xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision 357d8704e7b71e6f14cfde34e80d63f499af80c0)
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->free_a = PETSC_TRUE;
3304   PetscCall(PetscShmgetAllocateArray(c->nz, sizeof(PetscInt), (void **)&c->j));
3305   PetscCall(PetscShmgetAllocateArray(m + 1, sizeof(PetscInt), (void **)&c->i));
3306   c->free_ij = PETSC_TRUE;
3307   if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
3308     PetscInt      *d_i = c->i;
3309     THRUSTINTARRAY ii(Ccsr->row_offsets->size());
3310     THRUSTINTARRAY jj(Ccsr->column_indices->size());
3311     ii = *Ccsr->row_offsets;
3312     jj = *Ccsr->column_indices;
3313     if (ciscompressed) d_i = c->compressedrow.i;
3314     PetscCallCUDA(cudaMemcpy(d_i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3315     PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3316   } else {
3317     PetscInt *d_i = c->i;
3318     if (ciscompressed) d_i = c->compressedrow.i;
3319     PetscCallCUDA(cudaMemcpy(d_i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3320     PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
3321   }
3322   if (ciscompressed) { /* need to expand host row offsets */
3323     PetscInt r = 0;
3324     c->i[0]    = 0;
3325     for (k = 0; k < c->compressedrow.nrows; k++) {
3326       const PetscInt next = c->compressedrow.rindex[k];
3327       const PetscInt old  = c->compressedrow.i[k];
3328       for (; r < next; r++) c->i[r + 1] = old;
3329     }
3330     for (; r < m; r++) c->i[r + 1] = c->compressedrow.i[c->compressedrow.nrows];
3331   }
3332   PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
3333   PetscCall(PetscMalloc1(m, &c->ilen));
3334   PetscCall(PetscMalloc1(m, &c->imax));
3335   c->maxnz         = c->nz;
3336   c->nonzerorowcnt = 0;
3337   c->rmax          = 0;
3338   for (k = 0; k < m; k++) {
3339     const PetscInt nn = c->i[k + 1] - c->i[k];
3340     c->ilen[k] = c->imax[k] = nn;
3341     c->nonzerorowcnt += (PetscInt) !!nn;
3342     c->rmax = PetscMax(c->rmax, nn);
3343   }
3344   PetscCall(MatMarkDiagonal_SeqAIJ(C));
3345   PetscCall(PetscMalloc1(c->nz, &c->a));
3346   Ccsr->num_entries = c->nz;
3347 
3348   C->nonzerostate++;
3349   PetscCall(PetscLayoutSetUp(C->rmap));
3350   PetscCall(PetscLayoutSetUp(C->cmap));
3351   Ccusp->nonzerostate = C->nonzerostate;
3352   C->offloadmask      = PETSC_OFFLOAD_UNALLOCATED;
3353   C->preallocated     = PETSC_TRUE;
3354   C->assembled        = PETSC_FALSE;
3355   C->was_assembled    = PETSC_FALSE;
3356   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 */
3357     mmdata->reusesym = PETSC_TRUE;
3358     C->offloadmask   = PETSC_OFFLOAD_GPU;
3359   }
3360   C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3361   PetscFunctionReturn(PETSC_SUCCESS);
3362 }
3363 
3364 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat);
3365 
3366 /* handles sparse or dense B */
3367 static PetscErrorCode MatProductSetFromOptions_SeqAIJCUSPARSE(Mat mat)
3368 {
3369   Mat_Product *product = mat->product;
3370   PetscBool    isdense = PETSC_FALSE, Biscusp = PETSC_FALSE, Ciscusp = PETSC_TRUE;
3371 
3372   PetscFunctionBegin;
3373   MatCheckProduct(mat, 1);
3374   PetscCall(PetscObjectBaseTypeCompare((PetscObject)product->B, MATSEQDENSE, &isdense));
3375   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, MATSEQAIJCUSPARSE, &Biscusp));
3376   if (product->type == MATPRODUCT_ABC) {
3377     Ciscusp = PETSC_FALSE;
3378     if (!product->C->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->C, MATSEQAIJCUSPARSE, &Ciscusp));
3379   }
3380   if (Biscusp && Ciscusp) { /* we can always select the CPU backend */
3381     PetscBool usecpu = PETSC_FALSE;
3382     switch (product->type) {
3383     case MATPRODUCT_AB:
3384       if (product->api_user) {
3385         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
3386         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3387         PetscOptionsEnd();
3388       } else {
3389         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
3390         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
3391         PetscOptionsEnd();
3392       }
3393       break;
3394     case MATPRODUCT_AtB:
3395       if (product->api_user) {
3396         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
3397         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3398         PetscOptionsEnd();
3399       } else {
3400         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
3401         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
3402         PetscOptionsEnd();
3403       }
3404       break;
3405     case MATPRODUCT_PtAP:
3406       if (product->api_user) {
3407         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
3408         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3409         PetscOptionsEnd();
3410       } else {
3411         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
3412         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
3413         PetscOptionsEnd();
3414       }
3415       break;
3416     case MATPRODUCT_RARt:
3417       if (product->api_user) {
3418         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatRARt", "Mat");
3419         PetscCall(PetscOptionsBool("-matrart_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3420         PetscOptionsEnd();
3421       } else {
3422         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_RARt", "Mat");
3423         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
3424         PetscOptionsEnd();
3425       }
3426       break;
3427     case MATPRODUCT_ABC:
3428       if (product->api_user) {
3429         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMatMult", "Mat");
3430         PetscCall(PetscOptionsBool("-matmatmatmult_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3431         PetscOptionsEnd();
3432       } else {
3433         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_ABC", "Mat");
3434         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
3435         PetscOptionsEnd();
3436       }
3437       break;
3438     default:
3439       break;
3440     }
3441     if (usecpu) Biscusp = Ciscusp = PETSC_FALSE;
3442   }
3443   /* dispatch */
3444   if (isdense) {
3445     switch (product->type) {
3446     case MATPRODUCT_AB:
3447     case MATPRODUCT_AtB:
3448     case MATPRODUCT_ABt:
3449     case MATPRODUCT_PtAP:
3450     case MATPRODUCT_RARt:
3451       if (product->A->boundtocpu) {
3452         PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense(mat));
3453       } else {
3454         mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA;
3455       }
3456       break;
3457     case MATPRODUCT_ABC:
3458       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3459       break;
3460     default:
3461       break;
3462     }
3463   } else if (Biscusp && Ciscusp) {
3464     switch (product->type) {
3465     case MATPRODUCT_AB:
3466     case MATPRODUCT_AtB:
3467     case MATPRODUCT_ABt:
3468       mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
3469       break;
3470     case MATPRODUCT_PtAP:
3471     case MATPRODUCT_RARt:
3472     case MATPRODUCT_ABC:
3473       mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
3474       break;
3475     default:
3476       break;
3477     }
3478   } else { /* fallback for AIJ */
3479     PetscCall(MatProductSetFromOptions_SeqAIJ(mat));
3480   }
3481   PetscFunctionReturn(PETSC_SUCCESS);
3482 }
3483 
3484 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3485 {
3486   PetscFunctionBegin;
3487   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_FALSE, PETSC_FALSE));
3488   PetscFunctionReturn(PETSC_SUCCESS);
3489 }
3490 
3491 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3492 {
3493   PetscFunctionBegin;
3494   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_FALSE, PETSC_FALSE));
3495   PetscFunctionReturn(PETSC_SUCCESS);
3496 }
3497 
3498 static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3499 {
3500   PetscFunctionBegin;
3501   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_TRUE));
3502   PetscFunctionReturn(PETSC_SUCCESS);
3503 }
3504 
3505 static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3506 {
3507   PetscFunctionBegin;
3508   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_TRUE));
3509   PetscFunctionReturn(PETSC_SUCCESS);
3510 }
3511 
3512 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
3513 {
3514   PetscFunctionBegin;
3515   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_FALSE));
3516   PetscFunctionReturn(PETSC_SUCCESS);
3517 }
3518 
3519 __global__ static void ScatterAdd(PetscInt n, PetscInt *idx, const PetscScalar *x, PetscScalar *y)
3520 {
3521   int i = blockIdx.x * blockDim.x + threadIdx.x;
3522   if (i < n) y[idx[i]] += x[i];
3523 }
3524 
3525 /* z = op(A) x + y. If trans & !herm, op = ^T; if trans & herm, op = ^H; if !trans, op = no-op */
3526 static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz, PetscBool trans, PetscBool herm)
3527 {
3528   Mat_SeqAIJ                   *a              = (Mat_SeqAIJ *)A->data;
3529   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
3530   Mat_SeqAIJCUSPARSEMultStruct *matstruct;
3531   PetscScalar                  *xarray, *zarray, *dptr, *beta, *xptr;
3532   cusparseOperation_t           opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
3533   PetscBool                     compressed;
3534 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3535   PetscInt nx, ny;
3536 #endif
3537 
3538   PetscFunctionBegin;
3539   PetscCheck(!herm || trans, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Hermitian and not transpose not supported");
3540   if (!a->nz) {
3541     if (yy) PetscCall(VecSeq_CUDA::Copy(yy, zz));
3542     else PetscCall(VecSeq_CUDA::Set(zz, 0));
3543     PetscFunctionReturn(PETSC_SUCCESS);
3544   }
3545   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
3546   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
3547   if (!trans) {
3548     matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3549     PetscCheck(matstruct, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "SeqAIJCUSPARSE does not have a 'mat' (need to fix)");
3550   } else {
3551     if (herm || !A->form_explicit_transpose) {
3552       opA       = herm ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE : CUSPARSE_OPERATION_TRANSPOSE;
3553       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
3554     } else {
3555       if (!cusparsestruct->matTranspose) PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
3556       matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
3557     }
3558   }
3559   /* Does the matrix use compressed rows (i.e., drop zero rows)? */
3560   compressed = matstruct->cprowIndices ? PETSC_TRUE : PETSC_FALSE;
3561 
3562   try {
3563     PetscCall(VecCUDAGetArrayRead(xx, (const PetscScalar **)&xarray));
3564     if (yy == zz) PetscCall(VecCUDAGetArray(zz, &zarray)); /* read & write zz, so need to get up-to-date zarray on GPU */
3565     else PetscCall(VecCUDAGetArrayWrite(zz, &zarray));     /* write zz, so no need to init zarray on GPU */
3566 
3567     PetscCall(PetscLogGpuTimeBegin());
3568     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3569       /* z = A x + beta y.
