xref: /petsc/src/mat/impls/dense/mpi/mpidense.c (revision 62b4c0b38132a63aca20a38eff6e3f7572db1089)
1 #define PETSCMAT_DLL
2 
3 /*
4    Basic functions for basic parallel dense matrices.
5 */
6 
7 #include "src/mat/impls/dense/mpi/mpidense.h"    /*I   "petscmat.h"  I*/
8 
9 #undef __FUNCT__
10 #define __FUNCT__ "MatDenseGetLocalMatrix"
11 /*@
12 
13       MatDenseGetLocalMatrix - For a MATMPIDENSE or MATSEQDENSE matrix returns the sequential
14               matrix that represents the operator. For sequential matrices it returns itself.
15 
16     Input Parameter:
17 .      A - the Seq or MPI dense matrix
18 
19     Output Parameter:
20 .      B - the inner matrix
21 
22     Level: intermediate
23 
24 @*/
25 PetscErrorCode MatDenseGetLocalMatrix(Mat A,Mat *B)
26 {
27   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
28   PetscErrorCode ierr;
29   PetscTruth     flg;
30 
31   PetscFunctionBegin;
32   ierr = PetscTypeCompare((PetscObject)A,MATMPIDENSE,&flg);CHKERRQ(ierr);
33   if (flg) {
34     *B = mat->A;
35   } else {
36     *B = A;
37   }
38   PetscFunctionReturn(0);
39 }
40 
41 #undef __FUNCT__
42 #define __FUNCT__ "MatGetRow_MPIDense"
43 PetscErrorCode MatGetRow_MPIDense(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
44 {
45   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
46   PetscErrorCode ierr;
47   PetscInt       lrow,rstart = A->rmap.rstart,rend = A->rmap.rend;
48 
49   PetscFunctionBegin;
50   if (row < rstart || row >= rend) SETERRQ(PETSC_ERR_SUP,"only local rows")
51   lrow = row - rstart;
52   ierr = MatGetRow(mat->A,lrow,nz,(const PetscInt **)idx,(const PetscScalar **)v);CHKERRQ(ierr);
53   PetscFunctionReturn(0);
54 }
55 
56 #undef __FUNCT__
57 #define __FUNCT__ "MatRestoreRow_MPIDense"
58 PetscErrorCode MatRestoreRow_MPIDense(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
59 {
60   PetscErrorCode ierr;
61 
62   PetscFunctionBegin;
63   if (idx) {ierr = PetscFree(*idx);CHKERRQ(ierr);}
64   if (v) {ierr = PetscFree(*v);CHKERRQ(ierr);}
65   PetscFunctionReturn(0);
66 }
67 
68 EXTERN_C_BEGIN
69 #undef __FUNCT__
70 #define __FUNCT__ "MatGetDiagonalBlock_MPIDense"
71 PetscErrorCode PETSCMAT_DLLEXPORT MatGetDiagonalBlock_MPIDense(Mat A,PetscTruth *iscopy,MatReuse reuse,Mat *B)
72 {
73   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
74   PetscErrorCode ierr;
75   PetscInt       m = A->rmap.n,rstart = A->rmap.rstart;
76   PetscScalar    *array;
77   MPI_Comm       comm;
78 
79   PetscFunctionBegin;
80   if (A->rmap.N != A->cmap.N) SETERRQ(PETSC_ERR_SUP,"Only square matrices supported.");
81 
82   /* The reuse aspect is not implemented efficiently */
83   if (reuse) { ierr = MatDestroy(*B);CHKERRQ(ierr);}
84 
85   ierr = PetscObjectGetComm((PetscObject)(mdn->A),&comm);CHKERRQ(ierr);
86   ierr = MatGetArray(mdn->A,&array);CHKERRQ(ierr);
87   ierr = MatCreate(comm,B);CHKERRQ(ierr);
88   ierr = MatSetSizes(*B,m,m,m,m);CHKERRQ(ierr);
89   ierr = MatSetType(*B,((PetscObject)mdn->A)->type_name);CHKERRQ(ierr);
90   ierr = MatSeqDenseSetPreallocation(*B,array+m*rstart);CHKERRQ(ierr);
91   ierr = MatRestoreArray(mdn->A,&array);CHKERRQ(ierr);
92   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
93   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
94 
95   *iscopy = PETSC_TRUE;
96   PetscFunctionReturn(0);
97 }
98 EXTERN_C_END
99 
100 #undef __FUNCT__
101 #define __FUNCT__ "MatSetValues_MPIDense"
102 PetscErrorCode MatSetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
103 {
104   Mat_MPIDense   *A = (Mat_MPIDense*)mat->data;
105   PetscErrorCode ierr;
106   PetscInt       i,j,rstart = mat->rmap.rstart,rend = mat->rmap.rend,row;
107   PetscTruth     roworiented = A->roworiented;
108 
109   PetscFunctionBegin;
110   for (i=0; i<m; i++) {
111     if (idxm[i] < 0) continue;
112     if (idxm[i] >= mat->rmap.N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
113     if (idxm[i] >= rstart && idxm[i] < rend) {
114       row = idxm[i] - rstart;
115       if (roworiented) {
116         ierr = MatSetValues(A->A,1,&row,n,idxn,v+i*n,addv);CHKERRQ(ierr);
117       } else {
118         for (j=0; j<n; j++) {
119           if (idxn[j] < 0) continue;
120           if (idxn[j] >= mat->cmap.N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
121           ierr = MatSetValues(A->A,1,&row,1,&idxn[j],v+i+j*m,addv);CHKERRQ(ierr);
122         }
123       }
124     } else {
125       if (!A->donotstash) {
126         if (roworiented) {
127           ierr = MatStashValuesRow_Private(&mat->stash,idxm[i],n,idxn,v+i*n);CHKERRQ(ierr);
128         } else {
129           ierr = MatStashValuesCol_Private(&mat->stash,idxm[i],n,idxn,v+i,m);CHKERRQ(ierr);
130         }
131       }
132     }
133   }
134   PetscFunctionReturn(0);
135 }
136 
137 #undef __FUNCT__
138 #define __FUNCT__ "MatGetValues_MPIDense"
139 PetscErrorCode MatGetValues_MPIDense(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
140 {
141   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
142   PetscErrorCode ierr;
143   PetscInt       i,j,rstart = mat->rmap.rstart,rend = mat->rmap.rend,row;
144 
145   PetscFunctionBegin;
146   for (i=0; i<m; i++) {
147     if (idxm[i] < 0) continue; /* SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative row"); */
148     if (idxm[i] >= mat->rmap.N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
149     if (idxm[i] >= rstart && idxm[i] < rend) {
150       row = idxm[i] - rstart;
151       for (j=0; j<n; j++) {
152         if (idxn[j] < 0) continue; /* SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative column"); */
153         if (idxn[j] >= mat->cmap.N) {
154           SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
155         }
156         ierr = MatGetValues(mdn->A,1,&row,1,&idxn[j],v+i*n+j);CHKERRQ(ierr);
157       }
158     } else {
159       SETERRQ(PETSC_ERR_SUP,"Only local values currently supported");
160     }
161   }
162   PetscFunctionReturn(0);
163 }
164 
165 #undef __FUNCT__
166 #define __FUNCT__ "MatGetArray_MPIDense"
167 PetscErrorCode MatGetArray_MPIDense(Mat A,PetscScalar *array[])
168 {
169   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
170   PetscErrorCode ierr;
171 
172   PetscFunctionBegin;
173   ierr = MatGetArray(a->A,array);CHKERRQ(ierr);
174   PetscFunctionReturn(0);
175 }
176 
177 #undef __FUNCT__
178 #define __FUNCT__ "MatGetSubMatrix_MPIDense"
179 static PetscErrorCode MatGetSubMatrix_MPIDense(Mat A,IS isrow,IS iscol,PetscInt cs,MatReuse scall,Mat *B)
180 {
181   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data,*newmatd;
182   Mat_SeqDense   *lmat = (Mat_SeqDense*)mat->A->data;
183   PetscErrorCode ierr;
184   PetscInt       i,j,*irow,*icol,rstart,rend,nrows,ncols,nlrows,nlcols;
185   PetscScalar    *av,*bv,*v = lmat->v;
186   Mat            newmat;
187 
188   PetscFunctionBegin;
189   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
190   ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
191   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
192   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
193 
194   /* No parallel redistribution currently supported! Should really check each index set
195      to comfirm that it is OK.  ... Currently supports only submatrix same partitioning as
196      original matrix! */
197 
198   ierr = MatGetLocalSize(A,&nlrows,&nlcols);CHKERRQ(ierr);
199   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
200 
201   /* Check submatrix call */
202   if (scall == MAT_REUSE_MATRIX) {
203     /* SETERRQ(PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size"); */
204     /* Really need to test rows and column sizes! */
205     newmat = *B;
206   } else {
207     /* Create and fill new matrix */
208     ierr = MatCreate(((PetscObject)A)->comm,&newmat);CHKERRQ(ierr);
209     ierr = MatSetSizes(newmat,nrows,cs,PETSC_DECIDE,ncols);CHKERRQ(ierr);
210     ierr = MatSetType(newmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
211     ierr = MatMPIDenseSetPreallocation(newmat,PETSC_NULL);CHKERRQ(ierr);
212   }
213 
214   /* Now extract the data pointers and do the copy, column at a time */
215   newmatd = (Mat_MPIDense*)newmat->data;
216   bv      = ((Mat_SeqDense *)newmatd->A->data)->v;
217 
218   for (i=0; i<ncols; i++) {
219     av = v + nlrows*icol[i];
220     for (j=0; j<nrows; j++) {
221       *bv++ = av[irow[j] - rstart];
222     }
223   }
224 
225   /* Assemble the matrices so that the correct flags are set */
226   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
227   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
228 
229   /* Free work space */
230   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
231   ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
232   *B = newmat;
233   PetscFunctionReturn(0);
234 }
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "MatRestoreArray_MPIDense"
238 PetscErrorCode MatRestoreArray_MPIDense(Mat A,PetscScalar *array[])
239 {
240   PetscFunctionBegin;
241   PetscFunctionReturn(0);
242 }
243 
244 #undef __FUNCT__
245 #define __FUNCT__ "MatAssemblyBegin_MPIDense"
246 PetscErrorCode MatAssemblyBegin_MPIDense(Mat mat,MatAssemblyType mode)
247 {
248   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
249   MPI_Comm       comm = ((PetscObject)mat)->comm;
250   PetscErrorCode ierr;
251   PetscInt       nstash,reallocs;
252   InsertMode     addv;
253 
254   PetscFunctionBegin;
255   /* make sure all processors are either in INSERTMODE or ADDMODE */
256   ierr = MPI_Allreduce(&mat->insertmode,&addv,1,MPI_INT,MPI_BOR,comm);CHKERRQ(ierr);
257   if (addv == (ADD_VALUES|INSERT_VALUES)) {
258     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Cannot mix adds/inserts on different procs");
259   }
260   mat->insertmode = addv; /* in case this processor had no cache */
261 
262   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap.range);CHKERRQ(ierr);
263   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
264   ierr = PetscInfo2(mdn->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
265   PetscFunctionReturn(0);
266 }
267 
268 #undef __FUNCT__
269 #define __FUNCT__ "MatAssemblyEnd_MPIDense"
270 PetscErrorCode MatAssemblyEnd_MPIDense(Mat mat,MatAssemblyType mode)
271 {
272   Mat_MPIDense    *mdn=(Mat_MPIDense*)mat->data;
273   PetscErrorCode  ierr;
274   PetscInt        i,*row,*col,flg,j,rstart,ncols;
275   PetscMPIInt     n;
276   PetscScalar     *val;
277   InsertMode      addv=mat->insertmode;
278 
279   PetscFunctionBegin;
280   /*  wait on receives */
281   while (1) {
282     ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
283     if (!flg) break;
284 
285     for (i=0; i<n;) {
286       /* Now identify the consecutive vals belonging to the same row */
287       for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
288       if (j < n) ncols = j-i;
289       else       ncols = n-i;
290       /* Now assemble all these values with a single function call */
291       ierr = MatSetValues_MPIDense(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
292       i = j;
293     }
294   }
295   ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
296 
297   ierr = MatAssemblyBegin(mdn->A,mode);CHKERRQ(ierr);
298   ierr = MatAssemblyEnd(mdn->A,mode);CHKERRQ(ierr);
299 
300   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
301     ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
302   }
303   PetscFunctionReturn(0);
304 }
305 
306 #undef __FUNCT__
307 #define __FUNCT__ "MatZeroEntries_MPIDense"
308 PetscErrorCode MatZeroEntries_MPIDense(Mat A)
309 {
310   PetscErrorCode ierr;
311   Mat_MPIDense   *l = (Mat_MPIDense*)A->data;
312 
313   PetscFunctionBegin;
314   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
315   PetscFunctionReturn(0);
316 }
317 
318 /* the code does not do the diagonal entries correctly unless the
319    matrix is square and the column and row owerships are identical.
