xref: /petsc/src/mat/impls/dense/mpi/mpidense.c (revision fce0c873789145caee477924bfa4ad26b4cd6ea4)
1 
2 /*
3    Basic functions for basic parallel dense matrices.
4 */
5 
6 
7 #include <../src/mat/impls/dense/mpi/mpidense.h>    /*I   "petscmat.h"  I*/
8 #include <../src/mat/impls/aij/mpi/mpiaij.h>
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "MatDenseGetLocalMatrix"
12 /*@
13 
14       MatDenseGetLocalMatrix - For a MATMPIDENSE or MATSEQDENSE matrix returns the sequential
15               matrix that represents the operator. For sequential matrices it returns itself.
16 
17     Input Parameter:
18 .      A - the Seq or MPI dense matrix
19 
20     Output Parameter:
21 .      B - the inner matrix
22 
23     Level: intermediate
24 
25 @*/
26 PetscErrorCode MatDenseGetLocalMatrix(Mat A,Mat *B)
27 {
28   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
29   PetscErrorCode ierr;
30   PetscBool      flg;
31 
32   PetscFunctionBegin;
33   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIDENSE,&flg);CHKERRQ(ierr);
34   if (flg) *B = mat->A;
35   else *B = A;
36   PetscFunctionReturn(0);
37 }
38 
39 #undef __FUNCT__
40 #define __FUNCT__ "MatGetRow_MPIDense"
41 PetscErrorCode MatGetRow_MPIDense(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
42 {
43   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
44   PetscErrorCode ierr;
45   PetscInt       lrow,rstart = A->rmap->rstart,rend = A->rmap->rend;
46 
47   PetscFunctionBegin;
48   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"only local rows");
49   lrow = row - rstart;
50   ierr = MatGetRow(mat->A,lrow,nz,(const PetscInt**)idx,(const PetscScalar**)v);CHKERRQ(ierr);
51   PetscFunctionReturn(0);
52 }
53 
54 #undef __FUNCT__
55 #define __FUNCT__ "MatRestoreRow_MPIDense"
56 PetscErrorCode MatRestoreRow_MPIDense(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
57 {
58   PetscErrorCode ierr;
59 
60   PetscFunctionBegin;
61   if (idx) {ierr = PetscFree(*idx);CHKERRQ(ierr);}
62   if (v) {ierr = PetscFree(*v);CHKERRQ(ierr);}
63   PetscFunctionReturn(0);
64 }
65 
66 #undef __FUNCT__
67 #define __FUNCT__ "MatGetDiagonalBlock_MPIDense"
68 PetscErrorCode  MatGetDiagonalBlock_MPIDense(Mat A,Mat *a)
69 {
70   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
71   PetscErrorCode ierr;
72   PetscInt       m = A->rmap->n,rstart = A->rmap->rstart;
73   PetscScalar    *array;
74   MPI_Comm       comm;
75   Mat            B;
76 
77   PetscFunctionBegin;
78   if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only square matrices supported.");
79 
80   ierr = PetscObjectQuery((PetscObject)A,"DiagonalBlock",(PetscObject*)&B);CHKERRQ(ierr);
81   if (!B) {
82     ierr = PetscObjectGetComm((PetscObject)(mdn->A),&comm);CHKERRQ(ierr);
83     ierr = MatCreate(comm,&B);CHKERRQ(ierr);
84     ierr = MatSetSizes(B,m,m,m,m);CHKERRQ(ierr);
85     ierr = MatSetType(B,((PetscObject)mdn->A)->type_name);CHKERRQ(ierr);
86     ierr = MatDenseGetArray(mdn->A,&array);CHKERRQ(ierr);
87     ierr = MatSeqDenseSetPreallocation(B,array+m*rstart);CHKERRQ(ierr);
88     ierr = MatDenseRestoreArray(mdn->A,&array);CHKERRQ(ierr);
89     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
90     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
91     ierr = PetscObjectCompose((PetscObject)A,"DiagonalBlock",(PetscObject)B);CHKERRQ(ierr);
92     *a   = B;
93     ierr = MatDestroy(&B);CHKERRQ(ierr);
94   } else *a = B;
95   PetscFunctionReturn(0);
96 }
97 
98 #undef __FUNCT__
99 #define __FUNCT__ "MatSetValues_MPIDense"
100 PetscErrorCode MatSetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
101 {
102   Mat_MPIDense   *A = (Mat_MPIDense*)mat->data;
103   PetscErrorCode ierr;
104   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend,row;
105   PetscBool      roworiented = A->roworiented;
106 
107   PetscFunctionBegin;
108   for (i=0; i<m; i++) {
109     if (idxm[i] < 0) continue;
110     if (idxm[i] >= mat->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
111     if (idxm[i] >= rstart && idxm[i] < rend) {
112       row = idxm[i] - rstart;
113       if (roworiented) {
114         ierr = MatSetValues(A->A,1,&row,n,idxn,v+i*n,addv);CHKERRQ(ierr);
115       } else {
116         for (j=0; j<n; j++) {
117           if (idxn[j] < 0) continue;
118           if (idxn[j] >= mat->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
119           ierr = MatSetValues(A->A,1,&row,1,&idxn[j],v+i+j*m,addv);CHKERRQ(ierr);
120         }
121       }
122     } else if (!A->donotstash) {
123       mat->assembled = PETSC_FALSE;
124       if (roworiented) {
125         ierr = MatStashValuesRow_Private(&mat->stash,idxm[i],n,idxn,v+i*n,PETSC_FALSE);CHKERRQ(ierr);
126       } else {
127         ierr = MatStashValuesCol_Private(&mat->stash,idxm[i],n,idxn,v+i,m,PETSC_FALSE);CHKERRQ(ierr);
128       }
129     }
130   }
131   PetscFunctionReturn(0);
132 }
133 
134 #undef __FUNCT__
135 #define __FUNCT__ "MatGetValues_MPIDense"
136 PetscErrorCode MatGetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
137 {
138   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
139   PetscErrorCode ierr;
140   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend,row;
141 
142   PetscFunctionBegin;
143   for (i=0; i<m; i++) {
144     if (idxm[i] < 0) continue; /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row"); */
145     if (idxm[i] >= mat->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
146     if (idxm[i] >= rstart && idxm[i] < rend) {
147       row = idxm[i] - rstart;
148       for (j=0; j<n; j++) {
149         if (idxn[j] < 0) continue; /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column"); */
150         if (idxn[j] >= mat->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
151         ierr = MatGetValues(mdn->A,1,&row,1,&idxn[j],v+i*n+j);CHKERRQ(ierr);
152       }
153     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
154   }
155   PetscFunctionReturn(0);
156 }
157 
158 #undef __FUNCT__
159 #define __FUNCT__ "MatDenseGetArray_MPIDense"
160 PetscErrorCode MatDenseGetArray_MPIDense(Mat A,PetscScalar *array[])
161 {
162   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
163   PetscErrorCode ierr;
164 
165   PetscFunctionBegin;
166   ierr = MatDenseGetArray(a->A,array);CHKERRQ(ierr);
167   PetscFunctionReturn(0);
168 }
169 
170 #undef __FUNCT__
171 #define __FUNCT__ "MatGetSubMatrix_MPIDense"
172 static PetscErrorCode MatGetSubMatrix_MPIDense(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
173 {
174   Mat_MPIDense   *mat  = (Mat_MPIDense*)A->data,*newmatd;
175   Mat_SeqDense   *lmat = (Mat_SeqDense*)mat->A->data;
176   PetscErrorCode ierr;
177   PetscInt       i,j,rstart,rend,nrows,ncols,Ncols,nlrows,nlcols;
178   const PetscInt *irow,*icol;
179   PetscScalar    *av,*bv,*v = lmat->v;
180   Mat            newmat;
181   IS             iscol_local;
182 
183   PetscFunctionBegin;
184   ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
185   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
186   ierr = ISGetIndices(iscol_local,&icol);CHKERRQ(ierr);
187   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
188   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
189   ierr = ISGetSize(iscol,&Ncols);CHKERRQ(ierr); /* global number of columns, size of iscol_local */
190 
191   /* No parallel redistribution currently supported! Should really check each index set
192      to comfirm that it is OK.  ... Currently supports only submatrix same partitioning as
193      original matrix! */
194 
195   ierr = MatGetLocalSize(A,&nlrows,&nlcols);CHKERRQ(ierr);
196   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
197 
198   /* Check submatrix call */
199   if (scall == MAT_REUSE_MATRIX) {
200     /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size"); */
201     /* Really need to test rows and column sizes! */
202     newmat = *B;
203   } else {
204     /* Create and fill new matrix */
205     ierr = MatCreate(PetscObjectComm((PetscObject)A),&newmat);CHKERRQ(ierr);
206     ierr = MatSetSizes(newmat,nrows,ncols,PETSC_DECIDE,Ncols);CHKERRQ(ierr);
207     ierr = MatSetType(newmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
208     ierr = MatMPIDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
209   }
210 
211   /* Now extract the data pointers and do the copy, column at a time */
212   newmatd = (Mat_MPIDense*)newmat->data;
213   bv      = ((Mat_SeqDense*)newmatd->A->data)->v;
214 
215   for (i=0; i<Ncols; i++) {
216     av = v + ((Mat_SeqDense*)mat->A->data)->lda*icol[i];
217     for (j=0; j<nrows; j++) {
218       *bv++ = av[irow[j] - rstart];
219     }
220   }
221 
222   /* Assemble the matrices so that the correct flags are set */