3570          If A is compressed (with less rows), then Ax is shorter than the full z, so we need a work vector to store Ax.
3571          When A is non-compressed, and z = y, we can set beta=1 to compute y = Ax + y in one call.
3572       */
3573       xptr = xarray;
3574       dptr = compressed ? cusparsestruct->workVector->data().get() : zarray;
3575       beta = (yy == zz && !compressed) ? matstruct->beta_one : matstruct->beta_zero;
3576 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3577       /* Get length of x, y for y=Ax. ny might be shorter than the work vector's allocated length, since the work vector is
3578           allocated to accommodate different uses. So we get the length info directly from mat.
3579        */
3580       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3581         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3582         nx             = mat->num_cols;
3583         ny             = mat->num_rows;
3584       }
3585 #endif
3586     } else {
3587       /* z = A^T x + beta y
3588          If A is compressed, then we need a work vector as the shorter version of x to compute A^T x.
3589          Note A^Tx is of full length, so we set beta to 1.0 if y exists.
3590        */
3591       xptr = compressed ? cusparsestruct->workVector->data().get() : xarray;
3592       dptr = zarray;
3593       beta = yy ? matstruct->beta_one : matstruct->beta_zero;
3594       if (compressed) { /* Scatter x to work vector */
3595         thrust::device_ptr<PetscScalar> xarr = thrust::device_pointer_cast(xarray);
3596 
3597         thrust::for_each(
3598 #if PetscDefined(HAVE_THRUST_ASYNC)
3599           thrust::cuda::par.on(PetscDefaultCudaStream),
3600 #endif
3601           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))),
3602           thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(), VecCUDAEqualsReverse());
3603       }
3604 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3605       if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3606         CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3607         nx             = mat->num_rows;
3608         ny             = mat->num_cols;
3609       }
3610 #endif
3611     }
3612 
3613     /* csr_spmv does y = alpha op(A) x + beta y */
3614     if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
3615 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3616       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");
3617       if (!matstruct->cuSpMV[opA].initialized) { /* built on demand */
3618         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecXDescr, nx, xptr, cusparse_scalartype));
3619         PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecYDescr, ny, dptr, cusparse_scalartype));
3620         PetscCallCUSPARSE(
3621           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));
3622         PetscCallCUDA(cudaMalloc(&matstruct->cuSpMV[opA].spmvBuffer, matstruct->cuSpMV[opA].spmvBufferSize));
3623 
3624         matstruct->cuSpMV[opA].initialized = PETSC_TRUE;
3625       } else {
3626         /* x, y's value pointers might change between calls, but their shape is kept, so we just update pointers */
3627         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecXDescr, xptr));
3628         PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecYDescr, dptr));
3629       }
3630 
3631       PetscCallCUSPARSE(cusparseSpMV(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->matDescr, /* built in MatSeqAIJCUSPARSECopyToGPU() or MatSeqAIJCUSPARSEFormExplicitTranspose() */
3632                                      matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, matstruct->cuSpMV[opA].spmvBuffer));
3633 #else
3634       CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
3635       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));
3636 #endif
3637     } else {
3638       if (cusparsestruct->nrows) {
3639 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3640         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
3641 #else
3642         cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
3643         PetscCallCUSPARSE(cusparse_hyb_spmv(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->descr, hybMat, xptr, beta, dptr));
3644 #endif
3645       }
3646     }
3647     PetscCall(PetscLogGpuTimeEnd());
3648 
3649     if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
3650       if (yy) {                                      /* MatMultAdd: zz = A*xx + yy */
3651         if (compressed) {                            /* A is compressed. We first copy yy to zz, then ScatterAdd the work vector to zz */
3652           PetscCall(VecSeq_CUDA::Copy(yy, zz));      /* zz = yy */
3653         } else if (zz != yy) {                       /* A is not compressed. zz already contains A*xx, and we just need to add yy */
3654           PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3655         }
3656       } else if (compressed) { /* MatMult: zz = A*xx. A is compressed, so we zero zz first, then ScatterAdd the work vector to zz */
3657         PetscCall(VecSeq_CUDA::Set(zz, 0));
3658       }
3659 
3660       /* ScatterAdd the result from work vector into the full vector when A is compressed */
3661       if (compressed) {
3662         PetscCall(PetscLogGpuTimeBegin());
3663         /* I wanted to make this for_each asynchronous but failed. thrust::async::for_each() returns an event (internally registered)
3664            and in the destructor of the scope, it will call cudaStreamSynchronize() on this stream. One has to store all events to
3665            prevent that. So I just add a ScatterAdd kernel.
3666          */
3667 #if 0
3668         thrust::device_ptr<PetscScalar> zptr = thrust::device_pointer_cast(zarray);
3669         thrust::async::for_each(thrust::cuda::par.on(cusparsestruct->stream),
3670                          thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))),
3671                          thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(),
3672                          VecCUDAPlusEquals());
3673 #else
3674         PetscInt n = matstruct->cprowIndices->size();
3675         ScatterAdd<<<(n + 255) / 256, 256, 0, PetscDefaultCudaStream>>>(n, matstruct->cprowIndices->data().get(), cusparsestruct->workVector->data().get(), zarray);
3676 #endif
3677         PetscCall(PetscLogGpuTimeEnd());
3678       }
3679     } else {
3680       if (yy && yy != zz) PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
3681     }
3682     PetscCall(VecCUDARestoreArrayRead(xx, (const PetscScalar **)&xarray));
3683     if (yy == zz) PetscCall(VecCUDARestoreArray(zz, &zarray));
3684     else PetscCall(VecCUDARestoreArrayWrite(zz, &zarray));
3685   } catch (char *ex) {
3686     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
3687   }
3688   if (yy) {
3689     PetscCall(PetscLogGpuFlops(2.0 * a->nz));
3690   } else {
3691     PetscCall(PetscLogGpuFlops(2.0 * a->nz - a->nonzerorowcnt));
3692   }
3693   PetscFunctionReturn(PETSC_SUCCESS);
3694 }
3695 
3696 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
3697 {
3698   PetscFunctionBegin;
3699   PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_FALSE));
3700   PetscFunctionReturn(PETSC_SUCCESS);
3701 }
3702 
3703 static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A, MatAssemblyType mode)
3704 {
3705   PetscFunctionBegin;
3706   PetscCall(MatAssemblyEnd_SeqAIJ(A, mode));
3707   PetscFunctionReturn(PETSC_SUCCESS);
3708 }
3709 
3710 /*@
3711   MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in `MATAIJCUSPARSE` (compressed row) format
3712   (the default parallel PETSc format).
3713 
3714   Collective
3715 
3716   Input Parameters:
3717 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3718 . m    - number of rows
3719 . n    - number of columns
3720 . nz   - number of nonzeros per row (same for all rows), ignored if `nnz` is provide
3721 - nnz  - array containing the number of nonzeros in the various rows (possibly different for each row) or `NULL`
3722 
3723   Output Parameter:
3724 . A - the matrix
3725 
3726   Level: intermediate
3727 
3728   Notes:
3729   This matrix will ultimately pushed down to NVIDIA GPUs and use the CuSPARSE library for
3730   calculations. For good matrix assembly performance the user should preallocate the matrix
3731   storage by setting the parameter `nz` (or the array `nnz`).
3732 
3733   It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
3734   MatXXXXSetPreallocation() paradgm instead of this routine directly.
3735   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]
3736 
3737   The AIJ format, also called
3738   compressed row storage, is fully compatible with standard Fortran
3739   storage.  That is, the stored row and column indices can begin at
3740   either one (as in Fortran) or zero.
3741 
3742   Specify the preallocated storage with either nz or nnz (not both).
3743   Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
3744   allocation.
