xref: /petsc/src/ksp/pc/impls/tfs/xxt.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
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   xxt_ADT xxt_handle;
66 
67   /* rolling count on n_xxt ... pot. problem here */
68   n_xxt_handles++;
69   xxt_handle       = (xxt_ADT)malloc(sizeof(struct xxt_CDT));
70   xxt_handle->id   = ++n_xxt;
71   xxt_handle->info = NULL;
72   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   PCTFS_comm_init();
110   check_handle(xxt_handle);
111 
112   /* need to copy b into x? */
113   if (b) PCTFS_rvec_copy(x, b, xxt_handle->mvi->n);
114   return do_xxt_solve(xxt_handle, x);
115 }
116 
117 /**************************************xxt.c***********************************/
118 PetscInt XXT_free(xxt_ADT xxt_handle) {
119   PCTFS_comm_init();
120   check_handle(xxt_handle);
121   n_xxt_handles--;
122 
123   free(xxt_handle->info->nsep);
124   free(xxt_handle->info->lnsep);
125   free(xxt_handle->info->fo);
126   free(xxt_handle->info->stages);
127   free(xxt_handle->info->solve_uu);
128   free(xxt_handle->info->solve_w);
129   free(xxt_handle->info->x);
130   free(xxt_handle->info->col_vals);
131   free(xxt_handle->info->col_sz);
132   free(xxt_handle->info->col_indices);
133   free(xxt_handle->info);
134   free(xxt_handle->mvi->local2global);
135   PCTFS_gs_free(xxt_handle->mvi->PCTFS_gs_handle);
136   free(xxt_handle->mvi);
137   free(xxt_handle);
138 
139   /* if the check fails we nuke */
140   /* if NULL pointer passed to free we nuke */
141   /* if the calls to free fail that's not my problem */
142   return (0);
143 }
144 
145 /**************************************xxt.c***********************************/
146 PetscErrorCode XXT_stats(xxt_ADT xxt_handle) {
147   PetscInt    op[]  = {NON_UNIFORM, GL_MIN, GL_MAX, GL_ADD, GL_MIN, GL_MAX, GL_ADD, GL_MIN, GL_MAX, GL_ADD};
148   PetscInt    fop[] = {NON_UNIFORM, GL_MIN, GL_MAX, GL_ADD};
149   PetscInt    vals[9], work[9];
150   PetscScalar fvals[3], fwork[3];
151 
152   PetscFunctionBegin;
153   PetscCall(PCTFS_comm_init());
154   PetscCall(check_handle(xxt_handle));
155 
156   /* if factorization not done there are no stats */
157   if (!xxt_handle->info || !xxt_handle->mvi) {
158     if (!PCTFS_my_id) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "XXT_stats() :: no stats available!\n"));
159     PetscFunctionReturn(1);
160   }
161 
162   vals[0] = vals[1] = vals[2] = xxt_handle->info->nnz;
163   vals[3] = vals[4] = vals[5] = xxt_handle->mvi->n;
164   vals[6] = vals[7] = vals[8] = xxt_handle->info->msg_buf_sz;
165   PCTFS_giop(vals, work, PETSC_STATIC_ARRAY_LENGTH(op) - 1, op);
166 
167   fvals[0] = fvals[1] = fvals[2] = xxt_handle->info->tot_solve_time / xxt_handle->info->nsolves++;
168   PCTFS_grop(fvals, fwork, PETSC_STATIC_ARRAY_LENGTH(fop) - 1, fop);
169 
170   if (!PCTFS_my_id) {
171     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xxt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[0]));
172     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xxt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[1]));
173     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xxt_nnz=%g\n", PCTFS_my_id, (double)(1.0 * vals[2] / PCTFS_num_nodes)));
174     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: tot   xxt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[2]));
175     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: xxt   C(2d)  =%g\n", PCTFS_my_id, (double)(vals[2] / (PetscPowReal(1.0 * vals[5], 1.5)))));
176     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: xxt   C(3d)  =%g\n", PCTFS_my_id, (double)(vals[2] / (PetscPowReal(1.0 * vals[5], 1.6667)))));
177     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xxt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[3]));
178     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xxt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[4]));
179     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xxt_n  =%g\n", PCTFS_my_id, (double)(1.0 * vals[5] / PCTFS_num_nodes)));
180     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: tot   xxt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[5]));
181     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xxt_buf=%" PetscInt_FMT "\n", PCTFS_my_id, vals[6]));
182     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xxt_buf=%" PetscInt_FMT "\n", PCTFS_my_id, vals[7]));
183     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xxt_buf=%g\n", PCTFS_my_id, (double)(1.0 * vals[8] / PCTFS_num_nodes)));
184     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xxt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[0])));
185     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xxt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[1])));
186     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xxt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[2] / PCTFS_num_nodes)));
187   }
188   PetscFunctionReturn(0);
189 }
190 
191 /*************************************xxt.c************************************
192 
193 Description: get A_local, local portion of global coarse matrix which
194 is a row dist. nxm matrix w/ n<m.
