xref: /petsc/src/ksp/pc/impls/tfs/xyt.c (revision 2d30e087755efd99e28fdfe792ffbeb2ee1ea928)
1 
2 /*
3 Module Name: xyt
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 */
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 xyt_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     *xcol_sz, *xcol_indices;
30   PetscScalar **xcol_vals, *x, *solve_uu, *solve_w;
31   PetscInt     *ycol_sz, *ycol_indices;
32   PetscScalar **ycol_vals, *y;
33   PetscInt      nsolves;
34   PetscScalar   tot_solve_time;
35 } xyt_info;
36 
37 typedef struct matvec_info {
38   PetscInt     n, m, n_global, m_global;
39   PetscInt    *local2global;
40   PCTFS_gs_ADT PCTFS_gs_handle;
41   PetscErrorCode (*matvec)(struct matvec_info *, PetscScalar *, PetscScalar *);
42   void *grid_data;
43 } mv_info;
44 
45 struct xyt_CDT {
46   PetscInt  id;
47   PetscInt  ns;
48   PetscInt  level;
49   xyt_info *info;
50   mv_info  *mvi;
51 };
52 
53 static PetscInt n_xyt         = 0;
54 static PetscInt n_xyt_handles = 0;
55 
56 /* prototypes */
57 static PetscErrorCode do_xyt_solve(xyt_ADT xyt_handle, PetscScalar *rhs);
58 static PetscErrorCode check_handle(xyt_ADT xyt_handle);
59 static PetscErrorCode det_separators(xyt_ADT xyt_handle);
60 static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u);
61 static PetscErrorCode xyt_generate(xyt_ADT xyt_handle);
62 static PetscErrorCode do_xyt_factor(xyt_ADT xyt_handle);
63 static mv_info       *set_mvi(PetscInt *local2global, PetscInt n, PetscInt m, PetscErrorCode (*matvec)(mv_info *, PetscScalar *, PetscScalar *), void *grid_data);
64 
65 xyt_ADT XYT_new(void) {
66   xyt_ADT xyt_handle;
67 
68   /* rolling count on n_xyt ... pot. problem here */
69   n_xyt_handles++;
70   xyt_handle       = (xyt_ADT)malloc(sizeof(struct xyt_CDT));
71   xyt_handle->id   = ++n_xyt;
72   xyt_handle->info = NULL;
73   xyt_handle->mvi  = NULL;
74 
75   return (xyt_handle);
76 }
77 
78 PetscErrorCode XYT_factor(xyt_ADT   xyt_handle,                                           /* prev. allocated xyt  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(xyt_handle);
87 
88   /* only 2^k for now and all nodes participating */
89   PetscCheck((1 << (xyt_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   xyt_handle->info = (xyt_info *)malloc(sizeof(xyt_info));
93 
94   /* set up matvec handles */
95   xyt_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   xyt_handle->ns = 0;
100 
101   /* determine separators and generate firing order - NB xyt info set here */
102   det_separators(xyt_handle);
103 
104   return (do_xyt_factor(xyt_handle));
105 }
106 
107 PetscErrorCode XYT_solve(xyt_ADT xyt_handle, PetscScalar *x, PetscScalar *b) {
108   PCTFS_comm_init();
109   check_handle(xyt_handle);
110 
111   /* need to copy b into x? */
112   if (b) PCTFS_rvec_copy(x, b, xyt_handle->mvi->n);
113   return do_xyt_solve(xyt_handle, x);
114 }
115 
116 PetscErrorCode XYT_free(xyt_ADT xyt_handle) {
117   PCTFS_comm_init();
118   check_handle(xyt_handle);
119   n_xyt_handles--;
120 
121   free(xyt_handle->info->nsep);
122   free(xyt_handle->info->lnsep);
123   free(xyt_handle->info->fo);
124   free(xyt_handle->info->stages);
125   free(xyt_handle->info->solve_uu);
126   free(xyt_handle->info->solve_w);
127   free(xyt_handle->info->x);
128   free(xyt_handle->info->xcol_vals);
129   free(xyt_handle->info->xcol_sz);
130   free(xyt_handle->info->xcol_indices);
131   free(xyt_handle->info->y);
132   free(xyt_handle->info->ycol_vals);
133   free(xyt_handle->info->ycol_sz);
134   free(xyt_handle->info->ycol_indices);
135   free(xyt_handle->info);
136   free(xyt_handle->mvi->local2global);
137   PCTFS_gs_free(xyt_handle->mvi->PCTFS_gs_handle);
138   free(xyt_handle->mvi);