3745 
3746 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MATAIJCUSPARSE`
3747 @*/
3748 PetscErrorCode MatCreateSeqAIJCUSPARSE(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
3749 {
3750   PetscFunctionBegin;
3751   PetscCall(MatCreate(comm, A));
3752   PetscCall(MatSetSizes(*A, m, n, m, n));
3753   PetscCall(MatSetType(*A, MATSEQAIJCUSPARSE));
3754   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, (PetscInt *)nnz));
3755   PetscFunctionReturn(PETSC_SUCCESS);
3756 }
3757 
3758 static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
3759 {
3760   PetscFunctionBegin;
3761   if (A->factortype == MAT_FACTOR_NONE) {
3762     PetscCall(MatSeqAIJCUSPARSE_Destroy(A));
3763   } else {
3764     PetscCall(MatSeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors **)&A->spptr));
3765   }
3766   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3767   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetFormat_C", NULL));
3768   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetUseCPUSolve_C", NULL));
3769   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3770   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3771   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3772   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
3773   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3774   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3775   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijcusparse_hypre_C", NULL));
3776   PetscCall(MatDestroy_SeqAIJ(A));
3777   PetscFunctionReturn(PETSC_SUCCESS);
3778 }
3779 
3780 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
3781 static PetscErrorCode       MatBindToCPU_SeqAIJCUSPARSE(Mat, PetscBool);
3782 static PetscErrorCode       MatDuplicate_SeqAIJCUSPARSE(Mat A, MatDuplicateOption cpvalues, Mat *B)
3783 {
3784   PetscFunctionBegin;
3785   PetscCall(MatDuplicate_SeqAIJ(A, cpvalues, B));
3786   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(*B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, B));
3787   PetscFunctionReturn(PETSC_SUCCESS);
3788 }
3789 
3790 static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat Y, PetscScalar a, Mat X, MatStructure str)
3791 {
3792   Mat_SeqAIJ         *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
3793   Mat_SeqAIJCUSPARSE *cy;
3794   Mat_SeqAIJCUSPARSE *cx;
3795   PetscScalar        *ay;
3796   const PetscScalar  *ax;
3797   CsrMatrix          *csry, *csrx;
3798 
3799   PetscFunctionBegin;
3800   cy = (Mat_SeqAIJCUSPARSE *)Y->spptr;
3801   cx = (Mat_SeqAIJCUSPARSE *)X->spptr;
3802   if (X->ops->axpy != Y->ops->axpy) {
3803     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3804     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3805     PetscFunctionReturn(PETSC_SUCCESS);
3806   }
3807   /* if we are here, it means both matrices are bound to GPU */
3808   PetscCall(MatSeqAIJCUSPARSECopyToGPU(Y));
3809   PetscCall(MatSeqAIJCUSPARSECopyToGPU(X));
3810   PetscCheck(cy->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)Y), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3811   PetscCheck(cx->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)X), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
3812   csry = (CsrMatrix *)cy->mat->mat;
3813   csrx = (CsrMatrix *)cx->mat->mat;
3814   /* see if we can turn this into a cublas axpy */
3815   if (str != SAME_NONZERO_PATTERN && x->nz == y->nz && !x->compressedrow.use && !y->compressedrow.use) {
3816     bool eq = thrust::equal(thrust::device, csry->row_offsets->begin(), csry->row_offsets->end(), csrx->row_offsets->begin());
3817     if (eq) eq = thrust::equal(thrust::device, csry->column_indices->begin(), csry->column_indices->end(), csrx->column_indices->begin());
3818     if (eq) str = SAME_NONZERO_PATTERN;
3819   }
3820   /* spgeam is buggy with one column */
3821   if (Y->cmap->n == 1 && str != SAME_NONZERO_PATTERN) str = DIFFERENT_NONZERO_PATTERN;
3822 
3823   if (str == SUBSET_NONZERO_PATTERN) {
3824     PetscScalar b = 1.0;
3825 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3826     size_t bufferSize;
3827     void  *buffer;
3828 #endif
3829 
3830     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3831     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3832     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_HOST));
3833 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
3834     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(),
3835                                                      csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), &bufferSize));
3836     PetscCallCUDA(cudaMalloc(&buffer, bufferSize));
3837     PetscCall(PetscLogGpuTimeBegin());
3838     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(),
3839                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), buffer));
3840     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3841     PetscCall(PetscLogGpuTimeEnd());
3842     PetscCallCUDA(cudaFree(buffer));
3843 #else
3844     PetscCall(PetscLogGpuTimeBegin());
3845     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(),
3846                                           csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get()));
3847     PetscCall(PetscLogGpuFlops(x->nz + y->nz));
3848     PetscCall(PetscLogGpuTimeEnd());
3849 #endif
3850     PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_DEVICE));
3851     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3852     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3853     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3854   } else if (str == SAME_NONZERO_PATTERN) {
3855     cublasHandle_t cublasv2handle;
3856     PetscBLASInt   one = 1, bnz = 1;
3857 
3858     PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
3859     PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3860     PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3861     PetscCall(PetscBLASIntCast(x->nz, &bnz));
3862     PetscCall(PetscLogGpuTimeBegin());
3863     PetscCallCUBLAS(cublasXaxpy(cublasv2handle, bnz, &a, ax, one, ay, one));
3864     PetscCall(PetscLogGpuFlops(2.0 * bnz));
3865     PetscCall(PetscLogGpuTimeEnd());
3866     PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
3867     PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3868     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3869   } else {
3870     PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
3871     PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
3872   }
3873   PetscFunctionReturn(PETSC_SUCCESS);
3874 }
3875 
3876 static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat Y, PetscScalar a)
3877 {
3878   Mat_SeqAIJ    *y = (Mat_SeqAIJ *)Y->data;
3879   PetscScalar   *ay;
3880   cublasHandle_t cublasv2handle;
3881   PetscBLASInt   one = 1, bnz = 1;
3882 
3883   PetscFunctionBegin;
3884   PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
3885   PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
3886   PetscCall(PetscBLASIntCast(y->nz, &bnz));
3887   PetscCall(PetscLogGpuTimeBegin());
3888   PetscCallCUBLAS(cublasXscal(cublasv2handle, bnz, &a, ay, one));
3889   PetscCall(PetscLogGpuFlops(bnz));
3890   PetscCall(PetscLogGpuTimeEnd());
3891   PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
3892   PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3893   PetscFunctionReturn(PETSC_SUCCESS);
3894 }
3895 
3896 static PetscErrorCode MatZeroEntries_SeqAIJCUSPARSE(Mat A)
3897 {
3898   PetscBool   both = PETSC_FALSE;
3899   Mat_SeqAIJ *a    = (Mat_SeqAIJ *)A->data;
3900 
3901   PetscFunctionBegin;
3902   if (A->factortype == MAT_FACTOR_NONE) {
3903     Mat_SeqAIJCUSPARSE *spptr = (Mat_SeqAIJCUSPARSE *)A->spptr;
3904     if (spptr->mat) {
3905       CsrMatrix *matrix = (CsrMatrix *)spptr->mat->mat;
3906       if (matrix->values) {
3907         both = PETSC_TRUE;
3908         thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3909       }
3910     }
3911     if (spptr->matTranspose) {
3912       CsrMatrix *matrix = (CsrMatrix *)spptr->matTranspose->mat;
3913       if (matrix->values) thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
3914     }
3915   }
3916   PetscCall(PetscArrayzero(a->a, a->i[A->rmap->n]));
3917   PetscCall(MatSeqAIJInvalidateDiagonal(A));
3918   if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
3919   else A->offloadmask = PETSC_OFFLOAD_CPU;
3920   PetscFunctionReturn(PETSC_SUCCESS);
3921 }
3922 
3923 static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat A, PetscBool flg)
3924 {
3925   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
3926 
3927   PetscFunctionBegin;
3928   if (A->factortype != MAT_FACTOR_NONE) {
3929     A->boundtocpu = flg;
3930     PetscFunctionReturn(PETSC_SUCCESS);
3931   }
3932   if (flg) {
3933     PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
3934 
3935     A->ops->scale                     = MatScale_SeqAIJ;
3936     A->ops->axpy                      = MatAXPY_SeqAIJ;
3937     A->ops->zeroentries               = MatZeroEntries_SeqAIJ;
3938     A->ops->mult                      = MatMult_SeqAIJ;
3939     A->ops->multadd                   = MatMultAdd_SeqAIJ;
3940     A->ops->multtranspose             = MatMultTranspose_SeqAIJ;
3941     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJ;
3942     A->ops->multhermitiantranspose    = NULL;
3943     A->ops->multhermitiantransposeadd = NULL;
3944     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJ;
3945     PetscCall(PetscMemzero(a->ops, sizeof(Mat_SeqAIJOps)));
3946     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
3947     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
3948     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
3949     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
3950     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
