xref: /petsc/src/mat/impls/dense/mpi/mpidense.c (revision a4efd8ea4bb0600a5aef92b2c23cbfa314827193)
1 #define PETSCMAT_DLL
2 
3 /*
4    Basic functions for basic parallel dense matrices.
5 */
6 
7 
8 #include "src/mat/impls/dense/mpi/mpidense.h"    /*I   "petscmat.h"  I*/
9 #if defined(PETSC_HAVE_PLAPACK)
10 static PetscMPIInt Plapack_nprows,Plapack_npcols,Plapack_ierror,Plapack_nb_alg;
11 static MPI_Comm Plapack_comm_2d;
12 #endif
13 
14 #undef __FUNCT__
15 #define __FUNCT__ "MatDenseGetLocalMatrix"
16 /*@
17 
18       MatDenseGetLocalMatrix - For a MATMPIDENSE or MATSEQDENSE matrix returns the sequential
19               matrix that represents the operator. For sequential matrices it returns itself.
20 
21     Input Parameter:
22 .      A - the Seq or MPI dense matrix
23 
24     Output Parameter:
25 .      B - the inner matrix
26 
27     Level: intermediate
28 
29 @*/
30 PetscErrorCode MatDenseGetLocalMatrix(Mat A,Mat *B)
31 {
32   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
33   PetscErrorCode ierr;
34   PetscTruth     flg;
35 
36   PetscFunctionBegin;
37   ierr = PetscTypeCompare((PetscObject)A,MATMPIDENSE,&flg);CHKERRQ(ierr);
38   if (flg) {
39     *B = mat->A;
40   } else {
41     *B = A;
42   }
43   PetscFunctionReturn(0);
44 }
45 
46 #undef __FUNCT__
47 #define __FUNCT__ "MatGetRow_MPIDense"
48 PetscErrorCode MatGetRow_MPIDense(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
49 {
50   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
51   PetscErrorCode ierr;
52   PetscInt       lrow,rstart = A->rmap->rstart,rend = A->rmap->rend;
53 
54   PetscFunctionBegin;
55   if (row < rstart || row >= rend) SETERRQ(PETSC_ERR_SUP,"only local rows")
56   lrow = row - rstart;
57   ierr = MatGetRow(mat->A,lrow,nz,(const PetscInt **)idx,(const PetscScalar **)v);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 
61 #undef __FUNCT__
62 #define __FUNCT__ "MatRestoreRow_MPIDense"
63 PetscErrorCode MatRestoreRow_MPIDense(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
64 {
65   PetscErrorCode ierr;
66 
67   PetscFunctionBegin;
68   if (idx) {ierr = PetscFree(*idx);CHKERRQ(ierr);}
69   if (v) {ierr = PetscFree(*v);CHKERRQ(ierr);}
70   PetscFunctionReturn(0);
71 }
72 
73 EXTERN_C_BEGIN
74 #undef __FUNCT__
75 #define __FUNCT__ "MatGetDiagonalBlock_MPIDense"
76 PetscErrorCode PETSCMAT_DLLEXPORT MatGetDiagonalBlock_MPIDense(Mat A,PetscTruth *iscopy,MatReuse reuse,Mat *B)
77 {
78   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
79   PetscErrorCode ierr;
80   PetscInt       m = A->rmap->n,rstart = A->rmap->rstart;
81   PetscScalar    *array;
82   MPI_Comm       comm;
83 
84   PetscFunctionBegin;
85   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_SUP,"Only square matrices supported.");
86 
87   /* The reuse aspect is not implemented efficiently */
88   if (reuse) { ierr = MatDestroy(*B);CHKERRQ(ierr);}
89 
90   ierr = PetscObjectGetComm((PetscObject)(mdn->A),&comm);CHKERRQ(ierr);
91   ierr = MatGetArray(mdn->A,&array);CHKERRQ(ierr);
92   ierr = MatCreate(comm,B);CHKERRQ(ierr);
93   ierr = MatSetSizes(*B,m,m,m,m);CHKERRQ(ierr);
94   ierr = MatSetType(*B,((PetscObject)mdn->A)->type_name);CHKERRQ(ierr);
95   ierr = MatSeqDenseSetPreallocation(*B,array+m*rstart);CHKERRQ(ierr);
96   ierr = MatRestoreArray(mdn->A,&array);CHKERRQ(ierr);
97   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
98   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
99 
100   *iscopy = PETSC_TRUE;
101   PetscFunctionReturn(0);
102 }
103 EXTERN_C_END
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "MatSetValues_MPIDense"
107 PetscErrorCode MatSetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
108 {
109   Mat_MPIDense   *A = (Mat_MPIDense*)mat->data;
110   PetscErrorCode ierr;
111   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend,row;
112   PetscTruth     roworiented = A->roworiented;
113 
114   PetscFunctionBegin;
115   for (i=0; i<m; i++) {
116     if (idxm[i] < 0) continue;
117     if (idxm[i] >= mat->rmap->N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
118     if (idxm[i] >= rstart && idxm[i] < rend) {
119       row = idxm[i] - rstart;
120       if (roworiented) {
121         ierr = MatSetValues(A->A,1,&row,n,idxn,v+i*n,addv);CHKERRQ(ierr);
122       } else {
123         for (j=0; j<n; j++) {
124           if (idxn[j] < 0) continue;
125           if (idxn[j] >= mat->cmap->N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
126           ierr = MatSetValues(A->A,1,&row,1,&idxn[j],v+i+j*m,addv);CHKERRQ(ierr);
127         }
128       }
129     } else {
130       if (!A->donotstash) {
131         if (roworiented) {
132           ierr = MatStashValuesRow_Private(&mat->stash,idxm[i],n,idxn,v+i*n);CHKERRQ(ierr);
133         } else {
134           ierr = MatStashValuesCol_Private(&mat->stash,idxm[i],n,idxn,v+i,m);CHKERRQ(ierr);
135         }
136       }
137     }
138   }
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "MatGetValues_MPIDense"
144 PetscErrorCode MatGetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
145 {
146   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
147   PetscErrorCode ierr;
148   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend,row;
149 
150   PetscFunctionBegin;
151   for (i=0; i<m; i++) {
152     if (idxm[i] < 0) continue; /* SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative row"); */
153     if (idxm[i] >= mat->rmap->N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
154     if (idxm[i] >= rstart && idxm[i] < rend) {
155       row = idxm[i] - rstart;
156       for (j=0; j<n; j++) {
157         if (idxn[j] < 0) continue; /* SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative column"); */
158         if (idxn[j] >= mat->cmap->N) {
159           SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
160         }
161         ierr = MatGetValues(mdn->A,1,&row,1,&idxn[j],v+i*n+j);CHKERRQ(ierr);
162       }
163     } else {
164       SETERRQ(PETSC_ERR_SUP,"Only local values currently supported");
165     }
166   }
167   PetscFunctionReturn(0);
168 }
169 
170 #undef __FUNCT__
171 #define __FUNCT__ "MatGetArray_MPIDense"
172 PetscErrorCode MatGetArray_MPIDense(Mat A,PetscScalar *array[])
173 {
174   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
175   PetscErrorCode ierr;
176 
177   PetscFunctionBegin;
178   ierr = MatGetArray(a->A,array);CHKERRQ(ierr);
179   PetscFunctionReturn(0);
180 }
181 
182 #undef __FUNCT__
183 #define __FUNCT__ "MatGetSubMatrix_MPIDense"
184 static PetscErrorCode MatGetSubMatrix_MPIDense(Mat A,IS isrow,IS iscol,PetscInt cs,MatReuse scall,Mat *B)
185 {
186   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data,*newmatd;
187   Mat_SeqDense   *lmat = (Mat_SeqDense*)mat->A->data;
188   PetscErrorCode ierr;
189   PetscInt       i,j,*irow,*icol,rstart,rend,nrows,ncols,nlrows,nlcols;
190   PetscScalar    *av,*bv,*v = lmat->v;
191   Mat            newmat;
192 
193   PetscFunctionBegin;
194   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
195   ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
196   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
197   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
198 
199   /* No parallel redistribution currently supported! Should really check each index set
200      to comfirm that it is OK.  ... Currently supports only submatrix same partitioning as
201      original matrix! */
202 
203   ierr = MatGetLocalSize(A,&nlrows,&nlcols);CHKERRQ(ierr);
204   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
205 
206   /* Check submatrix call */
207   if (scall == MAT_REUSE_MATRIX) {
208     /* SETERRQ(PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size"); */
209     /* Really need to test rows and column sizes! */
210     newmat = *B;
211   } else {
212     /* Create and fill new matrix */
213     ierr = MatCreate(((PetscObject)A)->comm,&newmat);CHKERRQ(ierr);
214     ierr = MatSetSizes(newmat,nrows,cs,PETSC_DECIDE,ncols);CHKERRQ(ierr);
215     ierr = MatSetType(newmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
216     ierr = MatMPIDenseSetPreallocation(newmat,PETSC_NULL);CHKERRQ(ierr);
217   }
218 
219   /* Now extract the data pointers and do the copy, column at a time */
220   newmatd = (Mat_MPIDense*)newmat->data;
221   bv      = ((Mat_SeqDense *)newmatd->A->data)->v;
222 
223   for (i=0; i<ncols; i++) {
224     av = v + nlrows*icol[i];
225     for (j=0; j<nrows; j++) {
226       *bv++ = av[irow[j] - rstart];
227     }
228   }
229 
230   /* Assemble the matrices so that the correct flags are set */
231   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
232   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
233 
234   /* Free work space */
235   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
236   ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
237   *B = newmat;
238   PetscFunctionReturn(0);
239 }
240 
241 #undef __FUNCT__
242 #define __FUNCT__ "MatRestoreArray_MPIDense"
243 PetscErrorCode MatRestoreArray_MPIDense(Mat A,PetscScalar *array[])
244 {
245   PetscFunctionBegin;
246   PetscFunctionReturn(0);
247 }
248 
249 #undef __FUNCT__
250 #define __FUNCT__ "MatAssemblyBegin_MPIDense"
251 PetscErrorCode MatAssemblyBegin_MPIDense(Mat mat,MatAssemblyType mode)
252 {
253   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
254   MPI_Comm       comm = ((PetscObject)mat)->comm;
255   PetscErrorCode ierr;
256   PetscInt       nstash,reallocs;
257   InsertMode     addv;
258 
259   PetscFunctionBegin;
260   /* make sure all processors are either in INSERTMODE or ADDMODE */
261   ierr = MPI_Allreduce(&mat->insertmode,&addv,1,MPI_INT,MPI_BOR,comm);CHKERRQ(ierr);
262   if (addv == (ADD_VALUES|INSERT_VALUES)) {
263     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Cannot mix adds/inserts on different procs");
264   }
265   mat->insertmode = addv; /* in case this processor had no cache */
266 
267   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
268   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
269   ierr = PetscInfo2(mdn->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
270   PetscFunctionReturn(0);
271 }
272 
273 #undef __FUNCT__
274 #define __FUNCT__ "MatAssemblyEnd_MPIDense"
275 PetscErrorCode MatAssemblyEnd_MPIDense(Mat mat,MatAssemblyType mode)
276 {
277   Mat_MPIDense    *mdn=(Mat_MPIDense*)mat->data;
278   PetscErrorCode  ierr;
279   PetscInt        i,*row,*col,flg,j,rstart,ncols;
280   PetscMPIInt     n;
281   PetscScalar     *val;
282   InsertMode      addv=mat->insertmode;
283 
284   PetscFunctionBegin;
285   /*  wait on receives */
286   while (1) {
287     ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
288     if (!flg) break;
289 
290     for (i=0; i<n;) {
291       /* Now identify the consecutive vals belonging to the same row */
292       for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
293       if (j < n) ncols = j-i;
294       else       ncols = n-i;
295       /* Now assemble all these values with a single function call */
296       ierr = MatSetValues_MPIDense(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
297       i = j;
298     }
299   }
300   ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
301 
302   ierr = MatAssemblyBegin(mdn->A,mode);CHKERRQ(ierr);
303   ierr = MatAssemblyEnd(mdn->A,mode);CHKERRQ(ierr);
304 
305   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
306     ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
307   }
308   PetscFunctionReturn(0);
309 }
310 
311 #undef __FUNCT__
312 #define __FUNCT__ "MatZeroEntries_MPIDense"
313 PetscErrorCode MatZeroEntries_MPIDense(Mat A)
314 {
315   PetscErrorCode ierr;
316   Mat_MPIDense   *l = (Mat_MPIDense*)A->data;
317 
318   PetscFunctionBegin;
319   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
320   PetscFunctionReturn(0);
321 }
322 
323 /* the code does not do the diagonal entries correctly unless the
324    matrix is square and the column and row owerships are identical.
