin;
1225   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1226   matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
1227   PetscCheck(matstruct, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing mat struct");
1228   matstructT = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
1229   PetscCheck(!A->transupdated || matstructT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing matTranspose struct");
1230   if (A->transupdated) PetscFunctionReturn(PETSC_SUCCESS);
1231   PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1232   PetscCall(PetscLogGpuTimeBegin());
1233   if (cusparsestruct->format != MAT_CUSPARSE_CSR) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
1234   if (!cusparsestruct->matTranspose) { /* create cusparse matrix */
1235     matstructT = new Mat_SeqAIJCUSPARSEMultStruct;
1236     PetscCallCUSPARSE(cusparseCreateMatDescr(&matstructT->descr));
1237     indexBase = cusparseGetMatIndexBase(matstruct->descr);
1238     PetscCallCUSPARSE(cusparseSetMatIndexBase(matstructT->descr, indexBase));
1239     PetscCallCUSPARSE(cusparseSetMatType(matstructT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
1240 
1241     /* set alpha and beta */
1242     PetscCallCUDA(cudaMalloc((void **)&matstructT->alpha_one, sizeof(PetscScalar)));
1243     PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_zero, sizeof(PetscScalar)));
1244     PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_one, sizeof(PetscScalar)));
1245     PetscCallCUDA(cudaMemcpy(matstructT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1246     PetscCallCUDA(cudaMemcpy(matstructT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1247     PetscCallCUDA(cudaMemcpy(matstructT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
1248 
1249     if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
1250       CsrMatrix *matrixT      = new CsrMatrix;
1251       matstructT->mat         = matrixT;
1252       matrixT->num_rows       = A->cmap->n;
1253       matrixT->num_cols       = A->rmap->n;
1254       matrixT->num_entries    = a->nz;
1255       matrixT->row_offsets    = new THRUSTINTARRAY32(matrixT->num_rows + 1);
1256       matrixT->column_indices = new THRUSTINTARRAY32(a->nz);
1257       matrixT->values         = new THRUSTARRAY(a->nz);
1258 
1259       if (!cusparsestruct->rowoffsets_gpu) cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
1260       cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
1261 
1262 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1263   #if PETSC_PKG_CUDA_VERSION_GE(11, 2, 1)
1264       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 */
1265                                indexBase, cusparse_scalartype);
1266       PetscCallCUSPARSE(stat);
1267   #else
1268       /* cusparse-11.x returns errors with zero-sized matrices until 11.2.1,
1269            see https://docs.nvidia.com/cuda/cuda-toolkit-release-notes/index.html#cusparse-11.2.1
1270 
1271            I don't know what a proper value should be for matstructT->matDescr with empty matrices, so I just set
1272            it to NULL to blow it up if one relies on it. Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2,
1273            when nnz = 0, matrixT->row_offsets[] should be filled with indexBase. So I also set it accordingly.
1274         */
1275       if (matrixT->num_entries) {
1276         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);
1277         PetscCallCUSPARSE(stat);
1278 
1279       } else {
1280         matstructT->matDescr = NULL;
1281         matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
1282       }
1283   #endif
1284 #endif
1285     } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
1286 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1287       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
1288 #else
1289       CsrMatrix *temp  = new CsrMatrix;
1290       CsrMatrix *tempT = new CsrMatrix;
1291       /* First convert HYB to CSR */
1292       temp->num_rows       = A->rmap->n;
1293       temp->num_cols       = A->cmap->n;
1294       temp->num_entries    = a->nz;
1295       temp->row_offsets    = new THRUSTINTARRAY32(A->rmap->n + 1);
1296       temp->column_indices = new THRUSTINTARRAY32(a->nz);
1297       temp->values         = new THRUSTARRAY(a->nz);
1298 
1299       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());
1300       PetscCallCUSPARSE(stat);
1301 
1302       /* Next, convert CSR to CSC (i.e. the matrix transpose) */
1303       tempT->num_rows       = A->rmap->n;
1304       tempT->num_cols       = A->cmap->n;
1305       tempT->num_entries    = a->nz;
1306       tempT->row_offsets    = new THRUSTINTARRAY32(A->rmap->n + 1);
1307       tempT->column_indices = new THRUSTINTARRAY32(a->nz);
1308       tempT->values         = new THRUSTARRAY(a->nz);
1309 
1310       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(),
1311                               tempT->column_indices->data().get(), tempT->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1312       PetscCallCUSPARSE(stat);
1313 
1314       /* Last, convert CSC to HYB */
1315       cusparseHybMat_t hybMat;
1316       PetscCallCUSPARSE(cusparseCreateHybMat(&hybMat));
1317       cusparseHybPartition_t partition = cusparsestruct->format == MAT_CUSPARSE_ELL ? CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
1318       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);
1319       PetscCallCUSPARSE(stat);
1320 
1321       /* assign the pointer */
1322       matstructT->mat = hybMat;
1323       A->transupdated = PETSC_TRUE;
1324       /* delete temporaries */
1325       if (tempT) {
1326         if (tempT->values) delete (THRUSTARRAY *)tempT->values;
1327         if (tempT->column_indices) delete (THRUSTINTARRAY32 *)tempT->column_indices;
1328         if (tempT->row_offsets) delete (THRUSTINTARRAY32 *)tempT->row_offsets;
1329         delete (CsrMatrix *)tempT;
1330       }
1331       if (temp) {
1332         if (temp->values) delete (THRUSTARRAY *)temp->values;
1333         if (temp->column_indices) delete (THRUSTINTARRAY32 *)temp->column_indices;
1334         if (temp->row_offsets) delete (THRUSTINTARRAY32 *)temp->row_offsets;
1335         delete (CsrMatrix *)temp;
1336       }
1337 #endif
1338     }
1339   }
1340   if (cusparsestruct->format == MAT_CUSPARSE_CSR) { /* transpose mat struct may be already present, update data */
1341     CsrMatrix *matrix  = (CsrMatrix *)matstruct->mat;
1342     CsrMatrix *matrixT = (CsrMatrix *)matstructT->mat;
1343     PetscCheck(matrix, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix");
1344     PetscCheck(matrix->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix rows");
1345     PetscCheck(matrix->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix cols");
1346     PetscCheck(matrix->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix values");
1347     PetscCheck(matrixT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT");
1348     PetscCheck(matrixT->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT rows");
1349     PetscCheck(matrixT->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT cols");
1350     PetscCheck(matrixT->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT values");
1351     if (!cusparsestruct->rowoffsets_gpu) { /* this may be absent when we did not construct the transpose with csr2csc */
1352       cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
1353       cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
1354       PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
1355     }
1356     if (!cusparsestruct->csr2csc_i) {
1357       THRUSTARRAY csr2csc_a(matrix->num_entries);
1358       PetscCallThrust(thrust::sequence(thrust::device, csr2csc_a.begin(), csr2csc_a.end(), 0.0));
1359 
1360       indexBase = cusparseGetMatIndexBase(matstruct->descr);
1361 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1362       void  *csr2cscBuffer;
1363       size_t csr2cscBufferSize;
1364       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(),
1365                                            matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, &csr2cscBufferSize);
1366       PetscCallCUSPARSE(stat);
1367       PetscCallCUDA(cudaMalloc(&csr2cscBuffer, csr2cscBufferSize));
1368 #endif
1369 
1370       if (matrix->num_entries) {
1371         /* When there are no nonzeros, this routine mistakenly returns CUSPARSE_STATUS_INVALID_VALUE in
1372            mat_tests-ex62_15_mpiaijcusparse on ranks 0 and 2 with CUDA-11. But CUDA-10 is OK.
1373            I checked every parameters and they were just fine. I have no clue why cusparse complains.
1374 
1375            Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2, when nnz = 0, matrixT->row_offsets[]
1376            should be filled with indexBase. So I just take a shortcut here.
1377         */
1378         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(),
1379 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1380                                 matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, csr2cscBuffer);
1381         PetscCallCUSPARSE(stat);
1382 #else
1383                                 matrixT->column_indices->data().get(), matrixT->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
1384         PetscCallCUSPARSE(stat);
1385 #endif
1386       } else {
1387         matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
1388       }
1389 
1390       cusparsestruct->csr2csc_i = new THRUSTINTARRAY(matrix->num_entries);
1391       PetscCallThrust(thrust::transform(thrust::device, matrixT->values->begin(), matrixT->values->end(), cusparsestruct->csr2csc_i->begin(), PetscScalarToPetscInt()));
1392 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
1393       PetscCallCUDA(cudaFree(csr2cscBuffer));
1394 #endif
1395     }
1396     PetscCallThrust(
1397       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()));
1398   }
1399   PetscCall(PetscLogGpuTimeEnd());
1400   PetscCall(PetscLogEventEnd(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
1401   /* the compressed row indices is not used for matTranspose */
1402   matstructT->cprowIndices = NULL;
1403   /* assign the pointer */
1404   ((Mat_SeqAIJCUSPARSE *)A->spptr)->matTranspose = matstructT;
1405   A->transupdated                                = PETSC_TRUE;
1406   PetscFunctionReturn(PETSC_SUCCESS);
1407 }
1408 
1409 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1410 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
1411 {
1412   const PetscScalar                    *barray;
1413   PetscScalar                          *xarray;
1414   thrust::device_ptr<const PetscScalar> bGPU;
1415   thrust::device_ptr<PetscScalar>       xGPU;
1416   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
1417   const Mat_SeqAIJ                     *aij = static_cast<Mat_SeqAIJ *>(A->data);
1418   const cusparseOperation_t             op  = CUSPARSE_OPERATION_NON_TRANSPOSE;
1419   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
1420   PetscInt                              m   = A->rmap->n;
1421 
1422   PetscFunctionBegin;
1423   PetscCall(PetscLogGpuTimeBegin());
1424   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1425   PetscCall(VecCUDAGetArrayRead(b, &barray));
1426   xGPU = thrust::device_pointer_cast(xarray);
1427   bGPU = thrust::device_pointer_cast(barray);
1428 
1429   // Reorder b with the row permutation if needed, and wrap the result in fs->X
1430   if (fs->rpermIndices) {
1431     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)));
1432     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1433   } else {
1434     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1435   }
1436 
1437   // Solve L Y = X
1438   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1439   // Note that cusparseSpSV_solve() secretly uses the external buffer used in cusparseSpSV_analysis()!
1440   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_L));
1441 
1442   // Solve U X = Y
1443   if (fs->cpermIndices) {
1444     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1445   } else {
1446     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1447   }
1448   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_U));
1449 
1450   // Reorder X with the column permutation if needed, and put the result back to x
1451   if (fs->cpermIndices) {
1452     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
1453                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
1454   }
1455   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1456   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1457   PetscCall(PetscLogGpuTimeEnd());
1458   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - m));
1459   PetscFunctionReturn(PETSC_SUCCESS);
1460 }
1461 
1462 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
1463 {
1464   Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
1465   Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
1466   const PetscScalar                    *barray;
1467   PetscScalar                          *xarray;
1468   thrust::device_ptr<const PetscScalar> bGPU;
1469   thrust::device_ptr<PetscScalar>       xGPU;
1470   const cusparseOperation_t             opA = CUSPARSE_OPERATION_TRANSPOSE;
1471   const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
1472   PetscInt                              m   = A->rmap->n;
1473 
1474   PetscFunctionBegin;
1475   PetscCall(PetscLogGpuTimeBegin());
1476   if (!fs->createdTransposeSpSVDescr) { // Call MatSolveTranspose() for the first time
1477     PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
1478     PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* The matrix is still L. We only do transpose solve with it */
1479                                               fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Lt, &fs->spsvBufferSize_Lt));
1480 
1481     PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut));
1482     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));
1483     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
1484     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));
1485     fs->createdTransposeSpSVDescr = PETSC_TRUE;
1486   }
1487 
1488   if (!fs->updatedTransposeSpSVAnalysis) {
1489     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));
1490 
1491     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));
1492     fs->updatedTransposeSpSVAnalysis = PETSC_TRUE;
1493   }
1494 
1495   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1496   PetscCall(VecCUDAGetArrayRead(b, &barray));
1497   xGPU = thrust::device_pointer_cast(xarray);
1498   bGPU = thrust::device_pointer_cast(barray);
1499 
1500   // Reorder b with the row permutation if needed, and wrap the result in fs->X
1501   if (fs->rpermIndices) {
1502     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)));
1503     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1504   } else {
1505     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1506   }
1507 
1508   // Solve Ut Y = X
1509   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1510   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut));
1511 
1512   // Solve Lt X = Y
1513   if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
1514     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
1515   } else {
1516     PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1517   }
1518   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_Lt));
1519 
1520   // Reorder X with the column permutation if needed, and put the result back to x
1521   if (fs->cpermIndices) {
1522     PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
1523                                  thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
1524   }
1525 
1526   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1527   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1528   PetscCall(PetscLogGpuTimeEnd());
1529   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - A->rmap->n));
1530   PetscFunctionReturn(PETSC_SUCCESS);
1531 }
1532 #else
1533 /* Why do we need to analyze the transposed matrix again? Can't we just use op(A) = CUSPARSE_OPERATION_TRANSPOSE in MatSolve_SeqAIJCUSPARSE? */
1534 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat A, Vec bb, Vec xx)
1535 {
1536   PetscInt                              n = xx->map->n;
1537   const PetscScalar                    *barray;
1538   PetscScalar                          *xarray;
1539   thrust::device_ptr<const PetscScalar> bGPU;
1540   thrust::device_ptr<PetscScalar>       xGPU;
1541   Mat_SeqAIJCUSPARSETriFactors         *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1542   Mat_SeqAIJCUSPARSETriFactorStruct    *loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1543   Mat_SeqAIJCUSPARSETriFactorStruct    *upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1544   THRUSTARRAY                          *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1545 
1546   PetscFunctionBegin;
1547   /* Analyze the matrix and create the transpose ... on the fly */
1548   if (!loTriFactorT && !upTriFactorT) {
1549     PetscCall(MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A));
1550     loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1551     upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1552   }
1553 
1554   /* Get the GPU pointers */
1555   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1556   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1557   xGPU = thrust::device_pointer_cast(xarray);
1558   bGPU = thrust::device_pointer_cast(barray);
1559 
1560   PetscCall(PetscLogGpuTimeBegin());
1561   /* First, reorder with the row permutation */
1562   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);
1563 
1564   /* First, solve U */
1565   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(),
1566                                          upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, xarray, tempGPU->data().get(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1567 
1568   /* Then, solve L */
1569   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(),
1570                                          loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, tempGPU->data().get(), xarray, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1571 
1572   /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
1573   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());
1574 
1575   /* Copy the temporary to the full solution. */
1576   thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), tempGPU->begin(), tempGPU->end(), xGPU);
1577 
1578   /* restore */
1579   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1580   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1581   PetscCall(PetscLogGpuTimeEnd());
1582   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1583   PetscFunctionReturn(PETSC_SUCCESS);
1584 }
1585 
1586 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
1587 {
1588   const PetscScalar                 *barray;
1589   PetscScalar                       *xarray;
1590   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1591   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1592   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1593   THRUSTARRAY                       *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1594 
1595   PetscFunctionBegin;
1596   /* Analyze the matrix and create the transpose ... on the fly */
1597   if (!loTriFactorT && !upTriFactorT) {
1598     PetscCall(MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A));
1599     loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtrTranspose;
1600     upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtrTranspose;
1601   }
1602 
1603   /* Get the GPU pointers */
1604   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1605   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1606 
1607   PetscCall(PetscLogGpuTimeBegin());
1608   /* First, solve U */
1609   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(),
1610                                          upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->solveInfo, barray, tempGPU->data().get(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));
1611 
1612   /* Then, solve L */
1613   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(),
1614                                          loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->solveInfo, tempGPU->data().get(), xarray, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));
1615 
1616   /* restore */
1617   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1618   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1619   PetscCall(PetscLogGpuTimeEnd());
1620   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1621   PetscFunctionReturn(PETSC_SUCCESS);
1622 }
1623 
1624 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat A, Vec bb, Vec xx)
1625 {
1626   const PetscScalar                    *barray;
1627   PetscScalar                          *xarray;
1628   thrust::device_ptr<const PetscScalar> bGPU;
1629   thrust::device_ptr<PetscScalar>       xGPU;
1630   Mat_SeqAIJCUSPARSETriFactors         *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1631   Mat_SeqAIJCUSPARSETriFactorStruct    *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1632   Mat_SeqAIJCUSPARSETriFactorStruct    *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1633   THRUSTARRAY                          *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1634 
1635   PetscFunctionBegin;
1636   /* Get the GPU pointers */
1637   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1638   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1639   xGPU = thrust::device_pointer_cast(xarray);
1640   bGPU = thrust::device_pointer_cast(barray);
1641 
1642   PetscCall(PetscLogGpuTimeBegin());
1643   /* First, reorder with the row permutation */
1644   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());
1645 
1646   /* Next, solve L */
1647   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(),
1648                                          loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, tempGPU->data().get(), xarray, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
1649 
1650   /* Then, solve U */
1651   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(),
1652                                          upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, xarray, tempGPU->data().get(), upTriFactor->solvePolicy, upTriFactor->solveBuffer));
1653 
1654   /* Last, reorder with the column permutation */
1655   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);
1656 
1657   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1658   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1659   PetscCall(PetscLogGpuTimeEnd());
1660   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1661   PetscFunctionReturn(PETSC_SUCCESS);
1662 }
1663 
1664 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
1665 {
1666   const PetscScalar                 *barray;
1667   PetscScalar                       *xarray;
1668   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
1669   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->loTriFactorPtr;
1670   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor        = (Mat_SeqAIJCUSPARSETriFactorStruct *)cusparseTriFactors->upTriFactorPtr;
1671   THRUSTARRAY                       *tempGPU            = (THRUSTARRAY *)cusparseTriFactors->workVector;
1672 
1673   PetscFunctionBegin;
1674   /* Get the GPU pointers */
1675   PetscCall(VecCUDAGetArrayWrite(xx, &xarray));
1676   PetscCall(VecCUDAGetArrayRead(bb, &barray));
1677 
1678   PetscCall(PetscLogGpuTimeBegin());
1679   /* First, solve L */
1680   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(),
1681                                          loTriFactor->csrMat->row_offsets->data().get(), loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo, barray, tempGPU->data().get(), loTriFactor->solvePolicy, loTriFactor->solveBuffer));
1682 
1683   /* Next, solve U */
1684   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(),
1685                                          upTriFactor->csrMat->row_offsets->data().get(), upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo, tempGPU->data().get(), xarray, upTriFactor->solvePolicy, upTriFactor->solveBuffer));
1686 
1687   PetscCall(VecCUDARestoreArrayRead(bb, &barray));
1688   PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
1689   PetscCall(PetscLogGpuTimeEnd());
1690   PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
1691   PetscFunctionReturn(PETSC_SUCCESS);
1692 }
1693 #endif
1694 
1695 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
1696 static PetscErrorCode MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, const MatFactorInfo *)
1697 {
1698   Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1699   Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
1700   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
1701   CsrMatrix                    *Acsr;
1702   PetscInt                      m, nz;
1703   PetscBool                     flg;
1704 
1705   PetscFunctionBegin;
1706   if (PetscDefined(USE_DEBUG)) {
1707     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1708     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1709   }
1710 
1711   /* Copy A's value to fact */
1712   m  = fact->rmap->n;
1713   nz = aij->nz;
1714   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1715   Acsr = (CsrMatrix *)Acusp->mat->mat;
1716   PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1717 
1718   PetscCall(PetscLogGpuTimeBegin());
1719   /* Factorize fact inplace */
1720   if (m)
1721     PetscCallCUSPARSE(cusparseXcsrilu02(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1722                                         fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
1723   if (PetscDefined(USE_DEBUG)) {
1724     int              numerical_zero;
1725     cusparseStatus_t status;
1726     status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &numerical_zero);
1727     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);
1728   }
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   /* L, U values have changed, reset the flag to indicate we need to redo cusparseSpSV_analysis() for transpose solve */
1738   fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
1739 
1740   fact->offloadmask            = PETSC_OFFLOAD_GPU;
1741   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.
