xref: /petsc/src/ksp/pc/impls/tfs/xxt.c (revision fdf6c4e30aafdbc795e4f76379caa977fd5cdf5a)
1 
2 /*************************************xxt.c************************************
3 Module Name: xxt
4 Module Info:
5 
6 author:  Henry M. Tufo III
7 e-mail:  hmt@asci.uchicago.edu
8 contact:
9 +--------------------------------+--------------------------------+
10 |MCS Division - Building 221     |Department of Computer Science  |
11 |Argonne National Laboratory     |Ryerson 152                     |
12 |9700 S. Cass Avenue             |The University of Chicago       |
13 |Argonne, IL  60439              |Chicago, IL  60637              |
14 |(630) 252-5354/5986 ph/fx       |(773) 702-6019/8487 ph/fx       |
15 +--------------------------------+--------------------------------+
16 
17 Last Modification: 3.20.01
18 **************************************xxt.c***********************************/
19 #include <../src/ksp/pc/impls/tfs/tfs.h>
20 
21 #define LEFT  -1
22 #define RIGHT  1
23 #define BOTH   0
24 
25 typedef struct xxt_solver_info {
26   PetscInt    n, m, n_global, m_global;
27   PetscInt    nnz, max_nnz, msg_buf_sz;
28   PetscInt    *nsep, *lnsep, *fo, nfo, *stages;
29   PetscInt    *col_sz, *col_indices;
30   PetscScalar **col_vals, *x, *solve_uu, *solve_w;
31   PetscInt    nsolves;
32   PetscScalar tot_solve_time;
33 } xxt_info;
34 
35 typedef struct matvec_info {
36   PetscInt     n, m, n_global, m_global;
37   PetscInt     *local2global;
38   PCTFS_gs_ADT PCTFS_gs_handle;
39   PetscErrorCode (*matvec)(struct matvec_info*,PetscScalar*,PetscScalar*);
40   void *grid_data;
41 } mv_info;
42 
43 struct xxt_CDT {
44   PetscInt id;
45   PetscInt ns;
46   PetscInt level;
47   xxt_info *info;
48   mv_info  *mvi;
49 };
50 
51 static PetscInt n_xxt        =0;
52 static PetscInt n_xxt_handles=0;
53 
54 /* prototypes */
55 static PetscErrorCode do_xxt_solve(xxt_ADT xxt_handle, PetscScalar *rhs);
56 static PetscErrorCode check_handle(xxt_ADT xxt_handle);
57 static PetscErrorCode det_separators(xxt_ADT xxt_handle);
58 static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u);
59 static PetscErrorCode xxt_generate(xxt_ADT xxt_handle);
60 static PetscErrorCode do_xxt_factor(xxt_ADT xxt_handle);
61 static mv_info *set_mvi(PetscInt *local2global, PetscInt n, PetscInt m, PetscErrorCode (*matvec)(mv_info*,PetscScalar*,PetscScalar*), void *grid_data);
62 
63 /**************************************xxt.c***********************************/
64 xxt_ADT XXT_new(void)
65 {
66   xxt_ADT xxt_handle;
67 
68   /* rolling count on n_xxt ... pot. problem here */
69   n_xxt_handles++;
70   xxt_handle       = (xxt_ADT)malloc(sizeof(struct xxt_CDT));
71   xxt_handle->id   = ++n_xxt;
72   xxt_handle->info = NULL; xxt_handle->mvi  = NULL;
73 
74   return(xxt_handle);
75 }
76 
77 /**************************************xxt.c***********************************/
78 PetscErrorCode XXT_factor(xxt_ADT xxt_handle,     /* prev. allocated xxt  handle */
79                     PetscInt *local2global, /* global column mapping       */
80                     PetscInt n,             /* local num rows              */
81                     PetscInt m,             /* local num cols              */
82                     PetscErrorCode (*matvec)(void*,PetscScalar*,PetscScalar*), /* b_loc=A_local.x_loc         */
83                     void *grid_data)        /* grid data for matvec        */
84 {
85   PCTFS_comm_init();
86   check_handle(xxt_handle);
87 
88   /* only 2^k for now and all nodes participating */
89   PetscCheck((1<<(xxt_handle->level=PCTFS_i_log2_num_nodes))==PCTFS_num_nodes,PETSC_COMM_SELF,PETSC_ERR_PLIB,"only 2^k for now and MPI_COMM_WORLD!!! %d != %d",1<<PCTFS_i_log2_num_nodes,PCTFS_num_nodes);
90 
91   /* space for X info */
92   xxt_handle->info = (xxt_info*)malloc(sizeof(xxt_info));
93 
94   /* set up matvec handles */
95   xxt_handle->mvi = set_mvi(local2global, n, m, (PetscErrorCode (*)(mv_info*,PetscScalar*,PetscScalar*))matvec, grid_data);
96 
97   /* matrix is assumed to be of full rank */
98   /* LATER we can reset to indicate rank def. */
99   xxt_handle->ns=0;
100 
101   /* determine separators and generate firing order - NB xxt info set here */
102   det_separators(xxt_handle);
103 
104   return(do_xxt_factor(xxt_handle));
105 }
106 
107 /**************************************xxt.c***********************************/
