xref: /petsc/src/mat/impls/dense/mpi/mpidense.c (revision dced61a5cfeeeda68dfa4ee3e53b34d3cfb8da9f)
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 
566   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArray_C",NULL);CHKERRQ(ierr);
567   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArray_C",NULL);CHKERRQ(ierr);
568 #if defined(PETSC_HAVE_ELEMENTAL)
569   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpidense_elemental_C",NULL);CHKERRQ(ierr);
570 #endif
571   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",NULL);CHKERRQ(ierr);
572   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",NULL);CHKERRQ(ierr);
573   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
574   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
575   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
576   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMult_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
577   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultSymbolic_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
578   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultNumeric_mpiaij_mpidense_C",NULL);CHKERRQ(ierr);
579   PetscFunctionReturn(0);
580 }
581 
582 #undef __FUNCT__
583 #define __FUNCT__ "MatView_MPIDense_Binary"
584 static PetscErrorCode MatView_MPIDense_Binary(Mat mat,PetscViewer viewer)
585 {
586   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
587   PetscErrorCode    ierr;
588   PetscViewerFormat format;
589   int               fd;
590   PetscInt          header[4],mmax,N = mat->cmap->N,i,j,m,k;
591   PetscMPIInt       rank,tag  = ((PetscObject)viewer)->tag,size;
592   PetscScalar       *work,*v,*vv;
593   Mat_SeqDense      *a = (Mat_SeqDense*)mdn->A->data;
594 
595   PetscFunctionBegin;
596   if (mdn->size == 1) {
597     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
598   } else {
599     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
600     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
601     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
602 
603     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
604     if (format == PETSC_VIEWER_NATIVE) {
605 
606       if (!rank) {
607         /* store the matrix as a dense matrix */
608         header[0] = MAT_FILE_CLASSID;
609         header[1] = mat->rmap->N;
610         header[2] = N;
611         header[3] = MATRIX_BINARY_FORMAT_DENSE;
612         ierr      = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
613 
614         /* get largest work array needed for transposing array */
615         mmax = mat->rmap->n;
616         for (i=1; i<size; i++) {
617           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
618         }
619         ierr = PetscMalloc1(mmax*N,&work);CHKERRQ(ierr);
620 
621         /* write out local array, by rows */
622         m = mat->rmap->n;
623         v = a->v;
624         for (j=0; j<N; j++) {
625           for (i=0; i<m; i++) {
626             work[j + i*N] = *v++;
627           }
628         }
629         ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
630         /* get largest work array to receive messages from other processes, excludes process zero */
631         mmax = 0;
632         for (i=1; i<size; i++) {
633           mmax = PetscMax(mmax,mat->rmap->range[i+1] - mat->rmap->range[i]);
634         }
635         ierr = PetscMalloc1(mmax*N,&vv);CHKERRQ(ierr);
636         for (k = 1; k < size; k++) {
637           v    = vv;
638           m    = mat->rmap->range[k+1] - mat->rmap->range[k];
639           ierr = MPIULong_Recv(v,m*N,MPIU_SCALAR,k,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
640 
641           for (j = 0; j < N; j++) {
642             for (i = 0; i < m; i++) {
643               work[j + i*N] = *v++;
644             }
645           }
646           ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
647         }
648         ierr = PetscFree(work);CHKERRQ(ierr);
649         ierr = PetscFree(vv);CHKERRQ(ierr);
650       } else {
651         ierr = MPIULong_Send(a->v,mat->rmap->n*mat->cmap->N,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
652       }
653     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"To store a parallel dense matrix you must first call PetscViewerSetFormat(viewer,PETSC_VIEWER_NATIVE)");
654   }
655   PetscFunctionReturn(0);
656 }
657 
658 extern PetscErrorCode MatView_SeqDense(Mat,PetscViewer);
659 #include <petscdraw.h>
660 #undef __FUNCT__
661 #define __FUNCT__ "MatView_MPIDense_ASCIIorDraworSocket"
662 static PetscErrorCode MatView_MPIDense_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
663 {
664   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
665   PetscErrorCode    ierr;
666   PetscMPIInt       rank = mdn->rank;
667   PetscViewerType   vtype;
668   PetscBool         iascii,isdraw;
669   PetscViewer       sviewer;
670   PetscViewerFormat format;
671 
672   PetscFunctionBegin;
673   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
674   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
675   if (iascii) {
676     ierr = PetscViewerGetType(viewer,&vtype);CHKERRQ(ierr);
677     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
678     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
679       MatInfo info;
680       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
681       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
682       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);
683       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
684       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
685       ierr = VecScatterView(mdn->Mvctx,viewer);CHKERRQ(ierr);
686       PetscFunctionReturn(0);
687     } else if (format == PETSC_VIEWER_ASCII_INFO) {
688       PetscFunctionReturn(0);
689     }
690   } else if (isdraw) {
691     PetscDraw draw;
692     PetscBool isnull;
693 
694     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
695     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
696     if (isnull) PetscFunctionReturn(0);
697   }
698 
699   {
700     /* assemble the entire matrix onto first processor. */
701     Mat         A;
702     PetscInt    M = mat->rmap->N,N = mat->cmap->N,m,row,i,nz;
703     PetscInt    *cols;
704     PetscScalar *vals;
705 
706     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
707     if (!rank) {
708       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
709     } else {
710       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
711     }