320    This is a BUG. The only way to fix it seems to be to access
321    mdn->A and mdn->B directly and not through the MatZeroRows()
322    routine.
323 */
324 #undef __FUNCT__
325 #define __FUNCT__ "MatZeroRows_MPIDense"
326 PetscErrorCode MatZeroRows_MPIDense(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag)
327 {
328   Mat_MPIDense   *l = (Mat_MPIDense*)A->data;
329   PetscErrorCode ierr;
330   PetscInt       i,*owners = A->rmap.range;
331   PetscInt       *nprocs,j,idx,nsends;
332   PetscInt       nmax,*svalues,*starts,*owner,nrecvs;
333   PetscInt       *rvalues,tag = ((PetscObject)A)->tag,count,base,slen,*source;
334   PetscInt       *lens,*lrows,*values;
335   PetscMPIInt    n,imdex,rank = l->rank,size = l->size;
336   MPI_Comm       comm = ((PetscObject)A)->comm;
337   MPI_Request    *send_waits,*recv_waits;
338   MPI_Status     recv_status,*send_status;
339   PetscTruth     found;
340 
341   PetscFunctionBegin;
342   /*  first count number of contributors to each processor */
343   ierr  = PetscMalloc(2*size*sizeof(PetscInt),&nprocs);CHKERRQ(ierr);
344   ierr  = PetscMemzero(nprocs,2*size*sizeof(PetscInt));CHKERRQ(ierr);
345   ierr  = PetscMalloc((N+1)*sizeof(PetscInt),&owner);CHKERRQ(ierr); /* see note*/
346   for (i=0; i<N; i++) {
347     idx = rows[i];
348     found = PETSC_FALSE;
349     for (j=0; j<size; j++) {
350       if (idx >= owners[j] && idx < owners[j+1]) {
351         nprocs[2*j]++; nprocs[2*j+1] = 1; owner[i] = j; found = PETSC_TRUE; break;
352       }
353     }
354     if (!found) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
355   }
356   nsends = 0;  for (i=0; i<size; i++) { nsends += nprocs[2*i+1];}
357 
358   /* inform other processors of number of messages and max length*/
359   ierr = PetscMaxSum(comm,nprocs,&nmax,&nrecvs);CHKERRQ(ierr);
360 
361   /* post receives:   */
362   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(PetscInt),&rvalues);CHKERRQ(ierr);
363   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
364   for (i=0; i<nrecvs; i++) {
365     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPIU_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
366   }
367 
368   /* do sends:
369       1) starts[i] gives the starting index in svalues for stuff going to
370          the ith processor
371   */
372   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&svalues);CHKERRQ(ierr);
373   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
374   ierr = PetscMalloc((size+1)*sizeof(PetscInt),&starts);CHKERRQ(ierr);
375   starts[0]  = 0;
376   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
377   for (i=0; i<N; i++) {
378     svalues[starts[owner[i]]++] = rows[i];
379   }
380 
381   starts[0] = 0;
382   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[2*i-2];}
383   count = 0;
384   for (i=0; i<size; i++) {
385     if (nprocs[2*i+1]) {
386       ierr = MPI_Isend(svalues+starts[i],nprocs[2*i],MPIU_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
387     }
388   }
389   ierr = PetscFree(starts);CHKERRQ(ierr);
390 
391   base = owners[rank];
392 
393   /*  wait on receives */
394   ierr   = PetscMalloc(2*(nrecvs+1)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
395   source = lens + nrecvs;
396   count  = nrecvs; slen = 0;
397   while (count) {
398     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
399     /* unpack receives into our local space */
400     ierr = MPI_Get_count(&recv_status,MPIU_INT,&n);CHKERRQ(ierr);
401     source[imdex]  = recv_status.MPI_SOURCE;
402     lens[imdex]    = n;
403     slen += n;
404     count--;
405   }
406   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
407 
408   /* move the data into the send scatter */
409   ierr = PetscMalloc((slen+1)*sizeof(PetscInt),&lrows);CHKERRQ(ierr);
410   count = 0;
411   for (i=0; i<nrecvs; i++) {
412     values = rvalues + i*nmax;
413     for (j=0; j<lens[i]; j++) {
414       lrows[count++] = values[j] - base;
415     }
416   }
417   ierr = PetscFree(rvalues);CHKERRQ(ierr);
418   ierr = PetscFree(lens);CHKERRQ(ierr);
419   ierr = PetscFree(owner);CHKERRQ(ierr);
420   ierr = PetscFree(nprocs);CHKERRQ(ierr);
421 
422   /* actually zap the local rows */
423   ierr = MatZeroRows(l->A,slen,lrows,diag);CHKERRQ(ierr);
424   ierr = PetscFree(lrows);CHKERRQ(ierr);
425 
426   /* wait on sends */
427   if (nsends) {
428     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
429     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
430     ierr = PetscFree(send_status);CHKERRQ(ierr);
431   }
432   ierr = PetscFree(send_waits);CHKERRQ(ierr);
433   ierr = PetscFree(svalues);CHKERRQ(ierr);
434 
435   PetscFunctionReturn(0);
436 }
437 
438 #undef __FUNCT__
439 #define __FUNCT__ "MatMult_MPIDense"
440 PetscErrorCode MatMult_MPIDense(Mat mat,Vec xx,Vec yy)
441 {
442   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
443   PetscErrorCode ierr;
444 
445   PetscFunctionBegin;
446   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
447   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
448   ierr = MatMult_SeqDense(mdn->A,mdn->lvec,yy);CHKERRQ(ierr);
449   PetscFunctionReturn(0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "MatMultAdd_MPIDense"
454 PetscErrorCode MatMultAdd_MPIDense(Mat mat,Vec xx,Vec yy,Vec zz)
455 {
456   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
457   PetscErrorCode ierr;
458 
459   PetscFunctionBegin;
460   ierr = VecScatterBegin(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
461   ierr = VecScatterEnd(mdn->Mvctx,xx,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
462   ierr = MatMultAdd_SeqDense(mdn->A,mdn->lvec,yy,zz);CHKERRQ(ierr);
463   PetscFunctionReturn(0);
464 }
465 
466 #undef __FUNCT__
467 #define __FUNCT__ "MatMultTranspose_MPIDense"
468 PetscErrorCode MatMultTranspose_MPIDense(Mat A,Vec xx,Vec yy)
469 {
470   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
471   PetscErrorCode ierr;
472   PetscScalar    zero = 0.0;
473 
474   PetscFunctionBegin;
475   ierr = VecSet(yy,zero);CHKERRQ(ierr);
476   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
477   ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
478   ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
479   PetscFunctionReturn(0);
480 }
481 
482 #undef __FUNCT__
483 #define __FUNCT__ "MatMultTransposeAdd_MPIDense"
484 PetscErrorCode MatMultTransposeAdd_MPIDense(Mat A,Vec xx,Vec yy,Vec zz)
485 {
486   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
487   PetscErrorCode ierr;
488 
489   PetscFunctionBegin;
490   ierr = VecCopy(yy,zz);CHKERRQ(ierr);
491   ierr = MatMultTranspose_SeqDense(a->A,xx,a->lvec);CHKERRQ(ierr);
492   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
493   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
494   PetscFunctionReturn(0);
495 }
496 
497 #undef __FUNCT__
498 #define __FUNCT__ "MatGetDiagonal_MPIDense"
499 PetscErrorCode MatGetDiagonal_MPIDense(Mat A,Vec v)
500 {
501   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
502   Mat_SeqDense   *aloc = (Mat_SeqDense*)a->A->data;
503   PetscErrorCode ierr;
504   PetscInt       len,i,n,m = A->rmap.n,radd;
505   PetscScalar    *x,zero = 0.0;
506 
507   PetscFunctionBegin;
508   ierr = VecSet(v,zero);CHKERRQ(ierr);
509   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
510   ierr = VecGetSize(v,&n);CHKERRQ(ierr);
511   if (n != A->rmap.N) SETERRQ(PETSC_ERR_ARG_SIZ,"Nonconforming mat and vec");
512   len  = PetscMin(a->A->rmap.n,a->A->cmap.n);
513   radd = A->rmap.rstart*m;
514   for (i=0; i<len; i++) {
515     x[i] = aloc->v[radd + i*m + i];
516   }
517   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
518   PetscFunctionReturn(0);
519 }
520 
521 #undef __FUNCT__
522 #define __FUNCT__ "MatDestroy_MPIDense"
523 PetscErrorCode MatDestroy_MPIDense(Mat mat)
524 {
525   Mat_MPIDense   *mdn = (Mat_MPIDense*)mat->data;
526   PetscErrorCode ierr;
527 #if defined(PETSC_HAVE_PLAPACK)
528   Mat_Plapack   *lu=(Mat_Plapack*)(mat->spptr);
529 #endif
530 
531   PetscFunctionBegin;
532 
533 #if defined(PETSC_USE_LOG)
534   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap.N,mat->cmap.N);
535 #endif
536   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
537   ierr = MatDestroy(mdn->A);CHKERRQ(ierr);
538   if (mdn->lvec)   {ierr = VecDestroy(mdn->lvec);CHKERRQ(ierr);}
539   if (mdn->Mvctx)  {ierr = VecScatterDestroy(mdn->Mvctx);CHKERRQ(ierr);}
540 #if defined(PETSC_HAVE_PLAPACK)
541   if (lu->CleanUpPlapack) {
542     ierr = PLA_Obj_free(&lu->A);CHKERRQ(ierr);
543     ierr = PLA_Obj_free (&lu->pivots);CHKERRQ(ierr);
544     ierr = PLA_Temp_free(&lu->templ);CHKERRQ(ierr);