223   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
224   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
225 
226   /* Free work space */
227   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
228   ierr = ISRestoreIndices(iscol_local,&icol);CHKERRQ(ierr);
229   ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
230   *B   = newmat;
231   PetscFunctionReturn(0);
232 }
233 
234 #undef __FUNCT__
235 #define __FUNCT__ "MatDenseRestoreArray_MPIDense"
236 PetscErrorCode MatDenseRestoreArray_MPIDense(Mat A,PetscScalar *array[])
237 {
238   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
239   PetscErrorCode ierr;
240 
241   PetscFunctionBegin;
242   ierr = MatDenseRestoreArray(a->A,array);CHKERRQ(ierr);
243   PetscFunctionReturn(0);
244 }
245 
246 #undef __FUNCT__
247 #define __FUNCT__ "MatAssemblyBegin_MPIDense"
248 PetscErrorCode MatAssemblyBegin_MPIDense(Mat mat,MatAssemblyType mode)
249 {
250   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
251   MPI_Comm       comm;
252   PetscErrorCode ierr;
253   PetscInt       nstash,reallocs;
254   InsertMode     addv;
255 
256   PetscFunctionBegin;
257   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
258   /* make sure all processors are either in INSERTMODE or ADDMODE */
259   ierr = MPI_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,comm);CHKERRQ(ierr);
260   if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Cannot mix adds/inserts on different procs");
261   mat->insertmode = addv; /* in case this processor had no cache */
262 
263   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
264   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
265   ierr = PetscInfo2(mdn->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
266   PetscFunctionReturn(0);
267 }
268 
269 #undef __FUNCT__
270 #define __FUNCT__ "MatAssemblyEnd_MPIDense"
271 PetscErrorCode MatAssemblyEnd_MPIDense(Mat mat,MatAssemblyType mode)
272 {
273   Mat_MPIDense   *mdn=(Mat_MPIDense*)mat->data;
274   PetscErrorCode ierr;
275   PetscInt       i,*row,*col,flg,j,rstart,ncols;
276   PetscMPIInt    n;
277   PetscScalar    *val;
278   InsertMode     addv=mat->insertmode;
279 
280   PetscFunctionBegin;
281   /*  wait on receives */
282   while (1) {
283     ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
284     if (!flg) break;
285 
286     for (i=0; i<n;) {
287       /* Now identify the consecutive vals belonging to the same row */
288       for (j=i,rstart=row[j]; j<n; j++) {
289         if (row[j] != rstart) break;
290       }
291       if (j < n) ncols = j-i;
292       else       ncols = n-i;
293       /* Now assemble all these values with a single function call */
294       ierr = MatSetValues_MPIDense(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
295       i    = j;
296     }
297   }
298   ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
299 
300   ierr = MatAssemblyBegin(mdn->A,mode);CHKERRQ(ierr);
301   ierr = MatAssemblyEnd(mdn->A,mode);CHKERRQ(ierr);
302 
303   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
304     ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
305   }
306   PetscFunctionReturn(0);
307 }
308 
309 #undef __FUNCT__
310 #define __FUNCT__ "MatZeroEntries_MPIDense"
311 PetscErrorCode MatZeroEntries_MPIDense(Mat A)
312 {
313   PetscErrorCode ierr;
314   Mat_MPIDense   *l = (Mat_MPIDense*)A->data;
315 
316   PetscFunctionBegin;
317   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
318   PetscFunctionReturn(0);
319 }
320 
321 /* the code does not do the diagonal entries correctly unless the
322    matrix is square and the column and row owerships are identical.
323    This is a BUG. The only way to fix it seems to be to access
324    mdn->A and mdn->B directly and not through the MatZeroRows()
325    routine.
326 */
327 #undef __FUNCT__
328 #define __FUNCT__ "MatZeroRows_MPIDense"
329 PetscErrorCode MatZeroRows_MPIDense(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
330 {
331   Mat_MPIDense      *l = (Mat_MPIDense*)A->data;
332   PetscErrorCode    ierr;
333   PetscInt          i,*owners = A->rmap->range;
334   PetscInt          *sizes,j,idx,nsends;
335   PetscInt          nmax,*svalues,*starts,*owner,nrecvs;
336   PetscInt          *rvalues,tag = ((PetscObject)A)->tag,count,base,slen,*source;
337   PetscInt          *lens,*lrows,*values;
338   PetscMPIInt       n,imdex,rank = l->rank,size = l->size;
339   MPI_Comm          comm;
340   MPI_Request       *send_waits,*recv_waits;
341   MPI_Status        recv_status,*send_status;
342   PetscBool         found;
343   const PetscScalar *xx;
344   PetscScalar       *bb;
345 
346   PetscFunctionBegin;
347   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
348   if (A->rmap->N != A->cmap->N) SETERRQ(comm,PETSC_ERR_SUP,"Only handles square matrices");
349   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only handles matrices with identical column and row ownership");
350   /*  first count number of contributors to each processor */
351   ierr = PetscCalloc1(2*size,&sizes);CHKERRQ(ierr);
352   ierr = PetscMalloc1(N+1,&owner);CHKERRQ(ierr);  /* see note*/
353   for (i=0; i<N; i++) {
354     idx   = rows[i];
355     found = PETSC_FALSE;
356     for (j=0; j<size; j++) {
357       if (idx >= owners[j] && idx < owners[j+1]) {
358         sizes[2*j]++; sizes[2*j+1] = 1; owner[i] = j; found = PETSC_TRUE; break;
359       }
360     }
361     if (!found) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
362   }
363   nsends = 0;
364   for (i=0; i<size; i++) nsends += sizes[2*i+1];
365 
366   /* inform other processors of number of messages and max length*/
367   ierr = PetscMaxSum(comm,sizes,&nmax,&nrecvs);CHKERRQ(ierr);
368 
369   /* post receives:   */
370   ierr = PetscMalloc1((nrecvs+1)*(nmax+1),&rvalues);CHKERRQ(ierr);
371   ierr = PetscMalloc1((nrecvs+1),&recv_waits);CHKERRQ(ierr);
372   for (i=0; i<nrecvs; i++) {
373     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
374   }
375 
376   /* do sends:
377       1) starts[i] gives the starting index in svalues for stuff going to
378          the ith processor
379   */
380   ierr = PetscMalloc1((N+1),&svalues);CHKERRQ(ierr);
381   ierr = PetscMalloc1((nsends+1),&send_waits);CHKERRQ(ierr);
382   ierr = PetscMalloc1((size+1),&starts);CHKERRQ(ierr);
383 
384   starts[0] = 0;
385   for (i=1; i<size; i++) starts[i] = starts[i-1] + sizes[2*i-2];
386   for (i=0; i<N; i++) svalues[starts[owner[i]]++] = rows[i];
387 
388   starts[0] = 0;
389   for (i=1; i<size+1; i++) starts[i] = starts[i-1] + sizes[2*i-2];
390   count = 0;
391   for (i=0; i<size; i++) {
392     if (sizes[2*i+1]) {
393       ierr = MPI_Isend(svalues+starts[i],sizes[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
394     }
395   }
396   ierr = PetscFree(starts);CHKERRQ(ierr);
397 
398   base = owners[rank];
399 
400   /*  wait on receives */
401   ierr  = PetscMalloc2(nrecvs,&lens,nrecvs,&source);CHKERRQ(ierr);
402   count = nrecvs;
403   slen  = 0;
404   while (count) {
405     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
406     /* unpack receives into our local space */
407     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
408 
409     source[imdex] = recv_status.MPI_SOURCE;
410     lens[imdex]   = n;
411     slen += n;
412     count--;
413   }
414   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
415 
416   /* move the data into the send scatter */
417   ierr  = PetscMalloc1((slen+1),&lrows);CHKERRQ(ierr);
418   count = 0;
419   for (i=0; i<nrecvs; i++) {
420     values = rvalues + i*nmax;
421     for (j=0; j<lens[i]; j++) {
422       lrows[count++] = values[j] - base;
423     }
424   }
425   ierr = PetscFree(rvalues);CHKERRQ(ierr);
426   ierr = PetscFree2(lens,source);CHKERRQ(ierr);
427   ierr = PetscFree(owner);CHKERRQ(ierr);
428   ierr = PetscFree(sizes);CHKERRQ(ierr);
429 
430   /* fix right hand side if needed */
431   if (x && b) {
432     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
433     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
434     for (i=0; i<slen; i++) {
435       bb[lrows[i]] = diag*xx[lrows[i]];
436     }
437     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
438     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
439   }
440 
441   /* actually zap the local rows */
442   ierr = MatZeroRows(l->A,slen,lrows,0.0,0,0);CHKERRQ(ierr);
443   if (diag != 0.0) {
444     Mat_SeqDense *ll = (Mat_SeqDense*)l->A->data;
445     PetscInt     m   = ll->lda, i;
446 
447     for (i=0; i<slen; i++) {
448       ll->v[lrows[i] + m*(A->cmap->rstart + lrows[i])] = diag;
449     }
450   }
451   ierr = PetscFree(lrows);CHKERRQ(ierr);
452 
453   /* wait on sends */
454   if (nsends) {
