xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision d4c7638e66bfbab42594e49bfd8787d3c0f17499)
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_SPINLOCK
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 
15 const char *const MatCUSPARSEStorageFormats[] = {"CSR","ELL","HYB","MatCUSPARSEStorageFormat","MAT_CUSPARSE_",0};
16 
17 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,const MatFactorInfo*);
18 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,const MatFactorInfo*);
19 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat,Mat,const MatFactorInfo*);
20 
21 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,IS,const MatFactorInfo*);
22 static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,IS,const MatFactorInfo*);
23 static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat,Mat,const MatFactorInfo*);
24 
25 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat,Vec,Vec);
26 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat,Vec,Vec);
27 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat,Vec,Vec);
28 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat,Vec,Vec);
29 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(PetscOptionItems *PetscOptionsObject,Mat);
30 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat,Vec,Vec);
31 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec);
32 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat,Vec,Vec);
33 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec);
34 
35 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix**);
36 static PetscErrorCode Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct**);
37 static PetscErrorCode Mat_SeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct**,MatCUSPARSEStorageFormat);
38 static PetscErrorCode Mat_SeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors**);
39 static PetscErrorCode Mat_SeqAIJCUSPARSE_Destroy(Mat_SeqAIJCUSPARSE**);
40 
41 PetscErrorCode MatCUSPARSESetStream(Mat A,const cudaStream_t stream)
42 {
43   cusparseStatus_t   stat;
44   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
45 
46   PetscFunctionBegin;
47   cusparsestruct->stream = stream;
48   stat = cusparseSetStream(cusparsestruct->handle,cusparsestruct->stream);CHKERRCUDA(stat);
49   PetscFunctionReturn(0);
50 }
51 
52 PetscErrorCode MatCUSPARSESetHandle(Mat A,const cusparseHandle_t handle)
53 {
54   cusparseStatus_t   stat;
55   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
56 
57   PetscFunctionBegin;
58   if (cusparsestruct->handle != handle) {
59     if (cusparsestruct->handle) {
60       stat = cusparseDestroy(cusparsestruct->handle);CHKERRCUDA(stat);
61     }
62     cusparsestruct->handle = handle;
63   }
64   stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUDA(stat);
65   PetscFunctionReturn(0);
66 }
67 
68 PetscErrorCode MatCUSPARSEClearHandle(Mat A)
69 {
70   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
71   PetscFunctionBegin;
72   if (cusparsestruct->handle)
73     cusparsestruct->handle = 0;
74   PetscFunctionReturn(0);
75 }
76 
77 PetscErrorCode MatFactorGetSolverPackage_seqaij_cusparse(Mat A,const MatSolverPackage *type)
78 {
79   PetscFunctionBegin;
80   *type = MATSOLVERCUSPARSE;
81   PetscFunctionReturn(0);
82 }
83 
84 /*MC
85   MATSOLVERCUSPARSE = "cusparse" - A matrix type providing triangular solvers for seq matrices
86   on a single GPU of type, seqaijcusparse, aijcusparse, or seqaijcusp, aijcusp. Currently supported
87   algorithms are ILU(k) and ICC(k). Typically, deeper factorizations (larger k) results in poorer
88   performance in the triangular solves. Full LU, and Cholesky decompositions can be solved through the
89   CUSPARSE triangular solve algorithm. However, the performance can be quite poor and thus these
90   algorithms are not recommended. This class does NOT support direct solver operations.
91 
92   Level: beginner
93 
94 .seealso: PCFactorSetMatSolverPackage(), MatSolverPackage, MatCreateSeqAIJCUSPARSE(), MATAIJCUSPARSE, MatCreateAIJCUSPARSE(), MatCUSPARSESetFormat(), MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
95 M*/
96 
97 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat A,MatFactorType ftype,Mat *B)
98 {
99   PetscErrorCode ierr;
100   PetscInt       n = A->rmap->n;
101 
102   PetscFunctionBegin;
103   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
104   (*B)->factortype = ftype;
105   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
106   ierr = MatSetType(*B,MATSEQAIJCUSPARSE);CHKERRQ(ierr);
107 
108   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
109     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
110     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJCUSPARSE;
111     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJCUSPARSE;
112   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
113     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJCUSPARSE;
114     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJCUSPARSE;
115   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported for CUSPARSE Matrix Types");
116 
117   ierr = MatSeqAIJSetPreallocation(*B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
118   ierr = PetscObjectComposeFunction((PetscObject)(*B),"MatFactorGetSolverPackage_C",MatFactorGetSolverPackage_seqaij_cusparse);CHKERRQ(ierr);
119   PetscFunctionReturn(0);
120 }
121 
122 PETSC_INTERN PetscErrorCode MatCUSPARSESetFormat_SeqAIJCUSPARSE(Mat A,MatCUSPARSEFormatOperation op,MatCUSPARSEStorageFormat format)
123 {
124   Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
125 
126   PetscFunctionBegin;
127 #if CUDA_VERSION>=4020
128   switch (op) {
129   case MAT_CUSPARSE_MULT:
130     cusparsestruct->format = format;
131     break;
132   case MAT_CUSPARSE_ALL:
133     cusparsestruct->format = format;
134     break;
135   default:
136     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsupported operation %d for MatCUSPARSEFormatOperation. MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL are currently supported.",op);
137   }
138 #else
139   if (format==MAT_CUSPARSE_ELL || format==MAT_CUSPARSE_HYB) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ELL (Ellpack) and HYB (Hybrid) storage format require CUDA 4.2 or later.");
140 #endif
141   PetscFunctionReturn(0);
142 }
143 
144 /*@
145    MatCUSPARSESetFormat - Sets the storage format of CUSPARSE matrices for a particular
146    operation. Only the MatMult operation can use different GPU storage formats
147    for MPIAIJCUSPARSE matrices.
148    Not Collective
149 
150    Input Parameters:
151 +  A - Matrix of type SEQAIJCUSPARSE
152 .  op - MatCUSPARSEFormatOperation. SEQAIJCUSPARSE matrices support MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL. MPIAIJCUSPARSE matrices support MAT_CUSPARSE_MULT_DIAG, MAT_CUSPARSE_MULT_OFFDIAG, and MAT_CUSPARSE_ALL.
153 -  format - MatCUSPARSEStorageFormat (one of MAT_CUSPARSE_CSR, MAT_CUSPARSE_ELL, MAT_CUSPARSE_HYB. The latter two require CUDA 4.2)
154 
155    Output Parameter:
156 
157    Level: intermediate
158 
159 .seealso: MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
160 @*/
161 PetscErrorCode MatCUSPARSESetFormat(Mat A,MatCUSPARSEFormatOperation op,MatCUSPARSEStorageFormat format)
162 {
163   PetscErrorCode ierr;
164 
165   PetscFunctionBegin;
166   PetscValidHeaderSpecific(A, MAT_CLASSID,1);
167   ierr = PetscTryMethod(A, "MatCUSPARSESetFormat_C",(Mat,MatCUSPARSEFormatOperation,MatCUSPARSEStorageFormat),(A,op,format));CHKERRQ(ierr);
168   PetscFunctionReturn(0);
169 }
170 
171 static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(PetscOptionItems *PetscOptionsObject,Mat A)
172 {
173   PetscErrorCode           ierr;
174   MatCUSPARSEStorageFormat format;
175   PetscBool                flg;
176   Mat_SeqAIJCUSPARSE       *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
177 
178   PetscFunctionBegin;
179   ierr = PetscOptionsHead(PetscOptionsObject,"SeqAIJCUSPARSE options");CHKERRQ(ierr);
180   ierr = PetscObjectOptionsBegin((PetscObject)A);
181   if (A->factortype==MAT_FACTOR_NONE) {
182     ierr = PetscOptionsEnum("-mat_cusparse_mult_storage_format","sets storage format of (seq)aijcusparse gpu matrices for SpMV",
183                             "MatCUSPARSESetFormat",MatCUSPARSEStorageFormats,(PetscEnum)cusparsestruct->format,(PetscEnum*)&format,&flg);CHKERRQ(ierr);
184     if (flg) {
185       ierr = MatCUSPARSESetFormat(A,MAT_CUSPARSE_MULT,format);CHKERRQ(ierr);
186     }
187   }
188   ierr = PetscOptionsEnum("-mat_cusparse_storage_format","sets storage format of (seq)aijcusparse gpu matrices for SpMV and TriSolve",
189                           "MatCUSPARSESetFormat",MatCUSPARSEStorageFormats,(PetscEnum)cusparsestruct->format,(PetscEnum*)&format,&flg);CHKERRQ(ierr);
190   if (flg) {
191     ierr = MatCUSPARSESetFormat(A,MAT_CUSPARSE_ALL,format);CHKERRQ(ierr);
192   }
193   ierr = PetscOptionsEnd();CHKERRQ(ierr);
194   PetscFunctionReturn(0);
195 
196 }
197 
198 static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
199 {
200   PetscErrorCode ierr;
201 
202   PetscFunctionBegin;
203   ierr = MatILUFactorSymbolic_SeqAIJ(B,A,isrow,iscol,info);CHKERRQ(ierr);
204   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
205   PetscFunctionReturn(0);
206 }
207 
208 static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
209 {
210   PetscErrorCode ierr;
211 
212   PetscFunctionBegin;
213   ierr = MatLUFactorSymbolic_SeqAIJ(B,A,isrow,iscol,info);CHKERRQ(ierr);
214   B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
215   PetscFunctionReturn(0);
216 }
217 
218 static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS perm,const MatFactorInfo *info)
219 {
220   PetscErrorCode ierr;
221 
222   PetscFunctionBegin;
223   ierr = MatICCFactorSymbolic_SeqAIJ(B,A,perm,info);CHKERRQ(ierr);
224   B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
225   PetscFunctionReturn(0);
226 }
227 
228 static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS perm,const MatFactorInfo *info)
229 {
230   PetscErrorCode ierr;
231 
232   PetscFunctionBegin;
233   ierr = MatCholeskyFactorSymbolic_SeqAIJ(B,A,perm,info);CHKERRQ(ierr);
234   B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
235   PetscFunctionReturn(0);
236 }
237 
238 static PetscErrorCode MatSeqAIJCUSPARSEBuildILULowerTriMatrix(Mat A)
239 {
240   Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
241   PetscInt                          n = A->rmap->n;
242   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
243   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
244   cusparseStatus_t                  stat;
245   const PetscInt                    *ai = a->i,*aj = a->j,*vi;
246   const MatScalar                   *aa = a->a,*v;
247   PetscInt                          *AiLo, *AjLo;
248   PetscScalar                       *AALo;
249   PetscInt                          i,nz, nzLower, offset, rowOffset;
250   PetscErrorCode                    ierr;
251 
252   PetscFunctionBegin;
253   if (A->valid_GPU_matrix == PETSC_CUDA_UNALLOCATED || A->valid_GPU_matrix == PETSC_CUDA_CPU) {
254     try {
255       /* first figure out the number of nonzeros in the lower triangular matrix including 1's on the diagonal. */
256       nzLower=n+ai[n]-ai[1];
257 
258       /* Allocate Space for the lower triangular matrix */
259       ierr = cudaMallocHost((void**) &AiLo, (n+1)*sizeof(PetscInt));CHKERRCUDA(ierr);
260       ierr = cudaMallocHost((void**) &AjLo, nzLower*sizeof(PetscInt));CHKERRCUDA(ierr);
261       ierr = cudaMallocHost((void**) &AALo, nzLower*sizeof(PetscScalar));CHKERRCUDA(ierr);
262 
263       /* Fill the lower triangular matrix */
264       AiLo[0]  = (PetscInt) 0;
265       AiLo[n]  = nzLower;
266       AjLo[0]  = (PetscInt) 0;
267       AALo[0]  = (MatScalar) 1.0;
268       v        = aa;
269       vi       = aj;
270       offset   = 1;
271       rowOffset= 1;
272       for (i=1; i<n; i++) {
273         nz = ai[i+1] - ai[i];
274         /* additional 1 for the term on the diagonal */
275         AiLo[i]    = rowOffset;
276         rowOffset += nz+1;
277 
