Actual source code: sbaijfact.c
petsc-3.6.4 2016-04-12
2: #include <../src/mat/impls/baij/seq/baij.h>
3: #include <../src/mat/impls/sbaij/seq/sbaij.h>
4: #include <petsc/private/kernels/blockinvert.h>
5: #include <petscis.h>
7: /*
8: input:
9: F -- numeric factor
10: output:
11: nneg, nzero, npos: matrix inertia
12: */
16: PetscErrorCode MatGetInertia_SeqSBAIJ(Mat F,PetscInt *nneig,PetscInt *nzero,PetscInt *npos)
17: {
18: Mat_SeqSBAIJ *fact_ptr = (Mat_SeqSBAIJ*)F->data;
19: MatScalar *dd = fact_ptr->a;
20: PetscInt mbs =fact_ptr->mbs,bs=F->rmap->bs,i,nneig_tmp,npos_tmp,*fi = fact_ptr->diag;
23: if (bs != 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for bs: %D >1 yet",bs);
24: nneig_tmp = 0; npos_tmp = 0;
25: for (i=0; i<mbs; i++) {
26: if (PetscRealPart(dd[*fi]) > 0.0) npos_tmp++;
27: else if (PetscRealPart(dd[*fi]) < 0.0) nneig_tmp++;
28: fi++;
29: }
30: if (nneig) *nneig = nneig_tmp;
31: if (npos) *npos = npos_tmp;
32: if (nzero) *nzero = mbs - nneig_tmp - npos_tmp;
33: return(0);
34: }
36: /*
37: Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP.
38: Use Modified Sparse Row (MSR) storage for u and ju. See page 85, "Iterative Methods ..." by Saad.
39: */
42: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(Mat F,Mat A,IS perm,const MatFactorInfo *info)
43: {
44: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
46: const PetscInt *rip,*ai,*aj;
47: PetscInt i,mbs = a->mbs,*jutmp,bs = A->rmap->bs,bs2=a->bs2;
48: PetscInt m,reallocs = 0,prow;
49: PetscInt *jl,*q,jmin,jmax,juidx,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
50: PetscReal f = info->fill;
51: PetscBool perm_identity;
54: /* check whether perm is the identity mapping */
55: ISIdentity(perm,&perm_identity);
56: ISGetIndices(perm,&rip);
58: if (perm_identity) { /* without permutation */
59: a->permute = PETSC_FALSE;
61: ai = a->i; aj = a->j;
62: } else { /* non-trivial permutation */
63: a->permute = PETSC_TRUE;
65: MatReorderingSeqSBAIJ(A,perm);
67: ai = a->inew; aj = a->jnew;
68: }
70: /* initialization */
71: PetscMalloc1(mbs+1,&iu);
72: umax = (PetscInt)(f*ai[mbs] + 1); umax += mbs + 1;
73: PetscMalloc1(umax,&ju);
74: iu[0] = mbs+1;
75: juidx = mbs + 1; /* index for ju */
76: /* jl linked list for pivot row -- linked list for col index */
77: PetscMalloc2(mbs,&jl,mbs,&q);
78: for (i=0; i<mbs; i++) {
79: jl[i] = mbs;
80: q[i] = 0;
81: }
83: /* for each row k */
84: for (k=0; k<mbs; k++) {
85: for (i=0; i<mbs; i++) q[i] = 0; /* to be removed! */
86: nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
87: q[k] = mbs;
88: /* initialize nonzero structure of k-th row to row rip[k] of A */
89: jmin = ai[rip[k]] +1; /* exclude diag[k] */
90: jmax = ai[rip[k]+1];
91: for (j=jmin; j<jmax; j++) {
92: vj = rip[aj[j]]; /* col. value */
93: if (vj > k) {
94: qm = k;
95: do {
96: m = qm; qm = q[m];
97: } while (qm < vj);
98: if (qm == vj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Duplicate entry in A\n");
99: nzk++;
100: q[m] = vj;
101: q[vj] = qm;
102: } /* if (vj > k) */
103: } /* for (j=jmin; j<jmax; j++) */
105: /* modify nonzero structure of k-th row by computing fill-in
106: for each row i to be merged in */
107: prow = k;