3951     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
3952   } else {
3953     A->ops->scale                     = MatScale_SeqAIJCUSPARSE;
3954     A->ops->axpy                      = MatAXPY_SeqAIJCUSPARSE;
3955     A->ops->zeroentries               = MatZeroEntries_SeqAIJCUSPARSE;
3956     A->ops->mult                      = MatMult_SeqAIJCUSPARSE;
3957     A->ops->multadd                   = MatMultAdd_SeqAIJCUSPARSE;
3958     A->ops->multtranspose             = MatMultTranspose_SeqAIJCUSPARSE;
3959     A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJCUSPARSE;
3960     A->ops->multhermitiantranspose    = MatMultHermitianTranspose_SeqAIJCUSPARSE;
3961     A->ops->multhermitiantransposeadd = MatMultHermitianTransposeAdd_SeqAIJCUSPARSE;
3962     A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJCUSPARSE;
3963     a->ops->getarray                  = MatSeqAIJGetArray_SeqAIJCUSPARSE;
3964     a->ops->restorearray              = MatSeqAIJRestoreArray_SeqAIJCUSPARSE;
3965     a->ops->getarrayread              = MatSeqAIJGetArrayRead_SeqAIJCUSPARSE;
3966     a->ops->restorearrayread          = MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE;
3967     a->ops->getarraywrite             = MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE;
3968     a->ops->restorearraywrite         = MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE;
3969     a->ops->getcsrandmemtype          = MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE;
3970 
3971     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", MatSeqAIJCopySubArray_SeqAIJCUSPARSE));
3972     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3973     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3974     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJCUSPARSE));
3975     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJCUSPARSE));
3976     PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
3977   }
3978   A->boundtocpu = flg;
3979   if (flg && a->inode.size) {
3980     a->inode.use = PETSC_TRUE;
3981   } else {
3982     a->inode.use = PETSC_FALSE;
3983   }
3984   PetscFunctionReturn(PETSC_SUCCESS);
3985 }
3986 
3987 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat A, MatType, MatReuse reuse, Mat *newmat)
3988 {
3989   Mat B;
3990 
3991   PetscFunctionBegin;
3992   PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* first use of CUSPARSE may be via MatConvert */
3993   if (reuse == MAT_INITIAL_MATRIX) {
3994     PetscCall(MatDuplicate(A, MAT_COPY_VALUES, newmat));
3995   } else if (reuse == MAT_REUSE_MATRIX) {
3996     PetscCall(MatCopy(A, *newmat, SAME_NONZERO_PATTERN));
3997   }
3998   B = *newmat;
3999 
4000   PetscCall(PetscFree(B->defaultvectype));
4001   PetscCall(PetscStrallocpy(VECCUDA, &B->defaultvectype));
4002 
4003   if (reuse != MAT_REUSE_MATRIX && !B->spptr) {
4004     if (B->factortype == MAT_FACTOR_NONE) {
4005       Mat_SeqAIJCUSPARSE *spptr;
4006       PetscCall(PetscNew(&spptr));
4007       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4008       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4009       spptr->format = MAT_CUSPARSE_CSR;
4010 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4011   #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4012       spptr->spmvAlg = CUSPARSE_SPMV_CSR_ALG1; /* default, since we only support csr */
4013   #else
4014       spptr->spmvAlg = CUSPARSE_CSRMV_ALG1; /* default, since we only support csr */
4015   #endif
4016       spptr->spmmAlg    = CUSPARSE_SPMM_CSR_ALG1; /* default, only support column-major dense matrix B */
4017       spptr->csr2cscAlg = CUSPARSE_CSR2CSC_ALG1;
4018 #endif
4019       B->spptr = spptr;
4020     } else {
4021       Mat_SeqAIJCUSPARSETriFactors *spptr;
4022 
4023       PetscCall(PetscNew(&spptr));
4024       PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
4025       PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
4026       B->spptr = spptr;
4027     }
4028     B->offloadmask = PETSC_OFFLOAD_UNALLOCATED;
4029   }
4030   B->ops->assemblyend    = MatAssemblyEnd_SeqAIJCUSPARSE;
4031   B->ops->destroy        = MatDestroy_SeqAIJCUSPARSE;
4032   B->ops->setoption      = MatSetOption_SeqAIJCUSPARSE;
4033   B->ops->setfromoptions = MatSetFromOptions_SeqAIJCUSPARSE;
4034   B->ops->bindtocpu      = MatBindToCPU_SeqAIJCUSPARSE;
4035   B->ops->duplicate      = MatDuplicate_SeqAIJCUSPARSE;
4036 
4037   PetscCall(MatBindToCPU_SeqAIJCUSPARSE(B, PETSC_FALSE));
4038   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJCUSPARSE));
4039   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetFormat_C", MatCUSPARSESetFormat_SeqAIJCUSPARSE));
4040 #if defined(PETSC_HAVE_HYPRE)
4041   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijcusparse_hypre_C", MatConvert_AIJ_HYPRE));
4042 #endif
4043   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetUseCPUSolve_C", MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE));
4044   PetscFunctionReturn(PETSC_SUCCESS);
4045 }
4046 
4047 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
4048 {
4049   PetscFunctionBegin;
4050   PetscCall(MatCreate_SeqAIJ(B));
4051   PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, &B));
4052   PetscFunctionReturn(PETSC_SUCCESS);
4053 }
4054 
4055 /*MC
4056    MATSEQAIJCUSPARSE - MATAIJCUSPARSE = "(seq)aijcusparse" - A matrix type to be used for sparse matrices.
4057 
4058    A matrix type whose data resides on NVIDIA GPUs. These matrices can be in either
4059    CSR, ELL, or Hybrid format.
4060    All matrix calculations are performed on NVIDIA GPUs using the CuSPARSE library.
4061 
4062    Options Database Keys:
4063 +  -mat_type aijcusparse - sets the matrix type to "seqaijcusparse" during a call to `MatSetFromOptions()`
4064 .  -mat_cusparse_storage_format csr - sets the storage format of matrices (for `MatMult()` and factors in `MatSolve()`).
4065                                       Other options include ell (ellpack) or hyb (hybrid).
4066 .  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for `MatMult()`). Other options include ell (ellpack) or hyb (hybrid).
4067 -  -mat_cusparse_use_cpu_solve - Do `MatSolve()` on CPU
4068 
4069   Level: beginner
4070 
4071 .seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJCUSPARSE()`, `MatCUSPARSESetUseCPUSolve()`, `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
4072 M*/
4073 
4074 PETSC_INTERN PetscErrorCode MatSolverTypeRegister_CUSPARSE(void)
4075 {
4076   PetscFunctionBegin;
4077   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_LU, MatGetFactor_seqaijcusparse_cusparse));
4078   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_CHOLESKY, MatGetFactor_seqaijcusparse_cusparse));
4079   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ILU, MatGetFactor_seqaijcusparse_cusparse));
4080   PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ICC, MatGetFactor_seqaijcusparse_cusparse));
4081   PetscFunctionReturn(PETSC_SUCCESS);
4082 }
4083 
4084 static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat mat)
4085 {
4086   Mat_SeqAIJCUSPARSE *cusp = static_cast<Mat_SeqAIJCUSPARSE *>(mat->spptr);
4087 
4088   PetscFunctionBegin;
4089   if (cusp) {
4090     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->mat, cusp->format));
4091     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4092     delete cusp->workVector;
4093     delete cusp->rowoffsets_gpu;
4094     delete cusp->csr2csc_i;
4095     delete cusp->coords;
4096     if (cusp->handle) PetscCallCUSPARSE(cusparseDestroy(cusp->handle));
4097     PetscCall(PetscFree(mat->spptr));
4098   }
4099   PetscFunctionReturn(PETSC_SUCCESS);
4100 }
4101 
4102 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **mat)
4103 {
4104   PetscFunctionBegin;
4105   if (*mat) {
4106     delete (*mat)->values;
4107     delete (*mat)->column_indices;
4108     delete (*mat)->row_offsets;
4109     delete *mat;
4110     *mat = 0;
4111   }
4112   PetscFunctionReturn(PETSC_SUCCESS);
4113 }
4114 
4115 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4116 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
4117 {
4118   PetscFunctionBegin;
4119   if (*trifactor) {
4120     if ((*trifactor)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*trifactor)->descr));
4121     if ((*trifactor)->solveInfo) PetscCallCUSPARSE(cusparseDestroyCsrsvInfo((*trifactor)->solveInfo));
4122     PetscCall(CsrMatrix_Destroy(&(*trifactor)->csrMat));
4123     if ((*trifactor)->solveBuffer) PetscCallCUDA(cudaFree((*trifactor)->solveBuffer));
4124     if ((*trifactor)->AA_h) PetscCallCUDA(cudaFreeHost((*trifactor)->AA_h));
4125   #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4126     if ((*trifactor)->csr2cscBuffer) PetscCallCUDA(cudaFree((*trifactor)->csr2cscBuffer));
4127   #endif
4128     PetscCall(PetscFree(*trifactor));
4129   }
4130   PetscFunctionReturn(PETSC_SUCCESS);
4131 }
4132 #endif
4133 
4134 static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct, MatCUSPARSEStorageFormat format)
4135 {
4136   CsrMatrix *mat;
4137 
4138   PetscFunctionBegin;
4139   if (*matstruct) {
4140     if ((*matstruct)->mat) {
4141       if (format == MAT_CUSPARSE_ELL || format == MAT_CUSPARSE_HYB) {
4142 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4143         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
4144 #else
4145         cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
4146         PetscCallCUSPARSE(cusparseDestroyHybMat(hybMat));
4147 #endif
4148       } else {
4149         mat = (CsrMatrix *)(*matstruct)->mat;
4150         PetscCall(CsrMatrix_Destroy(&mat));
4151       }
4152     }
4153     if ((*matstruct)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*matstruct)->descr));
4154     delete (*matstruct)->cprowIndices;
4155     if ((*matstruct)->alpha_one) PetscCallCUDA(cudaFree((*matstruct)->alpha_one));