195    o my_ml holds address of ML struct associated w/A_local and coarse grid
196    o local2global holds global number of column i (i=0,...,m-1)
197    o local2global holds global number of row    i (i=0,...,n-1)
198    o mylocmatvec performs A_local . vec_local (note that gs is performed using
199    PCTFS_gs_init/gop).
200 
201 mylocmatvec = my_ml->Amat[grid_tag].matvec->external;
202 mylocmatvec (void :: void *data, double *in, double *out)
203 **************************************xxt.c***********************************/
204 static PetscErrorCode do_xxt_factor(xxt_ADT xxt_handle) {
205   return xxt_generate(xxt_handle);
206 }
207 
208 /**************************************xxt.c***********************************/
209 static PetscErrorCode xxt_generate(xxt_ADT xxt_handle) {
210   PetscInt      i, j, k, idex;
211   PetscInt      dim, col;
212   PetscScalar  *u, *uu, *v, *z, *w, alpha, alpha_w;
213   PetscInt     *segs;
214   PetscInt      op[] = {GL_ADD, 0};
215   PetscInt      off, len;
216   PetscScalar  *x_ptr;
217   PetscInt     *iptr, flag;
218   PetscInt      start = 0, end, work;
219   PetscInt      op2[] = {GL_MIN, 0};
220   PCTFS_gs_ADT  PCTFS_gs_handle;
221   PetscInt     *nsep, *lnsep, *fo;
222   PetscInt      a_n            = xxt_handle->mvi->n;
223   PetscInt      a_m            = xxt_handle->mvi->m;
224   PetscInt     *a_local2global = xxt_handle->mvi->local2global;
225   PetscInt      level;
226   PetscInt      xxt_nnz = 0, xxt_max_nnz = 0;
227   PetscInt      n, m;
228   PetscInt     *col_sz, *col_indices, *stages;
229   PetscScalar **col_vals, *x;
230   PetscInt      n_global;
231   PetscBLASInt  i1  = 1, dlen;
232   PetscScalar   dm1 = -1.0;
233 
234   n               = xxt_handle->mvi->n;
235   nsep            = xxt_handle->info->nsep;
236   lnsep           = xxt_handle->info->lnsep;
237   fo              = xxt_handle->info->fo;
238   end             = lnsep[0];
239   level           = xxt_handle->level;
240   PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;
241 
242   /* is there a null space? */
243   /* LATER add in ability to detect null space by checking alpha */
244   for (i = 0, j = 0; i <= level; i++) j += nsep[i];
245 
246   m = j - xxt_handle->ns;
247   if (m != j) { PetscCall(PetscPrintf(PETSC_COMM_WORLD, "xxt_generate() :: null space exists %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, j, xxt_handle->ns)); }
248 
249   /* get and initialize storage for x local         */
250   /* note that x local is nxm and stored by columns */
251   col_sz      = (PetscInt *)malloc(m * sizeof(PetscInt));
252   col_indices = (PetscInt *)malloc((2 * m + 1) * sizeof(PetscInt));
253   col_vals    = (PetscScalar **)malloc(m * sizeof(PetscScalar *));
254   for (i = j = 0; i < m; i++, j += 2) {
255     col_indices[j] = col_indices[j + 1] = col_sz[i] = -1;
256     col_vals[i]                                     = NULL;
257   }
258   col_indices[j] = -1;
259 
260   /* size of separators for each sub-hc working from bottom of tree to top */
261   /* this looks like nsep[]=segments */
262   stages = (PetscInt *)malloc((level + 1) * sizeof(PetscInt));
263   segs   = (PetscInt *)malloc((level + 1) * sizeof(PetscInt));