108: prow = jl[prow]; /* next pivot row (== mbs for symbolic factorization) */
110: while (prow < k) {
111: /* merge row prow into k-th row */
112: jmin = iu[prow] + 1; jmax = iu[prow+1];
113: qm = k;
114: for (j=jmin; j<jmax; j++) {
115: vj = ju[j];
116: do {
117: m = qm; qm = q[m];
118: } while (qm < vj);
119: if (qm != vj) {
120: nzk++; q[m] = vj; q[vj] = qm; qm = vj;
121: }
122: }
123: prow = jl[prow]; /* next pivot row */
124: }
126: /* add k to row list for first nonzero element in k-th row */
127: if (nzk > 0) {
128: i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
129: jl[k] = jl[i]; jl[i] = k;
130: }
131: iu[k+1] = iu[k] + nzk;
133: /* allocate more space to ju if needed */
134: if (iu[k+1] > umax) {
135: /* estimate how much additional space we will need */
136: /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
137: /* just double the memory each time */
138: maxadd = umax;
139: if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
140: umax += maxadd;
142: /* allocate a longer ju */
143: PetscMalloc1(umax,&jutmp);
144: PetscMemcpy(jutmp,ju,iu[k]*sizeof(PetscInt));
145: PetscFree(ju);
146: ju = jutmp;
147: reallocs++; /* count how many times we realloc */
148: }
150: /* save nonzero structure of k-th row in ju */
151: i=k;
152: while (nzk--) {
153: i = q[i];
154: ju[juidx++] = i;
155: }
156: }
158: #if defined(PETSC_USE_INFO)
159: if (ai[mbs] != 0) {
160: PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
161: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
162: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
163: PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
164: PetscInfo(A,"for best performance.\n");
165: } else {
166: PetscInfo(A,"Empty matrix.\n");
167: }
168: #endif
170: ISRestoreIndices(perm,&rip);
171: PetscFree2(jl,q);
173: /* put together the new matrix */
174: MatSeqSBAIJSetPreallocation_SeqSBAIJ(F,bs,MAT_SKIP_ALLOCATION,NULL);
176: /* PetscLogObjectParent((PetscObject)B,(PetscObject)iperm); */
177: b = (Mat_SeqSBAIJ*)(F)->data;
178: b->singlemalloc = PETSC_FALSE;
179: b->free_a = PETSC_TRUE;
180: b->free_ij = PETSC_TRUE;
182: PetscMalloc1((iu[mbs]+1)*bs2,&b->a);
183: b->j = ju;
184: b->i = iu;
185: b->diag = 0;
186: b->ilen = 0;
187: b->imax = 0;
188: b->row = perm;
190: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
192: PetscObjectReference((PetscObject)perm);
194: b->icol = perm;
195: PetscObjectReference((PetscObject)perm);
196: PetscMalloc1(bs*mbs+bs,&b->solve_work);
197: /* In b structure: Free imax, ilen, old a, old j.
198: Allocate idnew, solve_work, new a, new j */
199: PetscLogObjectMemory((PetscObject)F,(iu[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
200: b->maxnz = b->nz = iu[mbs];
202: (F)->info.factor_mallocs = reallocs;
203: (F)->info.fill_ratio_given = f;
204: if (ai[mbs] != 0) {
205: (F)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
206: } else {
207: (F)->info.fill_ratio_needed = 0.0;
208: }
209: MatSeqSBAIJSetNumericFactorization_inplace(F,perm_identity);
210: return(0);
211: }
212: /*
213: Symbolic U^T*D*U factorization for SBAIJ format.
214: See MatICCFactorSymbolic_SeqAIJ() for description of its data structure.