4156     if ((*matstruct)->beta_zero) PetscCallCUDA(cudaFree((*matstruct)->beta_zero));
4157     if ((*matstruct)->beta_one) PetscCallCUDA(cudaFree((*matstruct)->beta_one));
4158 
4159 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4160     Mat_SeqAIJCUSPARSEMultStruct *mdata = *matstruct;
4161     if (mdata->matDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr));
4162     for (int i = 0; i < 3; i++) {
4163       if (mdata->cuSpMV[i].initialized) {
4164         PetscCallCUDA(cudaFree(mdata->cuSpMV[i].spmvBuffer));
4165         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecXDescr));
4166         PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecYDescr));
4167       }
4168     }
4169 #endif
4170     delete *matstruct;
4171     *matstruct = NULL;
4172   }
4173   PetscFunctionReturn(PETSC_SUCCESS);
4174 }
4175 
4176 PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors_p *trifactors)
4177 {
4178   Mat_SeqAIJCUSPARSETriFactors *fs = *trifactors;
4179 
4180   PetscFunctionBegin;
4181   if (fs) {
4182 #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
4183     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtr));
4184     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtr));
4185     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtrTranspose));
4186     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtrTranspose));
4187     delete fs->workVector;
4188     fs->workVector = NULL;
4189 #endif
4190     delete fs->rpermIndices;
4191     delete fs->cpermIndices;
4192     fs->rpermIndices  = NULL;
4193     fs->cpermIndices  = NULL;
4194     fs->init_dev_prop = PETSC_FALSE;
4195 #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
4196     PetscCallCUDA(cudaFree(fs->csrRowPtr));
4197     PetscCallCUDA(cudaFree(fs->csrColIdx));
4198     PetscCallCUDA(cudaFree(fs->csrRowPtr32));
4199     PetscCallCUDA(cudaFree(fs->csrColIdx32));
4200     PetscCallCUDA(cudaFree(fs->csrVal));
4201     PetscCallCUDA(cudaFree(fs->diag));
4202     PetscCallCUDA(cudaFree(fs->X));
4203     PetscCallCUDA(cudaFree(fs->Y));
4204     // PetscCallCUDA(cudaFree(fs->factBuffer_M)); /* No needed since factBuffer_M shares with one of spsvBuffer_L/U */
4205     PetscCallCUDA(cudaFree(fs->spsvBuffer_L));
4206     PetscCallCUDA(cudaFree(fs->spsvBuffer_U));
4207     PetscCallCUDA(cudaFree(fs->spsvBuffer_Lt));
4208     PetscCallCUDA(cudaFree(fs->spsvBuffer_Ut));
4209     PetscCallCUSPARSE(cusparseDestroyMatDescr(fs->matDescr_M));
4210     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_L));
4211     PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_U));
4212     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_L));
4213     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Lt));
4214     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_U));
4215     PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Ut));
4216     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_X));
4217     PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_Y));
4218     PetscCallCUSPARSE(cusparseDestroyCsrilu02Info(fs->ilu0Info_M));
4219     PetscCallCUSPARSE(cusparseDestroyCsric02Info(fs->ic0Info_M));
4220     PetscCall(PetscFree(fs->csrRowPtr_h));
4221     PetscCall(PetscFree(fs->csrVal_h));
4222     PetscCall(PetscFree(fs->diag_h));
4223     fs->createdTransposeSpSVDescr    = PETSC_FALSE;
4224     fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
4225 #endif
4226   }
4227   PetscFunctionReturn(PETSC_SUCCESS);
4228 }
4229 
4230 static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **trifactors)
4231 {
4232   PetscFunctionBegin;
4233   if (*trifactors) {
4234     PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(trifactors));
4235     PetscCallCUSPARSE(cusparseDestroy((*trifactors)->handle));
4236     PetscCall(PetscFree(*trifactors));
4237   }
4238   PetscFunctionReturn(PETSC_SUCCESS);
4239 }
4240 
4241 struct IJCompare {
4242   __host__ __device__ inline bool operator()(const thrust::tuple<PetscInt, PetscInt> &t1, const thrust::tuple<PetscInt, PetscInt> &t2)
4243   {
4244     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4245     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4246     return false;
4247   }
4248 };
4249 
4250 static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat A, PetscBool destroy)
4251 {
4252   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4253 
4254   PetscFunctionBegin;
4255   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4256   if (!cusp) PetscFunctionReturn(PETSC_SUCCESS);
4257   if (destroy) {
4258     PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
4259     delete cusp->csr2csc_i;
4260     cusp->csr2csc_i = NULL;
4261   }
4262   A->transupdated = PETSC_FALSE;
4263   PetscFunctionReturn(PETSC_SUCCESS);
4264 }
4265 
4266 static PetscErrorCode MatCOOStructDestroy_SeqAIJCUSPARSE(void *data)
4267 {
4268   MatCOOStruct_SeqAIJ *coo = (MatCOOStruct_SeqAIJ *)data;
4269 
4270   PetscFunctionBegin;
4271   PetscCallCUDA(cudaFree(coo->perm));
4272   PetscCallCUDA(cudaFree(coo->jmap));
4273   PetscCall(PetscFree(coo));
4274   PetscFunctionReturn(PETSC_SUCCESS);
4275 }
4276 
4277 static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
4278 {
4279   PetscBool            dev_ij = PETSC_FALSE;
4280   PetscMemType         mtype  = PETSC_MEMTYPE_HOST;
4281   PetscInt            *i, *j;
4282   PetscContainer       container_h, container_d;
4283   MatCOOStruct_SeqAIJ *coo_h, *coo_d;
4284 
4285   PetscFunctionBegin;
4286   // The two MatResetPreallocationCOO_* must be done in order. The former relies on values that might be destroyed by the latter
4287   PetscCall(PetscGetMemType(coo_i, &mtype));
4288   if (PetscMemTypeDevice(mtype)) {
4289     dev_ij = PETSC_TRUE;
4290     PetscCall(PetscMalloc2(coo_n, &i, coo_n, &j));
4291     PetscCallCUDA(cudaMemcpy(i, coo_i, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4292     PetscCallCUDA(cudaMemcpy(j, coo_j, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4293   } else {
4294     i = coo_i;
4295     j = coo_j;
4296   }
4297 
4298   PetscCall(MatSetPreallocationCOO_SeqAIJ(mat, coo_n, i, j));
4299   if (dev_ij) PetscCall(PetscFree2(i, j));
4300   mat->offloadmask = PETSC_OFFLOAD_CPU;
4301   // Create the GPU memory
4302   PetscCall(MatSeqAIJCUSPARSECopyToGPU(mat));
4303 
4304   // Copy the COO struct to device
4305   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container_h));
4306   PetscCall(PetscContainerGetPointer(container_h, (void **)&coo_h));
4307   PetscCall(PetscMalloc1(1, &coo_d));
4308   *coo_d = *coo_h; // do a shallow copy and then amend some fields that need to be different
4309   PetscCallCUDA(cudaMalloc((void **)&coo_d->jmap, (coo_h->nz + 1) * sizeof(PetscCount)));
4310   PetscCallCUDA(cudaMemcpy(coo_d->jmap, coo_h->jmap, (coo_h->nz + 1) * sizeof(PetscCount), cudaMemcpyHostToDevice));
4311   PetscCallCUDA(cudaMalloc((void **)&coo_d->perm, coo_h->Atot * sizeof(PetscCount)));
4312   PetscCallCUDA(cudaMemcpy(coo_d->perm, coo_h->perm, coo_h->Atot * sizeof(PetscCount), cudaMemcpyHostToDevice));
4313 
4314   // Put the COO struct in a container and then attach that to the matrix
4315   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container_d));
4316   PetscCall(PetscContainerSetPointer(container_d, coo_d));
4317   PetscCall(PetscContainerSetUserDestroy(container_d, MatCOOStructDestroy_SeqAIJCUSPARSE));
4318   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Device", (PetscObject)container_d));
4319   PetscCall(PetscContainerDestroy(&container_d));
4320   PetscFunctionReturn(PETSC_SUCCESS);
4321 }
4322 
4323 __global__ static void MatAddCOOValues(const PetscScalar kv[], PetscCount nnz, const PetscCount jmap[], const PetscCount perm[], InsertMode imode, PetscScalar a[])
4324 {
4325   PetscCount       i         = blockIdx.x * blockDim.x + threadIdx.x;
4326   const PetscCount grid_size = gridDim.x * blockDim.x;
4327   for (; i < nnz; i += grid_size) {
4328     PetscScalar sum = 0.0;
4329     for (PetscCount k = jmap[i]; k < jmap[i + 1]; k++) sum += kv[perm[k]];
4330     a[i] = (imode == INSERT_VALUES ? 0.0 : a[i]) + sum;
4331   }
4332 }
4333 
4334 static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat A, const PetscScalar v[], InsertMode imode)
4335 {
4336   Mat_SeqAIJ          *seq  = (Mat_SeqAIJ *)A->data;
4337   Mat_SeqAIJCUSPARSE  *dev  = (Mat_SeqAIJCUSPARSE *)A->spptr;
4338   PetscCount           Annz = seq->nz;
4339   PetscMemType         memtype;
4340   const PetscScalar   *v1 = v;
4341   PetscScalar         *Aa;
4342   PetscContainer       container;
4343   MatCOOStruct_SeqAIJ *coo;
4344 
4345   PetscFunctionBegin;
4346   if (!dev->mat) PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4347 
4348   PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_MatCOOStruct_Device", (PetscObject *)&container));
4349   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
4350 
4351   PetscCall(PetscGetMemType(v, &memtype));
4352   if (PetscMemTypeHost(memtype)) { /* If user gave v[] in host, we might need to copy it to device if any */
4353     PetscCallCUDA(cudaMalloc((void **)&v1, coo->n * sizeof(PetscScalar)));
4354     PetscCallCUDA(cudaMemcpy((void *)v1, v, coo->n * sizeof(PetscScalar), cudaMemcpyHostToDevice));
4355   }
4356 
4357   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSEGetArrayWrite(A, &Aa));
4358   else PetscCall(MatSeqAIJCUSPARSEGetArray(A, &Aa));
4359 
4360   PetscCall(PetscLogGpuTimeBegin());
4361   if (Annz) {
4362     MatAddCOOValues<<<(Annz + 255) / 256, 256>>>(v1, Annz, coo->jmap, coo->perm, imode, Aa);
4363     PetscCallCUDA(cudaPeekAtLastError());
4364   }
4365   PetscCall(PetscLogGpuTimeEnd());
4366 
4367   if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSERestoreArrayWrite(A, &Aa));
4368   else PetscCall(MatSeqAIJCUSPARSERestoreArray(A, &Aa));
4369 
4370   if (PetscMemTypeHost(memtype)) PetscCallCUDA(cudaFree((void *)v1));