108 PetscErrorCode XXT_solve(xxt_ADT xxt_handle, PetscScalar *x, PetscScalar *b)
109 {
110 
111   PCTFS_comm_init();
112   check_handle(xxt_handle);
113 
114   /* need to copy b into x? */
115   if (b) PCTFS_rvec_copy(x,b,xxt_handle->mvi->n);
116   return do_xxt_solve(xxt_handle,x);
117 }
118 
119 /**************************************xxt.c***********************************/
120 PetscInt XXT_free(xxt_ADT xxt_handle)
121 {
122 
123   PCTFS_comm_init();
124   check_handle(xxt_handle);
125   n_xxt_handles--;
126 
127   free(xxt_handle->info->nsep);
128   free(xxt_handle->info->lnsep);
129   free(xxt_handle->info->fo);
130   free(xxt_handle->info->stages);
131   free(xxt_handle->info->solve_uu);
132   free(xxt_handle->info->solve_w);
133   free(xxt_handle->info->x);
134   free(xxt_handle->info->col_vals);
135   free(xxt_handle->info->col_sz);
136   free(xxt_handle->info->col_indices);
137   free(xxt_handle->info);
138   free(xxt_handle->mvi->local2global);
139   PCTFS_gs_free(xxt_handle->mvi->PCTFS_gs_handle);
140   free(xxt_handle->mvi);
141   free(xxt_handle);
142 
143   /* if the check fails we nuke */
144   /* if NULL pointer passed to free we nuke */
145   /* if the calls to free fail that's not my problem */
146   return(0);
147 }
148 
149 /**************************************xxt.c***********************************/
150 PetscErrorCode XXT_stats(xxt_ADT xxt_handle)
151 {
152   PetscInt       op[]  = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD};
153   PetscInt       fop[] = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD};
154   PetscInt       vals[9],  work[9];
155   PetscScalar    fvals[3], fwork[3];
156 
157   PetscFunctionBegin;
158   PetscCall(PCTFS_comm_init());
159   PetscCall(check_handle(xxt_handle));
160 
161   /* if factorization not done there are no stats */
162   if (!xxt_handle->info||!xxt_handle->mvi) {
163     if (!PCTFS_my_id) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"XXT_stats() :: no stats available!\n"));
164     PetscFunctionReturn(1);
165   }
166 
167   vals[0]=vals[1]=vals[2]=xxt_handle->info->nnz;
168   vals[3]=vals[4]=vals[5]=xxt_handle->mvi->n;
169   vals[6]=vals[7]=vals[8]=xxt_handle->info->msg_buf_sz;
170   PCTFS_giop(vals,work,PETSC_STATIC_ARRAY_LENGTH(op)-1,op);
171 
172   fvals[0]=fvals[1]=fvals[2] =xxt_handle->info->tot_solve_time/xxt_handle->info->nsolves++;
173   PCTFS_grop(fvals,fwork,PETSC_STATIC_ARRAY_LENGTH(fop)-1,fop);
174 
175   if (!PCTFS_my_id) {
176     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[0]));
177     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[1]));
178     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_nnz=%g\n",PCTFS_my_id,(double)(1.0*vals[2]/PCTFS_num_nodes)));
179     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: tot   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[2]));
180     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: xxt   C(2d)  =%g\n",PCTFS_my_id,(double)(vals[2]/(PetscPowReal(1.0*vals[5],1.5)))));
181     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: xxt   C(3d)  =%g\n",PCTFS_my_id,(double)(vals[2]/(PetscPowReal(1.0*vals[5],1.6667)))));
182     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[3]));
183     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[4]));
184     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_n  =%g\n",PCTFS_my_id,(double)(1.0*vals[5]/PCTFS_num_nodes)));
185     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: tot   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[5]));
186     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_buf=%" PetscInt_FMT "\n",PCTFS_my_id,vals[6]));
187     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_buf=%" PetscInt_FMT "\n",PCTFS_my_id,vals[7]));
188     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_buf=%g\n",PCTFS_my_id,(double)(1.0*vals[8]/PCTFS_num_nodes)));
189     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[0])));
190     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[1])));
191     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[2]/PCTFS_num_nodes)));
192   }
193   PetscFunctionReturn(0);
194 }
195 
196 /*************************************xxt.c************************************
197 
198 Description: get A_local, local portion of global coarse matrix which
199 is a row dist. nxm matrix w/ n<m.