139   free(xyt_handle);
140 
141   /* if the check fails we nuke */
142   /* if NULL pointer passed to free we nuke */
143   /* if the calls to free fail that's not my problem */
144   return (0);
145 }
146 
147 /* This function is currently not used */
148 PetscErrorCode XYT_stats(xyt_ADT xyt_handle) {
149   PetscInt    op[]  = {NON_UNIFORM, GL_MIN, GL_MAX, GL_ADD, GL_MIN, GL_MAX, GL_ADD, GL_MIN, GL_MAX, GL_ADD};
150   PetscInt    fop[] = {NON_UNIFORM, GL_MIN, GL_MAX, GL_ADD};
151   PetscInt    vals[9], work[9];
152   PetscScalar fvals[3], fwork[3];
153 
154   PetscFunctionBegin;
155   PetscCall(PCTFS_comm_init());
156   PetscCall(check_handle(xyt_handle));
157 
158   /* if factorization not done there are no stats */
159   if (!xyt_handle->info || !xyt_handle->mvi) {
160     if (!PCTFS_my_id) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "XYT_stats() :: no stats available!\n"));
161     PetscFunctionReturn(0);
162   }
163 
164   vals[0] = vals[1] = vals[2] = xyt_handle->info->nnz;
165   vals[3] = vals[4] = vals[5] = xyt_handle->mvi->n;
166   vals[6] = vals[7] = vals[8] = xyt_handle->info->msg_buf_sz;
167   PetscCall(PCTFS_giop(vals, work, PETSC_STATIC_ARRAY_LENGTH(op) - 1, op));
168 
169   fvals[0] = fvals[1] = fvals[2] = xyt_handle->info->tot_solve_time / xyt_handle->info->nsolves++;
170   PetscCall(PCTFS_grop(fvals, fwork, PETSC_STATIC_ARRAY_LENGTH(fop) - 1, fop));
171 
172   if (!PCTFS_my_id) {
173     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xyt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[0]));
174     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xyt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[1]));
175     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xyt_nnz=%g\n", PCTFS_my_id, (double)(1.0 * vals[2] / PCTFS_num_nodes)));
176     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: tot   xyt_nnz=%" PetscInt_FMT "\n", PCTFS_my_id, vals[2]));
177     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: xyt   C(2d)  =%g\n", PCTFS_my_id, (double)(vals[2] / (PetscPowReal(1.0 * vals[5], 1.5)))));
178     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: xyt   C(3d)  =%g\n", PCTFS_my_id, (double)(vals[2] / (PetscPowReal(1.0 * vals[5], 1.6667)))));
179     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xyt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[3]));
180     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xyt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[4]));
181     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xyt_n  =%g\n", PCTFS_my_id, (double)(1.0 * vals[5] / PCTFS_num_nodes)));
182     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: tot   xyt_n  =%" PetscInt_FMT "\n", PCTFS_my_id, vals[5]));
183     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xyt_buf=%" PetscInt_FMT "\n", PCTFS_my_id, vals[6]));
184     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xyt_buf=%" PetscInt_FMT "\n", PCTFS_my_id, vals[7]));
185     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xyt_buf=%g\n", PCTFS_my_id, (double)(1.0 * vals[8] / PCTFS_num_nodes)));
186     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: min   xyt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[0])));
187     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: max   xyt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[1])));
188     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%d :: avg   xyt_slv=%g\n", PCTFS_my_id, (double)PetscRealPart(fvals[2] / PCTFS_num_nodes)));
189   }
190   PetscFunctionReturn(0);
191 }
192 
193 /*
194 
195 Description: get A_local, local portion of global coarse matrix which
196 is a row dist. nxm matrix w/ n<m.