712     /* Since this is a temporary matrix, MATMPIDENSE instead of ((PetscObject)A)->type_name here is probably acceptable. */
713     ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
714     ierr = MatMPIDenseSetPreallocation(A,NULL);CHKERRQ(ierr);
715     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
716 
717     /* Copy the matrix ... This isn't the most efficient means,
718        but it's quick for now */
719     A->insertmode = INSERT_VALUES;
720 
721     row = mat->rmap->rstart;
722     m   = mdn->A->rmap->n;
723     for (i=0; i<m; i++) {
724       ierr = MatGetRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
725       ierr = MatSetValues_MPIDense(A,1,&row,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
726       ierr = MatRestoreRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
727       row++;
728     }
729 
730     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
731     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
732     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
733     if (!rank) {
734         ierr = MatView_SeqDense(((Mat_MPIDense*)(A->data))->A,sviewer);CHKERRQ(ierr);
735     }
736     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
737     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
738     ierr = MatDestroy(&A);CHKERRQ(ierr);
739   }
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "MatView_MPIDense"
745 PetscErrorCode MatView_MPIDense(Mat mat,PetscViewer viewer)
746 {
747   PetscErrorCode ierr;
748   PetscBool      iascii,isbinary,isdraw,issocket;
749 
750   PetscFunctionBegin;
751   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
752   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
753   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
754   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
755 
756   if (iascii || issocket || isdraw) {
757     ierr = MatView_MPIDense_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
758   } else if (isbinary) {
759     ierr = MatView_MPIDense_Binary(mat,viewer);CHKERRQ(ierr);
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->block_size = 1.0;
775 
776   ierr = MatGetInfo(mdn,MAT_LOCAL,info);CHKERRQ(ierr);
777 
778   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
779   isend[3] = info->memory;  isend[4] = info->mallocs;
780   if (flag == MAT_LOCAL) {
781     info->nz_used      = isend[0];
782     info->nz_allocated = isend[1];
783     info->nz_unneeded  = isend[2];
784     info->memory       = isend[3];
785     info->mallocs      = isend[4];
786   } else if (flag == MAT_GLOBAL_MAX) {
787     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
788 
789     info->nz_used      = irecv[0];
790     info->nz_allocated = irecv[1];
791     info->nz_unneeded  = irecv[2];
792     info->memory       = irecv[3];
793     info->mallocs      = irecv[4];
794   } else if (flag == MAT_GLOBAL_SUM) {
795     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
796 
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,PetscBool 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 
826     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
827     break;
828   case MAT_NEW_DIAGONALS:
829   case MAT_KEEP_NONZERO_PATTERN:
830   case MAT_USE_HASH_TABLE:
831     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
832     break;
833   case MAT_IGNORE_OFF_PROC_ENTRIES:
834     a->donotstash = flg;
835     break;
836   case MAT_SYMMETRIC:
837   case MAT_STRUCTURALLY_SYMMETRIC:
838   case MAT_HERMITIAN:
839   case MAT_SYMMETRY_ETERNAL:
840   case MAT_IGNORE_LOWER_TRIANGULAR:
841     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
842     break;
843   default:
844     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %s",MatOptions[op]);
845   }
846   PetscFunctionReturn(0);
847 }
848 
849 
850 #undef __FUNCT__
851 #define __FUNCT__ "MatDiagonalScale_MPIDense"
852 PetscErrorCode MatDiagonalScale_MPIDense(Mat A,Vec ll,Vec rr)
853 {
854   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
855   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
856   PetscScalar    *l,*r,x,*v;
857   PetscErrorCode ierr;
858   PetscInt       i,j,s2a,s3a,s2,s3,m=mdn->A->rmap->n,n=mdn->A->cmap->n;
859 
860   PetscFunctionBegin;
861   ierr = MatGetLocalSize(A,&s2,&s3);CHKERRQ(ierr);
862   if (ll) {
863     ierr = VecGetLocalSize(ll,&s2a);CHKERRQ(ierr);
864     if (s2a != s2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector non-conforming local size, %d != %d.", s2a, s2);
865     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
866     for (i=0; i<m; i++) {
867       x = l[i];
868       v = mat->v + i;
869       for (j=0; j<n; j++) { (*v) *= x; v+= m;}
870     }
871     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
872     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
873   }
874   if (rr) {
875     ierr = VecGetLocalSize(rr,&s3a);CHKERRQ(ierr);
876     if (s3a != s3) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vec non-conforming local size, %d != %d.", s3a, s3);
877     ierr = VecScatterBegin(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
878     ierr = VecScatterEnd(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
879     ierr = VecGetArray(mdn->lvec,&r);CHKERRQ(ierr);
880     for (i=0; i<n; i++) {
881       x = r[i];
882       v = mat->v + i*m;
883       for (j=0; j<m; j++) (*v++) *= x;
884     }
885     ierr = VecRestoreArray(mdn->lvec,&r);CHKERRQ(ierr);
886     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
887   }
888   PetscFunctionReturn(0);
889 }
890 
891 #undef __FUNCT__
892 #define __FUNCT__ "MatNorm_MPIDense"
893 PetscErrorCode MatNorm_MPIDense(Mat A,NormType type,PetscReal *nrm)
894 {
895   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
896   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
897   PetscErrorCode ierr;
898   PetscInt       i,j;
899   PetscReal      sum = 0.0;
900   PetscScalar    *v  = mat->v;
901 
902   PetscFunctionBegin;
903   if (mdn->size == 1) {
904     ierr =  MatNorm(mdn->A,type,nrm);CHKERRQ(ierr);
905   } else {
906     if (type == NORM_FROBENIUS) {
907       for (i=0; i<mdn->A->cmap->n*mdn->A->rmap->n; i++) {
908         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
909       }
910       ierr = MPI_Allreduce(&sum,nrm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
911       *nrm = PetscSqrtReal(*nrm);
912       ierr = PetscLogFlops(2.0*mdn->A->cmap->n*mdn->A->rmap->n);CHKERRQ(ierr);
913     } else if (type == NORM_1) {
914       PetscReal *tmp,*tmp2;
915       ierr = PetscMalloc2(A->cmap->N,&tmp,A->cmap->N,&tmp2);CHKERRQ(ierr);