264   PCTFS_ivec_zero(stages, level + 1);
265   PCTFS_ivec_copy(segs, nsep, level + 1);
266   for (i = 0; i < level; i++) segs[i + 1] += segs[i];
267   stages[0] = segs[0];
268 
269   /* temporary vectors  */
270   u  = (PetscScalar *)malloc(n * sizeof(PetscScalar));
271   z  = (PetscScalar *)malloc(n * sizeof(PetscScalar));
272   v  = (PetscScalar *)malloc(a_m * sizeof(PetscScalar));
273   uu = (PetscScalar *)malloc(m * sizeof(PetscScalar));
274   w  = (PetscScalar *)malloc(m * sizeof(PetscScalar));
275 
276   /* extra nnz due to replication of vertices across separators */
277   for (i = 1, j = 0; i <= level; i++) j += nsep[i];
278 
279   /* storage for sparse x values */
280   n_global    = xxt_handle->info->n_global;
281   xxt_max_nnz = (PetscInt)(2.5 * PetscPowReal(1.0 * n_global, 1.6667) + j * n / 2) / PCTFS_num_nodes;
282   x           = (PetscScalar *)malloc(xxt_max_nnz * sizeof(PetscScalar));
283   xxt_nnz     = 0;
284 
285   /* LATER - can embed next sep to fire in gs */
286   /* time to make the donuts - generate X factor */
287   for (dim = i = j = 0; i < m; i++) {
288     /* time to move to the next level? */
289     while (i == segs[dim]) {
290       PetscCheck(dim != level, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim about to exceed level");
291       stages[dim++] = i;
292       end += lnsep[dim];
293     }
294     stages[dim] = i;
295 
296     /* which column are we firing? */
297     /* i.e. set v_l */
298     /* use new seps and do global min across hc to determine which one to fire */
299     (start < end) ? (col = fo[start]) : (col = INT_MAX);
300     PCTFS_giop_hc(&col, &work, 1, op2, dim);
301 
302     /* shouldn't need this */
303     if (col == INT_MAX) {
304       PetscCall(PetscInfo(0, "hey ... col==INT_MAX??\n"));
305       continue;
306     }
307 
308     /* do I own it? I should */
309     PCTFS_rvec_zero(v, a_m);
310     if (col == fo[start]) {
311       start++;
312       idex = PCTFS_ivec_linear_search(col, a_local2global, a_n);
313       if (idex != -1) {
314         v[idex] = 1.0;
315         j++;
316       } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "NOT FOUND!");
317     } else {
318       idex = PCTFS_ivec_linear_search(col, a_local2global, a_m);
319       if (idex != -1) v[idex] = 1.0;
320     }
321 
322     /* perform u = A.v_l */
323     PCTFS_rvec_zero(u, n);
324     do_matvec(xxt_handle->mvi, v, u);
325 
326     /* uu =  X^T.u_l (local portion) */
327     /* technically only need to zero out first i entries */
328     /* later turn this into an XXT_solve call ? */
329     PCTFS_rvec_zero(uu, m);
330     x_ptr = x;
331     iptr  = col_indices;
332     for (k = 0; k < i; k++) {
333       off = *iptr++;
334       len = *iptr++;
335       PetscCall(PetscBLASIntCast(len, &dlen));
336       PetscCallBLAS("BLASdot", uu[k] = BLASdot_(&dlen, u + off, &i1, x_ptr, &i1));
337       x_ptr += len;
338     }
339 
340     /* uu = X^T.u_l (comm portion) */
341     PetscCall(PCTFS_ssgl_radd(uu, w, dim, stages));
342 
343     /* z = X.uu */
344     PCTFS_rvec_zero(z, n);
345     x_ptr = x;
346     iptr  = col_indices;
347     for (k = 0; k < i; k++) {
348       off = *iptr++;
349       len = *iptr++;