200    o my_ml holds address of ML struct associated w/A_local and coarse grid
201    o local2global holds global number of column i (i=0,...,m-1)
202    o local2global holds global number of row    i (i=0,...,n-1)
203    o mylocmatvec performs A_local . vec_local (note that gs is performed using
204    PCTFS_gs_init/gop).
205 
206 mylocmatvec = my_ml->Amat[grid_tag].matvec->external;
207 mylocmatvec (void :: void *data, double *in, double *out)
208 **************************************xxt.c***********************************/
209 static PetscErrorCode do_xxt_factor(xxt_ADT xxt_handle)
210 {
211   return xxt_generate(xxt_handle);
212 }
213 
214 /**************************************xxt.c***********************************/
215 static PetscErrorCode xxt_generate(xxt_ADT xxt_handle)
216 {
217   PetscInt       i,j,k,idex;
218   PetscInt       dim, col;
219   PetscScalar    *u, *uu, *v, *z, *w, alpha, alpha_w;
220   PetscInt       *segs;
221   PetscInt       op[] = {GL_ADD,0};
222   PetscInt       off, len;
223   PetscScalar    *x_ptr;
224   PetscInt       *iptr, flag;
225   PetscInt       start =0, end, work;
226   PetscInt       op2[] = {GL_MIN,0};
227   PCTFS_gs_ADT   PCTFS_gs_handle;
228   PetscInt       *nsep, *lnsep, *fo;
229   PetscInt       a_n            =xxt_handle->mvi->n;
230   PetscInt       a_m            =xxt_handle->mvi->m;
231   PetscInt       *a_local2global=xxt_handle->mvi->local2global;
232   PetscInt       level;
233   PetscInt       xxt_nnz=0, xxt_max_nnz=0;
234   PetscInt       n, m;
235   PetscInt       *col_sz, *col_indices, *stages;
236   PetscScalar    **col_vals, *x;
237   PetscInt       n_global;
238   PetscBLASInt   i1            = 1,dlen;
239   PetscScalar    dm1           = -1.0;
240 
241   n               = xxt_handle->mvi->n;
242   nsep            = xxt_handle->info->nsep;
243   lnsep           = xxt_handle->info->lnsep;
244   fo              = xxt_handle->info->fo;
245   end             = lnsep[0];
246   level           = xxt_handle->level;
247   PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;
248 
249   /* is there a null space? */
250   /* LATER add in ability to detect null space by checking alpha */
251   for (i=0, j=0; i<=level; i++) j+=nsep[i];
252 
253   m = j-xxt_handle->ns;
254   if (m!=j) {
255     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"xxt_generate() :: null space exists %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",m,j,xxt_handle->ns));
256   }
257 
258   /* get and initialize storage for x local         */
259   /* note that x local is nxm and stored by columns */
260   col_sz      = (PetscInt*) malloc(m*sizeof(PetscInt));
261   col_indices = (PetscInt*) malloc((2*m+1)*sizeof(PetscInt));
262   col_vals    = (PetscScalar**) malloc(m*sizeof(PetscScalar*));
263   for (i=j=0; i<m; i++, j+=2) {
264     col_indices[j]=col_indices[j+1]=col_sz[i]=-1;
265     col_vals[i]   = NULL;
266   }
267   col_indices[j]=-1;
268 
269   /* size of separators for each sub-hc working from bottom of tree to top */
270   /* this looks like nsep[]=segments */
271   stages = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
272   segs   = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
273   PCTFS_ivec_zero(stages,level+1);
274   PCTFS_ivec_copy(segs,nsep,level+1);
275   for (i=0; i<level; i++) segs[i+1] += segs[i];
276   stages[0] = segs[0];
277 
278   /* temporary vectors  */
279   u  = (PetscScalar*) malloc(n*sizeof(PetscScalar));
280   z  = (PetscScalar*) malloc(n*sizeof(PetscScalar));
281   v  = (PetscScalar*) malloc(a_m*sizeof(PetscScalar));
282   uu = (PetscScalar*) malloc(m*sizeof(PetscScalar));
283   w  = (PetscScalar*) malloc(m*sizeof(PetscScalar));