278         ierr = PetscMemcpy(&(AjLo[offset]), vi, nz*sizeof(PetscInt));CHKERRQ(ierr);
279         ierr = PetscMemcpy(&(AALo[offset]), v, nz*sizeof(PetscScalar));CHKERRQ(ierr);
280 
281         offset      += nz;
282         AjLo[offset] = (PetscInt) i;
283         AALo[offset] = (MatScalar) 1.0;
284         offset      += 1;
285 
286         v  += nz;
287         vi += nz;
288       }
289 
290       /* allocate space for the triangular factor information */
291       loTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;
292 
293       /* Create the matrix description */
294       stat = cusparseCreateMatDescr(&loTriFactor->descr);CHKERRCUDA(stat);
295       stat = cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUDA(stat);
296       stat = cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUDA(stat);
297       stat = cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_LOWER);CHKERRCUDA(stat);
298       stat = cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT);CHKERRCUDA(stat);
299 
300       /* Create the solve analysis information */
301       stat = cusparseCreateSolveAnalysisInfo(&loTriFactor->solveInfo);CHKERRCUDA(stat);
302 
303       /* set the operation */
304       loTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
305 
306       /* set the matrix */
307       loTriFactor->csrMat = new CsrMatrix;
308       loTriFactor->csrMat->num_rows = n;
309       loTriFactor->csrMat->num_cols = n;
310       loTriFactor->csrMat->num_entries = nzLower;
311 
312       loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n+1);
313       loTriFactor->csrMat->row_offsets->assign(AiLo, AiLo+n+1);
314 
315       loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzLower);
316       loTriFactor->csrMat->column_indices->assign(AjLo, AjLo+nzLower);
317 
318       loTriFactor->csrMat->values = new THRUSTARRAY(nzLower);
319       loTriFactor->csrMat->values->assign(AALo, AALo+nzLower);
320 
321       /* perform the solve analysis */
322       stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactor->solveOp,
323                                loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr,
324                                loTriFactor->csrMat->values->data().get(), loTriFactor->csrMat->row_offsets->data().get(),
325                                loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo);CHKERRCUDA(stat);
326 
327       /* assign the pointer. Is this really necessary? */
328       ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtr = loTriFactor;
329 
330       ierr = cudaFreeHost(AiLo);CHKERRCUDA(ierr);
331       ierr = cudaFreeHost(AjLo);CHKERRCUDA(ierr);
332       ierr = cudaFreeHost(AALo);CHKERRCUDA(ierr);
333     } catch(char *ex) {
334       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
335     }
336   }
337   PetscFunctionReturn(0);
338 }
339 
340 static PetscErrorCode MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(Mat A)
341 {
342   Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
343   PetscInt                          n = A->rmap->n;
344   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
345   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
346   cusparseStatus_t                  stat;
347   const PetscInt                    *aj = a->j,*adiag = a->diag,*vi;
348   const MatScalar                   *aa = a->a,*v;
349   PetscInt                          *AiUp, *AjUp;
350   PetscScalar                       *AAUp;
351   PetscInt                          i,nz, nzUpper, offset;
352   PetscErrorCode                    ierr;
353 
354   PetscFunctionBegin;
355   if (A->valid_GPU_matrix == PETSC_CUDA_UNALLOCATED || A->valid_GPU_matrix == PETSC_CUDA_CPU) {
356     try {
357       /* next, figure out the number of nonzeros in the upper triangular matrix. */
358       nzUpper = adiag[0]-adiag[n];
359 
360       /* Allocate Space for the upper triangular matrix */
361       ierr = cudaMallocHost((void**) &AiUp, (n+1)*sizeof(PetscInt));CHKERRCUDA(ierr);
362       ierr = cudaMallocHost((void**) &AjUp, nzUpper*sizeof(PetscInt));CHKERRCUDA(ierr);
363       ierr = cudaMallocHost((void**) &AAUp, nzUpper*sizeof(PetscScalar));CHKERRCUDA(ierr);
364 
365       /* Fill the upper triangular matrix */
366       AiUp[0]=(PetscInt) 0;
367       AiUp[n]=nzUpper;
368       offset = nzUpper;
369       for (i=n-1; i>=0; i--) {
370         v  = aa + adiag[i+1] + 1;
371         vi = aj + adiag[i+1] + 1;
372 
373         /* number of elements NOT on the diagonal */
374         nz = adiag[i] - adiag[i+1]-1;
375 
376         /* decrement the offset */
377         offset -= (nz+1);
378 
379         /* first, set the diagonal elements */
380         AjUp[offset] = (PetscInt) i;
381         AAUp[offset] = (MatScalar)1./v[nz];
382         AiUp[i]      = AiUp[i+1] - (nz+1);
383 
384         ierr = PetscMemcpy(&(AjUp[offset+1]), vi, nz*sizeof(PetscInt));CHKERRQ(ierr);
385         ierr = PetscMemcpy(&(AAUp[offset+1]), v, nz*sizeof(PetscScalar));CHKERRQ(ierr);
386       }
387 
388       /* allocate space for the triangular factor information */
389       upTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;
390 
391       /* Create the matrix description */
392       stat = cusparseCreateMatDescr(&upTriFactor->descr);CHKERRCUDA(stat);
393       stat = cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUDA(stat);
394       stat = cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUDA(stat);
395       stat = cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUDA(stat);
396       stat = cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT);CHKERRCUDA(stat);
397 
398       /* Create the solve analysis information */
399       stat = cusparseCreateSolveAnalysisInfo(&upTriFactor->solveInfo);CHKERRCUDA(stat);
400 
401       /* set the operation */
402       upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
403 
404       /* set the matrix */
405       upTriFactor->csrMat = new CsrMatrix;
406       upTriFactor->csrMat->num_rows = n;
407       upTriFactor->csrMat->num_cols = n;
408       upTriFactor->csrMat->num_entries = nzUpper;
409 
410       upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n+1);
411       upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+n+1);
412 
413       upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzUpper);
414       upTriFactor->csrMat->column_indices->assign(AjUp, AjUp+nzUpper);
415 
416       upTriFactor->csrMat->values = new THRUSTARRAY(nzUpper);
417       upTriFactor->csrMat->values->assign(AAUp, AAUp+nzUpper);
418 
419       /* perform the solve analysis */
420       stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactor->solveOp,
421                                upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr,
422                                upTriFactor->csrMat->values->data().get(), upTriFactor->csrMat->row_offsets->data().get(),
423                                upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo);CHKERRCUDA(stat);
424 
425       /* assign the pointer. Is this really necessary? */
426       ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtr = upTriFactor;
427 
428       ierr = cudaFreeHost(AiUp);CHKERRCUDA(ierr);
429       ierr = cudaFreeHost(AjUp);CHKERRCUDA(ierr);
430       ierr = cudaFreeHost(AAUp);CHKERRCUDA(ierr);
431     } catch(char *ex) {
432       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
433     }
434   }
435   PetscFunctionReturn(0);
436 }
437 
438 static PetscErrorCode MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(Mat A)
439 {
440   PetscErrorCode               ierr;
441   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ*)A->data;
442   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
443   IS                           isrow = a->row,iscol = a->icol;
444   PetscBool                    row_identity,col_identity;
445   const PetscInt               *r,*c;
446   PetscInt                     n = A->rmap->n;
447 
448   PetscFunctionBegin;
449   ierr = MatSeqAIJCUSPARSEBuildILULowerTriMatrix(A);CHKERRQ(ierr);
450   ierr = MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(A);CHKERRQ(ierr);
451 
452   cusparseTriFactors->workVector = new THRUSTARRAY;
453   cusparseTriFactors->workVector->resize(n);
454   cusparseTriFactors->nnz=a->nz;
455 
456   A->valid_GPU_matrix = PETSC_CUDA_BOTH;
457   /*lower triangular indices */
458   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
459   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
460   if (!row_identity) {
461     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
462     cusparseTriFactors->rpermIndices->assign(r, r+n);
463   }
464   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
465 
466   /*upper triangular indices */
467   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr);
468   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
469   if (!col_identity) {
470     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
471     cusparseTriFactors->cpermIndices->assign(c, c+n);
472   }
473   ierr = ISRestoreIndices(iscol,&c);CHKERRQ(ierr);
474   PetscFunctionReturn(0);
475 }
476 
477 static PetscErrorCode MatSeqAIJCUSPARSEBuildICCTriMatrices(Mat A)
478 {
479   Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
480   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
481   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
482   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
483   cusparseStatus_t                  stat;
484   PetscErrorCode                    ierr;
485   PetscInt                          *AiUp, *AjUp;
486   PetscScalar                       *AAUp;
487   PetscScalar                       *AALo;
488   PetscInt                          nzUpper = a->nz,n = A->rmap->n,i,offset,nz,j;
489   Mat_SeqSBAIJ                      *b = (Mat_SeqSBAIJ*)A->data;
490   const PetscInt                    *ai = b->i,*aj = b->j,*vj;
491   const MatScalar                   *aa = b->a,*v;
492 
493   PetscFunctionBegin;
494   if (A->valid_GPU_matrix == PETSC_CUDA_UNALLOCATED || A->valid_GPU_matrix == PETSC_CUDA_CPU) {
495     try {
496       /* Allocate Space for the upper triangular matrix */
497       ierr = cudaMallocHost((void**) &AiUp, (n+1)*sizeof(PetscInt));CHKERRCUDA(ierr);
498       ierr = cudaMallocHost((void**) &AjUp, nzUpper*sizeof(PetscInt));CHKERRCUDA(ierr);
499       ierr = cudaMallocHost((void**) &AAUp, nzUpper*sizeof(PetscScalar));CHKERRCUDA(ierr);
500       ierr = cudaMallocHost((void**) &AALo, nzUpper*sizeof(PetscScalar));CHKERRCUDA(ierr);
501 
502       /* Fill the upper triangular matrix */
503       AiUp[0]=(PetscInt) 0;
504       AiUp[n]=nzUpper;
505       offset = 0;
506       for (i=0; i<n; i++) {
507         /* set the pointers */
508         v  = aa + ai[i];
509         vj = aj + ai[i];
510         nz = ai[i+1] - ai[i] - 1; /* exclude diag[i] */
511 
512         /* first, set the diagonal elements */
513         AjUp[offset] = (PetscInt) i;
514         AAUp[offset] = (MatScalar)1.0/v[nz];
515         AiUp[i]      = offset;
516         AALo[offset] = (MatScalar)1.0/v[nz];
517 
518         offset+=1;
519         if (nz>0) {
520           ierr = PetscMemcpy(&(AjUp[offset]), vj, nz*sizeof(PetscInt));CHKERRQ(ierr);
521           ierr = PetscMemcpy(&(AAUp[offset]), v, nz*sizeof(PetscScalar));CHKERRQ(ierr);
522           for (j=offset; j<offset+nz; j++) {
523             AAUp[j] = -AAUp[j];
524             AALo[j] = AAUp[j]/v[nz];
525           }
526           offset+=nz;
527         }
528       }
529 
530       /* allocate space for the triangular factor information */
531       upTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;
532 
533       /* Create the matrix description */
534       stat = cusparseCreateMatDescr(&upTriFactor->descr);CHKERRCUDA(stat);
535       stat = cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUDA(stat);
536       stat = cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUDA(stat);
537       stat = cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUDA(stat);
538       stat = cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT);CHKERRCUDA(stat);
539 
540       /* Create the solve analysis information */