455     ierr = PetscMalloc1(nsends,&send_status);CHKERRQ(ierr);
456     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
457     ierr = PetscFree(send_status);CHKERRQ(ierr);
458   }
459   ierr = PetscFree(send_waits);CHKERRQ(ierr);
460   ierr = PetscFree(svalues);CHKERRQ(ierr);
461   PetscFunctionReturn(0);
462 }
463 
464 #undef __FUNCT__
465 #define __FUNCT__ "MatMult_MPIDense"
466 PetscErrorCode MatMult_MPIDense(Mat mat,Vec xx,Vec yy)
467 {
468   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
469   PetscErrorCode ierr;
470 
471   PetscFunctionBegin;
472   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
473   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
474   ierr = MatMult_SeqDense(mdn->A,mdn->lvec,yy);CHKERRQ(ierr);
475   PetscFunctionReturn(0);
476 }
477 
478 #undef __FUNCT__
479 #define __FUNCT__ "MatMultAdd_MPIDense"
480 PetscErrorCode MatMultAdd_MPIDense(Mat mat,Vec xx,Vec yy,Vec zz)
481 {
482   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
483   PetscErrorCode ierr;
484 
485   PetscFunctionBegin;
486   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
487   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
488   ierr = MatMultAdd_SeqDense(mdn->A,mdn->lvec,yy,zz);CHKERRQ(ierr);
489   PetscFunctionReturn(0);
490 }
491 
492 #undef __FUNCT__
493 #define __FUNCT__ "MatMultTranspose_MPIDense"
494 PetscErrorCode MatMultTranspose_MPIDense(Mat A,Vec xx,Vec yy)
495 {
496   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
497   PetscErrorCode ierr;
498   PetscScalar    zero = 0.0;
499 
500   PetscFunctionBegin;
501   ierr = VecSet(yy,zero);CHKERRQ(ierr);
502   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
503   ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
504   ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
505   PetscFunctionReturn(0);
506 }
507 
508 #undef __FUNCT__
509 #define __FUNCT__ "MatMultTransposeAdd_MPIDense"
510 PetscErrorCode MatMultTransposeAdd_MPIDense(Mat A,Vec xx,Vec yy,Vec zz)
511 {
512   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
513   PetscErrorCode ierr;
514 
515   PetscFunctionBegin;
516   ierr = VecCopy(yy,zz);CHKERRQ(ierr);
517   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
518   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
519   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
520   PetscFunctionReturn(0);
521 }
522 
523 #undef __FUNCT__
524 #define __FUNCT__ "MatGetDiagonal_MPIDense"
525 PetscErrorCode MatGetDiagonal_MPIDense(Mat A,Vec v)
526 {
527   Mat_MPIDense   *a    = (Mat_MPIDense*)A->data;
528   Mat_SeqDense   *aloc = (Mat_SeqDense*)a->A->data;
529   PetscErrorCode ierr;
530   PetscInt       len,i,n,m = A->rmap->n,radd;
531   PetscScalar    *x,zero = 0.0;
532 
533   PetscFunctionBegin;
534   ierr = VecSet(v,zero);CHKERRQ(ierr);
535   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
536   ierr = VecGetSize(v,&n);CHKERRQ(ierr);
537   if (n != A->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming mat and vec");
538   len  = PetscMin(a->A->rmap->n,a->A->cmap->n);
539   radd = A->rmap->rstart*m;
540   for (i=0; i<len; i++) {
541     x[i] = aloc->v[radd + i*m + i];
542   }
543   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
544   PetscFunctionReturn(0);
545 }
546 
547 #undef __FUNCT__
548 #define __FUNCT__ "MatDestroy_MPIDense"
549 PetscErrorCode MatDestroy_MPIDense(Mat mat)
550 {
551   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
552   PetscErrorCode ierr;
553 
554   PetscFunctionBegin;
555 #if defined(PETSC_USE_LOG)
556   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
557 #endif
558   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
559   ierr = MatDestroy(&mdn->A);CHKERRQ(ierr);
560   ierr = VecDestroy(&mdn->lvec);CHKERRQ(ierr);
561   ierr = VecScatterDestroy(&mdn->Mvctx);CHKERRQ(ierr);
562 
563   ierr = PetscFree(mat->data);CHKERRQ(ierr);
564   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
565   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
566   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",NULL);CHKERRQ(ierr);
567   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
568   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
569   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
570   PetscFunctionReturn(0);
571 }
572 
573 #undef __FUNCT__
574 #define __FUNCT__ "MatView_MPIDense_Binary"
575 static PetscErrorCode MatView_MPIDense_Binary(Mat mat,PetscViewer viewer)
576 {
577   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
578   PetscErrorCode    ierr;
579   PetscViewerFormat format;
580   int               fd;
581   PetscInt          header[4],mmax,N = mat->cmap->N,i,j,m,k;
582   PetscMPIInt       rank,tag  = ((PetscObject)viewer)->tag,size;
583   PetscScalar       *work,*v,*vv;
584   Mat_SeqDense      *a = (Mat_SeqDense*)mdn->A->data;
585 
586   PetscFunctionBegin;
587   if (mdn->size == 1) {
588     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
589   } else {
590     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
591     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
592     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
593 
594     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
595     if (format == PETSC_VIEWER_NATIVE) {
596 
597       if (!rank) {
598         /* store the matrix as a dense matrix */
599         header[0] = MAT_FILE_CLASSID;
600         header[1] = mat->rmap->N;
601         header[2] = N;
602         header[3] = MATRIX_BINARY_FORMAT_DENSE;
603         ierr      = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
604 
605         /* get largest work array needed for transposing array */
606         mmax = mat->rmap->n;
607         for (i=1; i<size; i++) {
608           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
609         }
610         ierr = PetscMalloc1(mmax*N,&work);CHKERRQ(ierr);
611 
612         /* write out local array, by rows */
613         m = mat->rmap->n;
614         v = a->v;
615         for (j=0; j<N; j++) {
616           for (i=0; i<m; i++) {
617             work[j + i*N] = *v++;
618           }
619         }
620         ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
621         /* get largest work array to receive messages from other processes, excludes process zero */
622         mmax = 0;
623         for (i=1; i<size; i++) {
624           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
625         }
626         ierr = PetscMalloc1(mmax*N,&vv);CHKERRQ(ierr);
627         for (k = 1; k < size; k++) {
628           v    = vv;
629           m    = mat->rmap->range[k+1] - mat->rmap->range[k];
630           ierr = MPIULong_Recv(v,m*N,MPIU_SCALAR,k,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
631 
632           for (j = 0; j < N; j++) {
633             for (i = 0; i < m; i++) {
634               work[j + i*N] = *v++;
635             }
636           }
637           ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
638         }
639         ierr = PetscFree(work);CHKERRQ(ierr);
640         ierr = PetscFree(vv);CHKERRQ(ierr);
641       } else {
642         ierr = MPIULong_Send(a->v,mat->rmap->n*mat->cmap->N,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
643       }
644     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"To store a parallel dense matrix you must first call PetscViewerSetFormat(viewer,PETSC_VIEWER_NATIVE)");
645   }
646   PetscFunctionReturn(0);
647 }
648 
649 extern PetscErrorCode MatView_SeqDense(Mat,PetscViewer);
650 #include <petscdraw.h>
651 #undef __FUNCT__
652 #define __FUNCT__ "MatView_MPIDense_ASCIIorDraworSocket"
653 static PetscErrorCode MatView_MPIDense_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
654 {
655   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
656   PetscErrorCode    ierr;
657   PetscMPIInt       rank = mdn->rank;
658   PetscViewerType   vtype;
659   PetscBool         iascii,isdraw;
660   PetscViewer       sviewer;
661   PetscViewerFormat format;
662 
663   PetscFunctionBegin;
664   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
665   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&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 = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
673       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  [%d] local rows %D nz %D nz alloced %D mem %D \n",rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
674       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
675       ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
676       ierr = VecScatterView(mdn->Mvctx,viewer);CHKERRQ(ierr);
677       PetscFunctionReturn(0);
678     } else if (format == PETSC_VIEWER_ASCII_INFO) {
679       PetscFunctionReturn(0);