284 
285   /* extra nnz due to replication of vertices across separators */
286   for (i=1, j=0; i<=level; i++) j+=nsep[i];
287 
288   /* storage for sparse x values */
289   n_global    = xxt_handle->info->n_global;
290   xxt_max_nnz = (PetscInt)(2.5*PetscPowReal(1.0*n_global,1.6667) + j*n/2)/PCTFS_num_nodes;
291   x           = (PetscScalar*) malloc(xxt_max_nnz*sizeof(PetscScalar));
292   xxt_nnz     = 0;
293 
294   /* LATER - can embed next sep to fire in gs */
295   /* time to make the donuts - generate X factor */
296   for (dim=i=j=0; i<m; i++) {
297     /* time to move to the next level? */
298     while (i==segs[dim]) {
299       PetscCheck(dim!=level,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim about to exceed level");
300       stages[dim++]=i;
301       end         +=lnsep[dim];
302     }
303     stages[dim]=i;
304 
305     /* which column are we firing? */
306     /* i.e. set v_l */
307     /* use new seps and do global min across hc to determine which one to fire */
308     (start<end) ? (col=fo[start]) : (col=INT_MAX);
309     PCTFS_giop_hc(&col,&work,1,op2,dim);
310 
311     /* shouldn't need this */
312     if (col==INT_MAX) {
313       PetscCall(PetscInfo(0,"hey ... col==INT_MAX??\n"));
314       continue;
315     }
316 
317     /* do I own it? I should */
318     PCTFS_rvec_zero(v,a_m);
319     if (col==fo[start]) {
320       start++;
321       idex=PCTFS_ivec_linear_search(col, a_local2global, a_n);
322       if (idex!=-1) {
323         v[idex] = 1.0; j++;
324       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"NOT FOUND!");
325     } else {
326       idex=PCTFS_ivec_linear_search(col, a_local2global, a_m);
327       if (idex!=-1) v[idex] = 1.0;
328     }
329 
330     /* perform u = A.v_l */
331     PCTFS_rvec_zero(u,n);
332     do_matvec(xxt_handle->mvi,v,u);
333 
334     /* uu =  X^T.u_l (local portion) */
335     /* technically only need to zero out first i entries */
336     /* later turn this into an XXT_solve call ? */
337     PCTFS_rvec_zero(uu,m);
338     x_ptr=x;
339     iptr = col_indices;
340     for (k=0; k<i; k++) {
341       off   = *iptr++;
342       len   = *iptr++;
343       PetscCall(PetscBLASIntCast(len,&dlen));
344       PetscStackCallBLAS("BLASdot",uu[k] = BLASdot_(&dlen,u+off,&i1,x_ptr,&i1));
345       x_ptr+=len;
346     }
347 
348     /* uu = X^T.u_l (comm portion) */
349     PetscCall(PCTFS_ssgl_radd  (uu, w, dim, stages));
350 
351     /* z = X.uu */
352     PCTFS_rvec_zero(z,n);
353     x_ptr=x;
354     iptr = col_indices;
355     for (k=0; k<i; k++) {
356       off  = *iptr++;
357       len  = *iptr++;
358       PetscCall(PetscBLASIntCast(len,&dlen));
359       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&dlen,&uu[k],x_ptr,&i1,z+off,&i1));
360       x_ptr+=len;
361     }
362 
363     /* compute v_l = v_l - z */
364     PCTFS_rvec_zero(v+a_n,a_m-a_n);
365     PetscCall(PetscBLASIntCast(n,&dlen));
366     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&dlen,&dm1,z,&i1,v,&i1));
367 
368     /* compute u_l = A.v_l */
369     if (a_n!=a_m) PCTFS_gs_gop_hc(PCTFS_gs_handle,v,"+\0",dim);
370     PCTFS_rvec_zero(u,n);
371     do_matvec(xxt_handle->mvi,v,u);
372 
373     /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - local portion */
374     PetscCall(PetscBLASIntCast(n,&dlen));
375     PetscStackCallBLAS("BLASdot",alpha = BLASdot_(&dlen,u,&i1,v,&i1));
376     /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - comm portion */
377     PCTFS_grop_hc(&alpha, &alpha_w, 1, op, dim);
378 
379     alpha = (PetscScalar) PetscSqrtReal((PetscReal)alpha);
380 
381     /* check for small alpha                             */