541       stat = cusparseCreateSolveAnalysisInfo(&upTriFactor->solveInfo);CHKERRCUDA(stat);
542 
543       /* set the operation */
544       upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
545 
546       /* set the matrix */
547       upTriFactor->csrMat = new CsrMatrix;
548       upTriFactor->csrMat->num_rows = A->rmap->n;
549       upTriFactor->csrMat->num_cols = A->cmap->n;
550       upTriFactor->csrMat->num_entries = a->nz;
551 
552       upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
553       upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+A->rmap->n+1);
554 
555       upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
556       upTriFactor->csrMat->column_indices->assign(AjUp, AjUp+a->nz);
557 
558       upTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
559       upTriFactor->csrMat->values->assign(AAUp, AAUp+a->nz);
560 
561       /* perform the solve analysis */
562       stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactor->solveOp,
563                                upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr,
564                                upTriFactor->csrMat->values->data().get(), upTriFactor->csrMat->row_offsets->data().get(),
565                                upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo);CHKERRCUDA(stat);
566 
567       /* assign the pointer. Is this really necessary? */
568       ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtr = upTriFactor;
569 
570       /* allocate space for the triangular factor information */
571       loTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;
572 
573       /* Create the matrix description */
574       stat = cusparseCreateMatDescr(&loTriFactor->descr);CHKERRCUDA(stat);
575       stat = cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUDA(stat);
576       stat = cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUDA(stat);
577       stat = cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUDA(stat);
578       stat = cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT);CHKERRCUDA(stat);
579 
580       /* Create the solve analysis information */
581       stat = cusparseCreateSolveAnalysisInfo(&loTriFactor->solveInfo);CHKERRCUDA(stat);
582 
583       /* set the operation */
584       loTriFactor->solveOp = CUSPARSE_OPERATION_TRANSPOSE;
585 
586       /* set the matrix */
587       loTriFactor->csrMat = new CsrMatrix;
588       loTriFactor->csrMat->num_rows = A->rmap->n;
589       loTriFactor->csrMat->num_cols = A->cmap->n;
590       loTriFactor->csrMat->num_entries = a->nz;
591 
592       loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
593       loTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+A->rmap->n+1);
594 
595       loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
596       loTriFactor->csrMat->column_indices->assign(AjUp, AjUp+a->nz);
597 
598       loTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
599       loTriFactor->csrMat->values->assign(AALo, AALo+a->nz);
600 
601       /* perform the solve analysis */
602       stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactor->solveOp,
603                                loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr,
604                                loTriFactor->csrMat->values->data().get(), loTriFactor->csrMat->row_offsets->data().get(),
605                                loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo);CHKERRCUDA(stat);
606 
607       /* assign the pointer. Is this really necessary? */
608       ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtr = loTriFactor;
609 
610       A->valid_GPU_matrix = PETSC_CUDA_BOTH;
611       ierr = cudaFreeHost(AiUp);CHKERRCUDA(ierr);
612       ierr = cudaFreeHost(AjUp);CHKERRCUDA(ierr);
613       ierr = cudaFreeHost(AAUp);CHKERRCUDA(ierr);
614       ierr = cudaFreeHost(AALo);CHKERRCUDA(ierr);
615     } catch(char *ex) {
616       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
617     }
618   }
619   PetscFunctionReturn(0);
620 }
621 
622 static PetscErrorCode MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(Mat A)
623 {
624   PetscErrorCode               ierr;
625   Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ*)A->data;
626   Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
627   IS                           ip = a->row;
628   const PetscInt               *rip;
629   PetscBool                    perm_identity;
630   PetscInt                     n = A->rmap->n;
631 
632   PetscFunctionBegin;
633   ierr = MatSeqAIJCUSPARSEBuildICCTriMatrices(A);CHKERRQ(ierr);
634   cusparseTriFactors->workVector = new THRUSTARRAY;
635   cusparseTriFactors->workVector->resize(n);
636   cusparseTriFactors->nnz=(a->nz-n)*2 + n;
637 
638   /*lower triangular indices */
639   ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr);
640   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
641   if (!perm_identity) {
642     cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
643     cusparseTriFactors->rpermIndices->assign(rip, rip+n);
644     cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
645     cusparseTriFactors->cpermIndices->assign(rip, rip+n);
646   }
647   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
648   PetscFunctionReturn(0);
649 }
650 
651 static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat B,Mat A,const MatFactorInfo *info)
652 {
653   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
654   IS             isrow = b->row,iscol = b->col;
655   PetscBool      row_identity,col_identity;
656   PetscErrorCode ierr;
657 
658   PetscFunctionBegin;
659   ierr = MatLUFactorNumeric_SeqAIJ(B,A,info);CHKERRQ(ierr);
660   /* determine which version of MatSolve needs to be used. */
661   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
662   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
663   if (row_identity && col_identity) {
664     B->ops->solve = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
665     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
666   } else {
667     B->ops->solve = MatSolve_SeqAIJCUSPARSE;
668     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
669   }
670 
671   /* get the triangular factors */
672   ierr = MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(B);CHKERRQ(ierr);
673   PetscFunctionReturn(0);
674 }
675 
676 static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat B,Mat A,const MatFactorInfo *info)
677 {
678   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
679   IS             ip = b->row;
680   PetscBool      perm_identity;
681   PetscErrorCode ierr;
682 
683   PetscFunctionBegin;
684   ierr = MatCholeskyFactorNumeric_SeqAIJ(B,A,info);CHKERRQ(ierr);
685 
686   /* determine which version of MatSolve needs to be used. */
687   ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
688   if (perm_identity) {
689     B->ops->solve = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
690     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
691   } else {
692     B->ops->solve = MatSolve_SeqAIJCUSPARSE;
693     B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
694   }
695 
696   /* get the triangular factors */
697   ierr = MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(B);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 static PetscErrorCode MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(Mat A)
702 {
703   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
704   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
705   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
706   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
707   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
708   cusparseStatus_t                  stat;
709   cusparseIndexBase_t               indexBase;
710   cusparseMatrixType_t              matrixType;
711   cusparseFillMode_t                fillMode;
712   cusparseDiagType_t                diagType;
713 
714   PetscFunctionBegin;
715 
716   /*********************************************/
717   /* Now the Transpose of the Lower Tri Factor */
718   /*********************************************/
719 
720   /* allocate space for the transpose of the lower triangular factor */
721   loTriFactorT = new Mat_SeqAIJCUSPARSETriFactorStruct;
722 
723   /* set the matrix descriptors of the lower triangular factor */
724   matrixType = cusparseGetMatType(loTriFactor->descr);
725   indexBase = cusparseGetMatIndexBase(loTriFactor->descr);
726   fillMode = cusparseGetMatFillMode(loTriFactor->descr)==CUSPARSE_FILL_MODE_UPPER ?
727     CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
728   diagType = cusparseGetMatDiagType(loTriFactor->descr);
729 
730   /* Create the matrix description */
731   stat = cusparseCreateMatDescr(&loTriFactorT->descr);CHKERRCUDA(stat);
732   stat = cusparseSetMatIndexBase(loTriFactorT->descr, indexBase);CHKERRCUDA(stat);
733   stat = cusparseSetMatType(loTriFactorT->descr, matrixType);CHKERRCUDA(stat);
734   stat = cusparseSetMatFillMode(loTriFactorT->descr, fillMode);CHKERRCUDA(stat);
735   stat = cusparseSetMatDiagType(loTriFactorT->descr, diagType);CHKERRCUDA(stat);
736 
737   /* Create the solve analysis information */
738   stat = cusparseCreateSolveAnalysisInfo(&loTriFactorT->solveInfo);CHKERRCUDA(stat);
739 
740   /* set the operation */
741   loTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
742 
743   /* allocate GPU space for the CSC of the lower triangular factor*/
744   loTriFactorT->csrMat = new CsrMatrix;
745   loTriFactorT->csrMat->num_rows = loTriFactor->csrMat->num_rows;
746   loTriFactorT->csrMat->num_cols = loTriFactor->csrMat->num_cols;
747   loTriFactorT->csrMat->num_entries = loTriFactor->csrMat->num_entries;
748   loTriFactorT->csrMat->row_offsets = new THRUSTINTARRAY32(loTriFactor->csrMat->num_rows+1);
749   loTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(loTriFactor->csrMat->num_entries);
750   loTriFactorT->csrMat->values = new THRUSTARRAY(loTriFactor->csrMat->num_entries);
751 
752   /* compute the transpose of the lower triangular factor, i.e. the CSC */
753   stat = cusparse_csr2csc(cusparseTriFactors->handle, loTriFactor->csrMat->num_rows,
754                           loTriFactor->csrMat->num_cols, loTriFactor->csrMat->num_entries,
755                           loTriFactor->csrMat->values->data().get(),
756                           loTriFactor->csrMat->row_offsets->data().get(),
757                           loTriFactor->csrMat->column_indices->data().get(),
758                           loTriFactorT->csrMat->values->data().get(),
759                           loTriFactorT->csrMat->column_indices->data().get(),
760                           loTriFactorT->csrMat->row_offsets->data().get(),
761                           CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUDA(stat);
762 
763   /* perform the solve analysis on the transposed matrix */
764   stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactorT->solveOp,
765                            loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries,
766                            loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
767                            loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(),
768                            loTriFactorT->solveInfo);CHKERRCUDA(stat);
769 
770   /* assign the pointer. Is this really necessary? */
771   ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtrTranspose = loTriFactorT;
772 
773   /*********************************************/
774   /* Now the Transpose of the Upper Tri Factor */
775   /*********************************************/
776 
777   /* allocate space for the transpose of the upper triangular factor */
778   upTriFactorT = new Mat_SeqAIJCUSPARSETriFactorStruct;
779 
780   /* set the matrix descriptors of the upper triangular factor */
781   matrixType = cusparseGetMatType(upTriFactor->descr);
782   indexBase = cusparseGetMatIndexBase(upTriFactor->descr);
783   fillMode = cusparseGetMatFillMode(upTriFactor->descr)==CUSPARSE_FILL_MODE_UPPER ?