197    o my_ml holds address of ML struct associated w/A_local and coarse grid
198    o local2global holds global number of column i (i=0,...,m-1)
199    o local2global holds global number of row    i (i=0,...,n-1)
200    o mylocmatvec performs A_local . vec_local (note that gs is performed using
201    PCTFS_gs_init/gop).
202 
203 mylocmatvec = my_ml->Amat[grid_tag].matvec->external;
204 mylocmatvec (void :: void *data, double *in, double *out)
205 */
206 static PetscErrorCode do_xyt_factor(xyt_ADT xyt_handle) {
207   return xyt_generate(xyt_handle);
208 }
209 
210 static PetscErrorCode xyt_generate(xyt_ADT xyt_handle) {
211   PetscInt      i, j, k, idx;
212   PetscInt      dim, col;
213   PetscScalar  *u, *uu, *v, *z, *w, alpha, alpha_w;
214   PetscInt     *segs;
215   PetscInt      op[] = {GL_ADD, 0};
216   PetscInt      off, len;
217   PetscScalar  *x_ptr, *y_ptr;
218   PetscInt     *iptr, flag;
219   PetscInt      start = 0, end, work;
220   PetscInt      op2[] = {GL_MIN, 0};
221   PCTFS_gs_ADT  PCTFS_gs_handle;
222   PetscInt     *nsep, *lnsep, *fo;
223   PetscInt      a_n            = xyt_handle->mvi->n;
224   PetscInt      a_m            = xyt_handle->mvi->m;
225   PetscInt     *a_local2global = xyt_handle->mvi->local2global;
226   PetscInt      level;
227   PetscInt      n, m;
228   PetscInt     *xcol_sz, *xcol_indices, *stages;
229   PetscScalar **xcol_vals, *x;
230   PetscInt     *ycol_sz, *ycol_indices;
231   PetscScalar **ycol_vals, *y;
232   PetscInt      n_global;
233   PetscInt      xt_nnz = 0, xt_max_nnz = 0;
234   PetscInt      yt_nnz = 0, yt_max_nnz = 0;
235   PetscBLASInt  i1  = 1, dlen;
236   PetscScalar   dm1 = -1.0;
237 
238   n               = xyt_handle->mvi->n;
239   nsep            = xyt_handle->info->nsep;
240   lnsep           = xyt_handle->info->lnsep;
241   fo              = xyt_handle->info->fo;
242   end             = lnsep[0];
243   level           = xyt_handle->level;
244   PCTFS_gs_handle = xyt_handle->mvi->PCTFS_gs_handle;
245 
246   /* is there a null space? */
247   /* LATER add in ability to detect null space by checking alpha */
248   for (i = 0, j = 0; i <= level; i++) j += nsep[i];
249 
250   m = j - xyt_handle->ns;
251   if (m != j) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "xyt_generate() :: null space exists %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, j, xyt_handle->ns));
252 
253   PetscCall(PetscInfo(0, "xyt_generate() :: X(%" PetscInt_FMT ",%" PetscInt_FMT ")\n", n, m));
254 
255   /* get and initialize storage for x local         */
256   /* note that x local is nxm and stored by columns */
257   xcol_sz      = (PetscInt *)malloc(m * sizeof(PetscInt));
258   xcol_indices = (PetscInt *)malloc((2 * m + 1) * sizeof(PetscInt));
259   xcol_vals    = (PetscScalar **)malloc(m * sizeof(PetscScalar *));
260   for (i = j = 0; i < m; i++, j += 2) {
261     xcol_indices[j] = xcol_indices[j + 1] = xcol_sz[i] = -1;
262     xcol_vals[i]                                       = NULL;
263   }
264   xcol_indices[j] = -1;
265 
266   /* get and initialize storage for y local         */
267   /* note that y local is nxm and stored by columns */
268   ycol_sz      = (PetscInt *)malloc(m * sizeof(PetscInt));
269   ycol_indices = (PetscInt *)malloc((2 * m + 1) * sizeof(PetscInt));
270   ycol_vals    = (PetscScalar **)malloc(m * sizeof(PetscScalar *));
271   for (i = j = 0; i < m; i++, j += 2) {
272     ycol_indices[j] = ycol_indices[j + 1] = ycol_sz[i] = -1;