1742   fact->ops->solvetranspose    = MatSolveTranspose_SeqAIJCUSPARSE_LU;
1743   fact->ops->matsolve          = NULL;
1744   fact->ops->matsolvetranspose = NULL;
1745   PetscCall(PetscLogGpuTimeEnd());
1746   PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
1747   PetscFunctionReturn(PETSC_SUCCESS);
1748 }
1749 
1750 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, IS, IS, const MatFactorInfo *info)
1751 {
1752   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1753   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
1754   PetscInt                      m, nz;
1755 
1756   PetscFunctionBegin;
1757   if (PetscDefined(USE_DEBUG)) {
1758     PetscInt  i;
1759     PetscBool flg, missing;
1760 
1761     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1762     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1763     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);
1764     PetscCall(MatMissingDiagonal(A, &missing, &i));
1765     PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
1766   }
1767 
1768   /* Free the old stale stuff */
1769   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));
1770 
1771   /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
1772      but they will not be used. Allocate them just for easy debugging.
1773    */
1774   PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));
1775 
1776   fact->offloadmask            = PETSC_OFFLOAD_BOTH;
1777   fact->factortype             = MAT_FACTOR_ILU;
1778   fact->info.factor_mallocs    = 0;
1779   fact->info.fill_ratio_given  = info->fill;
1780   fact->info.fill_ratio_needed = 1.0;
1781 
1782   aij->row = NULL;
1783   aij->col = NULL;
1784 
1785   /* ====================================================================== */
1786   /* Copy A's i, j to fact and also allocate the value array of fact.       */
1787   /* We'll do in-place factorization on fact                                */
1788   /* ====================================================================== */
1789   const int *Ai, *Aj;
1790 
1791   m  = fact->rmap->n;
1792   nz = aij->nz;
1793 
1794   PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
1795   PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
1796   PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(*fs->csrVal) * nz));
1797   PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai.  The returned Ai, Aj are 32-bit */
1798   PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1799   PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1800 
1801   /* ====================================================================== */
1802   /* Create descriptors for M, L, U                                         */
1803   /* ====================================================================== */
1804   cusparseFillMode_t fillMode;
1805   cusparseDiagType_t diagType;
1806 
1807   PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
1808   PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
1809   PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));
1810 
1811   /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
1812     cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
1813     assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
1814     all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
1815     assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
1816   */
1817   fillMode = CUSPARSE_FILL_MODE_LOWER;
1818   diagType = CUSPARSE_DIAG_TYPE_UNIT;
1819   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));
1820   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
1821   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
1822 
1823   fillMode = CUSPARSE_FILL_MODE_UPPER;
1824   diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
1825   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));
1826   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
1827   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
1828 
1829   /* ========================================================================= */
1830   /* Query buffer sizes for csrilu0, SpSV and allocate buffers                 */
1831   /* ========================================================================= */
1832   PetscCallCUSPARSE(cusparseCreateCsrilu02Info(&fs->ilu0Info_M));
1833   if (m)
1834     PetscCallCUSPARSE(cusparseXcsrilu02_bufferSize(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1835                                                    fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, &fs->factBufferSize_M));
1836 
1837   PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
1838   PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));
1839 
1840   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
1841   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
1842 
1843   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
1844   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));
1845 
1846   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
1847   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));
1848 
1849   /* From my experiment with the example at https://github.com/NVIDIA/CUDALibrarySamples/tree/master/cuSPARSE/bicgstab,
1850      and discussion at https://github.com/NVIDIA/CUDALibrarySamples/issues/77,
1851      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.
1852      To save memory, we make factBuffer_M share with the bigger of spsvBuffer_L/U.
1853    */
1854   if (fs->spsvBufferSize_L > fs->spsvBufferSize_U) {
1855     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
1856     fs->spsvBuffer_L = fs->factBuffer_M;
1857     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
1858   } else {
1859     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_U, (size_t)fs->factBufferSize_M)));
1860     fs->spsvBuffer_U = fs->factBuffer_M;
1861     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
1862   }
1863 
1864   /* ========================================================================== */
1865   /* Perform analysis of ilu0 on M, SpSv on L and U                             */
1866   /* The lower(upper) triangular part of M has the same sparsity pattern as L(U)*/
1867   /* ========================================================================== */
1868   int              structural_zero;
1869   cusparseStatus_t status;
1870 
1871   fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
1872   if (m)
1873     PetscCallCUSPARSE(cusparseXcsrilu02_analysis(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
1874                                                  fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
1875   if (PetscDefined(USE_DEBUG)) {
1876     /* Function cusparseXcsrilu02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
1877     status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &structural_zero);
1878     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);
1879   }
1880 
1881   /* Estimate FLOPs of the numeric factorization */
1882   {
1883     Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
1884     PetscInt      *Ai, *Adiag, nzRow, nzLeft;
1885     PetscLogDouble flops = 0.0;
1886 
1887     PetscCall(MatMarkDiagonal_SeqAIJ(A));
1888     Ai    = Aseq->i;
1889     Adiag = Aseq->diag;
1890     for (PetscInt i = 0; i < m; i++) {
1891       if (Ai[i] < Adiag[i] && Adiag[i] < Ai[i + 1]) { /* There are nonzeros left to the diagonal of row i */
1892         nzRow  = Ai[i + 1] - Ai[i];
1893         nzLeft = Adiag[i] - Ai[i];
1894         /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
1895           and include the eliminated one will be updated, which incurs a multiplication and an addition.
1896         */
1897         nzLeft = (nzRow - 1) / 2;
1898         flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
1899       }
1900     }
1901     fs->numericFactFlops = flops;
1902   }
1903   fact->ops->lufactornumeric = MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0;
1904   PetscFunctionReturn(PETSC_SUCCESS);
1905 }
1906 
1907 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_ICC0(Mat fact, Vec b, Vec x)
1908 {
1909   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1910   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
1911   const PetscScalar            *barray;
1912   PetscScalar                  *xarray;
1913 
1914   PetscFunctionBegin;
1915   PetscCall(VecCUDAGetArrayWrite(x, &xarray));
1916   PetscCall(VecCUDAGetArrayRead(b, &barray));
1917   PetscCall(PetscLogGpuTimeBegin());
1918 
1919   /* Solve L*y = b */
1920   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
1921   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
1922   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* L Y = X */
1923                                        fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L));
1924 
1925   /* Solve Lt*x = y */
1926   PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
1927   PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* Lt X = Y */
1928                                        fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt));
1929 
1930   PetscCall(VecCUDARestoreArrayRead(b, &barray));
1931   PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
1932 
1933   PetscCall(PetscLogGpuTimeEnd());
1934   PetscCall(PetscLogGpuFlops(2.0 * aij->nz - fact->rmap->n));
1935   PetscFunctionReturn(PETSC_SUCCESS);
1936 }
1937 
1938 static PetscErrorCode MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, const MatFactorInfo *)
1939 {
1940   Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1941   Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
1942   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
1943   CsrMatrix                    *Acsr;
1944   PetscInt                      m, nz;
1945   PetscBool                     flg;
1946 
1947   PetscFunctionBegin;
1948   if (PetscDefined(USE_DEBUG)) {
1949     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
1950     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
1951   }
1952 
1953   /* Copy A's value to fact */
1954   m  = fact->rmap->n;
1955   nz = aij->nz;
1956   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
1957   Acsr = (CsrMatrix *)Acusp->mat->mat;
1958   PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
1959 
1960   /* Factorize fact inplace */
1961   /* https://docs.nvidia.com/cuda/cusparse/index.html#csric02_solve
1962      Function csric02() only takes the lower triangular part of matrix A to perform factorization.
1963      The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, the fill mode and diagonal type are ignored,
1964      and the strictly upper triangular part is ignored and never touched. It does not matter if A is Hermitian or not.
1965      In other words, from the point of view of csric02() A is Hermitian and only the lower triangular part is provided.
1966    */
1967   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));
1968   if (PetscDefined(USE_DEBUG)) {
1969     int              numerical_zero;
1970     cusparseStatus_t status;
1971     status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &numerical_zero);
1972     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);
1973   }
1974 
1975   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));
1976 
1977   /* Note that cusparse reports this error if we use double and CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE
1978     ** On entry to cusparseSpSV_analysis(): conjugate transpose (opA) is not supported for matA data type, current -> CUDA_R_64F
1979   */
1980   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));
1981 
1982   fact->offloadmask            = PETSC_OFFLOAD_GPU;
1983   fact->ops->solve             = MatSolve_SeqAIJCUSPARSE_ICC0;
1984   fact->ops->solvetranspose    = MatSolve_SeqAIJCUSPARSE_ICC0;
1985   fact->ops->matsolve          = NULL;
1986   fact->ops->matsolvetranspose = NULL;
1987   PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
1988   PetscFunctionReturn(PETSC_SUCCESS);
1989 }
1990 
1991 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, IS, const MatFactorInfo *info)
1992 {
1993   Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
1994   Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
1995   PetscInt                      m, nz;
1996 
1997   PetscFunctionBegin;
1998   if (PetscDefined(USE_DEBUG)) {
1999     PetscInt  i;
2000     PetscBool flg, missing;
2001 
2002     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2003     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
2004     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);
2005     PetscCall(MatMissingDiagonal(A, &missing, &i));
2006     PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
2007   }
2008 
2009   /* Free the old stale stuff */
2010   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));
2011 
2012   /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
2013      but they will not be used. Allocate them just for easy debugging.
2014    */
2015   PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));
2016 
2017   fact->offloadmask            = PETSC_OFFLOAD_BOTH;
2018   fact->factortype             = MAT_FACTOR_ICC;
2019   fact->info.factor_mallocs    = 0;
2020   fact->info.fill_ratio_given  = info->fill;
2021   fact->info.fill_ratio_needed = 1.0;
2022 
2023   aij->row = NULL;
2024   aij->col = NULL;
2025 
2026   /* ====================================================================== */
2027   /* Copy A's i, j to fact and also allocate the value array of fact.       */
2028   /* We'll do in-place factorization on fact                                */
2029   /* ====================================================================== */
2030   const int *Ai, *Aj;
2031 
2032   m  = fact->rmap->n;
2033   nz = aij->nz;
2034 
2035   PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
2036   PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
2037   PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(PetscScalar) * nz));
2038   PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai */
2039   PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
2040   PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
2041 
2042   /* ====================================================================== */
2043   /* Create mat descriptors for M, L                                        */
2044   /* ====================================================================== */
2045   cusparseFillMode_t fillMode;
2046   cusparseDiagType_t diagType;
2047 
2048   PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
2049   PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
2050   PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));
2051 
2052   /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
2053     cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
2054     assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
2055     all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
2056     assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
2057   */
2058   fillMode = CUSPARSE_FILL_MODE_LOWER;
2059   diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
2060   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));
2061   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
2062   PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));
2063 
2064   /* ========================================================================= */
2065   /* Query buffer sizes for csric0, SpSV of L and Lt, and allocate buffers     */
2066   /* ========================================================================= */
2067   PetscCallCUSPARSE(cusparseCreateCsric02Info(&fs->ic0Info_M));
2068   if (m) PetscCallCUSPARSE(cusparseXcsric02_bufferSize(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, &fs->factBufferSize_M));
2069 
2070   PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
2071   PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));
2072 
2073   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
2074   PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));
2075 
2076   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
2077   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));
2078 
2079   PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
2080   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));
2081 
2082   /* To save device memory, we make the factorization buffer share with one of the solver buffer.
2083      See also comments in MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0().
2084    */
2085   if (fs->spsvBufferSize_L > fs->spsvBufferSize_Lt) {
2086     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
2087     fs->spsvBuffer_L = fs->factBuffer_M;
2088     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
2089   } else {
2090     PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_Lt, (size_t)fs->factBufferSize_M)));
2091     fs->spsvBuffer_Lt = fs->factBuffer_M;
2092     PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
2093   }
2094 
2095   /* ========================================================================== */
2096   /* Perform analysis of ic0 on M                                               */
2097   /* The lower triangular part of M has the same sparsity pattern as L          */
2098   /* ========================================================================== */
2099   int              structural_zero;
2100   cusparseStatus_t status;
2101 
2102   fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
2103   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));
2104   if (PetscDefined(USE_DEBUG)) {
2105     /* Function cusparseXcsric02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
2106     status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &structural_zero);
2107     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);
2108   }
2109 
2110   /* Estimate FLOPs of the numeric factorization */
2111   {
2112     Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
2113     PetscInt      *Ai, nzRow, nzLeft;
2114     PetscLogDouble flops = 0.0;
2115 
2116     Ai = Aseq->i;
2117     for (PetscInt i = 0; i < m; i++) {
2118       nzRow = Ai[i + 1] - Ai[i];
2119       if (nzRow > 1) {
2120         /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
2121           and include the eliminated one will be updated, which incurs a multiplication and an addition.
2122         */
2123         nzLeft = (nzRow - 1) / 2;
2124         flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
2125       }
2126     }
2127     fs->numericFactFlops = flops;
2128   }
2129   fact->ops->choleskyfactornumeric = MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0;
2130   PetscFunctionReturn(PETSC_SUCCESS);
2131 }
2132 #endif
2133 
2134 static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
2135 {
2136   // use_cpu_solve is a field in Mat_SeqAIJCUSPARSE. B, a factored matrix, uses Mat_SeqAIJCUSPARSETriFactors.
2137   Mat_SeqAIJCUSPARSE *cusparsestruct = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);
2138 
2139   PetscFunctionBegin;
2140   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2141   PetscCall(MatLUFactorNumeric_SeqAIJ(B, A, info));
2142   B->offloadmask = PETSC_OFFLOAD_CPU;
2143 
2144   if (!cusparsestruct->use_cpu_solve) {
2145 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2146     B->ops->solve          = MatSolve_SeqAIJCUSPARSE_LU;
2147     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_LU;
2148 #else
2149     /* determine which version of MatSolve needs to be used. */
2150     Mat_SeqAIJ *b     = (Mat_SeqAIJ *)B->data;
2151     IS          isrow = b->row, iscol = b->col;
2152     PetscBool   row_identity, col_identity;
2153 
2154     PetscCall(ISIdentity(isrow, &row_identity));
2155     PetscCall(ISIdentity(iscol, &col_identity));
2156     if (row_identity && col_identity) {
2157       B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
2158       B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
2159     } else {
2160       B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
2161       B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
2162     }
2163 #endif
2164   }
2165   B->ops->matsolve          = NULL;
2166   B->ops->matsolvetranspose = NULL;
2167 
2168   /* get the triangular factors */
2169   if (!cusparsestruct->use_cpu_solve) PetscCall(MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(B));
2170   PetscFunctionReturn(PETSC_SUCCESS);
2171 }
2172 
2173 static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2174 {
2175   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(B->spptr);
2176 
2177   PetscFunctionBegin;
2178   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2179   PetscCall(MatLUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
2180   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
2181   PetscFunctionReturn(PETSC_SUCCESS);
2182 }
2183 
2184 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
2185 {
2186   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2187 
2188   PetscFunctionBegin;
2189 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2190   PetscBool row_identity = PETSC_FALSE, col_identity = PETSC_FALSE;
2191   if (cusparseTriFactors->factorizeOnDevice) {
2192     PetscCall(ISIdentity(isrow, &row_identity));
2193     PetscCall(ISIdentity(iscol, &col_identity));
2194   }
2195   if (!info->levels && row_identity && col_identity) {
2196     PetscCall(MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(B, A, isrow, iscol, info));
2197   } else
2198 #endif
2199   {
2200     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2201     PetscCall(MatILUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
2202     B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
2203   }
2204   PetscFunctionReturn(PETSC_SUCCESS);
2205 }
2206 
2207 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
2208 {
2209   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2210 
2211   PetscFunctionBegin;
2212 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2213   PetscBool perm_identity = PETSC_FALSE;
2214   if (cusparseTriFactors->factorizeOnDevice) PetscCall(ISIdentity(perm, &perm_identity));
2215   if (!info->levels && perm_identity) {
2216     PetscCall(MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(B, A, perm, info));
2217   } else
2218 #endif
2219   {
2220     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2221     PetscCall(MatICCFactorSymbolic_SeqAIJ(B, A, perm, info));
2222     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
2223   }
2224   PetscFunctionReturn(PETSC_SUCCESS);
2225 }
2226 
2227 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
2228 {
2229   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;
2230 
2231   PetscFunctionBegin;
2232   PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
2233   PetscCall(MatCholeskyFactorSymbolic_SeqAIJ(B, A, perm, info));
2234   B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
2235   PetscFunctionReturn(PETSC_SUCCESS);
2236 }
2237 
2238 static PetscErrorCode MatFactorGetSolverType_seqaij_cusparse(Mat, MatSolverType *type)
2239 {
2240   PetscFunctionBegin;
2241   *type = MATSOLVERCUSPARSE;
2242   PetscFunctionReturn(PETSC_SUCCESS);
2243 }
2244 
2245 /*MC
2246   MATSOLVERCUSPARSE = "cusparse" - A matrix type providing triangular solvers for seq matrices
2247   on a single GPU of type, `MATSEQAIJCUSPARSE`. Currently supported
2248   algorithms are ILU(k) and ICC(k). Typically, deeper factorizations (larger k) results in poorer
2249   performance in the triangular solves. Full LU, and Cholesky decompositions can be solved through the
2250   CuSPARSE triangular solve algorithm. However, the performance can be quite poor and thus these
2251   algorithms are not recommended. This class does NOT support direct solver operations.