784     CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
785   diagType = cusparseGetMatDiagType(upTriFactor->descr);
786 
787   /* Create the matrix description */
788   stat = cusparseCreateMatDescr(&upTriFactorT->descr);CHKERRCUDA(stat);
789   stat = cusparseSetMatIndexBase(upTriFactorT->descr, indexBase);CHKERRCUDA(stat);
790   stat = cusparseSetMatType(upTriFactorT->descr, matrixType);CHKERRCUDA(stat);
791   stat = cusparseSetMatFillMode(upTriFactorT->descr, fillMode);CHKERRCUDA(stat);
792   stat = cusparseSetMatDiagType(upTriFactorT->descr, diagType);CHKERRCUDA(stat);
793 
794   /* Create the solve analysis information */
795   stat = cusparseCreateSolveAnalysisInfo(&upTriFactorT->solveInfo);CHKERRCUDA(stat);
796 
797   /* set the operation */
798   upTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;
799 
800   /* allocate GPU space for the CSC of the upper triangular factor*/
801   upTriFactorT->csrMat = new CsrMatrix;
802   upTriFactorT->csrMat->num_rows = upTriFactor->csrMat->num_rows;
803   upTriFactorT->csrMat->num_cols = upTriFactor->csrMat->num_cols;
804   upTriFactorT->csrMat->num_entries = upTriFactor->csrMat->num_entries;
805   upTriFactorT->csrMat->row_offsets = new THRUSTINTARRAY32(upTriFactor->csrMat->num_rows+1);
806   upTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(upTriFactor->csrMat->num_entries);
807   upTriFactorT->csrMat->values = new THRUSTARRAY(upTriFactor->csrMat->num_entries);
808 
809   /* compute the transpose of the upper triangular factor, i.e. the CSC */
810   stat = cusparse_csr2csc(cusparseTriFactors->handle, upTriFactor->csrMat->num_rows,
811                           upTriFactor->csrMat->num_cols, upTriFactor->csrMat->num_entries,
812                           upTriFactor->csrMat->values->data().get(),
813                           upTriFactor->csrMat->row_offsets->data().get(),
814                           upTriFactor->csrMat->column_indices->data().get(),
815                           upTriFactorT->csrMat->values->data().get(),
816                           upTriFactorT->csrMat->column_indices->data().get(),
817                           upTriFactorT->csrMat->row_offsets->data().get(),
818                           CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUDA(stat);
819 
820   /* perform the solve analysis on the transposed matrix */
821   stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactorT->solveOp,
822                            upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries,
823                            upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
824                            upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(),
825                            upTriFactorT->solveInfo);CHKERRCUDA(stat);
826 
827   /* assign the pointer. Is this really necessary? */
828   ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtrTranspose = upTriFactorT;
829   PetscFunctionReturn(0);
830 }
831 
832 static PetscErrorCode MatSeqAIJCUSPARSEGenerateTransposeForMult(Mat A)
833 {
834   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
835   Mat_SeqAIJCUSPARSEMultStruct *matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
836   Mat_SeqAIJCUSPARSEMultStruct *matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
837   Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
838   cusparseStatus_t             stat;
839   cusparseIndexBase_t          indexBase;
840   cudaError_t                  err;
841 
842   PetscFunctionBegin;
843 
844   /* allocate space for the triangular factor information */
845   matstructT = new Mat_SeqAIJCUSPARSEMultStruct;
846   stat = cusparseCreateMatDescr(&matstructT->descr);CHKERRCUDA(stat);
847   indexBase = cusparseGetMatIndexBase(matstruct->descr);
848   stat = cusparseSetMatIndexBase(matstructT->descr, indexBase);CHKERRCUDA(stat);
849   stat = cusparseSetMatType(matstructT->descr, CUSPARSE_MATRIX_TYPE_GENERAL);CHKERRCUDA(stat);
850 
851   /* set alpha and beta */
852   err = cudaMalloc((void **)&(matstructT->alpha),sizeof(PetscScalar));CHKERRCUDA(err);
853   err = cudaMemcpy(matstructT->alpha,&ALPHA,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
854   err = cudaMalloc((void **)&(matstructT->beta),sizeof(PetscScalar));CHKERRCUDA(err);
855   err = cudaMemcpy(matstructT->beta,&BETA,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
856   stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUDA(stat);
857 
858   if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
859     CsrMatrix *matrix = (CsrMatrix*)matstruct->mat;
860     CsrMatrix *matrixT= new CsrMatrix;
861     matrixT->num_rows = A->rmap->n;
862     matrixT->num_cols = A->cmap->n;
863     matrixT->num_entries = a->nz;
864     matrixT->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
865     matrixT->column_indices = new THRUSTINTARRAY32(a->nz);
866     matrixT->values = new THRUSTARRAY(a->nz);
867 
868     /* compute the transpose of the upper triangular factor, i.e. the CSC */
869     indexBase = cusparseGetMatIndexBase(matstruct->descr);
870     stat = cusparse_csr2csc(cusparsestruct->handle, matrix->num_rows,
871                             matrix->num_cols, matrix->num_entries,
872                             matrix->values->data().get(),
873                             matrix->row_offsets->data().get(),
874                             matrix->column_indices->data().get(),
875                             matrixT->values->data().get(),
876                             matrixT->column_indices->data().get(),
877                             matrixT->row_offsets->data().get(),
878                             CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUDA(stat);
879 
880     /* assign the pointer */
881     matstructT->mat = matrixT;
882 
883   } else if (cusparsestruct->format==MAT_CUSPARSE_ELL || cusparsestruct->format==MAT_CUSPARSE_HYB) {
884 #if CUDA_VERSION>=5000
885     /* First convert HYB to CSR */
886     CsrMatrix *temp= new CsrMatrix;
887     temp->num_rows = A->rmap->n;
888     temp->num_cols = A->cmap->n;
889     temp->num_entries = a->nz;
890     temp->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
891     temp->column_indices = new THRUSTINTARRAY32(a->nz);
892     temp->values = new THRUSTARRAY(a->nz);
893 
894 
895     stat = cusparse_hyb2csr(cusparsestruct->handle,
896                             matstruct->descr, (cusparseHybMat_t)matstruct->mat,
897                             temp->values->data().get(),
898                             temp->row_offsets->data().get(),
899                             temp->column_indices->data().get());CHKERRCUDA(stat);
900 
901     /* Next, convert CSR to CSC (i.e. the matrix transpose) */
902     CsrMatrix *tempT= new CsrMatrix;
903     tempT->num_rows = A->rmap->n;
904     tempT->num_cols = A->cmap->n;
905     tempT->num_entries = a->nz;
906     tempT->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
907     tempT->column_indices = new THRUSTINTARRAY32(a->nz);
908     tempT->values = new THRUSTARRAY(a->nz);
909 
910     stat = cusparse_csr2csc(cusparsestruct->handle, temp->num_rows,
911                             temp->num_cols, temp->num_entries,
912                             temp->values->data().get(),
913                             temp->row_offsets->data().get(),
914                             temp->column_indices->data().get(),
915                             tempT->values->data().get(),
916                             tempT->column_indices->data().get(),
917                             tempT->row_offsets->data().get(),
918                             CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUDA(stat);
919 
920     /* Last, convert CSC to HYB */
921     cusparseHybMat_t hybMat;
922     stat = cusparseCreateHybMat(&hybMat);CHKERRCUDA(stat);
923     cusparseHybPartition_t partition = cusparsestruct->format==MAT_CUSPARSE_ELL ?