545     ierr = PLA_Finalize();CHKERRQ(ierr);
546 
547     ierr = ISDestroy(lu->is_pla);CHKERRQ(ierr);
548     ierr = ISDestroy(lu->is_petsc);CHKERRQ(ierr);
549     ierr = VecScatterDestroy(lu->ctx);CHKERRQ(ierr);
550   }
551 #endif
552 
553   ierr = PetscFree(mdn);CHKERRQ(ierr);
554   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
555   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatGetDiagonalBlock_C","",PETSC_NULL);CHKERRQ(ierr);
556   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMPIDenseSetPreallocation_C","",PETSC_NULL);CHKERRQ(ierr);
557   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
558   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
559   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C","",PETSC_NULL);CHKERRQ(ierr);
560   PetscFunctionReturn(0);
561 }
562 
563 #undef __FUNCT__
564 #define __FUNCT__ "MatView_MPIDense_Binary"
565 static PetscErrorCode MatView_MPIDense_Binary(Mat mat,PetscViewer viewer)
566 {
567   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
568   PetscErrorCode    ierr;
569   PetscViewerFormat format;
570   int               fd;
571   PetscInt          header[4],mmax,N = mat->cmap.N,i,j,m,k;
572   PetscMPIInt       rank,tag  = ((PetscObject)viewer)->tag,size;
573   PetscScalar       *work,*v,*vv;
574   Mat_SeqDense      *a = (Mat_SeqDense*)mdn->A->data;
575   MPI_Status        status;
576 
577   PetscFunctionBegin;
578   if (mdn->size == 1) {
579     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
580   } else {
581     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
582     ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&rank);CHKERRQ(ierr);
583     ierr = MPI_Comm_size(((PetscObject)mat)->comm,&size);CHKERRQ(ierr);
584 
585     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
586     if (format == PETSC_VIEWER_BINARY_NATIVE) {
587 
588       if (!rank) {
589 	/* store the matrix as a dense matrix */
590 	header[0] = MAT_FILE_COOKIE;
591 	header[1] = mat->rmap.N;
592 	header[2] = N;
593 	header[3] = MATRIX_BINARY_FORMAT_DENSE;
594 	ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
595 
596 	/* get largest work array needed for transposing array */
597         mmax = mat->rmap.n;
598         for (i=1; i<size; i++) {
599           mmax = PetscMax(mmax,mat->rmap.range[i+1] - mat->rmap.range[i]);
600         }
601 	ierr = PetscMalloc(mmax*N*sizeof(PetscScalar),&work);CHKERRQ(ierr);
602 
603 	/* write out local array, by rows */
604         m    = mat->rmap.n;
605 	v    = a->v;
606         for (j=0; j<N; j++) {
607           for (i=0; i<m; i++) {
608 	    work[j + i*N] = *v++;
609 	  }
610 	}
611 	ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
612         /* get largest work array to receive messages from other processes, excludes process zero */
613         mmax = 0;
614         for (i=1; i<size; i++) {
615           mmax = PetscMax(mmax,mat->rmap.range[i+1] - mat->rmap.range[i]);
616         }
617 	ierr = PetscMalloc(mmax*N*sizeof(PetscScalar),&vv);CHKERRQ(ierr);
618         v = vv;
619         for (k=1; k<size; k++) {
620           m    = mat->rmap.range[k+1] - mat->rmap.range[k];
621           ierr = MPI_Recv(v,m*N,MPIU_SCALAR,k,tag,((PetscObject)mat)->comm,&status);CHKERRQ(ierr);
622 
623           for (j=0; j<N; j++) {
624             for (i=0; i<m; i++) {
625               work[j + i*N] = *v++;
626 	    }
627 	  }
628 	  ierr = PetscBinaryWrite(fd,work,m*N,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
629         }
630         ierr = PetscFree(work);CHKERRQ(ierr);
631         ierr = PetscFree(vv);CHKERRQ(ierr);
632       } else {
633         ierr = MPI_Send(a->v,mat->rmap.n*mat->cmap.N,MPIU_SCALAR,0,tag,((PetscObject)mat)->comm);CHKERRQ(ierr);
634       }
635     }
636   }
637   PetscFunctionReturn(0);
638 }
639 
640 #undef __FUNCT__
641 #define __FUNCT__ "MatView_MPIDense_ASCIIorDraworSocket"
642 static PetscErrorCode MatView_MPIDense_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
643 {
644   Mat_MPIDense      *mdn = (Mat_MPIDense*)mat->data;
645   PetscErrorCode    ierr;
646   PetscMPIInt       size = mdn->size,rank = mdn->rank;
647   PetscViewerType   vtype;
648   PetscTruth        iascii,isdraw;
649   PetscViewer       sviewer;
650   PetscViewerFormat format;
651 #if defined(PETSC_HAVE_PLAPACK)
652   Mat_Plapack       *lu=(Mat_Plapack*)(mat->spptr);
653 #endif
654 
655   PetscFunctionBegin;
656   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
657   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
658   if (iascii) {
659     ierr = PetscViewerGetType(viewer,&vtype);CHKERRQ(ierr);
660     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
661     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
662       MatInfo info;
663       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
664       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"  [%d] local rows %D nz %D nz alloced %D mem %D \n",rank,mat->rmap.n,
665                    (PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
666       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
667       ierr = VecScatterView(mdn->Mvctx,viewer);CHKERRQ(ierr);
668 #if defined(PETSC_HAVE_PLAPACK)
669       ierr = PetscViewerASCIIPrintf(viewer,"PLAPACK run parameters:\n");CHKERRQ(ierr);
670       ierr = PetscViewerASCIIPrintf(viewer,"  Processor mesh: nprows %d, npcols %d\n",lu->nprows, lu->npcols);CHKERRQ(ierr);
671       ierr = PetscViewerASCIIPrintf(viewer,"  Distr. block size nb: %d \n",lu->nb);CHKERRQ(ierr);
672       ierr = PetscViewerASCIIPrintf(viewer,"  Error checking: %d\n",lu->ierror);CHKERRQ(ierr);
673       ierr = PetscViewerASCIIPrintf(viewer,"  Algorithmic block size: %d\n",lu->nb_alg);CHKERRQ(ierr);
674 #endif
675       PetscFunctionReturn(0);
676     } else if (format == PETSC_VIEWER_ASCII_INFO) {
677       PetscFunctionReturn(0);
678     }
679   } else if (isdraw) {
680     PetscDraw  draw;
681     PetscTruth isnull;
682 
683     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
684     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
685     if (isnull) PetscFunctionReturn(0);
686   }
687 
688   if (size == 1) {
689     ierr = MatView(mdn->A,viewer);CHKERRQ(ierr);
690   } else {
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(((PetscObject)mat)->comm,&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,PETSC_NULL);
706     ierr = PetscLogObjectParent(mat,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     row = mat->rmap.rstart; m = mdn->A->rmap.n;
712     for (i=0; i<m; i++) {
713       ierr = MatGetRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
714       ierr = MatSetValues_MPIDense(A,1,&row,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
715       ierr = MatRestoreRow_MPIDense(mat,row,&nz,&cols,&vals);CHKERRQ(ierr);
716       row++;
717     }
718 
719     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
720     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
721     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
722     if (!rank) {
723       ierr = MatView(((Mat_MPIDense*)(A->data))->A,sviewer);CHKERRQ(ierr);
724     }
725     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
726     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
727     ierr = MatDestroy(A);CHKERRQ(ierr);
728   }
729   PetscFunctionReturn(0);
730 }
731 
732 #undef __FUNCT__
733 #define __FUNCT__ "MatView_MPIDense"
734 PetscErrorCode MatView_MPIDense(Mat mat,PetscViewer viewer)
735 {
736   PetscErrorCode ierr;
737   PetscTruth     iascii,isbinary,isdraw,issocket;
738 
739   PetscFunctionBegin;
740 
741   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
742   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
743   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
744   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
745 
746   if (iascii || issocket || isdraw) {
747     ierr = MatView_MPIDense_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
748   } else if (isbinary) {
749     ierr = MatView_MPIDense_Binary(mat,viewer);CHKERRQ(ierr);
750   } else {
751     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported by MPI dense matrix",((PetscObject)viewer)->type_name);
752   }
753   PetscFunctionReturn(0);
754 }
755 
756 #undef __FUNCT__
757 #define __FUNCT__ "MatGetInfo_MPIDense"
758 PetscErrorCode MatGetInfo_MPIDense(Mat A,MatInfoType flag,MatInfo *info)
759 {
760   Mat_MPIDense   *mat = (Mat_MPIDense*)A->data;
761   Mat            mdn = mat->A;
762   PetscErrorCode ierr;
763   PetscReal      isend[5],irecv[5];
764 
765   PetscFunctionBegin;
766   info->rows_global    = (double)A->rmap.N;