2252 
2253   Level: beginner
2254 
2255 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatCreateSeqAIJCUSPARSE()`,
2256           `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
2257 M*/
2258 
2259 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat A, MatFactorType ftype, Mat *B)
2260 {
2261   PetscInt  n = A->rmap->n;
2262   PetscBool factOnDevice, factOnHost;
2263   char     *prefix;
2264   char      factPlace[32] = "device"; /* the default */
2265 
2266   PetscFunctionBegin;
2267   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
2268   PetscCall(MatSetSizes(*B, n, n, n, n));
2269   (*B)->factortype = ftype; // factortype makes MatSetType() allocate spptr of type Mat_SeqAIJCUSPARSETriFactors
2270   PetscCall(MatSetType(*B, MATSEQAIJCUSPARSE));
2271 
2272   prefix = (*B)->factorprefix ? (*B)->factorprefix : ((PetscObject)A)->prefix;
2273   PetscOptionsBegin(PetscObjectComm((PetscObject)*B), prefix, "MatGetFactor", "Mat");
2274   PetscCall(PetscOptionsString("-mat_factor_bind_factorization", "Do matrix factorization on host or device when possible", "MatGetFactor", NULL, factPlace, sizeof(factPlace), NULL));
2275   PetscOptionsEnd();
2276   PetscCall(PetscStrcasecmp("device", factPlace, &factOnDevice));
2277   PetscCall(PetscStrcasecmp("host", factPlace, &factOnHost));
2278   PetscCheck(factOnDevice || factOnHost, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_OUTOFRANGE, "Wrong option %s to -mat_factor_bind_factorization <string>. Only host and device are allowed", factPlace);
2279   ((Mat_SeqAIJCUSPARSETriFactors *)(*B)->spptr)->factorizeOnDevice = factOnDevice;
2280 
2281   if (A->boundtocpu && A->bindingpropagates) PetscCall(MatBindToCPU(*B, PETSC_TRUE));
2282   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
2283     PetscCall(MatSetBlockSizesFromMats(*B, A, A));
2284     if (!A->boundtocpu) {
2285       (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJCUSPARSE;
2286       (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJCUSPARSE;
2287     } else {
2288       (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
2289       (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
2290     }
2291     PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]));
2292     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILU]));
2293     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILUDT]));
2294   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
2295     if (!A->boundtocpu) {
2296       (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJCUSPARSE;
2297       (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJCUSPARSE;
2298     } else {
2299       (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
2300       (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
2301     }
2302     PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_CHOLESKY]));
2303     PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ICC]));
2304   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor type not supported for CUSPARSE Matrix Types");
2305 
2306   PetscCall(MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL));
2307   (*B)->canuseordering = PETSC_TRUE;
2308   PetscCall(PetscObjectComposeFunction((PetscObject)*B, "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_cusparse));
2309   PetscFunctionReturn(PETSC_SUCCESS);
2310 }
2311 
2312 static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat A)
2313 {
2314   Mat_SeqAIJ         *a    = (Mat_SeqAIJ *)A->data;
2315   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2316 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2317   Mat_SeqAIJCUSPARSETriFactors *fs = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
2318 #endif
2319 
2320   PetscFunctionBegin;
2321   if (A->offloadmask == PETSC_OFFLOAD_GPU) {
2322     PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
2323     if (A->factortype == MAT_FACTOR_NONE) {
2324       CsrMatrix *matrix = (CsrMatrix *)cusp->mat->mat;
2325       PetscCallCUDA(cudaMemcpy(a->a, matrix->values->data().get(), a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
2326     }
2327 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2328     else if (fs->csrVal) {
2329       /* We have a factorized matrix on device and are able to copy it to host */
2330       PetscCallCUDA(cudaMemcpy(a->a, fs->csrVal, a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
2331     }
2332 #endif
2333     else
2334       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for copying this type of factorized matrix from device to host");
2335     PetscCall(PetscLogGpuToCpu(a->nz * sizeof(PetscScalar)));
2336     PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
2337     A->offloadmask = PETSC_OFFLOAD_BOTH;
2338   }
2339   PetscFunctionReturn(PETSC_SUCCESS);
2340 }
2341 
2342 static PetscErrorCode MatSeqAIJGetArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2343 {
2344   PetscFunctionBegin;
2345   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2346   *array = ((Mat_SeqAIJ *)A->data)->a;
2347   PetscFunctionReturn(PETSC_SUCCESS);
2348 }
2349 
2350 static PetscErrorCode MatSeqAIJRestoreArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2351 {
2352   PetscFunctionBegin;
2353   A->offloadmask = PETSC_OFFLOAD_CPU;
2354   *array         = NULL;
2355   PetscFunctionReturn(PETSC_SUCCESS);
2356 }
2357 
2358 static PetscErrorCode MatSeqAIJGetArrayRead_SeqAIJCUSPARSE(Mat A, const PetscScalar *array[])
2359 {
2360   PetscFunctionBegin;
2361   PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
2362   *array = ((Mat_SeqAIJ *)A->data)->a;
2363   PetscFunctionReturn(PETSC_SUCCESS);
2364 }
2365 
2366 static PetscErrorCode MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE(Mat, const PetscScalar *array[])
2367 {
2368   PetscFunctionBegin;
2369   *array = NULL;
2370   PetscFunctionReturn(PETSC_SUCCESS);
2371 }
2372 
2373 static PetscErrorCode MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2374 {
2375   PetscFunctionBegin;
2376   *array = ((Mat_SeqAIJ *)A->data)->a;
2377   PetscFunctionReturn(PETSC_SUCCESS);
2378 }
2379 
2380 static PetscErrorCode MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
2381 {
2382   PetscFunctionBegin;
2383   A->offloadmask = PETSC_OFFLOAD_CPU;
2384   *array         = NULL;
2385   PetscFunctionReturn(PETSC_SUCCESS);
2386 }
2387 
2388 static PetscErrorCode MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE(Mat A, const PetscInt **i, const PetscInt **j, PetscScalar **a, PetscMemType *mtype)
2389 {
2390   Mat_SeqAIJCUSPARSE *cusp;
2391   CsrMatrix          *matrix;
2392 
2393   PetscFunctionBegin;
2394   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2395   PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2396   cusp = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);
2397   PetscCheck(cusp != NULL, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "cusp is NULL");
2398   matrix = (CsrMatrix *)cusp->mat->mat;
2399 
2400   if (i) {
2401 #if !defined(PETSC_USE_64BIT_INDICES)
2402     *i = matrix->row_offsets->data().get();
2403 #else
2404     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
2405 #endif
2406   }
2407   if (j) {
2408 #if !defined(PETSC_USE_64BIT_INDICES)
2409     *j = matrix->column_indices->data().get();
2410 #else
2411     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
2412 #endif
2413   }
2414   if (a) *a = matrix->values->data().get();
2415   if (mtype) *mtype = PETSC_MEMTYPE_CUDA;
2416   PetscFunctionReturn(PETSC_SUCCESS);
2417 }
2418 
2419 PETSC_INTERN PetscErrorCode MatSeqAIJCUSPARSECopyToGPU(Mat A)
2420 {
2421   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
2422   Mat_SeqAIJCUSPARSEMultStruct *matstruct      = cusparsestruct->mat;
2423   Mat_SeqAIJ                   *a              = (Mat_SeqAIJ *)A->data;
2424   PetscInt                      m              = A->rmap->n, *ii, *ridx, tmp;
2425   cusparseStatus_t              stat;
2426   PetscBool                     both = PETSC_TRUE;
2427 
2428   PetscFunctionBegin;
2429   PetscCheck(!A->boundtocpu, PETSC_COMM_SELF, PETSC_ERR_GPU, "Cannot copy to GPU");
2430   if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
2431     if (A->nonzerostate == cusparsestruct->nonzerostate && cusparsestruct->format == MAT_CUSPARSE_CSR) { /* Copy values only */
2432       CsrMatrix *matrix;
2433       matrix = (CsrMatrix *)cusparsestruct->mat->mat;
2434 
2435       PetscCheck(!a->nz || a->a, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR values");
2436       PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2437       matrix->values->assign(a->a, a->a + a->nz);
2438       PetscCallCUDA(WaitForCUDA());
2439       PetscCall(PetscLogCpuToGpu(a->nz * sizeof(PetscScalar)));
2440       PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2441       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
2442     } else {
2443       PetscInt nnz;
2444       PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2445       PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusparsestruct->mat, cusparsestruct->format));
2446       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
2447       delete cusparsestruct->workVector;
2448       delete cusparsestruct->rowoffsets_gpu;
2449       cusparsestruct->workVector     = NULL;
2450       cusparsestruct->rowoffsets_gpu = NULL;
2451       try {
2452         if (a->compressedrow.use) {
2453           m    = a->compressedrow.nrows;
2454           ii   = a->compressedrow.i;
2455           ridx = a->compressedrow.rindex;
2456         } else {
2457           m    = A->rmap->n;
2458           ii   = a->i;
2459           ridx = NULL;
2460         }
2461         PetscCheck(ii, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR row data");
2462         if (!a->a) {
2463           nnz  = ii[m];
2464           both = PETSC_FALSE;
2465         } else nnz = a->nz;
2466         PetscCheck(!nnz || a->j, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR column data");
2467 
2468         /* create cusparse matrix */
2469         cusparsestruct->nrows = m;
2470         matstruct             = new Mat_SeqAIJCUSPARSEMultStruct;
2471         PetscCallCUSPARSE(cusparseCreateMatDescr(&matstruct->descr));
2472         PetscCallCUSPARSE(cusparseSetMatIndexBase(matstruct->descr, CUSPARSE_INDEX_BASE_ZERO));
2473         PetscCallCUSPARSE(cusparseSetMatType(matstruct->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
2474 
2475         PetscCallCUDA(cudaMalloc((void **)&matstruct->alpha_one, sizeof(PetscScalar)));
2476         PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_zero, sizeof(PetscScalar)));
2477         PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_one, sizeof(PetscScalar)));
2478         PetscCallCUDA(cudaMemcpy(matstruct->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2479         PetscCallCUDA(cudaMemcpy(matstruct->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2480         PetscCallCUDA(cudaMemcpy(matstruct->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
2481         PetscCallCUSPARSE(cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE));
2482 
2483         /* Build a hybrid/ellpack matrix if this option is chosen for the storage */
2484         if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
2485           /* set the matrix */
2486           CsrMatrix *mat   = new CsrMatrix;
2487           mat->num_rows    = m;
2488           mat->num_cols    = A->cmap->n;
2489           mat->num_entries = nnz;
2490           PetscCallCXX(mat->row_offsets = new THRUSTINTARRAY32(m + 1));
2491           mat->row_offsets->assign(ii, ii + m + 1);
2492 
2493           PetscCallCXX(mat->column_indices = new THRUSTINTARRAY32(nnz));
2494           mat->column_indices->assign(a->j, a->j + nnz);
2495 
2496           PetscCallCXX(mat->values = new THRUSTARRAY(nnz));
2497           if (a->a) mat->values->assign(a->a, a->a + nnz);
2498 
2499           /* assign the pointer */
2500           matstruct->mat = mat;
2501 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2502           if (mat->num_rows) { /* cusparse errors on empty matrices! */
2503             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 */
2504                                      CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
2505             PetscCallCUSPARSE(stat);
2506           }
2507 #endif
2508         } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
2509 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2510           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
2511 #else
2512           CsrMatrix *mat   = new CsrMatrix;
2513           mat->num_rows    = m;
2514           mat->num_cols    = A->cmap->n;
2515           mat->num_entries = nnz;
2516           PetscCallCXX(mat->row_offsets = new THRUSTINTARRAY32(m + 1));
2517           mat->row_offsets->assign(ii, ii + m + 1);
2518 
2519           PetscCallCXX(mat->column_indices = new THRUSTINTARRAY32(nnz));
2520           mat->column_indices->assign(a->j, a->j + nnz);
2521 
2522           PetscCallCXX(mat->values = new THRUSTARRAY(nnz));
2523           if (a->a) mat->values->assign(a->a, a->a + nnz);
2524 
2525           cusparseHybMat_t hybMat;
2526           PetscCallCUSPARSE(cusparseCreateHybMat(&hybMat));
2527           cusparseHybPartition_t partition = cusparsestruct->format == MAT_CUSPARSE_ELL ? CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
2528           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);
2529           PetscCallCUSPARSE(stat);
2530           /* assign the pointer */
2531           matstruct->mat = hybMat;
2532 
2533           if (mat) {
2534             if (mat->values) delete (THRUSTARRAY *)mat->values;
2535             if (mat->column_indices) delete (THRUSTINTARRAY32 *)mat->column_indices;
2536             if (mat->row_offsets) delete (THRUSTINTARRAY32 *)mat->row_offsets;
2537             delete (CsrMatrix *)mat;
2538           }
2539 #endif
2540         }
2541 
2542         /* assign the compressed row indices */
2543         if (a->compressedrow.use) {
2544           PetscCallCXX(cusparsestruct->workVector = new THRUSTARRAY(m));
2545           PetscCallCXX(matstruct->cprowIndices = new THRUSTINTARRAY(m));
2546           matstruct->cprowIndices->assign(ridx, ridx + m);
2547           tmp = m;
2548         } else {
2549           cusparsestruct->workVector = NULL;
2550           matstruct->cprowIndices    = NULL;
2551           tmp                        = 0;
2552         }
2553         PetscCall(PetscLogCpuToGpu(((m + 1) + (a->nz)) * sizeof(int) + tmp * sizeof(PetscInt) + (3 + (a->nz)) * sizeof(PetscScalar)));
2554 
2555         /* assign the pointer */
2556         cusparsestruct->mat = matstruct;
2557       } catch (char *ex) {
2558         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
2559       }
2560       PetscCallCUDA(WaitForCUDA());
2561       PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
2562       cusparsestruct->nonzerostate = A->nonzerostate;
2563     }
2564     if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
2565   }
2566   PetscFunctionReturn(PETSC_SUCCESS);
2567 }
2568 
2569 struct VecCUDAPlusEquals {
2570   template <typename Tuple>
2571   __host__ __device__ void operator()(Tuple t)
2572   {
2573     thrust::get<1>(t) = thrust::get<1>(t) + thrust::get<0>(t);
2574   }
2575 };
2576 
2577 struct VecCUDAEquals {
2578   template <typename Tuple>
2579   __host__ __device__ void operator()(Tuple t)
2580   {
2581     thrust::get<1>(t) = thrust::get<0>(t);
2582   }
2583 };
2584 
2585 struct VecCUDAEqualsReverse {
2586   template <typename Tuple>
2587   __host__ __device__ void operator()(Tuple t)
2588   {
2589     thrust::get<0>(t) = thrust::get<1>(t);
2590   }
2591 };
2592 
2593 struct MatMatCusparse {
2594   PetscBool      cisdense;
2595   PetscScalar   *Bt;
2596   Mat            X;
2597   PetscBool      reusesym; /* Cusparse does not have split symbolic and numeric phases for sparse matmat operations */
2598   PetscLogDouble flops;
2599   CsrMatrix     *Bcsr;
2600 
2601 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2602   cusparseSpMatDescr_t matSpBDescr;
2603   PetscBool            initialized; /* C = alpha op(A) op(B) + beta C */
2604   cusparseDnMatDescr_t matBDescr;
2605   cusparseDnMatDescr_t matCDescr;
2606   PetscInt             Blda, Clda; /* Record leading dimensions of B and C here to detect changes*/
2607   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2608   void *dBuffer4;
2609   void *dBuffer5;
2610   #endif
2611   size_t                mmBufferSize;
2612   void                 *mmBuffer;
2613   void                 *mmBuffer2; /* SpGEMM WorkEstimation buffer */
2614   cusparseSpGEMMDescr_t spgemmDesc;
2615 #endif
2616 };
2617 
2618 static PetscErrorCode MatDestroy_MatMatCusparse(void *data)
2619 {
2620   MatMatCusparse *mmdata = (MatMatCusparse *)data;
2621 
2622   PetscFunctionBegin;
2623   PetscCallCUDA(cudaFree(mmdata->Bt));
2624   delete mmdata->Bcsr;
2625 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2626   if (mmdata->matSpBDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mmdata->matSpBDescr));
2627   if (mmdata->matBDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
2628   if (mmdata->matCDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
2629   if (mmdata->spgemmDesc) PetscCallCUSPARSE(cusparseSpGEMM_destroyDescr(mmdata->spgemmDesc));
2630   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2631   if (mmdata->dBuffer4) PetscCallCUDA(cudaFree(mmdata->dBuffer4));
2632   if (mmdata->dBuffer5) PetscCallCUDA(cudaFree(mmdata->dBuffer5));
2633   #endif
2634   if (mmdata->mmBuffer) PetscCallCUDA(cudaFree(mmdata->mmBuffer));
2635   if (mmdata->mmBuffer2) PetscCallCUDA(cudaFree(mmdata->mmBuffer2));
2636 #endif
2637   PetscCall(MatDestroy(&mmdata->X));
2638   PetscCall(PetscFree(data));
2639   PetscFunctionReturn(PETSC_SUCCESS);
2640 }
2641 
2642 #include <../src/mat/impls/dense/seq/dense.h> // MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal()
2643 
2644 static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
2645 {
2646   Mat_Product                  *product = C->product;
2647   Mat                           A, B;
2648   PetscInt                      m, n, blda, clda;
2649   PetscBool                     flg, biscuda;
2650   Mat_SeqAIJCUSPARSE           *cusp;
2651   cusparseStatus_t              stat;
2652   cusparseOperation_t           opA;
2653   const PetscScalar            *barray;
2654   PetscScalar                  *carray;
2655   MatMatCusparse               *mmdata;
2656   Mat_SeqAIJCUSPARSEMultStruct *mat;
2657   CsrMatrix                    *csrmat;
2658 
2659   PetscFunctionBegin;
2660   MatCheckProduct(C, 1);
2661   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
2662   mmdata = (MatMatCusparse *)product->data;
2663   A      = product->A;
2664   B      = product->B;
2665   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2666   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2667   /* currently CopyToGpu does not copy if the matrix is bound to CPU
2668      Instead of silently accepting the wrong answer, I prefer to raise the error */
2669   PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2670   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2671   cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2672   switch (product->type) {
2673   case MATPRODUCT_AB:
2674   case MATPRODUCT_PtAP:
2675     mat = cusp->mat;
2676     opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2677     m   = A->rmap->n;
2678     n   = B->cmap->n;
2679     break;
2680   case MATPRODUCT_AtB:
2681     if (!A->form_explicit_transpose) {
2682       mat = cusp->mat;
2683       opA = CUSPARSE_OPERATION_TRANSPOSE;
2684     } else {
2685       PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
2686       mat = cusp->matTranspose;
2687       opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2688     }
2689     m = A->cmap->n;
2690     n = B->cmap->n;
2691     break;
2692   case MATPRODUCT_ABt:
2693   case MATPRODUCT_RARt:
2694     mat = cusp->mat;
2695     opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
2696     m   = A->rmap->n;
2697     n   = B->rmap->n;
2698     break;
2699   default:
2700     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2701   }
2702   PetscCheck(mat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing Mat_SeqAIJCUSPARSEMultStruct");
2703   csrmat = (CsrMatrix *)mat->mat;
2704   /* if the user passed a CPU matrix, copy the data to the GPU */
2705   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSECUDA, &biscuda));
2706   if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSECUDA, MAT_INPLACE_MATRIX, &B));
2707   PetscCall(MatDenseGetArrayReadAndMemType(B, &barray, nullptr));
2708 
2709   PetscCall(MatDenseGetLDA(B, &blda));
2710   if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
2711     PetscCall(MatDenseGetArrayWriteAndMemType(mmdata->X, &carray, nullptr));
2712     PetscCall(MatDenseGetLDA(mmdata->X, &clda));
2713   } else {
2714     PetscCall(MatDenseGetArrayWriteAndMemType(C, &carray, nullptr));
2715     PetscCall(MatDenseGetLDA(C, &clda));
2716   }
2717 
2718   PetscCall(PetscLogGpuTimeBegin());
2719 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2720   cusparseOperation_t opB = (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) ? CUSPARSE_OPERATION_TRANSPOSE : CUSPARSE_OPERATION_NON_TRANSPOSE;