924       CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
925     stat = cusparse_csr2hyb(cusparsestruct->handle, A->rmap->n, A->cmap->n,
926                             matstructT->descr, tempT->values->data().get(),
927                             tempT->row_offsets->data().get(),
928                             tempT->column_indices->data().get(),
929                             hybMat, 0, partition);CHKERRCUDA(stat);
930 
931     /* assign the pointer */
932     matstructT->mat = hybMat;
933 
934     /* delete temporaries */
935     if (tempT) {
936       if (tempT->values) delete (THRUSTARRAY*) tempT->values;
937       if (tempT->column_indices) delete (THRUSTINTARRAY32*) tempT->column_indices;
938       if (tempT->row_offsets) delete (THRUSTINTARRAY32*) tempT->row_offsets;
939       delete (CsrMatrix*) tempT;
940     }
941     if (temp) {
942       if (temp->values) delete (THRUSTARRAY*) temp->values;
943       if (temp->column_indices) delete (THRUSTINTARRAY32*) temp->column_indices;
944       if (temp->row_offsets) delete (THRUSTINTARRAY32*) temp->row_offsets;
945       delete (CsrMatrix*) temp;
946     }
947 #else
948     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ELL (Ellpack) and HYB (Hybrid) storage format for the Matrix Transpose (in MatMultTranspose) require CUDA 5.0 or later.");
949 #endif
950   }
951   /* assign the compressed row indices */
952   matstructT->cprowIndices = new THRUSTINTARRAY;
953 
954   /* assign the pointer */
955   ((Mat_SeqAIJCUSPARSE*)A->spptr)->matTranspose = matstructT;
956   PetscFunctionReturn(0);
957 }
958 
959 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat A,Vec bb,Vec xx)
960 {
961   PetscInt                              n = xx->map->n;
962   const PetscScalar                     *barray;
963   PetscScalar                           *xarray;
964   thrust::device_ptr<const PetscScalar> bGPU;
965   thrust::device_ptr<PetscScalar>       xGPU;
966   cusparseStatus_t                      stat;
967   Mat_SeqAIJCUSPARSETriFactors          *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
968   Mat_SeqAIJCUSPARSETriFactorStruct     *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
969   Mat_SeqAIJCUSPARSETriFactorStruct     *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
970   THRUSTARRAY                           *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
971   PetscErrorCode                        ierr;
972 
973   PetscFunctionBegin;
974   /* Analyze the matrix and create the transpose ... on the fly */
975   if (!loTriFactorT && !upTriFactorT) {
976     ierr = MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A);CHKERRQ(ierr);
977     loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
978     upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
979   }
980 
981   /* Get the GPU pointers */
982   ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
983   ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
984   xGPU = thrust::device_pointer_cast(xarray);
985   bGPU = thrust::device_pointer_cast(barray);
986 
987   /* First, reorder with the row permutation */
988   thrust::copy(thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()),
989                thrust::make_permutation_iterator(bGPU+n, cusparseTriFactors->rpermIndices->end()),
990                xGPU);
991 
992   /* First, solve U */
993   stat = cusparse_solve(cusparseTriFactors->handle, upTriFactorT->solveOp,
994                         upTriFactorT->csrMat->num_rows, &ALPHA, upTriFactorT->descr,
995                         upTriFactorT->csrMat->values->data().get(),
996                         upTriFactorT->csrMat->row_offsets->data().get(),
997                         upTriFactorT->csrMat->column_indices->data().get(),
998                         upTriFactorT->solveInfo,
999                         xarray, tempGPU->data().get());CHKERRCUDA(stat);
1000 
1001   /* Then, solve L */
1002   stat = cusparse_solve(cusparseTriFactors->handle, loTriFactorT->solveOp,
1003                         loTriFactorT->csrMat->num_rows, &ALPHA, loTriFactorT->descr,
1004                         loTriFactorT->csrMat->values->data().get(),
1005                         loTriFactorT->csrMat->row_offsets->data().get(),
1006                         loTriFactorT->csrMat->column_indices->data().get(),
1007                         loTriFactorT->solveInfo,
1008                         tempGPU->data().get(), xarray);CHKERRCUDA(stat);
1009 
1010   /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
1011   thrust::copy(thrust::make_permutation_iterator(xGPU, cusparseTriFactors->cpermIndices->begin()),
1012                thrust::make_permutation_iterator(xGPU+n, cusparseTriFactors->cpermIndices->end()),
1013                tempGPU->begin());
1014 
1015   /* Copy the temporary to the full solution. */
1016   thrust::copy(tempGPU->begin(), tempGPU->end(), xGPU);
1017 
1018   /* restore */
1019   ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
1020   ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
1021   ierr = WaitForGPU();CHKERRCUDA(ierr);
1022 
1023   ierr = PetscLogFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat A,Vec bb,Vec xx)
1028 {
1029   const PetscScalar                 *barray;
1030   PetscScalar                       *xarray;
1031   cusparseStatus_t                  stat;
1032   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
1033   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
1034   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
1035   THRUSTARRAY                       *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
1036   PetscErrorCode                    ierr;
1037 
1038   PetscFunctionBegin;
1039   /* Analyze the matrix and create the transpose ... on the fly */
1040   if (!loTriFactorT && !upTriFactorT) {
1041     ierr = MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A);CHKERRQ(ierr);
1042     loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
1043     upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
1044   }
1045 
1046   /* Get the GPU pointers */
1047   ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
1048   ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
1049 
1050   /* First, solve U */
1051   stat = cusparse_solve(cusparseTriFactors->handle, upTriFactorT->solveOp,
1052                         upTriFactorT->csrMat->num_rows, &ALPHA, upTriFactorT->descr,
1053                         upTriFactorT->csrMat->values->data().get(),
1054                         upTriFactorT->csrMat->row_offsets->data().get(),
1055                         upTriFactorT->csrMat->column_indices->data().get(),
1056                         upTriFactorT->solveInfo,
1057                         barray, tempGPU->data().get());CHKERRCUDA(stat);
1058 
1059   /* Then, solve L */
1060   stat = cusparse_solve(cusparseTriFactors->handle, loTriFactorT->solveOp,
1061                         loTriFactorT->csrMat->num_rows, &ALPHA, loTriFactorT->descr,
1062                         loTriFactorT->csrMat->values->data().get(),
1063                         loTriFactorT->csrMat->row_offsets->data().get(),
1064                         loTriFactorT->csrMat->column_indices->data().get(),
1065                         loTriFactorT->solveInfo,
1066                         tempGPU->data().get(), xarray);CHKERRCUDA(stat);
1067 
1068   /* restore */
1069   ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
1070   ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
1071   ierr = WaitForGPU();CHKERRCUDA(ierr);
1072   ierr = PetscLogFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat A,Vec bb,Vec xx)
1077 {
1078   const PetscScalar                     *barray;
1079   PetscScalar                           *xarray;
1080   thrust::device_ptr<const PetscScalar> bGPU;
1081   thrust::device_ptr<PetscScalar>       xGPU;
1082   cusparseStatus_t                      stat;
1083   Mat_SeqAIJCUSPARSETriFactors          *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
1084   Mat_SeqAIJCUSPARSETriFactorStruct     *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
1085   Mat_SeqAIJCUSPARSETriFactorStruct     *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
1086   THRUSTARRAY                           *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
1087   PetscErrorCode                        ierr;
1088   VecType                               t;
1089   PetscBool                             flg;
1090 
1091   PetscFunctionBegin;
1092   ierr = VecGetType(bb,&t);CHKERRQ(ierr);
1093   ierr = PetscStrcmp(t,VECSEQCUDA,&flg);CHKERRQ(ierr);
1094   if (!flg) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Vector of type %s passed into MatSolve_SeqAIJCUSPARSE (Arg #2). Can only deal with %s\n.",t,VECSEQCUDA);
1095   ierr = VecGetType(xx,&t);CHKERRQ(ierr);
1096   ierr = PetscStrcmp(t,VECSEQCUDA,&flg);CHKERRQ(ierr);
1097   if (!flg) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Vector of type %s passed into MatSolve_SeqAIJCUSPARSE (Arg #3). Can only deal with %s\n.",t,VECSEQCUDA);
1098 
1099   /* Get the GPU pointers */
1100   ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
1101   ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
1102   xGPU = thrust::device_pointer_cast(xarray);
1103   bGPU = thrust::device_pointer_cast(barray);
1104 
1105   /* First, reorder with the row permutation */
1106   thrust::copy(thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()),
1107                thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->end()),
1108                xGPU);
1109 
1110   /* Next, solve L */
1111   stat = cusparse_solve(cusparseTriFactors->handle, loTriFactor->solveOp,
1112                         loTriFactor->csrMat->num_rows, &ALPHA, loTriFactor->descr,
1113                         loTriFactor->csrMat->values->data().get(),
1114                         loTriFactor->csrMat->row_offsets->data().get(),
1115                         loTriFactor->csrMat->column_indices->data().get(),
1116                         loTriFactor->solveInfo,
1117                         xarray, tempGPU->data().get());CHKERRCUDA(stat);
1118 
1119   /* Then, solve U */
1120   stat = cusparse_solve(cusparseTriFactors->handle, upTriFactor->solveOp,
1121                         upTriFactor->csrMat->num_rows, &ALPHA, upTriFactor->descr,
1122                         upTriFactor->csrMat->values->data().get(),
1123                         upTriFactor->csrMat->row_offsets->data().get(),
1124                         upTriFactor->csrMat->column_indices->data().get(),
1125                         upTriFactor->solveInfo,
1126                         tempGPU->data().get(), xarray);CHKERRCUDA(stat);
1127 
1128   /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
1129   thrust::copy(thrust::make_permutation_iterator(xGPU, cusparseTriFactors->cpermIndices->begin()),
1130                thrust::make_permutation_iterator(xGPU, cusparseTriFactors->cpermIndices->end()),
1131                tempGPU->begin());
1132 
1133   /* Copy the temporary to the full solution. */
1134   thrust::copy(tempGPU->begin(), tempGPU->end(), xGPU);
1135 
1136   ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
1137   ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
1138   ierr = WaitForGPU();CHKERRCUDA(ierr);
1139   ierr = PetscLogFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat A,Vec bb,Vec xx)
1144 {
1145   const PetscScalar                 *barray;
1146   PetscScalar                       *xarray;
1147   cusparseStatus_t                  stat;
1148   Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
1149   Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
1150   Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