767   info->columns_global = (double)A->cmap.N;
768   info->rows_local     = (double)A->rmap.n;
769   info->columns_local  = (double)A->cmap.N;
770   info->block_size     = 1.0;
771   ierr = MatGetInfo(mdn,MAT_LOCAL,info);CHKERRQ(ierr);
772   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
773   isend[3] = info->memory;  isend[4] = info->mallocs;
774   if (flag == MAT_LOCAL) {
775     info->nz_used      = isend[0];
776     info->nz_allocated = isend[1];
777     info->nz_unneeded  = isend[2];
778     info->memory       = isend[3];
779     info->mallocs      = isend[4];
780   } else if (flag == MAT_GLOBAL_MAX) {
781     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_MAX,((PetscObject)A)->comm);CHKERRQ(ierr);
782     info->nz_used      = irecv[0];
783     info->nz_allocated = irecv[1];
784     info->nz_unneeded  = irecv[2];
785     info->memory       = irecv[3];
786     info->mallocs      = irecv[4];
787   } else if (flag == MAT_GLOBAL_SUM) {
788     ierr = MPI_Allreduce(isend,irecv,5,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
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   }
795   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
796   info->fill_ratio_needed = 0;
797   info->factor_mallocs    = 0;
798   PetscFunctionReturn(0);
799 }
800 
801 #undef __FUNCT__
802 #define __FUNCT__ "MatSetOption_MPIDense"
803 PetscErrorCode MatSetOption_MPIDense(Mat A,MatOption op,PetscTruth flg)
804 {
805   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
806   PetscErrorCode ierr;
807 
808   PetscFunctionBegin;
809   switch (op) {
810   case MAT_NEW_NONZERO_LOCATIONS:
811   case MAT_NEW_NONZERO_LOCATION_ERR:
812   case MAT_NEW_NONZERO_ALLOCATION_ERR:
813     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
814     break;
815   case MAT_ROW_ORIENTED:
816     a->roworiented = flg;
817     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
818     break;
819   case MAT_NEW_DIAGONALS:
820   case MAT_USE_HASH_TABLE:
821     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
822     break;
823   case MAT_IGNORE_OFF_PROC_ENTRIES:
824     a->donotstash = flg;
825     break;
826   case MAT_SYMMETRIC:
827   case MAT_STRUCTURALLY_SYMMETRIC:
828   case MAT_HERMITIAN:
829   case MAT_SYMMETRY_ETERNAL:
830   case MAT_IGNORE_LOWER_TRIANGULAR:
831     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
832     break;
833   default:
834     SETERRQ1(PETSC_ERR_SUP,"unknown option %s",MatOptions[op]);
835   }
836   PetscFunctionReturn(0);
837 }
838 
839 
840 #undef __FUNCT__
841 #define __FUNCT__ "MatDiagonalScale_MPIDense"
842 PetscErrorCode MatDiagonalScale_MPIDense(Mat A,Vec ll,Vec rr)
843 {
844   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
845   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
846   PetscScalar    *l,*r,x,*v;
847   PetscErrorCode ierr;
848   PetscInt       i,j,s2a,s3a,s2,s3,m=mdn->A->rmap.n,n=mdn->A->cmap.n;
849 
850   PetscFunctionBegin;
851   ierr = MatGetLocalSize(A,&s2,&s3);CHKERRQ(ierr);
852   if (ll) {
853     ierr = VecGetLocalSize(ll,&s2a);CHKERRQ(ierr);
854     if (s2a != s2) SETERRQ2(PETSC_ERR_ARG_SIZ,"Left scaling vector non-conforming local size, %d != %d.", s2a, s2);
855     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
856     for (i=0; i<m; i++) {
857       x = l[i];
858       v = mat->v + i;
859       for (j=0; j<n; j++) { (*v) *= x; v+= m;}
860     }
861     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
862     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
863   }
864   if (rr) {
865     ierr = VecGetLocalSize(rr,&s3a);CHKERRQ(ierr);
866     if (s3a != s3) SETERRQ2(PETSC_ERR_ARG_SIZ,"Right scaling vec non-conforming local size, %d != %d.", s3a, s3);
867     ierr = VecScatterBegin(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
868     ierr = VecScatterEnd(mdn->Mvctx,rr,mdn->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869     ierr = VecGetArray(mdn->lvec,&r);CHKERRQ(ierr);
870     for (i=0; i<n; i++) {
871       x = r[i];
872       v = mat->v + i*m;
873       for (j=0; j<m; j++) { (*v++) *= x;}
874     }
875     ierr = VecRestoreArray(mdn->lvec,&r);CHKERRQ(ierr);
876     ierr = PetscLogFlops(n*m);CHKERRQ(ierr);
877   }
878   PetscFunctionReturn(0);
879 }
880 
881 #undef __FUNCT__
882 #define __FUNCT__ "MatNorm_MPIDense"
883 PetscErrorCode MatNorm_MPIDense(Mat A,NormType type,PetscReal *nrm)
884 {
885   Mat_MPIDense   *mdn = (Mat_MPIDense*)A->data;
886   Mat_SeqDense   *mat = (Mat_SeqDense*)mdn->A->data;
887   PetscErrorCode ierr;
888   PetscInt       i,j;
889   PetscReal      sum = 0.0;
890   PetscScalar    *v = mat->v;
891 
892   PetscFunctionBegin;
893   if (mdn->size == 1) {
894     ierr =  MatNorm(mdn->A,type,nrm);CHKERRQ(ierr);
895   } else {
896     if (type == NORM_FROBENIUS) {
897       for (i=0; i<mdn->A->cmap.n*mdn->A->rmap.n; i++) {
898 #if defined(PETSC_USE_COMPLEX)
899         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
900 #else
901         sum += (*v)*(*v); v++;
902 #endif
903       }
904       ierr = MPI_Allreduce(&sum,nrm,1,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
905       *nrm = sqrt(*nrm);
906       ierr = PetscLogFlops(2*mdn->A->cmap.n*mdn->A->rmap.n);CHKERRQ(ierr);
907     } else if (type == NORM_1) {
908       PetscReal *tmp,*tmp2;
909       ierr = PetscMalloc(2*A->cmap.N*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
910       tmp2 = tmp + A->cmap.N;
911       ierr = PetscMemzero(tmp,2*A->cmap.N*sizeof(PetscReal));CHKERRQ(ierr);
912       *nrm = 0.0;
913       v = mat->v;
914       for (j=0; j<mdn->A->cmap.n; j++) {
915         for (i=0; i<mdn->A->rmap.n; i++) {
916           tmp[j] += PetscAbsScalar(*v);  v++;
917         }
918       }
919       ierr = MPI_Allreduce(tmp,tmp2,A->cmap.N,MPIU_REAL,MPI_SUM,((PetscObject)A)->comm);CHKERRQ(ierr);
920       for (j=0; j<A->cmap.N; j++) {
921         if (tmp2[j] > *nrm) *nrm = tmp2[j];
922       }
923       ierr = PetscFree(tmp);CHKERRQ(ierr);
924       ierr = PetscLogFlops(A->cmap.n*A->rmap.n);CHKERRQ(ierr);
925     } else if (type == NORM_INFINITY) { /* max row norm */
926       PetscReal ntemp;
927       ierr = MatNorm(mdn->A,type,&ntemp);CHKERRQ(ierr);
928       ierr = MPI_Allreduce(&ntemp,nrm,1,MPIU_REAL,MPI_MAX,((PetscObject)A)->comm);CHKERRQ(ierr);
929     } else {
930       SETERRQ(PETSC_ERR_SUP,"No support for two norm");
931     }
932   }
933   PetscFunctionReturn(0);
934 }
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "MatTranspose_MPIDense"
938 PetscErrorCode MatTranspose_MPIDense(Mat A,MatReuse reuse,Mat *matout)
939 {
940   Mat_MPIDense   *a = (Mat_MPIDense*)A->data;
941   Mat_SeqDense   *Aloc = (Mat_SeqDense*)a->A->data;
942   Mat            B;
943   PetscInt       M = A->rmap.N,N = A->cmap.N,m,n,*rwork,rstart = A->rmap.rstart;
944   PetscErrorCode ierr;
945   PetscInt       j,i;
946   PetscScalar    *v;
947 
948   PetscFunctionBegin;
949   if (A == *matout && M != N) {
950     SETERRQ(PETSC_ERR_SUP,"Supports square matrix only in-place");
951   }
952   if (reuse == MAT_INITIAL_MATRIX || A == *matout) {
953     ierr = MatCreate(((PetscObject)A)->comm,&B);CHKERRQ(ierr);
954     ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,M);CHKERRQ(ierr);
955     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
956     ierr = MatMPIDenseSetPreallocation(B,PETSC_NULL);CHKERRQ(ierr);
957   } else {
958     B = *matout;
959   }
960 
961   m = a->A->rmap.n; n = a->A->cmap.n; v = Aloc->v;
962   ierr = PetscMalloc(m*sizeof(PetscInt),&rwork);CHKERRQ(ierr);
963   for (i=0; i<m; i++) rwork[i] = rstart + i;
964   for (j=0; j<n; j++) {
965     ierr = MatSetValues(B,1,&j,m,rwork,v,INSERT_VALUES);CHKERRQ(ierr);
966     v   += m;
967   }
968   ierr = PetscFree(rwork);CHKERRQ(ierr);
969   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
970   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
971   if (*matout != A) {
972     *matout = B;
973   } else {
974     ierr = MatHeaderCopy(A,B);CHKERRQ(ierr);
975   }
976   PetscFunctionReturn(0);
977 }
978 
979 #include "petscblaslapack.h"
980 #undef __FUNCT__
981 #define __FUNCT__ "MatScale_MPIDense"
982 PetscErrorCode MatScale_MPIDense(Mat inA,PetscScalar alpha)
983 {
984   Mat_MPIDense   *A = (Mat_MPIDense*)inA->data;
985   Mat_SeqDense   *a = (Mat_SeqDense*)A->A->data;
986   PetscScalar    oalpha = alpha;
987   PetscErrorCode ierr;
988   PetscBLASInt   one = 1,nz = PetscBLASIntCast(inA->rmap.n*inA->cmap.N);
989 
990   PetscFunctionBegin;
991   BLASscal_(&nz,&oalpha,a->v,&one);
992   ierr = PetscLogFlops(nz);CHKERRQ(ierr);
993   PetscFunctionReturn(0);
994 }
995 