382     /* LATER use this to detect and determine null space */
383     PetscCheck(PetscAbsScalar(alpha)>=1.0e-14,PETSC_COMM_SELF,PETSC_ERR_PLIB,"bad alpha! %g",(double)PetscAbsScalar(alpha));
384 
385     /* compute v_l = v_l/sqrt(alpha) */
386     PCTFS_rvec_scale(v,1.0/alpha,n);
387 
388     /* add newly generated column, v_l, to X */
389     flag = 1;
390     off=len=0;
391     for (k=0; k<n; k++) {
392       if (v[k]!=0.0) {
393         len=k;
394         if (flag) { off=k; flag=0; }
395       }
396     }
397 
398     len -= (off-1);
399 
400     if (len>0) {
401       if ((xxt_nnz+len)>xxt_max_nnz) {
402         PetscCall(PetscInfo(0,"increasing space for X by 2x!\n"));
403         xxt_max_nnz *= 2;
404         x_ptr        = (PetscScalar*) malloc(xxt_max_nnz*sizeof(PetscScalar));
405         PCTFS_rvec_copy(x_ptr,x,xxt_nnz);
406         free(x);
407         x     = x_ptr;
408         x_ptr+=xxt_nnz;
409       }
410       xxt_nnz += len;
411       PCTFS_rvec_copy(x_ptr,v+off,len);
412 
413       col_indices[2*i] = off;
414       col_sz[i] = col_indices[2*i+1] = len;
415       col_vals[i] = x_ptr;
416     }
417     else {
418       col_indices[2*i] = 0;
419       col_sz[i]        = col_indices[2*i+1] = 0;
420       col_vals[i]      = x_ptr;
421     }
422   }
423 
424   /* close off stages for execution phase */
425   while (dim!=level) {
426     stages[dim++] = i;
427     PetscCall(PetscInfo(0,"disconnected!!! dim(%" PetscInt_FMT ")!=level(%" PetscInt_FMT ")\n",dim,level));
428   }
429   stages[dim]=i;
430 
431   xxt_handle->info->n              = xxt_handle->mvi->n;
432   xxt_handle->info->m              = m;
433   xxt_handle->info->nnz            = xxt_nnz;
434   xxt_handle->info->max_nnz        = xxt_max_nnz;
435   xxt_handle->info->msg_buf_sz     = stages[level]-stages[0];
436   xxt_handle->info->solve_uu       = (PetscScalar*) malloc(m*sizeof(PetscScalar));
437   xxt_handle->info->solve_w        = (PetscScalar*) malloc(m*sizeof(PetscScalar));
438   xxt_handle->info->x              = x;
439   xxt_handle->info->col_vals       = col_vals;
440   xxt_handle->info->col_sz         = col_sz;
441   xxt_handle->info->col_indices    = col_indices;
442   xxt_handle->info->stages         = stages;
443   xxt_handle->info->nsolves        = 0;
444   xxt_handle->info->tot_solve_time = 0.0;
445 
446   free(segs);
447   free(u);
448   free(v);
449   free(uu);
450   free(z);
451   free(w);
452 
453   return(0);
454 }
455 
456 /**************************************xxt.c***********************************/
457 static PetscErrorCode do_xxt_solve(xxt_ADT xxt_handle,  PetscScalar *uc)
458 {
459   PetscInt       off, len, *iptr;
460   PetscInt       level        = xxt_handle->level;
461   PetscInt       n            = xxt_handle->info->n;
462   PetscInt       m            = xxt_handle->info->m;
463   PetscInt       *stages      = xxt_handle->info->stages;
464   PetscInt       *col_indices = xxt_handle->info->col_indices;
465   PetscScalar    *x_ptr, *uu_ptr;
466   PetscScalar    *solve_uu = xxt_handle->info->solve_uu;
467   PetscScalar    *solve_w  = xxt_handle->info->solve_w;
468   PetscScalar    *x        = xxt_handle->info->x;
469   PetscBLASInt   i1        = 1,dlen;
470 
471   PetscFunctionBegin;
472   uu_ptr=solve_uu;
473   PCTFS_rvec_zero(uu_ptr,m);
474 
475   /* x  = X.Y^T.b */
476   /* uu = Y^T.b */
477   for (x_ptr=x,iptr=col_indices; *iptr!=-1; x_ptr+=len) {
478     off       =*iptr++;
479     len       =*iptr++;
480     PetscCall(PetscBLASIntCast(len,&dlen));
481     PetscStackCallBLAS("BLASdot",*uu_ptr++ = BLASdot_(&dlen,uc+off,&i1,x_ptr,&i1));
482   }
483 
484   /* comunication of beta */