916       ierr = PetscMemzero(tmp,A->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
917       ierr = PetscMemzero(tmp2,A->cmap->N*sizeof(PetscReal));CHKERRQ(ierr);
918       *nrm = 0.0;
919       v    = mat->v;
920       for (j=0; j<mdn->A->cmap->n; j++) {
921         for (i=0; i<mdn->A->rmap->n; i++) {
922           tmp[j] += PetscAbsScalar(*v);  v++;
923         }
924       }
925       ierr = MPI_Allreduce(tmp,tmp2,A->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
926       for (j=0; j<A->cmap->N; j++) {
927         if (tmp2[j] > *nrm) *nrm = tmp2[j];
928       }
929       ierr = PetscFree2(tmp,tmp);CHKERRQ(ierr);
930       ierr = PetscLogFlops(A->cmap->n*A->rmap->n);CHKERRQ(ierr);
931     } else if (type == NORM_INFINITY) { /* max row norm */
932       PetscReal ntemp;
933       ierr = MatNorm(mdn->A,type,&ntemp);CHKERRQ(ierr);
934       ierr = MPI_Allreduce(&ntemp,nrm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
935     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for two norm");
936   }
937   PetscFunctionReturn(0);
938 }
939 
940 #undef __FUNCT__
941 #define __FUNCT__ "MatTranspose_MPIDense"
942 PetscErrorCode MatTranspose_MPIDense(Mat A,MatReuse reuse,Mat *matout)
943 {
944   Mat_MPIDense   *a    = (Mat_MPIDense*)A->data;
945   Mat_SeqDense   *Aloc = (Mat_SeqDense*)a->A->data;
946   Mat            B;
947   PetscInt       M = A->rmap->N,N = A->cmap->N,m,n,*rwork,rstart = A->rmap->rstart;
948   PetscErrorCode ierr;
949   PetscInt       j,i;
950   PetscScalar    *v;
951 
952   PetscFunctionBegin;
953   if (reuse == MAT_REUSE_MATRIX && A == *matout && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports square matrix only in-place");
954   if (reuse == MAT_INITIAL_MATRIX || A == *matout) {
955     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
956     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
957     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
958     ierr = MatMPIDenseSetPreallocation(B,NULL);CHKERRQ(ierr);
959   } else {
960     B = *matout;
961   }
962 
963   m    = a->A->rmap->n; n = a->A->cmap->n; v = Aloc->v;
964   ierr = PetscMalloc1(m,&rwork);CHKERRQ(ierr);
965   for (i=0; i<m; i++) rwork[i] = rstart + i;
966   for (j=0; j<n; j++) {
967     ierr = MatSetValues(B,1,&j,m,rwork,v,INSERT_VALUES);CHKERRQ(ierr);
968     v   += m;
969   }
970   ierr = PetscFree(rwork);CHKERRQ(ierr);
971   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
972   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
973   if (reuse == MAT_INITIAL_MATRIX || *matout != A) {
974     *matout = B;
975   } else {
976     ierr = MatHeaderMerge(A,B);CHKERRQ(ierr);
977   }
978   PetscFunctionReturn(0);
979 }
980 
981 
982 static PetscErrorCode MatDuplicate_MPIDense(Mat,MatDuplicateOption,Mat*);
983 extern PetscErrorCode MatScale_MPIDense(Mat,PetscScalar);
984 
985 #undef __FUNCT__
986 #define __FUNCT__ "MatSetUp_MPIDense"
987 PetscErrorCode MatSetUp_MPIDense(Mat A)
988 {
989   PetscErrorCode ierr;
990 
991   PetscFunctionBegin;
992   ierr =  MatMPIDenseSetPreallocation(A,0);CHKERRQ(ierr);
993   PetscFunctionReturn(0);
994 }
995 
996 #undef __FUNCT__
997 #define __FUNCT__ "MatAXPY_MPIDense"
998 PetscErrorCode MatAXPY_MPIDense(Mat Y,PetscScalar alpha,Mat X,MatStructure str)
999 {
1000   PetscErrorCode ierr;
1001   Mat_MPIDense   *A = (Mat_MPIDense*)Y->data, *B = (Mat_MPIDense*)X->data;
1002 
1003   PetscFunctionBegin;
1004   ierr = MatAXPY(A->A,alpha,B->A,str);CHKERRQ(ierr);
1005   ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 #undef __FUNCT__
1010 #define __FUNCT__ "MatConjugate_MPIDense"
1011 PetscErrorCode  MatConjugate_MPIDense(Mat mat)
1012 {
1013   Mat_MPIDense   *a = (Mat_MPIDense*)mat->data;
1014   PetscErrorCode ierr;
1015 
1016   PetscFunctionBegin;
1017   ierr = MatConjugate(a->A);CHKERRQ(ierr);
1018   PetscFunctionReturn(0);
1019 }
1020 
1021 #undef __FUNCT__
1022 #define __FUNCT__ "MatRealPart_MPIDense"
1023 PetscErrorCode MatRealPart_MPIDense(Mat A)
1024 {
1025   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
1026   PetscErrorCode ierr;
1027 
1028   PetscFunctionBegin;
1029   ierr = MatRealPart(a->A);CHKERRQ(ierr);
1030   PetscFunctionReturn(0);
1031 }
1032 
1033 #undef __FUNCT__
1034 #define __FUNCT__ "MatImaginaryPart_MPIDense"
1035 PetscErrorCode MatImaginaryPart_MPIDense(Mat A)
1036 {
1037   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
1038   PetscErrorCode ierr;
1039 
1040   PetscFunctionBegin;
1041   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
1042   PetscFunctionReturn(0);
1043 }
1044 
1045 extern PetscErrorCode MatGetColumnNorms_SeqDense(Mat,NormType,PetscReal*);
1046 #undef __FUNCT__
1047 #define __FUNCT__ "MatGetColumnNorms_MPIDense"
1048 PetscErrorCode MatGetColumnNorms_MPIDense(Mat A,NormType type,PetscReal *norms)
1049 {
1050   PetscErrorCode ierr;
1051   PetscInt       i,n;
1052   Mat_MPIDense   *a = (Mat_MPIDense*) A->data;
1053   PetscReal      *work;
1054 
1055   PetscFunctionBegin;
1056   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
1057   ierr = PetscMalloc1(n,&work);CHKERRQ(ierr);
1058   ierr = MatGetColumnNorms_SeqDense(a->A,type,work);CHKERRQ(ierr);
1059   if (type == NORM_2) {
1060     for (i=0; i<n; i++) work[i] *= work[i];
1061   }
1062   if (type == NORM_INFINITY) {
1063     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,A->hdr.comm);CHKERRQ(ierr);
1064   } else {
1065     ierr = MPI_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,A->hdr.comm);CHKERRQ(ierr);
1066   }
1067   ierr = PetscFree(work);CHKERRQ(ierr);
1068   if (type == NORM_2) {
1069     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
1070   }
1071   PetscFunctionReturn(0);
1072 }
1073 
1074 #undef __FUNCT__
1075 #define __FUNCT__ "MatSetRandom_MPIDense"
1076 static PetscErrorCode  MatSetRandom_MPIDense(Mat x,PetscRandom rctx)
1077 {
1078   Mat_MPIDense   *d = (Mat_MPIDense*)x->data;
1079   PetscErrorCode ierr;
1080   PetscScalar    *a;
1081   PetscInt       m,n,i;
1082 
1083   PetscFunctionBegin;
1084   ierr = MatGetSize(d->A,&m,&n);CHKERRQ(ierr);
1085   ierr = MatDenseGetArray(d->A,&a);CHKERRQ(ierr);
1086   for (i=0; i<m*n; i++) {
1087     ierr = PetscRandomGetValue(rctx,a+i);CHKERRQ(ierr);
1088   }
1089   ierr = MatDenseRestoreArray(d->A,&a);CHKERRQ(ierr);
1090   PetscFunctionReturn(0);
1091 }
1092 
1093 extern PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat,Mat);
1094 
1095 /* -------------------------------------------------------------------*/
1096 static struct _MatOps MatOps_Values = { MatSetValues_MPIDense,