273     ycol_vals[i]                                       = NULL;
274   }
275   ycol_indices[j] = -1;
276 
277   /* size of separators for each sub-hc working from bottom of tree to top */
278   /* this looks like nsep[]=segments */
279   stages = (PetscInt *)malloc((level + 1) * sizeof(PetscInt));
280   segs   = (PetscInt *)malloc((level + 1) * sizeof(PetscInt));
281   PCTFS_ivec_zero(stages, level + 1);
282   PCTFS_ivec_copy(segs, nsep, level + 1);
283   for (i = 0; i < level; i++) segs[i + 1] += segs[i];
284   stages[0] = segs[0];
285 
286   /* temporary vectors  */
287   u  = (PetscScalar *)malloc(n * sizeof(PetscScalar));
288   z  = (PetscScalar *)malloc(n * sizeof(PetscScalar));
289   v  = (PetscScalar *)malloc(a_m * sizeof(PetscScalar));
290   uu = (PetscScalar *)malloc(m * sizeof(PetscScalar));
291   w  = (PetscScalar *)malloc(m * sizeof(PetscScalar));
292 
293   /* extra nnz due to replication of vertices across separators */
294   for (i = 1, j = 0; i <= level; i++) j += nsep[i];
295 
296   /* storage for sparse x values */
297   n_global   = xyt_handle->info->n_global;
298   xt_max_nnz = yt_max_nnz = (PetscInt)(2.5 * PetscPowReal(1.0 * n_global, 1.6667) + j * n / 2) / PCTFS_num_nodes;
299   x                       = (PetscScalar *)malloc(xt_max_nnz * sizeof(PetscScalar));
300   y                       = (PetscScalar *)malloc(yt_max_nnz * sizeof(PetscScalar));
301 
302   /* LATER - can embed next sep to fire in gs */
303   /* time to make the donuts - generate X factor */
304   for (dim = i = j = 0; i < m; i++) {
305     /* time to move to the next level? */
306     while (i == segs[dim]) {
307       PetscCheck(dim != level, PETSC_COMM_SELF, PETSC_ERR_PLIB, "dim about to exceed level");
308       stages[dim++] = i;
309       end += lnsep[dim];
310     }
311     stages[dim] = i;
312 
313     /* which column are we firing? */
314     /* i.e. set v_l */
315     /* use new seps and do global min across hc to determine which one to fire */
316     (start < end) ? (col = fo[start]) : (col = INT_MAX);
317     PCTFS_giop_hc(&col, &work, 1, op2, dim);
318 
319     /* shouldn't need this */
320     if (col == INT_MAX) {
321       PetscCall(PetscInfo(0, "hey ... col==INT_MAX??\n"));
322       continue;
323     }
324 
325     /* do I own it? I should */
326     PCTFS_rvec_zero(v, a_m);
327     if (col == fo[start]) {
328       start++;
329       idx = PCTFS_ivec_linear_search(col, a_local2global, a_n);
330       if (idx != -1) {
331         v[idx] = 1.0;
332         j++;
333       } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "NOT FOUND!");
334     } else {
335       idx = PCTFS_ivec_linear_search(col, a_local2global, a_m);
336       if (idx != -1) v[idx] = 1.0;
337     }
338 
339     /* perform u = A.v_l */
340     PCTFS_rvec_zero(u, n);
341     do_matvec(xyt_handle->mvi, v, u);
342 
343     /* uu =  X^T.u_l (local portion) */
344     /* technically only need to zero out first i entries */
345     /* later turn this into an XYT_solve call ? */
346     PCTFS_rvec_zero(uu, m);
347     y_ptr = y;
348     iptr  = ycol_indices;
349     for (k = 0; k < i; k++) {
350       off = *iptr++;
351       len = *iptr++;
352       PetscCall(PetscBLASIntCast(len, &dlen));
353       PetscCallBLAS("BLASdot", uu[k] = BLASdot_(&dlen, u + off, &i1, y_ptr, &i1));
354       y_ptr += len;
355     }
356 
357     /* uu = X^T.u_l (comm portion) */
358     PetscCall(PCTFS_ssgl_radd(uu, w, dim, stages));
359 
360     /* z = X.uu */
361     PCTFS_rvec_zero(z, n);
362     x_ptr = x;