680     }
681   } else if (isdraw) {
682     PetscDraw draw;
683     PetscBool isnull;
684 
685     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
686     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
687     if (isnull) PetscFunctionReturn(0);
688   }
689 
690   {
691     /* assemble the entire matrix onto first processor. */
692     Mat         A;
693     PetscInt    M = mat->rmap->N,N = mat->cmap->N,m,row,i,nz;
694     PetscInt    *cols;
695     PetscScalar *vals;
696 
697     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
698     if (!rank) {
699       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
700     } else {
701       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
702     }
703     /* Since this is a temporary matrix, MATMPIDENSE instead of ((PetscObject)A)->type_name here is probably acceptable. */
704     ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
705     ierr = MatMPIDenseSetPreallocation(A,NULL);CHKERRQ(ierr);
706     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
707 
708     /* Copy the matrix ... This isn't the most efficient means,
709        but it's quick for now */
710     A->insertmode = INSERT_VALUES;
711 
712     row = mat->rmap->rstart;
713     m   = mdn->A->rmap->n;
714     for (i=0; i<m; i++) {
715       ierr = MatGetRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
716       ierr = MatSetValues_MPIDense(A,1,&row,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
717       ierr = MatRestoreRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
718       row++;
719     }
720 
721     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
722     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
723     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
724     if (!rank) {
725         ierr = MatView_SeqDense(((Mat_MPIDense*)(A->data))->A,sviewer);CHKERRQ(ierr);
726     }
727     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
728     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
729     ierr = MatDestroy(&A);CHKERRQ(ierr);
730   }
731   PetscFunctionReturn(0);
732 }
733 
734 #undef __FUNCT__
735 #define __FUNCT__ "MatView_MPIDense"
736 PetscErrorCode MatView_MPIDense(Mat mat,PetscViewer viewer)
737 {
738   PetscErrorCode ierr;
739   PetscBool      iascii,isbinary,isdraw,issocket;
740 
741   PetscFunctionBegin;
742   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
743   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
744   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
745   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
746 
747   if (iascii || issocket || isdraw) {
748     ierr = MatView_MPIDense_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
749   } else if (isbinary) {
750     ierr = MatView_MPIDense_Binary(mat,viewer);CHKERRQ(ierr);
751   }
752   PetscFunctionReturn(0);
753 }
754 
755 #undef __FUNCT__
756 #define __FUNCT__ "MatGetInfo_MPIDense"
757 PetscErrorCode MatGetInfo_MPIDense(Mat A,MatInfoType flag,MatInfo *info)
758 {
759   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
760   Mat            mdn  = mat->A;
761   PetscErrorCode ierr;
762   PetscReal      isend[5],irecv[5];
763 
764   PetscFunctionBegin;
765   info->block_size = 1.0;
766 
767   ierr = MatGetInfo(mdn,MAT_LOCAL,info);CHKERRQ(ierr);
768 
769   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
770   isend[3] = info->memory;  isend[4] = info->mallocs;
771   if (flag == MAT_LOCAL) {
772     info->nz_used      = isend[0];
773     info->nz_allocated = isend[1];
774     info->nz_unneeded  = isend[2];
775     info->memory       = isend[3];
776     info->mallocs      = isend[4];
777   } else if (flag == MAT_GLOBAL_MAX) {
778     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
779 
780     info->nz_used      = irecv[0];
781     info->nz_allocated = irecv[1];
782     info->nz_unneeded  = irecv[2];
783     info->memory       = irecv[3];
784     info->mallocs      = irecv[4];
785   } else if (flag == MAT_GLOBAL_SUM) {
786     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
787 
788     info->nz_used      = irecv[0];
789     info->nz_allocated = irecv[1];
790     info->nz_unneeded  = irecv[2];
791     info->memory       = irecv[3];
792     info->mallocs      = irecv[4];
793   }
794   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
795   info->fill_ratio_needed = 0;
796   info->factor_mallocs    = 0;
797   PetscFunctionReturn(0);
798 }
799 
800 #undef __FUNCT__
801 #define __FUNCT__ "MatSetOption_MPIDense"
802 PetscErrorCode MatSetOption_MPIDense(Mat A,MatOption op,PetscBool flg)
803 {
804   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
805   PetscErrorCode ierr;
806 
807   PetscFunctionBegin;
808   switch (op) {
809   case MAT_NEW_NONZERO_LOCATIONS:
810   case MAT_NEW_NONZERO_LOCATION_ERR:
811   case MAT_NEW_NONZERO_ALLOCATION_ERR:
812     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
813     break;
814   case MAT_ROW_ORIENTED:
815     a->roworiented = flg;
816 
817     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
818     break;
819   case MAT_NEW_DIAGONALS:
820   case MAT_KEEP_NONZERO_PATTERN:
821   case MAT_USE_HASH_TABLE:
822     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
823     break;
824   case MAT_IGNORE_OFF_PROC_ENTRIES:
825     a->donotstash = flg;
826     break;
827   case MAT_SYMMETRIC:
828   case MAT_STRUCTURALLY_SYMMETRIC:
829   case MAT_HERMITIAN:
830   case MAT_SYMMETRY_ETERNAL:
831   case MAT_IGNORE_LOWER_TRIANGULAR:
832     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
833     break;
834   default:
835     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %s",MatOptions[op]);
836   }
837   PetscFunctionReturn(0);
838 }
839 
840 
841 #undef __FUNCT__
842 #define __FUNCT__ "MatDiagonalScale_MPIDense"
843 PetscErrorCode MatDiagonalScale_MPIDense(Mat A,Vec ll,Vec rr)
844 {
845   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
846   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
847   PetscScalar    *l,*r,x,*v;
848   PetscErrorCode ierr;
849   PetscInt       i,j,s2a,s3a,s2,s3,m=mdn->A->rmap->n,n=mdn->A->cmap->n;
850 
851   PetscFunctionBegin;
852   ierr = MatGetLocalSize(A,&s2,&s3);CHKERRQ(ierr);
853   if (ll) {
854     ierr = VecGetLocalSize(ll,&s2a);CHKERRQ(ierr);
855     if (s2a != s2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector non-conforming local size, %d != %d.", s2a, s2);
856     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
857     for (i=0; i<m; i++) {
858       x = l[i];
859       v = mat->v + i;
860       for (j=0; j<n; j++) { (*v) *= x; v+= m;}
861     }
862     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
863     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
864   }
865   if (rr) {
866     ierr = VecGetLocalSize(rr,&s3a);CHKERRQ(ierr);
867     if (s3a != s3) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vec non-conforming local size, %d != %d.", s3a, s3);
868     ierr = VecScatterBegin(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869     ierr = VecScatterEnd(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
870     ierr = VecGetArray(mdn->lvec,&r);CHKERRQ(ierr);
871     for (i=0; i<n; i++) {
872       x = r[i];
873       v = mat->v + i*m;
874       for (j=0; j<m; j++) (*v++) *= x;
875     }
876     ierr = VecRestoreArray(mdn->lvec,&r);CHKERRQ(ierr);
877     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
878   }
879   PetscFunctionReturn(0);
880 }
881 
882 #undef __FUNCT__
883 #define __FUNCT__ "MatNorm_MPIDense"
884 PetscErrorCode MatNorm_MPIDense(Mat A,NormType type,PetscReal *nrm)
885 {
886   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
887   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
888   PetscErrorCode ierr;
889   PetscInt       i,j;
890   PetscReal      sum = 0.0;
891   PetscScalar    *v  = mat->v;
892 
893   PetscFunctionBegin;
894   if (mdn->size == 1) {
895     ierr =  MatNorm(mdn->A,type,nrm);CHKERRQ(ierr);
896   } else {
897     if (type == NORM_FROBENIUS) {
898       for (i=0; i<mdn->A->cmap->n*mdn->A->rmap->n; i++) {
899         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
900       }
901       ierr = MPI_Allreduce(&sum,nrm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
902       *nrm = PetscSqrtReal(*nrm);
903       ierr = PetscLogFlops(2.0*mdn->A->cmap->n*mdn->A->rmap->n);CHKERRQ(ierr);
904     } else if (type == NORM_1) {
905       PetscReal *tmp,*tmp2;
906       ierr = PetscMalloc2(A->cmap->N,&tmp,A->cmap->N,&tmp2);CHKERRQ(ierr);
907       ierr = PetscMemzero(tmp,A->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
908       ierr = PetscMemzero(tmp2,A->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