325    This is a BUG. The only way to fix it seems to be to access
326    mdn->A and mdn->B directly and not through the MatZeroRows()
327    routine.
328 */
329 #undef __FUNCT__
330 #define __FUNCT__ "MatZeroRows_MPIDense"
331 PetscErrorCode MatZeroRows_MPIDense(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag)
332 {
333   Mat_MPIDense   *l = (Mat_MPIDense*)A->data;
334   PetscErrorCode ierr;
335   PetscInt       i,*owners = A->rmap->range;
336   PetscInt       *nprocs,j,idx,nsends;
337   PetscInt       nmax,*svalues,*starts,*owner,nrecvs;
338   PetscInt       *rvalues,tag = ((PetscObject)A)->tag,count,base,slen,*source;
339   PetscInt       *lens,*lrows,*values;
340   PetscMPIInt    n,imdex,rank = l->rank,size = l->size;
341   MPI_Comm       comm = ((PetscObject)A)->comm;
342   MPI_Request    *send_waits,*recv_waits;
343   MPI_Status     recv_status,*send_status;
344   PetscTruth     found;
345 
346   PetscFunctionBegin;
347   /*  first count number of contributors to each processor */
348   ierr  = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
349   ierr  = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
350   ierr  = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
351   for (i=0; i<N; i++) {
352     idx = rows[i];
353     found = PETSC_FALSE;
354     for (j=0; j<size; j++) {
355       if (idx >= owners[j] && idx < owners[j+1]) {
356         nprocs[2*j]++; nprocs[2*j+1] = 1; owner[i] = j; found = PETSC_TRUE; break;
357       }
358     }
359     if (!found) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
360   }
361   nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}
362 
363   /* inform other processors of number of messages and max length*/
364   ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
365 
366   /* post receives:   */
367   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
368   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
369   for (i=0; i<nrecvs; i++) {
370     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
371   }
372 
373   /* do sends:
374       1) starts[i] gives the starting index in svalues for stuff going to
375          the ith processor
376   */
377   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
378   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
379   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
380   starts[0]  = 0;
381   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
382   for (i=0; i<N; i++) {
383     svalues[starts[owner[i]]++] = rows[i];
384   }
385 
386   starts[0] = 0;
387   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
388   count = 0;
389   for (i=0; i<size; i++) {
390     if (nprocs[2*i+1]) {
391       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
392     }
393   }
394   ierr = PetscFree(starts);CHKERRQ(ierr);
395 
396   base = owners[rank];
397 
398   /*  wait on receives */
399   ierr   = PetscMalloc(2*(nrecvs+1)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
400   source = lens + nrecvs;
401   count  = nrecvs; slen = 0;
402   while (count) {
403     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
404     /* unpack receives into our local space */
405     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
406     source[imdex]  = recv_status.MPI_SOURCE;
407     lens[imdex]    = n;
408     slen += n;
409     count--;
410   }
411   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
412 
413   /* move the data into the send scatter */
414   ierr = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
415   count = 0;
416   for (i=0; i<nrecvs; i++) {
417     values = rvalues + i*nmax;
418     for (j=0; j<lens[i]; j++) {
419       lrows[count++] = values[j] - base;
420     }
421   }
422   ierr = PetscFree(rvalues);CHKERRQ(ierr);
423   ierr = PetscFree(lens);CHKERRQ(ierr);
424   ierr = PetscFree(owner);CHKERRQ(ierr);
425   ierr = PetscFree(nprocs);CHKERRQ(ierr);
426 
427   /* actually zap the local rows */
428   ierr = MatZeroRows(l->A,slen,lrows,diag);CHKERRQ(ierr);
429   ierr = PetscFree(lrows);CHKERRQ(ierr);
430 
431   /* wait on sends */
432   if (nsends) {
433     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
434     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
435     ierr = PetscFree(send_status);CHKERRQ(ierr);
436   }
437   ierr = PetscFree(send_waits);CHKERRQ(ierr);
438   ierr = PetscFree(svalues);CHKERRQ(ierr);
439 
440   PetscFunctionReturn(0);
441 }
442 
443 #undef __FUNCT__
444 #define __FUNCT__ "MatMult_MPIDense"
445 PetscErrorCode MatMult_MPIDense(Mat mat,Vec xx,Vec yy)
446 {
447   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
448   PetscErrorCode ierr;
449 
450   PetscFunctionBegin;
451   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
452   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
453   ierr = MatMult_SeqDense(mdn->A,mdn->lvec,yy);CHKERRQ(ierr);
454   PetscFunctionReturn(0);
455 }
456 
457 #undef __FUNCT__
458 #define __FUNCT__ "MatMultAdd_MPIDense"
459 PetscErrorCode MatMultAdd_MPIDense(Mat mat,Vec xx,Vec yy,Vec zz)
460 {
461   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
462   PetscErrorCode ierr;
463 
464   PetscFunctionBegin;
465   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
466   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
467   ierr = MatMultAdd_SeqDense(mdn->A,mdn->lvec,yy,zz);CHKERRQ(ierr);
468   PetscFunctionReturn(0);
469 }
470 
471 #undef __FUNCT__
472 #define __FUNCT__ "MatMultTranspose_MPIDense"
473 PetscErrorCode MatMultTranspose_MPIDense(Mat A,Vec xx,Vec yy)
474 {
475   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
476   PetscErrorCode ierr;
477   PetscScalar    zero = 0.0;
478 
479   PetscFunctionBegin;
480   ierr = VecSet(yy,zero);CHKERRQ(ierr);
481   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
482   ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
483   ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
484   PetscFunctionReturn(0);
485 }
486 
487 #undef __FUNCT__
488 #define __FUNCT__ "MatMultTransposeAdd_MPIDense"
489 PetscErrorCode MatMultTransposeAdd_MPIDense(Mat A,Vec xx,Vec yy,Vec zz)
490 {
491   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
492   PetscErrorCode ierr;
493 
494   PetscFunctionBegin;
495   ierr = VecCopy(yy,zz);CHKERRQ(ierr);
496   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
497   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
498   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
499   PetscFunctionReturn(0);
500 }
501 
502 #undef __FUNCT__
503 #define __FUNCT__ "MatGetDiagonal_MPIDense"
504 PetscErrorCode MatGetDiagonal_MPIDense(Mat A,Vec v)
505 {
506   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
507   Mat_SeqDense   *aloc = (Mat_SeqDense*)a->A->data;
508   PetscErrorCode ierr;
509   PetscInt       len,i,n,m = A->rmap->n,radd;
510   PetscScalar    *x,zero = 0.0;
511 
512   PetscFunctionBegin;
513   ierr = VecSet(v,zero);CHKERRQ(ierr);
514   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
515   ierr = VecGetSize(v,&n);CHKERRQ(ierr);
516   if (n != A->rmap->N) SETERRQ(PETSC_ERR_ARG_SIZ,"Nonconforming mat and vec");
517   len  = PetscMin(a->A->rmap->n,a->A->cmap->n);
518   radd = A->rmap->rstart*m;
519   for (i=0; i<len; i++) {
520     x[i] = aloc->v[radd + i*m + i];
521   }
522   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatDestroy_MPIDense"
528 PetscErrorCode MatDestroy_MPIDense(Mat mat)
529 {
530   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
531   PetscErrorCode ierr;
532 #if defined(PETSC_HAVE_PLAPACK)
533   Mat_Plapack   *lu=(Mat_Plapack*)(mat->spptr);
534 #endif
535 
536   PetscFunctionBegin;
537 
538 #if defined(PETSC_USE_LOG)
539   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
540 #endif
541   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
542   ierr = MatDestroy(mdn->A);CHKERRQ(ierr);
543   if (mdn->lvec)   {ierr = VecDestroy(mdn->lvec);CHKERRQ(ierr);}
544   if (mdn->Mvctx)  {ierr = VecScatterDestroy(mdn->Mvctx);CHKERRQ(ierr);}
545 #if defined(PETSC_HAVE_PLAPACK)
546   if (lu) {
547     ierr = PLA_Obj_free(&lu->A);CHKERRQ(ierr);
548     ierr = PLA_Obj_free (&lu->pivots);CHKERRQ(ierr);
549     ierr = PLA_Temp_free(&lu->templ);CHKERRQ(ierr);
550 
551     if (lu->is_pla) {
552       ierr = ISDestroy(lu->is_pla);CHKERRQ(ierr);
553       ierr = ISDestroy(lu->is_petsc);CHKERRQ(ierr);
554       ierr = VecScatterDestroy(lu->ctx);CHKERRQ(ierr);
555     }
556   }
557 #endif
558 
559   ierr = PetscFree(mdn);CHKERRQ(ierr);
560   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
561   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatGetDiagonalBlock_C","",PETSC_NULL);CHKERRQ(ierr);
562   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMPIDenseSetPreallocation_C","",PETSC_NULL);CHKERRQ(ierr);
563   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
564   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
565   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
566   PetscFunctionReturn(0);
567 }
568 
569 #undef __FUNCT__
570 #define __FUNCT__ "MatView_MPIDense_Binary"
571 static PetscErrorCode MatView_MPIDense_Binary(Mat mat,PetscViewer viewer)
572 {
573   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
574   PetscErrorCode    ierr;
575   PetscViewerFormat format;
576   int               fd;
577   PetscInt          header[4],mmax,N = mat->cmap->N,i,j,m,k;
578   PetscMPIInt       rank,tag  = ((PetscObject)viewer)->tag,size;
579   PetscScalar       *work,*v,*vv;
580   Mat_SeqDense      *a = (Mat_SeqDense*)mdn->A->data;
581   MPI_Status        status;
582 
583   PetscFunctionBegin;
584   if (mdn->size == 1) {
585     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
586   } else {
587     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
588     ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&rank);CHKERRQ(ierr);
589     ierr = MPI_Comm_size(((PetscObject)mat)->comm,&size);CHKERRQ(ierr);
590 