215: */
216: #include <petscbt.h>
217: #include <../src/mat/utils/freespace.h>
220: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
221: {
222: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;
223: Mat_SeqSBAIJ *b;
224: PetscErrorCode ierr;
225: PetscBool perm_identity,missing;
226: PetscReal fill = info->fill;
227: const PetscInt *rip,*ai=a->i,*aj=a->j;
228: PetscInt i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow;
229: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
230: PetscInt nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
231: PetscFreeSpaceList free_space=NULL,current_space=NULL;
232: PetscBT lnkbt;
235: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
236: MatMissingDiagonal(A,&missing,&i);
237: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
238: if (bs > 1) {
239: MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(fact,A,perm,info);
240: return(0);
241: }
243: /* check whether perm is the identity mapping */
244: ISIdentity(perm,&perm_identity);
245: if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported for sbaij matrix. Use aij format");
246: a->permute = PETSC_FALSE;
247: ISGetIndices(perm,&rip);
249: /* initialization */
250: PetscMalloc1(mbs+1,&ui);
251: PetscMalloc1(mbs+1,&udiag);
252: ui[0] = 0;
254: /* jl: linked list for storing indices of the pivot rows
255: il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
256: PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
257: for (i=0; i<mbs; i++) {
258: jl[i] = mbs; il[i] = 0;
259: }
261: /* create and initialize a linked list for storing column indices of the active row k */
262: nlnk = mbs + 1;
263: PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);
265: /* initial FreeSpace size is fill*(ai[mbs]+1) */
266: PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+1)),&free_space);
267: current_space = free_space;
269: for (k=0; k<mbs; k++) { /* for each active row k */
270: /* initialize lnk by the column indices of row rip[k] of A */
271: nzk = 0;
272: ncols = ai[k+1] - ai[k];
273: if (!ncols) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row %D in matrix ",k);
274: for (j=0; j<ncols; j++) {
275: i = *(aj + ai[k] + j);
276: cols[j] = i;
277: }
278: PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
279: nzk += nlnk;
281: /* update lnk by computing fill-in for each pivot row to be merged in */
282: prow = jl[k]; /* 1st pivot row */
284: while (prow < k) {
285: nextprow = jl[prow];
286: /* merge prow into k-th row */
287: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
288: jmax = ui[prow+1];
289: ncols = jmax-jmin;
290: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
291: PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
292: nzk += nlnk;
294: /* update il and jl for prow */
295: if (jmin < jmax) {
296: il[prow] = jmin;
297: j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
298: }
299: prow = nextprow;
300: }
302: /* if free space is not available, make more free space */
303: if (current_space->local_remaining<nzk) {
304: i = mbs - k + 1; /* num of unfactored rows */
305: i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */
306: PetscFreeSpaceGet(i,¤t_space);
307: reallocs++;
308: }
310: /* copy data into free space, then initialize lnk */
311: PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);
313: /* add the k-th row into il and jl */
314: if (nzk > 1) {
315: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
316: jl[k] = jl[i]; jl[i] = k;
317: il[k] = ui[k] + 1;
318: }
319: ui_ptr[k] = current_space->array;
321: current_space->array += nzk;
322: current_space->local_used += nzk;
323: current_space->local_remaining -= nzk;
325: ui[k+1] = ui[k] + nzk;
326: }
328: ISRestoreIndices(perm,&rip);
329: PetscFree4(ui_ptr,il,jl,cols);
331: /* destroy list of free space and other temporary array(s) */
332: PetscMalloc1(ui[mbs]+1,&uj);
333: PetscFreeSpaceContiguous_Cholesky(&free_space,uj,mbs,ui,udiag); /* store matrix factor */
334: PetscLLDestroy(lnk,lnkbt);
336: /* put together the new matrix in MATSEQSBAIJ format */
337: MatSeqSBAIJSetPreallocation_SeqSBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);
339: b = (Mat_SeqSBAIJ*)fact->data;
340: b->singlemalloc = PETSC_FALSE;
341: b->free_a = PETSC_TRUE;
342: b->free_ij = PETSC_TRUE;
344: PetscMalloc1(ui[mbs]+1,&b->a);