485   uu_ptr=solve_uu;
486   if (level) PetscCall(PCTFS_ssgl_radd(uu_ptr, solve_w, level, stages));
487 
488   PCTFS_rvec_zero(uc,n);
489 
490   /* x = X.uu */
491   for (x_ptr=x,iptr=col_indices; *iptr!=-1; x_ptr+=len) {
492     off  =*iptr++;
493     len  =*iptr++;
494     PetscCall(PetscBLASIntCast(len,&dlen));
495     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&dlen,uu_ptr++,x_ptr,&i1,uc+off,&i1));
496   }
497   PetscFunctionReturn(0);
498 }
499 
500 /**************************************xxt.c***********************************/
501 static PetscErrorCode check_handle(xxt_ADT xxt_handle)
502 {
503   PetscInt vals[2], work[2], op[] = {NON_UNIFORM,GL_MIN,GL_MAX};
504 
505   PetscFunctionBegin;
506   PetscCheck(xxt_handle,PETSC_COMM_SELF,PETSC_ERR_PLIB,"check_handle() :: bad handle :: NULL %p",xxt_handle);
507 
508   vals[0]=vals[1]=xxt_handle->id;
509   PCTFS_giop(vals,work,PETSC_STATIC_ARRAY_LENGTH(op)-1,op);
510   PetscCheck(!(vals[0]!=vals[1])&&!(xxt_handle->id<=0),PETSC_COMM_SELF,PETSC_ERR_PLIB,"check_handle() :: bad handle :: id mismatch min/max %" PetscInt_FMT "/%" PetscInt_FMT " %" PetscInt_FMT,vals[0],vals[1], xxt_handle->id);
511   PetscFunctionReturn(0);
512 }
513 
514 /**************************************xxt.c***********************************/
515 static PetscErrorCode det_separators(xxt_ADT xxt_handle)
516 {
517   PetscInt     i, ct, id;
518   PetscInt     mask, edge, *iptr;
519   PetscInt     *dir, *used;
520   PetscInt     sum[4], w[4];
521   PetscScalar  rsum[4], rw[4];
522   PetscInt     op[] = {GL_ADD,0};
523   PetscScalar  *lhs, *rhs;
524   PetscInt     *nsep, *lnsep, *fo, nfo=0;
525   PCTFS_gs_ADT PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;
526   PetscInt     *local2global   = xxt_handle->mvi->local2global;
527   PetscInt     n               = xxt_handle->mvi->n;
528   PetscInt     m               = xxt_handle->mvi->m;
529   PetscInt     level           = xxt_handle->level;
530   PetscInt     shared          = 0;
531 
532   PetscFunctionBegin;
533   dir  = (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
534   nsep = (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
535   lnsep= (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
536   fo   = (PetscInt*)malloc(sizeof(PetscInt)*(n+1));
537   used = (PetscInt*)malloc(sizeof(PetscInt)*n);
538 
539   PCTFS_ivec_zero(dir,level+1);
540   PCTFS_ivec_zero(nsep,level+1);
541   PCTFS_ivec_zero(lnsep,level+1);
542   PCTFS_ivec_set (fo,-1,n+1);
543   PCTFS_ivec_zero(used,n);
544 
545   lhs = (PetscScalar*)malloc(sizeof(PetscScalar)*m);
546   rhs = (PetscScalar*)malloc(sizeof(PetscScalar)*m);
547 
548   /* determine the # of unique dof */
549   PCTFS_rvec_zero(lhs,m);
550   PCTFS_rvec_set(lhs,1.0,n);
551   PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",level);
552   PCTFS_rvec_zero(rsum,2);
553   for (i=0; i<n; i++) {
554     if (lhs[i]!=0.0) {
555       rsum[0]+=1.0/lhs[i]; rsum[1]+=lhs[i];
556     }
557   }
558   PCTFS_grop_hc(rsum,rw,2,op,level);
559   rsum[0]+=0.1;
560   rsum[1]+=0.1;
561 
562   if (PetscAbsScalar(rsum[0]-rsum[1])>EPS) shared=1;
563 
564   xxt_handle->info->n_global=xxt_handle->info->m_global=(PetscInt) rsum[0];
565   xxt_handle->mvi->n_global =xxt_handle->mvi->m_global =(PetscInt) rsum[0];
566 
567   /* determine separator sets top down */
568   if (shared) {
569     for (iptr=fo+n,id=PCTFS_my_id,mask=PCTFS_num_nodes>>1,edge=level;edge>0;edge--,mask>>=1) {
570 
571       /* set rsh of hc, fire, and collect lhs responses */
572       (id<mask) ? PCTFS_rvec_zero(lhs,m) : PCTFS_rvec_set(lhs,1.0,m);
573       PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge);