350       PetscCall(PetscBLASIntCast(len, &dlen));
351       PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, &uu[k], x_ptr, &i1, z + off, &i1));
352       x_ptr += len;
353     }
354 
355     /* compute v_l = v_l - z */
356     PCTFS_rvec_zero(v + a_n, a_m - a_n);
357     PetscCall(PetscBLASIntCast(n, &dlen));
358     PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, &dm1, z, &i1, v, &i1));
359 
360     /* compute u_l = A.v_l */
361     if (a_n != a_m) PCTFS_gs_gop_hc(PCTFS_gs_handle, v, "+\0", dim);
362     PCTFS_rvec_zero(u, n);
363     do_matvec(xxt_handle->mvi, v, u);
364 
365     /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - local portion */
366     PetscCall(PetscBLASIntCast(n, &dlen));
367     PetscCallBLAS("BLASdot", alpha = BLASdot_(&dlen, u, &i1, v, &i1));
368     /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - comm portion */
369     PCTFS_grop_hc(&alpha, &alpha_w, 1, op, dim);
370 
371     alpha = (PetscScalar)PetscSqrtReal((PetscReal)alpha);
372 
373     /* check for small alpha                             */
374     /* LATER use this to detect and determine null space */
375     PetscCheck(PetscAbsScalar(alpha) >= 1.0e-14, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bad alpha! %g", (double)PetscAbsScalar(alpha));
376 
377     /* compute v_l = v_l/sqrt(alpha) */
378     PCTFS_rvec_scale(v, 1.0 / alpha, n);
379 
380     /* add newly generated column, v_l, to X */
381     flag = 1;
382     off = len = 0;
383     for (k = 0; k < n; k++) {
384       if (v[k] != 0.0) {
385         len = k;
386         if (flag) {
387           off  = k;
388           flag = 0;
389         }
390       }
391     }
392 
393     len -= (off - 1);
394 
395     if (len > 0) {
396       if ((xxt_nnz + len) > xxt_max_nnz) {
397         PetscCall(PetscInfo(0, "increasing space for X by 2x!\n"));
398         xxt_max_nnz *= 2;
399         x_ptr = (PetscScalar *)malloc(xxt_max_nnz * sizeof(PetscScalar));
400         PCTFS_rvec_copy(x_ptr, x, xxt_nnz);
401         free(x);
402         x = x_ptr;
403         x_ptr += xxt_nnz;
404       }
405       xxt_nnz += len;
406       PCTFS_rvec_copy(x_ptr, v + off, len);
407 
408       col_indices[2 * i] = off;
409       col_sz[i] = col_indices[2 * i + 1] = len;
410       col_vals[i]                        = x_ptr;
411     } else {
412       col_indices[2 * i] = 0;
413       col_sz[i] = col_indices[2 * i + 1] = 0;
414       col_vals[i]                        = x_ptr;
415     }
416   }
417 
418   /* close off stages for execution phase */
419   while (dim != level) {
420     stages[dim++] = i;
421     PetscCall(PetscInfo(0, "disconnected!!! dim(%" PetscInt_FMT ")!=level(%" PetscInt_FMT ")\n", dim, level));
422   }
423   stages[dim] = i;
424 
425   xxt_handle->info->n              = xxt_handle->mvi->n;
426   xxt_handle->info->m              = m;
427   xxt_handle->info->nnz            = xxt_nnz;
428   xxt_handle->info->max_nnz        = xxt_max_nnz;
429   xxt_handle->info->msg_buf_sz     = stages[level] - stages[0];
430   xxt_handle->info->solve_uu       = (PetscScalar *)malloc(m * sizeof(PetscScalar));
431   xxt_handle->info->solve_w        = (PetscScalar *)malloc(m * sizeof(PetscScalar));
432   xxt_handle->info->x              = x;