591     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
592     if (format == PETSC_VIEWER_BINARY_NATIVE) {
593 
594       if (!rank) {
595         /* store the matrix as a dense matrix */
596         header[0] = MAT_FILE_COOKIE;
597         header[1] = mat->rmap->N;
598         header[2] = N;
599         header[3] = MATRIX_BINARY_FORMAT_DENSE;
600         ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
601 
602         /* get largest work array needed for transposing array */
603         mmax = mat->rmap->n;
604         for (i=1; i<size; i++) {
605           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
606         }
607         ierr = PetscMalloc(mmax*N*sizeof(PetscScalar),&work);CHKERRQ(ierr);
608 
609         /* write out local array, by rows */
610         m    = mat->rmap->n;
611         v    = a->v;
612         for (j=0; j<N; j++) {
613           for (i=0; i<m; i++) {
614             work[j + i*N] = *v++;
615           }
616         }
617         ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
618         /* get largest work array to receive messages from other processes, excludes process zero */
619         mmax = 0;
620         for (i=1; i<size; i++) {
621           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
622         }
623         ierr = PetscMalloc(mmax*N*sizeof(PetscScalar),&vv);CHKERRQ(ierr);
624         for(k = 1; k < size; k++) {
625           v    = vv;
626           m    = mat->rmap->range[k+1] - mat->rmap->range[k];
627           ierr = MPI_Recv(v,m*N,MPIU_SCALAR,k,tag,((PetscObject)mat)->comm,&status);CHKERRQ(ierr);
628 
629           for(j = 0; j < N; j++) {
630             for(i = 0; i < m; i++) {
631               work[j + i*N] = *v++;
632             }
633           }
634           ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
635         }
636         ierr = PetscFree(work);CHKERRQ(ierr);
637         ierr = PetscFree(vv);CHKERRQ(ierr);
638       } else {
639         ierr = MPI_Send(a->v,mat->rmap->n*mat->cmap->N,MPIU_SCALAR,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
640       }
641     } else {
642       SETERRQ(PETSC_ERR_SUP,"To store a parallel dense matrix you must first call PetscViewerSetFormat(viewer,PETSC_VIEWER_BINARY_NATIVE");
643     }
644   }
645   PetscFunctionReturn(0);
646 }
647 
648 #undef __FUNCT__
649 #define __FUNCT__ "MatView_MPIDense_ASCIIorDraworSocket"
650 static PetscErrorCode MatView_MPIDense_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
651 {
652   Mat_MPIDense          *mdn = (Mat_MPIDense*)mat->data;
653   PetscErrorCode        ierr;
654   PetscMPIInt           size = mdn->size,rank = mdn->rank;
655   const PetscViewerType vtype;
656   PetscTruth            iascii,isdraw;
657   PetscViewer           sviewer;
658   PetscViewerFormat     format;
659 #if defined(PETSC_HAVE_PLAPACK)
660   Mat_Plapack           *lu=(Mat_Plapack*)(mat->spptr);
661 #endif
662 
663   PetscFunctionBegin;
664   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
665   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
666   if (iascii) {
667     ierr = PetscViewerGetType(viewer,&vtype);CHKERRQ(ierr);
668     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
669     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
670       MatInfo info;
671       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
672       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  [%d] local rows %D nz %D nz alloced %D mem %D \n",rank,mat->rmap->n,
673                    (PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
674       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
675       ierr = VecScatterView(mdn->Mvctx,viewer);CHKERRQ(ierr);
676 #if defined(PETSC_HAVE_PLAPACK)
677       ierr = PetscViewerASCIIPrintf(viewer,"PLAPACK run parameters:\n");CHKERRQ(ierr);
678       ierr = PetscViewerASCIIPrintf(viewer,"  Processor mesh: nprows %d, npcols %d\n",lu->Plapack_nprows, lu->Plapack_npcols);CHKERRQ(ierr);
679       ierr = PetscViewerASCIIPrintf(viewer,"  Distr. block size nb: %d \n",lu->nb);CHKERRQ(ierr);
680       ierr = PetscViewerASCIIPrintf(viewer,"  Error checking: %d\n",lu->Plapack_ierror);CHKERRQ(ierr);
681       ierr = PetscViewerASCIIPrintf(viewer,"  Algorithmic block size: %d\n",lu->Plapack_nb_alg);CHKERRQ(ierr);
682 #endif
683       PetscFunctionReturn(0);
684     } else if (format == PETSC_VIEWER_ASCII_INFO) {
685       PetscFunctionReturn(0);
686     }
687   } else if (isdraw) {
688     PetscDraw  draw;
689     PetscTruth isnull;
690 
691     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
692     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
693     if (isnull) PetscFunctionReturn(0);
694   }
695 
696   if (size == 1) {
697     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
698   } else {
699     /* assemble the entire matrix onto first processor. */
700     Mat         A;
701     PetscInt    M = mat->rmap->N,N = mat->cmap->N,m,row,i,nz;
702     PetscInt    *cols;
703     PetscScalar *vals;
704 
705     ierr = MatCreate(((PetscObject)mat)->comm,&A);CHKERRQ(ierr);
706     if (!rank) {
707       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
708     } else {
709       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
710     }
711     /* Since this is a temporary matrix, MATMPIDENSE instead of ((PetscObject)A)->type_name here is probably acceptable. */
712     ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
713     ierr = MatMPIDenseSetPreallocation(A,PETSC_NULL);
714     ierr = PetscLogObjectParent(mat,A);CHKERRQ(ierr);
715 
716     /* Copy the matrix ... This isn't the most efficient means,
717        but it's quick for now */
718     A->insertmode = INSERT_VALUES;
719     row = mat->rmap->rstart; m = mdn->A->rmap->n;
720     for (i=0; i<m; i++) {
721       ierr = MatGetRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
722       ierr = MatSetValues_MPIDense(A,1,&row,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
723       ierr = MatRestoreRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
724       row++;
725     }
726 
727     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
728     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
729     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
730     if (!rank) {
731       ierr = MatView(((Mat_MPIDense*)(A->data))->A,sviewer);CHKERRQ(ierr);
732     }
733     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
734     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
735     ierr = MatDestroy(A);CHKERRQ(ierr);
736   }
737   PetscFunctionReturn(0);
738 }
739 
740 #undef __FUNCT__
741 #define __FUNCT__ "MatView_MPIDense"
742 PetscErrorCode MatView_MPIDense(Mat mat,PetscViewer viewer)
743 {
744   PetscErrorCode ierr;
745   PetscTruth     iascii,isbinary,isdraw,issocket;
746 
747   PetscFunctionBegin;
748 
749   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
750   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
751   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
752   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
753 
754   if (iascii || issocket || isdraw) {
755     ierr = MatView_MPIDense_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
756   } else if (isbinary) {
757     ierr = MatView_MPIDense_Binary(mat,viewer);CHKERRQ(ierr);
758   } else {
759     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported by MPI dense matrix",((PetscObject)viewer)->type_name);
760   }
761   PetscFunctionReturn(0);
762 }
763 
764 #undef __FUNCT__
765 #define __FUNCT__ "MatGetInfo_MPIDense"
766 PetscErrorCode MatGetInfo_MPIDense(Mat A,MatInfoType flag,MatInfo *info)
767 {
768   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
769   Mat            mdn = mat->A;
770   PetscErrorCode ierr;
771   PetscReal      isend[5],irecv[5];
772 
773   PetscFunctionBegin;
774   info->rows_global    = (double)A->rmap->N;
775   info->columns_global = (double)A->cmap->N;
776   info->rows_local     = (double)A->rmap->n;
777   info->columns_local  = (double)A->cmap->N;
778   info->block_size     = 1.0;
779   ierr = MatGetInfo(mdn,MAT_LOCAL,info);CHKERRQ(ierr);
780   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
781   isend[3] = info->memory;  isend[4] = info->mallocs;
782   if (flag == MAT_LOCAL) {
783     info->nz_used      = isend[0];
784     info->nz_allocated = isend[1];
785     info->nz_unneeded  = isend[2];
786     info->memory       = isend[3];
787     info->mallocs      = isend[4];
788   } else if (flag == MAT_GLOBAL_MAX) {
789     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_MAX,((PetscObject)A)->comm);CHKERRQ(ierr);
790     info->nz_used      = irecv[0];
791     info->nz_allocated = irecv[1];
792     info->nz_unneeded  = irecv[2];
793     info->memory       = irecv[3];
794     info->mallocs      = irecv[4];
795   } else if (flag == MAT_GLOBAL_SUM) {
796     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
797     info->nz_used      = irecv[0];
798     info->nz_allocated = irecv[1];
799     info->nz_unneeded  = irecv[2];
800     info->memory       = irecv[3];
801     info->mallocs      = irecv[4];
802   }
803   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
804   info->fill_ratio_needed = 0;
805   info->factor_mallocs    = 0;
806   PetscFunctionReturn(0);
807 }
808 
809 #undef __FUNCT__
810 #define __FUNCT__ "MatSetOption_MPIDense"
811 PetscErrorCode MatSetOption_MPIDense(Mat A,MatOption op,PetscTruth flg)
812 {
813   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
814   PetscErrorCode ierr;
815 
816   PetscFunctionBegin;
817   switch (op) {
818   case MAT_NEW_NONZERO_LOCATIONS:
819   case MAT_NEW_NONZERO_LOCATION_ERR:
820   case MAT_NEW_NONZERO_ALLOCATION_ERR:
821     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
822     break;
823   case MAT_ROW_ORIENTED:
824     a->roworiented = flg;
825     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