2721   /* (re)allocate mmBuffer if not initialized or LDAs are different */
2722   if (!mmdata->initialized || mmdata->Blda != blda || mmdata->Clda != clda) {
2723     size_t mmBufferSize;
2724     if (mmdata->initialized && mmdata->Blda != blda) {
2725       PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
2726       mmdata->matBDescr = NULL;
2727     }
2728     if (!mmdata->matBDescr) {
2729       PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matBDescr, B->rmap->n, B->cmap->n, blda, (void *)barray, cusparse_scalartype, CUSPARSE_ORDER_COL));
2730       mmdata->Blda = blda;
2731     }
2732 
2733     if (mmdata->initialized && mmdata->Clda != clda) {
2734       PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
2735       mmdata->matCDescr = NULL;
2736     }
2737     if (!mmdata->matCDescr) { /* matCDescr is for C or mmdata->X */
2738       PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matCDescr, m, n, clda, (void *)carray, cusparse_scalartype, CUSPARSE_ORDER_COL));
2739       mmdata->Clda = clda;
2740     }
2741 
2742     if (!mat->matDescr) {
2743       stat = cusparseCreateCsr(&mat->matDescr, 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 */
2744                                CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
2745       PetscCallCUSPARSE(stat);
2746     }
2747     stat = cusparseSpMM_bufferSize(cusp->handle, opA, opB, mat->alpha_one, mat->matDescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, &mmBufferSize);
2748     PetscCallCUSPARSE(stat);
2749     if ((mmdata->mmBuffer && mmdata->mmBufferSize < mmBufferSize) || !mmdata->mmBuffer) {
2750       PetscCallCUDA(cudaFree(mmdata->mmBuffer));
2751       PetscCallCUDA(cudaMalloc(&mmdata->mmBuffer, mmBufferSize));
2752       mmdata->mmBufferSize = mmBufferSize;
2753     }
2754     mmdata->initialized = PETSC_TRUE;
2755   } else {
2756     /* to be safe, always update pointers of the mats */
2757     PetscCallCUSPARSE(cusparseSpMatSetValues(mat->matDescr, csrmat->values->data().get()));
2758     PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matBDescr, (void *)barray));
2759     PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matCDescr, (void *)carray));
2760   }
2761 
2762   /* do cusparseSpMM, which supports transpose on B */
2763   stat = cusparseSpMM(cusp->handle, opA, opB, mat->alpha_one, mat->matDescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, mmdata->mmBuffer);
2764   PetscCallCUSPARSE(stat);
2765 #else
2766   PetscInt k;
2767   /* cusparseXcsrmm does not support transpose on B */
2768   if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) {
2769     cublasHandle_t cublasv2handle;
2770     cublasStatus_t cerr;
2771 
2772     PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
2773     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);
2774     PetscCallCUBLAS(cerr);
2775     blda = B->cmap->n;
2776     k    = B->cmap->n;
2777   } else {
2778     k = B->rmap->n;
2779   }
2780 
2781   /* perform the MatMat operation, op(A) is m x k, op(B) is k x n */
2782   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);
2783   PetscCallCUSPARSE(stat);
2784 #endif
2785   PetscCall(PetscLogGpuTimeEnd());
2786   PetscCall(PetscLogGpuFlops(n * 2.0 * csrmat->num_entries));
2787   PetscCall(MatDenseRestoreArrayReadAndMemType(B, &barray));
2788   if (product->type == MATPRODUCT_RARt) {
2789     PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
2790     PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_FALSE, PETSC_FALSE));
2791   } else if (product->type == MATPRODUCT_PtAP) {
2792     PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
2793     PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_TRUE, PETSC_FALSE));
2794   } else {
2795     PetscCall(MatDenseRestoreArrayWriteAndMemType(C, &carray));
2796   }
2797   if (mmdata->cisdense) PetscCall(MatConvert(C, MATSEQDENSE, MAT_INPLACE_MATRIX, &C));
2798   if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSE, MAT_INPLACE_MATRIX, &B));
2799   PetscFunctionReturn(PETSC_SUCCESS);
2800 }
2801 
2802 static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
2803 {
2804   Mat_Product        *product = C->product;
2805   Mat                 A, B;
2806   PetscInt            m, n;
2807   PetscBool           cisdense, flg;
2808   MatMatCusparse     *mmdata;
2809   Mat_SeqAIJCUSPARSE *cusp;
2810 
2811   PetscFunctionBegin;
2812   MatCheckProduct(C, 1);
2813   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
2814   A = product->A;
2815   B = product->B;
2816   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2817   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2818   cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2819   PetscCheck(cusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2820   switch (product->type) {
2821   case MATPRODUCT_AB:
2822     m = A->rmap->n;
2823     n = B->cmap->n;
2824     break;
2825   case MATPRODUCT_AtB:
2826     m = A->cmap->n;
2827     n = B->cmap->n;
2828     break;
2829   case MATPRODUCT_ABt:
2830     m = A->rmap->n;
2831     n = B->rmap->n;
2832     break;
2833   case MATPRODUCT_PtAP:
2834     m = B->cmap->n;
2835     n = B->cmap->n;
2836     break;
2837   case MATPRODUCT_RARt:
2838     m = B->rmap->n;
2839     n = B->rmap->n;
2840     break;
2841   default:
2842     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2843   }
2844   PetscCall(MatSetSizes(C, m, n, m, n));
2845   /* if C is of type MATSEQDENSE (CPU), perform the operation on the GPU and then copy on the CPU */
2846   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &cisdense));
2847   PetscCall(MatSetType(C, MATSEQDENSECUDA));
2848 
2849   /* product data */
2850   PetscCall(PetscNew(&mmdata));
2851   mmdata->cisdense = cisdense;
2852 #if PETSC_PKG_CUDA_VERSION_LT(11, 0, 0)
2853   /* cusparseXcsrmm does not support transpose on B, so we allocate buffer to store B^T */
2854   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)));
2855 #endif
2856   /* for these products we need intermediate storage */
2857   if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
2858     PetscCall(MatCreate(PetscObjectComm((PetscObject)C), &mmdata->X));
2859     PetscCall(MatSetType(mmdata->X, MATSEQDENSECUDA));
2860     if (product->type == MATPRODUCT_RARt) { /* do not preallocate, since the first call to MatDenseCUDAGetArray will preallocate on the GPU for us */
2861       PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->rmap->n, A->rmap->n, B->rmap->n));
2862     } else {
2863       PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->cmap->n, A->rmap->n, B->cmap->n));
2864     }
2865   }
2866   C->product->data    = mmdata;
2867   C->product->destroy = MatDestroy_MatMatCusparse;
2868 
2869   C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA;
2870   PetscFunctionReturn(PETSC_SUCCESS);
2871 }
2872 
2873 static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
2874 {
2875   Mat_Product                  *product = C->product;
2876   Mat                           A, B;
2877   Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
2878   Mat_SeqAIJ                   *c = (Mat_SeqAIJ *)C->data;
2879   Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
2880   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
2881   PetscBool                     flg;
2882   cusparseStatus_t              stat;
2883   MatProductType                ptype;
2884   MatMatCusparse               *mmdata;
2885 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2886   cusparseSpMatDescr_t BmatSpDescr;
2887 #endif
2888   cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */
2889 
2890   PetscFunctionBegin;
2891   MatCheckProduct(C, 1);
2892   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
2893   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQAIJCUSPARSE, &flg));
2894   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for C of type %s", ((PetscObject)C)->type_name);
2895   mmdata = (MatMatCusparse *)C->product->data;
2896   A      = product->A;
2897   B      = product->B;
2898   if (mmdata->reusesym) { /* this happens when api_user is true, meaning that the matrix values have been already computed in the MatProductSymbolic phase */
2899     mmdata->reusesym = PETSC_FALSE;
2900     Ccusp            = (Mat_SeqAIJCUSPARSE *)C->spptr;
2901     PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2902     Cmat = Ccusp->mat;
2903     PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[C->product->type]);
2904     Ccsr = (CsrMatrix *)Cmat->mat;
2905     PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
2906     goto finalize;
2907   }
2908   if (!c->nz) goto finalize;
2909   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
2910   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
2911   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
2912   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
2913   PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2914   PetscCheck(!B->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
2915   Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
2916   Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
2917   Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
2918   PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2919   PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2920   PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
2921   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
2922   PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
2923 
2924   ptype = product->type;
2925   if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
2926     ptype = MATPRODUCT_AB;
2927     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");
2928   }
2929   if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
2930     ptype = MATPRODUCT_AB;
2931     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");
2932   }
2933   switch (ptype) {
2934   case MATPRODUCT_AB:
2935     Amat = Acusp->mat;
2936     Bmat = Bcusp->mat;
2937     break;
2938   case MATPRODUCT_AtB:
2939     Amat = Acusp->matTranspose;
2940     Bmat = Bcusp->mat;
2941     break;
2942   case MATPRODUCT_ABt:
2943     Amat = Acusp->mat;
2944     Bmat = Bcusp->matTranspose;
2945     break;
2946   default:
2947     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
2948   }
2949   Cmat = Ccusp->mat;
2950   PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
2951   PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
2952   PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[ptype]);
2953   Acsr = (CsrMatrix *)Amat->mat;
2954   Bcsr = mmdata->Bcsr ? mmdata->Bcsr : (CsrMatrix *)Bmat->mat; /* B may be in compressed row storage */
2955   Ccsr = (CsrMatrix *)Cmat->mat;
2956   PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
2957   PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
2958   PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
2959   PetscCall(PetscLogGpuTimeBegin());
2960 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
2961   BmatSpDescr = mmdata->Bcsr ? mmdata->matSpBDescr : Bmat->matDescr; /* B may be in compressed row storage */
2962   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
2963   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
2964   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);
2965   PetscCallCUSPARSE(stat);
2966   #else
2967   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);
2968   PetscCallCUSPARSE(stat);
2969   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);
2970   PetscCallCUSPARSE(stat);
2971   #endif
2972 #else
2973   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,
2974                              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());
2975   PetscCallCUSPARSE(stat);
2976 #endif
2977   PetscCall(PetscLogGpuFlops(mmdata->flops));
2978   PetscCallCUDA(WaitForCUDA());
2979   PetscCall(PetscLogGpuTimeEnd());
2980   C->offloadmask = PETSC_OFFLOAD_GPU;
2981 finalize:
2982   /* shorter version of MatAssemblyEnd_SeqAIJ */
2983   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));
2984   PetscCall(PetscInfo(C, "Number of mallocs during MatSetValues() is 0\n"));
2985   PetscCall(PetscInfo(C, "Maximum nonzeros in any row is %" PetscInt_FMT "\n", c->rmax));
2986   c->reallocs = 0;
2987   C->info.mallocs += 0;
2988   C->info.nz_unneeded = 0;
2989   C->assembled = C->was_assembled = PETSC_TRUE;
2990   C->num_ass++;
2991   PetscFunctionReturn(PETSC_SUCCESS);
2992 }
2993 
2994 static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
2995 {
2996   Mat_Product                  *product = C->product;
2997   Mat                           A, B;
2998   Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
2999   Mat_SeqAIJ                   *a, *b, *c;
3000   Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
3001   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
3002   PetscInt                      i, j, m, n, k;
3003   PetscBool                     flg;
3004   cusparseStatus_t              stat;
3005   MatProductType                ptype;
3006   MatMatCusparse               *mmdata;
3007   PetscLogDouble                flops;
3008   PetscBool                     biscompressed, ciscompressed;
3009 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3010   int64_t              C_num_rows1, C_num_cols1, C_nnz1;
3011   cusparseSpMatDescr_t BmatSpDescr;
3012 #else
3013   int cnz;
3014 #endif
3015   cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */
3016 
3017   PetscFunctionBegin;
3018   MatCheckProduct(C, 1);
3019   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
3020   A = product->A;
3021   B = product->B;
3022   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
3023   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
3024   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
3025   PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
3026   a = (Mat_SeqAIJ *)A->data;
3027   b = (Mat_SeqAIJ *)B->data;
3028   /* product data */
3029   PetscCall(PetscNew(&mmdata));
3030   C->product->data    = mmdata;
3031   C->product->destroy = MatDestroy_MatMatCusparse;
3032 
3033   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
3034   PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
3035   Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr; /* Access spptr after MatSeqAIJCUSPARSECopyToGPU, not before */
3036   Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
3037   PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
3038   PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
3039 
3040   ptype = product->type;
3041   if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
3042     ptype                                          = MATPRODUCT_AB;
3043     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
3044   }
3045   if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
3046     ptype                                          = MATPRODUCT_AB;
3047     product->symbolic_used_the_fact_B_is_symmetric = PETSC_TRUE;
3048   }
3049   biscompressed = PETSC_FALSE;
3050   ciscompressed = PETSC_FALSE;
3051   switch (ptype) {
3052   case MATPRODUCT_AB:
3053     m    = A->rmap->n;
3054     n    = B->cmap->n;
3055     k    = A->cmap->n;
3056     Amat = Acusp->mat;
3057     Bmat = Bcusp->mat;
3058     if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
3059     if (b->compressedrow.use) biscompressed = PETSC_TRUE;
3060     break;
3061   case MATPRODUCT_AtB:
3062     m = A->cmap->n;
3063     n = B->cmap->n;
3064     k = A->rmap->n;
3065     PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
3066     Amat = Acusp->matTranspose;
3067     Bmat = Bcusp->mat;
3068     if (b->compressedrow.use) biscompressed = PETSC_TRUE;
3069     break;
3070   case MATPRODUCT_ABt:
3071     m = A->rmap->n;
3072     n = B->rmap->n;
3073     k = A->cmap->n;
3074     PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
3075     Amat = Acusp->mat;
3076     Bmat = Bcusp->matTranspose;
3077     if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
3078     break;
3079   default:
3080     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
3081   }
3082 
3083   /* create cusparse matrix */
3084   PetscCall(MatSetSizes(C, m, n, m, n));
3085   PetscCall(MatSetType(C, MATSEQAIJCUSPARSE));
3086   c     = (Mat_SeqAIJ *)C->data;
3087   Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
3088   Cmat  = new Mat_SeqAIJCUSPARSEMultStruct;
3089   Ccsr  = new CsrMatrix;
3090 
3091   c->compressedrow.use = ciscompressed;
3092   if (c->compressedrow.use) { /* if a is in compressed row, than c will be in compressed row format */
3093     c->compressedrow.nrows = a->compressedrow.nrows;
3094     PetscCall(PetscMalloc2(c->compressedrow.nrows + 1, &c->compressedrow.i, c->compressedrow.nrows, &c->compressedrow.rindex));
3095     PetscCall(PetscArraycpy(c->compressedrow.rindex, a->compressedrow.rindex, c->compressedrow.nrows));
3096     Ccusp->workVector  = new THRUSTARRAY(c->compressedrow.nrows);
3097     Cmat->cprowIndices = new THRUSTINTARRAY(c->compressedrow.nrows);
3098     Cmat->cprowIndices->assign(c->compressedrow.rindex, c->compressedrow.rindex + c->compressedrow.nrows);
3099   } else {
3100     c->compressedrow.nrows  = 0;
3101     c->compressedrow.i      = NULL;
3102     c->compressedrow.rindex = NULL;
3103     Ccusp->workVector       = NULL;
3104     Cmat->cprowIndices      = NULL;
3105   }
3106   Ccusp->nrows      = ciscompressed ? c->compressedrow.nrows : m;
3107   Ccusp->mat        = Cmat;
3108   Ccusp->mat->mat   = Ccsr;
3109   Ccsr->num_rows    = Ccusp->nrows;
3110   Ccsr->num_cols    = n;
3111   Ccsr->row_offsets = new THRUSTINTARRAY32(Ccusp->nrows + 1);
3112   PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
3113   PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
3114   PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
3115   PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
3116   PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
3117   PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
3118   PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3119   PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3120   PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
3121   if (!Ccsr->num_rows || !Ccsr->num_cols || !a->nz || !b->nz) { /* cusparse raise errors in different calls when matrices have zero rows/columns! */
3122     PetscCallThrust(thrust::fill(thrust::device, Ccsr->row_offsets->begin(), Ccsr->row_offsets->end(), 0));
3123     c->nz                = 0;
3124     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3125     Ccsr->values         = new THRUSTARRAY(c->nz);
3126     goto finalizesym;
3127   }
3128 
3129   PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
3130   PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
3131   Acsr = (CsrMatrix *)Amat->mat;
3132   if (!biscompressed) {
3133     Bcsr = (CsrMatrix *)Bmat->mat;
3134 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3135     BmatSpDescr = Bmat->matDescr;
3136 #endif
3137   } else { /* we need to use row offsets for the full matrix */
3138     CsrMatrix *cBcsr     = (CsrMatrix *)Bmat->mat;
3139     Bcsr                 = new CsrMatrix;
3140     Bcsr->num_rows       = B->rmap->n;
3141     Bcsr->num_cols       = cBcsr->num_cols;
3142     Bcsr->num_entries    = cBcsr->num_entries;
3143     Bcsr->column_indices = cBcsr->column_indices;
3144     Bcsr->values         = cBcsr->values;
3145     if (!Bcusp->rowoffsets_gpu) {
3146       Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
3147       Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
3148       PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
3149     }
3150     Bcsr->row_offsets = Bcusp->rowoffsets_gpu;
3151     mmdata->Bcsr      = Bcsr;
3152 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3153     if (Bcsr->num_rows && Bcsr->num_cols) {
3154       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);
3155       PetscCallCUSPARSE(stat);
3156     }
3157     BmatSpDescr = mmdata->matSpBDescr;
3158 #endif
3159   }
3160   PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
3161   PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
3162   /* precompute flops count */
3163   if (ptype == MATPRODUCT_AB) {
3164     for (i = 0, flops = 0; i < A->rmap->n; i++) {
3165       const PetscInt st = a->i[i];
3166       const PetscInt en = a->i[i + 1];
3167       for (j = st; j < en; j++) {
3168         const PetscInt brow = a->j[j];
3169         flops += 2. * (b->i[brow + 1] - b->i[brow]);
3170       }
3171     }
3172   } else if (ptype == MATPRODUCT_AtB) {
3173     for (i = 0, flops = 0; i < A->rmap->n; i++) {
3174       const PetscInt anzi = a->i[i + 1] - a->i[i];
3175       const PetscInt bnzi = b->i[i + 1] - b->i[i];
3176       flops += (2. * anzi) * bnzi;
3177     }
3178   } else { /* TODO */
3179     flops = 0.;
3180   }
3181 
3182   mmdata->flops = flops;
3183   PetscCall(PetscLogGpuTimeBegin());
3184 
3185 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3186   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
3187   // cuda-12.2 requires non-null csrRowOffsets
3188   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);
3189   PetscCallCUSPARSE(stat);
3190   PetscCallCUSPARSE(cusparseSpGEMM_createDescr(&mmdata->spgemmDesc));
3191   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
3192   {
3193     /* cusparseSpGEMMreuse has more reasonable APIs than cusparseSpGEMM, so we prefer to use it.