346: b->j = uj;
347: b->i = ui;
348: b->diag = udiag;
349: b->free_diag = PETSC_TRUE;
350: b->ilen = 0;
351: b->imax = 0;
352: b->row = perm;
353: b->icol = perm;
355: PetscObjectReference((PetscObject)perm);
356: PetscObjectReference((PetscObject)perm);
358: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
360: PetscMalloc1(mbs+1,&b->solve_work);
361: PetscLogObjectMemory((PetscObject)fact,ui[mbs]*(sizeof(PetscInt)+sizeof(MatScalar)));
363: b->maxnz = b->nz = ui[mbs];
365: fact->info.factor_mallocs = reallocs;
366: fact->info.fill_ratio_given = fill;
367: if (ai[mbs] != 0) {
368: fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
369: } else {
370: fact->info.fill_ratio_needed = 0.0;
371: }
372: #if defined(PETSC_USE_INFO)
373: if (ai[mbs] != 0) {
374: PetscReal af = fact->info.fill_ratio_needed;
375: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
376: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
377: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
378: } else {
379: PetscInfo(A,"Empty matrix.\n");
380: }
381: #endif
382: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering;
383: return(0);
384: }
388: PetscErrorCode MatCholeskyFactorSymbolic_SeqSBAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
389: {
390: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;
391: Mat_SeqSBAIJ *b;
392: PetscErrorCode ierr;
393: PetscBool perm_identity,missing;
394: PetscReal fill = info->fill;
395: const PetscInt *rip,*ai,*aj;
396: PetscInt i,mbs=a->mbs,bs=A->rmap->bs,reallocs=0,prow,d;
397: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
398: PetscInt nlnk,*lnk,ncols,*cols,*uj,**ui_ptr,*uj_ptr;
399: PetscFreeSpaceList free_space=NULL,current_space=NULL;
400: PetscBT lnkbt;
403: MatMissingDiagonal(A,&missing,&d);
404: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
406: /*
407: This code originally uses Modified Sparse Row (MSR) storage
408: (see page 85, "Iterative Methods ..." by Saad) for the output matrix B - bad choise!
409: Then it is rewritten so the factor B takes seqsbaij format. However the associated
410: MatCholeskyFactorNumeric_() have not been modified for the cases of bs>1 or !perm_identity,
411: thus the original code in MSR format is still used for these cases.
412: The code below should replace MatCholeskyFactorSymbolic_SeqSBAIJ_MSR() whenever
413: MatCholeskyFactorNumeric_() is modified for using sbaij symbolic factor.
414: */
415: if (bs > 1) {
416: MatCholeskyFactorSymbolic_SeqSBAIJ_MSR(fact,A,perm,info);
417: return(0);
418: }
420: /* check whether perm is the identity mapping */
421: ISIdentity(perm,&perm_identity);
423: if (perm_identity) {
424: a->permute = PETSC_FALSE;
426: ai = a->i; aj = a->j;
427: } else {
428: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported for sbaij matrix. Use aij format");
429: #if 0
430: /* There are bugs for reordeing. Needs further work.
431: MatReordering for sbaij cannot be efficient. User should use aij formt! */
432: a->permute = PETSC_TRUE;
434: MatReorderingSeqSBAIJ(A,perm);
435: ai = a->inew; aj = a->jnew;
436: #endif
437: }
438: ISGetIndices(perm,&rip);
440: /* initialization */
441: PetscMalloc1(mbs+1,&ui);
442: ui[0] = 0;
444: /* jl: linked list for storing indices of the pivot rows
445: il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
446: PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
447: for (i=0; i<mbs; i++) {
448: jl[i] = mbs; il[i] = 0;
449: }
451: /* create and initialize a linked list for storing column indices of the active row k */
452: nlnk = mbs + 1;
453: PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);
455: /* initial FreeSpace size is fill*(ai[mbs]+1) */
456: PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+1)),&free_space);
457: current_space = free_space;
459: for (k=0; k<mbs; k++) { /* for each active row k */
460: /* initialize lnk by the column indices of row rip[k] of A */
461: nzk = 0;
462: ncols = ai[rip[k]+1] - ai[rip[k]];
463: for (j=0; j<ncols; j++) {
464: i = *(aj + ai[rip[k]] + j);
465: cols[j] = rip[i];
466: }
467: PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
468: nzk += nlnk;
470: /* update lnk by computing fill-in for each pivot row to be merged in */
471: prow = jl[k]; /* 1st pivot row */
473: while (prow < k) {
474: nextprow = jl[prow];