909       *nrm = 0.0;
910       v    = mat->v;
911       for (j=0; j<mdn->A->cmap->n; j++) {
912         for (i=0; i<mdn->A->rmap->n; i++) {
913           tmp[j] += PetscAbsScalar(*v);  v++;
914         }
915       }
916       ierr = MPI_Allreduce(tmp,tmp2,A->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
917       for (j=0; j<A->cmap->N; j++) {
918         if (tmp2[j] > *nrm) *nrm = tmp2[j];
919       }
920       ierr = PetscFree2(tmp,tmp);CHKERRQ(ierr);
921       ierr = PetscLogFlops(A->cmap->n*A->rmap->n);CHKERRQ(ierr);
922     } else if (type == NORM_INFINITY) { /* max row norm */
923       PetscReal ntemp;
924       ierr = MatNorm(mdn->A,type,&ntemp);CHKERRQ(ierr);
925       ierr = MPI_Allreduce(&ntemp,nrm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
926     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for two norm");
927   }
928   PetscFunctionReturn(0);
929 }
930 
931 #undef __FUNCT__
932 #define __FUNCT__ "MatTranspose_MPIDense"
933 PetscErrorCode MatTranspose_MPIDense(Mat A,MatReuse reuse,Mat *matout)
934 {
935   Mat_MPIDense   *a    = (Mat_MPIDense*)A->data;
936   Mat_SeqDense   *Aloc = (Mat_SeqDense*)a->A->data;
937   Mat            B;
938   PetscInt       M = A->rmap->N,N = A->cmap->N,m,n,*rwork,rstart = A->rmap->rstart;
939   PetscErrorCode ierr;
940   PetscInt       j,i;
941   PetscScalar    *v;
942 
943   PetscFunctionBegin;
944   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports square matrix only in-place");
945   if (reuse == MAT_INITIAL_MATRIX || A == *matout) {
946     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
947     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
948     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
949     ierr = MatMPIDenseSetPreallocation(B,NULL);CHKERRQ(ierr);
950   } else {
951     B = *matout;
952   }
953 
954   m    = a->A->rmap->n; n = a->A->cmap->n; v = Aloc->v;
955   ierr = PetscMalloc1(m,&rwork);CHKERRQ(ierr);
956   for (i=0; i<m; i++) rwork[i] = rstart + i;
957   for (j=0; j<n; j++) {
958     ierr = MatSetValues(B,1,&j,m,rwork,v,INSERT_VALUES);CHKERRQ(ierr);
959     v   += m;
960   }
961   ierr = PetscFree(rwork);CHKERRQ(ierr);
962   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
963   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
964   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
965     *matout = B;
966   } else {
967     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
968   }
969   PetscFunctionReturn(0);
970 }
971 
972 
973 static PetscErrorCode MatDuplicate_MPIDense(Mat,MatDuplicateOption,Mat*);
974 extern PetscErrorCode MatScale_MPIDense(Mat,PetscScalar);
975 
976 #undef __FUNCT__
977 #define __FUNCT__ "MatSetUp_MPIDense"
978 PetscErrorCode MatSetUp_MPIDense(Mat A)
979 {
980   PetscErrorCode ierr;
981 
982   PetscFunctionBegin;
983   ierr =  MatMPIDenseSetPreallocation(A,0);CHKERRQ(ierr);
984   PetscFunctionReturn(0);
985 }
986 
987 #undef __FUNCT__
988 #define __FUNCT__ "MatAXPY_MPIDense"
989 PetscErrorCode MatAXPY_MPIDense(Mat Y,PetscScalar alpha,Mat X,MatStructure str)
990 {
991   PetscErrorCode ierr;
992   Mat_MPIDense   *A = (Mat_MPIDense*)Y->data, *B = (Mat_MPIDense*)X->data;
993 
994   PetscFunctionBegin;
995   ierr = MatAXPY(A->A,alpha,B->A,str);CHKERRQ(ierr);
996   ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 #undef __FUNCT__
1001 #define __FUNCT__ "MatConjugate_MPIDense"
1002 PetscErrorCode  MatConjugate_MPIDense(Mat mat)
1003 {
1004   Mat_MPIDense   *a = (Mat_MPIDense*)mat->data;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = MatConjugate(a->A);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 #undef __FUNCT__
1013 #define __FUNCT__ "MatRealPart_MPIDense"
1014 PetscErrorCode MatRealPart_MPIDense(Mat A)
1015 {
1016   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
1017   PetscErrorCode ierr;
1018 
1019   PetscFunctionBegin;
1020   ierr = MatRealPart(a->A);CHKERRQ(ierr);
1021   PetscFunctionReturn(0);
1022 }
1023 
1024 #undef __FUNCT__
1025 #define __FUNCT__ "MatImaginaryPart_MPIDense"
1026 PetscErrorCode MatImaginaryPart_MPIDense(Mat A)
1027 {
1028   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
1029   PetscErrorCode ierr;
1030 
1031   PetscFunctionBegin;
1032   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
1033   PetscFunctionReturn(0);
1034 }
1035 
1036 extern PetscErrorCode MatGetColumnNorms_SeqDense(Mat,NormType,PetscReal*);
1037 #undef __FUNCT__
1038 #define __FUNCT__ "MatGetColumnNorms_MPIDense"
1039 PetscErrorCode MatGetColumnNorms_MPIDense(Mat A,NormType type,PetscReal *norms)
1040 {
1041   PetscErrorCode ierr;
1042   PetscInt       i,n;
1043   Mat_MPIDense   *a = (Mat_MPIDense*) A->data;
1044   PetscReal      *work;
1045 
1046   PetscFunctionBegin;
1047   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
1048   ierr = PetscMalloc1(n,&work);CHKERRQ(ierr);
1049   ierr = MatGetColumnNorms_SeqDense(a->A,type,work);CHKERRQ(ierr);
1050   if (type == NORM_2) {
1051     for (i=0; i<n; i++) work[i] *= work[i];
1052   }
1053   if (type == NORM_INFINITY) {
1054     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,A->hdr.comm);CHKERRQ(ierr);
1055   } else {
1056     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,A->hdr.comm);CHKERRQ(ierr);
1057   }
1058   ierr = PetscFree(work);CHKERRQ(ierr);
1059   if (type == NORM_2) {
1060     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
1061   }
1062   PetscFunctionReturn(0);
1063 }
1064 
1065 #undef __FUNCT__
1066 #define __FUNCT__ "MatSetRandom_MPIDense"
1067 static PetscErrorCode  MatSetRandom_MPIDense(Mat x,PetscRandom rctx)
1068 {
1069   Mat_MPIDense   *d = (Mat_MPIDense*)x->data;
1070   PetscErrorCode ierr;
1071   PetscScalar    *a;
1072   PetscInt       m,n,i;
1073 
1074   PetscFunctionBegin;
1075   ierr = MatGetSize(d->A,&m,&n);CHKERRQ(ierr);
1076   ierr = MatDenseGetArray(d->A,&a);CHKERRQ(ierr);
1077   for (i=0; i<m*n; i++) {
1078     ierr = PetscRandomGetValue(rctx,a+i);CHKERRQ(ierr);
1079   }
1080   ierr = MatDenseRestoreArray(d->A,&a);CHKERRQ(ierr);
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 /* -------------------------------------------------------------------*/
1085 static struct _MatOps MatOps_Values = { MatSetValues_MPIDense,
1086                                         MatGetRow_MPIDense,
1087                                         MatRestoreRow_MPIDense,
1088                                         MatMult_MPIDense,
1089                                 /*  4*/ MatMultAdd_MPIDense,
1090                                         MatMultTranspose_MPIDense,
1091                                         MatMultTransposeAdd_MPIDense,
1092                                         0,
1093                                         0,
1094                                         0,
1095                                 /* 10*/ 0,
1096                                         0,
1097                                         0,
1098                                         0,
1099                                         MatTranspose_MPIDense,
1100                                 /* 15*/ MatGetInfo_MPIDense,
1101                                         MatEqual_MPIDense,
1102                                         MatGetDiagonal_MPIDense,
1103                                         MatDiagonalScale_MPIDense,
1104                                         MatNorm_MPIDense,
1105                                 /* 20*/ MatAssemblyBegin_MPIDense,
1106                                         MatAssemblyEnd_MPIDense,
1107                                         MatSetOption_MPIDense,
1108                                         MatZeroEntries_MPIDense,
1109                                 /* 24*/ MatZeroRows_MPIDense,
1110                                         0,
1111                                         0,
1112                                         0,
1113                                         0,
1114                                 /* 29*/ MatSetUp_MPIDense,
1115                                         0,
1116                                         0,
1117                                         0,
1118                                         0,
1119                                 /* 34*/ MatDuplicate_MPIDense,
1120                                         0,
1121                                         0,
1122                                         0,
1123                                         0,
1124                                 /* 39*/ MatAXPY_MPIDense,
1125                                         MatGetSubMatrices_MPIDense,
1126                                         0,
1127                                         MatGetValues_MPIDense,