433   xxt_handle->info->col_vals       = col_vals;
434   xxt_handle->info->col_sz         = col_sz;
435   xxt_handle->info->col_indices    = col_indices;
436   xxt_handle->info->stages         = stages;
437   xxt_handle->info->nsolves        = 0;
438   xxt_handle->info->tot_solve_time = 0.0;
439 
440   free(segs);
441   free(u);
442   free(v);
443   free(uu);
444   free(z);
445   free(w);
446 
447   return (0);
448 }
449 
450 /**************************************xxt.c***********************************/
451 static PetscErrorCode do_xxt_solve(xxt_ADT xxt_handle, PetscScalar *uc) {
452   PetscInt     off, len, *iptr;
453   PetscInt     level       = xxt_handle->level;
454   PetscInt     n           = xxt_handle->info->n;
455   PetscInt     m           = xxt_handle->info->m;
456   PetscInt    *stages      = xxt_handle->info->stages;
457   PetscInt    *col_indices = xxt_handle->info->col_indices;
458   PetscScalar *x_ptr, *uu_ptr;
459   PetscScalar *solve_uu = xxt_handle->info->solve_uu;
460   PetscScalar *solve_w  = xxt_handle->info->solve_w;
461   PetscScalar *x        = xxt_handle->info->x;
462   PetscBLASInt i1       = 1, dlen;
463 
464   PetscFunctionBegin;
465   uu_ptr = solve_uu;
466   PCTFS_rvec_zero(uu_ptr, m);
467 
468   /* x  = X.Y^T.b */
469   /* uu = Y^T.b */
470   for (x_ptr = x, iptr = col_indices; *iptr != -1; x_ptr += len) {
471     off = *iptr++;
472     len = *iptr++;
473     PetscCall(PetscBLASIntCast(len, &dlen));
474     PetscCallBLAS("BLASdot", *uu_ptr++ = BLASdot_(&dlen, uc + off, &i1, x_ptr, &i1));
475   }
476 
477   /* comunication of beta */
478   uu_ptr = solve_uu;
479   if (level) PetscCall(PCTFS_ssgl_radd(uu_ptr, solve_w, level, stages));
480 
481   PCTFS_rvec_zero(uc, n);
482 
483   /* x = X.uu */
484   for (x_ptr = x, iptr = col_indices; *iptr != -1; x_ptr += len) {
485     off = *iptr++;
486     len = *iptr++;
487     PetscCall(PetscBLASIntCast(len, &dlen));
488     PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, uu_ptr++, x_ptr, &i1, uc + off, &i1));
489   }
490   PetscFunctionReturn(0);
491 }
492 
493 /**************************************xxt.c***********************************/
494 static PetscErrorCode check_handle(xxt_ADT xxt_handle) {
495   PetscInt vals[2], work[2], op[] = {NON_UNIFORM, GL_MIN, GL_MAX};
496 
497   PetscFunctionBegin;
498   PetscCheck(xxt_handle, PETSC_COMM_SELF, PETSC_ERR_PLIB, "check_handle() :: bad handle :: NULL %p", xxt_handle);
499 
500   vals[0] = vals[1] = xxt_handle->id;
501   PCTFS_giop(vals, work, PETSC_STATIC_ARRAY_LENGTH(op) - 1, op);
502   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);
503   PetscFunctionReturn(0);
504 }
505 
506 /**************************************xxt.c***********************************/
507 static PetscErrorCode det_separators(xxt_ADT xxt_handle) {
508   PetscInt     i, ct, id;
509   PetscInt     mask, edge, *iptr;
510   PetscInt    *dir, *used;
511   PetscInt     sum[4], w[4];
512   PetscScalar  rsum[4], rw[4];
513   PetscInt     op[] = {GL_ADD, 0};
514   PetscScalar *lhs, *rhs;
515   PetscInt    *nsep, *lnsep, *fo, nfo = 0;
516   PCTFS_gs_ADT PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;