1151   THRUSTARRAY                       *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
1152   PetscErrorCode                    ierr;
1153 
1154   PetscFunctionBegin;
1155   /* Get the GPU pointers */
1156   ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
1157   ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
1158 
1159   /* First, solve L */
1160   stat = cusparse_solve(cusparseTriFactors->handle, loTriFactor->solveOp,
1161                         loTriFactor->csrMat->num_rows, &ALPHA, loTriFactor->descr,
1162                         loTriFactor->csrMat->values->data().get(),
1163                         loTriFactor->csrMat->row_offsets->data().get(),
1164                         loTriFactor->csrMat->column_indices->data().get(),
1165                         loTriFactor->solveInfo,
1166                         barray, tempGPU->data().get());CHKERRCUDA(stat);
1167 
1168   /* Next, solve U */
1169   stat = cusparse_solve(cusparseTriFactors->handle, upTriFactor->solveOp,
1170                         upTriFactor->csrMat->num_rows, &ALPHA, upTriFactor->descr,
1171                         upTriFactor->csrMat->values->data().get(),
1172                         upTriFactor->csrMat->row_offsets->data().get(),
1173                         upTriFactor->csrMat->column_indices->data().get(),
1174                         upTriFactor->solveInfo,
1175                         tempGPU->data().get(), xarray);CHKERRCUDA(stat);
1176 
1177   ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
1178   ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
1179   ierr = WaitForGPU();CHKERRCUDA(ierr);
1180   ierr = PetscLogFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
1181   PetscFunctionReturn(0);
1182 }
1183 
1184 static PetscErrorCode MatSeqAIJCUSPARSECopyToGPU(Mat A)
1185 {
1186 
1187   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
1188   Mat_SeqAIJCUSPARSEMultStruct *matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
1189   Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
1190   PetscInt                     m = A->rmap->n,*ii,*ridx;
1191   PetscErrorCode               ierr;
1192   cusparseStatus_t             stat;
1193   cudaError_t                  err;
1194 
1195   PetscFunctionBegin;
1196   if (A->valid_GPU_matrix == PETSC_CUDA_UNALLOCATED || A->valid_GPU_matrix == PETSC_CUDA_CPU) {
1197     ierr = PetscLogEventBegin(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);
1198     if (A->assembled && A->nonzerostate == cusparsestruct->nonzerostate && cusparsestruct->format == MAT_CUSPARSE_CSR) {
1199       CsrMatrix *matrix = (CsrMatrix*)matstruct->mat;
1200       /* copy values only */
1201       matrix->values->assign(a->a, a->a+a->nz);
1202     } else {
1203       Mat_SeqAIJCUSPARSEMultStruct_Destroy(&matstruct,cusparsestruct->format);
1204       try {
1205         cusparsestruct->nonzerorow=0;
1206         for (int j = 0; j<m; j++) cusparsestruct->nonzerorow += ((a->i[j+1]-a->i[j])>0);
1207 
1208         if (a->compressedrow.use) {
1209           m    = a->compressedrow.nrows;
1210           ii   = a->compressedrow.i;
1211           ridx = a->compressedrow.rindex;
1212         } else {
1213           /* Forcing compressed row on the GPU */
1214           int k=0;
1215           ierr = PetscMalloc1(cusparsestruct->nonzerorow+1, &ii);CHKERRQ(ierr);
1216           ierr = PetscMalloc1(cusparsestruct->nonzerorow, &ridx);CHKERRQ(ierr);
1217           ii[0]=0;
1218           for (int j = 0; j<m; j++) {
1219             if ((a->i[j+1]-a->i[j])>0) {
1220               ii[k]  = a->i[j];
1221               ridx[k]= j;
1222               k++;
1223             }
1224           }
1225           ii[cusparsestruct->nonzerorow] = a->nz;
1226           m = cusparsestruct->nonzerorow;
1227         }
1228 
1229         /* allocate space for the triangular factor information */
1230         matstruct = new Mat_SeqAIJCUSPARSEMultStruct;
1231         stat = cusparseCreateMatDescr(&matstruct->descr);CHKERRCUDA(stat);
1232         stat = cusparseSetMatIndexBase(matstruct->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUDA(stat);
1233         stat = cusparseSetMatType(matstruct->descr, CUSPARSE_MATRIX_TYPE_GENERAL);CHKERRCUDA(stat);
1234 
1235         err = cudaMalloc((void **)&(matstruct->alpha),sizeof(PetscScalar));CHKERRCUDA(err);
1236         err = cudaMemcpy(matstruct->alpha,&ALPHA,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
1237         err = cudaMalloc((void **)&(matstruct->beta),sizeof(PetscScalar));CHKERRCUDA(err);
1238         err = cudaMemcpy(matstruct->beta,&BETA,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
1239         stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUDA(stat);
1240 
1241         /* Build a hybrid/ellpack matrix if this option is chosen for the storage */
1242         if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
1243           /* set the matrix */
1244           CsrMatrix *matrix= new CsrMatrix;
1245           matrix->num_rows = m;
1246           matrix->num_cols = A->cmap->n;
1247           matrix->num_entries = a->nz;
1248           matrix->row_offsets = new THRUSTINTARRAY32(m+1);
1249           matrix->row_offsets->assign(ii, ii + m+1);
1250 
1251           matrix->column_indices = new THRUSTINTARRAY32(a->nz);
1252           matrix->column_indices->assign(a->j, a->j+a->nz);
1253 
1254           matrix->values = new THRUSTARRAY(a->nz);
1255           matrix->values->assign(a->a, a->a+a->nz);
1256 
1257           /* assign the pointer */
1258           matstruct->mat = matrix;
1259 
1260         } else if (cusparsestruct->format==MAT_CUSPARSE_ELL || cusparsestruct->format==MAT_CUSPARSE_HYB) {
1261 #if CUDA_VERSION>=4020
1262           CsrMatrix *matrix= new CsrMatrix;
1263           matrix->num_rows = m;
1264           matrix->num_cols = A->cmap->n;
1265           matrix->num_entries = a->nz;
1266           matrix->row_offsets = new THRUSTINTARRAY32(m+1);
1267           matrix->row_offsets->assign(ii, ii + m+1);
1268 
1269           matrix->column_indices = new THRUSTINTARRAY32(a->nz);
1270           matrix->column_indices->assign(a->j, a->j+a->nz);
1271 
1272           matrix->values = new THRUSTARRAY(a->nz);
1273           matrix->values->assign(a->a, a->a+a->nz);
1274 
1275           cusparseHybMat_t hybMat;
1276           stat = cusparseCreateHybMat(&hybMat);CHKERRCUDA(stat);
1277           cusparseHybPartition_t partition = cusparsestruct->format==MAT_CUSPARSE_ELL ?
1278             CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
1279           stat = cusparse_csr2hyb(cusparsestruct->handle, matrix->num_rows, matrix->num_cols,
1280               matstruct->descr, matrix->values->data().get(),
1281               matrix->row_offsets->data().get(),
1282               matrix->column_indices->data().get(),
1283               hybMat, 0, partition);CHKERRCUDA(stat);
1284           /* assign the pointer */
1285           matstruct->mat = hybMat;
1286 
1287           if (matrix) {
1288             if (matrix->values) delete (THRUSTARRAY*)matrix->values;
1289             if (matrix->column_indices) delete (THRUSTINTARRAY32*)matrix->column_indices;
1290             if (matrix->row_offsets) delete (THRUSTINTARRAY32*)matrix->row_offsets;
1291             delete (CsrMatrix*)matrix;
1292           }
1293 #endif
1294         }
1295 
1296         /* assign the compressed row indices */
1297         matstruct->cprowIndices = new THRUSTINTARRAY(m);
1298         matstruct->cprowIndices->assign(ridx,ridx+m);
1299 
1300         /* assign the pointer */
1301         cusparsestruct->mat = matstruct;
1302 
1303         if (!a->compressedrow.use) {
1304           ierr = PetscFree(ii);CHKERRQ(ierr);
1305           ierr = PetscFree(ridx);CHKERRQ(ierr);
1306         }
1307         cusparsestruct->workVector = new THRUSTARRAY;
1308         cusparsestruct->workVector->resize(m);
1309       } catch(char *ex) {
1310         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
1311       }
1312       cusparsestruct->nonzerostate = A->nonzerostate;
1313     }
1314     ierr = WaitForGPU();CHKERRCUDA(ierr);
1315     A->valid_GPU_matrix = PETSC_CUDA_BOTH;
1316     ierr = PetscLogEventEnd(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);
1317   }
1318   PetscFunctionReturn(0);
1319 }
1320 
1321 static PetscErrorCode MatCreateVecs_SeqAIJCUSPARSE(Mat mat, Vec *right, Vec *left)
1322 {
1323   PetscErrorCode ierr;
1324   PetscInt rbs,cbs;
1325 
1326   PetscFunctionBegin;
1327   ierr = MatGetBlockSizes(mat,&rbs,&cbs);CHKERRQ(ierr);
1328   if (right) {
1329     ierr = VecCreate(PetscObjectComm((PetscObject)mat),right);CHKERRQ(ierr);
1330     ierr = VecSetSizes(*right,mat->cmap->n,PETSC_DETERMINE);CHKERRQ(ierr);
1331     ierr = VecSetBlockSize(*right,cbs);CHKERRQ(ierr);
1332     ierr = VecSetType(*right,VECSEQCUDA);CHKERRQ(ierr);
1333     ierr = PetscLayoutReference(mat->cmap,&(*right)->map);CHKERRQ(ierr);
1334   }
1335   if (left) {
1336     ierr = VecCreate(PetscObjectComm((PetscObject)mat),left);CHKERRQ(ierr);
1337     ierr = VecSetSizes(*left,mat->rmap->n,PETSC_DETERMINE);CHKERRQ(ierr);
1338     ierr = VecSetBlockSize(*left,rbs);CHKERRQ(ierr);
1339     ierr = VecSetType(*left,VECSEQCUDA);CHKERRQ(ierr);
1340     ierr = PetscLayoutReference(mat->rmap,&(*left)->map);CHKERRQ(ierr);
1341   }
1342   PetscFunctionReturn(0);
1343 }
1344 
1345 struct VecCUDAPlusEquals
1346 {
1347   template <typename Tuple>
1348   __host__ __device__
1349   void operator()(Tuple t)
1350   {
1351     thrust::get<1>(t) = thrust::get<1>(t) + thrust::get<0>(t);
1352   }
1353 };
1354 
1355 static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy)
1356 {
1357   Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
1358   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
1359   Mat_SeqAIJCUSPARSEMultStruct *matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
1360   const PetscScalar            *xarray;
1361   PetscScalar                  *yarray;
1362   PetscErrorCode               ierr;
1363   cusparseStatus_t             stat;
1364 
1365   PetscFunctionBegin;
1366   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
1367   ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
1368   ierr = VecCUDAGetArrayRead(xx,&xarray);CHKERRQ(ierr);
1369   ierr = VecSet(yy,0);CHKERRQ(ierr);
1370   ierr = VecCUDAGetArrayWrite(yy,&yarray);CHKERRQ(ierr);
1371   if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
1372     CsrMatrix *mat = (CsrMatrix*)matstruct->mat;
1373     stat = cusparse_csr_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1374                              mat->num_rows, mat->num_cols, mat->num_entries,
1375                              matstruct->alpha, matstruct->descr, mat->values->data().get(), mat->row_offsets->data().get(),
1376                              mat->column_indices->data().get(), xarray, matstruct->beta,
1377                              yarray);CHKERRCUDA(stat);
1378   } else {
1379 #if CUDA_VERSION>=4020
1380     cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
1381     stat = cusparse_hyb_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1382                              matstruct->alpha, matstruct->descr, hybMat,
1383                              xarray, matstruct->beta,
1384                              yarray);CHKERRCUDA(stat);
1385 #endif
1386   }
1387   ierr = VecCUDARestoreArrayRead(xx,&xarray);CHKERRQ(ierr);
1388   ierr = VecCUDARestoreArrayWrite(yy,&yarray);CHKERRQ(ierr);
1389   if (!cusparsestruct->stream) {
1390     ierr = WaitForGPU();CHKERRCUDA(ierr);
1391   }
1392   ierr = PetscLogFlops(2.0*a->nz - cusparsestruct->nonzerorow);CHKERRQ(ierr);
1393   PetscFunctionReturn(0);
1394 }