1128                                         0,
1129                                 /* 44*/ 0,
1130                                         MatScale_MPIDense,
1131                                         0,
1132                                         0,
1133                                         0,
1134                                 /* 49*/ MatSetRandom_MPIDense,
1135                                         0,
1136                                         0,
1137                                         0,
1138                                         0,
1139                                 /* 54*/ 0,
1140                                         0,
1141                                         0,
1142                                         0,
1143                                         0,
1144                                 /* 59*/ MatGetSubMatrix_MPIDense,
1145                                         MatDestroy_MPIDense,
1146                                         MatView_MPIDense,
1147                                         0,
1148                                         0,
1149                                 /* 64*/ 0,
1150                                         0,
1151                                         0,
1152                                         0,
1153                                         0,
1154                                 /* 69*/ 0,
1155                                         0,
1156                                         0,
1157                                         0,
1158                                         0,
1159                                 /* 74*/ 0,
1160                                         0,
1161                                         0,
1162                                         0,
1163                                         0,
1164                                 /* 79*/ 0,
1165                                         0,
1166                                         0,
1167                                         0,
1168                                 /* 83*/ MatLoad_MPIDense,
1169                                         0,
1170                                         0,
1171                                         0,
1172                                         0,
1173                                         0,
1174                                 /* 89*/
1175                                         0,
1176                                         0,
1177                                         0,
1178                                         0,
1179                                         0,
1180                                 /* 94*/ 0,
1181                                         0,
1182                                         0,
1183                                         0,
1184                                         0,
1185                                 /* 99*/ 0,
1186                                         0,
1187                                         0,
1188                                         MatConjugate_MPIDense,
1189                                         0,
1190                                 /*104*/ 0,
1191                                         MatRealPart_MPIDense,
1192                                         MatImaginaryPart_MPIDense,
1193                                         0,
1194                                         0,
1195                                 /*109*/ 0,
1196                                         0,
1197                                         0,
1198                                         0,
1199                                         0,
1200                                 /*114*/ 0,
1201                                         0,
1202                                         0,
1203                                         0,
1204                                         0,
1205                                 /*119*/ 0,
1206                                         0,
1207                                         0,
1208                                         0,
1209                                         0,
1210                                 /*124*/ 0,
1211                                         MatGetColumnNorms_MPIDense,
1212                                         0,
1213                                         0,
1214                                         0,
1215                                 /*129*/ 0,
1216                                         0,
1217                                         0,
1218                                         0,
1219                                         0,
1220                                 /*134*/ 0,
1221                                         0,
1222                                         0,
1223                                         0,
1224                                         0,
1225                                 /*139*/ 0,
1226                                         0,
1227                                         0
1228 };
1229 
1230 #undef __FUNCT__
1231 #define __FUNCT__ "MatMPIDenseSetPreallocation_MPIDense"
1232 PetscErrorCode  MatMPIDenseSetPreallocation_MPIDense(Mat mat,PetscScalar *data)
1233 {
1234   Mat_MPIDense   *a;
1235   PetscErrorCode ierr;
1236 
1237   PetscFunctionBegin;
1238   mat->preallocated = PETSC_TRUE;
1239   /* Note:  For now, when data is specified above, this assumes the user correctly
1240    allocates the local dense storage space.  We should add error checking. */
1241 
1242   a       = (Mat_MPIDense*)mat->data;
1243   ierr    = PetscLayoutSetUp(mat->rmap);CHKERRQ(ierr);
1244   ierr    = PetscLayoutSetUp(mat->cmap);CHKERRQ(ierr);
1245   a->nvec = mat->cmap->n;
1246 
1247   ierr = MatCreate(PETSC_COMM_SELF,&a->A);CHKERRQ(ierr);
1248   ierr = MatSetSizes(a->A,mat->rmap->n,mat->cmap->N,mat->rmap->n,mat->cmap->N);CHKERRQ(ierr);
1249   ierr = MatSetType(a->A,MATSEQDENSE);CHKERRQ(ierr);
1250   ierr = MatSeqDenseSetPreallocation(a->A,data);CHKERRQ(ierr);
1251   ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
1252   PetscFunctionReturn(0);
1253 }
1254 
1255 #undef __FUNCT__
1256 #define __FUNCT__ "MatCreate_MPIDense"
1257 PETSC_EXTERN PetscErrorCode MatCreate_MPIDense(Mat mat)
1258 {
1259   Mat_MPIDense   *a;
1260   PetscErrorCode ierr;
1261 
1262   PetscFunctionBegin;
1263   ierr      = PetscNewLog(mat,&a);CHKERRQ(ierr);
1264   mat->data = (void*)a;
1265   ierr      = PetscMemcpy(mat->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1266 
1267   mat->insertmode = NOT_SET_VALUES;
1268   ierr            = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&a->rank);CHKERRQ(ierr);
1269   ierr            = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&a->size);CHKERRQ(ierr);
1270 
1271   /* build cache for off array entries formed */
1272   a->donotstash = PETSC_FALSE;
1273 
1274   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)mat),1,&mat->stash);CHKERRQ(ierr);
1275 
1276   /* stuff used for matrix vector multiply */
1277   a->lvec        = 0;
1278   a->Mvctx       = 0;
1279   a->roworiented = PETSC_TRUE;
1280 
1281   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArray_C",MatDenseGetArray_MPIDense);CHKERRQ(ierr);
1282   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArray_C",MatDenseRestoreArray_MPIDense);CHKERRQ(ierr);
1283 
1284   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIDense);CHKERRQ(ierr);
1285   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",MatMPIDenseSetPreallocation_MPIDense);CHKERRQ(ierr);
1286   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",MatMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1287   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",MatMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1288   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",MatMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1289 
1290   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMult_mpiaij_mpidense_C",MatTransposeMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1291   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultSymbolic_mpiaij_mpidense_C",MatTransposeMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1292   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultNumeric_mpiaij_mpidense_C",MatTransposeMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1293   ierr = PetscObjectChangeTypeName((PetscObject)mat,MATMPIDENSE);CHKERRQ(ierr);
1294   PetscFunctionReturn(0);
1295 }
1296 
1297 /*MC
1298    MATDENSE - MATDENSE = "dense" - A matrix type to be used for dense matrices.
1299 
1300    This matrix type is identical to MATSEQDENSE when constructed with a single process communicator,
1301    and MATMPIDENSE otherwise.