996 static PetscErrorCode MatDuplicate_MPIDense(Mat,MatDuplicateOption,Mat *);
997 
998 #undef __FUNCT__
999 #define __FUNCT__ "MatSetUpPreallocation_MPIDense"
1000 PetscErrorCode MatSetUpPreallocation_MPIDense(Mat A)
1001 {
1002   PetscErrorCode ierr;
1003 
1004   PetscFunctionBegin;
1005   ierr =  MatMPIDenseSetPreallocation(A,0);CHKERRQ(ierr);
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 #undef __FUNCT__
1010 #define __FUNCT__ "MatMatMultSymbolic_MPIDense_MPIDense"
1011 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
1012 {
1013   PetscErrorCode ierr;
1014   PetscInt       m=A->rmap.n,n=B->cmap.n;
1015   Mat            Cmat;
1016 
1017   PetscFunctionBegin;
1018   if (A->cmap.n != B->rmap.n) SETERRQ2(PETSC_ERR_ARG_SIZ,"A->cmap.n %d != B->rmap.n %d\n",A->cmap.n,B->rmap.n);
1019   ierr = MatCreate(((PetscObject)B)->comm,&Cmat);CHKERRQ(ierr);
1020   ierr = MatSetSizes(Cmat,m,n,A->rmap.N,B->cmap.N);CHKERRQ(ierr);
1021   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
1022   ierr = MatMPIDenseSetPreallocation(Cmat,PETSC_NULL);CHKERRQ(ierr);
1023   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1024   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1025   *C = Cmat;
1026   PetscFunctionReturn(0);
1027 }
1028 
1029 #if defined(PETSC_HAVE_PLAPACK)
1030 #undef __FUNCT__
1031 #define __FUNCT__ "MatSolve_MPIDense"
1032 PetscErrorCode MatSolve_MPIDense(Mat A,Vec b,Vec x)
1033 {
1034   MPI_Comm       comm = ((PetscObject)A)->comm;
1035   Mat_Plapack    *lu = (Mat_Plapack*)A->spptr;
1036   PetscErrorCode ierr;
1037   PetscInt       M=A->rmap.N,m=A->rmap.n,rstart,i,j,*idx_pla,*idx_petsc,loc_m,loc_stride;
1038   PetscScalar    *array;
1039   PetscReal      one = 1.0;
1040   PetscMPIInt    size,rank,r_rank,r_nproc,c_rank,c_nproc;;
1041   PLA_Obj        v_pla = NULL;
1042   PetscScalar    *loc_buf;
1043   Vec            loc_x;
1044 
1045   PetscFunctionBegin;
1046   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1047   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1048 
1049   /* Create PLAPACK vector objects, then copy b into PLAPACK b */
1050   ierr = PLA_Mvector_create(lu->datatype,M,1,lu->templ,PLA_ALIGN_FIRST,&v_pla);CHKERRQ(ierr);
1051   ierr = PLA_Obj_set_to_zero(v_pla);CHKERRQ(ierr);
1052 
1053   /* Copy b into rhs_pla */
1054   ierr = PLA_API_begin();CHKERRQ(ierr);
1055   ierr = PLA_Obj_API_open(v_pla);CHKERRQ(ierr);
1056   ierr = VecGetArray(b,&array);CHKERRQ(ierr);
1057   ierr = PLA_API_axpy_vector_to_global(m,&one,(void *)array,1,v_pla,lu->rstart);CHKERRQ(ierr);
1058   ierr = VecRestoreArray(b,&array);CHKERRQ(ierr);
1059   ierr = PLA_Obj_API_close(v_pla);CHKERRQ(ierr);
1060   ierr = PLA_API_end();CHKERRQ(ierr);
1061 
1062   if (A->factor == FACTOR_LU){
1063     /* Apply the permutations to the right hand sides */
1064     ierr = PLA_Apply_pivots_to_rows (v_pla,lu->pivots);CHKERRQ(ierr);
1065 
1066     /* Solve L y = b, overwriting b with y */
1067     ierr = PLA_Trsv( PLA_LOWER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_UNIT_DIAG,lu->A,v_pla );CHKERRQ(ierr);
1068 
1069     /* Solve U x = y (=b), overwriting b with x */
1070     ierr = PLA_Trsv( PLA_UPPER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_NONUNIT_DIAG,lu->A,v_pla );CHKERRQ(ierr);
1071   } else { /* FACTOR_CHOLESKY */
1072     ierr = PLA_Trsv( PLA_LOWER_TRIANGULAR,PLA_NO_TRANSPOSE,PLA_NONUNIT_DIAG,lu->A,v_pla);CHKERRQ(ierr);
1073     ierr = PLA_Trsv( PLA_LOWER_TRIANGULAR,(lu->datatype == MPI_DOUBLE ? PLA_TRANSPOSE : PLA_CONJUGATE_TRANSPOSE),PLA_NONUNIT_DIAG,lu->A,v_pla);CHKERRQ(ierr);
1074   }
1075 
1076   /* Copy PLAPACK x into Petsc vector x  */
1077   ierr = PLA_Obj_local_length(v_pla, &loc_m);CHKERRQ(ierr);
1078   ierr = PLA_Obj_local_buffer(v_pla, (void**)&loc_buf);CHKERRQ(ierr);
1079   ierr = PLA_Obj_local_stride(v_pla, &loc_stride);CHKERRQ(ierr);
1080   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,loc_m*loc_stride,loc_buf,&loc_x);CHKERRQ(ierr);
1081   if (!lu->pla_solved){
1082 
1083     ierr = PLA_Temp_comm_row_info(lu->templ,&lu->comm_2d,&r_rank,&r_nproc);CHKERRQ(ierr);
1084     ierr = PLA_Temp_comm_col_info(lu->templ,&lu->comm_2d,&c_rank,&c_nproc);CHKERRQ(ierr);
1085     /* printf(" [%d] rank: %d %d, nproc: %d %d\n",rank,r_rank,c_rank,r_nproc,c_nproc); */
1086 
1087     /* Create IS and cts for VecScatterring */
1088     ierr = PLA_Obj_local_length(v_pla, &loc_m);CHKERRQ(ierr);
1089     ierr = PLA_Obj_local_stride(v_pla, &loc_stride);CHKERRQ(ierr);
1090     ierr = PetscMalloc((2*loc_m+1)*sizeof(PetscInt),&idx_pla);CHKERRQ(ierr);
1091     idx_petsc = idx_pla + loc_m;
1092 
1093     rstart = (r_rank*c_nproc+c_rank)*lu->nb;
1094     for (i=0; i<loc_m; i+=lu->nb){
1095       j = 0;
1096       while (j < lu->nb && i+j < loc_m){
1097         idx_petsc[i+j] = rstart + j; j++;
1098       }
1099       rstart += size*lu->nb;
1100     }
1101 
1102     for (i=0; i<loc_m; i++) idx_pla[i] = i*loc_stride;
1103 
1104     ierr = ISCreateGeneral(PETSC_COMM_SELF,loc_m,idx_pla,&lu->is_pla);CHKERRQ(ierr);
1105     ierr = ISCreateGeneral(PETSC_COMM_SELF,loc_m,idx_petsc,&lu->is_petsc);CHKERRQ(ierr);
1106     ierr = PetscFree(idx_pla);CHKERRQ(ierr);
1107     ierr = VecScatterCreate(loc_x,lu->is_pla,x,lu->is_petsc,&lu->ctx);CHKERRQ(ierr);
1108   }
1109   ierr = VecScatterBegin(lu->ctx,loc_x,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1110   ierr = VecScatterEnd(lu->ctx,loc_x,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1111 
1112   /* Free data */
1113   ierr = VecDestroy(loc_x);CHKERRQ(ierr);
1114   ierr = PLA_Obj_free(&v_pla);CHKERRQ(ierr);
1115 
1116   lu->pla_solved = PETSC_TRUE;
1117   PetscFunctionReturn(0);
1118 }
1119 
1120 #undef __FUNCT__
1121 #define __FUNCT__ "MatLUFactorNumeric_MPIDense"
1122 PetscErrorCode MatLUFactorNumeric_MPIDense(Mat A,MatFactorInfo *info,Mat *F)
1123 {
1124   Mat_Plapack    *lu = (Mat_Plapack*)(*F)->spptr;
1125   PetscErrorCode ierr;
1126   PetscInt       M=A->rmap.N,m=A->rmap.n,rstart,rend;
1127   PetscInt       info_pla=0;
1128   PetscScalar    *array,one = 1.0;
1129 
1130   PetscFunctionBegin;
1131   ierr = PLA_Obj_set_to_zero(lu->A);CHKERRQ(ierr);
1132 
1133   /* Copy A into lu->A */
1134   ierr = PLA_API_begin();CHKERRQ(ierr);
1135   ierr = PLA_Obj_API_open(lu->A);CHKERRQ(ierr);
1136   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
1137   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1138   ierr = PLA_API_axpy_matrix_to_global(m,M, &one,(void *)array,m,lu->A,rstart,0);CHKERRQ(ierr);
1139   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1140   ierr = PLA_Obj_API_close(lu->A);CHKERRQ(ierr);
1141   ierr = PLA_API_end();CHKERRQ(ierr);
1142 
1143   /* Factor P A -> L U overwriting lower triangular portion of A with L, upper, U */
1144   info_pla = PLA_LU(lu->A,lu->pivots);
1145   if (info_pla != 0)
1146     SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot encountered at row %d from PLA_LU()",info_pla);
1147 
1148   lu->CleanUpPlapack = PETSC_TRUE;
1149   lu->rstart         = rstart;
1150 
1151   (*F)->assembled    = PETSC_TRUE;  /* required by -ksp_view */
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 #undef __FUNCT__
1156 #define __FUNCT__ "MatCholeskyFactorNumeric_MPIDense"
1157 PetscErrorCode MatCholeskyFactorNumeric_MPIDense(Mat A,MatFactorInfo *info,Mat *F)
1158 {
1159   Mat_Plapack    *lu = (Mat_Plapack*)(*F)->spptr;
1160   PetscErrorCode ierr;
1161   PetscInt       M=A->rmap.N,m=A->rmap.n,rstart,rend;
1162   PetscInt       info_pla=0;
1163   PetscScalar    *array,one = 1.0;
1164 
1165   PetscFunctionBegin;
1166 
1167   /* Copy A into lu->A */
1168   ierr = PLA_Obj_set_to_zero(lu->A);CHKERRQ(ierr);
1169   ierr = PLA_API_begin();CHKERRQ(ierr);
1170   ierr = PLA_Obj_API_open(lu->A);CHKERRQ(ierr);
1171   ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
1172   ierr = MatGetArray(A,&array);CHKERRQ(ierr);
1173   ierr = PLA_API_axpy_matrix_to_global(m,M, &one,(void *)array,m,lu->A,rstart,0);CHKERRQ(ierr);
1174   ierr = MatRestoreArray(A,&array);CHKERRQ(ierr);
1175   ierr = PLA_Obj_API_close(lu->A);CHKERRQ(ierr);
1176   ierr = PLA_API_end();CHKERRQ(ierr);
1177 
1178   /* Factor P A -> Chol */
1179   info_pla = PLA_Chol(PLA_LOWER_TRIANGULAR,lu->A);
1180   if (info_pla != 0)
1181     SETERRQ1( PETSC_ERR_MAT_CH_ZRPVT,"Nonpositive definite matrix detected at row %d from PLA_Chol()",info_pla);
1182 
1183   lu->CleanUpPlapack = PETSC_TRUE;
1184   lu->rstart         = rstart;
1185 
1186   (*F)->assembled    = PETSC_TRUE;  /* required by -ksp_view */
1187   PetscFunctionReturn(0);
1188 }
1189 
1190 #undef __FUNCT__
1191 #define __FUNCT__ "MatFactorSymbolic_MPIDense_Private"