363     iptr  = xcol_indices;
364     for (k = 0; k < i; k++) {
365       off = *iptr++;
366       len = *iptr++;
367       PetscCall(PetscBLASIntCast(len, &dlen));
368       PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, &uu[k], x_ptr, &i1, z + off, &i1));
369       x_ptr += len;
370     }
371 
372     /* compute v_l = v_l - z */
373     PCTFS_rvec_zero(v + a_n, a_m - a_n);
374     PetscCall(PetscBLASIntCast(n, &dlen));
375     PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, &dm1, z, &i1, v, &i1));
376 
377     /* compute u_l = A.v_l */
378     if (a_n != a_m) PCTFS_gs_gop_hc(PCTFS_gs_handle, v, "+\0", dim);
379     PCTFS_rvec_zero(u, n);
380     do_matvec(xyt_handle->mvi, v, u);
381 
382     /* compute sqrt(alpha) = sqrt(u_l^T.u_l) - local portion */
383     PetscCall(PetscBLASIntCast(n, &dlen));
384     PetscCallBLAS("BLASdot", alpha = BLASdot_(&dlen, u, &i1, u, &i1));
385     /* compute sqrt(alpha) = sqrt(u_l^T.u_l) - comm portion */
386     PCTFS_grop_hc(&alpha, &alpha_w, 1, op, dim);
387 
388     alpha = (PetscScalar)PetscSqrtReal((PetscReal)alpha);
389 
390     /* check for small alpha                             */
391     /* LATER use this to detect and determine null space */
392     PetscCheck(PetscAbsScalar(alpha) >= 1.0e-14, PETSC_COMM_SELF, PETSC_ERR_PLIB, "bad alpha! %g", (double)PetscAbsScalar(alpha));
393 
394     /* compute v_l = v_l/sqrt(alpha) */
395     PCTFS_rvec_scale(v, 1.0 / alpha, n);
396     PCTFS_rvec_scale(u, 1.0 / alpha, n);
397 
398     /* add newly generated column, v_l, to X */
399     flag = 1;
400     off = len = 0;
401     for (k = 0; k < n; k++) {
402       if (v[k] != 0.0) {
403         len = k;
404         if (flag) {
405           off  = k;
406           flag = 0;
407         }
408       }
409     }
410 
411     len -= (off - 1);
412 
413     if (len > 0) {
414       if ((xt_nnz + len) > xt_max_nnz) {
415         PetscCall(PetscInfo(0, "increasing space for X by 2x!\n"));
416         xt_max_nnz *= 2;
417         x_ptr = (PetscScalar *)malloc(xt_max_nnz * sizeof(PetscScalar));
418         PCTFS_rvec_copy(x_ptr, x, xt_nnz);
419         free(x);
420         x = x_ptr;
421         x_ptr += xt_nnz;
422       }
423       xt_nnz += len;
424       PCTFS_rvec_copy(x_ptr, v + off, len);
425 
426       xcol_indices[2 * i] = off;
427       xcol_sz[i] = xcol_indices[2 * i + 1] = len;
428       xcol_vals[i]                         = x_ptr;
429     } else {
430       xcol_indices[2 * i] = 0;
431       xcol_sz[i] = xcol_indices[2 * i + 1] = 0;
432       xcol_vals[i]                         = x_ptr;
433     }
434 
435     /* add newly generated column, u_l, to Y */
436     flag = 1;
437     off = len = 0;
438     for (k = 0; k < n; k++) {
439       if (u[k] != 0.0) {
440         len = k;
441         if (flag) {
442           off  = k;
443           flag = 0;
444         }
445       }
446     }
447 
448     len -= (off - 1);
449 
450     if (len > 0) {
451       if ((yt_nnz + len) > yt_max_nnz) {
452         PetscCall(PetscInfo(0, "increasing space for Y by 2x!\n"));
453         yt_max_nnz *= 2;
454         y_ptr = (PetscScalar *)malloc(yt_max_nnz * sizeof(PetscScalar));
455         PCTFS_rvec_copy(y_ptr, y, yt_nnz);
456         free(y);
457         y = y_ptr;
458         y_ptr += yt_nnz;
459       }
460       yt_nnz += len;
461       PCTFS_rvec_copy(y_ptr, u + off, len);
462 
463       ycol_indices[2 * i] = off;
464       ycol_sz[i] = ycol_indices[2 * i + 1] = len;
465       ycol_vals[i]                         = y_ptr;