3194      We follow the sample code at https://github.com/NVIDIA/CUDALibrarySamples/blob/master/cuSPARSE/spgemm_reuse
3195   */
3196     void *dBuffer1 = NULL;
3197     void *dBuffer2 = NULL;
3198     void *dBuffer3 = NULL;
3199     /* dBuffer4, dBuffer5 are needed by cusparseSpGEMMreuse_compute, and therefore are stored in mmdata */
3200     size_t bufferSize1 = 0;
3201     size_t bufferSize2 = 0;
3202     size_t bufferSize3 = 0;
3203     size_t bufferSize4 = 0;
3204     size_t bufferSize5 = 0;
3205 
3206     /* ask bufferSize1 bytes for external memory */
3207     stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, NULL);
3208     PetscCallCUSPARSE(stat);
3209     PetscCallCUDA(cudaMalloc((void **)&dBuffer1, bufferSize1));
3210     /* inspect the matrices A and B to understand the memory requirement for the next step */
3211     stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, dBuffer1);
3212     PetscCallCUSPARSE(stat);
3213 
3214     stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, NULL, &bufferSize3, NULL, &bufferSize4, NULL);
3215     PetscCallCUSPARSE(stat);
3216     PetscCallCUDA(cudaMalloc((void **)&dBuffer2, bufferSize2));
3217     PetscCallCUDA(cudaMalloc((void **)&dBuffer3, bufferSize3));
3218     PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer4, bufferSize4));
3219     stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, dBuffer2, &bufferSize3, dBuffer3, &bufferSize4, mmdata->dBuffer4);
3220     PetscCallCUSPARSE(stat);
3221     PetscCallCUDA(cudaFree(dBuffer1));
3222     PetscCallCUDA(cudaFree(dBuffer2));
3223 
3224     /* get matrix C non-zero entries C_nnz1 */
3225     PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
3226     c->nz = (PetscInt)C_nnz1;
3227     /* allocate matrix C */
3228     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3229     PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3230     Ccsr->values = new THRUSTARRAY(c->nz);
3231     PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3232     /* update matC with the new pointers */
3233     stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
3234     PetscCallCUSPARSE(stat);
3235 
3236     stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, NULL);
3237     PetscCallCUSPARSE(stat);
3238     PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer5, bufferSize5));
3239     stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, mmdata->dBuffer5);
3240     PetscCallCUSPARSE(stat);
3241     PetscCallCUDA(cudaFree(dBuffer3));
3242     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);
3243     PetscCallCUSPARSE(stat);
3244     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));
3245   }
3246   #else
3247   size_t bufSize2;
3248   /* ask bufferSize bytes for external memory */
3249   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);
3250   PetscCallCUSPARSE(stat);
3251   PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer2, bufSize2));
3252   /* inspect the matrices A and B to understand the memory requirement for the next step */
3253   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);
3254   PetscCallCUSPARSE(stat);
3255   /* ask bufferSize again bytes for external memory */
3256   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);
3257   PetscCallCUSPARSE(stat);
3258   /* The CUSPARSE documentation is not clear, nor the API
3259      We need both buffers to perform the operations properly!
3260      mmdata->mmBuffer2 does not appear anywhere in the compute/copy API
3261      it only appears for the workEstimation stuff, but it seems it is needed in compute, so probably the address
3262      is stored in the descriptor! What a messy API... */
3263   PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer, mmdata->mmBufferSize));
3264   /* compute the intermediate product of A * B */
3265   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);
3266   PetscCallCUSPARSE(stat);
3267   /* get matrix C non-zero entries C_nnz1 */
3268   PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
3269   c->nz = (PetscInt)C_nnz1;
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, bufSize2 / 1024,
3271                       mmdata->mmBufferSize / 1024));
3272   Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3273   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3274   Ccsr->values = new THRUSTARRAY(c->nz);
3275   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3276   stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
3277   PetscCallCUSPARSE(stat);
3278   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);
3279   PetscCallCUSPARSE(stat);
3280   #endif // PETSC_PKG_CUDA_VERSION_GE(11,4,0)
3281 #else
3282   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_HOST));
3283   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,
3284                              Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->row_offsets->data().get(), &cnz);
3285   PetscCallCUSPARSE(stat);
3286   c->nz                = cnz;
3287   Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
3288   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3289   Ccsr->values = new THRUSTARRAY(c->nz);
3290   PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
3291 
3292   PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
3293   /* with the old gemm interface (removed from 11.0 on) we cannot compute the symbolic factorization only.
3294      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
3295      D is NULL, despite the fact that CUSPARSE documentation claims it is supported! */
3296   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,
3297                              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());
3298   PetscCallCUSPARSE(stat);
3299 #endif
3300   PetscCall(PetscLogGpuFlops(mmdata->flops));
3301   PetscCall(PetscLogGpuTimeEnd());
3302 finalizesym:
3303   c->singlemalloc = PETSC_FALSE;
3304   c->free_a       = PETSC_TRUE;
3305   c->free_ij      = PETSC_TRUE;
3306   PetscCall(PetscMalloc1(m + 1, &c->i));
3307   PetscCall(PetscMalloc1(c->nz, &c->j));
3308   if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
3309     PetscInt      *d_i = c->i;
3310     THRUSTINTARRAY ii(Ccsr->row_offsets->size());
3311     THRUSTINTARRAY jj(Ccsr->column_indices->size());
3312     ii = *Ccsr->row_offsets;
3313     jj = *Ccsr->column_indices;
3314     if (ciscompressed) d_i = c->compressedrow.i;
3315     PetscCallCUDA(cudaMemcpy(d_i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3316     PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3317   } else {
3318     PetscInt *d_i = c->i;
3319     if (ciscompressed) d_i = c->compressedrow.i;
3320     PetscCallCUDA(cudaMemcpy(d_i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3321     PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3322   }
3323   if (ciscompressed) { /* need to expand host row offsets */
3324     PetscInt r = 0;
3325     c->i[0]    = 0;
3326     for (k = 0; k < c->compressedrow.nrows; k++) {
3327       const PetscInt next = c->compressedrow.rindex[k];
3328       const PetscInt old  = c->compressedrow.i[k];
3329       for (; r < next; r++) c->i[r + 1] = old;
3330     }
3331     for (; r < m; r++) c->i[r + 1] = c->compressedrow.i[c->compressedrow.nrows];
3332   }
3333   PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
3334   PetscCall(PetscMalloc1(m, &c->ilen));
3335   PetscCall(PetscMalloc1(m, &c->imax));
3336   c->maxnz         = c->nz;
3337   c->nonzerorowcnt = 0;
3338   c->rmax          = 0;
3339   for (k = 0; k < m; k++) {
3340     const PetscInt nn = c->i[k + 1] - c->i[k];
3341     c->ilen[k] = c->imax[k] = nn;
3342     c->nonzerorowcnt += (PetscInt) !!nn;
3343     c->rmax = PetscMax(c->rmax, nn);
3344   }
3345   PetscCall(MatMarkDiagonal_SeqAIJ(C));
3346   PetscCall(PetscMalloc1(c->nz, &c->a));
3347   Ccsr->num_entries = c->nz;
3348 
3349   C->nonzerostate++;
3350   PetscCall(PetscLayoutSetUp(C->rmap));
3351   PetscCall(PetscLayoutSetUp(C->cmap));
3352   Ccusp->nonzerostate = C->nonzerostate;
3353   C->offloadmask      = PETSC_OFFLOAD_UNALLOCATED;
3354   C->preallocated     = PETSC_TRUE;
3355   C->assembled        = PETSC_FALSE;
3356   C->was_assembled    = PETSC_FALSE;
3357   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 */
3358     mmdata->reusesym = PETSC_TRUE;
3359     C->offloadmask   = PETSC_OFFLOAD_GPU;
3360   }
3361   C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3362   PetscFunctionReturn(PETSC_SUCCESS);
3363 }
3364 
3365 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat);
3366 
3367 /* handles sparse or dense B */
3368 static PetscErrorCode MatProductSetFromOptions_SeqAIJCUSPARSE(Mat mat)
3369 {
3370   Mat_Product *product = mat->product;
3371   PetscBool    isdense = PETSC_FALSE, Biscusp = PETSC_FALSE, Ciscusp = PETSC_TRUE;
3372 
3373   PetscFunctionBegin;
3374   MatCheckProduct(mat, 1);
3375   PetscCall(PetscObjectBaseTypeCompare((PetscObject)product->B, MATSEQDENSE, &isdense));
3376   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, MATSEQAIJCUSPARSE, &Biscusp));
3377   if (product->type == MATPRODUCT_ABC) {
3378     Ciscusp = PETSC_FALSE;
3379     if (!product->C->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->C, MATSEQAIJCUSPARSE, &Ciscusp));
3380   }
3381   if (Biscusp && Ciscusp) { /* we can always select the CPU backend */
3382     PetscBool usecpu = PETSC_FALSE;
3383     switch (product->type) {
3384     case MATPRODUCT_AB:
3385       if (product->api_user) {
3386         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
3387         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3388         PetscOptionsEnd();
3389       } else {
3390         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
3391         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3392         PetscOptionsEnd();
3393       }
3394       break;
3395     case MATPRODUCT_AtB:
3396       if (product->api_user) {
3397         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
3398         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3399         PetscOptionsEnd();
3400       } else {
3401         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
3402         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3403         PetscOptionsEnd();
3404       }
3405       break;
3406     case MATPRODUCT_PtAP:
3407       if (product->api_user) {
3408         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
3409         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3410         PetscOptionsEnd();
3411       } else {
3412         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
3413         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3414         PetscOptionsEnd();
3415       }
3416       break;
3417     case MATPRODUCT_RARt:
3418       if (product->api_user) {
3419         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatRARt", "Mat");
3420         PetscCall(PetscOptionsBool("-matrart_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3421         PetscOptionsEnd();
3422       } else {
3423         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_RARt", "Mat");
3424         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3425         PetscOptionsEnd();
3426       }
3427       break;
3428     case MATPRODUCT_ABC:
3429       if (product->api_user) {
3430         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMatMult", "Mat");
3431         PetscCall(PetscOptionsBool("-matmatmatmult_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3432         PetscOptionsEnd();
3433       } else {
3434         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_ABC", "Mat");
3435         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3436         PetscOptionsEnd();
3437       }
3438       break;
3439     default:
3440       break;
3441     }
3442     if (usecpu) Biscusp = Ciscusp = PETSC_FALSE;
3443   }
3444   /* dispatch */
3445   if (isdense) {
3446     switch (product->type) {
3447     case MATPRODUCT_AB:
3448     case MATPRODUCT_AtB:
3449     case MATPRODUCT_ABt:
3450     case MATPRODUCT_PtAP:
3451     case MATPRODUCT_RARt:
3452       if (product->A->boundtocpu) {
3453         PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense(mat));
3454       } else {
3455         mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA;
3456       }
3457       break;
3458     case MATPRODUCT_ABC:
3459       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3460       break;
3461     default:
3462       break;
3463     }
3464   } else if (Biscusp && Ciscusp) {
3465     switch (product->type) {
3466     case MATPRODUCT_AB:
3467     case MATPRODUCT_AtB:
3468     case MATPRODUCT_ABt:
3469       mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3470       break;
3471     case MATPRODUCT_PtAP:
3472     case MATPRODUCT_RARt:
3473     case MATPRODUCT_ABC:
3474       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3475       break;
3476     default:
3477       break;
3478     }
3479   } else { /* fallback for AIJ */
3480     PetscCall(MatProductSetFromOptions_SeqAIJ(mat));
3481   }
3482   PetscFunctionReturn(PETSC_SUCCESS);
3483 }
3484 
3485 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3486 {
3487   PetscFunctionBegin;
3488   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_FALSE, PETSC_FALSE));
3489   PetscFunctionReturn(PETSC_SUCCESS);
3490 }
3491 
3492 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3493 {
3494   PetscFunctionBegin;
3495   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_FALSE, PETSC_FALSE));
3496   PetscFunctionReturn(PETSC_SUCCESS);
3497 }
3498 
3499 static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3500 {
3501   PetscFunctionBegin;
3502   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_TRUE));
3503   PetscFunctionReturn(PETSC_SUCCESS);
3504 }
3505 
3506 static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3507 {
3508   PetscFunctionBegin;
3509   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_TRUE));
3510   PetscFunctionReturn(PETSC_SUCCESS);
3511 }
3512 
3513 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3514 {
3515   PetscFunctionBegin;
3516   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_FALSE));
3517   PetscFunctionReturn(PETSC_SUCCESS);
3518 }
3519 
3520 __global__ static void ScatterAdd(PetscInt n, PetscInt *idx, const PetscScalar *x, PetscScalar *y)
3521 {
3522   int i = blockIdx.x * blockDim.x + threadIdx.x;
3523   if (i < n) y[idx[i]] += x[i];
3524 }
3525 
3526 /* z = op(A) x + y. If trans & !herm, op = ^T; if trans & herm, op = ^H; if !trans, op = no-op */
3527 static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz, PetscBool trans, PetscBool herm)
3528 {
3529   Mat_SeqAIJ                   *a              = (Mat_SeqAIJ *)A->data;
3530   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
3531   Mat_SeqAIJCUSPARSEMultStruct *matstruct;
3532   PetscScalar                  *xarray, *zarray, *dptr, *beta, *xptr;
3533   cusparseOperation_t           opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
3534   PetscBool                     compressed;
3535 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3536   PetscInt nx, ny;
3537 #endif
3538 
3539   PetscFunctionBegin;
3540   PetscCheck(!herm || trans, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Hermitian and not transpose not supported");
3541   if (!a->nz) {
3542     if (yy) PetscCall(VecSeq_CUDA::Copy(yy, zz));
3543     else PetscCall(VecSeq_CUDA::Set(zz, 0));
3544     PetscFunctionReturn(PETSC_SUCCESS);
3545   }
3546   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
3547   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
3548   if (!trans) {
3549     matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3550     PetscCheck(matstruct, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "SeqAIJCUSPARSE does not have a 'mat' (need to fix)");
3551   } else {
3552     if (herm || !A->form_explicit_transpose) {
3553       opA       = herm ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE : CUSPARSE_OPERATION_TRANSPOSE;
3554       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3555     } else {
3556       if (!cusparsestruct->matTranspose) PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
3557       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
3558     }
3559   }
3560   /* Does the matrix use compressed rows (i.e., drop zero rows)? */
3561   compressed = matstruct->cprowIndices ? PETSC_TRUE : PETSC_FALSE;
3562 
3563   try {
3564     PetscCall(VecCUDAGetArrayRead(xx, (const PetscScalar **)&xarray));
3565     if (yy == zz) PetscCall(VecCUDAGetArray(zz, &zarray)); /* read & write zz, so need to get up-to-date zarray on GPU */
3566     else PetscCall(VecCUDAGetArrayWrite(zz, &zarray));     /* write zz, so no need to init zarray on GPU */
3567 
3568     PetscCall(PetscLogGpuTimeBegin());
3569     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3570       /* z = A x + beta y.
3571          If A is compressed (with less rows), then Ax is shorter than the full z, so we need a work vector to store Ax.
3572          When A is non-compressed, and z = y, we can set beta=1 to compute y = Ax + y in one call.
3573       */
3574       xptr = xarray;
3575       dptr = compressed ? cusparsestruct->workVector->data().get() : zarray;
3576       beta = (yy == zz && !compressed) ? matstruct->beta_one : matstruct->beta_zero;
3577 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3578       /* Get length of x, y for y=Ax. ny might be shorter than the work vector's allocated length, since the work vector is
3579           allocated to accommodate different uses. So we get the length info directly from mat.
3580        */
3581       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3582         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3583         nx             = mat->num_cols;
3584         ny             = mat->num_rows;
3585       }
3586 #endif
3587     } else {
3588       /* z = A^T x + beta y
3589          If A is compressed, then we need a work vector as the shorter version of x to compute A^T x.
3590          Note A^Tx is of full length, so we set beta to 1.0 if y exists.
3591        */
3592       xptr = compressed ? cusparsestruct->workVector->data().get() : xarray;
3593       dptr = zarray;
3594       beta = yy ? matstruct->beta_one : matstruct->beta_zero;
3595       if (compressed) { /* Scatter x to work vector */
3596         thrust::device_ptr<PetscScalar> xarr = thrust::device_pointer_cast(xarray);
3597 
3598         thrust::for_each(
3599 #if PetscDefined(HAVE_THRUST_ASYNC)
3600           thrust::cuda::par.on(PetscDefaultCudaStream),
3601 #endif
3602           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))),
3603           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(), VecCUDAEqualsReverse());
3604       }
3605 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3606       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3607         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3608         nx             = mat->num_rows;
3609         ny             = mat->num_cols;
3610       }
3611 #endif
3612     }
3613 
3614     /* csr_spmv does y = alpha op(A) x + beta y */
3615     if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3616 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3617       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");
3618       if (!matstruct->cuSpMV[opA].initialized) { /* built on demand */
3619         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecXDescr, nx, xptr, cusparse_scalartype));
3620         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecYDescr, ny, dptr, cusparse_scalartype));
3621         PetscCallCUSPARSE(
3622           cusparseSpMV_bufferSize(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->matDescr, matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, &matstruct->cuSpMV[opA].spmvBufferSize));
3623         PetscCallCUDA(cudaMalloc(&matstruct->cuSpMV[opA].spmvBuffer, matstruct->cuSpMV[opA].spmvBufferSize));
3624 
3625         matstruct->cuSpMV[opA].initialized = PETSC_TRUE;
3626       } else {
3627         /* x, y's value pointers might change between calls, but their shape is kept, so we just update pointers */
3628         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecXDescr, xptr));
3629         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecYDescr, dptr));
3630       }
3631 
3632       PetscCallCUSPARSE(cusparseSpMV(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->matDescr, /* built in MatSeqAIJCUSPARSECopyToGPU() or MatSeqAIJCUSPARSEFormExplicitTranspose() */
3633                                      matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, matstruct->cuSpMV[opA].spmvBuffer));
3634 #else
3635       CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3636       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));
3637 #endif
3638     } else {
3639       if (cusparsestruct->nrows) {
3640 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3641         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
3642 #else
3643         cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
3644         PetscCallCUSPARSE(cusparse_hyb_spmv(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->descr, hybMat, xptr, beta, dptr));
3645 #endif
3646       }
3647     }
3648     PetscCall(PetscLogGpuTimeEnd());
3649 
3650     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3651       if (yy) {                                      /* MatMultAdd: zz = A*xx + yy */
3652         if (compressed) {                            /* A is compressed. We first copy yy to zz, then ScatterAdd the work vector to zz */
3653           PetscCall(VecSeq_CUDA::Copy(yy, zz));      /* zz = yy */
3654         } else if (zz != yy) {                       /* A is not compressed. zz already contains A*xx, and we just need to add yy */
3655           PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3656         }
3657       } else if (compressed) { /* MatMult: zz = A*xx. A is compressed, so we zero zz first, then ScatterAdd the work vector to zz */
3658         PetscCall(VecSeq_CUDA::Set(zz, 0));
3659       }
3660 
3661       /* ScatterAdd the result from work vector into the full vector when A is compressed */
3662       if (compressed) {
3663         PetscCall(PetscLogGpuTimeBegin());
3664         /* I wanted to make this for_each asynchronous but failed. thrust::async::for_each() returns an event (internally registered)
3665            and in the destructor of the scope, it will call cudaStreamSynchronize() on this stream. One has to store all events to
3666            prevent that. So I just add a ScatterAdd kernel.