1192 PetscErrorCode MatFactorSymbolic_MPIDense_Private(Mat A,MatFactorInfo *info,Mat *F)
1193 {
1194   Mat            B;
1195   Mat_Plapack    *lu;
1196   PetscErrorCode ierr;
1197   PetscInt       M=A->rmap.N,N=A->cmap.N;
1198   MPI_Comm       comm=((PetscObject)A)->comm,comm_2d;
1199   PetscMPIInt    size;
1200   PetscInt       ierror;
1201 
1202   PetscFunctionBegin;
1203   /* Create the factorization matrix */
1204   ierr = MatCreate(((PetscObject)A)->comm,&B);CHKERRQ(ierr);
1205   ierr = MatSetSizes(B,A->rmap.n,A->cmap.n,M,N);CHKERRQ(ierr);
1206   ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1207 
1208   lu = (Mat_Plapack*)(B->spptr);
1209 
1210   /* Set default Plapack parameters */
1211   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1212   lu->nprows = 1; lu->npcols = size;
1213   ierror = 0;
1214   lu->nb     = M/size;
1215   if (M - lu->nb*size) lu->nb++; /* without cyclic distribution */
1216 
1217   /* Set runtime options */
1218   ierr = PetscOptionsBegin(((PetscObject)A)->comm,((PetscObject)A)->prefix,"PLAPACK Options","Mat");CHKERRQ(ierr);
1219   ierr = PetscOptionsInt("-mat_plapack_nprows","row dimension of 2D processor mesh","None",lu->nprows,&lu->nprows,PETSC_NULL);CHKERRQ(ierr);
1220   ierr = PetscOptionsInt("-mat_plapack_npcols","column dimension of 2D processor mesh","None",lu->npcols,&lu->npcols,PETSC_NULL);CHKERRQ(ierr);
1221 
1222   ierr = PetscOptionsInt("-mat_plapack_nb","block size of template vector","None",lu->nb,&lu->nb,PETSC_NULL);CHKERRQ(ierr);
1223   ierr = PetscOptionsInt("-mat_plapack_ckerror","error checking flag","None",ierror,&ierror,PETSC_NULL);CHKERRQ(ierr);
1224   if (ierror){
1225     ierr = PLA_Set_error_checking(ierror,PETSC_TRUE,PETSC_TRUE,PETSC_FALSE );CHKERRQ(ierr);
1226   } else {
1227     ierr = PLA_Set_error_checking(ierror,PETSC_FALSE,PETSC_FALSE,PETSC_FALSE );CHKERRQ(ierr);
1228   }
1229   lu->ierror = ierror;
1230 
1231   lu->nb_alg = 0;
1232   ierr = PetscOptionsInt("-mat_plapack_nb_alg","algorithmic block size","None",lu->nb_alg,&lu->nb_alg,PETSC_NULL);CHKERRQ(ierr);
1233   if (lu->nb_alg){
1234     ierr = pla_Environ_set_nb_alg (PLA_OP_ALL_ALG,lu->nb_alg);CHKERRQ(ierr);
1235   }
1236   PetscOptionsEnd();
1237 
1238 
1239   /* Create a 2D communicator */
1240   ierr = PLA_Comm_1D_to_2D(comm,lu->nprows,lu->npcols,&comm_2d);CHKERRQ(ierr);
1241   lu->comm_2d = comm_2d;
1242 
1243   /* Initialize PLAPACK */
1244   ierr = PLA_Init(comm_2d);CHKERRQ(ierr);
1245 
1246   /* Create object distribution template */
1247   lu->templ = NULL;
1248   ierr = PLA_Temp_create(lu->nb, 0, &lu->templ);CHKERRQ(ierr);
1249 
1250   /* Use suggested nb_alg if it is not provided by user */
1251   if (lu->nb_alg == 0){
1252     ierr = PLA_Environ_nb_alg(PLA_OP_PAN_PAN,lu->templ,&lu->nb_alg);CHKERRQ(ierr);
1253     ierr = pla_Environ_set_nb_alg(PLA_OP_ALL_ALG,lu->nb_alg);CHKERRQ(ierr);
1254   }
1255 
1256   /* Set the datatype */
1257 #if defined(PETSC_USE_COMPLEX)
1258   lu->datatype = MPI_DOUBLE_COMPLEX;
1259 #else
1260   lu->datatype = MPI_DOUBLE;
1261 #endif
1262 
1263   ierr = PLA_Matrix_create(lu->datatype,M,M,lu->templ,PLA_ALIGN_FIRST,PLA_ALIGN_FIRST,&lu->A);CHKERRQ(ierr);
1264 
1265   lu->pla_solved     = PETSC_FALSE; /* MatSolve_Plapack() is called yet */
1266   lu->CleanUpPlapack = PETSC_TRUE;
1267   *F                 = B;
1268   PetscFunctionReturn(0);
1269 }
1270 
1271 /* Note the Petsc r and c permutations are ignored */
1272 #undef __FUNCT__
1273 #define __FUNCT__ "MatLUFactorSymbolic_MPIDense"
1274 PetscErrorCode MatLUFactorSymbolic_MPIDense(Mat A,IS r,IS c,MatFactorInfo *info,Mat *F)
1275 {
1276   PetscErrorCode ierr;
1277   PetscInt       M = A->rmap.N;
1278   Mat_Plapack    *lu;
1279 
1280   PetscFunctionBegin;
1281   ierr = MatFactorSymbolic_MPIDense_Private(A,info,F);CHKERRQ(ierr);
1282   lu = (Mat_Plapack*)(*F)->spptr;
1283   ierr = PLA_Mvector_create(MPI_INT,M,1,lu->templ,PLA_ALIGN_FIRST,&lu->pivots);CHKERRQ(ierr);
1284   (*F)->factor = FACTOR_LU;
1285   PetscFunctionReturn(0);
1286 }
1287 
1288 /* Note the Petsc perm permutation is ignored */
1289 #undef __FUNCT__
1290 #define __FUNCT__ "MatCholeskyFactorSymbolic_MPIDense"
1291 PetscErrorCode MatCholeskyFactorSymbolic_MPIDense(Mat A,IS perm,MatFactorInfo *info,Mat *F)
1292 {
1293   PetscErrorCode ierr;
1294   PetscTruth     issymmetric,set;
1295 
1296   PetscFunctionBegin;
1297   ierr = MatIsSymmetricKnown(A,&set,&issymmetric); CHKERRQ(ierr);
1298   if (!set || !issymmetric) SETERRQ(PETSC_ERR_USER,"Matrix must be set as MAT_SYMMETRIC for CholeskyFactor()");
1299   ierr = MatFactorSymbolic_MPIDense_Private(A,info,F);CHKERRQ(ierr);
1300   (*F)->factor = FACTOR_CHOLESKY;
1301   PetscFunctionReturn(0);
1302 }
1303 #endif
1304 
1305 /* -------------------------------------------------------------------*/
1306 static struct _MatOps MatOps_Values = {MatSetValues_MPIDense,
1307        MatGetRow_MPIDense,
1308        MatRestoreRow_MPIDense,
1309        MatMult_MPIDense,
1310 /* 4*/ MatMultAdd_MPIDense,
1311        MatMultTranspose_MPIDense,
1312        MatMultTransposeAdd_MPIDense,
1313 #if defined(PETSC_HAVE_PLAPACK)
1314        MatSolve_MPIDense,
1315 #else
1316        0,
1317 #endif
1318        0,
1319        0,
1320 /*10*/ 0,
1321        0,
1322        0,
1323        0,
1324        MatTranspose_MPIDense,
1325 /*15*/ MatGetInfo_MPIDense,
1326        MatEqual_MPIDense,
1327        MatGetDiagonal_MPIDense,
1328        MatDiagonalScale_MPIDense,
1329        MatNorm_MPIDense,
1330 /*20*/ MatAssemblyBegin_MPIDense,
1331        MatAssemblyEnd_MPIDense,
1332        0,
1333        MatSetOption_MPIDense,
1334        MatZeroEntries_MPIDense,
1335 /*25*/ MatZeroRows_MPIDense,
1336 #if defined(PETSC_HAVE_PLAPACK)
1337        MatLUFactorSymbolic_MPIDense,
1338        MatLUFactorNumeric_MPIDense,
1339        MatCholeskyFactorSymbolic_MPIDense,
1340        MatCholeskyFactorNumeric_MPIDense,
1341 #else
1342        0,
1343        0,
1344        0,
1345        0,
1346 #endif
1347 /*30*/ MatSetUpPreallocation_MPIDense,
1348        0,
1349        0,
1350        MatGetArray_MPIDense,
1351        MatRestoreArray_MPIDense,
1352 /*35*/ MatDuplicate_MPIDense,
1353        0,
1354        0,
1355        0,
1356        0,
1357 /*40*/ 0,
1358        MatGetSubMatrices_MPIDense,
1359        0,
1360        MatGetValues_MPIDense,
1361        0,
1362 /*45*/ 0,
1363        MatScale_MPIDense,
1364        0,
1365        0,
1366        0,
1367 /*50*/ 0,
1368        0,
1369        0,
1370        0,
1371        0,
1372 /*55*/ 0,
1373        0,
1374        0,
1375        0,
1376        0,
1377 /*60*/ MatGetSubMatrix_MPIDense,
1378        MatDestroy_MPIDense,
1379        MatView_MPIDense,
1380        0,
1381        0,
1382 /*65*/ 0,
1383        0,
1384        0,
1385        0,
1386        0,
1387 /*70*/ 0,
1388        0,
1389        0,
1390        0,
1391        0,
1392 /*75*/ 0,
1393        0,
1394        0,
1395        0,
1396        0,
1397 /*80*/ 0,
1398        0,
1399        0,
1400        0,
1401 /*84*/ MatLoad_MPIDense,
1402        0,
1403        0,
1404        0,
1405        0,
1406        0,
1407 /*90*/ 0,
1408        MatMatMultSymbolic_MPIDense_MPIDense,
1409        0,
1410        0,
1411        0,
1412 /*95*/ 0,
1413        0,
1414        0,
1415        0};
1416 
1417 EXTERN_C_BEGIN
1418 #undef __FUNCT__
1419 #define __FUNCT__ "MatMPIDenseSetPreallocation_MPIDense"
1420 PetscErrorCode PETSCMAT_DLLEXPORT MatMPIDenseSetPreallocation_MPIDense(Mat mat,PetscScalar *data)
1421 {
1422   Mat_MPIDense   *a;
1423   PetscErrorCode ierr;
1424 
1425   PetscFunctionBegin;
1426   mat->preallocated = PETSC_TRUE;
1427   /* Note:  For now, when data is specified above, this assumes the user correctly
1428    allocates the local dense storage space.  We should add error checking. */
1429 
1430   a    = (Mat_MPIDense*)mat->data;
1431   ierr = MatCreate(PETSC_COMM_SELF,&a->A);CHKERRQ(ierr);
1432   ierr = MatSetSizes(a->A,mat->rmap.n,mat->cmap.N,mat->rmap.n,mat->cmap.N);CHKERRQ(ierr);
1433   ierr = MatSetType(a->A,MATSEQDENSE);CHKERRQ(ierr);
1434   ierr = MatSeqDenseSetPreallocation(a->A,data);CHKERRQ(ierr);
1435   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
1436   PetscFunctionReturn(0);
1437 }
1438 EXTERN_C_END
1439 
1440 EXTERN_C_BEGIN
1441 #if defined(PETSC_HAVE_PLAPACK)
1442 #undef __FUNCT__
1443 #define __FUNCT__ "MatSetSolverType_MPIDense_PLAPACK"
1444 PetscErrorCode PETSCMAT_DLLEXPORT MatSetSolverType_MPIDense_PLAPACK(Mat mat,const char *type)
1445 {
1446   PetscFunctionBegin;
1447   /* dummy function so that -mat_solver_type plapack or MatSetSolverType(mat,"plapack"); silently work (since PLAPACK is on by default) */