1395 
1396 static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy)
1397 {
1398   Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
1399   Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
1400   Mat_SeqAIJCUSPARSEMultStruct *matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
1401   const PetscScalar            *xarray;
1402   PetscScalar                  *yarray;
1403   PetscErrorCode               ierr;
1404   cusparseStatus_t             stat;
1405 
1406   PetscFunctionBegin;
1407   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
1408   ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
1409   if (!matstructT) {
1410     ierr = MatSeqAIJCUSPARSEGenerateTransposeForMult(A);CHKERRQ(ierr);
1411     matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
1412   }
1413   ierr = VecCUDAGetArrayRead(xx,&xarray);CHKERRQ(ierr);
1414   ierr = VecSet(yy,0);CHKERRQ(ierr);
1415   ierr = VecCUDAGetArrayWrite(yy,&yarray);CHKERRQ(ierr);
1416 
1417   if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
1418     CsrMatrix *mat = (CsrMatrix*)matstructT->mat;
1419     stat = cusparse_csr_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1420                              mat->num_rows, mat->num_cols,
1421                              mat->num_entries, matstructT->alpha, matstructT->descr,
1422                              mat->values->data().get(), mat->row_offsets->data().get(),
1423                              mat->column_indices->data().get(), xarray, matstructT->beta,
1424                              yarray);CHKERRCUDA(stat);
1425   } else {
1426 #if CUDA_VERSION>=4020
1427     cusparseHybMat_t hybMat = (cusparseHybMat_t)matstructT->mat;
1428     stat = cusparse_hyb_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1429                              matstructT->alpha, matstructT->descr, hybMat,
1430                              xarray, matstructT->beta,
1431                              yarray);CHKERRCUDA(stat);
1432 #endif
1433   }
1434   ierr = VecCUDARestoreArrayRead(xx,&xarray);CHKERRQ(ierr);
1435   ierr = VecCUDARestoreArrayWrite(yy,&yarray);CHKERRQ(ierr);
1436   if (!cusparsestruct->stream) {
1437     ierr = WaitForGPU();CHKERRCUDA(ierr);
1438   }
1439   ierr = PetscLogFlops(2.0*a->nz - cusparsestruct->nonzerorow);CHKERRQ(ierr);
1440   PetscFunctionReturn(0);
1441 }
1442 
1443 
1444 static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy,Vec zz)
1445 {
1446   Mat_SeqAIJ                      *a = (Mat_SeqAIJ*)A->data;
1447   Mat_SeqAIJCUSPARSE              *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
1448   Mat_SeqAIJCUSPARSEMultStruct    *matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
1449   thrust::device_ptr<PetscScalar> zptr;
1450   const PetscScalar               *xarray;
1451   PetscScalar                     *zarray;
1452   PetscErrorCode                  ierr;
1453   cusparseStatus_t                stat;
1454 
1455   PetscFunctionBegin;
1456   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
1457   ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
1458   try {
1459     ierr = VecCopy_SeqCUDA(yy,zz);CHKERRQ(ierr);
1460     ierr = VecCUDAGetArrayRead(xx,&xarray);CHKERRQ(ierr);
1461     ierr = VecCUDAGetArrayReadWrite(zz,&zarray);CHKERRQ(ierr);
1462     zptr = thrust::device_pointer_cast(zarray);
1463 
1464     /* multiply add */
1465     if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
1466       CsrMatrix *mat = (CsrMatrix*)matstruct->mat;
1467     /* here we need to be careful to set the number of rows in the multiply to the
1468        number of compressed rows in the matrix ... which is equivalent to the
1469        size of the workVector */
1470       stat = cusparse_csr_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1471                                mat->num_rows, mat->num_cols,
1472                                mat->num_entries, matstruct->alpha, matstruct->descr,
1473                                mat->values->data().get(), mat->row_offsets->data().get(),
1474                                mat->column_indices->data().get(), xarray, matstruct->beta,
1475                                cusparsestruct->workVector->data().get());CHKERRCUDA(stat);
1476     } else {
1477 #if CUDA_VERSION>=4020
1478       cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
1479       if (cusparsestruct->workVector->size()) {
1480         stat = cusparse_hyb_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1481             matstruct->alpha, matstruct->descr, hybMat,
1482             xarray, matstruct->beta,
1483             cusparsestruct->workVector->data().get());CHKERRCUDA(stat);
1484       }
1485 #endif
1486     }
1487 
1488     /* scatter the data from the temporary into the full vector with a += operation */
1489     thrust::for_each(thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))),
1490         thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))) + cusparsestruct->workVector->size(),
1491         VecCUDAPlusEquals());
1492     ierr = VecCUDARestoreArrayRead(xx,&xarray);CHKERRQ(ierr);
1493     ierr = VecCUDARestoreArrayReadWrite(zz,&zarray);CHKERRQ(ierr);
1494 
1495   } catch(char *ex) {
1496     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
1497   }
1498   ierr = WaitForGPU();CHKERRCUDA(ierr);
1499   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1500   PetscFunctionReturn(0);
1501 }
1502 
1503 static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy,Vec zz)
1504 {
1505   Mat_SeqAIJ                      *a = (Mat_SeqAIJ*)A->data;
1506   Mat_SeqAIJCUSPARSE              *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
1507   Mat_SeqAIJCUSPARSEMultStruct    *matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
1508   thrust::device_ptr<PetscScalar> zptr;
1509   const PetscScalar               *xarray;
1510   PetscScalar                     *zarray;
1511   PetscErrorCode                  ierr;
1512   cusparseStatus_t                stat;
1513 
1514   PetscFunctionBegin;
1515   /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
1516   ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
1517   if (!matstructT) {
1518     ierr = MatSeqAIJCUSPARSEGenerateTransposeForMult(A);CHKERRQ(ierr);
1519     matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
1520   }
1521 
1522   try {
1523     ierr = VecCopy_SeqCUDA(yy,zz);CHKERRQ(ierr);
1524     ierr = VecCUDAGetArrayRead(xx,&xarray);CHKERRQ(ierr);
1525     ierr = VecCUDAGetArrayReadWrite(zz,&zarray);CHKERRQ(ierr);
1526     zptr = thrust::device_pointer_cast(zarray);
1527 
1528     /* multiply add with matrix transpose */
1529     if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
1530       CsrMatrix *mat = (CsrMatrix*)matstructT->mat;
1531       /* here we need to be careful to set the number of rows in the multiply to the
1532          number of compressed rows in the matrix ... which is equivalent to the
1533          size of the workVector */
1534       stat = cusparse_csr_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1535                                mat->num_rows, mat->num_cols,
1536                                mat->num_entries, matstructT->alpha, matstructT->descr,
1537                                mat->values->data().get(), mat->row_offsets->data().get(),
1538                                mat->column_indices->data().get(), xarray, matstructT->beta,
1539                                cusparsestruct->workVector->data().get());CHKERRCUDA(stat);
1540     } else {
1541 #if CUDA_VERSION>=4020
1542       cusparseHybMat_t hybMat = (cusparseHybMat_t)matstructT->mat;
1543       if (cusparsestruct->workVector->size()) {
1544         stat = cusparse_hyb_spmv(cusparsestruct->handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
1545             matstructT->alpha, matstructT->descr, hybMat,
1546             xarray, matstructT->beta,
1547             cusparsestruct->workVector->data().get());CHKERRCUDA(stat);
1548       }
1549 #endif
1550     }
1551 
1552     /* scatter the data from the temporary into the full vector with a += operation */
1553     thrust::for_each(thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstructT->cprowIndices->begin()))),
1554         thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstructT->cprowIndices->begin()))) + cusparsestruct->workVector->size(),
1555         VecCUDAPlusEquals());
1556 
1557     ierr = VecCUDARestoreArrayRead(xx,&xarray);CHKERRQ(ierr);
1558     ierr = VecCUDARestoreArrayReadWrite(zz,&zarray);CHKERRQ(ierr);
1559 
1560   } catch(char *ex) {
1561     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
1562   }
1563   ierr = WaitForGPU();CHKERRCUDA(ierr);
1564   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1565   PetscFunctionReturn(0);
1566 }
1567 
1568 static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A,MatAssemblyType mode)
1569 {
1570   PetscErrorCode ierr;
1571 
1572   PetscFunctionBegin;
1573   ierr = MatAssemblyEnd_SeqAIJ(A,mode);CHKERRQ(ierr);
1574   if (A->factortype==MAT_FACTOR_NONE) {
1575     ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
1576   }
1577   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
1578   A->ops->mult             = MatMult_SeqAIJCUSPARSE;
1579   A->ops->multadd          = MatMultAdd_SeqAIJCUSPARSE;
1580   A->ops->multtranspose    = MatMultTranspose_SeqAIJCUSPARSE;
1581   A->ops->multtransposeadd = MatMultTransposeAdd_SeqAIJCUSPARSE;
1582   PetscFunctionReturn(0);
1583 }
1584 
1585 /* --------------------------------------------------------------------------------*/
1586 /*@
1587    MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in AIJ (compressed row) format
1588    (the default parallel PETSc format). This matrix will ultimately pushed down
1589    to NVidia GPUs and use the CUSPARSE library for calculations. For good matrix
1590    assembly performance the user should preallocate the matrix storage by setting
1591    the parameter nz (or the array nnz).  By setting these parameters accurately,
1592    performance during matrix assembly can be increased by more than a factor of 50.
1593 
1594    Collective on MPI_Comm
1595 
1596    Input Parameters:
1597 +  comm - MPI communicator, set to PETSC_COMM_SELF
1598 .  m - number of rows
1599 .  n - number of columns
1600 .  nz - number of nonzeros per row (same for all rows)
1601 -  nnz - array containing the number of nonzeros in the various rows
1602          (possibly different for each row) or NULL
1603 
1604    Output Parameter:
1605 .  A - the matrix
1606 
1607    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
1608    MatXXXXSetPreallocation() paradgm instead of this routine directly.
1609    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
1610 
1611    Notes:
1612    If nnz is given then nz is ignored
1613 
1614    The AIJ format (also called the Yale sparse matrix format or
1615    compressed row storage), is fully compatible with standard Fortran 77
1616    storage.  That is, the stored row and column indices can begin at
1617    either one (as in Fortran) or zero.  See the users' manual for details.
1618 
1619    Specify the preallocated storage with either nz or nnz (not both).
1620    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
1621    allocation.  For large problems you MUST preallocate memory or you
1622    will get TERRIBLE performance, see the users' manual chapter on matrices.
1623 
1624    By default, this format uses inodes (identical nodes) when possible, to
1625    improve numerical efficiency of matrix-vector products and solves. We
1626    search for consecutive rows with the same nonzero structure, thereby
1627    reusing matrix information to achieve increased efficiency.