466     } else {
467       ycol_indices[2 * i] = 0;
468       ycol_sz[i] = ycol_indices[2 * i + 1] = 0;
469       ycol_vals[i]                         = y_ptr;
470     }
471   }
472 
473   /* close off stages for execution phase */
474   while (dim != level) {
475     stages[dim++] = i;
476     PetscCall(PetscInfo(0, "disconnected!!! dim(%" PetscInt_FMT ")!=level(%" PetscInt_FMT ")\n", dim, level));
477   }
478   stages[dim] = i;
479 
480   xyt_handle->info->n            = xyt_handle->mvi->n;
481   xyt_handle->info->m            = m;
482   xyt_handle->info->nnz          = xt_nnz + yt_nnz;
483   xyt_handle->info->max_nnz      = xt_max_nnz + yt_max_nnz;
484   xyt_handle->info->msg_buf_sz   = stages[level] - stages[0];
485   xyt_handle->info->solve_uu     = (PetscScalar *)malloc(m * sizeof(PetscScalar));
486   xyt_handle->info->solve_w      = (PetscScalar *)malloc(m * sizeof(PetscScalar));
487   xyt_handle->info->x            = x;
488   xyt_handle->info->xcol_vals    = xcol_vals;
489   xyt_handle->info->xcol_sz      = xcol_sz;
490   xyt_handle->info->xcol_indices = xcol_indices;
491   xyt_handle->info->stages       = stages;
492   xyt_handle->info->y            = y;
493   xyt_handle->info->ycol_vals    = ycol_vals;
494   xyt_handle->info->ycol_sz      = ycol_sz;
495   xyt_handle->info->ycol_indices = ycol_indices;
496 
497   free(segs);
498   free(u);
499   free(v);
500   free(uu);
501   free(z);
502   free(w);
503 
504   return (0);
505 }
506 
507 static PetscErrorCode do_xyt_solve(xyt_ADT xyt_handle, PetscScalar *uc) {
508   PetscInt     off, len, *iptr;
509   PetscInt     level        = xyt_handle->level;
510   PetscInt     n            = xyt_handle->info->n;
511   PetscInt     m            = xyt_handle->info->m;
512   PetscInt    *stages       = xyt_handle->info->stages;
513   PetscInt    *xcol_indices = xyt_handle->info->xcol_indices;
514   PetscInt    *ycol_indices = xyt_handle->info->ycol_indices;
515   PetscScalar *x_ptr, *y_ptr, *uu_ptr;
516   PetscScalar *solve_uu = xyt_handle->info->solve_uu;
517   PetscScalar *solve_w  = xyt_handle->info->solve_w;
518   PetscScalar *x        = xyt_handle->info->x;
519   PetscScalar *y        = xyt_handle->info->y;
520   PetscBLASInt i1       = 1, dlen;
521 
522   PetscFunctionBegin;
523   uu_ptr = solve_uu;
524   PCTFS_rvec_zero(uu_ptr, m);
525 
526   /* x  = X.Y^T.b */
527   /* uu = Y^T.b */
528   for (y_ptr = y, iptr = ycol_indices; *iptr != -1; y_ptr += len) {
529     off = *iptr++;
530     len = *iptr++;
531     PetscCall(PetscBLASIntCast(len, &dlen));
532     PetscCallBLAS("BLASdot", *uu_ptr++ = BLASdot_(&dlen, uc + off, &i1, y_ptr, &i1));
533   }
534 
535   /* comunication of beta */
536   uu_ptr = solve_uu;
537   if (level) PetscCall(PCTFS_ssgl_radd(uu_ptr, solve_w, level, stages));
538   PCTFS_rvec_zero(uc, n);
539 
540   /* x = X.uu */
541   for (x_ptr = x, iptr = xcol_indices; *iptr != -1; x_ptr += len) {
542     off = *iptr++;
543     len = *iptr++;
544     PetscCall(PetscBLASIntCast(len, &dlen));
545     PetscCallBLAS("BLASaxpy", BLASaxpy_(&dlen, uu_ptr++, x_ptr, &i1, uc + off, &i1));
546   }
547   PetscFunctionReturn(0);
548 }
549 
550 static PetscErrorCode check_handle(xyt_ADT xyt_handle) {
551   PetscInt vals[2], work[2], op[] = {NON_UNIFORM, GL_MIN, GL_MAX};
552 
553   PetscFunctionBegin;
554   PetscCheck(xyt_handle, PETSC_COMM_SELF, PETSC_ERR_PLIB, "check_handle() :: bad handle :: NULL %p", xyt_handle);
555 
556   vals[0] = vals[1] = xyt_handle->id;