1302 
1303    Options Database Keys:
1304 . -mat_type dense - sets the matrix type to "dense" during a call to MatSetFromOptions()
1305 
1306   Level: beginner
1307 
1308 
1309 .seealso: MatCreateMPIDense,MATSEQDENSE,MATMPIDENSE
1310 M*/
1311 
1312 #undef __FUNCT__
1313 #define __FUNCT__ "MatMPIDenseSetPreallocation"
1314 /*@C
1315    MatMPIDenseSetPreallocation - Sets the array used to store the matrix entries
1316 
1317    Not collective
1318 
1319    Input Parameters:
1320 .  A - the matrix
1321 -  data - optional location of matrix data.  Set data=NULL for PETSc
1322    to control all matrix memory allocation.
1323 
1324    Notes:
1325    The dense format is fully compatible with standard Fortran 77
1326    storage by columns.
1327 
1328    The data input variable is intended primarily for Fortran programmers
1329    who wish to allocate their own matrix memory space.  Most users should
1330    set data=NULL.
1331 
1332    Level: intermediate
1333 
1334 .keywords: matrix,dense, parallel
1335 
1336 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1337 @*/
1338 PetscErrorCode  MatMPIDenseSetPreallocation(Mat mat,PetscScalar *data)
1339 {
1340   PetscErrorCode ierr;
1341 
1342   PetscFunctionBegin;
1343   ierr = PetscTryMethod(mat,"MatMPIDenseSetPreallocation_C",(Mat,PetscScalar*),(mat,data));CHKERRQ(ierr);
1344   PetscFunctionReturn(0);
1345 }
1346 
1347 #undef __FUNCT__
1348 #define __FUNCT__ "MatCreateDense"
1349 /*@C
1350    MatCreateDense - Creates a parallel matrix in dense format.
1351 
1352    Collective on MPI_Comm
1353 
1354    Input Parameters:
1355 +  comm - MPI communicator
1356 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
1357 .  n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
1358 .  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
1359 .  N - number of global columns (or PETSC_DECIDE to have calculated if n is given)
1360 -  data - optional location of matrix data.  Set data=NULL (NULL_SCALAR for Fortran users) for PETSc
1361    to control all matrix memory allocation.
1362 
1363    Output Parameter:
1364 .  A - the matrix
1365 
1366    Notes:
1367    The dense format is fully compatible with standard Fortran 77
1368    storage by columns.
1369 
1370    The data input variable is intended primarily for Fortran programmers
1371    who wish to allocate their own matrix memory space.  Most users should
1372    set data=NULL (NULL_SCALAR for Fortran users).
1373 
1374    The user MUST specify either the local or global matrix dimensions
1375    (possibly both).
1376 
1377    Level: intermediate
1378 
1379 .keywords: matrix,dense, parallel
1380 
1381 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1382 @*/
1383 PetscErrorCode  MatCreateDense(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscScalar *data,Mat *A)
1384 {
1385   PetscErrorCode ierr;
1386   PetscMPIInt    size;
1387 
1388   PetscFunctionBegin;
1389   ierr = MatCreate(comm,A);CHKERRQ(ierr);
1390   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
1391   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1392   if (size > 1) {
1393     ierr = MatSetType(*A,MATMPIDENSE);CHKERRQ(ierr);
1394     ierr = MatMPIDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1395   } else {
1396     ierr = MatSetType(*A,MATSEQDENSE);CHKERRQ(ierr);
1397     ierr = MatSeqDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1398   }
1399   PetscFunctionReturn(0);
1400 }
1401 
1402 #undef __FUNCT__
1403 #define __FUNCT__ "MatDuplicate_MPIDense"
1404 static PetscErrorCode MatDuplicate_MPIDense(Mat A,MatDuplicateOption cpvalues,Mat *newmat)
1405 {
1406   Mat            mat;
1407   Mat_MPIDense   *a,*oldmat = (Mat_MPIDense*)A->data;
1408   PetscErrorCode ierr;
1409 
1410   PetscFunctionBegin;
1411   *newmat = 0;
1412   ierr    = MatCreate(PetscObjectComm((PetscObject)A),&mat);CHKERRQ(ierr);
1413   ierr    = MatSetSizes(mat,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
1414   ierr    = MatSetType(mat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1415   a       = (Mat_MPIDense*)mat->data;
1416   ierr    = PetscMemcpy(mat->ops,A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
1417 
1418   mat->factortype   = A->factortype;
1419   mat->assembled    = PETSC_TRUE;
1420   mat->preallocated = PETSC_TRUE;
1421 
1422   a->size         = oldmat->size;
1423   a->rank         = oldmat->rank;
1424   mat->insertmode = NOT_SET_VALUES;
1425   a->nvec         = oldmat->nvec;
1426   a->donotstash   = oldmat->donotstash;
1427 
1428   ierr = PetscLayoutReference(A->rmap,&mat->rmap);CHKERRQ(ierr);
1429   ierr = PetscLayoutReference(A->cmap,&mat->cmap);CHKERRQ(ierr);
1430 
1431   ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
1432   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1433   ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
1434 
1435   *newmat = mat;
1436   PetscFunctionReturn(0);
1437 }
1438 
1439 #undef __FUNCT__
1440 #define __FUNCT__ "MatLoad_MPIDense_DenseInFile"
1441 PetscErrorCode MatLoad_MPIDense_DenseInFile(MPI_Comm comm,PetscInt fd,PetscInt M,PetscInt N,Mat newmat,PetscInt sizesset)
1442 {
1443   PetscErrorCode ierr;
1444   PetscMPIInt    rank,size;
1445   PetscInt       *rowners,i,m,nz,j;
1446   PetscScalar    *array,*vals,*vals_ptr;
1447 
1448   PetscFunctionBegin;
1449   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1450   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1451 
1452   /* determine ownership of all rows */
1453   if (newmat->rmap->n < 0) m = M/size + ((M % size) > rank);
1454   else m = newmat->rmap->n;
1455   ierr       = PetscMalloc1((size+2),&rowners);CHKERRQ(ierr);
1456   ierr       = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
1457   rowners[0] = 0;
1458   for (i=2; i<=size; i++) {
1459     rowners[i] += rowners[i-1];
1460   }
1461 
1462   if (!sizesset) {
1463     ierr = MatSetSizes(newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
1464   }
1465   ierr = MatMPIDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
1466   ierr = MatDenseGetArray(newmat,&array);CHKERRQ(ierr);
1467 
1468   if (!rank) {
1469     ierr = PetscMalloc1(m*N,&vals);CHKERRQ(ierr);
1470 
1471     /* read in my part of the matrix numerical values  */
1472     ierr = PetscBinaryRead(fd,vals,m*N,PETSC_SCALAR);CHKERRQ(ierr);
1473 
1474     /* insert into matrix-by row (this is why cannot directly read into array */
1475     vals_ptr = vals;
1476     for (i=0; i<m; i++) {
1477       for (j=0; j<N; j++) {
1478         array[i + j*m] = *vals_ptr++;
1479       }
1480     }
1481 
1482     /* read in other processors and ship out */
1483     for (i=1; i<size; i++) {
1484       nz   = (rowners[i+1] - rowners[i])*N;
1485       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1486       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)(newmat))->tag,comm);CHKERRQ(ierr);
1487     }
1488   } else {
1489     /* receive numeric values */
1490     ierr = PetscMalloc1(m*N,&vals);CHKERRQ(ierr);
1491 
1492     /* receive message of values*/
1493     ierr = MPIULong_Recv(vals,m*N,MPIU_SCALAR,0,((PetscObject)(newmat))->tag,comm);CHKERRQ(ierr);
1494 
1495     /* insert into matrix-by row (this is why cannot directly read into array */
1496     vals_ptr = vals;
1497     for (i=0; i<m; i++) {
1498       for (j=0; j<N; j++) {
1499         array[i + j*m] = *vals_ptr++;
1500       }
1501     }
1502   }
1503   ierr = MatDenseRestoreArray(newmat,&array);CHKERRQ(ierr);
1504   ierr = PetscFree(rowners);CHKERRQ(ierr);
1505   ierr = PetscFree(vals);CHKERRQ(ierr);
1506   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1507   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1508   PetscFunctionReturn(0);
1509 }
1510 
1511 #undef __FUNCT__
1512 #define __FUNCT__ "MatLoad_MPIDense"
1513 PetscErrorCode MatLoad_MPIDense(Mat newmat,PetscViewer viewer)
1514 {
1515   PetscScalar    *vals,*svals;
1516   MPI_Comm       comm;
1517   MPI_Status     status;
1518   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag,*rowners,*sndcounts,m,maxnz;
1519   PetscInt       header[4],*rowlengths = 0,M,N,*cols;