826     break;
827   case MAT_NEW_DIAGONALS:
828   case MAT_USE_HASH_TABLE:
829     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
830     break;
831   case MAT_IGNORE_OFF_PROC_ENTRIES:
832     a->donotstash = flg;
833     break;
834   case MAT_SYMMETRIC:
835   case MAT_STRUCTURALLY_SYMMETRIC:
836   case MAT_HERMITIAN:
837   case MAT_SYMMETRY_ETERNAL:
838   case MAT_IGNORE_LOWER_TRIANGULAR:
839     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
840     break;
841   default:
842     SETERRQ1(PETSC_ERR_SUP,"unknown option %s",MatOptions[op]);
843   }
844   PetscFunctionReturn(0);
845 }
846 
847 
848 #undef __FUNCT__
849 #define __FUNCT__ "MatDiagonalScale_MPIDense"
850 PetscErrorCode MatDiagonalScale_MPIDense(Mat A,Vec ll,Vec rr)
851 {
852   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
853   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
854   PetscScalar    *l,*r,x,*v;
855   PetscErrorCode ierr;
856   PetscInt       i,j,s2a,s3a,s2,s3,m=mdn->A->rmap->n,n=mdn->A->cmap->n;
857 
858   PetscFunctionBegin;
859   ierr = MatGetLocalSize(A,&s2,&s3);CHKERRQ(ierr);
860   if (ll) {
861     ierr = VecGetLocalSize(ll,&s2a);CHKERRQ(ierr);
862     if (s2a != s2) SETERRQ2(PETSC_ERR_ARG_SIZ,"Left scaling vector non-conforming local size, %d != %d.", s2a, s2);
863     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
864     for (i=0; i<m; i++) {
865       x = l[i];
866       v = mat->v + i;
867       for (j=0; j<n; j++) { (*v) *= x; v+= m;}
868     }
869     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
870     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
871   }
872   if (rr) {
873     ierr = VecGetLocalSize(rr,&s3a);CHKERRQ(ierr);
874     if (s3a != s3) SETERRQ2(PETSC_ERR_ARG_SIZ,"Right scaling vec non-conforming local size, %d != %d.", s3a, s3);
875     ierr = VecScatterBegin(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
876     ierr = VecScatterEnd(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
877     ierr = VecGetArray(mdn->lvec,&r);CHKERRQ(ierr);
878     for (i=0; i<n; i++) {
879       x = r[i];
880       v = mat->v + i*m;
881       for (j=0; j<m; j++) { (*v++) *= x;}
882     }
883     ierr = VecRestoreArray(mdn->lvec,&r);CHKERRQ(ierr);
884     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
885   }
886   PetscFunctionReturn(0);
887 }
888 
889 #undef __FUNCT__
890 #define __FUNCT__ "MatNorm_MPIDense"
891 PetscErrorCode MatNorm_MPIDense(Mat A,NormType type,PetscReal *nrm)
892 {
893   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
894   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
895   PetscErrorCode ierr;
896   PetscInt       i,j;
897   PetscReal      sum = 0.0;
898   PetscScalar    *v = mat->v;
899 
900   PetscFunctionBegin;
901   if (mdn->size == 1) {
902     ierr =  MatNorm(mdn->A,type,nrm);CHKERRQ(ierr);
903   } else {
904     if (type == NORM_FROBENIUS) {
905       for (i=0; i<mdn->A->cmap->n*mdn->A->rmap->n; i++) {
906 #if defined(PETSC_USE_COMPLEX)
907         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
908 #else
909         sum += (*v)*(*v); v++;
910 #endif
911       }
912       ierr = MPI_Allreduce(&sum,nrm,1,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
913       *nrm = sqrt(*nrm);
914       ierr = PetscLogFlops(2*mdn->A->cmap->n*mdn->A->rmap->n);CHKERRQ(ierr);
915     } else if (type == NORM_1) {
916       PetscReal *tmp,*tmp2;
917       ierr = PetscMalloc(2*A->cmap->N*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
918       tmp2 = tmp + A->cmap->N;
919       ierr = PetscMemzero(tmp,2*A->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
920       *nrm = 0.0;
921       v = mat->v;
922       for (j=0; j<mdn->A->cmap->n; j++) {
923         for (i=0; i<mdn->A->rmap->n; i++) {
924           tmp[j] += PetscAbsScalar(*v);  v++;
925         }
926       }
927       ierr = MPI_Allreduce(tmp,tmp2,A->cmap->N,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
928       for (j=0; j<A->cmap->N; j++) {
929         if (tmp2[j] > *nrm) *nrm = tmp2[j];
930       }
931       ierr = PetscFree(tmp);CHKERRQ(ierr);
932       ierr = PetscLogFlops(A->cmap->n*A->rmap->n);CHKERRQ(ierr);
933     } else if (type == NORM_INFINITY) { /* max row norm */
934       PetscReal ntemp;
935       ierr = MatNorm(mdn->A,type,&ntemp);CHKERRQ(ierr);
936       ierr = MPI_Allreduce(&ntemp,nrm,1,MPIU_REAL,MPI_MAX,((PetscObject)A)->comm);CHKERRQ(ierr);
937     } else {
938       SETERRQ(PETSC_ERR_SUP,"No support for two norm");
939     }
940   }
941   PetscFunctionReturn(0);
942 }
943 
944 #undef __FUNCT__
945 #define __FUNCT__ "MatTranspose_MPIDense"
946 PetscErrorCode MatTranspose_MPIDense(Mat A,MatReuse reuse,Mat *matout)
947 {
948   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
949   Mat_SeqDense   *Aloc = (Mat_SeqDense*)a->A->data;
950   Mat            B;
951   PetscInt       M = A->rmap->N,N = A->cmap->N,m,n,*rwork,rstart = A->rmap->rstart;
952   PetscErrorCode ierr;
953   PetscInt       j,i;
954   PetscScalar    *v;
955 
956   PetscFunctionBegin;
957   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PETSC_ERR_SUP,"Supports square matrix only in-place");
958   if (reuse == MAT_INITIAL_MATRIX || A == *matout) {
959     ierr = MatCreate(((PetscObject)A)->comm,&B);CHKERRQ(ierr);
960     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
961     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
962     ierr = MatMPIDenseSetPreallocation(B,PETSC_NULL);CHKERRQ(ierr);
963   } else {
964     B = *matout;
965   }
966 
967   m = a->A->rmap->n; n = a->A->cmap->n; v = Aloc->v;
968   ierr = PetscMalloc(m*sizeof(PetscInt),&rwork);CHKERRQ(ierr);
969   for (i=0; i<m; i++) rwork[i] = rstart + i;
970   for (j=0; j<n; j++) {
971     ierr = MatSetValues(B,1,&j,m,rwork,v,INSERT_VALUES);CHKERRQ(ierr);
972     v   += m;
973   }
974   ierr = PetscFree(rwork);CHKERRQ(ierr);
975   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
976   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
977   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
978     *matout = B;
979   } else {
980     ierr = MatHeaderCopy(A,B);CHKERRQ(ierr);
981   }
982   PetscFunctionReturn(0);
983 }
984 
985 #include "petscblaslapack.h"
986 #undef __FUNCT__
987 #define __FUNCT__ "MatScale_MPIDense"
988 PetscErrorCode MatScale_MPIDense(Mat inA,PetscScalar alpha)
989 {
990   Mat_MPIDense   *A = (Mat_MPIDense*)inA->data;
991   Mat_SeqDense   *a = (Mat_SeqDense*)A->A->data;
992   PetscScalar    oalpha = alpha;
993   PetscErrorCode ierr;
994   PetscBLASInt   one = 1,nz = PetscBLASIntCast(inA->rmap->n*inA->cmap->N);
995 
996   PetscFunctionBegin;
997   BLASscal_(&nz,&oalpha,a->v,&one);
998   ierr = PetscLogFlops(nz);CHKERRQ(ierr);
999   PetscFunctionReturn(0);
1000 }
1001 
1002 static PetscErrorCode MatDuplicate_MPIDense(Mat,MatDuplicateOption,Mat *);
1003 
1004 #undef __FUNCT__
1005 #define __FUNCT__ "MatSetUpPreallocation_MPIDense"
1006 PetscErrorCode MatSetUpPreallocation_MPIDense(Mat A)
1007 {
1008   PetscErrorCode ierr;
1009 
1010   PetscFunctionBegin;
1011   ierr =  MatMPIDenseSetPreallocation(A,0);CHKERRQ(ierr);
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 #if defined(PETSC_HAVE_PLAPACK)
1016 
1017 #undef __FUNCT__
1018 #define __FUNCT__ "MatMPIDenseCopyToPlapack"
1019 PetscErrorCode MatMPIDenseCopyToPlapack(Mat A,Mat F)
1020 {
1021   Mat_Plapack    *lu = (Mat_Plapack*)(F)->spptr;
1022   PetscErrorCode ierr;
1023   PetscInt       M=A->cmap->N,m=A->rmap->n,rstart;
1024   PetscScalar    *array;
1025   PetscReal      one = 1.0;
1026 
1027   PetscFunctionBegin;
1028   /* Copy A into F->lu->A */
1029   ierr = PLA_Obj_set_to_zero(lu->A);CHKERRQ(ierr);
1030   ierr = PLA_API_begin();CHKERRQ(ierr);
1031   ierr = PLA_Obj_API_open(lu->A);CHKERRQ(ierr);
1032   ierr = MatGetOwnershipRange(A,&rstart,PETSC_NULL);CHKERRQ(ierr);
1033   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1034   ierr = PLA_API_axpy_matrix_to_global(m,M, &one,(void *)array,m,lu->A,rstart,0);CHKERRQ(ierr);
1035   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1036   ierr = PLA_Obj_API_close(lu->A);CHKERRQ(ierr);
1037   ierr = PLA_API_end();CHKERRQ(ierr);
1038   lu->rstart = rstart;
1039   PetscFunctionReturn(0);
1040 }
1041 
1042 #undef __FUNCT__
1043 #define __FUNCT__ "MatMPIDenseCopyFromPlapack"
1044 PetscErrorCode MatMPIDenseCopyFromPlapack(Mat F,Mat A)
1045 {
1046   Mat_Plapack    *lu = (Mat_Plapack*)(F)->spptr;
1047   PetscErrorCode ierr;
1048   PetscInt       M=A->cmap->N,m=A->rmap->n,rstart;
1049   PetscScalar    *array;
1050   PetscReal      one = 1.0;
1051 
1052   PetscFunctionBegin;
1053   /* Copy F into A->lu->A */
1054   ierr = MatZeroEntries(A);CHKERRQ(ierr);
1055   ierr = PLA_API_begin();CHKERRQ(ierr);
1056   ierr = PLA_Obj_API_open(lu->A);CHKERRQ(ierr);
1057   ierr = MatGetOwnershipRange(A,&rstart,PETSC_NULL);CHKERRQ(ierr);
1058   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1059   ierr = PLA_API_axpy_global_to_matrix(m,M, &one,lu->A,rstart,0,(void *)array,m);CHKERRQ(ierr);
1060   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1061   ierr = PLA_Obj_API_close(lu->A);CHKERRQ(ierr);
1062   ierr = PLA_API_end();CHKERRQ(ierr);
1063   lu->rstart = rstart;
1064   PetscFunctionReturn(0);
1065 }
1066 
1067 #undef __FUNCT__
1068 #define __FUNCT__ "MatMatMultNumeric_MPIDense_MPIDense"
1069 PetscErrorCode MatMatMultNumeric_MPIDense_MPIDense(Mat A,Mat B,Mat C)
1070 {
1071   PetscErrorCode ierr;
1072   Mat_Plapack    *luA = (Mat_Plapack*)A->spptr;
1073   Mat_Plapack    *luB = (Mat_Plapack*)B->spptr;
1074   Mat_Plapack    *luC = (Mat_Plapack*)C->spptr;
1075   PLA_Obj        alpha = NULL,beta = NULL;
1076 
1077   PetscFunctionBegin;
1078   ierr = MatMPIDenseCopyToPlapack(A,A);CHKERRQ(ierr);
1079   ierr = MatMPIDenseCopyToPlapack(B,B);CHKERRQ(ierr);
1080 
1081   /*
1082   ierr = PLA_Global_show("A = ",luA->A,"%g ","");CHKERRQ(ierr);
1083   ierr = PLA_Global_show("B = ",luB->A,"%g ","");CHKERRQ(ierr);