574 
575       /* set lsh of hc, fire, and collect rhs responses */
576       (id<mask) ? PCTFS_rvec_set(rhs,1.0,m) : PCTFS_rvec_zero(rhs,m);
577       PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge);
578 
579       for (i=0;i<n;i++) {
580         if (id< mask) {
581           if (lhs[i]!=0.0) lhs[i]=1.0;
582         }
583         if (id>=mask) {
584           if (rhs[i]!=0.0) rhs[i]=1.0;
585         }
586       }
587 
588       if (id< mask) PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge-1);
589       else          PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge-1);
590 
591       /* count number of dofs I own that have signal and not in sep set */
592       PCTFS_rvec_zero(rsum,4);
593       for (PCTFS_ivec_zero(sum,4),ct=i=0;i<n;i++) {
594         if (!used[i]) {
595           /* number of unmarked dofs on node */
596           ct++;
597           /* number of dofs to be marked on lhs hc */
598           if (id< mask) {
599             if (lhs[i]!=0.0) { sum[0]++; rsum[0]+=1.0/lhs[i]; }
600           }
601           /* number of dofs to be marked on rhs hc */
602           if (id>=mask) {
603             if (rhs[i]!=0.0) { sum[1]++; rsum[1]+=1.0/rhs[i]; }
604           }
605         }
606       }
607 
608       /* go for load balance - choose half with most unmarked dofs, bias LHS */
609       (id<mask) ? (sum[2]=ct) : (sum[3]=ct);
610       (id<mask) ? (rsum[2]=ct) : (rsum[3]=ct);
611       PCTFS_giop_hc(sum,w,4,op,edge);
612       PCTFS_grop_hc(rsum,rw,4,op,edge);
613       rsum[0]+=0.1; rsum[1]+=0.1; rsum[2]+=0.1; rsum[3]+=0.1;
614 
615       if (id<mask) {
616         /* mark dofs I own that have signal and not in sep set */
617         for (ct=i=0;i<n;i++) {
618           if ((!used[i])&&(lhs[i]!=0.0)) {
619             ct++; nfo++;
620 
621             PetscCheck(nfo<=n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"nfo about to exceed n");
622 
623             *--iptr = local2global[i];
624             used[i] = edge;
625           }
626         }
627         if (ct>1) PCTFS_ivec_sort(iptr,ct);
628 
629         lnsep[edge]=ct;
630         nsep[edge]=(PetscInt) rsum[0];
631         dir [edge]=LEFT;
632       }
633 
634       if (id>=mask) {
635         /* mark dofs I own that have signal and not in sep set */
636         for (ct=i=0;i<n;i++) {
637           if ((!used[i])&&(rhs[i]!=0.0)) {
638             ct++; nfo++;
639 
640             PetscCheck(nfo<=n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"nfo about to exceed n");
641 
642             *--iptr = local2global[i];
643             used[i] = edge;
644           }
645         }
646         if (ct>1) PCTFS_ivec_sort(iptr,ct);
647 
648         lnsep[edge] = ct;
649         nsep[edge]  = (PetscInt) rsum[1];
650         dir [edge]  = RIGHT;
651       }
652 
653       /* LATER or we can recur on these to order seps at this level */
654       /* do we need full set of separators for this?                */
655 
656       /* fold rhs hc into lower */
657       if (id>=mask) id-=mask;
658     }
659   } else {
660     for (iptr=fo+n,id=PCTFS_my_id,mask=PCTFS_num_nodes>>1,edge=level;edge>0;edge--,mask>>=1) {
661       /* set rsh of hc, fire, and collect lhs responses */
662       (id<mask) ? PCTFS_rvec_zero(lhs,m) : PCTFS_rvec_set(lhs,1.0,m);
663       PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge);
664 
665       /* set lsh of hc, fire, and collect rhs responses */
666       (id<mask) ? PCTFS_rvec_set(rhs,1.0,m) : PCTFS_rvec_zero(rhs,m);
667       PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge);
668 
669       /* count number of dofs I own that have signal and not in sep set */