517   PetscInt    *local2global    = xxt_handle->mvi->local2global;
518   PetscInt     n               = xxt_handle->mvi->n;
519   PetscInt     m               = xxt_handle->mvi->m;
520   PetscInt     level           = xxt_handle->level;
521   PetscInt     shared          = 0;
522 
523   PetscFunctionBegin;
524   dir   = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
525   nsep  = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
526   lnsep = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
527   fo    = (PetscInt *)malloc(sizeof(PetscInt) * (n + 1));
528   used  = (PetscInt *)malloc(sizeof(PetscInt) * n);
529 
530   PCTFS_ivec_zero(dir, level + 1);
531   PCTFS_ivec_zero(nsep, level + 1);
532   PCTFS_ivec_zero(lnsep, level + 1);
533   PCTFS_ivec_set(fo, -1, n + 1);
534   PCTFS_ivec_zero(used, n);
535 
536   lhs = (PetscScalar *)malloc(sizeof(PetscScalar) * m);
537   rhs = (PetscScalar *)malloc(sizeof(PetscScalar) * m);
538 
539   /* determine the # of unique dof */
540   PCTFS_rvec_zero(lhs, m);
541   PCTFS_rvec_set(lhs, 1.0, n);
542   PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", level);
543   PCTFS_rvec_zero(rsum, 2);
544   for (i = 0; i < n; i++) {
545     if (lhs[i] != 0.0) {
546       rsum[0] += 1.0 / lhs[i];
547       rsum[1] += lhs[i];
548     }
549   }
550   PCTFS_grop_hc(rsum, rw, 2, op, level);
551   rsum[0] += 0.1;
552   rsum[1] += 0.1;
553 
554   if (PetscAbsScalar(rsum[0] - rsum[1]) > EPS) shared = 1;
555 
556   xxt_handle->info->n_global = xxt_handle->info->m_global = (PetscInt)rsum[0];
557   xxt_handle->mvi->n_global = xxt_handle->mvi->m_global = (PetscInt)rsum[0];
558 
559   /* determine separator sets top down */
560   if (shared) {
561     for (iptr = fo + n, id = PCTFS_my_id, mask = PCTFS_num_nodes >> 1, edge = level; edge > 0; edge--, mask >>= 1) {
562       /* set rsh of hc, fire, and collect lhs responses */
563       (id < mask) ? PCTFS_rvec_zero(lhs, m) : PCTFS_rvec_set(lhs, 1.0, m);
564       PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", edge);
565 
566       /* set lsh of hc, fire, and collect rhs responses */
567       (id < mask) ? PCTFS_rvec_set(rhs, 1.0, m) : PCTFS_rvec_zero(rhs, m);
568       PCTFS_gs_gop_hc(PCTFS_gs_handle, rhs, "+\0", edge);
569 
570       for (i = 0; i < n; i++) {
571         if (id < mask) {
572           if (lhs[i] != 0.0) lhs[i] = 1.0;
573         }
574         if (id >= mask) {
575           if (rhs[i] != 0.0) rhs[i] = 1.0;
576         }
577       }
578 
579       if (id < mask) PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", edge - 1);
580       else PCTFS_gs_gop_hc(PCTFS_gs_handle, rhs, "+\0", edge - 1);
581 
582       /* count number of dofs I own that have signal and not in sep set */
583       PCTFS_rvec_zero(rsum, 4);
584       for (PCTFS_ivec_zero(sum, 4), ct = i = 0; i < n; i++) {
585         if (!used[i]) {
586           /* number of unmarked dofs on node */
587           ct++;
588           /* number of dofs to be marked on lhs hc */
589           if (id < mask) {
590             if (lhs[i] != 0.0) {
591               sum[0]++;
592               rsum[0] += 1.0 / lhs[i];
593             }
594           }
595           /* number of dofs to be marked on rhs hc */