1097                                         MatGetRow_MPIDense,
1098                                         MatRestoreRow_MPIDense,
1099                                         MatMult_MPIDense,
1100                                 /*  4*/ MatMultAdd_MPIDense,
1101                                         MatMultTranspose_MPIDense,
1102                                         MatMultTransposeAdd_MPIDense,
1103                                         0,
1104                                         0,
1105                                         0,
1106                                 /* 10*/ 0,
1107                                         0,
1108                                         0,
1109                                         0,
1110                                         MatTranspose_MPIDense,
1111                                 /* 15*/ MatGetInfo_MPIDense,
1112                                         MatEqual_MPIDense,
1113                                         MatGetDiagonal_MPIDense,
1114                                         MatDiagonalScale_MPIDense,
1115                                         MatNorm_MPIDense,
1116                                 /* 20*/ MatAssemblyBegin_MPIDense,
1117                                         MatAssemblyEnd_MPIDense,
1118                                         MatSetOption_MPIDense,
1119                                         MatZeroEntries_MPIDense,
1120                                 /* 24*/ MatZeroRows_MPIDense,
1121                                         0,
1122                                         0,
1123                                         0,
1124                                         0,
1125                                 /* 29*/ MatSetUp_MPIDense,
1126                                         0,
1127                                         0,
1128                                         0,
1129                                         0,
1130                                 /* 34*/ MatDuplicate_MPIDense,
1131                                         0,
1132                                         0,
1133                                         0,
1134                                         0,
1135                                 /* 39*/ MatAXPY_MPIDense,
1136                                         MatGetSubMatrices_MPIDense,
1137                                         0,
1138                                         MatGetValues_MPIDense,
1139                                         0,
1140                                 /* 44*/ 0,
1141                                         MatScale_MPIDense,
1142                                         MatShift_Basic,
1143                                         0,
1144                                         0,
1145                                 /* 49*/ MatSetRandom_MPIDense,
1146                                         0,
1147                                         0,
1148                                         0,
1149                                         0,
1150                                 /* 54*/ 0,
1151                                         0,
1152                                         0,
1153                                         0,
1154                                         0,
1155                                 /* 59*/ MatGetSubMatrix_MPIDense,
1156                                         MatDestroy_MPIDense,
1157                                         MatView_MPIDense,
1158                                         0,
1159                                         0,
1160                                 /* 64*/ 0,
1161                                         0,
1162                                         0,
1163                                         0,
1164                                         0,
1165                                 /* 69*/ 0,
1166                                         0,
1167                                         0,
1168                                         0,
1169                                         0,
1170                                 /* 74*/ 0,
1171                                         0,
1172                                         0,
1173                                         0,
1174                                         0,
1175                                 /* 79*/ 0,
1176                                         0,
1177                                         0,
1178                                         0,
1179                                 /* 83*/ MatLoad_MPIDense,
1180                                         0,
1181                                         0,
1182                                         0,
1183                                         0,
1184                                         0,
1185                                 /* 89*/
1186                                         0,
1187                                         0,
1188                                         MatMatMultNumeric_MPIDense,
1189                                         0,
1190                                         0,
1191                                 /* 94*/ 0,
1192                                         0,
1193                                         0,
1194                                         0,
1195                                         0,
1196                                 /* 99*/ 0,
1197                                         0,
1198                                         0,
1199                                         MatConjugate_MPIDense,
1200                                         0,
1201                                 /*104*/ 0,
1202                                         MatRealPart_MPIDense,
1203                                         MatImaginaryPart_MPIDense,
1204                                         0,
1205                                         0,
1206                                 /*109*/ 0,
1207                                         0,
1208                                         0,
1209                                         0,
1210                                         0,
1211                                 /*114*/ 0,
1212                                         0,
1213                                         0,
1214                                         0,
1215                                         0,
1216                                 /*119*/ 0,
1217                                         0,
1218                                         0,
1219                                         0,
1220                                         0,