475: /* merge prow into k-th row */
476: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
477: jmax = ui[prow+1];
478: ncols = jmax-jmin;
479: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
480: PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
481: nzk += nlnk;
483: /* update il and jl for prow */
484: if (jmin < jmax) {
485: il[prow] = jmin;
487: j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
488: }
489: prow = nextprow;
490: }
492: /* if free space is not available, make more free space */
493: if (current_space->local_remaining<nzk) {
494: i = mbs - k + 1; /* num of unfactored rows */
495: i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
496: PetscFreeSpaceGet(i,¤t_space);
497: reallocs++;
498: }
500: /* copy data into free space, then initialize lnk */
501: PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);
503: /* add the k-th row into il and jl */
504: if (nzk-1 > 0) {
505: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
506: jl[k] = jl[i]; jl[i] = k;
507: il[k] = ui[k] + 1;
508: }
509: ui_ptr[k] = current_space->array;
511: current_space->array += nzk;
512: current_space->local_used += nzk;
513: current_space->local_remaining -= nzk;
515: ui[k+1] = ui[k] + nzk;
516: }
518: ISRestoreIndices(perm,&rip);
519: PetscFree4(ui_ptr,il,jl,cols);
521: /* destroy list of free space and other temporary array(s) */
522: PetscMalloc1(ui[mbs]+1,&uj);
523: PetscFreeSpaceContiguous(&free_space,uj);
524: PetscLLDestroy(lnk,lnkbt);
526: /* put together the new matrix in MATSEQSBAIJ format */
527: MatSeqSBAIJSetPreallocation_SeqSBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);
529: b = (Mat_SeqSBAIJ*)fact->data;
530: b->singlemalloc = PETSC_FALSE;
531: b->free_a = PETSC_TRUE;
532: b->free_ij = PETSC_TRUE;
534: PetscMalloc1(ui[mbs]+1,&b->a);
536: b->j = uj;
537: b->i = ui;
538: b->diag = 0;
539: b->ilen = 0;
540: b->imax = 0;
541: b->row = perm;
543: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
545: PetscObjectReference((PetscObject)perm);
546: b->icol = perm;
547: PetscObjectReference((PetscObject)perm);
548: PetscMalloc1(mbs+1,&b->solve_work);
549: PetscLogObjectMemory((PetscObject)fact,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
550: b->maxnz = b->nz = ui[mbs];
552: fact->info.factor_mallocs = reallocs;
553: fact->info.fill_ratio_given = fill;
554: if (ai[mbs] != 0) {
555: fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
556: } else {
557: fact->info.fill_ratio_needed = 0.0;
558: }
559: #if defined(PETSC_USE_INFO)
560: if (ai[mbs] != 0) {
561: PetscReal af = fact->info.fill_ratio_needed;
562: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
563: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
564: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
565: } else {
566: PetscInfo(A,"Empty matrix.\n");
567: }
568: #endif
569: MatSeqSBAIJSetNumericFactorization_inplace(fact,perm_identity);
570: return(0);
571: }
575: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
576: {
577: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
578: IS perm = b->row;
580: const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
581: PetscInt i,j;
582: PetscInt *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
583: PetscInt bs =A->rmap->bs,bs2 = a->bs2,bslog = 0;
584: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
585: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
586: MatScalar *work;
587: PetscInt *pivots;
590: /* initialization */
591: PetscCalloc1(bs2*mbs,&rtmp);
592: PetscMalloc2(mbs,&il,mbs,&jl);
593: for (i=0; i<mbs; i++) {
594: jl[i] = mbs; il[0] = 0;
595: }
596: PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
597: PetscMalloc1(bs,&pivots);
599: ISGetIndices(perm,&perm_ptr);
601: /* check permutation */
602: if (!a->permute) {
603: ai = a->i; aj = a->j; aa = a->a;
604: } else {
605: ai = a->inew; aj = a->jnew;
606: PetscMalloc1(bs2*ai[mbs],&aa);
607: PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));
608: PetscMalloc1(ai[mbs],&a2anew);
609: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
611: /* flops in while loop */
612: bslog = 2*bs*bs2;
614: for (i=0; i<mbs; i++) {
615: jmin = ai[i]; jmax = ai[i+1];
616: for (j=jmin; j<jmax; j++) {
617: while (a2anew[j] != j) {
618: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
619: for (k1=0; k1<bs2; k1++) {