1084   */
1085 
1086   /* do the multiply in PLA  */
1087   ierr = PLA_Create_constants_conf_to(luA->A,NULL,NULL,&alpha);CHKERRQ(ierr);
1088   ierr = PLA_Create_constants_conf_to(luC->A,NULL,&beta,NULL);CHKERRQ(ierr);
1089   CHKMEMQ;
1090 
1091   ierr = PLA_Gemm(PLA_NO_TRANSPOSE,PLA_NO_TRANSPOSE,alpha,luA->A,luB->A,beta,luC->A); /* CHKERRQ(ierr); */
1092   CHKMEMQ;
1093   ierr = PLA_Obj_free(&alpha);CHKERRQ(ierr);
1094   ierr = PLA_Obj_free(&beta);CHKERRQ(ierr);
1095 
1096   /*
1097   ierr = PLA_Global_show("C = ",luC->A,"%g ","");CHKERRQ(ierr);
1098   */
1099   ierr = MatMPIDenseCopyFromPlapack(C,C);CHKERRQ(ierr);
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 #undef __FUNCT__
1104 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIDense"
1105 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
1106 {
1107   PetscErrorCode ierr;
1108   PetscInt       m=A->rmap->n,n=B->cmap->n;
1109   Mat            Cmat;
1110 
1111   PetscFunctionBegin;
1112   if (A->cmap->n != B->rmap->n) SETERRQ2(PETSC_ERR_ARG_SIZ,"A->cmap->n %d != B->rmap->n %d\n",A->cmap->n,B->rmap->n);
1113   SETERRQ(PETSC_ERR_LIB,"Due to aparent bugs in PLAPACK,this is not currently supported");
1114   ierr = MatCreate(((PetscObject)B)->comm,&Cmat);CHKERRQ(ierr);
1115   ierr = MatSetSizes(Cmat,m,n,A->rmap->N,B->cmap->N);CHKERRQ(ierr);
1116   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
1117   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1118   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1119   //ierr = MatMPIDenseCreatePlapack(A);CHKERRQ(ierr);
1120   //ierr = MatMPIDenseCreatePlapack(B);CHKERRQ(ierr);
1121   //ierr = MatMPIDenseCreatePlapack(Cmat);CHKERRQ(ierr);
1122   *C = Cmat;
1123   PetscFunctionReturn(0);
1124 }
1125 
1126 #undef __FUNCT__
1127 #define __FUNCT__ "MatMatMult_MPIDense_MPIDense"
1128 PetscErrorCode MatMatMult_MPIDense_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1129 {
1130   PetscErrorCode ierr;
1131 
1132   PetscFunctionBegin;
1133   if (scall == MAT_INITIAL_MATRIX){
1134     ierr = MatMatMultSymbolic_MPIDense_MPIDense(A,B,fill,C);CHKERRQ(ierr);
1135   }
1136   ierr = MatMatMultNumeric_MPIDense_MPIDense(A,B,*C);CHKERRQ(ierr);
1137   PetscFunctionReturn(0);
1138 }
1139 
1140 #undef __FUNCT__
1141 #define __FUNCT__ "MatSolve_MPIDense"
1142 PetscErrorCode MatSolve_MPIDense(Mat A,Vec b,Vec x)
1143 {
1144   MPI_Comm       comm = ((PetscObject)A)->comm;
1145   Mat_Plapack    *lu = (Mat_Plapack*)A->spptr;
1146   PetscErrorCode ierr;
1147   PetscInt       M=A->rmap->N,m=A->rmap->n,rstart,i,j,*idx_pla,*idx_petsc,loc_m,loc_stride;
1148   PetscScalar    *array;
1149   PetscReal      one = 1.0;
1150   PetscMPIInt    size,rank,r_rank,r_nproc,c_rank,c_nproc;;
1151   PLA_Obj        v_pla = NULL;
1152   PetscScalar    *loc_buf;
1153   Vec            loc_x;
1154 
1155   PetscFunctionBegin;
1156   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1157   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1158 
1159   /* Create PLAPACK vector objects, then copy b into PLAPACK b */
1160   PLA_Mvector_create(lu->datatype,M,1,lu->templ,PLA_ALIGN_FIRST,&v_pla);
1161   PLA_Obj_set_to_zero(v_pla);
1162 
1163   /* Copy b into rhs_pla */
1164   PLA_API_begin();
1165   PLA_Obj_API_open(v_pla);
1166   ierr = VecGetArray(b,&array);CHKERRQ(ierr);
1167   PLA_API_axpy_vector_to_global(m,&one,(void *)array,1,v_pla,lu->rstart);
1168   ierr = VecRestoreArray(b,&array);CHKERRQ(ierr);
1169   PLA_Obj_API_close(v_pla);
1170   PLA_API_end();
1171 
1172   if (A->factor == MAT_FACTOR_LU){
1173     /* Apply the permutations to the right hand sides */
1174     PLA_Apply_pivots_to_rows (v_pla,lu->pivots);
1175 
1176     /* Solve L y = b, overwriting b with y */
1177     PLA_Trsv( PLA_LOWER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_UNIT_DIAG,lu->A,v_pla );
1178 
1179     /* Solve U x = y (=b), overwriting b with x */
1180     PLA_Trsv( PLA_UPPER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_NONUNIT_DIAG,lu->A,v_pla );
1181   } else { /*MAT_FACTOR_CHOLESKY */
1182     PLA_Trsv( PLA_LOWER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_NONUNIT_DIAG,lu->A,v_pla);
1183     PLA_Trsv( PLA_LOWER_TRIANGULAR,(lu->datatype == MPI_DOUBLE ? PLA_TRANSPOSE : PLA_CONJUGATE_TRANSPOSE),
1184                                     PLA_NONUNIT_DIAG,lu->A,v_pla);
1185   }
1186 
1187   /* Copy PLAPACK x into Petsc vector x  */
1188   PLA_Obj_local_length(v_pla, &loc_m);
1189   PLA_Obj_local_buffer(v_pla, (void**)&loc_buf);
1190   PLA_Obj_local_stride(v_pla, &loc_stride);
1191   /*
1192     PetscPrintf(PETSC_COMM_SELF," [%d] b - local_m %d local_stride %d, loc_buf: %g %g, nb: %d\n",rank,loc_m,loc_stride,loc_buf[0],loc_buf[(loc_m-1)*loc_stride],lu->nb);
1193   */
1194   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,loc_m*loc_stride,loc_buf,&loc_x);CHKERRQ(ierr);
1195   if (!lu->pla_solved){
1196 
1197     PLA_Temp_comm_row_info(lu->templ,&lu->comm_2d,&r_rank,&r_nproc);
1198     PLA_Temp_comm_col_info(lu->templ,&lu->comm_2d,&c_rank,&c_nproc);
1199     /* printf(" [%d] rank: %d %d, nproc: %d %d\n",rank,r_rank,c_rank,r_nproc,c_nproc); */
1200 
1201     /* Create IS and cts for VecScatterring */
1202     PLA_Obj_local_length(v_pla, &loc_m);
1203     PLA_Obj_local_stride(v_pla, &loc_stride);
1204     ierr = PetscMalloc((2*loc_m+1)*sizeof(PetscInt),&idx_pla);CHKERRQ(ierr);
1205     idx_petsc = idx_pla + loc_m;
1206 
1207     rstart = (r_rank*c_nproc+c_rank)*lu->nb;
1208     for (i=0; i<loc_m; i+=lu->nb){
1209       j = 0;
1210       while (j < lu->nb && i+j < loc_m){
1211         idx_petsc[i+j] = rstart + j; j++;
1212       }
1213       rstart += size*lu->nb;
1214     }
1215 
1216     for (i=0; i<loc_m; i++) idx_pla[i] = i*loc_stride;
1217 
1218     ierr = ISCreateGeneral(PETSC_COMM_SELF,loc_m,idx_pla,&lu->is_pla);CHKERRQ(ierr);
1219     ierr = ISCreateGeneral(PETSC_COMM_SELF,loc_m,idx_petsc,&lu->is_petsc);CHKERRQ(ierr);
1220     ierr = PetscFree(idx_pla);CHKERRQ(ierr);
1221     ierr = VecScatterCreate(loc_x,lu->is_pla,x,lu->is_petsc,&lu->ctx);CHKERRQ(ierr);
1222   }
1223   ierr = VecScatterBegin(lu->ctx,loc_x,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1224   ierr = VecScatterEnd(lu->ctx,loc_x,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1225 
1226   /* Free data */
1227   ierr = VecDestroy(loc_x);CHKERRQ(ierr);
1228   PLA_Obj_free(&v_pla);
1229 
1230   lu->pla_solved = PETSC_TRUE;
1231   PetscFunctionReturn(0);
1232 }
1233 
1234 #undef __FUNCT__
1235 #define __FUNCT__ "MatLUFactorNumeric_MPIDense"
1236 PetscErrorCode MatLUFactorNumeric_MPIDense(Mat A,MatFactorInfo *info,Mat *F)
1237 {
1238   Mat_Plapack    *lu = (Mat_Plapack*)(*F)->spptr;
1239   PetscErrorCode ierr;
1240   PetscInt       M=A->rmap->N,m=A->rmap->n,rstart,rend;
1241   PetscInt       info_pla=0;
1242   PetscScalar    *array,one = 1.0;
1243 
1244   PetscFunctionBegin;
1245   if (lu->mstruct == SAME_NONZERO_PATTERN){
1246     PLA_Obj_free(&lu->A);
1247     PLA_Obj_free (&lu->pivots);
1248   }
1249   /* Create PLAPACK matrix object */
1250   lu->A = NULL; lu->pivots = NULL;
1251   PLA_Matrix_create(lu->datatype,M,M,lu->templ,PLA_ALIGN_FIRST,PLA_ALIGN_FIRST,&lu->A);
1252   PLA_Obj_set_to_zero(lu->A);
1253   PLA_Mvector_create(MPI_INT,M,1,lu->templ,PLA_ALIGN_FIRST,&lu->pivots);
1254 
1255   /* Copy A into lu->A */
1256   PLA_API_begin();
1257   PLA_Obj_API_open(lu->A);
1258   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
1259   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1260   PLA_API_axpy_matrix_to_global(m,M, &one,(void *)array,m,lu->A,rstart,0);
1261   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1262   PLA_Obj_API_close(lu->A);
1263   PLA_API_end();
1264 
1265   /* Factor P A -> L U overwriting lower triangular portion of A with L, upper, U */
1266   info_pla = PLA_LU(lu->A,lu->pivots);
1267   if (info_pla != 0)
1268     SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot encountered at row %d from PLA_LU()",info_pla);
1269 
1270   lu->CleanUpPlapack = PETSC_TRUE;
1271   lu->rstart         = rstart;
1272   lu->mstruct        = SAME_NONZERO_PATTERN;
1273 
1274   (*F)->assembled    = PETSC_TRUE;  /* required by -ksp_view */
1275   PetscFunctionReturn(0);
1276 }
1277 
1278 #undef __FUNCT__
1279 #define __FUNCT__ "MatCholeskyFactorNumeric_MPIDense"
1280 PetscErrorCode MatCholeskyFactorNumeric_MPIDense(Mat A,MatFactorInfo *info,Mat *F)
1281 {
1282   Mat_Plapack    *lu = (Mat_Plapack*)(*F)->spptr;
1283   PetscErrorCode ierr;
1284   PetscInt       M=A->rmap->N,m=A->rmap->n,rstart,rend;
1285   PetscInt       info_pla=0;
1286   PetscScalar    *array,one = 1.0;
1287 
1288   PetscFunctionBegin;
1289   if (lu->mstruct == SAME_NONZERO_PATTERN){
1290     PLA_Obj_free(&lu->A);
1291   }
1292   /* Create PLAPACK matrix object */
1293   lu->A      = NULL;
1294   lu->pivots = NULL;
1295   PLA_Matrix_create(lu->datatype,M,M,lu->templ,PLA_ALIGN_FIRST,PLA_ALIGN_FIRST,&lu->A);
1296 
1297   /* Copy A into lu->A */
1298   PLA_API_begin();
1299   PLA_Obj_API_open(lu->A);
1300   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
1301   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1302   PLA_API_axpy_matrix_to_global(m,M, &one,(void *)array,m,lu->A,rstart,0);
1303   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1304   PLA_Obj_API_close(lu->A);
1305   PLA_API_end();
1306 
1307   /* Factor P A -> Chol */
1308   info_pla = PLA_Chol(PLA_LOWER_TRIANGULAR,lu->A);
1309   if (info_pla != 0)
1310     SETERRQ1( PETSC_ERR_MAT_CH_ZRPVT,"Nonpositive definite matrix detected at row %d from PLA_Chol()",info_pla);
1311 
1312   lu->CleanUpPlapack = PETSC_TRUE;
1313   lu->rstart         = rstart;
1314   lu->mstruct        = SAME_NONZERO_PATTERN;
1315 
1316   (*F)->assembled    = PETSC_TRUE;  /* required by -ksp_view */
1317   PetscFunctionReturn(0);
1318 }
1319 
1320 #undef __FUNCT__
1321 #define __FUNCT__ "MatFactorSymbolic_Plapack_Private"