1221                                 /*124*/ 0,
1222                                         MatGetColumnNorms_MPIDense,
1223                                         0,
1224                                         0,
1225                                         0,
1226                                 /*129*/ 0,
1227                                         0,
1228                                         0,
1229                                         0,
1230                                         0,
1231                                 /*134*/ 0,
1232                                         0,
1233                                         0,
1234                                         0,
1235                                         0,
1236                                 /*139*/ 0,
1237                                         0,
1238                                         0
1239 };
1240 
1241 #undef __FUNCT__
1242 #define __FUNCT__ "MatMPIDenseSetPreallocation_MPIDense"
1243 PetscErrorCode  MatMPIDenseSetPreallocation_MPIDense(Mat mat,PetscScalar *data)
1244 {
1245   Mat_MPIDense   *a;
1246   PetscErrorCode ierr;
1247 
1248   PetscFunctionBegin;
1249   mat->preallocated = PETSC_TRUE;
1250   /* Note:  For now, when data is specified above, this assumes the user correctly
1251    allocates the local dense storage space.  We should add error checking. */
1252 
1253   a       = (Mat_MPIDense*)mat->data;
1254   ierr    = PetscLayoutSetUp(mat->rmap);CHKERRQ(ierr);
1255   ierr    = PetscLayoutSetUp(mat->cmap);CHKERRQ(ierr);
1256   a->nvec = mat->cmap->n;
1257 
1258   ierr = MatCreate(PETSC_COMM_SELF,&a->A);CHKERRQ(ierr);
1259   ierr = MatSetSizes(a->A,mat->rmap->n,mat->cmap->N,mat->rmap->n,mat->cmap->N);CHKERRQ(ierr);
1260   ierr = MatSetType(a->A,MATSEQDENSE);CHKERRQ(ierr);
1261   ierr = MatSeqDenseSetPreallocation(a->A,data);CHKERRQ(ierr);
1262   ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
1263   PetscFunctionReturn(0);
1264 }
1265 
1266 #if defined(PETSC_HAVE_ELEMENTAL)
1267 #undef __FUNCT__
1268 #define __FUNCT__ "MatConvert_MPIDense_Elemental"
1269 PETSC_EXTERN PetscErrorCode MatConvert_MPIDense_Elemental(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
1270 {
1271   Mat            mat_elemental;
1272   PetscErrorCode ierr;
1273   PetscScalar    *array,*v_rowwise;
1274   PetscInt       m=A->rmap->n,N=A->cmap->N,rstart=A->rmap->rstart,i,j,k,*rows,*cols;
1275 
1276   PetscFunctionBegin;
1277   ierr = PetscMalloc3(m*N,&v_rowwise,m,&rows,N,&cols);CHKERRQ(ierr);
1278   ierr = MatDenseGetArray(A,&array);CHKERRQ(ierr);
1279   /* convert column-wise array into row-wise v_rowwise, see MatSetValues_Elemental() */
1280   k = 0;
1281   for (j=0; j<N; j++) {
1282     cols[j] = j;
1283     for (i=0; i<m; i++) {
1284       v_rowwise[i*N+j] = array[k++];
1285     }
1286   }
1287   for (i=0; i<m; i++) {
1288     rows[i] = rstart + i;
1289   }
1290   ierr = MatDenseRestoreArray(A,&array);CHKERRQ(ierr);
1291 
1292   ierr = MatCreate(PetscObjectComm((PetscObject)A), &mat_elemental);CHKERRQ(ierr);
1293   ierr = MatSetSizes(mat_elemental,PETSC_DECIDE,PETSC_DECIDE,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
1294   ierr = MatSetType(mat_elemental,MATELEMENTAL);CHKERRQ(ierr);
1295   ierr = MatSetUp(mat_elemental);CHKERRQ(ierr);
1296 
1297   /* PETSc-Elemental interaface uses axpy for setting off-processor entries, only ADD_VALUES is allowed */
1298   ierr = MatSetValues(mat_elemental,m,rows,N,cols,v_rowwise,ADD_VALUES);CHKERRQ(ierr);
1299   ierr = MatAssemblyBegin(mat_elemental, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1300   ierr = MatAssemblyEnd(mat_elemental, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1301   ierr = PetscFree3(v_rowwise,rows,cols);CHKERRQ(ierr);
1302 
1303   if (reuse == MAT_REUSE_MATRIX) {
1304     ierr = MatHeaderReplace(A,mat_elemental);CHKERRQ(ierr);
1305   } else {
1306     *newmat = mat_elemental;
1307   }
1308   PetscFunctionReturn(0);
1309 }
1310 #endif
1311 
1312 #undef __FUNCT__
1313 #define __FUNCT__ "MatCreate_MPIDense"
1314 PETSC_EXTERN PetscErrorCode MatCreate_MPIDense(Mat mat)
1315 {
1316   Mat_MPIDense   *a;
1317   PetscErrorCode ierr;
1318 
1319   PetscFunctionBegin;
1320   ierr      = PetscNewLog(mat,&a);CHKERRQ(ierr);
1321   mat->data = (void*)a;
1322   ierr      = PetscMemcpy(mat->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1323 
1324   mat->insertmode = NOT_SET_VALUES;
1325   ierr            = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&a->rank);CHKERRQ(ierr);
1326   ierr            = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&a->size);CHKERRQ(ierr);
1327 
1328   /* build cache for off array entries formed */
1329   a->donotstash = PETSC_FALSE;
1330 
1331   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)mat),1,&mat->stash);CHKERRQ(ierr);
1332 
1333   /* stuff used for matrix vector multiply */
1334   a->lvec        = 0;
1335   a->Mvctx       = 0;
1336   a->roworiented = PETSC_TRUE;
1337 
1338   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArray_C",MatDenseGetArray_MPIDense);CHKERRQ(ierr);
1339   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArray_C",MatDenseRestoreArray_MPIDense);CHKERRQ(ierr);
1340 #if defined(PETSC_HAVE_ELEMENTAL)
1341   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpidense_elemental_C",MatConvert_MPIDense_Elemental);CHKERRQ(ierr);
1342 #endif
1343   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatGetDiagonalBlock_C",MatGetDiagonalBlock_MPIDense);CHKERRQ(ierr);
1344   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",MatMPIDenseSetPreallocation_MPIDense);CHKERRQ(ierr);
1345   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",MatMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1346   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",MatMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1347   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",MatMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1348 
1349   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMult_mpiaij_mpidense_C",MatTransposeMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1350   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultSymbolic_mpiaij_mpidense_C",MatTransposeMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1351   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatTransposeMatMultNumeric_mpiaij_mpidense_C",MatTransposeMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1352   ierr = PetscObjectChangeTypeName((PetscObject)mat,MATMPIDENSE);CHKERRQ(ierr);