596           if (id >= mask) {
597             if (rhs[i] != 0.0) {
598               sum[1]++;
599               rsum[1] += 1.0 / rhs[i];
600             }
601           }
602         }
603       }
604 
605       /* go for load balance - choose half with most unmarked dofs, bias LHS */
606       (id < mask) ? (sum[2] = ct) : (sum[3] = ct);
607       (id < mask) ? (rsum[2] = ct) : (rsum[3] = ct);
608       PCTFS_giop_hc(sum, w, 4, op, edge);
609       PCTFS_grop_hc(rsum, rw, 4, op, edge);
610       rsum[0] += 0.1;
611       rsum[1] += 0.1;
612       rsum[2] += 0.1;
613       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++;
620             nfo++;
621 
622             PetscCheck(nfo <= n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nfo about to exceed n");
623 
624             *--iptr = local2global[i];
625             used[i] = edge;
626           }
627         }
628         if (ct > 1) PCTFS_ivec_sort(iptr, ct);
629 
630         lnsep[edge] = ct;
631         nsep[edge]  = (PetscInt)rsum[0];
632         dir[edge]   = LEFT;
633       }
634 
635       if (id >= mask) {
636         /* mark dofs I own that have signal and not in sep set */
637         for (ct = i = 0; i < n; i++) {
638           if ((!used[i]) && (rhs[i] != 0.0)) {
639             ct++;
640             nfo++;
641 
642             PetscCheck(nfo <= n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nfo about to exceed n");
643 
644             *--iptr = local2global[i];
645             used[i] = edge;
646           }
647         }
648         if (ct > 1) PCTFS_ivec_sort(iptr, ct);
649 
650         lnsep[edge] = ct;
651         nsep[edge]  = (PetscInt)rsum[1];
652         dir[edge]   = RIGHT;
653       }
654 
655       /* LATER or we can recur on these to order seps at this level */
656       /* do we need full set of separators for this?                */
657 
658       /* fold rhs hc into lower */
659       if (id >= mask) id -= mask;
660     }
661   } else {
662     for (iptr = fo + n, id = PCTFS_my_id, mask = PCTFS_num_nodes >> 1, edge = level; edge > 0; edge--, mask >>= 1) {
663       /* set rsh of hc, fire, and collect lhs responses */
664       (id < mask) ? PCTFS_rvec_zero(lhs, m) : PCTFS_rvec_set(lhs, 1.0, m);
665       PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", edge);
666 
667       /* set lsh of hc, fire, and collect rhs responses */
668       (id < mask) ? PCTFS_rvec_set(rhs, 1.0, m) : PCTFS_rvec_zero(rhs, m);
669       PCTFS_gs_gop_hc(PCTFS_gs_handle, rhs, "+\0", edge);
670 
671       /* count number of dofs I own that have signal and not in sep set */
672       for (PCTFS_ivec_zero(sum, 4), ct = i = 0; i < n; i++) {
673         if (!used[i]) {
674           /* number of unmarked dofs on node */
675           ct++;
676           /* number of dofs to be marked on lhs hc */
677           if ((id < mask) && (lhs[i] != 0.0)) sum[0]++;
678           /* number of dofs to be marked on rhs hc */
679           if ((id >= mask) && (rhs[i] != 0.0)) sum[1]++;
680         }
681       }
682 
683       /* go for load balance - choose half with most unmarked dofs, bias LHS */
684       (id < mask) ? (sum[2] = ct) : (sum[3] = ct);
685       PCTFS_giop_hc(sum, w, 4, op, edge);