557   PCTFS_giop(vals, work, PETSC_STATIC_ARRAY_LENGTH(op) - 1, op);
558   PetscCheck(!(vals[0] != vals[1]) && !(xyt_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], xyt_handle->id);
559   PetscFunctionReturn(0);
560 }
561 
562 static PetscErrorCode det_separators(xyt_ADT xyt_handle) {
563   PetscInt     i, ct, id;
564   PetscInt     mask, edge, *iptr;
565   PetscInt    *dir, *used;
566   PetscInt     sum[4], w[4];
567   PetscScalar  rsum[4], rw[4];
568   PetscInt     op[] = {GL_ADD, 0};
569   PetscScalar *lhs, *rhs;
570   PetscInt    *nsep, *lnsep, *fo, nfo = 0;
571   PCTFS_gs_ADT PCTFS_gs_handle = xyt_handle->mvi->PCTFS_gs_handle;
572   PetscInt    *local2global    = xyt_handle->mvi->local2global;
573   PetscInt     n               = xyt_handle->mvi->n;
574   PetscInt     m               = xyt_handle->mvi->m;
575   PetscInt     level           = xyt_handle->level;
576   PetscInt     shared          = 0;
577 
578   PetscFunctionBegin;
579   dir   = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
580   nsep  = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
581   lnsep = (PetscInt *)malloc(sizeof(PetscInt) * (level + 1));
582   fo    = (PetscInt *)malloc(sizeof(PetscInt) * (n + 1));
583   used  = (PetscInt *)malloc(sizeof(PetscInt) * n);
584 
585   PCTFS_ivec_zero(dir, level + 1);
586   PCTFS_ivec_zero(nsep, level + 1);
587   PCTFS_ivec_zero(lnsep, level + 1);
588   PCTFS_ivec_set(fo, -1, n + 1);
589   PCTFS_ivec_zero(used, n);
590 
591   lhs = (PetscScalar *)malloc(sizeof(PetscScalar) * m);
592   rhs = (PetscScalar *)malloc(sizeof(PetscScalar) * m);
593 
594   /* determine the # of unique dof */
595   PCTFS_rvec_zero(lhs, m);
596   PCTFS_rvec_set(lhs, 1.0, n);
597   PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", level);
598   PetscCall(PetscInfo(0, "done first PCTFS_gs_gop_hc\n"));
599   PCTFS_rvec_zero(rsum, 2);
600   for (i = 0; i < n; i++) {
601     if (lhs[i] != 0.0) {
602       rsum[0] += 1.0 / lhs[i];
603       rsum[1] += lhs[i];
604     }
605     if (lhs[i] != 1.0) shared = 1;
606   }
607 
608   PCTFS_grop_hc(rsum, rw, 2, op, level);
609   rsum[0] += 0.1;
610   rsum[1] += 0.1;
611 
612   xyt_handle->info->n_global = xyt_handle->info->m_global = (PetscInt)rsum[0];
613   xyt_handle->mvi->n_global = xyt_handle->mvi->m_global = (PetscInt)rsum[0];
614 
615   /* determine separator sets top down */
616   if (shared) {
617     /* solution is to do as in the symmetric shared case but then */
618     /* pick the sub-hc with the most free dofs and do a mat-vec   */
619     /* and pick up the responses on the other sub-hc from the     */
620     /* initial separator set obtained from the symm. shared case  */
621     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "shared dof separator determination not ready ... see hmt!!!");
622     /* [dead code deleted since it is unlikely to be completed] */
623   } else {
624     for (iptr = fo + n, id = PCTFS_my_id, mask = PCTFS_num_nodes >> 1, edge = level; edge > 0; edge--, mask >>= 1) {
625       /* set rsh of hc, fire, and collect lhs responses */
626       (id < mask) ? PCTFS_rvec_zero(lhs, m) : PCTFS_rvec_set(lhs, 1.0, m);
627       PCTFS_gs_gop_hc(PCTFS_gs_handle, lhs, "+\0", edge);
628 
629       /* set lsh of hc, fire, and collect rhs responses */
630       (id < mask) ? PCTFS_rvec_set(rhs, 1.0, m) : PCTFS_rvec_zero(rhs, m);
631       PCTFS_gs_gop_hc(PCTFS_gs_handle, rhs, "+\0", edge);
632 
633       /* count number of dofs I own that have signal and not in sep set */