1353   PetscFunctionReturn(0);
1354 }
1355 
1356 /*MC
1357    MATDENSE - MATDENSE = "dense" - A matrix type to be used for dense matrices.
1358 
1359    This matrix type is identical to MATSEQDENSE when constructed with a single process communicator,
1360    and MATMPIDENSE otherwise.
1361 
1362    Options Database Keys:
1363 . -mat_type dense - sets the matrix type to "dense" during a call to MatSetFromOptions()
1364 
1365   Level: beginner
1366 
1367 
1368 .seealso: MatCreateMPIDense,MATSEQDENSE,MATMPIDENSE
1369 M*/
1370 
1371 #undef __FUNCT__
1372 #define __FUNCT__ "MatMPIDenseSetPreallocation"
1373 /*@C
1374    MatMPIDenseSetPreallocation - Sets the array used to store the matrix entries
1375 
1376    Not collective
1377 
1378    Input Parameters:
1379 .  B - the matrix
1380 -  data - optional location of matrix data.  Set data=NULL for PETSc
1381    to control all matrix memory allocation.
1382 
1383    Notes:
1384    The dense format is fully compatible with standard Fortran 77
1385    storage by columns.
1386 
1387    The data input variable is intended primarily for Fortran programmers
1388    who wish to allocate their own matrix memory space.  Most users should
1389    set data=NULL.
1390 
1391    Level: intermediate
1392 
1393 .keywords: matrix,dense, parallel
1394 
1395 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1396 @*/
1397 PetscErrorCode  MatMPIDenseSetPreallocation(Mat B,PetscScalar *data)
1398 {
1399   PetscErrorCode ierr;
1400 
1401   PetscFunctionBegin;
1402   ierr = PetscTryMethod(B,"MatMPIDenseSetPreallocation_C",(Mat,PetscScalar*),(B,data));CHKERRQ(ierr);
1403   PetscFunctionReturn(0);
1404 }
1405 
1406 #undef __FUNCT__
1407 #define __FUNCT__ "MatCreateDense"
1408 /*@C
1409    MatCreateDense - Creates a parallel matrix in dense format.
1410 
1411    Collective on MPI_Comm
1412 
1413    Input Parameters:
1414 +  comm - MPI communicator
1415 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
1416 .  n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
1417 .  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
1418 .  N - number of global columns (or PETSC_DECIDE to have calculated if n is given)
1419 -  data - optional location of matrix data.  Set data=NULL (PETSC_NULL_SCALAR for Fortran users) for PETSc
1420    to control all matrix memory allocation.
1421 
1422    Output Parameter:
1423 .  A - the matrix
1424 
1425    Notes:
1426    The dense format is fully compatible with standard Fortran 77
1427    storage by columns.
1428 
1429    The data input variable is intended primarily for Fortran programmers
1430    who wish to allocate their own matrix memory space.  Most users should
1431    set data=NULL (PETSC_NULL_SCALAR for Fortran users).
1432 
1433    The user MUST specify either the local or global matrix dimensions
1434    (possibly both).
1435 
1436    Level: intermediate
1437 
1438 .keywords: matrix,dense, parallel
1439 
1440 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1441 @*/
1442 PetscErrorCode  MatCreateDense(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscScalar *data,Mat *A)
1443 {
1444   PetscErrorCode ierr;
1445   PetscMPIInt    size;
1446 
1447   PetscFunctionBegin;
1448   ierr = MatCreate(comm,A);CHKERRQ(ierr);
1449   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
1450   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1451   if (size > 1) {
1452     ierr = MatSetType(*A,MATMPIDENSE);CHKERRQ(ierr);
1453     ierr = MatMPIDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1454     if (data) {  /* user provided data array, so no need to assemble */
1455       ierr = MatSetUpMultiply_MPIDense(*A);CHKERRQ(ierr);
1456       (*A)->assembled = PETSC_TRUE;
1457     }
1458   } else {
1459     ierr = MatSetType(*A,MATSEQDENSE);CHKERRQ(ierr);
1460     ierr = MatSeqDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1461   }
1462   PetscFunctionReturn(0);
1463 }
1464 
1465 #undef __FUNCT__
1466 #define __FUNCT__ "MatDuplicate_MPIDense"
1467 static PetscErrorCode MatDuplicate_MPIDense(Mat A,MatDuplicateOption cpvalues,Mat *newmat)
1468 {
1469   Mat            mat;
1470   Mat_MPIDense   *a,*oldmat = (Mat_MPIDense*)A->data;
1471   PetscErrorCode ierr;
1472 
1473   PetscFunctionBegin;
1474   *newmat = 0;
1475   ierr    = MatCreate(PetscObjectComm((PetscObject)A),&mat);CHKERRQ(ierr);
1476   ierr    = MatSetSizes(mat,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
1477   ierr    = MatSetType(mat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1478   a       = (Mat_MPIDense*)mat->data;
1479   ierr    = PetscMemcpy(mat->ops,A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
1480 
1481   mat->factortype   = A->factortype;
1482   mat->assembled    = PETSC_TRUE;
1483   mat->preallocated = PETSC_TRUE;
1484 
1485   a->size         = oldmat->size;
1486   a->rank         = oldmat->rank;
1487   mat->insertmode = NOT_SET_VALUES;
1488   a->nvec         = oldmat->nvec;
1489   a->donotstash   = oldmat->donotstash;
1490 
1491   ierr = PetscLayoutReference(A->rmap,&mat->rmap);CHKERRQ(ierr);
1492   ierr = PetscLayoutReference(A->cmap,&mat->cmap);CHKERRQ(ierr);
1493 
1494   ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
1495   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1496   ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
1497 
1498   *newmat = mat;
1499   PetscFunctionReturn(0);