670       for (PCTFS_ivec_zero(sum,4),ct=i=0;i<n;i++) {
671         if (!used[i]) {
672           /* number of unmarked dofs on node */
673           ct++;
674           /* number of dofs to be marked on lhs hc */
675           if ((id< mask)&&(lhs[i]!=0.0)) sum[0]++;
676           /* number of dofs to be marked on rhs hc */
677           if ((id>=mask)&&(rhs[i]!=0.0)) sum[1]++;
678         }
679       }
680 
681       /* go for load balance - choose half with most unmarked dofs, bias LHS */
682       (id<mask) ? (sum[2]=ct) : (sum[3]=ct);
683       PCTFS_giop_hc(sum,w,4,op,edge);
684 
685       /* lhs hc wins */
686       if (sum[2]>=sum[3]) {
687         if (id<mask) {
688           /* mark dofs I own that have signal and not in sep set */
689           for (ct=i=0;i<n;i++) {
690             if ((!used[i])&&(lhs[i]!=0.0)) {
691               ct++; nfo++;
692               *--iptr = local2global[i];
693               used[i]=edge;
694             }
695           }
696           if (ct>1) PCTFS_ivec_sort(iptr,ct);
697           lnsep[edge]=ct;
698         }
699         nsep[edge]=sum[0];
700         dir [edge]=LEFT;
701       } else { /* rhs hc wins */
702         if (id>=mask) {
703           /* mark dofs I own that have signal and not in sep set */
704           for (ct=i=0;i<n;i++) {
705             if ((!used[i])&&(rhs[i]!=0.0)) {
706               ct++; nfo++;
707               *--iptr = local2global[i];
708               used[i]=edge;
709             }
710           }
711           if (ct>1) PCTFS_ivec_sort(iptr,ct);
712           lnsep[edge]=ct;
713         }
714         nsep[edge]=sum[1];
715         dir [edge]=RIGHT;
716       }
717       /* LATER or we can recur on these to order seps at this level */
718       /* do we need full set of separators for this?                */
719 
720       /* fold rhs hc into lower */
721       if (id>=mask) id-=mask;
722     }
723   }
724 
725   /* level 0 is on processor case - so mark the remainder */
726   for (ct=i=0; i<n; i++) {
727     if (!used[i]) {
728       ct++; nfo++;
729       *--iptr = local2global[i];
730       used[i] = edge;
731     }
732   }
733   if (ct>1) PCTFS_ivec_sort(iptr,ct);
734   lnsep[edge]=ct;
735   nsep [edge]=ct;
736   dir  [edge]=LEFT;
737 
738   xxt_handle->info->nsep  = nsep;
739   xxt_handle->info->lnsep = lnsep;
740   xxt_handle->info->fo    = fo;
741   xxt_handle->info->nfo   = nfo;
742 
743   free(dir);
744   free(lhs);
745   free(rhs);
746   free(used);
747   PetscFunctionReturn(0);
748 }
749 
750 /**************************************xxt.c***********************************/
751 static mv_info *set_mvi(PetscInt *local2global,PetscInt n,PetscInt m,PetscErrorCode (*matvec)(mv_info*,PetscScalar*,PetscScalar*),void *grid_data)
752 {
753   mv_info *mvi;
754 
755   mvi               = (mv_info*)malloc(sizeof(mv_info));
756   mvi->n            = n;
757   mvi->m            = m;
758   mvi->n_global     = -1;
759   mvi->m_global     = -1;
760   mvi->local2global = (PetscInt*)malloc((m+1)*sizeof(PetscInt));
761   PCTFS_ivec_copy(mvi->local2global,local2global,m);
762   mvi->local2global[m] = INT_MAX;
763   mvi->matvec          = matvec;
764   mvi->grid_data       = grid_data;
765 
766   /* set xxt communication handle to perform restricted matvec */
767   mvi->PCTFS_gs_handle = PCTFS_gs_init(local2global, m, PCTFS_num_nodes);
768 
769   return(mvi);
770 }
771 
772 /**************************************xxt.c***********************************/
773 static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u)
774 {
775   PetscFunctionBegin;
776   A->matvec((mv_info*)A->grid_data,v,u);
777   PetscFunctionReturn(0);
778 }
779