1322 PetscErrorCode MatFactorSymbolic_Plapack_Private(Mat A,MatFactorInfo *info,Mat *F)
1323 {
1324   Mat            B = *F;
1325   Mat_Plapack    *lu;
1326   PetscErrorCode ierr;
1327   PetscInt       M=A->rmap->N;
1328   MPI_Comm       comm=((PetscObject)A)->comm,comm_2d;
1329   PetscMPIInt    size;
1330   PetscInt       ierror;
1331 
1332   PetscFunctionBegin;
1333   lu = (Mat_Plapack*)(B->spptr);
1334 
1335   /* Set default Plapack parameters */
1336   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1337   lu->nprows = 1; lu->npcols = size;
1338   ierror = 0;
1339   lu->nb     = M/size;
1340   if (M - lu->nb*size) lu->nb++; /* without cyclic distribution */
1341 
1342   /* Set runtime options */
1343   ierr = PetscOptionsBegin(((PetscObject)A)->comm,((PetscObject)A)->prefix,"PLAPACK Options","Mat");CHKERRQ(ierr);
1344   ierr = PetscOptionsInt("-mat_plapack_nprows","row dimension of 2D processor mesh","None",lu->nprows,&lu->nprows,PETSC_NULL);CHKERRQ(ierr);
1345   ierr = PetscOptionsInt("-mat_plapack_npcols","column dimension of 2D processor mesh","None",lu->npcols,&lu->npcols,PETSC_NULL);CHKERRQ(ierr);
1346 
1347   ierr = PetscOptionsInt("-mat_plapack_nb","block size of template vector","None",lu->nb,&lu->nb,PETSC_NULL);CHKERRQ(ierr);
1348   ierr = PetscOptionsInt("-mat_plapack_ckerror","error checking flag","None",ierror,&ierror,PETSC_NULL);CHKERRQ(ierr);
1349   if (ierror){
1350     PLA_Set_error_checking(ierror,PETSC_TRUE,PETSC_TRUE,PETSC_FALSE );
1351   } else {
1352     PLA_Set_error_checking(ierror,PETSC_FALSE,PETSC_FALSE,PETSC_FALSE );
1353   }
1354   lu->ierror = ierror;
1355 
1356   lu->nb_alg = 0;
1357   ierr = PetscOptionsInt("-mat_plapack_nb_alg","algorithmic block size","None",lu->nb_alg,&lu->nb_alg,PETSC_NULL);CHKERRQ(ierr);
1358   if (lu->nb_alg){
1359     pla_Environ_set_nb_alg (PLA_OP_ALL_ALG,lu->nb_alg);
1360   }
1361   PetscOptionsEnd();
1362 
1363 
1364   /* Create a 2D communicator */
1365   PLA_Comm_1D_to_2D(comm,lu->nprows,lu->npcols,&comm_2d);
1366   lu->comm_2d = comm_2d;
1367 
1368   /* Initialize PLAPACK */
1369   PLA_Init(comm_2d);
1370 
1371   /* Create object distribution template */
1372   lu->templ = NULL;
1373   PLA_Temp_create(lu->nb, 0, &lu->templ);
1374 
1375   /* Use suggested nb_alg if it is not provided by user */
1376   if (lu->nb_alg == 0){
1377     PLA_Environ_nb_alg(PLA_OP_PAN_PAN,lu->templ,&lu->nb_alg);
1378     pla_Environ_set_nb_alg(PLA_OP_ALL_ALG,lu->nb_alg);
1379   }
1380 
1381   /* Set the datatype */
1382 #if defined(PETSC_USE_COMPLEX)
1383   lu->datatype = MPI_DOUBLE_COMPLEX;
1384 #else
1385   lu->datatype = MPI_DOUBLE;
1386 #endif
1387 
1388   lu->pla_solved     = PETSC_FALSE; /* MatSolve_Plapack() is called yet */
1389   lu->mstruct        = DIFFERENT_NONZERO_PATTERN;
1390   lu->CleanUpPlapack = PETSC_TRUE;
1391   *F                 = B;
1392   PetscFunctionReturn(0);
1393 }
1394 
1395 /* Note the Petsc perm permutation is ignored */
1396 #undef __FUNCT__
1397 #define __FUNCT__ "MatCholeskyFactorSymbolic_MPIDense"
1398 PetscErrorCode MatCholeskyFactorSymbolic_MPIDense(Mat A,IS perm,MatFactorInfo *info,Mat *F)
1399 {
1400   PetscErrorCode ierr;
1401   PetscTruth     issymmetric,set;
1402 
1403   PetscFunctionBegin;
1404   ierr = MatIsSymmetricKnown(A,&set,&issymmetric); CHKERRQ(ierr);
1405   if (!set || !issymmetric) SETERRQ(PETSC_ERR_USER,"Matrix must be set as MAT_SYMMETRIC for CholeskyFactor()");
1406   ierr = MatFactorSymbolic_Plapack_Private(A,info,F);CHKERRQ(ierr);
1407   (*F)->factor = MAT_FACTOR_CHOLESKY;
1408   PetscFunctionReturn(0);
1409 }
1410 
1411 /* Note the Petsc r and c permutations are ignored */
1412 #undef __FUNCT__
1413 #define __FUNCT__ "MatLUFactorSymbolic_MPIDense"
1414 PetscErrorCode MatLUFactorSymbolic_MPIDense(Mat A,IS r,IS c,MatFactorInfo *info,Mat *F)
1415 {
1416   PetscErrorCode ierr;
1417   PetscInt       M = A->rmap->N;
1418   Mat_Plapack    *lu;
1419 
1420   PetscFunctionBegin;
1421   ierr = MatFactorSymbolic_Plapack_Private(A,info,F);CHKERRQ(ierr);
1422   lu = (Mat_Plapack*)(*F)->spptr;
1423   ierr = PLA_Mvector_create(MPI_INT,M,1,lu->templ,PLA_ALIGN_FIRST,&lu->pivots);CHKERRQ(ierr);
1424   (*F)->factor = MAT_FACTOR_LU;
1425   PetscFunctionReturn(0);
1426 }
1427 
1428 #undef __FUNCT__
1429 #define __FUNCT__ "MatGetFactor_mpidense_plapack"
1430 PetscErrorCode MatGetFactor_mpidense_plapack(Mat A,MatFactorType ftype,Mat *F)
1431 {
1432   PetscErrorCode ierr;
1433   Mat_Plapack    *lu;
1434   PetscMPIInt    size;
1435   PetscInt       M;
1436 
1437   PetscFunctionBegin;
1438   /* Create the factorization matrix */
1439   ierr = MatCreate(((PetscObject)A)->comm,F);CHKERRQ(ierr);
1440   ierr = MatSetSizes(*F,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
1441   ierr = MatSetType(*F,((PetscObject)A)->type_name);CHKERRQ(ierr);
1442   ierr = PetscNewLog(A,Mat_Plapack,&lu);CHKERRQ(ierr);
1443   A->spptr = (void*)lu;
1444 
1445   lu = (Mat_Plapack*)(A->spptr);
1446 
1447   /* Set default Plapack parameters */
1448   ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
1449   lu->nb     = M/size;
1450   if (M - lu->nb*size) lu->nb++; /* without cyclic distribution */
1451 
1452   /* Set runtime options */
1453   ierr = PetscOptionsBegin(((PetscObject)A)->comm,((PetscObject)A)->prefix,"PLAPACK Options","Mat");CHKERRQ(ierr);
1454     ierr = PetscOptionsInt("-mat_plapack_nb","block size of template vector","None",lu->nb,&lu->nb,PETSC_NULL);CHKERRQ(ierr);
1455   PetscOptionsEnd();
1456 
1457   /* Create object distribution template */
1458   lu->templ = NULL;
1459   ierr = PLA_Temp_create(lu->nb, 0, &lu->templ);CHKERRQ(ierr);
1460 
1461   /* Set the datatype */
1462 #if defined(PETSC_USE_COMPLEX)
1463   lu->datatype = MPI_DOUBLE_COMPLEX;
1464 #else
1465   lu->datatype = MPI_DOUBLE;
1466 #endif
1467 
1468   ierr = PLA_Matrix_create(lu->datatype,M,A->cmap->N,lu->templ,PLA_ALIGN_FIRST,PLA_ALIGN_FIRST,&lu->A);CHKERRQ(ierr);
1469 
1470 
1471   lu->pla_solved     = PETSC_FALSE; /* MatSolve_Plapack() is called yet */
1472 
1473   if (ftype == MAT_FACTOR_LU) {
1474     (*F)->ops->lufactorsymbolic = MatLUFactorSymbolic_MPIDense;
1475     (*F)->ops->lufactornumeric  = MatLUFactorNumeric_MPIDense;
1476     (*F)->ops->solve            = MatSolve_MPIDense;
1477   } else if (ftype == MAT_FACTOR_CHOLESKY) {
1478     (*F)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_MPIDense;
1479     (*F)->ops->choleskyfactornumeric  = MatCholeskyFactorNumeric_MPIDense;
1480     (*F)->ops->solve                  = MatSolve_MPIDense;
1481   } else SETERRQ(PETSC_ERR_SUP,"No incomplete factorizations for dense matrices");
1482 
1483   PetscFunctionReturn(0);
1484 }
1485 #endif
1486 
1487 /* -------------------------------------------------------------------*/
1488 static struct _MatOps MatOps_Values = {MatSetValues_MPIDense,
1489        MatGetRow_MPIDense,
1490        MatRestoreRow_MPIDense,
1491        MatMult_MPIDense,
1492 /* 4*/ MatMultAdd_MPIDense,
1493        MatMultTranspose_MPIDense,
1494        MatMultTransposeAdd_MPIDense,
1495        0,
1496        0,
1497        0,
1498 /*10*/ 0,
1499        0,
1500        0,
1501        0,
1502        MatTranspose_MPIDense,
1503 /*15*/ MatGetInfo_MPIDense,
1504        MatEqual_MPIDense,
1505        MatGetDiagonal_MPIDense,
1506        MatDiagonalScale_MPIDense,
1507        MatNorm_MPIDense,
1508 /*20*/ MatAssemblyBegin_MPIDense,
1509        MatAssemblyEnd_MPIDense,
1510        0,
1511        MatSetOption_MPIDense,
1512        MatZeroEntries_MPIDense,
1513 /*25*/ MatZeroRows_MPIDense,
1514        0,
1515        0,
1516        0,
1517        0,
1518 /*30*/ MatSetUpPreallocation_MPIDense,
1519        0,
1520        0,
1521        MatGetArray_MPIDense,
1522        MatRestoreArray_MPIDense,
1523 /*35*/ MatDuplicate_MPIDense,
1524        0,
1525        0,
1526        0,
1527        0,
1528 /*40*/ 0,
1529        MatGetSubMatrices_MPIDense,
1530        0,
1531        MatGetValues_MPIDense,
1532        0,
1533 /*45*/ 0,
1534        MatScale_MPIDense,
1535        0,
1536        0,
1537        0,
1538 /*50*/ 0,
1539        0,
1540        0,
1541        0,
1542        0,
1543 /*55*/ 0,
1544        0,
1545        0,
1546        0,
1547        0,
1548 /*60*/ MatGetSubMatrix_MPIDense,
1549        MatDestroy_MPIDense,
1550        MatView_MPIDense,
1551        0,
1552        0,
1553 /*65*/ 0,
1554        0,
1555        0,
1556        0,
1557        0,
1558 /*70*/ 0,
1559        0,
1560        0,
1561        0,
1562        0,
1563 /*75*/ 0,
1564        0,
1565        0,
1566        0,
1567        0,
1568 /*80*/ 0,
1569        0,
1570        0,
1571        0,
1572 /*84*/ MatLoad_MPIDense,
1573        0,
1574        0,
1575        0,
1576        0,
1577        0,
1578 /*90*/
1579 #if defined(PETSC_HAVE_PLAPACK)
1580        MatMatMult_MPIDense_MPIDense,
1581        MatMatMultSymbolic_MPIDense_MPIDense,
1582        MatMatMultNumeric_MPIDense_MPIDense,
1583 #else
1584        0,
1585        0,
1586        0,
1587 #endif
1588        0,
1589 /*95*/ 0,
1590        0,
1591        0,
1592        0};
1593 
1594 EXTERN_C_BEGIN
1595 #undef __FUNCT__
1596 #define __FUNCT__ "MatMPIDenseSetPreallocation_MPIDense"
1597 PetscErrorCode PETSCMAT_DLLEXPORT MatMPIDenseSetPreallocation_MPIDense(Mat mat,PetscScalar *data)
1598 {
1599   Mat_MPIDense   *a;
1600   PetscErrorCode ierr;
1601 
1602   PetscFunctionBegin;
1603   mat->preallocated = PETSC_TRUE;
1604   /* Note:  For now, when data is specified above, this assumes the user correctly
1605    allocates the local dense storage space.  We should add error checking. */
1606 
1607   a    = (Mat_MPIDense*)mat->data;
1608   ierr = MatCreate(PETSC_COMM_SELF,&a->A);CHKERRQ(ierr);
1609   ierr = MatSetSizes(a->A,mat->rmap->n,mat->cmap->N,mat->rmap->n,mat->cmap->N);CHKERRQ(ierr);
1610   ierr = MatSetType(a->A,MATSEQDENSE);CHKERRQ(ierr);
1611   ierr = MatSeqDenseSetPreallocation(a->A,data);CHKERRQ(ierr);