1500 }
1501 
1502 #undef __FUNCT__
1503 #define __FUNCT__ "MatLoad_MPIDense_DenseInFile"
1504 PetscErrorCode MatLoad_MPIDense_DenseInFile(MPI_Comm comm,PetscInt fd,PetscInt M,PetscInt N,Mat newmat)
1505 {
1506   PetscErrorCode ierr;
1507   PetscMPIInt    rank,size;
1508   const PetscInt *rowners;
1509   PetscInt       i,m,n,nz,j,mMax;
1510   PetscScalar    *array,*vals,*vals_ptr;
1511   Mat_MPIDense   *a = (Mat_MPIDense*)newmat->data;
1512 
1513   PetscFunctionBegin;
1514   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1515   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1516 
1517   /* determine ownership of rows and columns */
1518   m = (newmat->rmap->n < 0) ? PETSC_DECIDE : newmat->rmap->n;
1519   n = (newmat->cmap->n < 0) ? PETSC_DECIDE : newmat->cmap->n;
1520 
1521   ierr = MatSetSizes(newmat,m,n,M,N);CHKERRQ(ierr);
1522   if (!a->A || !((Mat_SeqDense*)(a->A->data))->user_alloc) {
1523     ierr = MatMPIDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
1524   }
1525   ierr = MatDenseGetArray(newmat,&array);CHKERRQ(ierr);
1526   ierr = MatGetLocalSize(newmat,&m,NULL);CHKERRQ(ierr);
1527   ierr = MatGetOwnershipRanges(newmat,&rowners);CHKERRQ(ierr);
1528   ierr = MPI_Reduce(&m,&mMax,1,MPIU_INT,MPI_MAX,0,comm);CHKERRQ(ierr);
1529   if (!rank) {
1530     ierr = PetscMalloc1(mMax*N,&vals);CHKERRQ(ierr);
1531 
1532     /* read in my part of the matrix numerical values  */
1533     ierr = PetscBinaryRead(fd,vals,m*N,PETSC_SCALAR);CHKERRQ(ierr);
1534 
1535     /* insert into matrix-by row (this is why cannot directly read into array */
1536     vals_ptr = vals;
1537     for (i=0; i<m; i++) {
1538       for (j=0; j<N; j++) {
1539         array[i + j*m] = *vals_ptr++;
1540       }
1541     }
1542 
1543     /* read in other processors and ship out */
1544     for (i=1; i<size; i++) {
1545       nz   = (rowners[i+1] - rowners[i])*N;
1546       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1547       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)(newmat))->tag,comm);CHKERRQ(ierr);
1548     }
1549   } else {
1550     /* receive numeric values */
1551     ierr = PetscMalloc1(m*N,&vals);CHKERRQ(ierr);
1552 
1553     /* receive message of values*/
1554     ierr = MPIULong_Recv(vals,m*N,MPIU_SCALAR,0,((PetscObject)(newmat))->tag,comm);CHKERRQ(ierr);
1555 
1556     /* insert into matrix-by row (this is why cannot directly read into array */
1557     vals_ptr = vals;
1558     for (i=0; i<m; i++) {
1559       for (j=0; j<N; j++) {
1560         array[i + j*m] = *vals_ptr++;
1561       }
1562     }
1563   }
1564   ierr = MatDenseRestoreArray(newmat,&array);CHKERRQ(ierr);
1565   ierr = PetscFree(vals);CHKERRQ(ierr);
1566   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1567   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1568   PetscFunctionReturn(0);
1569 }
1570 
1571 #undef __FUNCT__
1572 #define __FUNCT__ "MatLoad_MPIDense"
1573 PetscErrorCode MatLoad_MPIDense(Mat newmat,PetscViewer viewer)
1574 {
1575   Mat_MPIDense   *a;
1576   PetscScalar    *vals,*svals;
1577   MPI_Comm       comm;
1578   MPI_Status     status;
1579   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag,*rowners,*sndcounts,m,n,maxnz;
1580   PetscInt       header[4],*rowlengths = 0,M,N,*cols;
1581   PetscInt       *ourlens,*procsnz = 0,jj,*mycols,*smycols;
1582   PetscInt       i,nz,j,rstart,rend;
1583   int            fd;
1584   PetscErrorCode ierr;
1585 
1586   PetscFunctionBegin;
1587   /* force binary viewer to load .info file if it has not yet done so */
1588   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
1589   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
1590   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1591   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1592   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1593   if (!rank) {
1594     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
1595     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
1596   }
1597   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
1598   M    = header[1]; N = header[2]; nz = header[3];
1599 
1600   /* If global rows/cols are set to PETSC_DECIDE, set it to the sizes given in the file */
1601   if (newmat->rmap->N < 0) newmat->rmap->N = M;
1602   if (newmat->cmap->N < 0) newmat->cmap->N = N;
1603 
1604   if (newmat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",M,newmat->rmap->N);
1605   if (newmat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",N,newmat->cmap->N);
1606 
1607   /*
1608        Handle case where matrix is stored on disk as a dense matrix
1609   */
1610   if (nz == MATRIX_BINARY_FORMAT_DENSE) {
1611     ierr = MatLoad_MPIDense_DenseInFile(comm,fd,M,N,newmat);CHKERRQ(ierr);
1612     PetscFunctionReturn(0);
1613   }
1614 
1615   /* determine ownership of all rows */
1616   if (newmat->rmap->n < 0) {
1617     ierr = PetscMPIIntCast(M/size + ((M % size) > rank),&m);CHKERRQ(ierr);
1618   } else {
1619     ierr = PetscMPIIntCast(newmat->rmap->n,&m);CHKERRQ(ierr);
1620   }
1621   if (newmat->cmap->n < 0) {
1622     n = PETSC_DECIDE;
1623   } else {
1624     ierr = PetscMPIIntCast(newmat->cmap->n,&n);CHKERRQ(ierr);
1625   }
1626 
1627   ierr       = PetscMalloc1(size+2,&rowners);CHKERRQ(ierr);
1628   ierr       = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
1629   rowners[0] = 0;