1520   PetscInt       *ourlens,*procsnz = 0,*offlens,jj,*mycols,*smycols;
1521   PetscInt       i,nz,j,rstart,rend,sizesset=1,grows,gcols;
1522   int            fd;
1523   PetscErrorCode ierr;
1524 
1525   PetscFunctionBegin;
1526   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
1527   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1528   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1529   if (!rank) {
1530     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1531     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
1532     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
1533   }
1534   if (newmat->rmap->n < 0 && newmat->rmap->N < 0 && newmat->cmap->n < 0 && newmat->cmap->N < 0) sizesset = 0;
1535 
1536   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
1537   M    = header[1]; N = header[2]; nz = header[3];
1538 
1539   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
1540   if (sizesset && newmat->rmap->N < 0) newmat->rmap->N = M;
1541   if (sizesset && newmat->cmap->N < 0) newmat->cmap->N = N;
1542 
1543   /* If global sizes are set, check if they are consistent with that given in the file */
1544   if (sizesset) {
1545     ierr = MatGetSize(newmat,&grows,&gcols);CHKERRQ(ierr);
1546   }
1547   if (sizesset && newmat->rmap->N != grows) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows:Matrix in file has (%d) and input matrix has (%d)",M,grows);
1548   if (sizesset && newmat->cmap->N != gcols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of cols:Matrix in file has (%d) and input matrix has (%d)",N,gcols);
1549 
1550   /*
1551        Handle case where matrix is stored on disk as a dense matrix
1552   */
1553   if (nz == MATRIX_BINARY_FORMAT_DENSE) {
1554     ierr = MatLoad_MPIDense_DenseInFile(comm,fd,M,N,newmat,sizesset);CHKERRQ(ierr);
1555     PetscFunctionReturn(0);
1556   }
1557 
1558   /* determine ownership of all rows */
1559   if (newmat->rmap->n < 0) {
1560     ierr = PetscMPIIntCast(M/size + ((M % size) > rank),&m);CHKERRQ(ierr);
1561   } else {
1562     ierr = PetscMPIIntCast(newmat->rmap->n,&m);CHKERRQ(ierr);
1563   }
1564   ierr       = PetscMalloc1((size+2),&rowners);CHKERRQ(ierr);
1565   ierr       = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
1566   rowners[0] = 0;
1567   for (i=2; i<=size; i++) {
1568     rowners[i] += rowners[i-1];
1569   }
1570   rstart = rowners[rank];
1571   rend   = rowners[rank+1];
1572 
1573   /* distribute row lengths to all processors */
1574   ierr = PetscMalloc2(rend-rstart,&ourlens,rend-rstart,&offlens);CHKERRQ(ierr);
1575   if (!rank) {
1576     ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
1577     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
1578     ierr = PetscMalloc1(size,&sndcounts);CHKERRQ(ierr);
1579     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
1580     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1581     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
1582   } else {
1583     ierr = MPI_Scatterv(0,0,0,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1584   }
1585 
1586   if (!rank) {
1587     /* calculate the number of nonzeros on each processor */
1588     ierr = PetscMalloc1(size,&procsnz);CHKERRQ(ierr);
1589     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
1590     for (i=0; i<size; i++) {
1591       for (j=rowners[i]; j< rowners[i+1]; j++) {
1592         procsnz[i] += rowlengths[j];
1593       }
1594     }
1595     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
1596 
1597     /* determine max buffer needed and allocate it */
1598     maxnz = 0;
1599     for (i=0; i<size; i++) {
1600       maxnz = PetscMax(maxnz,procsnz[i]);
1601     }
1602     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
1603 
1604     /* read in my part of the matrix column indices  */
1605     nz   = procsnz[0];
1606     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
1607     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
1608 
1609     /* read in every one elses and ship off */
1610     for (i=1; i<size; i++) {
1611       nz   = procsnz[i];
1612       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
1613       ierr = MPI_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
1614     }
1615     ierr = PetscFree(cols);CHKERRQ(ierr);
1616   } else {
1617     /* determine buffer space needed for message */
1618     nz = 0;
1619     for (i=0; i<m; i++) {
1620       nz += ourlens[i];
1621     }
1622     ierr = PetscMalloc1((nz+1),&mycols);CHKERRQ(ierr);
1623 
1624     /* receive message of column indices*/
1625     ierr = MPI_Recv(mycols,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
1626     ierr = MPI_Get_count(&status,MPIU_INT,&maxnz);CHKERRQ(ierr);
1627     if (maxnz != nz) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1628   }
1629 
1630   /* loop over local rows, determining number of off diagonal entries */
1631   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
1632   jj   = 0;
1633   for (i=0; i<m; i++) {
1634     for (j=0; j<ourlens[i]; j++) {
1635       if (mycols[jj] < rstart || mycols[jj] >= rend) offlens[i]++;
1636       jj++;
1637     }
1638   }
1639 
1640   /* create our matrix */
1641   for (i=0; i<m; i++) ourlens[i] -= offlens[i];
1642 
1643   if (!sizesset) {
1644     ierr = MatSetSizes(newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
1645   }
1646   ierr = MatMPIDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
1647   for (i=0; i<m; i++) ourlens[i] += offlens[i];
1648 
1649   if (!rank) {
1650     ierr = PetscMalloc1(maxnz,&vals);CHKERRQ(ierr);
1651 
1652     /* read in my part of the matrix numerical values  */
1653     nz   = procsnz[0];
1654     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1655 
1656     /* insert into matrix */
1657     jj      = rstart;
1658     smycols = mycols;
1659     svals   = vals;
1660     for (i=0; i<m; i++) {
1661       ierr     = MatSetValues(newmat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1662       smycols += ourlens[i];
1663       svals   += ourlens[i];
1664       jj++;
1665     }
1666 
1667     /* read in other processors and ship out */
1668     for (i=1; i<size; i++) {
1669       nz   = procsnz[i];
1670       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1671       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newmat)->tag,comm);CHKERRQ(ierr);
1672     }
1673     ierr = PetscFree(procsnz);CHKERRQ(ierr);
1674   } else {
1675     /* receive numeric values */
1676     ierr = PetscMalloc1((nz+1),&vals);CHKERRQ(ierr);
1677 
1678     /* receive message of values*/
1679     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newmat)->tag,comm,&status);CHKERRQ(ierr);
1680     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
1681     if (maxnz != nz) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1682 
1683     /* insert into matrix */
1684     jj      = rstart;
1685     smycols = mycols;
1686     svals   = vals;
1687     for (i=0; i<m; i++) {
1688       ierr     = MatSetValues(newmat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1689       smycols += ourlens[i];
1690       svals   += ourlens[i];
1691       jj++;
1692     }
1693   }
1694   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
1695   ierr = PetscFree(vals);CHKERRQ(ierr);
1696   ierr = PetscFree(mycols);CHKERRQ(ierr);
1697   ierr = PetscFree(rowners);CHKERRQ(ierr);
1698 
1699   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1700   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1701   PetscFunctionReturn(0);
1702 }
1703 
1704 #undef __FUNCT__
1705 #define __FUNCT__ "MatEqual_MPIDense"
1706 PetscErrorCode MatEqual_MPIDense(Mat A,Mat B,PetscBool  *flag)
1707 {
1708   Mat_MPIDense   *matB = (Mat_MPIDense*)B->data,*matA = (Mat_MPIDense*)A->data;
1709   Mat            a,b;
1710   PetscBool      flg;
1711   PetscErrorCode ierr;
1712 
1713   PetscFunctionBegin;
1714   a    = matA->A;
1715   b    = matB->A;
1716   ierr = MatEqual(a,b,&flg);CHKERRQ(ierr);
1717   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1718   PetscFunctionReturn(0);
1719 }
1720 
1721