1448   PetscFunctionReturn(0);
1449 }
1450 #endif
1451 EXTERN_C_END
1452 
1453 /*MC
1454    MATMPIDENSE - MATMPIDENSE = "mpidense" - A matrix type to be used for distributed dense matrices.
1455 
1456    Options Database Keys:
1457 . -mat_type mpidense - sets the matrix type to "mpidense" during a call to MatSetFromOptions()
1458 
1459   Level: beginner
1460 
1461   MATMPIDENSE matrices may use direct solvers (LU, Cholesky, and QR)
1462   for parallel dense matrices via the external package PLAPACK, if PLAPACK is installed
1463   (run config/configure.py with the option --download-plapack)
1464 
1465 
1466   Options Database Keys:
1467 . -mat_plapack_nprows <n> - number of rows in processor partition
1468 . -mat_plapack_npcols <n> - number of columns in processor partition
1469 . -mat_plapack_nb <n> - block size of template vector
1470 . -mat_plapack_nb_alg <n> - algorithmic block size
1471 - -mat_plapack_ckerror <n> - error checking flag
1472 
1473 .seealso: MatCreateMPIDense(), MATDENSE, MATSEQDENSE
1474 M*/
1475 
1476 EXTERN_C_BEGIN
1477 #undef __FUNCT__
1478 #define __FUNCT__ "MatCreate_MPIDense"
1479 PetscErrorCode PETSCMAT_DLLEXPORT MatCreate_MPIDense(Mat mat)
1480 {
1481   Mat_MPIDense   *a;
1482   PetscErrorCode ierr;
1483 #if defined(PETSC_HAVE_PLAPACK)
1484   Mat_Plapack    *lu;
1485 #endif
1486 
1487   PetscFunctionBegin;
1488   ierr              = PetscNewLog(mat,Mat_MPIDense,&a);CHKERRQ(ierr);
1489   mat->data         = (void*)a;
1490   ierr              = PetscMemcpy(mat->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1491   mat->factor       = 0;
1492   mat->mapping      = 0;
1493 
1494   mat->insertmode = NOT_SET_VALUES;
1495   ierr = MPI_Comm_rank(((PetscObject)mat)->comm,&a->rank);CHKERRQ(ierr);
1496   ierr = MPI_Comm_size(((PetscObject)mat)->comm,&a->size);CHKERRQ(ierr);
1497 
1498   mat->rmap.bs = mat->cmap.bs = 1;
1499   ierr = PetscMapSetUp(&mat->rmap);CHKERRQ(ierr);
1500   ierr = PetscMapSetUp(&mat->cmap);CHKERRQ(ierr);
1501   a->nvec = mat->cmap.n;
1502 
1503   /* build cache for off array entries formed */
1504   a->donotstash = PETSC_FALSE;
1505   ierr = MatStashCreate_Private(((PetscObject)mat)->comm,1,&mat->stash);CHKERRQ(ierr);
1506 
1507   /* stuff used for matrix vector multiply */
1508   a->lvec        = 0;
1509   a->Mvctx       = 0;
1510   a->roworiented = PETSC_TRUE;
1511 
1512   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatGetDiagonalBlock_C",
1513                                      "MatGetDiagonalBlock_MPIDense",
1514                                      MatGetDiagonalBlock_MPIDense);CHKERRQ(ierr);
1515   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMPIDenseSetPreallocation_C",
1516                                      "MatMPIDenseSetPreallocation_MPIDense",
1517                                      MatMPIDenseSetPreallocation_MPIDense);CHKERRQ(ierr);
1518   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMult_mpiaij_mpidense_C",
1519                                      "MatMatMult_MPIAIJ_MPIDense",
1520                                       MatMatMult_MPIAIJ_MPIDense);CHKERRQ(ierr);
1521   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMultSymbolic_mpiaij_mpidense_C",
1522                                      "MatMatMultSymbolic_MPIAIJ_MPIDense",
1523                                       MatMatMultSymbolic_MPIAIJ_MPIDense);CHKERRQ(ierr);
1524   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatMatMultNumeric_mpiaij_mpidense_C",
1525                                      "MatMatMultNumeric_MPIAIJ_MPIDense",
1526                                       MatMatMultNumeric_MPIAIJ_MPIDense);CHKERRQ(ierr);
1527 #if defined(PETSC_HAVE_PLAPACK)
1528   ierr = PetscObjectComposeFunctionDynamic((PetscObject)mat,"MatSetSolverType_mpidense_plapack_C",
1529                                      "MatSetSolverType_MPIDense_PLAPACK",
1530                                       MatSetSolverType_MPIDense_PLAPACK);CHKERRQ(ierr);
1531 #endif
1532   ierr = PetscObjectChangeTypeName((PetscObject)mat,MATMPIDENSE);CHKERRQ(ierr);
1533 
1534 #if defined(PETSC_HAVE_PLAPACK)
1535   ierr = PetscNewLog(mat,Mat_Plapack,&lu);CHKERRQ(ierr);
1536   lu->CleanUpPlapack       = PETSC_FALSE;
1537   mat->spptr                 = (void*)lu;
1538 #endif
1539   PetscFunctionReturn(0);
1540 }
1541 EXTERN_C_END
1542 
1543 /*MC
1544    MATDENSE - MATDENSE = "dense" - A matrix type to be used for dense matrices.
1545 
1546    This matrix type is identical to MATSEQDENSE when constructed with a single process communicator,
1547    and MATMPIDENSE otherwise.
1548 
1549    Options Database Keys:
1550 . -mat_type dense - sets the matrix type to "dense" during a call to MatSetFromOptions()
1551 
1552   Level: beginner
1553 
1554 
1555 .seealso: MatCreateMPIDense,MATSEQDENSE,MATMPIDENSE
1556 M*/
1557 
1558 EXTERN_C_BEGIN
1559 #undef __FUNCT__
1560 #define __FUNCT__ "MatCreate_Dense"
1561 PetscErrorCode PETSCMAT_DLLEXPORT MatCreate_Dense(Mat A)
1562 {
1563   PetscErrorCode ierr;
1564   PetscMPIInt    size;
1565 
1566   PetscFunctionBegin;
1567   ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
1568   if (size == 1) {
1569     ierr = MatSetType(A,MATSEQDENSE);CHKERRQ(ierr);
1570   } else {
1571     ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
1572   }
1573   PetscFunctionReturn(0);
1574 }
1575 EXTERN_C_END
1576 
1577 #undef __FUNCT__
1578 #define __FUNCT__ "MatMPIDenseSetPreallocation"
1579 /*@C
1580    MatMPIDenseSetPreallocation - Sets the array used to store the matrix entries
1581 
1582    Not collective
1583 
1584    Input Parameters:
1585 .  A - the matrix
1586 -  data - optional location of matrix data.  Set data=PETSC_NULL for PETSc
1587    to control all matrix memory allocation.
1588 
1589    Notes:
1590    The dense format is fully compatible with standard Fortran 77
1591    storage by columns.
1592 
1593    The data input variable is intended primarily for Fortran programmers
1594    who wish to allocate their own matrix memory space.  Most users should
1595    set data=PETSC_NULL.
1596 
1597    Level: intermediate
1598 
1599 .keywords: matrix,dense, parallel
1600 
1601 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1602 @*/
1603 PetscErrorCode PETSCMAT_DLLEXPORT MatMPIDenseSetPreallocation(Mat mat,PetscScalar *data)
1604 {
1605   PetscErrorCode ierr,(*f)(Mat,PetscScalar *);
1606 
1607   PetscFunctionBegin;
1608   ierr = PetscObjectQueryFunction((PetscObject)mat,"MatMPIDenseSetPreallocation_C",(void (**)(void))&f);CHKERRQ(ierr);
1609   if (f) {
1610     ierr = (*f)(mat,data);CHKERRQ(ierr);
1611   }
1612   PetscFunctionReturn(0);
1613 }
1614 
1615 #undef __FUNCT__
1616 #define __FUNCT__ "MatCreateMPIDense"
1617 /*@C
1618    MatCreateMPIDense - Creates a sparse parallel matrix in dense format.
1619 
1620    Collective on MPI_Comm
1621 
1622    Input Parameters:
1623 +  comm - MPI communicator
1624 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
1625 .  n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
1626 .  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
1627 .  N - number of global columns (or PETSC_DECIDE to have calculated if n is given)
1628 -  data - optional location of matrix data.  Set data=PETSC_NULL (PETSC_NULL_SCALAR for Fortran users) for PETSc
1629    to control all matrix memory allocation.
1630 
1631    Output Parameter:
1632 .  A - the matrix
1633 
1634    Notes:
1635    The dense format is fully compatible with standard Fortran 77
1636    storage by columns.
1637 
1638    The data input variable is intended primarily for Fortran programmers
1639    who wish to allocate their own matrix memory space.  Most users should
1640    set data=PETSC_NULL (PETSC_NULL_SCALAR for Fortran users).
1641 
1642    The user MUST specify either the local or global matrix dimensions
1643    (possibly both).