1630   for (i=2; i<=size; i++) {
1631     rowners[i] += rowners[i-1];
1632   }
1633   rstart = rowners[rank];
1634   rend   = rowners[rank+1];
1635 
1636   /* distribute row lengths to all processors */
1637   ierr = PetscMalloc1(rend-rstart,&ourlens);CHKERRQ(ierr);
1638   if (!rank) {
1639     ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
1640     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
1641     ierr = PetscMalloc1(size,&sndcounts);CHKERRQ(ierr);
1642     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
1643     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1644     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
1645   } else {
1646     ierr = MPI_Scatterv(0,0,0,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1647   }
1648 
1649   if (!rank) {
1650     /* calculate the number of nonzeros on each processor */
1651     ierr = PetscMalloc1(size,&procsnz);CHKERRQ(ierr);
1652     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
1653     for (i=0; i<size; i++) {
1654       for (j=rowners[i]; j< rowners[i+1]; j++) {
1655         procsnz[i] += rowlengths[j];
1656       }
1657     }
1658     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
1659 
1660     /* determine max buffer needed and allocate it */
1661     maxnz = 0;
1662     for (i=0; i<size; i++) {
1663       maxnz = PetscMax(maxnz,procsnz[i]);
1664     }
1665     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
1666 
1667     /* read in my part of the matrix column indices  */
1668     nz   = procsnz[0];
1669     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
1670     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
1671 
1672     /* read in every one elses and ship off */
1673     for (i=1; i<size; i++) {
1674       nz   = procsnz[i];
1675       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
1676       ierr = MPI_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
1677     }
1678     ierr = PetscFree(cols);CHKERRQ(ierr);
1679   } else {
1680     /* determine buffer space needed for message */
1681     nz = 0;
1682     for (i=0; i<m; i++) {
1683       nz += ourlens[i];
1684     }
1685     ierr = PetscMalloc1(nz+1,&mycols);CHKERRQ(ierr);
1686 
1687     /* receive message of column indices*/
1688     ierr = MPI_Recv(mycols,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
1689     ierr = MPI_Get_count(&status,MPIU_INT,&maxnz);CHKERRQ(ierr);
1690     if (maxnz != nz) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1691   }
1692 
1693   ierr = MatSetSizes(newmat,m,n,M,N);CHKERRQ(ierr);
1694   a = (Mat_MPIDense*)newmat->data;
1695   if (!a->A || !((Mat_SeqDense*)(a->A->data))->user_alloc) {
1696     ierr = MatMPIDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
1697   }
1698 
1699   if (!rank) {
1700     ierr = PetscMalloc1(maxnz,&vals);CHKERRQ(ierr);
1701 
1702     /* read in my part of the matrix numerical values  */
1703     nz   = procsnz[0];
1704     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1705 
1706     /* insert into matrix */
1707     jj      = rstart;
1708     smycols = mycols;
1709     svals   = vals;
1710     for (i=0; i<m; i++) {
1711       ierr     = MatSetValues(newmat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1712       smycols += ourlens[i];
1713       svals   += ourlens[i];
1714       jj++;
1715     }
1716 
1717     /* read in other processors and ship out */
1718     for (i=1; i<size; i++) {
1719       nz   = procsnz[i];
1720       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1721       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newmat)->tag,comm);CHKERRQ(ierr);
1722     }
1723     ierr = PetscFree(procsnz);CHKERRQ(ierr);
1724   } else {
1725     /* receive numeric values */
1726     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
1727 
1728     /* receive message of values*/
1729     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newmat)->tag,comm,&status);CHKERRQ(ierr);
1730     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
1731     if (maxnz != nz) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1732 
1733     /* insert into matrix */
1734     jj      = rstart;
1735     smycols = mycols;
1736     svals   = vals;
1737     for (i=0; i<m; i++) {
1738       ierr     = MatSetValues(newmat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1739       smycols += ourlens[i];
1740       svals   += ourlens[i];
1741       jj++;
1742     }
1743   }
1744   ierr = PetscFree(ourlens);CHKERRQ(ierr);
1745   ierr = PetscFree(vals);CHKERRQ(ierr);
1746   ierr = PetscFree(mycols);CHKERRQ(ierr);
1747   ierr = PetscFree(rowners);CHKERRQ(ierr);
1748 
1749   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1750   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1751   PetscFunctionReturn(0);
1752 }
1753 
1754 #undef __FUNCT__
1755 #define __FUNCT__ "MatEqual_MPIDense"
1756 PetscErrorCode MatEqual_MPIDense(Mat A,Mat B,PetscBool  *flag)
1757 {
1758   Mat_MPIDense   *matB = (Mat_MPIDense*)B->data,*matA = (Mat_MPIDense*)A->data;
1759   Mat            a,b;
1760   PetscBool      flg;
1761   PetscErrorCode ierr;
1762 
1763   PetscFunctionBegin;
1764   a    = matA->A;
1765   b    = matB->A;
1766   ierr = MatEqual(a,b,&flg);CHKERRQ(ierr);
1767   ierr = MPI_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1768   PetscFunctionReturn(0);
1769 }
1770 
1771