3667          */
3668 #if 0
3669         thrust::device_ptr<PetscScalar> zptr = thrust::device_pointer_cast(zarray);
3670         thrust::async::for_each(thrust::cuda::par.on(cusparsestruct->stream),
3671                          thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))),
3672                          thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(),
3673                          VecCUDAPlusEquals());
3674 #else
3675         PetscInt n = matstruct->cprowIndices->size();
3676         ScatterAdd<<<(n + 255) / 256, 256, 0, PetscDefaultCudaStream>>>(n, matstruct->cprowIndices->data().get(), cusparsestruct->workVector->data().get(), zarray);
3677 #endif
3678         PetscCall(PetscLogGpuTimeEnd());
3679       }
3680     } else {
3681       if (yy && yy != zz) PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3682     }
3683     PetscCall(VecCUDARestoreArrayRead(xx, (const PetscScalar **)&xarray));
3684     if (yy == zz) PetscCall(VecCUDARestoreArray(zz, &zarray));
3685     else PetscCall(VecCUDARestoreArrayWrite(zz, &zarray));
3686   } catch (char *ex) {
3687     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
3688   }
3689   if (yy) {
3690     PetscCall(PetscLogGpuFlops(2.0 * a->nz));
3691   } else {
3692     PetscCall(PetscLogGpuFlops(2.0 * a->nz - a->nonzerorowcnt));
3693   }
3694   PetscFunctionReturn(PETSC_SUCCESS);
3695 }
3696 
3697 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3698 {
3699   PetscFunctionBegin;
3700   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_FALSE));
3701   PetscFunctionReturn(PETSC_SUCCESS);
3702 }
3703 
3704 static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A, MatAssemblyType mode)
3705 {
3706   PetscFunctionBegin;
3707   PetscCall(MatAssemblyEnd_SeqAIJ(A, mode));
3708   PetscFunctionReturn(PETSC_SUCCESS);
3709 }
3710 
3711 /*@
3712   MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in `MATAIJCUSPARSE` (compressed row) format
3713   (the default parallel PETSc format).
3714 
3715   Collective
3716 
3717   Input Parameters:
3718 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3719 . m    - number of rows
3720 . n    - number of columns
3721 . nz   - number of nonzeros per row (same for all rows), ignored if `nnz` is provide
3722 - nnz  - array containing the number of nonzeros in the various rows (possibly different for each row) or `NULL`
3723 
3724   Output Parameter:
3725 . A - the matrix
3726 
3727   Level: intermediate
3728 
3729   Notes:
3730   This matrix will ultimately pushed down to NVIDIA GPUs and use the CuSPARSE library for
3731   calculations. For good matrix assembly performance the user should preallocate the matrix
3732   storage by setting the parameter `nz` (or the array `nnz`).
3733 
3734   It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
3735   MatXXXXSetPreallocation() paradgm instead of this routine directly.
3736   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]
3737 
3738   The AIJ format, also called
3739   compressed row storage, is fully compatible with standard Fortran
3740   storage.  That is, the stored row and column indices can begin at
3741   either one (as in Fortran) or zero.
3742 
3743   Specify the preallocated storage with either nz or nnz (not both).
3744   Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
3745   allocation.
3746 
3747 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MATAIJCUSPARSE`
3748 @*/
3749 PetscErrorCode MatCreateSeqAIJCUSPARSE(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
3750 {
3751   PetscFunctionBegin;
3752   PetscCall(MatCreate(comm, A));
3753   PetscCall(MatSetSizes(*A, m, n, m, n));
3754   PetscCall(MatSetType(*A, MATSEQAIJCUSPARSE));
3755   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, (PetscInt *)nnz));
3756   PetscFunctionReturn(PETSC_SUCCESS);
3757 }
3758 
3759 static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
3760 {
3761   PetscFunctionBegin;
3762   if (A->factortype == MAT_FACTOR_NONE) {
3763     PetscCall(MatSeqAIJCUSPARSE_Destroy(A));
3764   } else {
3765     PetscCall(MatSeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors **)&A->spptr));
3766   }
3767   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3768   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetFormat_C", NULL));
3769   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetUseCPUSolve_C", NULL));
3770   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3771   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3772   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3773   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
3774   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3775   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3776   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijcusparse_hypre_C", NULL));
3777   PetscCall(MatDestroy_SeqAIJ(A));
3778   PetscFunctionReturn(PETSC_SUCCESS);
3779 }
3780 
3781 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
3782 static PetscErrorCode       MatBindToCPU_SeqAIJCUSPARSE(Mat, PetscBool);
3783 static PetscErrorCode       MatDuplicate_SeqAIJCUSPARSE(Mat A, MatDuplicateOption cpvalues, Mat *B)
3784 {
3785   PetscFunctionBegin;
3786   PetscCall(MatDuplicate_SeqAIJ(A, cpvalues, B));
3787   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(*B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, B));
3788   PetscFunctionReturn(PETSC_SUCCESS);
3789 }
3790 
3791 static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat Y, PetscScalar a, Mat X, MatStructure str)
3792 {
3793   Mat_SeqAIJ         *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
3794   Mat_SeqAIJCUSPARSE *cy;
3795   Mat_SeqAIJCUSPARSE *cx;
3796   PetscScalar        *ay;
3797   const PetscScalar  *ax;
3798   CsrMatrix          *csry, *csrx;
3799 
3800   PetscFunctionBegin;
3801   cy = (Mat_SeqAIJCUSPARSE *)Y->spptr;
3802   cx = (Mat_SeqAIJCUSPARSE *)X->spptr;
3803   if (X->ops->axpy != Y->ops->axpy) {
3804     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3805     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3806     PetscFunctionReturn(PETSC_SUCCESS);
3807   }
3808   /* if we are here, it means both matrices are bound to GPU */
3809   PetscCall(MatSeqAIJCUSPARSECopyToGPU(Y));
3810   PetscCall(MatSeqAIJCUSPARSECopyToGPU(X));
3811   PetscCheck(cy->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)Y), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3812   PetscCheck(cx->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)X), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3813   csry = (CsrMatrix *)cy->mat->mat;
3814   csrx = (CsrMatrix *)cx->mat->mat;
3815   /* see if we can turn this into a cublas axpy */
3816   if (str != SAME_NONZERO_PATTERN && x->nz == y->nz && !x->compressedrow.use && !y->compressedrow.use) {
3817     bool eq = thrust::equal(thrust::device, csry->row_offsets->begin(), csry->row_offsets->end(), csrx->row_offsets->begin());
3818     if (eq) eq = thrust::equal(thrust::device, csry->column_indices->begin(), csry->column_indices->end(), csrx->column_indices->begin());
3819     if (eq) str = SAME_NONZERO_PATTERN;
3820   }
3821   /* spgeam is buggy with one column */
3822   if (Y->cmap->n == 1 && str != SAME_NONZERO_PATTERN) str = DIFFERENT_NONZERO_PATTERN;
3823 
3824   if (str == SUBSET_NONZERO_PATTERN) {
3825     PetscScalar b = 1.0;
3826 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3827     size_t bufferSize;
3828     void  *buffer;
3829 #endif
3830 
3831     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3832     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3833     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_HOST));
3834 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3835     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(),
3836                                                      csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), &bufferSize));
3837     PetscCallCUDA(cudaMalloc(&buffer, bufferSize));
3838     PetscCall(PetscLogGpuTimeBegin());
3839     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(),
3840                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), buffer));
3841     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3842     PetscCall(PetscLogGpuTimeEnd());
3843     PetscCallCUDA(cudaFree(buffer));
3844 #else
3845     PetscCall(PetscLogGpuTimeBegin());
3846     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(),
3847                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get()));
3848     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3849     PetscCall(PetscLogGpuTimeEnd());
3850 #endif
3851     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_DEVICE));
3852     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3853     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3854     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3855   } else if (str == SAME_NONZERO_PATTERN) {
3856     cublasHandle_t cublasv2handle;
3857     PetscBLASInt   one = 1, bnz = 1;
3858 
3859     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3860     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3861     PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3862     PetscCall(PetscBLASIntCast(x->nz, &bnz));
3863     PetscCall(PetscLogGpuTimeBegin());
3864     PetscCallCUBLAS(cublasXaxpy(cublasv2handle, bnz, &a, ax, one, ay, one));
3865     PetscCall(PetscLogGpuFlops(2.0 * bnz));
3866     PetscCall(PetscLogGpuTimeEnd());
3867     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3868     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3869     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3870   } else {
3871     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3872     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3873   }
3874   PetscFunctionReturn(PETSC_SUCCESS);
3875 }
3876 
3877 static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat Y, PetscScalar a)
3878 {
3879   Mat_SeqAIJ    *y = (Mat_SeqAIJ *)Y->data;
3880   PetscScalar   *ay;
3881   cublasHandle_t cublasv2handle;
3882   PetscBLASInt   one = 1, bnz = 1;
3883 
3884   PetscFunctionBegin;
3885   PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3886   PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3887   PetscCall(PetscBLASIntCast(y->nz, &bnz));
3888   PetscCall(PetscLogGpuTimeBegin());
3889   PetscCallCUBLAS(cublasXscal(cublasv2handle, bnz, &a, ay, one));
3890   PetscCall(PetscLogGpuFlops(bnz));
3891   PetscCall(PetscLogGpuTimeEnd());
3892   PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3893   PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3894   PetscFunctionReturn(PETSC_SUCCESS);
3895 }
3896 
3897 static PetscErrorCode MatZeroEntries_SeqAIJCUSPARSE(Mat A)
3898 {
3899   PetscBool   both = PETSC_FALSE;
3900   Mat_SeqAIJ *a    = (Mat_SeqAIJ *)A->data;
3901 
3902   PetscFunctionBegin;
3903   if (A->factortype == MAT_FACTOR_NONE) {
3904     Mat_SeqAIJCUSPARSE *spptr = (Mat_SeqAIJCUSPARSE *)A->spptr;
3905     if (spptr->mat) {
3906       CsrMatrix *matrix = (CsrMatrix *)spptr->mat->mat;
3907       if (matrix->values) {
3908         both = PETSC_TRUE;
3909         thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3910       }
3911     }
3912     if (spptr->matTranspose) {
3913       CsrMatrix *matrix = (CsrMatrix *)spptr->matTranspose->mat;
3914       if (matrix->values) thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3915     }
3916   }
3917   PetscCall(PetscArrayzero(a->a, a->i[A->rmap->n]));
3918   PetscCall(MatSeqAIJInvalidateDiagonal(A));
3919   if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
3920   else A->offloadmask = PETSC_OFFLOAD_CPU;
3921   PetscFunctionReturn(PETSC_SUCCESS);
3922 }
3923 
3924 static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat A, PetscBool flg)
3925 {
3926   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
3927 
3928   PetscFunctionBegin;
3929   if (A->factortype != MAT_FACTOR_NONE) {
3930     A->boundtocpu = flg;
3931     PetscFunctionReturn(PETSC_SUCCESS);
3932   }
3933   if (flg) {
3934     PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
3935 
3936     A->ops->scale                     = MatScale_SeqAIJ;
3937     A->ops->axpy                      = MatAXPY_SeqAIJ;
3938     A->ops->zeroentries               = MatZeroEntries_SeqAIJ;
3939     A->ops->mult                      = MatMult_SeqAIJ;
3940     A->ops->multadd                   = MatMultAdd_SeqAIJ;
3941     A->ops->multtranspose             = MatMultTranspose_SeqAIJ;
3942     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJ;
3943     A->ops->multhermitiantranspose    = NULL;
3944     A->ops->multhermitiantransposeadd = NULL;
3945     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJ;
3946     PetscCall(PetscMemzero(a->ops, sizeof(Mat_SeqAIJOps)));
3947     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3948     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3949     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3950     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3951     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3952     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3953   } else {
3954     A->ops->scale                     = MatScale_SeqAIJCUSPARSE;
3955     A->ops->axpy                      = MatAXPY_SeqAIJCUSPARSE;
3956     A->ops->zeroentries               = MatZeroEntries_SeqAIJCUSPARSE;
3957     A->ops->mult                      = MatMult_SeqAIJCUSPARSE;
3958     A->ops->multadd                   = MatMultAdd_SeqAIJCUSPARSE;
3959     A->ops->multtranspose             = MatMultTranspose_SeqAIJCUSPARSE;
3960     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJCUSPARSE;
3961     A->ops->multhermitiantranspose    = MatMultHermitianTranspose_SeqAIJCUSPARSE;
3962     A->ops->multhermitiantransposeadd = MatMultHermitianTransposeAdd_SeqAIJCUSPARSE;
3963     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJCUSPARSE;
3964     a->ops->getarray                  = MatSeqAIJGetArray_SeqAIJCUSPARSE;
3965     a->ops->restorearray              = MatSeqAIJRestoreArray_SeqAIJCUSPARSE;
3966     a->ops->getarrayread              = MatSeqAIJGetArrayRead_SeqAIJCUSPARSE;
3967     a->ops->restorearrayread          = MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE;
3968     a->ops->getarraywrite             = MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE;
3969     a->ops->restorearraywrite         = MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE;
3970     a->ops->getcsrandmemtype          = MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE;
3971 
3972     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", MatSeqAIJCopySubArray_SeqAIJCUSPARSE));
3973     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3974     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3975     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJCUSPARSE));
3976     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJCUSPARSE));
3977     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3978   }
3979   A->boundtocpu = flg;
3980   if (flg && a->inode.size) {
3981     a->inode.use = PETSC_TRUE;
3982   } else {
3983     a->inode.use = PETSC_FALSE;
3984   }
3985   PetscFunctionReturn(PETSC_SUCCESS);
3986 }
3987 
3988 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat A, MatType, MatReuse reuse, Mat *newmat)
3989 {
3990   Mat B;
3991 
3992   PetscFunctionBegin;
3993   PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* first use of CUSPARSE may be via MatConvert */
3994   if (reuse == MAT_INITIAL_MATRIX) {
3995     PetscCall(MatDuplicate(A, MAT_COPY_VALUES, newmat));
3996   } else if (reuse == MAT_REUSE_MATRIX) {
3997     PetscCall(MatCopy(A, *newmat, SAME_NONZERO_PATTERN));
3998   }
3999   B = *newmat;
4000 
4001   PetscCall(PetscFree(B->defaultvectype));
4002   PetscCall(PetscStrallocpy(VECCUDA, &B->defaultvectype));
4003 
4004   if (reuse != MAT_REUSE_MATRIX && !B->spptr) {
4005     if (B->factortype == MAT_FACTOR_NONE) {
4006       Mat_SeqAIJCUSPARSE *spptr;
4007       PetscCall(PetscNew(&spptr));
4008       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4009       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4010       spptr->format = MAT_CUSPARSE_CSR;
4011 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4012   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4013       spptr->spmvAlg = CUSPARSE_SPMV_CSR_ALG1; /* default, since we only support csr */
4014   #else
4015       spptr->spmvAlg = CUSPARSE_CSRMV_ALG1; /* default, since we only support csr */
4016   #endif
4017       spptr->spmmAlg    = CUSPARSE_SPMM_CSR_ALG1; /* default, only support column-major dense matrix B */
4018       spptr->csr2cscAlg = CUSPARSE_CSR2CSC_ALG1;
4019 #endif
4020       B->spptr = spptr;
4021     } else {
4022       Mat_SeqAIJCUSPARSETriFactors *spptr;
4023 
4024       PetscCall(PetscNew(&spptr));
4025       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4026       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4027       B->spptr = spptr;
4028     }
4029     B->offloadmask = PETSC_OFFLOAD_UNALLOCATED;
4030   }
4031   B->ops->assemblyend    = MatAssemblyEnd_SeqAIJCUSPARSE;
4032   B->ops->destroy        = MatDestroy_SeqAIJCUSPARSE;
4033   B->ops->setoption      = MatSetOption_SeqAIJCUSPARSE;
4034   B->ops->setfromoptions = MatSetFromOptions_SeqAIJCUSPARSE;
4035   B->ops->bindtocpu      = MatBindToCPU_SeqAIJCUSPARSE;
4036   B->ops->duplicate      = MatDuplicate_SeqAIJCUSPARSE;
4037 
4038   PetscCall(MatBindToCPU_SeqAIJCUSPARSE(B, PETSC_FALSE));
4039   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJCUSPARSE));
4040   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetFormat_C", MatCUSPARSESetFormat_SeqAIJCUSPARSE));
4041 #if defined(PETSC_HAVE_HYPRE)
4042   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijcusparse_hypre_C", MatConvert_AIJ_HYPRE));
4043 #endif
4044   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetUseCPUSolve_C", MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE));
4045   PetscFunctionReturn(PETSC_SUCCESS);
4046 }
4047 
4048 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
4049 {
4050   PetscFunctionBegin;
4051   PetscCall(MatCreate_SeqAIJ(B));
4052   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, &B));
4053   PetscFunctionReturn(PETSC_SUCCESS);
4054 }
4055 
4056 /*MC
4057    MATSEQAIJCUSPARSE - MATAIJCUSPARSE = "(seq)aijcusparse" - A matrix type to be used for sparse matrices.
4058 
4059    A matrix type whose data resides on NVIDIA GPUs. These matrices can be in either
4060    CSR, ELL, or Hybrid format.
4061    All matrix calculations are performed on NVIDIA GPUs using the CuSPARSE library.
4062 
4063    Options Database Keys:
4064 +  -mat_type aijcusparse - sets the matrix type to "seqaijcusparse" during a call to `MatSetFromOptions()`
4065 .  -mat_cusparse_storage_format csr - sets the storage format of matrices (for `MatMult()` and factors in `MatSolve()`).
4066                                       Other options include ell (ellpack) or hyb (hybrid).
4067 .  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for `MatMult()`). Other options include ell (ellpack) or hyb (hybrid).