634       for (PCTFS_ivec_zero(sum, 4), ct = i = 0; i < n; i++) {
635         if (!used[i]) {
636           /* number of unmarked dofs on node */
637           ct++;
638           /* number of dofs to be marked on lhs hc */
639           if ((id < mask) && (lhs[i] != 0.0)) sum[0]++;
640           /* number of dofs to be marked on rhs hc */
641           if ((id >= mask) && (rhs[i] != 0.0)) sum[1]++;
642         }
643       }
644 
645       /* for the non-symmetric case we need separators of width 2 */
646       /* so take both sides */
647       (id < mask) ? (sum[2] = ct) : (sum[3] = ct);
648       PCTFS_giop_hc(sum, w, 4, op, edge);
649 
650       ct = 0;
651       if (id < mask) {
652         /* mark dofs I own that have signal and not in sep set */
653         for (i = 0; i < n; i++) {
654           if ((!used[i]) && (lhs[i] != 0.0)) {
655             ct++;
656             nfo++;
657             *--iptr = local2global[i];
658             used[i] = edge;
659           }
660         }
661         /* LSH hc summation of ct should be sum[0] */
662       } else {
663         /* mark dofs I own that have signal and not in sep set */
664         for (i = 0; i < n; i++) {
665           if ((!used[i]) && (rhs[i] != 0.0)) {
666             ct++;
667             nfo++;
668             *--iptr = local2global[i];
669             used[i] = edge;
670           }
671         }
672         /* RSH hc summation of ct should be sum[1] */
673       }
674 
675       if (ct > 1) PCTFS_ivec_sort(iptr, ct);
676       lnsep[edge] = ct;
677       nsep[edge]  = sum[0] + sum[1];
678       dir[edge]   = BOTH;
679 
680       /* LATER or we can recur on these to order seps at this level */
681       /* do we need full set of separators for this?                */
682 
683       /* fold rhs hc into lower */
684       if (id >= mask) id -= mask;
685     }
686   }
687 
688   /* level 0 is on processor case - so mark the remainder */
689   for (ct = i = 0; i < n; i++) {
690     if (!used[i]) {
691       ct++;
692       nfo++;
693       *--iptr = local2global[i];
694       used[i] = edge;
695     }
696   }
697   if (ct > 1) PCTFS_ivec_sort(iptr, ct);
698   lnsep[edge] = ct;
699   nsep[edge]  = ct;
700   dir[edge]   = BOTH;
701 
702   xyt_handle->info->nsep  = nsep;
703   xyt_handle->info->lnsep = lnsep;
704   xyt_handle->info->fo    = fo;
705   xyt_handle->info->nfo   = nfo;
706 
707   free(dir);
708   free(lhs);
709   free(rhs);
710   free(used);
711   PetscFunctionReturn(0);
712 }
713 
714 static mv_info *set_mvi(PetscInt *local2global, PetscInt n, PetscInt m, PetscErrorCode (*matvec)(mv_info *, PetscScalar *, PetscScalar *), void *grid_data) {
715   mv_info *mvi;
716 
717   mvi               = (mv_info *)malloc(sizeof(mv_info));
718   mvi->n            = n;
719   mvi->m            = m;
720   mvi->n_global     = -1;
721   mvi->m_global     = -1;
722   mvi->local2global = (PetscInt *)malloc((m + 1) * sizeof(PetscInt));
723 
724   PCTFS_ivec_copy(mvi->local2global, local2global, m);
725   mvi->local2global[m] = INT_MAX;
726   mvi->matvec          = matvec;
727   mvi->grid_data       = grid_data;
728 
729   /* set xyt communication handle to perform restricted matvec */
730   mvi->PCTFS_gs_handle = PCTFS_gs_init(local2global, m, PCTFS_num_nodes);
731 
732   return (mvi);
733 }
734 
735 static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u) {
736   PetscFunctionBegin;
737   A->matvec((mv_info *)A->grid_data, v, u);
738   PetscFunctionReturn(0);
739 }
740