686 
687       /* lhs hc wins */
688       if (sum[2] >= sum[3]) {
689         if (id < mask) {
690           /* mark dofs I own that have signal and not in sep set */
691           for (ct = i = 0; i < n; i++) {
692             if ((!used[i]) && (lhs[i] != 0.0)) {
693               ct++;
694               nfo++;
695               *--iptr = local2global[i];
696               used[i] = edge;
697             }
698           }
699           if (ct > 1) PCTFS_ivec_sort(iptr, ct);
700           lnsep[edge] = ct;
701         }
702         nsep[edge] = sum[0];
703         dir[edge]  = LEFT;
704       } else { /* rhs hc wins */
705         if (id >= mask) {
706           /* mark dofs I own that have signal and not in sep set */
707           for (ct = i = 0; i < n; i++) {
708             if ((!used[i]) && (rhs[i] != 0.0)) {
709               ct++;
710               nfo++;
711               *--iptr = local2global[i];
712               used[i] = edge;
713             }
714           }
715           if (ct > 1) PCTFS_ivec_sort(iptr, ct);
716           lnsep[edge] = ct;
717         }
718         nsep[edge] = sum[1];
719         dir[edge]  = RIGHT;
720       }
721       /* LATER or we can recur on these to order seps at this level */
722       /* do we need full set of separators for this?                */
723 
724       /* fold rhs hc into lower */
725       if (id >= mask) id -= mask;
726     }
727   }
728 
729   /* level 0 is on processor case - so mark the remainder */
730   for (ct = i = 0; i < n; i++) {
731     if (!used[i]) {
732       ct++;
733       nfo++;
734       *--iptr = local2global[i];
735       used[i] = edge;
736     }
737   }
738   if (ct > 1) PCTFS_ivec_sort(iptr, ct);
739   lnsep[edge] = ct;
740   nsep[edge]  = ct;
741   dir[edge]   = LEFT;
742 
743   xxt_handle->info->nsep  = nsep;
744   xxt_handle->info->lnsep = lnsep;
745   xxt_handle->info->fo    = fo;
746   xxt_handle->info->nfo   = nfo;
747 
748   free(dir);
749   free(lhs);
750   free(rhs);
751   free(used);
752   PetscFunctionReturn(0);
753 }
754 
755 /**************************************xxt.c***********************************/
756 static mv_info *set_mvi(PetscInt *local2global, PetscInt n, PetscInt m, PetscErrorCode (*matvec)(mv_info *, PetscScalar *, PetscScalar *), void *grid_data) {
757   mv_info *mvi;
758 
759   mvi               = (mv_info *)malloc(sizeof(mv_info));
760   mvi->n            = n;
761   mvi->m            = m;
762   mvi->n_global     = -1;
763   mvi->m_global     = -1;
764   mvi->local2global = (PetscInt *)malloc((m + 1) * sizeof(PetscInt));
765   PCTFS_ivec_copy(mvi->local2global, local2global, m);
766   mvi->local2global[m] = INT_MAX;
767   mvi->matvec          = matvec;
768   mvi->grid_data       = grid_data;
769 
770   /* set xxt communication handle to perform restricted matvec */
771   mvi->PCTFS_gs_handle = PCTFS_gs_init(local2global, m, PCTFS_num_nodes);
772 
773   return (mvi);
774 }
775 
776 /**************************************xxt.c***********************************/
777 static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u) {
778   PetscFunctionBegin;
779   A->matvec((mv_info *)A->grid_data, v, u);
780   PetscFunctionReturn(0);
781 }
782