1628 
1629    Level: intermediate
1630 
1631 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatCreateAIJ(), MATSEQAIJCUSPARSE, MATAIJCUSPARSE
1632 @*/
1633 PetscErrorCode  MatCreateSeqAIJCUSPARSE(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
1634 {
1635   PetscErrorCode ierr;
1636 
1637   PetscFunctionBegin;
1638   ierr = MatCreate(comm,A);CHKERRQ(ierr);
1639   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
1640   ierr = MatSetType(*A,MATSEQAIJCUSPARSE);CHKERRQ(ierr);
1641   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,(PetscInt*)nnz);CHKERRQ(ierr);
1642   PetscFunctionReturn(0);
1643 }
1644 
1645 static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
1646 {
1647   PetscErrorCode   ierr;
1648 
1649   PetscFunctionBegin;
1650   if (A->factortype==MAT_FACTOR_NONE) {
1651     if (A->valid_GPU_matrix != PETSC_CUDA_UNALLOCATED) {
1652       ierr = Mat_SeqAIJCUSPARSE_Destroy((Mat_SeqAIJCUSPARSE**)&A->spptr);CHKERRQ(ierr);
1653     }
1654   } else {
1655     ierr = Mat_SeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors**)&A->spptr);CHKERRQ(ierr);
1656   }
1657   ierr = MatDestroy_SeqAIJ(A);CHKERRQ(ierr);
1658   PetscFunctionReturn(0);
1659 }
1660 
1661 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
1662 {
1663   PetscErrorCode ierr;
1664   cusparseStatus_t stat;
1665   cusparseHandle_t handle=0;
1666 
1667   PetscFunctionBegin;
1668   ierr = MatCreate_SeqAIJ(B);CHKERRQ(ierr);
1669   if (B->factortype==MAT_FACTOR_NONE) {
1670     /* you cannot check the inode.use flag here since the matrix was just created.
1671        now build a GPU matrix data structure */
1672     B->spptr = new Mat_SeqAIJCUSPARSE;
1673     ((Mat_SeqAIJCUSPARSE*)B->spptr)->mat          = 0;
1674     ((Mat_SeqAIJCUSPARSE*)B->spptr)->matTranspose = 0;
1675     ((Mat_SeqAIJCUSPARSE*)B->spptr)->workVector   = 0;
1676     ((Mat_SeqAIJCUSPARSE*)B->spptr)->format       = MAT_CUSPARSE_CSR;
1677     ((Mat_SeqAIJCUSPARSE*)B->spptr)->stream       = 0;
1678     ((Mat_SeqAIJCUSPARSE*)B->spptr)->handle       = 0;
1679     stat = cusparseCreate(&handle);CHKERRCUDA(stat);
1680     ((Mat_SeqAIJCUSPARSE*)B->spptr)->handle       = handle;
1681     ((Mat_SeqAIJCUSPARSE*)B->spptr)->stream       = 0;
1682   } else {
1683     /* NEXT, set the pointers to the triangular factors */
1684     B->spptr = new Mat_SeqAIJCUSPARSETriFactors;
1685     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->loTriFactorPtr          = 0;
1686     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->upTriFactorPtr          = 0;
1687     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->loTriFactorPtrTranspose = 0;
1688     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->upTriFactorPtrTranspose = 0;
1689     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->rpermIndices            = 0;
1690     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->cpermIndices            = 0;
1691     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->workVector              = 0;
1692     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->handle                  = 0;
1693     stat = cusparseCreate(&handle);CHKERRCUDA(stat);
1694     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->handle                  = handle;
1695     ((Mat_SeqAIJCUSPARSETriFactors*)B->spptr)->nnz                     = 0;
1696   }
1697 
1698   B->ops->assemblyend      = MatAssemblyEnd_SeqAIJCUSPARSE;
1699   B->ops->destroy          = MatDestroy_SeqAIJCUSPARSE;
1700   B->ops->getvecs          = MatCreateVecs_SeqAIJCUSPARSE;
1701   B->ops->setfromoptions   = MatSetFromOptions_SeqAIJCUSPARSE;
1702   B->ops->mult             = MatMult_SeqAIJCUSPARSE;
1703   B->ops->multadd          = MatMultAdd_SeqAIJCUSPARSE;
1704   B->ops->multtranspose    = MatMultTranspose_SeqAIJCUSPARSE;
1705   B->ops->multtransposeadd = MatMultTransposeAdd_SeqAIJCUSPARSE;
1706 
1707   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJCUSPARSE);CHKERRQ(ierr);
1708 
1709   B->valid_GPU_matrix = PETSC_CUDA_UNALLOCATED;
1710 
1711   ierr = PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetFormat_C", MatCUSPARSESetFormat_SeqAIJCUSPARSE);CHKERRQ(ierr);
1712   PetscFunctionReturn(0);
1713 }
1714 
1715 /*M
1716    MATSEQAIJCUSPARSE - MATAIJCUSPARSE = "(seq)aijcusparse" - A matrix type to be used for sparse matrices.
1717 
1718    A matrix type type whose data resides on Nvidia GPUs. These matrices can be in either
1719    CSR, ELL, or Hybrid format. The ELL and HYB formats require CUDA 4.2 or later.
1720    All matrix calculations are performed on Nvidia GPUs using the CUSPARSE library.
1721 
1722    Options Database Keys:
1723 +  -mat_type aijcusparse - sets the matrix type to "seqaijcusparse" during a call to MatSetFromOptions()
1724 .  -mat_cusparse_storage_format csr - sets the storage format of matrices (for MatMult and factors in MatSolve) during a call to MatSetFromOptions(). Other options include ell (ellpack) or hyb (hybrid).
1725 .  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for MatMult) during a call to MatSetFromOptions(). Other options include ell (ellpack) or hyb (hybrid).
1726 
1727   Level: beginner
1728 
1729 .seealso: MatCreateSeqAIJCUSPARSE(), MATAIJCUSPARSE, MatCreateAIJCUSPARSE(), MatCUSPARSESetFormat(), MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
1730 M*/
1731 
1732 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat,MatFactorType,Mat*);
1733 
1734 
1735 PETSC_EXTERN PetscErrorCode MatSolverPackageRegister_CUSPARSE(void)
1736 {
1737   PetscErrorCode ierr;
1738 
1739   PetscFunctionBegin;
1740   ierr = MatSolverPackageRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_LU,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
1741   ierr = MatSolverPackageRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_CHOLESKY,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
1742   ierr = MatSolverPackageRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_ILU,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
1743   ierr = MatSolverPackageRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_ICC,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
1744   PetscFunctionReturn(0);
1745 }
1746 
1747 
1748 static PetscErrorCode Mat_SeqAIJCUSPARSE_Destroy(Mat_SeqAIJCUSPARSE **cusparsestruct)
1749 {
1750   cusparseStatus_t stat;
1751   cusparseHandle_t handle;
1752 
1753   PetscFunctionBegin;
1754   if (*cusparsestruct) {
1755     Mat_SeqAIJCUSPARSEMultStruct_Destroy(&(*cusparsestruct)->mat,(*cusparsestruct)->format);
1756     Mat_SeqAIJCUSPARSEMultStruct_Destroy(&(*cusparsestruct)->matTranspose,(*cusparsestruct)->format);
1757     delete (*cusparsestruct)->workVector;
1758     if (handle = (*cusparsestruct)->handle) {
1759       stat = cusparseDestroy(handle);CHKERRCUDA(stat);
1760     }
1761     delete *cusparsestruct;
1762     *cusparsestruct = 0;
1763   }
1764   PetscFunctionReturn(0);
1765 }
1766 
1767 static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **mat)
1768 {
1769   PetscFunctionBegin;
1770   if (*mat) {
1771     delete (*mat)->values;
1772     delete (*mat)->column_indices;
1773     delete (*mat)->row_offsets;
1774     delete *mat;
1775     *mat = 0;
1776   }
1777   PetscFunctionReturn(0);
1778 }
1779 
1780 static PetscErrorCode Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
1781 {
1782   cusparseStatus_t stat;
1783   PetscErrorCode   ierr;
1784 
1785   PetscFunctionBegin;
1786   if (*trifactor) {
1787     if ((*trifactor)->descr) { stat = cusparseDestroyMatDescr((*trifactor)->descr);CHKERRCUDA(stat); }
1788     if ((*trifactor)->solveInfo) { stat = cusparseDestroySolveAnalysisInfo((*trifactor)->solveInfo);CHKERRCUDA(stat); }
1789     ierr = CsrMatrix_Destroy(&(*trifactor)->csrMat);CHKERRQ(ierr);
1790     delete *trifactor;
1791     *trifactor = 0;
1792   }
1793   PetscFunctionReturn(0);
1794 }
1795 
1796 static PetscErrorCode Mat_SeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct,MatCUSPARSEStorageFormat format)
1797 {
1798   CsrMatrix        *mat;
1799   cusparseStatus_t stat;
1800   cudaError_t      err;
1801 
1802   PetscFunctionBegin;
1803   if (*matstruct) {
1804     if ((*matstruct)->mat) {
1805       if (format==MAT_CUSPARSE_ELL || format==MAT_CUSPARSE_HYB) {
1806         cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
1807         stat = cusparseDestroyHybMat(hybMat);CHKERRCUDA(stat);
1808       } else {
1809         mat = (CsrMatrix*)(*matstruct)->mat;
1810         CsrMatrix_Destroy(&mat);
1811       }
1812     }
1813     if ((*matstruct)->descr) { stat = cusparseDestroyMatDescr((*matstruct)->descr);CHKERRCUDA(stat); }
1814     delete (*matstruct)->cprowIndices;
1815     if ((*matstruct)->alpha) { err=cudaFree((*matstruct)->alpha);CHKERRCUDA(err); }
1816     if ((*matstruct)->beta) { err=cudaFree((*matstruct)->beta);CHKERRCUDA(err); }
1817     delete *matstruct;
1818     *matstruct = 0;
1819   }
1820   PetscFunctionReturn(0);
1821 }
1822 
1823 static PetscErrorCode Mat_SeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors** trifactors)
1824 {
1825   cusparseHandle_t handle;
1826   cusparseStatus_t stat;
1827 
1828   PetscFunctionBegin;
1829   if (*trifactors) {
1830     Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(&(*trifactors)->loTriFactorPtr);
1831     Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(&(*trifactors)->upTriFactorPtr);
1832     Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(&(*trifactors)->loTriFactorPtrTranspose);
1833     Mat_SeqAIJCUSPARSETriFactorStruct_Destroy(&(*trifactors)->upTriFactorPtrTranspose);
1834     delete (*trifactors)->rpermIndices;
1835     delete (*trifactors)->cpermIndices;
1836     delete (*trifactors)->workVector;
1837     if (handle = (*trifactors)->handle) {
1838       stat = cusparseDestroy(handle);CHKERRCUDA(stat);
1839     }
1840     delete *trifactors;
1841     *trifactors = 0;
1842   }
1843   PetscFunctionReturn(0);
1844 }
1845 
1846