4371   PetscFunctionReturn(PETSC_SUCCESS);
4372 }
4373 
4374 /*@C
4375   MatSeqAIJCUSPARSEGetIJ - returns the device row storage `i` and `j` indices for `MATSEQAIJCUSPARSE` matrices.
4376 
4377   Not Collective
4378 
4379   Input Parameters:
4380 + A          - the matrix
4381 - compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4382 
4383   Output Parameters:
4384 + i - the CSR row pointers
4385 - j - the CSR column indices
4386 
4387   Level: developer
4388 
4389   Note:
4390   When compressed is true, the CSR structure does not contain empty rows
4391 
4392 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSERestoreIJ()`, `MatSeqAIJCUSPARSEGetArrayRead()`
4393 @*/
4394 PetscErrorCode MatSeqAIJCUSPARSEGetIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4395 {
4396   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4397   CsrMatrix          *csr;
4398   Mat_SeqAIJ         *a = (Mat_SeqAIJ *)A->data;
4399 
4400   PetscFunctionBegin;
4401   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4402   if (!i || !j) PetscFunctionReturn(PETSC_SUCCESS);
4403   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4404   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4405   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4406   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4407   csr = (CsrMatrix *)cusp->mat->mat;
4408   if (i) {
4409     if (!compressed && a->compressedrow.use) { /* need full row offset */
4410       if (!cusp->rowoffsets_gpu) {
4411         cusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4412         cusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4413         PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4414       }
4415       *i = cusp->rowoffsets_gpu->data().get();
4416     } else *i = csr->row_offsets->data().get();
4417   }
4418   if (j) *j = csr->column_indices->data().get();
4419   PetscFunctionReturn(PETSC_SUCCESS);
4420 }
4421 
4422 /*@C
4423   MatSeqAIJCUSPARSERestoreIJ - restore the device row storage `i` and `j` indices obtained with `MatSeqAIJCUSPARSEGetIJ()`
4424 
4425   Not Collective
4426 
4427   Input Parameters:
4428 + A          - the matrix
4429 . compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
4430 . i          - the CSR row pointers
4431 - j          - the CSR column indices
4432 
4433   Level: developer
4434 
4435 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetIJ()`
4436 @*/
4437 PetscErrorCode MatSeqAIJCUSPARSERestoreIJ(Mat A, PetscBool compressed, const int **i, const int **j)
4438 {
4439   PetscFunctionBegin;
4440   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4441   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4442   if (i) *i = NULL;
4443   if (j) *j = NULL;
4444   (void)compressed;
4445   PetscFunctionReturn(PETSC_SUCCESS);
4446 }
4447 
4448 /*@C
4449   MatSeqAIJCUSPARSEGetArrayRead - gives read-only access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4450 
4451   Not Collective
4452 
4453   Input Parameter:
4454 . A - a `MATSEQAIJCUSPARSE` matrix
4455 
4456   Output Parameter:
4457 . a - pointer to the device data
4458 
4459   Level: developer
4460 
4461   Note:
4462   May trigger host-device copies if up-to-date matrix data is on host
4463 
4464 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArrayRead()`
4465 @*/
4466 PetscErrorCode MatSeqAIJCUSPARSEGetArrayRead(Mat A, const PetscScalar **a)
4467 {
4468   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4469   CsrMatrix          *csr;
4470 
4471   PetscFunctionBegin;
4472   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4473   PetscAssertPointer(a, 2);
4474   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4475   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4476   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4477   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4478   csr = (CsrMatrix *)cusp->mat->mat;
4479   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4480   *a = csr->values->data().get();
4481   PetscFunctionReturn(PETSC_SUCCESS);
4482 }
4483 
4484 /*@C
4485   MatSeqAIJCUSPARSERestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJCUSPARSEGetArrayRead()`
4486 
4487   Not Collective
4488 
4489   Input Parameters:
4490 + A - a `MATSEQAIJCUSPARSE` matrix
4491 - a - pointer to the device data
4492 
4493   Level: developer
4494 
4495 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`
4496 @*/
4497 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayRead(Mat A, const PetscScalar **a)
4498 {
4499   PetscFunctionBegin;
4500   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4501   PetscAssertPointer(a, 2);
4502   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4503   *a = NULL;
4504   PetscFunctionReturn(PETSC_SUCCESS);
4505 }
4506 
4507 /*@C
4508   MatSeqAIJCUSPARSEGetArray - gives read-write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4509 
4510   Not Collective
4511 
4512   Input Parameter:
4513 . A - a `MATSEQAIJCUSPARSE` matrix
4514 
4515   Output Parameter:
4516 . a - pointer to the device data
4517 
4518   Level: developer
4519 
4520   Note:
4521   May trigger host-device copies if up-to-date matrix data is on host
4522 
4523 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArray()`
4524 @*/
4525 PetscErrorCode MatSeqAIJCUSPARSEGetArray(Mat A, PetscScalar **a)
4526 {
4527   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4528   CsrMatrix          *csr;
4529 
4530   PetscFunctionBegin;
4531   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4532   PetscAssertPointer(a, 2);
4533   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4534   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4535   PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4536   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4537   csr = (CsrMatrix *)cusp->mat->mat;
4538   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4539   *a             = csr->values->data().get();
4540   A->offloadmask = PETSC_OFFLOAD_GPU;
4541   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4542   PetscFunctionReturn(PETSC_SUCCESS);
4543 }
4544 /*@C
4545   MatSeqAIJCUSPARSERestoreArray - restore the read-write access array obtained from `MatSeqAIJCUSPARSEGetArray()`
4546 
4547   Not Collective
4548 
4549   Input Parameters:
4550 + A - a `MATSEQAIJCUSPARSE` matrix
4551 - a - pointer to the device data
4552 
4553   Level: developer
4554 
4555 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`
4556 @*/
4557 PetscErrorCode MatSeqAIJCUSPARSERestoreArray(Mat A, PetscScalar **a)
4558 {
4559   PetscFunctionBegin;
4560   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4561   PetscAssertPointer(a, 2);
4562   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4563   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4564   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4565   *a = NULL;
4566   PetscFunctionReturn(PETSC_SUCCESS);
4567 }
4568 
4569 /*@C
4570   MatSeqAIJCUSPARSEGetArrayWrite - gives write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored
4571 
4572   Not Collective
4573 
4574   Input Parameter:
4575 . A - a `MATSEQAIJCUSPARSE` matrix
4576 
4577   Output Parameter:
4578 . a - pointer to the device data
4579 
4580   Level: developer
4581 
4582   Note:
4583   Does not trigger host-device copies and flags data validity on the GPU
4584 
4585 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSERestoreArrayWrite()`
4586 @*/
4587 PetscErrorCode MatSeqAIJCUSPARSEGetArrayWrite(Mat A, PetscScalar **a)
4588 {
4589   Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
4590   CsrMatrix          *csr;
4591 
4592   PetscFunctionBegin;
4593   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4594   PetscAssertPointer(a, 2);
4595   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4596   PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4597   PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4598   csr = (CsrMatrix *)cusp->mat->mat;
4599   PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
4600   *a             = csr->values->data().get();
4601   A->offloadmask = PETSC_OFFLOAD_GPU;
4602   PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
4603   PetscFunctionReturn(PETSC_SUCCESS);
4604 }
4605 
4606 /*@C
4607   MatSeqAIJCUSPARSERestoreArrayWrite - restore the write-only access array obtained from `MatSeqAIJCUSPARSEGetArrayWrite()`
4608 
4609   Not Collective
4610 
4611   Input Parameters:
4612 + A - a `MATSEQAIJCUSPARSE` matrix
4613 - a - pointer to the device data
4614 
4615   Level: developer
4616 
4617 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayWrite()`
4618 @*/
4619 PetscErrorCode MatSeqAIJCUSPARSERestoreArrayWrite(Mat A, PetscScalar **a)
4620 {
4621   PetscFunctionBegin;
4622   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4623   PetscAssertPointer(a, 2);
4624   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4625   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4626   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4627   *a = NULL;
4628   PetscFunctionReturn(PETSC_SUCCESS);
4629 }
4630 
4631 struct IJCompare4 {
4632   __host__ __device__ inline bool operator()(const thrust::tuple<int, int, PetscScalar, int> &t1, const thrust::tuple<int, int, PetscScalar, int> &t2)