4068 -  -mat_cusparse_use_cpu_solve - Do `MatSolve()` on CPU
4069 
4070   Level: beginner
4071 
4072 .seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJCUSPARSE()`, `MatCUSPARSESetUseCPUSolve()`, `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
4073 M*/
4074 
4075 PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_CUSPARSE(void)
4076 {
4077   PetscFunctionBegin;
4078   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_LU, MatGetFactor_seqaijcusparse_cusparse));
4079   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_CHOLESKY, MatGetFactor_seqaijcusparse_cusparse));
4080   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ILU, MatGetFactor_seqaijcusparse_cusparse));
4081   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ICC, MatGetFactor_seqaijcusparse_cusparse));
4082   PetscFunctionReturn(PETSC_SUCCESS);
4083 }
4084 
4085 static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat mat)
4086 {
4087   Mat_SeqAIJCUSPARSE *cusp = static_cast<Mat_SeqAIJCUSPARSE *>(mat->spptr);
4088 
4089   PetscFunctionBegin;
4090   if (cusp) {
4091     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->mat, cusp->format));
4092     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4093     delete cusp->workVector;
4094     delete cusp->rowoffsets_gpu;
4095     delete cusp->csr2csc_i;
4096     delete cusp->coords;
4097     if (cusp->handle) PetscCallCUSPARSE(cusparseDestroy(cusp->handle));
4098     PetscCall(PetscFree(mat->spptr));
4099   }
4100   PetscFunctionReturn(PETSC_SUCCESS);
4101 }
4102 
4103 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **mat)
4104 {
4105   PetscFunctionBegin;
4106   if (*mat) {
4107     delete (*mat)->values;
4108     delete (*mat)->column_indices;
4109     delete (*mat)->row_offsets;
4110     delete *mat;
4111     *mat = 0;
4112   }
4113   PetscFunctionReturn(PETSC_SUCCESS);
4114 }
4115 
4116 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4117 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
4118 {
4119   PetscFunctionBegin;
4120   if (*trifactor) {
4121     if ((*trifactor)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*trifactor)->descr));
4122     if ((*trifactor)->solveInfo) PetscCallCUSPARSE(cusparseDestroyCsrsvInfo((*trifactor)->solveInfo));
4123     PetscCall(CsrMatrix_Destroy(&(*trifactor)->csrMat));
4124     if ((*trifactor)->solveBuffer) PetscCallCUDA(cudaFree((*trifactor)->solveBuffer));
4125     if ((*trifactor)->AA_h) PetscCallCUDA(cudaFreeHost((*trifactor)->AA_h));
4126   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4127     if ((*trifactor)->csr2cscBuffer) PetscCallCUDA(cudaFree((*trifactor)->csr2cscBuffer));
4128   #endif
4129     PetscCall(PetscFree(*trifactor));
4130   }
4131   PetscFunctionReturn(PETSC_SUCCESS);
4132 }
4133 #endif
4134 
4135 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct, MatCUSPARSEStorageFormat format)
4136 {
4137   CsrMatrix *mat;
4138 
4139   PetscFunctionBegin;
4140   if (*matstruct) {
4141     if ((*matstruct)->mat) {
4142       if (format == MAT_CUSPARSE_ELL || format == MAT_CUSPARSE_HYB) {
4143 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4144         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
4145 #else
4146         cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
4147         PetscCallCUSPARSE(cusparseDestroyHybMat(hybMat));
4148 #endif
4149       } else {
4150         mat = (CsrMatrix *)(*matstruct)->mat;
4151         PetscCall(CsrMatrix_Destroy(&mat));
4152       }
4153     }
4154     if ((*matstruct)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*matstruct)->descr));
4155     delete (*matstruct)->cprowIndices;
4156     if ((*matstruct)->alpha_one) PetscCallCUDA(cudaFree((*matstruct)->alpha_one));
4157     if ((*matstruct)->beta_zero) PetscCallCUDA(cudaFree((*matstruct)->beta_zero));
4158     if ((*matstruct)->beta_one) PetscCallCUDA(cudaFree((*matstruct)->beta_one));
4159 
4160 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4161     Mat_SeqAIJCUSPARSEMultStruct *mdata = *matstruct;
4162     if (mdata->matDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr));
4163     for (int i = 0; i < 3; i++) {
4164       if (mdata->cuSpMV[i].initialized) {
4165         PetscCallCUDA(cudaFree(mdata->cuSpMV[i].spmvBuffer));
4166         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecXDescr));
4167         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecYDescr));
4168       }
4169     }
4170 #endif
4171     delete *matstruct;
4172     *matstruct = NULL;
4173   }
4174   PetscFunctionReturn(PETSC_SUCCESS);
4175 }
4176 
4177 PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors_p *trifactors)
4178 {
4179   Mat_SeqAIJCUSPARSETriFactors *fs = *trifactors;
4180 
4181   PetscFunctionBegin;
4182   if (fs) {
4183 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4184     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtr));
4185     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtr));
4186     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtrTranspose));
4187     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtrTranspose));
4188     delete fs->workVector;
4189     fs->workVector = NULL;
4190 #endif
4191     delete fs->rpermIndices;
4192     delete fs->cpermIndices;
4193     fs->rpermIndices  = NULL;
4194     fs->cpermIndices  = NULL;
4195     fs->init_dev_prop = PETSC_FALSE;
4196 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4197     PetscCallCUDA(cudaFree(fs->csrRowPtr));
4198     PetscCallCUDA(cudaFree(fs->csrColIdx));
4199     PetscCallCUDA(cudaFree(fs->csrRowPtr32));
4200     PetscCallCUDA(cudaFree(fs->csrColIdx32));
4201     PetscCallCUDA(cudaFree(fs->csrVal));
4202     PetscCallCUDA(cudaFree(fs->diag));
4203     PetscCallCUDA(cudaFree(fs->X));
4204     PetscCallCUDA(cudaFree(fs->Y));
4205     // PetscCallCUDA(cudaFree(fs->factBuffer_M)); /* No needed since factBuffer_M shares with one of spsvBuffer_L/U */
4206     PetscCallCUDA(cudaFree(fs->spsvBuffer_L));
4207     PetscCallCUDA(cudaFree(fs->spsvBuffer_U));
4208     PetscCallCUDA(cudaFree(fs->spsvBuffer_Lt));
4209     PetscCallCUDA(cudaFree(fs->spsvBuffer_Ut));
4210     PetscCallCUSPARSE(cusparseDestroyMatDescr(fs->matDescr_M));
4211     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_L));
4212     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_U));
4213     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_L));
4214     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Lt));
4215     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_U));
4216     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Ut));
4217     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_X));
4218     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_Y));
4219     PetscCallCUSPARSE(cusparseDestroyCsrilu02Info(fs->ilu0Info_M));
4220     PetscCallCUSPARSE(cusparseDestroyCsric02Info(fs->ic0Info_M));
4221     PetscCall(PetscFree(fs->csrRowPtr_h));
4222     PetscCall(PetscFree(fs->csrVal_h));
4223     PetscCall(PetscFree(fs->diag_h));
4224     fs->createdTransposeSpSVDescr    = PETSC_FALSE;
4225     fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
4226 #endif
4227   }
4228   PetscFunctionReturn(PETSC_SUCCESS);
4229 }
4230 
4231 static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **trifactors)
4232 {
4233   PetscFunctionBegin;
4234   if (*trifactors) {
4235     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(trifactors));
4236     PetscCallCUSPARSE(cusparseDestroy((*trifactors)->handle));
4237     PetscCall(PetscFree(*trifactors));
4238   }
4239   PetscFunctionReturn(PETSC_SUCCESS);
4240 }
4241 
4242 struct IJCompare {
4243   __host__ __device__ inline bool operator()(const thrust::tuple<PetscInt, PetscInt> &t1, const thrust::tuple<PetscInt, PetscInt> &t2)
4244   {
4245     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4246     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4247     return false;
4248   }
4249 };
4250 
4251 static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat A, PetscBool destroy)
4252 {
4253   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4254 
4255   PetscFunctionBegin;
4256   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4257   if (!cusp) PetscFunctionReturn(PETSC_SUCCESS);
4258   if (destroy) {
4259     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4260     delete cusp->csr2csc_i;
4261     cusp->csr2csc_i = NULL;
4262   }
4263   A->transupdated = PETSC_FALSE;
4264   PetscFunctionReturn(PETSC_SUCCESS);
4265 }
4266 
4267 static PetscErrorCode MatCOOStructDestroy_SeqAIJCUSPARSE(void *data)
4268 {
4269   MatCOOStruct_SeqAIJ *coo = (MatCOOStruct_SeqAIJ *)data;
4270 
4271   PetscFunctionBegin;
4272   PetscCallCUDA(cudaFree(coo->perm));
4273   PetscCallCUDA(cudaFree(coo->jmap));
4274   PetscCall(PetscFree(coo));
4275   PetscFunctionReturn(PETSC_SUCCESS);
4276 }
4277 
4278 static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
4279 {
4280   PetscBool            dev_ij = PETSC_FALSE;
4281   PetscMemType         mtype  = PETSC_MEMTYPE_HOST;
4282   PetscInt            *i, *j;
4283   PetscContainer       container_h, container_d;
4284   MatCOOStruct_SeqAIJ *coo_h, *coo_d;
4285 
4286   PetscFunctionBegin;
4287   // The two MatResetPreallocationCOO_* must be done in order. The former relies on values that might be destroyed by the latter
4288   PetscCall(PetscGetMemType(coo_i, &mtype));
4289   if (PetscMemTypeDevice(mtype)) {
4290     dev_ij = PETSC_TRUE;
4291     PetscCall(PetscMalloc2(coo_n, &i, coo_n, &j));
4292     PetscCallCUDA(cudaMemcpy(i, coo_i, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4293     PetscCallCUDA(cudaMemcpy(j, coo_j, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4294   } else {
4295     i = coo_i;
4296     j = coo_j;
4297   }
4298 
4299   PetscCall(MatSetPreallocationCOO_SeqAIJ(mat, coo_n, i, j));
4300   if (dev_ij) PetscCall(PetscFree2(i, j));
4301   mat->offloadmask = PETSC_OFFLOAD_CPU;
4302   // Create the GPU memory
4303   PetscCall(MatSeqAIJCUSPARSECopyToGPU(mat));
4304 
4305   // Copy the COO struct to device
4306   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container_h));
4307   PetscCall(PetscContainerGetPointer(container_h, (void **)&coo_h));
4308   PetscCall(PetscMalloc1(1, &coo_d));
4309   *coo_d = *coo_h; // do a shallow copy and then amend some fields that need to be different
4310   PetscCallCUDA(cudaMalloc((void **)&coo_d->jmap, (coo_h->nz + 1) * sizeof(PetscCount)));
4311   PetscCallCUDA(cudaMemcpy(coo_d->jmap, coo_h->jmap, (coo_h->nz + 1) * sizeof(PetscCount), cudaMemcpyHostToDevice));
4312   PetscCallCUDA(cudaMalloc((void **)&coo_d->perm, coo_h->Atot * sizeof(PetscCount)));
4313   PetscCallCUDA(cudaMemcpy(coo_d->perm, coo_h->perm, coo_h->Atot * sizeof(PetscCount), cudaMemcpyHostToDevice));
4314 
4315   // Put the COO struct in a container and then attach that to the matrix
4316   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container_d));
4317   PetscCall(PetscContainerSetPointer(container_d, coo_d));
4318   PetscCall(PetscContainerSetUserDestroy(container_d, MatCOOStructDestroy_SeqAIJCUSPARSE));
4319   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Device", (PetscObject)container_d));
4320   PetscCall(PetscContainerDestroy(&container_d));
4321   PetscFunctionReturn(PETSC_SUCCESS);
4322 }
4323 
4324 __global__ static void MatAddCOOValues(const PetscScalar kv[], PetscCount nnz, const PetscCount jmap[], const PetscCount perm[], InsertMode imode, PetscScalar a[])
4325 {
4326   PetscCount       i         = blockIdx.x * blockDim.x + threadIdx.x;
4327   const PetscCount grid_size = gridDim.x * blockDim.x;
4328   for (; i < nnz; i += grid_size) {
4329     PetscScalar sum = 0.0;
4330     for (PetscCount k = jmap[i]; k < jmap[i + 1]; k++) sum += kv[perm[k]];
4331     a[i] = (imode == INSERT_VALUES ? 0.0 : a[i]) + sum;
4332   }
4333 }
4334 
4335 static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat A, const PetscScalar v[], InsertMode imode)
4336 {
4337   Mat_SeqAIJ          *seq  = (Mat_SeqAIJ *)A->data;
4338   Mat_SeqAIJCUSPARSE  *dev  = (Mat_SeqAIJCUSPARSE *)A->spptr;
4339   PetscCount           Annz = seq->nz;
4340   PetscMemType         memtype;
4341   const PetscScalar   *v1 = v;
4342   PetscScalar         *Aa;
4343   PetscContainer       container;
4344   MatCOOStruct_SeqAIJ *coo;
4345 
4346   PetscFunctionBegin;
4347   if (!dev->mat) PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4348 
4349   PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_MatCOOStruct_Device", (PetscObject *)&container));
4350   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
4351 
4352   PetscCall(PetscGetMemType(v, &memtype));
4353   if (PetscMemTypeHost(memtype)) { /* If user gave v[] in host, we might need to copy it to device if any */
4354     PetscCallCUDA(cudaMalloc((void **)&v1, coo->n * sizeof(PetscScalar)));
4355     PetscCallCUDA(cudaMemcpy((void *)v1, v, coo->n * sizeof(PetscScalar), cudaMemcpyHostToDevice));
4356   }
4357 
4358   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSEGetArrayWrite(A, &Aa));
4359   else PetscCall(MatSeqAIJCUSPARSEGetArray(A, &Aa));
4360 
4361   PetscCall(PetscLogGpuTimeBegin());
4362   if (Annz) {
4363     MatAddCOOValues<<<(Annz + 255) / 256, 256>>>(v1, Annz, coo->jmap, coo->perm, imode, Aa);
4364     PetscCallCUDA(cudaPeekAtLastError());
4365   }
4366   PetscCall(PetscLogGpuTimeEnd());
4367 
4368   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSERestoreArrayWrite(A, &Aa));
4369   else PetscCall(MatSeqAIJCUSPARSERestoreArray(A, &Aa));
4370 
4371   if (PetscMemTypeHost(memtype)) PetscCallCUDA(cudaFree((void *)v1));