1612   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
1613   PetscFunctionReturn(0);
1614 }
1615 EXTERN_C_END
1616 
1617 /*MC
1618    MATMPIDENSE - MATMPIDENSE = "mpidense" - A matrix type to be used for distributed dense matrices.
1619 
1620    Options Database Keys:
1621 . -mat_type mpidense - sets the matrix type to "mpidense" during a call to MatSetFromOptions()
1622 
1623   Level: beginner
1624 
1625   MATMPIDENSE matrices may use direct solvers (LU, Cholesky, and QR)
1626   for parallel dense matrices via the external package PLAPACK, if PLAPACK is installed
1627   (run config/configure.py with the option --download-plapack)
1628 
1629 
1630   Options Database Keys:
1631 . -mat_plapack_nprows <n> - number of rows in processor partition
1632 . -mat_plapack_npcols <n> - number of columns in processor partition
1633 . -mat_plapack_nb <n> - block size of template vector
1634 . -mat_plapack_nb_alg <n> - algorithmic block size
1635 - -mat_plapack_ckerror <n> - error checking flag
1636 
1637 .seealso: MatCreateMPIDense(), MATDENSE, MATSEQDENSE
1638 M*/
1639 
1640 EXTERN_C_BEGIN
1641 #undef __FUNCT__
1642 #define __FUNCT__ "MatCreate_MPIDense"
1643 PetscErrorCode PETSCMAT_DLLEXPORT MatCreate_MPIDense(Mat mat)
1644 {
1645   Mat_MPIDense   *a;
1646   PetscErrorCode ierr;
1647 
1648   PetscFunctionBegin;
1649   ierr              = PetscNewLog(mat,Mat_MPIDense,&a);CHKERRQ(ierr);
1650   mat->data         = (void*)a;
1651   ierr              = PetscMemcpy(mat->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1652   mat->mapping      = 0;
1653 
1654   mat->insertmode = NOT_SET_VALUES;
1655   ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&a->rank);CHKERRQ(ierr);
1656   ierr = MPI_Comm_size(((PetscObject)mat)->comm,&a->size);CHKERRQ(ierr);
1657 
1658   mat->rmap->bs = mat->cmap->bs = 1;
1659   ierr = PetscMapSetUp(mat->rmap);CHKERRQ(ierr);
1660   ierr = PetscMapSetUp(mat->cmap);CHKERRQ(ierr);
1661   a->nvec = mat->cmap->n;
1662 
1663   /* build cache for off array entries formed */
1664   a->donotstash = PETSC_FALSE;
1665   ierr = MatStashCreate_Private(((PetscObject)mat)->comm,1,&mat->stash);CHKERRQ(ierr);
1666 
1667   /* stuff used for matrix vector multiply */
1668   a->lvec        = 0;
1669   a->Mvctx       = 0;
1670   a->roworiented = PETSC_TRUE;
1671 
1672   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatGetDiagonalBlock_C",
1673                                      "MatGetDiagonalBlock_MPIDense",
1674                                      MatGetDiagonalBlock_MPIDense);CHKERRQ(ierr);
1675   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMPIDenseSetPreallocation_C",
1676                                      "MatMPIDenseSetPreallocation_MPIDense",
1677                                      MatMPIDenseSetPreallocation_MPIDense);CHKERRQ(ierr);
1678   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",
1679                                      "MatMatMult_MPIAIJ_MPIDense",
1680                                       MatMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1681   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",
1682                                      "MatMatMultSymbolic_MPIAIJ_MPIDense",
1683                                       MatMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1684   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",
1685                                      "MatMatMultNumeric_MPIAIJ_MPIDense",
1686                                       MatMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1687 #if defined(PETSC_HAVE_PLAPACK)
1688   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatGetFactor_mpidense_plapack_C",
1689                                      "MatGetFactor_mpidense_plapack",
1690                                       MatGetFactor_mpidense_plapack);CHKERRQ(ierr);
1691 #if defined(PETSC_HAVE_PLAPACK)
1692   ierr = PetscPLAPACKInitializePackage(((PetscObject)mat)->comm);CHKERRQ(ierr);
1693 #endif
1694 
1695 #endif
1696   ierr = PetscObjectChangeTypeName((PetscObject)mat,MATMPIDENSE);CHKERRQ(ierr);
1697 
1698   PetscFunctionReturn(0);
1699 }
1700 EXTERN_C_END
1701 
1702 /*MC
1703    MATDENSE - MATDENSE = "dense" - A matrix type to be used for dense matrices.
1704 
1705    This matrix type is identical to MATSEQDENSE when constructed with a single process communicator,
1706    and MATMPIDENSE otherwise.
1707 
1708    Options Database Keys:
1709 . -mat_type dense - sets the matrix type to "dense" during a call to MatSetFromOptions()
1710 
1711   Level: beginner
1712 
1713 
1714 .seealso: MatCreateMPIDense,MATSEQDENSE,MATMPIDENSE
1715 M*/
1716 
1717 EXTERN_C_BEGIN
1718 #undef __FUNCT__
1719 #define __FUNCT__ "MatCreate_Dense"
1720 PetscErrorCode PETSCMAT_DLLEXPORT MatCreate_Dense(Mat A)
1721 {
1722   PetscErrorCode ierr;
1723   PetscMPIInt    size;
1724 
1725   PetscFunctionBegin;
1726   ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
1727   if (size == 1) {
1728     ierr = MatSetType(A,MATSEQDENSE);CHKERRQ(ierr);
1729   } else {
1730     ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
1731   }
1732   PetscFunctionReturn(0);
1733 }
1734 EXTERN_C_END
1735 
1736 #undef __FUNCT__
1737 #define __FUNCT__ "MatMPIDenseSetPreallocation"
1738 /*@C
1739    MatMPIDenseSetPreallocation - Sets the array used to store the matrix entries
1740 
1741    Not collective
1742 
1743    Input Parameters:
1744 .  A - the matrix
1745 -  data - optional location of matrix data.  Set data=PETSC_NULL for PETSc
1746    to control all matrix memory allocation.
1747 
1748    Notes:
1749    The dense format is fully compatible with standard Fortran 77
1750    storage by columns.
1751 
1752    The data input variable is intended primarily for Fortran programmers
1753    who wish to allocate their own matrix memory space.  Most users should
1754    set data=PETSC_NULL.
1755 
1756    Level: intermediate
1757 
1758 .keywords: matrix,dense, parallel
1759 
1760 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1761 @*/
1762 PetscErrorCode PETSCMAT_DLLEXPORT MatMPIDenseSetPreallocation(Mat mat,PetscScalar *data)
1763 {
1764   PetscErrorCode ierr,(*f)(Mat,PetscScalar *);
1765 
1766   PetscFunctionBegin;
1767   ierr = PetscObjectQueryFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",(void (**)(void))&f);CHKERRQ(ierr);
1768   if (f) {
1769     ierr = (*f)(mat,data);CHKERRQ(ierr);
1770   }
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 #undef __FUNCT__
1775 #define __FUNCT__ "MatCreateMPIDense"
1776 /*@C
1777    MatCreateMPIDense - Creates a sparse parallel matrix in dense format.
1778 
1779    Collective on MPI_Comm
1780 
1781    Input Parameters:
1782 +  comm - MPI communicator
1783 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
1784 .  n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
1785 .  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
1786 .  N - number of global columns (or PETSC_DECIDE to have calculated if n is given)
1787 -  data - optional location of matrix data.  Set data=PETSC_NULL (PETSC_NULL_SCALAR for Fortran users) for PETSc
1788    to control all matrix memory allocation.
1789 
1790    Output Parameter:
1791 .  A - the matrix
1792 
1793    Notes:
1794    The dense format is fully compatible with standard Fortran 77
1795    storage by columns.
1796 
1797    The data input variable is intended primarily for Fortran programmers
1798    who wish to allocate their own matrix memory space.  Most users should
1799    set data=PETSC_NULL (PETSC_NULL_SCALAR for Fortran users).
1800 
1801    The user MUST specify either the local or global matrix dimensions
1802    (possibly both).
1803 
1804    Level: intermediate
1805 
1806 .keywords: matrix,dense, parallel
1807 
1808 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1809 @*/
1810 PetscErrorCode PETSCMAT_DLLEXPORT MatCreateMPIDense(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscScalar *data,Mat *A)
1811 {
1812   PetscErrorCode ierr;
1813   PetscMPIInt    size;
1814 
1815   PetscFunctionBegin;
1816   ierr = MatCreate(comm,A);CHKERRQ(ierr);
1817   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
1818   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1819   if (size > 1) {
1820     ierr = MatSetType(*A,MATMPIDENSE);CHKERRQ(ierr);
1821     ierr = MatMPIDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1822   } else {
1823     ierr = MatSetType(*A,MATSEQDENSE);CHKERRQ(ierr);
1824     ierr = MatSeqDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1825   }
1826   PetscFunctionReturn(0);
1827 }
1828 
1829 #undef __FUNCT__
1830 #define __FUNCT__ "MatDuplicate_MPIDense"
1831 static PetscErrorCode MatDuplicate_MPIDense(Mat A,MatDuplicateOption cpvalues,Mat *newmat)
1832 {
1833   Mat            mat;
1834   Mat_MPIDense   *a,*oldmat = (Mat_MPIDense*)A->data;
1835   PetscErrorCode ierr;
1836 
1837   PetscFunctionBegin;
1838   *newmat       = 0;
1839   ierr = MatCreate(((PetscObject)A)->comm,&mat);CHKERRQ(ierr);
1840   ierr = MatSetSizes(mat,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
1841   ierr = MatSetType(mat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1842   a                 = (Mat_MPIDense*)mat->data;
1843   ierr              = PetscMemcpy(mat->ops,A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
1844   mat->factor       = A->factor;
1845   mat->assembled    = PETSC_TRUE;
1846   mat->preallocated = PETSC_TRUE;
1847 
1848   mat->rmap->rstart     = A->rmap->rstart;
1849   mat->rmap->rend       = A->rmap->rend;
1850   a->size              = oldmat->size;
1851   a->rank              = oldmat->rank;
1852   mat->insertmode      = NOT_SET_VALUES;
1853   a->nvec              = oldmat->nvec;
1854   a->donotstash        = oldmat->donotstash;
1855 
1856   ierr = PetscMemcpy(mat->rmap->range,A->rmap->range,(a->size+1)*sizeof(PetscInt));CHKERRQ(ierr);
1857   ierr = PetscMemcpy(mat->cmap->range,A->cmap->range,(a->size+1)*sizeof(PetscInt));CHKERRQ(ierr);
1858   ierr = MatStashCreate_Private(((PetscObject)A)->comm,1,&mat->stash);CHKERRQ(ierr);
1859 
1860   ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
1861   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1862   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
1863 
1864 #if defined(PETSC_HAVE_PLAPACK)
1865   ierr = PetscMemcpy(mat->spptr,A->spptr,sizeof(Mat_Plapack));CHKERRQ(ierr);
1866 #endif
1867   *newmat = mat;
1868   PetscFunctionReturn(0);
1869 }
1870 
1871 #include "petscsys.h"
1872 
1873 #undef __FUNCT__
1874 #define __FUNCT__ "MatLoad_MPIDense_DenseInFile"
1875 PetscErrorCode MatLoad_MPIDense_DenseInFile(MPI_Comm comm,PetscInt fd,PetscInt M,PetscInt N, const MatType type,Mat *newmat)
1876 {
1877   PetscErrorCode ierr;
1878   PetscMPIInt    rank,size;
1879   PetscInt       *rowners,i,m,nz,j;
1880   PetscScalar    *array,*vals,*vals_ptr;
1881   MPI_Status     status;
1882 
1883   PetscFunctionBegin;
1884   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1885   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1886 
1887   /* determine ownership of all rows */
1888   m          = M/size + ((M % size) > rank);
1889   ierr       = PetscMalloc((size+2)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
1890   ierr       = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
1891   rowners[0] = 0;
1892   for (i=2; i<=size; i++) {
1893     rowners[i] += rowners[i-1];
1894   }
1895 
1896   ierr = MatCreate(comm,newmat);CHKERRQ(ierr);
1897   ierr = MatSetSizes(*newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
1898   ierr = MatSetType(*newmat,type);CHKERRQ(ierr);
1899   ierr = MatMPIDenseSetPreallocation(*newmat,PETSC_NULL);CHKERRQ(ierr);
1900   ierr = MatGetArray(*newmat,&array);CHKERRQ(ierr);
1901 
1902   if (!rank) {
1903     ierr = PetscMalloc(m*N*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1904 
1905     /* read in my part of the matrix numerical values  */
1906     ierr = PetscBinaryRead(fd,vals,m*N,PETSC_SCALAR);CHKERRQ(ierr);
1907 
1908     /* insert into matrix-by row (this is why cannot directly read into array */
1909     vals_ptr = vals;
1910     for (i=0; i<m; i++) {
1911       for (j=0; j<N; j++) {
1912         array[i + j*m] = *vals_ptr++;
1913       }
1914     }
1915 
1916     /* read in other processors and ship out */