4633   {
4634     if (thrust::get<0>(t1) < thrust::get<0>(t2)) return true;
4635     if (thrust::get<0>(t1) == thrust::get<0>(t2)) return thrust::get<1>(t1) < thrust::get<1>(t2);
4636     return false;
4637   }
4638 };
4639 
4640 struct Shift {
4641   int _shift;
4642 
4643   Shift(int shift) : _shift(shift) { }
4644   __host__ __device__ inline int operator()(const int &c) { return c + _shift; }
4645 };
4646 
4647 /* merges two SeqAIJCUSPARSE matrices A, B by concatenating their rows. [A';B']' operation in MATLAB notation */
4648 PetscErrorCode MatSeqAIJCUSPARSEMergeMats(Mat A, Mat B, MatReuse reuse, Mat *C)
4649 {
4650   Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
4651   Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr, *Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr, *Ccusp;
4652   Mat_SeqAIJCUSPARSEMultStruct *Cmat;
4653   CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
4654   PetscInt                      Annz, Bnnz;
4655   cusparseStatus_t              stat;
4656   PetscInt                      i, m, n, zero = 0;
4657 
4658   PetscFunctionBegin;
4659   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4660   PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
4661   PetscAssertPointer(C, 4);
4662   PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
4663   PetscCheckTypeName(B, MATSEQAIJCUSPARSE);
4664   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);
4665   PetscCheck(reuse != MAT_INPLACE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_INPLACE_MATRIX not supported");
4666   PetscCheck(Acusp->format != MAT_CUSPARSE_ELL && Acusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4667   PetscCheck(Bcusp->format != MAT_CUSPARSE_ELL && Bcusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4668   if (reuse == MAT_INITIAL_MATRIX) {
4669     m = A->rmap->n;
4670     n = A->cmap->n + B->cmap->n;
4671     PetscCall(MatCreate(PETSC_COMM_SELF, C));
4672     PetscCall(MatSetSizes(*C, m, n, m, n));
4673     PetscCall(MatSetType(*C, MATSEQAIJCUSPARSE));
4674     c                       = (Mat_SeqAIJ *)(*C)->data;
4675     Ccusp                   = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4676     Cmat                    = new Mat_SeqAIJCUSPARSEMultStruct;
4677     Ccsr                    = new CsrMatrix;
4678     Cmat->cprowIndices      = NULL;
4679     c->compressedrow.use    = PETSC_FALSE;
4680     c->compressedrow.nrows  = 0;
4681     c->compressedrow.i      = NULL;
4682     c->compressedrow.rindex = NULL;
4683     Ccusp->workVector       = NULL;
4684     Ccusp->nrows            = m;
4685     Ccusp->mat              = Cmat;
4686     Ccusp->mat->mat         = Ccsr;
4687     Ccsr->num_rows          = m;
4688     Ccsr->num_cols          = n;
4689     PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
4690     PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
4691     PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4692     PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
4693     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
4694     PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
4695     PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4696     PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4697     PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4698     PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4699     PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4700     PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4701     PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4702 
4703     Acsr                 = (CsrMatrix *)Acusp->mat->mat;
4704     Bcsr                 = (CsrMatrix *)Bcusp->mat->mat;
4705     Annz                 = (PetscInt)Acsr->column_indices->size();
4706     Bnnz                 = (PetscInt)Bcsr->column_indices->size();
4707     c->nz                = Annz + Bnnz;
4708     Ccsr->row_offsets    = new THRUSTINTARRAY32(m + 1);
4709     Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
4710     Ccsr->values         = new THRUSTARRAY(c->nz);
4711     Ccsr->num_entries    = c->nz;
4712     Ccusp->coords        = new THRUSTINTARRAY(c->nz);
4713     if (c->nz) {
4714       auto              Acoo = new THRUSTINTARRAY32(Annz);
4715       auto              Bcoo = new THRUSTINTARRAY32(Bnnz);
4716       auto              Ccoo = new THRUSTINTARRAY32(c->nz);
4717       THRUSTINTARRAY32 *Aroff, *Broff;
4718 
4719       if (a->compressedrow.use) { /* need full row offset */
4720         if (!Acusp->rowoffsets_gpu) {
4721           Acusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
4722           Acusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
4723           PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
4724         }
4725         Aroff = Acusp->rowoffsets_gpu;
4726       } else Aroff = Acsr->row_offsets;
4727       if (b->compressedrow.use) { /* need full row offset */
4728         if (!Bcusp->rowoffsets_gpu) {
4729           Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
4730           Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
4731           PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
4732         }
4733         Broff = Bcusp->rowoffsets_gpu;
4734       } else Broff = Bcsr->row_offsets;
4735       PetscCall(PetscLogGpuTimeBegin());
4736       stat = cusparseXcsr2coo(Acusp->handle, Aroff->data().get(), Annz, m, Acoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4737       PetscCallCUSPARSE(stat);
4738       stat = cusparseXcsr2coo(Bcusp->handle, Broff->data().get(), Bnnz, m, Bcoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4739       PetscCallCUSPARSE(stat);
4740       /* Issues when using bool with large matrices on SUMMIT 10.2.89 */
4741       auto Aperm = thrust::make_constant_iterator(1);
4742       auto Bperm = thrust::make_constant_iterator(0);
4743 #if PETSC_PKG_CUDA_VERSION_GE(10, 0, 0)
4744       auto Bcib = thrust::make_transform_iterator(Bcsr->column_indices->begin(), Shift(A->cmap->n));
4745       auto Bcie = thrust::make_transform_iterator(Bcsr->column_indices->end(), Shift(A->cmap->n));
4746 #else
4747       /* there are issues instantiating the merge operation using a transform iterator for the columns of B */
4748       auto Bcib = Bcsr->column_indices->begin();
4749       auto Bcie = Bcsr->column_indices->end();
4750       thrust::transform(Bcib, Bcie, Bcib, Shift(A->cmap->n));
4751 #endif
4752       auto wPerm = new THRUSTINTARRAY32(Annz + Bnnz);
4753       auto Azb   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->begin(), Acsr->column_indices->begin(), Acsr->values->begin(), Aperm));
4754       auto Aze   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->end(), Acsr->column_indices->end(), Acsr->values->end(), Aperm));
4755       auto Bzb   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->begin(), Bcib, Bcsr->values->begin(), Bperm));
4756       auto Bze   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->end(), Bcie, Bcsr->values->end(), Bperm));
4757       auto Czb   = thrust::make_zip_iterator(thrust::make_tuple(Ccoo->begin(), Ccsr->column_indices->begin(), Ccsr->values->begin(), wPerm->begin()));
4758       auto p1    = Ccusp->coords->begin();
4759       auto p2    = Ccusp->coords->begin();
4760       thrust::advance(p2, Annz);
4761       PetscCallThrust(thrust::merge(thrust::device, Azb, Aze, Bzb, Bze, Czb, IJCompare4()));
4762 #if PETSC_PKG_CUDA_VERSION_LT(10, 0, 0)
4763       thrust::transform(Bcib, Bcie, Bcib, Shift(-A->cmap->n));
4764 #endif
4765       auto cci = thrust::make_counting_iterator(zero);
4766       auto cce = thrust::make_counting_iterator(c->nz);
4767 #if 0 //Errors on SUMMIT cuda 11.1.0
4768       PetscCallThrust(thrust::partition_copy(thrust::device,cci,cce,wPerm->begin(),p1,p2,thrust::identity<int>()));
4769 #else
4770       auto pred = thrust::identity<int>();
4771       PetscCallThrust(thrust::copy_if(thrust::device, cci, cce, wPerm->begin(), p1, pred));
4772       PetscCallThrust(thrust::remove_copy_if(thrust::device, cci, cce, wPerm->begin(), p2, pred));
4773 #endif
4774       stat = cusparseXcoo2csr(Ccusp->handle, Ccoo->data().get(), c->nz, m, Ccsr->row_offsets->data().get(), CUSPARSE_INDEX_BASE_ZERO);
4775       PetscCallCUSPARSE(stat);
4776       PetscCall(PetscLogGpuTimeEnd());
4777       delete wPerm;
4778       delete Acoo;
4779       delete Bcoo;
4780       delete Ccoo;
4781 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4782       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);
4783       PetscCallCUSPARSE(stat);
4784 #endif
4785       if (A->form_explicit_transpose && B->form_explicit_transpose) { /* if A and B have the transpose, generate C transpose too */
4786         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
4787         PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
4788         PetscBool                     AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4789         Mat_SeqAIJCUSPARSEMultStruct *CmatT = new Mat_SeqAIJCUSPARSEMultStruct;
4790         CsrMatrix                    *CcsrT = new CsrMatrix;