1644 
1645    Level: intermediate
1646 
1647 .keywords: matrix,dense, parallel
1648 
1649 .seealso: MatCreate(), MatCreateSeqDense(), MatSetValues()
1650 @*/
1651 PetscErrorCode PETSCMAT_DLLEXPORT MatCreateMPIDense(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscScalar *data,Mat *A)
1652 {
1653   PetscErrorCode ierr;
1654   PetscMPIInt    size;
1655 
1656   PetscFunctionBegin;
1657   ierr = MatCreate(comm,A);CHKERRQ(ierr);
1658   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
1659   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1660   if (size > 1) {
1661     ierr = MatSetType(*A,MATMPIDENSE);CHKERRQ(ierr);
1662     ierr = MatMPIDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1663   } else {
1664     ierr = MatSetType(*A,MATSEQDENSE);CHKERRQ(ierr);
1665     ierr = MatSeqDenseSetPreallocation(*A,data);CHKERRQ(ierr);
1666   }
1667   PetscFunctionReturn(0);
1668 }
1669 
1670 #undef __FUNCT__
1671 #define __FUNCT__ "MatDuplicate_MPIDense"
1672 static PetscErrorCode MatDuplicate_MPIDense(Mat A,MatDuplicateOption cpvalues,Mat *newmat)
1673 {
1674   Mat            mat;
1675   Mat_MPIDense   *a,*oldmat = (Mat_MPIDense*)A->data;
1676   PetscErrorCode ierr;
1677 
1678   PetscFunctionBegin;
1679   *newmat       = 0;
1680   ierr = MatCreate(((PetscObject)A)->comm,&mat);CHKERRQ(ierr);
1681   ierr = MatSetSizes(mat,A->rmap.n,A->cmap.n,A->rmap.N,A->cmap.N);CHKERRQ(ierr);
1682   ierr = MatSetType(mat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1683   a                 = (Mat_MPIDense*)mat->data;
1684   ierr              = PetscMemcpy(mat->ops,A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
1685   mat->factor       = A->factor;
1686   mat->assembled    = PETSC_TRUE;
1687   mat->preallocated = PETSC_TRUE;
1688 
1689   mat->rmap.rstart     = A->rmap.rstart;
1690   mat->rmap.rend       = A->rmap.rend;
1691   a->size              = oldmat->size;
1692   a->rank              = oldmat->rank;
1693   mat->insertmode      = NOT_SET_VALUES;
1694   a->nvec              = oldmat->nvec;
1695   a->donotstash        = oldmat->donotstash;
1696 
1697   ierr = PetscMemcpy(mat->rmap.range,A->rmap.range,(a->size+1)*sizeof(PetscInt));CHKERRQ(ierr);
1698   ierr = PetscMemcpy(mat->cmap.range,A->cmap.range,(a->size+1)*sizeof(PetscInt));CHKERRQ(ierr);
1699   ierr = MatStashCreate_Private(((PetscObject)A)->comm,1,&mat->stash);CHKERRQ(ierr);
1700 
1701   ierr = MatSetUpMultiply_MPIDense(mat);CHKERRQ(ierr);
1702   ierr = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1703   ierr = PetscLogObjectParent(mat,a->A);CHKERRQ(ierr);
1704 
1705 #if defined(PETSC_HAVE_PLAPACK)
1706   ierr = PetscMemcpy(mat->spptr,A->spptr,sizeof(Mat_Plapack));CHKERRQ(ierr);
1707 #endif
1708   *newmat = mat;
1709   PetscFunctionReturn(0);
1710 }
1711 
1712 #include "petscsys.h"
1713 
1714 #undef __FUNCT__
1715 #define __FUNCT__ "MatLoad_MPIDense_DenseInFile"
1716 PetscErrorCode MatLoad_MPIDense_DenseInFile(MPI_Comm comm,PetscInt fd,PetscInt M,PetscInt N, MatType type,Mat *newmat)
1717 {
1718   PetscErrorCode ierr;
1719   PetscMPIInt    rank,size;
1720   PetscInt       *rowners,i,m,nz,j;
1721   PetscScalar    *array,*vals,*vals_ptr;
1722   MPI_Status     status;
1723 
1724   PetscFunctionBegin;
1725   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1726   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1727 
1728   /* determine ownership of all rows */
1729   m          = M/size + ((M % size) > rank);
1730   ierr       = PetscMalloc((size+2)*sizeof(PetscInt),&rowners);CHKERRQ(ierr);
1731   ierr       = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
1732   rowners[0] = 0;
1733   for (i=2; i<=size; i++) {
1734     rowners[i] += rowners[i-1];
1735   }
1736 
1737   ierr = MatCreate(comm,newmat);CHKERRQ(ierr);
1738   ierr = MatSetSizes(*newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
1739   ierr = MatSetType(*newmat,type);CHKERRQ(ierr);
1740   ierr = MatMPIDenseSetPreallocation(*newmat,PETSC_NULL);CHKERRQ(ierr);
1741   ierr = MatGetArray(*newmat,&array);CHKERRQ(ierr);
1742 
1743   if (!rank) {
1744     ierr = PetscMalloc(m*N*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1745 
1746     /* read in my part of the matrix numerical values  */
1747     ierr = PetscBinaryRead(fd,vals,m*N,PETSC_SCALAR);CHKERRQ(ierr);
1748 
1749     /* insert into matrix-by row (this is why cannot directly read into array */
1750     vals_ptr = vals;
1751     for (i=0; i<m; i++) {
1752       for (j=0; j<N; j++) {
1753         array[i + j*m] = *vals_ptr++;
1754       }
1755     }
1756 
1757     /* read in other processors and ship out */
1758     for (i=1; i<size; i++) {
1759       nz   = (rowners[i+1] - rowners[i])*N;
1760       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1761       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)(*newmat))->tag,comm);CHKERRQ(ierr);
1762     }
1763   } else {
1764     /* receive numeric values */
1765     ierr = PetscMalloc(m*N*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1766 
1767     /* receive message of values*/
1768     ierr = MPI_Recv(vals,m*N,MPIU_SCALAR,0,((PetscObject)(*newmat))->tag,comm,&status);CHKERRQ(ierr);
1769 
1770     /* insert into matrix-by row (this is why cannot directly read into array */
1771     vals_ptr = vals;
1772     for (i=0; i<m; i++) {
1773       for (j=0; j<N; j++) {
1774         array[i + j*m] = *vals_ptr++;
1775       }
1776     }
1777   }
1778   ierr = PetscFree(rowners);CHKERRQ(ierr);
1779   ierr = PetscFree(vals);CHKERRQ(ierr);
1780   ierr = MatAssemblyBegin(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1781   ierr = MatAssemblyEnd(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1782   PetscFunctionReturn(0);
1783 }
1784 
1785 #undef __FUNCT__
1786 #define __FUNCT__ "MatLoad_MPIDense"
1787 PetscErrorCode MatLoad_MPIDense(PetscViewer viewer, MatType type,Mat *newmat)
1788 {
1789   Mat            A;
1790   PetscScalar    *vals,*svals;
1791   MPI_Comm       comm = ((PetscObject)viewer)->comm;
1792   MPI_Status     status;
1793   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag,*rowners,*sndcounts,m,maxnz;
1794   PetscInt       header[4],*rowlengths = 0,M,N,*cols;
1795   PetscInt       *ourlens,*procsnz = 0,*offlens,jj,*mycols,*smycols;
1796   PetscInt       i,nz,j,rstart,rend;
1797   int            fd;
1798   PetscErrorCode ierr;
1799 
1800   PetscFunctionBegin;
1801   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1802   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1803   if (!rank) {
1804     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1805     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
1806     if (header[0] != MAT_FILE_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
1807   }
1808 
1809   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
1810   M = header[1]; N = header[2]; nz = header[3];
1811 
1812   /*
1813        Handle case where matrix is stored on disk as a dense matrix
1814   */
1815   if (nz == MATRIX_BINARY_FORMAT_DENSE) {
1816     ierr = MatLoad_MPIDense_DenseInFile(comm,fd,M,N,type,newmat);CHKERRQ(ierr);
1817     PetscFunctionReturn(0);
1818   }
1819 
1820   /* determine ownership of all rows */
1821   m          = PetscMPIIntCast(M/size + ((M % size) > rank));
1822   ierr       = PetscMalloc((size+2)*sizeof(PetscMPIInt),&rowners);CHKERRQ(ierr);
1823   ierr       = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
1824   rowners[0] = 0;
1825   for (i=2; i<=size; i++) {
1826     rowners[i] += rowners[i-1];
1827   }
1828   rstart = rowners[rank];
1829   rend   = rowners[rank+1];
1830 
1831   /* distribute row lengths to all processors */
1832   ierr    = PetscMalloc(2*(rend-rstart+1)*sizeof(PetscInt),&ourlens);CHKERRQ(ierr);
1833   offlens = ourlens + (rend-rstart);
1834   if (!rank) {
1835     ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
1836     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
1837     ierr = PetscMalloc(size*sizeof(PetscMPIInt),&sndcounts);CHKERRQ(ierr);
1838     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
1839     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1840     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
1841   } else {
1842     ierr = MPI_Scatterv(0,0,0,MPIU_INT,ourlens,rend-rstart,MPIU_INT,0,comm);CHKERRQ(ierr);
1843   }
1844 
1845   if (!rank) {
1846     /* calculate the number of nonzeros on each processor */
1847     ierr = PetscMalloc(size*sizeof(PetscInt),&procsnz);CHKERRQ(ierr);
1848     ierr = PetscMemzero(procsnz,size*sizeof(PetscInt));CHKERRQ(ierr);
1849     for (i=0; i<size; i++) {
1850       for (j=rowners[i]; j< rowners[i+1]; j++) {
1851         procsnz[i] += rowlengths[j];
1852       }
1853     }
1854     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
1855 
1856     /* determine max buffer needed and allocate it */
1857     maxnz = 0;
1858     for (i=0; i<size; i++) {
1859       maxnz = PetscMax(maxnz,procsnz[i]);
1860     }
1861     ierr = PetscMalloc(maxnz*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1862 
1863     /* read in my part of the matrix column indices  */
1864     nz = procsnz[0];
1865     ierr = PetscMalloc(nz*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
1866     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
1867 
1868     /* read in every one elses and ship off */
1869     for (i=1; i<size; i++) {
1870       nz   = procsnz[i];
1871       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
1872       ierr = MPI_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
1873     }
1874     ierr = PetscFree(cols);CHKERRQ(ierr);
1875   } else {
1876     /* determine buffer space needed for message */
1877     nz = 0;
1878     for (i=0; i<m; i++) {
1879       nz += ourlens[i];
1880     }
1881     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&mycols);CHKERRQ(ierr);
1882 
1883     /* receive message of column indices*/
1884     ierr = MPI_Recv(mycols,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
1885     ierr = MPI_Get_count(&status,MPIU_INT,&maxnz);CHKERRQ(ierr);
1886     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1887   }
1888 
1889   /* loop over local rows, determining number of off diagonal entries */
1890   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
1891   jj = 0;
1892   for (i=0; i<m; i++) {
1893     for (j=0; j<ourlens[i]; j++) {
1894       if (mycols[jj] < rstart || mycols[jj] >= rend) offlens[i]++;
1895       jj++;
1896     }
1897   }
1898 
1899   /* create our matrix */
1900   for (i=0; i<m; i++) {
1901     ourlens[i] -= offlens[i];
1902   }
1903   ierr = MatCreate(comm,newmat);CHKERRQ(ierr);
1904   ierr = MatSetSizes(*newmat,m,PETSC_DECIDE,M,N);CHKERRQ(ierr);
1905   ierr = MatSetType(*newmat,type);CHKERRQ(ierr);
1906   ierr = MatMPIDenseSetPreallocation(*newmat,PETSC_NULL);CHKERRQ(ierr);
1907   A = *newmat;
1908   for (i=0; i<m; i++) {
1909     ourlens[i] += offlens[i];
1910   }
1911 
1912   if (!rank) {
1913     ierr = PetscMalloc(maxnz*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1914 
1915     /* read in my part of the matrix numerical values  */
1916     nz = procsnz[0];
1917     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1918 
1919     /* insert into matrix */
1920     jj      = rstart;
1921     smycols = mycols;
1922     svals   = vals;
1923     for (i=0; i<m; i++) {
1924       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1925       smycols += ourlens[i];
1926       svals   += ourlens[i];
1927       jj++;
1928     }
1929 
1930     /* read in other processors and ship out */
1931     for (i=1; i<size; i++) {
1932       nz   = procsnz[i];
1933       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1934       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)A)->tag,comm);CHKERRQ(ierr);
1935     }
1936     ierr = PetscFree(procsnz);CHKERRQ(ierr);
1937   } else {
1938     /* receive numeric values */
1939     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1940 
1941     /* receive message of values*/
1942     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)A)->tag,comm,&status);CHKERRQ(ierr);
1943     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
1944     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1945 
1946     /* insert into matrix */
1947     jj      = rstart;
1948     smycols = mycols;
1949     svals   = vals;
1950     for (i=0; i<m; i++) {
1951       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1952       smycols += ourlens[i];
1953       svals   += ourlens[i];
1954       jj++;
1955     }
1956   }
1957   ierr = PetscFree(ourlens);CHKERRQ(ierr);
1958   ierr = PetscFree(vals);CHKERRQ(ierr);
1959   ierr = PetscFree(mycols);CHKERRQ(ierr);
1960   ierr = PetscFree(rowners);CHKERRQ(ierr);
1961 
1962   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1963   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1964   PetscFunctionReturn(0);
1965 }
1966 
1967 #undef __FUNCT__
1968 #define __FUNCT__ "MatEqual_MPIDense"
1969 PetscErrorCode MatEqual_MPIDense(Mat A,Mat B,PetscTruth *flag)
1970 {
1971   Mat_MPIDense   *matB = (Mat_MPIDense*)B->data,*matA = (Mat_MPIDense*)A->data;
1972   Mat            a,b;
1973   PetscTruth     flg;
1974   PetscErrorCode ierr;
1975 
1976   PetscFunctionBegin;
1977   a = matA->A;
1978   b = matB->A;
1979   ierr = MatEqual(a,b,&flg);CHKERRQ(ierr);
1980   ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,((PetscObject)A)->comm);CHKERRQ(ierr);
1981   PetscFunctionReturn(0);
1982 }
1983 
1984 
1985 
1986