4372   PetscFunctionReturn(PETSC_SUCCESS);
4373 }
4374 
4375 /*@C
4376   MatSeqAIJCUSPARSEGetIJ - returns the device row storage `i` and `j` indices for `MATSEQAIJCUSPARSE` matrices.
4377 
4378   Not Collective
4379 
4380   Input Parameters:
4381 + A          - the matrix
4382 - compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4383 
4384   Output Parameters:
4385 + i - the CSR row pointers
4386 - j - the CSR column indices
4387 
4388   Level: developer
4389 
4390   Note:
4391   When compressed is true, the CSR structure does not contain empty rows
4392 
4393 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSERestoreIJ()`, `MatSeqAIJCUSPARSEGetArrayRead()`
4394 @*/
4395 PetscErrorCode MatSeqAIJCUSPARSEGetIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4396 {
4397   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4398   CsrMatrix          *csr;
4399   Mat_SeqAIJ         *a = (Mat_SeqAIJ *)A->data;
4400 
4401   PetscFunctionBegin;
4402   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4403   if (!i || !j) PetscFunctionReturn(PETSC_SUCCESS);
4404   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4405   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4406   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4407   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4408   csr = (CsrMatrix *)cusp->mat->mat;
4409   if (i) {
4410     if (!compressed && a->compressedrow.use) { /* need full row offset */
4411       if (!cusp->rowoffsets_gpu) {
4412         cusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4413         cusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4414         PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4415       }
4416       *i = cusp->rowoffsets_gpu->data().get();
4417     } else *i = csr->row_offsets->data().get();
4418   }
4419   if (j) *j = csr->column_indices->data().get();
4420   PetscFunctionReturn(PETSC_SUCCESS);
4421 }
4422 
4423 /*@C
4424   MatSeqAIJCUSPARSERestoreIJ - restore the device row storage `i` and `j` indices obtained with `MatSeqAIJCUSPARSEGetIJ()`
4425 
4426   Not Collective
4427 
4428   Input Parameters:
4429 + A          - the matrix
4430 . compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4431 . i          - the CSR row pointers
4432 - j          - the CSR column indices
4433 
4434   Level: developer
4435 
4436 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetIJ()`
4437 @*/
4438 PetscErrorCode MatSeqAIJCUSPARSERestoreIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4439 {
4440   PetscFunctionBegin;
4441   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4442   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4443   if (i) *i = NULL;
4444   if (j) *j = NULL;
4445   (void)compressed;
4446   PetscFunctionReturn(PETSC_SUCCESS);
4447 }
4448 
4449 /*@C
4450   MatSeqAIJCUSPARSEGetArrayRead - gives read-only access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4451 
4452   Not Collective
4453 
4454   Input Parameter:
4455 . A - a `MATSEQAIJCUSPARSE` matrix
4456 
4457   Output Parameter:
4458 . a - pointer to the device data
4459 
4460   Level: developer
4461 
4462   Note:
4463   May trigger host-device copies if up-to-date matrix data is on host
4464 
4465 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArrayRead()`
4466 @*/
4467 PetscErrorCode MatSeqAIJCUSPARSEGetArrayRead(Mat A, const PetscScalar **a)
4468 {
4469   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4470   CsrMatrix          *csr;
4471 
4472   PetscFunctionBegin;
4473   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4474   PetscAssertPointer(a, 2);
4475   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4476   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4477   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4478   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4479   csr = (CsrMatrix *)cusp->mat->mat;
4480   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4481   *a = csr->values->data().get();
4482   PetscFunctionReturn(PETSC_SUCCESS);
4483 }
4484 
4485 /*@C
4486   MatSeqAIJCUSPARSERestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJCUSPARSEGetArrayRead()`
4487 
4488   Not Collective
4489 
4490   Input Parameters:
4491 + A - a `MATSEQAIJCUSPARSE` matrix
4492 - a - pointer to the device data
4493 
4494   Level: developer
4495 
4496 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`
4497 @*/
4498 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayRead(Mat A, const PetscScalar **a)
4499 {
4500   PetscFunctionBegin;
4501   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4502   PetscAssertPointer(a, 2);
4503   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4504   *a = NULL;
4505   PetscFunctionReturn(PETSC_SUCCESS);
4506 }
4507 
4508 /*@C
4509   MatSeqAIJCUSPARSEGetArray - gives read-write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4510 
4511   Not Collective
4512 
4513   Input Parameter:
4514 . A - a `MATSEQAIJCUSPARSE` matrix
4515 
4516   Output Parameter:
4517 . a - pointer to the device data
4518 
4519   Level: developer
4520 
4521   Note:
4522   May trigger host-device copies if up-to-date matrix data is on host
4523 
4524 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArray()`
4525 @*/
4526 PetscErrorCode MatSeqAIJCUSPARSEGetArray(Mat A, PetscScalar **a)
4527 {
4528   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4529   CsrMatrix          *csr;
4530 
4531   PetscFunctionBegin;
4532   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4533   PetscAssertPointer(a, 2);
4534   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4535   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4536   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4537   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4538   csr = (CsrMatrix *)cusp->mat->mat;
4539   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4540   *a             = csr->values->data().get();
4541   A->offloadmask = PETSC_OFFLOAD_GPU;
4542   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4543   PetscFunctionReturn(PETSC_SUCCESS);
4544 }
4545 /*@C
4546   MatSeqAIJCUSPARSERestoreArray - restore the read-write access array obtained from `MatSeqAIJCUSPARSEGetArray()`
4547 
4548   Not Collective
4549 
4550   Input Parameters:
4551 + A - a `MATSEQAIJCUSPARSE` matrix
4552 - a - pointer to the device data
4553 
4554   Level: developer
4555 
4556 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`
4557 @*/
4558 PetscErrorCode MatSeqAIJCUSPARSERestoreArray(Mat A, PetscScalar **a)
4559 {
4560   PetscFunctionBegin;
4561   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4562   PetscAssertPointer(a, 2);
4563   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4564   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4565   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4566   *a = NULL;
4567   PetscFunctionReturn(PETSC_SUCCESS);
4568 }
4569 
4570 /*@C
4571   MatSeqAIJCUSPARSEGetArrayWrite - gives write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4572 
4573   Not Collective
4574 
4575   Input Parameter:
4576 . A - a `MATSEQAIJCUSPARSE` matrix
4577 
4578   Output Parameter:
4579 . a - pointer to the device data
4580 
4581   Level: developer
4582 
4583   Note:
4584   Does not trigger host-device copies and flags data validity on the GPU
4585 
4586 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSERestoreArrayWrite()`
4587 @*/
4588 PetscErrorCode MatSeqAIJCUSPARSEGetArrayWrite(Mat A, PetscScalar **a)
4589 {
4590   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4591   CsrMatrix          *csr;
4592 
4593   PetscFunctionBegin;
4594   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4595   PetscAssertPointer(a, 2);
4596   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4597   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4598   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4599   csr = (CsrMatrix *)cusp->mat->mat;
4600   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4601   *a             = csr->values->data().get();
4602   A->offloadmask = PETSC_OFFLOAD_GPU;
4603   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4604   PetscFunctionReturn(PETSC_SUCCESS);
4605 }
4606 
4607 /*@C
4608   MatSeqAIJCUSPARSERestoreArrayWrite - restore the write-only access array obtained from `MatSeqAIJCUSPARSEGetArrayWrite()`
4609 
4610   Not Collective
4611 
4612   Input Parameters:
4613 + A - a `MATSEQAIJCUSPARSE` matrix
4614 - a - pointer to the device data
4615 
4616   Level: developer
4617 
4618 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayWrite()`
4619 @*/
4620 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayWrite(Mat A, PetscScalar **a)
4621 {
4622   PetscFunctionBegin;
4623   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4624   PetscAssertPointer(a, 2);
4625   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4626   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4627   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4628   *a = NULL;
4629   PetscFunctionReturn(PETSC_SUCCESS);
4630 }
4631 
4632 struct IJCompare4 {
4633   __host__ __device__ inline bool operator()(const thrust::tuple<int, int, PetscScalar, int> &t1, const thrust::tuple<int, int, PetscScalar, int> &t2)
4634   {
4635     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4636     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4637     return false;
4638   }
4639 };
4640 
4641 struct Shift {
4642   int _shift;
4643 
4644   Shift(int shift) : _shift(shift) { }
4645   __host__ __device__ inline int operator()(const int &c) { return c + _shift; }
4646 };
4647 
4648 /* merges two SeqAIJCUSPARSE matrices A, B by concatenating their rows. [A';B']' operation in MATLAB notation */
4649 PetscErrorCode MatSeqAIJCUSPARSEMergeMats(Mat A, Mat B, MatReuse reuse, Mat *C)
4650 {
4651   Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
4652   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr, *Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr, *Ccusp;
4653   Mat_SeqAIJCUSPARSEMultStruct *Cmat;
4654   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
4655   PetscInt                      Annz, Bnnz;
4656   cusparseStatus_t              stat;
4657   PetscInt                      i, m, n, zero = 0;
4658 
4659   PetscFunctionBegin;
4660   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4661   PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
4662   PetscAssertPointer(C, 4);
4663   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4664   PetscCheckTypeName(B, MATSEQAIJCUSPARSE);
4665   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);
4666   PetscCheck(reuse != MAT_INPLACE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_INPLACE_MATRIX not supported");
4667   PetscCheck(Acusp->format != MAT_CUSPARSE_ELL && Acusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4668   PetscCheck(Bcusp->format != MAT_CUSPARSE_ELL && Bcusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4669   if (reuse == MAT_INITIAL_MATRIX) {
4670     m = A->rmap->n;
4671     n = A->cmap->n + B->cmap->n;
4672     PetscCall(MatCreate(PETSC_COMM_SELF, C));
4673     PetscCall(MatSetSizes(*C, m, n, m, n));
4674     PetscCall(MatSetType(*C, MATSEQAIJCUSPARSE));
4675     c                       = (Mat_SeqAIJ *)(*C)->data;
4676     Ccusp                   = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4677     Cmat                    = new Mat_SeqAIJCUSPARSEMultStruct;
4678     Ccsr                    = new CsrMatrix;
4679     Cmat->cprowIndices      = NULL;
4680     c->compressedrow.use    = PETSC_FALSE;
4681     c->compressedrow.nrows  = 0;
4682     c->compressedrow.i      = NULL;
4683     c->compressedrow.rindex = NULL;
4684     Ccusp->workVector       = NULL;
4685     Ccusp->nrows            = m;
4686     Ccusp->mat              = Cmat;
4687     Ccusp->mat->mat         = Ccsr;
4688     Ccsr->num_rows          = m;
4689     Ccsr->num_cols          = n;
4690     PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
4691     PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
4692     PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4693     PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
4694     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
4695     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
4696     PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4697     PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4698     PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4699     PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4700     PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4701     PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4702     PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4703 
4704     Acsr                 = (CsrMatrix *)Acusp->mat->mat;
4705     Bcsr                 = (CsrMatrix *)Bcusp->mat->mat;
4706     Annz                 = (PetscInt)Acsr->column_indices->size();
4707     Bnnz                 = (PetscInt)Bcsr->column_indices->size();
4708     c->nz                = Annz + Bnnz;
4709     Ccsr->row_offsets    = new THRUSTINTARRAY32(m + 1);
4710     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
4711     Ccsr->values         = new THRUSTARRAY(c->nz);
4712     Ccsr->num_entries    = c->nz;
4713     Ccusp->coords        = new THRUSTINTARRAY(c->nz);
4714     if (c->nz) {
4715       auto              Acoo = new THRUSTINTARRAY32(Annz);
4716       auto              Bcoo = new THRUSTINTARRAY32(Bnnz);
4717       auto              Ccoo = new THRUSTINTARRAY32(c->nz);
4718       THRUSTINTARRAY32 *Aroff, *Broff;
4719 
4720       if (a->compressedrow.use) { /* need full row offset */
4721         if (!Acusp->rowoffsets_gpu) {
4722           Acusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4723           Acusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4724           PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4725         }
4726         Aroff = Acusp->rowoffsets_gpu;
4727       } else Aroff = Acsr->row_offsets;
4728       if (b->compressedrow.use) { /* need full row offset */
4729         if (!Bcusp->rowoffsets_gpu) {
4730           Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
4731           Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
4732           PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
4733         }
4734         Broff = Bcusp->rowoffsets_gpu;
4735       } else Broff = Bcsr->row_offsets;
4736       PetscCall(PetscLogGpuTimeBegin());
4737       stat = cusparseXcsr2coo(Acusp->handle, Aroff->data().get(), Annz, m, Acoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4738       PetscCallCUSPARSE(stat);
4739       stat = cusparseXcsr2coo(Bcusp->handle, Broff->data().get(), Bnnz, m, Bcoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4740       PetscCallCUSPARSE(stat);
4741       /* Issues when using bool with large matrices on SUMMIT 10.2.89 */
4742       auto Aperm = thrust::make_constant_iterator(1);
4743       auto Bperm = thrust::make_constant_iterator(0);
4744 #if PETSC_PKG_CUDA_VERSION_GE(10, 0, 0)
4745       auto Bcib = thrust::make_transform_iterator(Bcsr->column_indices->begin(), Shift(A->cmap->n));
4746       auto Bcie = thrust::make_transform_iterator(Bcsr->column_indices->end(), Shift(A->cmap->n));
4747 #else
4748       /* there are issues instantiating the merge operation using a transform iterator for the columns of B */
4749       auto Bcib = Bcsr->column_indices->begin();
4750       auto Bcie = Bcsr->column_indices->end();
4751       thrust::transform(Bcib, Bcie, Bcib, Shift(A->cmap->n));
4752 #endif
4753       auto wPerm = new THRUSTINTARRAY32(Annz + Bnnz);
4754       auto Azb   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->begin(), Acsr->column_indices->begin(), Acsr->values->begin(), Aperm));
4755       auto Aze   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->end(), Acsr->column_indices->end(), Acsr->values->end(), Aperm));
4756       auto Bzb   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->begin(), Bcib, Bcsr->values->begin(), Bperm));
4757       auto Bze   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->end(), Bcie, Bcsr->values->end(), Bperm));
4758       auto Czb   = thrust::make_zip_iterator(thrust::make_tuple(Ccoo->begin(), Ccsr->column_indices->begin(), Ccsr->values->begin(), wPerm->begin()));
4759       auto p1    = Ccusp->coords->begin();
4760       auto p2    = Ccusp->coords->begin();
4761       thrust::advance(p2, Annz);
4762       PetscCallThrust(thrust::merge(thrust::device, Azb, Aze, Bzb, Bze, Czb, IJCompare4()));
4763 #if PETSC_PKG_CUDA_VERSION_LT(10, 0, 0)
4764       thrust::transform(Bcib, Bcie, Bcib, Shift(-A->cmap->n));
4765 #endif
4766       auto cci = thrust::make_counting_iterator(zero);
4767       auto cce = thrust::make_counting_iterator(c->nz);
4768 #if 0 //Errors on SUMMIT cuda 11.1.0
4769       PetscCallThrust(thrust::partition_copy(thrust::device,cci,cce,wPerm->begin(),p1,p2,thrust::identity<int>()));
4770 #else
4771       auto pred = thrust::identity<int>();
4772       PetscCallThrust(thrust::copy_if(thrust::device, cci, cce, wPerm->begin(), p1, pred));
4773       PetscCallThrust(thrust::remove_copy_if(thrust::device, cci, cce, wPerm->begin(), p2, pred));
4774 #endif
4775       stat = cusparseXcoo2csr(Ccusp->handle, Ccoo->data().get(), c->nz, m, Ccsr->row_offsets->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4776       PetscCallCUSPARSE(stat);
4777       PetscCall(PetscLogGpuTimeEnd());
4778       delete wPerm;
4779       delete Acoo;
4780       delete Bcoo;
4781       delete Ccoo;
4782 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4783       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);
4784       PetscCallCUSPARSE(stat);
4785 #endif
4786       if (A->form_explicit_transpose && B->form_explicit_transpose) { /* if A and B have the transpose, generate C transpose too */
4787         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
4788         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
4789         PetscBool                     AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4790         Mat_SeqAIJCUSPARSEMultStruct *CmatT = new Mat_SeqAIJCUSPARSEMultStruct;
4791         CsrMatrix                    *CcsrT = new CsrMatrix;
4792         CsrMatrix                    *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4793         CsrMatrix                    *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4794 
4795         (*C)->form_explicit_transpose = PETSC_TRUE;
4796         (*C)->transupdated            = PETSC_TRUE;
4797         Ccusp->rowoffsets_gpu         = NULL;
4798         CmatT->cprowIndices           = NULL;
4799         CmatT->mat                    = CcsrT;
4800         CcsrT->num_rows               = n;
4801         CcsrT->num_cols               = m;
4802         CcsrT->num_entries            = c->nz;
4803 
4804         CcsrT->row_offsets    = new THRUSTINTARRAY32(n + 1);
4805         CcsrT->column_indices = new THRUSTINTARRAY32(c->nz);
4806         CcsrT->values         = new THRUSTARRAY(c->nz);
4807 
4808         PetscCall(PetscLogGpuTimeBegin());
4809         auto rT = CcsrT->row_offsets->begin();
4810         if (AT) {
4811           rT = thrust::copy(AcsrT->row_offsets->begin(), AcsrT->row_offsets->end(), rT);
4812           thrust::advance(rT, -1);
4813         }
4814         if (BT) {
4815           auto titb = thrust::make_transform_iterator(BcsrT->row_offsets->begin(), Shift(a->nz));
4816           auto tite = thrust::make_transform_iterator(BcsrT->row_offsets->end(), Shift(a->nz));
4817           thrust::copy(titb, tite, rT);
4818         }
4819         auto cT = CcsrT->column_indices->begin();
4820         if (AT) cT = thrust::copy(AcsrT->column_indices->begin(), AcsrT->column_indices->end(), cT);
4821         if (BT) thrust::copy(BcsrT->column_indices->begin(), BcsrT->column_indices->end(), cT);
4822         auto vT = CcsrT->values->begin();
4823         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4824         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4825         PetscCall(PetscLogGpuTimeEnd());
4826 
4827         PetscCallCUSPARSE(cusparseCreateMatDescr(&CmatT->descr));
4828         PetscCallCUSPARSE(cusparseSetMatIndexBase(CmatT->descr, CUSPARSE_INDEX_BASE_ZERO));
4829         PetscCallCUSPARSE(cusparseSetMatType(CmatT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4830         PetscCallCUDA(cudaMalloc((void **)&CmatT->alpha_one, sizeof(PetscScalar)));
4831         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_zero, sizeof(PetscScalar)));
4832         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_one, sizeof(PetscScalar)));
4833         PetscCallCUDA(cudaMemcpy(CmatT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4834         PetscCallCUDA(cudaMemcpy(CmatT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4835         PetscCallCUDA(cudaMemcpy(CmatT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4836 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4837         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);
4838         PetscCallCUSPARSE(stat);
4839 #endif
4840         Ccusp->matTranspose = CmatT;
4841       }
4842     }
4843 
4844     c->singlemalloc = PETSC_FALSE;
4845     c->free_a       = PETSC_TRUE;
4846     c->free_ij      = PETSC_TRUE;
4847     PetscCall(PetscMalloc1(m + 1, &c->i));
4848     PetscCall(PetscMalloc1(c->nz, &c->j));
4849     if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
4850       THRUSTINTARRAY ii(Ccsr->row_offsets->size());
4851       THRUSTINTARRAY jj(Ccsr->column_indices->size());
4852       ii = *Ccsr->row_offsets;
4853       jj = *Ccsr->column_indices;
4854       PetscCallCUDA(cudaMemcpy(c->i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4855       PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4856     } else {
4857       PetscCallCUDA(cudaMemcpy(c->i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4858       PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4859     }
4860     PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
4861     PetscCall(PetscMalloc1(m, &c->ilen));
4862     PetscCall(PetscMalloc1(m, &c->imax));
4863     c->maxnz         = c->nz;
4864     c->nonzerorowcnt = 0;
4865     c->rmax          = 0;
4866     for (i = 0; i < m; i++) {
4867       const PetscInt nn = c->i[i + 1] - c->i[i];
4868       c->ilen[i] = c->imax[i] = nn;
4869       c->nonzerorowcnt += (PetscInt) !!nn;
4870       c->rmax = PetscMax(c->rmax, nn);
4871     }
4872     PetscCall(MatMarkDiagonal_SeqAIJ(*C));
4873     PetscCall(PetscMalloc1(c->nz, &c->a));
4874     (*C)->nonzerostate++;
4875     PetscCall(PetscLayoutSetUp((*C)->rmap));
4876     PetscCall(PetscLayoutSetUp((*C)->cmap));
4877     Ccusp->nonzerostate = (*C)->nonzerostate;
4878     (*C)->preallocated  = PETSC_TRUE;
4879   } else {
4880     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);
4881     c = (Mat_SeqAIJ *)(*C)->data;
4882     if (c->nz) {
4883       Ccusp = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4884       PetscCheck(Ccusp->coords, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing coords");
4885       PetscCheck(Ccusp->format != MAT_CUSPARSE_ELL && Ccusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4886       PetscCheck(Ccusp->nonzerostate == (*C)->nonzerostate, PETSC_COMM_SELF, PETSC_ERR_COR, "Wrong nonzerostate");
4887       PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4888       PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4889       PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4890       PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4891       Acsr = (CsrMatrix *)Acusp->mat->mat;
4892       Bcsr = (CsrMatrix *)Bcusp->mat->mat;
4893       Ccsr = (CsrMatrix *)Ccusp->mat->mat;
4894       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());
4895       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());
4896       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());
4897       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);
4898       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());
4899       auto pmid = Ccusp->coords->begin();
4900       thrust::advance(pmid, Acsr->num_entries);
4901       PetscCall(PetscLogGpuTimeBegin());
4902       auto zibait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->begin())));
4903       auto zieait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4904       thrust::for_each(zibait, zieait, VecCUDAEquals());
4905       auto zibbit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4906       auto ziebit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->end())));
4907       thrust::for_each(zibbit, ziebit, VecCUDAEquals());
4908       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(*C, PETSC_FALSE));
4909       if (A->form_explicit_transpose && B->form_explicit_transpose && (*C)->form_explicit_transpose) {
4910         PetscCheck(Ccusp->matTranspose, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing transpose Mat_SeqAIJCUSPARSEMultStruct");
4911         PetscBool  AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4912         CsrMatrix *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4913         CsrMatrix *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4914         CsrMatrix *CcsrT = (CsrMatrix *)Ccusp->matTranspose->mat;
4915         auto       vT    = CcsrT->values->begin();
4916         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4917         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4918         (*C)->transupdated = PETSC_TRUE;
4919       }
4920       PetscCall(PetscLogGpuTimeEnd());
4921     }
4922   }
4923   PetscCall(PetscObjectStateIncrease((PetscObject)*C));
4924   (*C)->assembled     = PETSC_TRUE;
4925   (*C)->was_assembled = PETSC_FALSE;
4926   (*C)->offloadmask   = PETSC_OFFLOAD_GPU;
4927   PetscFunctionReturn(PETSC_SUCCESS);
4928 }
4929 
4930 static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
4931 {
4932   bool               dmem;
4933   const PetscScalar *av;
4934 
4935   PetscFunctionBegin;
4936   dmem = isCudaMem(v);
4937   PetscCall(MatSeqAIJCUSPARSEGetArrayRead(A, &av));
4938   if (n && idx) {
4939     THRUSTINTARRAY widx(n);
4940     widx.assign(idx, idx + n);
4941     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
4942 
4943     THRUSTARRAY                    *w = NULL;
4944     thrust::device_ptr<PetscScalar> dv;
4945     if (dmem) {
4946       dv = thrust::device_pointer_cast(v);
4947     } else {
4948       w  = new THRUSTARRAY(n);
4949       dv = w->data();
4950     }
4951     thrust::device_ptr<const PetscScalar> dav = thrust::device_pointer_cast(av);
4952 
4953     auto zibit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.begin()), dv));
4954     auto zieit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.end()), dv + n));
4955     thrust::for_each(zibit, zieit, VecCUDAEquals());
4956     if (w) PetscCallCUDA(cudaMemcpy(v, w->data().get(), n * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
4957     delete w;
4958   } else {
4959     PetscCallCUDA(cudaMemcpy(v, av, n * sizeof(PetscScalar), dmem ? cudaMemcpyDeviceToDevice : cudaMemcpyDeviceToHost));
4960   }
4961   if (!dmem) PetscCall(PetscLogCpuToGpu(n * sizeof(PetscScalar)));
4962   PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(A, &av));
4963   PetscFunctionReturn(PETSC_SUCCESS);
4964 }
4965