4791         CsrMatrix                    *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4792         CsrMatrix                    *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4793 
4794         (*C)->form_explicit_transpose = PETSC_TRUE;
4795         (*C)->transupdated            = PETSC_TRUE;
4796         Ccusp->rowoffsets_gpu         = NULL;
4797         CmatT->cprowIndices           = NULL;
4798         CmatT->mat                    = CcsrT;
4799         CcsrT->num_rows               = n;
4800         CcsrT->num_cols               = m;
4801         CcsrT->num_entries            = c->nz;
4802 
4803         CcsrT->row_offsets    = new THRUSTINTARRAY32(n + 1);
4804         CcsrT->column_indices = new THRUSTINTARRAY32(c->nz);
4805         CcsrT->values         = new THRUSTARRAY(c->nz);
4806 
4807         PetscCall(PetscLogGpuTimeBegin());
4808         auto rT = CcsrT->row_offsets->begin();
4809         if (AT) {
4810           rT = thrust::copy(AcsrT->row_offsets->begin(), AcsrT->row_offsets->end(), rT);
4811           thrust::advance(rT, -1);
4812         }
4813         if (BT) {
4814           auto titb = thrust::make_transform_iterator(BcsrT->row_offsets->begin(), Shift(a->nz));
4815           auto tite = thrust::make_transform_iterator(BcsrT->row_offsets->end(), Shift(a->nz));
4816           thrust::copy(titb, tite, rT);
4817         }
4818         auto cT = CcsrT->column_indices->begin();
4819         if (AT) cT = thrust::copy(AcsrT->column_indices->begin(), AcsrT->column_indices->end(), cT);
4820         if (BT) thrust::copy(BcsrT->column_indices->begin(), BcsrT->column_indices->end(), cT);
4821         auto vT = CcsrT->values->begin();
4822         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4823         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4824         PetscCall(PetscLogGpuTimeEnd());
4825 
4826         PetscCallCUSPARSE(cusparseCreateMatDescr(&CmatT->descr));
4827         PetscCallCUSPARSE(cusparseSetMatIndexBase(CmatT->descr, CUSPARSE_INDEX_BASE_ZERO));
4828         PetscCallCUSPARSE(cusparseSetMatType(CmatT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
4829         PetscCallCUDA(cudaMalloc((void **)&CmatT->alpha_one, sizeof(PetscScalar)));
4830         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_zero, sizeof(PetscScalar)));
4831         PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_one, sizeof(PetscScalar)));
4832         PetscCallCUDA(cudaMemcpy(CmatT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4833         PetscCallCUDA(cudaMemcpy(CmatT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4834         PetscCallCUDA(cudaMemcpy(CmatT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
4835 #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
4836         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);
4837         PetscCallCUSPARSE(stat);
4838 #endif
4839         Ccusp->matTranspose = CmatT;
4840       }
4841     }
4842 
4843     c->free_a = PETSC_TRUE;
4844     PetscCall(PetscShmgetAllocateArray(c->nz, sizeof(PetscInt), (void **)&c->j));
4845     PetscCall(PetscShmgetAllocateArray(m + 1, sizeof(PetscInt), (void **)&c->i));
4846     c->free_ij = PETSC_TRUE;
4847     if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
4848       THRUSTINTARRAY ii(Ccsr->row_offsets->size());
4849       THRUSTINTARRAY jj(Ccsr->column_indices->size());
4850       ii = *Ccsr->row_offsets;
4851       jj = *Ccsr->column_indices;
4852       PetscCallCUDA(cudaMemcpy(c->i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4853       PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4854     } else {
4855       PetscCallCUDA(cudaMemcpy(c->i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4856       PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
4857     }
4858     PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
4859     PetscCall(PetscMalloc1(m, &c->ilen));
4860     PetscCall(PetscMalloc1(m, &c->imax));
4861     c->maxnz         = c->nz;
4862     c->nonzerorowcnt = 0;
4863     c->rmax          = 0;
4864     for (i = 0; i < m; i++) {
4865       const PetscInt nn = c->i[i + 1] - c->i[i];
4866       c->ilen[i] = c->imax[i] = nn;
4867       c->nonzerorowcnt += (PetscInt) !!nn;
4868       c->rmax = PetscMax(c->rmax, nn);
4869     }
4870     PetscCall(MatMarkDiagonal_SeqAIJ(*C));
4871     PetscCall(PetscMalloc1(c->nz, &c->a));
4872     (*C)->nonzerostate++;
4873     PetscCall(PetscLayoutSetUp((*C)->rmap));
4874     PetscCall(PetscLayoutSetUp((*C)->cmap));
4875     Ccusp->nonzerostate = (*C)->nonzerostate;
4876     (*C)->preallocated  = PETSC_TRUE;
4877   } else {
4878     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);
4879     c = (Mat_SeqAIJ *)(*C)->data;
4880     if (c->nz) {
4881       Ccusp = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
4882       PetscCheck(Ccusp->coords, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing coords");
4883       PetscCheck(Ccusp->format != MAT_CUSPARSE_ELL && Ccusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
4884       PetscCheck(Ccusp->nonzerostate == (*C)->nonzerostate, PETSC_COMM_SELF, PETSC_ERR_COR, "Wrong nonzerostate");
4885       PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
4886       PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
4887       PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4888       PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
4889       Acsr = (CsrMatrix *)Acusp->mat->mat;
4890       Bcsr = (CsrMatrix *)Bcusp->mat->mat;
4891       Ccsr = (CsrMatrix *)Ccusp->mat->mat;
4892       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());
4893       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());
4894       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());
4895       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);
4896       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());
4897       auto pmid = Ccusp->coords->begin();
4898       thrust::advance(pmid, Acsr->num_entries);
4899       PetscCall(PetscLogGpuTimeBegin());
4900       auto zibait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->begin())));
4901       auto zieait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4902       thrust::for_each(zibait, zieait, VecCUDAEquals());
4903       auto zibbit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
4904       auto ziebit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->end())));
4905       thrust::for_each(zibbit, ziebit, VecCUDAEquals());
4906       PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(*C, PETSC_FALSE));
4907       if (A->form_explicit_transpose && B->form_explicit_transpose && (*C)->form_explicit_transpose) {
4908         PetscCheck(Ccusp->matTranspose, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing transpose Mat_SeqAIJCUSPARSEMultStruct");
4909         PetscBool  AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
4910         CsrMatrix *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
4911         CsrMatrix *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
4912         CsrMatrix *CcsrT = (CsrMatrix *)Ccusp->matTranspose->mat;
4913         auto       vT    = CcsrT->values->begin();
4914         if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
4915         if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
4916         (*C)->transupdated = PETSC_TRUE;
4917       }
4918       PetscCall(PetscLogGpuTimeEnd());
4919     }
4920   }
4921   PetscCall(PetscObjectStateIncrease((PetscObject)*C));
4922   (*C)->assembled     = PETSC_TRUE;
4923   (*C)->was_assembled = PETSC_FALSE;
4924   (*C)->offloadmask   = PETSC_OFFLOAD_GPU;
4925   PetscFunctionReturn(PETSC_SUCCESS);
4926 }
4927 
4928 static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
4929 {
4930   bool               dmem;
4931   const PetscScalar *av;
4932 
4933   PetscFunctionBegin;
4934   dmem = isCudaMem(v);
4935   PetscCall(MatSeqAIJCUSPARSEGetArrayRead(A, &av));
4936   if (n && idx) {
4937     THRUSTINTARRAY widx(n);
4938     widx.assign(idx, idx + n);
4939     PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
4940 
4941     THRUSTARRAY                    *w = NULL;
4942     thrust::device_ptr<PetscScalar> dv;
4943     if (dmem) {
4944       dv = thrust::device_pointer_cast(v);
4945     } else {
4946       w  = new THRUSTARRAY(n);
4947       dv = w->data();
4948     }
4949     thrust::device_ptr<const PetscScalar> dav = thrust::device_pointer_cast(av);
4950 
4951     auto zibit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.begin()), dv));
4952     auto zieit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.end()), dv + n));
4953     thrust::for_each(zibit, zieit, VecCUDAEquals());
4954     if (w) PetscCallCUDA(cudaMemcpy(v, w->data().get(), n * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
4955     delete w;
4956   } else {
4957     PetscCallCUDA(cudaMemcpy(v, av, n * sizeof(PetscScalar), dmem ? cudaMemcpyDeviceToDevice : cudaMemcpyDeviceToHost));
4958   }
4959   if (!dmem) PetscCall(PetscLogCpuToGpu(n * sizeof(PetscScalar)));
4960   PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(A, &av));
4961   PetscFunctionReturn(PETSC_SUCCESS);
4962 }
4963