1917     for (i=1; i<size; i++) {
1918       nz   = (rowners[i+1] - rowners[i])*N;
1919       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1920       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)(*newmat))->tag,comm);CHKERRQ(ierr);
1921     }
1922   } else {
1923     /* receive numeric values */
1924     ierr = PetscMalloc(m*N*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1925 
1926     /* receive message of values*/
1927     ierr = MPI_Recv(vals,m*N,MPIU_SCALAR,0,((PetscObject)(*newmat))->tag,comm,&status);CHKERRQ(ierr);
1928 
1929     /* insert into matrix-by row (this is why cannot directly read into array */
1930     vals_ptr = vals;
1931     for (i=0; i<m; i++) {
1932       for (j=0; j<N; j++) {
1933         array[i + j*m] = *vals_ptr++;
1934       }
1935     }
1936   }
1937   ierr = PetscFree(rowners);CHKERRQ(ierr);
1938   ierr = PetscFree(vals);CHKERRQ(ierr);
1939   ierr = MatAssemblyBegin(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1940   ierr = MatAssemblyEnd(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1941   PetscFunctionReturn(0);
1942 }
1943 
1944 #undef __FUNCT__
1945 #define __FUNCT__ "MatLoad_MPIDense"
1946 PetscErrorCode MatLoad_MPIDense(PetscViewer viewer,const MatType type,Mat *newmat)
1947 {
1948   Mat            A;
1949   PetscScalar    *vals,*svals;
1950   MPI_Comm       comm = ((PetscObject)viewer)->comm;
1951   MPI_Status     status;
1952   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag,*rowners,*sndcounts,m,maxnz;
1953   PetscInt       header[4],*rowlengths = 0,M,N,*cols;
1954   PetscInt       *ourlens,*procsnz = 0,*offlens,jj,*mycols,*smycols;
1955   PetscInt       i,nz,j,rstart,rend;
1956   int            fd;
1957   PetscErrorCode ierr;
1958 
1959   PetscFunctionBegin;
1960   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1961   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1962   if (!rank) {
1963     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1964     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
1965     if (header[0] != MAT_FILE_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
1966   }
1967 
1968   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
1969   M = header[1]; N = header[2]; nz = header[3];
1970 
1971   /*
1972        Handle case where matrix is stored on disk as a dense matrix
1973   */
1974   if (nz == MATRIX_BINARY_FORMAT_DENSE) {
1975     ierr = MatLoad_MPIDense_DenseInFile(comm,fd,M,N,type,newmat);CHKERRQ(ierr);
1976     PetscFunctionReturn(0);
1977   }
1978 
1979   /* determine ownership of all rows */
1980   m          = PetscMPIIntCast(M/size + ((M % size) > rank));
1981   ierr       = PetscMalloc((size+2)*sizeof(PetscMPIInt),&rowners);CHKERRQ(ierr);
1982   ierr       = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
1983   rowners[0] = 0;
1984   for (i=2; i<=size; i++) {
1985     rowners[i] += rowners[i-1];
1986   }
1987   rstart = rowners[rank];
1988   rend   = rowners[rank+1];
1989 
1990   /* distribute row lengths to all processors */
1991   ierr    = PetscMalloc(2*(rend-rstart+1)*sizeof(PetscInt),&ourlens);CHKERRQ(ierr);
1992   offlens = ourlens + (rend-rstart);
1993   if (!rank) {
1994     ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
1995     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
1996     ierr = PetscMalloc(size*sizeof(PetscMPIInt),&sndcounts);CHKERRQ(ierr);
1997     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
1998     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1999     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
2000   } else {
2001     ierr = MPI_Scatterv(0,0,0,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
2002   }
2003 
2004   if (!rank) {
2005     /* calculate the number of nonzeros on each processor */
2006     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
2007     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
2008     for (i=0; i<size; i++) {
2009       for (j=rowners[i]; j< rowners[i+1]; j++) {
2010         procsnz[i] += rowlengths[j];
2011       }
2012     }
2013     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2014 
2015     /* determine max buffer needed and allocate it */
2016     maxnz = 0;
2017     for (i=0; i<size; i++) {
2018       maxnz = PetscMax(maxnz,procsnz[i]);
2019     }
2020     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
2021 
2022     /* read in my part of the matrix column indices  */
2023     nz = procsnz[0];
2024     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
2025     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2026 
2027     /* read in every one elses and ship off */
2028     for (i=1; i<size; i++) {
2029       nz   = procsnz[i];
2030       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2031       ierr = MPI_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2032     }
2033     ierr = PetscFree(cols);CHKERRQ(ierr);
2034   } else {
2035     /* determine buffer space needed for message */
2036     nz = 0;
2037     for (i=0; i<m; i++) {
2038       nz += ourlens[i];
2039     }
2040     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
2041 
2042     /* receive message of column indices*/
2043     ierr = MPI_Recv(mycols,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
2044     ierr = MPI_Get_count(&status,MPIU_INT,&maxnz);CHKERRQ(ierr);
2045     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
2046   }
2047 
2048   /* loop over local rows, determining number of off diagonal entries */
2049   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2050   jj = 0;
2051   for (i=0; i<m; i++) {
2052     for (j=0; j<ourlens[i]; j++) {
2053       if (mycols[jj] < rstart || mycols[jj] >= rend) offlens[i]++;
2054       jj++;
2055     }
2056   }
2057 
2058   /* create our matrix */
2059   for (i=0; i<m; i++) {
2060     ourlens[i] -= offlens[i];
2061   }
2062   ierr = MatCreate(comm,newmat);CHKERRQ(ierr);
2063   ierr = MatSetSizes(*newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
2064   ierr = MatSetType(*newmat,type);CHKERRQ(ierr);
2065   ierr = MatMPIDenseSetPreallocation(*newmat,PETSC_NULL);CHKERRQ(ierr);
2066   A = *newmat;
2067   for (i=0; i<m; i++) {
2068     ourlens[i] += offlens[i];
2069   }
2070 
2071   if (!rank) {
2072     ierr = PetscMalloc(maxnz*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
2073 
2074     /* read in my part of the matrix numerical values  */
2075     nz = procsnz[0];
2076     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2077 
2078     /* insert into matrix */
2079     jj      = rstart;
2080     smycols = mycols;
2081     svals   = vals;
2082     for (i=0; i<m; i++) {
2083       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2084       smycols += ourlens[i];
2085       svals   += ourlens[i];
2086       jj++;
2087     }
2088 
2089     /* read in other processors and ship out */
2090     for (i=1; i<size; i++) {
2091       nz   = procsnz[i];
2092       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2093       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)A)->tag,comm);CHKERRQ(ierr);
2094     }
2095     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2096   } else {
2097     /* receive numeric values */
2098     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
2099 
2100     /* receive message of values*/
2101     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)A)->tag,comm,&status);CHKERRQ(ierr);
2102     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
2103     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
2104 
2105     /* insert into matrix */
2106     jj      = rstart;
2107     smycols = mycols;
2108     svals   = vals;
2109     for (i=0; i<m; i++) {
2110       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2111       smycols += ourlens[i];
2112       svals   += ourlens[i];
2113       jj++;
2114     }
2115   }
2116   ierr = PetscFree(ourlens);CHKERRQ(ierr);
2117   ierr = PetscFree(vals);CHKERRQ(ierr);
2118   ierr = PetscFree(mycols);CHKERRQ(ierr);
2119   ierr = PetscFree(rowners);CHKERRQ(ierr);
2120 
2121   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2122   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2123   PetscFunctionReturn(0);
2124 }
2125 
2126 #undef __FUNCT__
2127 #define __FUNCT__ "MatEqual_MPIDense"
2128 PetscErrorCode MatEqual_MPIDense(Mat A,Mat B,PetscTruth *flag)
2129 {
2130   Mat_MPIDense   *matB = (Mat_MPIDense*)B->data,*matA = (Mat_MPIDense*)A->data;
2131   Mat            a,b;
2132   PetscTruth     flg;
2133   PetscErrorCode ierr;
2134 
2135   PetscFunctionBegin;
2136   a = matA->A;
2137   b = matB->A;
2138   ierr = MatEqual(a,b,&flg);CHKERRQ(ierr);
2139   ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,((PetscObject)A)->comm);CHKERRQ(ierr);
2140   PetscFunctionReturn(0);
2141 }
2142 
2143 #if defined(PETSC_HAVE_PLAPACK)
2144 
2145 #undef __FUNCT__
2146 #define __FUNCT__ "PetscPLAPACKFinalizePackage"
2147 /*@C
2148   PetscPLAPACKFinalizePackage - This function destroys everything in the Petsc interface to PLAPACK.
2149   Level: developer
2150 
2151 .keywords: Petsc, destroy, package, PLAPACK
2152 .seealso: PetscFinalize()
2153 @*/
2154 PetscErrorCode PETSC_DLLEXPORT PetscPLAPACKFinalizePackage(void)
2155 {
2156   PetscErrorCode ierr;
2157 
2158   PetscFunctionBegin;
2159   ierr = PLA_Finalize();CHKERRQ(ierr);
2160   PetscFunctionReturn(0);
2161 }
2162 
2163 #undef __FUNCT__
2164 #define __FUNCT__ "PetscPLAPACKInitializePackage"
2165 /*@C
2166   PetscPLAPACKInitializePackage - This function initializes everything in the Petsc interface to PLAPACK. It is
2167   called from MatCreate_MPIDense() the first time an MPI dense matrix is called.
2168 
2169   Input Parameter:
2170 .   comm - the communicator the matrix lives on
2171 
2172   Level: developer
2173 
2174    Notes: PLAPACK does not have a good fit with MPI communicators; all (parallel) PLAPACK objects have to live in the
2175   same communicator (because there is some global state that is initialized and used for all matrices). In addition if
2176   PLAPACK is initialized (that is the initial matrices created) are on subcommunicators of MPI_COMM_WORLD, these subcommunicators
2177   cannot overlap.
2178 
2179 .keywords: Petsc, initialize, package, PLAPACK
2180 .seealso: PetscInitializePackage(), PetscInitialize()
2181 @*/
2182 PetscErrorCode PETSC_DLLEXPORT PetscPLAPACKInitializePackage(MPI_Comm comm)
2183 {
2184   PetscMPIInt    size;
2185   PetscErrorCode ierr;
2186 
2187   PetscFunctionBegin;
2188   if (!PLA_Initialized(PETSC_NULL)) {
2189 
2190     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2191     Plapack_nprows = 1;
2192     Plapack_npcols = size;
2193 
2194     ierr = PetscOptionsBegin(comm,PETSC_NULL,"PLAPACK Options","Mat");CHKERRQ(ierr);
2195       ierr = PetscOptionsInt("-plapack_nprows","row dimension of 2D processor mesh","None",Plapack_nprows,&Plapack_nprows,PETSC_NULL);CHKERRQ(ierr);
2196       ierr = PetscOptionsInt("-plapack_npcols","column dimension of 2D processor mesh","None",Plapack_npcols,&Plapack_npcols,PETSC_NULL);CHKERRQ(ierr);
2197 #if defined(PETSC_USE_DEBUG)
2198       Plapack_ierror = 3;
2199 #else
2200       Plapack_ierror = 0;
2201 #endif
2202       ierr = PetscOptionsInt("-plapack_ckerror","error checking flag","None",Plapack_ierror,&Plapack_ierror,PETSC_NULL);CHKERRQ(ierr);
2203       if (Plapack_ierror){
2204 	ierr = PLA_Set_error_checking(Plapack_ierror,PETSC_TRUE,PETSC_TRUE,PETSC_FALSE );CHKERRQ(ierr);
2205       } else {
2206 	ierr = PLA_Set_error_checking(Plapack_ierror,PETSC_FALSE,PETSC_FALSE,PETSC_FALSE );CHKERRQ(ierr);
2207       }
2208 
2209       Plapack_nb_alg = 0;
2210       ierr = PetscOptionsInt("-plapack_nb_alg","algorithmic block size","None",Plapack_nb_alg,&Plapack_nb_alg,PETSC_NULL);CHKERRQ(ierr);
2211       if (Plapack_nb_alg) {
2212         ierr = pla_Environ_set_nb_alg (PLA_OP_ALL_ALG,Plapack_nb_alg);CHKERRQ(ierr);
2213       }
2214     PetscOptionsEnd();
2215 
2216     ierr = PLA_Comm_1D_to_2D(comm,Plapack_nprows,Plapack_npcols,&Plapack_comm_2d);CHKERRQ(ierr);
2217     ierr = PLA_Init(Plapack_comm_2d);CHKERRQ(ierr);
2218     ierr = PetscRegisterFinalize(PetscPLAPACKFinalizePackage);CHKERRQ(ierr);
2219   }
2220   PetscFunctionReturn(0);
2221 }
2222 
2223 
2224 #endif
2225