620: dk[k1] = aa[k*bs2+k1];
621: aa[k*bs2+k1] = aa[j*bs2+k1];
622: aa[j*bs2+k1] = dk[k1];
623: }
624: }
625: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
626: if (i > aj[j]) {
627: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
628: ap = aa + j*bs2; /* ptr to the beginning of j-th block of aa */
629: for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
630: for (k=0; k<bs; k++) { /* j-th block of aa <- dk^T */
631: for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1];
632: }
633: }
634: }
635: }
636: PetscFree(a2anew);
637: }
639: /* for each row k */
640: for (k = 0; k<mbs; k++) {
642: /*initialize k-th row with elements nonzero in row perm(k) of A */
643: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
645: ap = aa + jmin*bs2;
646: for (j = jmin; j < jmax; j++) {
647: vj = perm_ptr[aj[j]]; /* block col. index */
648: rtmp_ptr = rtmp + vj*bs2;
649: for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
650: }
652: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
653: PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
654: i = jl[k]; /* first row to be added to k_th row */
656: while (i < k) {
657: nexti = jl[i]; /* next row to be added to k_th row */
659: /* compute multiplier */
660: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
662: /* uik = -inv(Di)*U_bar(i,k) */
663: diag = ba + i*bs2;
664: u = ba + ili*bs2;
665: PetscMemzero(uik,bs2*sizeof(MatScalar));
666: PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);
668: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
669: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
670: PetscLogFlops(bslog*2.0);
672: /* update -U(i,k) */
673: PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));
675: /* add multiple of row i to k-th row ... */
676: jmin = ili + 1; jmax = bi[i+1];
677: if (jmin < jmax) {
678: for (j=jmin; j<jmax; j++) {
679: /* rtmp += -U(i,k)^T * U_bar(i,j) */
680: rtmp_ptr = rtmp + bj[j]*bs2;
681: u = ba + j*bs2;
682: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
683: }
684: PetscLogFlops(bslog*(jmax-jmin));
686: /* ... add i to row list for next nonzero entry */
687: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
688: j = bj[jmin];
689: jl[i] = jl[j]; jl[j] = i; /* update jl */
690: }
691: i = nexti;
692: }
694: /* save nonzero entries in k-th row of U ... */
696: /* invert diagonal block */
697: diag = ba+k*bs2;
698: PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
699: PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);
701: jmin = bi[k]; jmax = bi[k+1];
702: if (jmin < jmax) {
703: for (j=jmin; j<jmax; j++) {
704: vj = bj[j]; /* block col. index of U */
705: u = ba + j*bs2;
706: rtmp_ptr = rtmp + vj*bs2;
707: for (k1=0; k1<bs2; k1++) {
708: *u++ = *rtmp_ptr;
709: *rtmp_ptr++ = 0.0;
710: }
711: }
713: /* ... add k to row list for first nonzero entry in k-th row */
714: il[k] = jmin;
715: i = bj[jmin];
716: jl[k] = jl[i]; jl[i] = k;
717: }
718: }
720: PetscFree(rtmp);
721: PetscFree2(il,jl);
722: PetscFree3(dk,uik,work);
723: PetscFree(pivots);
724: if (a->permute) {
725: PetscFree(aa);
726: }
728: ISRestoreIndices(perm,&perm_ptr);
730: C->ops->solve = MatSolve_SeqSBAIJ_N_inplace;
731: C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_inplace;
732: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_N_inplace;
733: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_N_inplace;
735: C->assembled = PETSC_TRUE;
736: C->preallocated = PETSC_TRUE;
738: PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
739: return(0);
740: }
744: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
745: {
746: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
748: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
749: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
750: PetscInt bs =A->rmap->bs,bs2 = a->bs2,bslog;
751: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
752: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
753: MatScalar *work;
754: PetscInt *pivots;
757: PetscCalloc1(bs2*mbs,&rtmp);
758: PetscMalloc2(mbs,&il,mbs,&jl);
759: for (i=0; i<mbs; i++) {
760: jl[i] = mbs; il[0] = 0;
761: }
762: PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
763: PetscMalloc1(bs,&pivots);
765: ai = a->i; aj = a->j; aa = a->a;
767: /* flops in while loop */
768: bslog = 2*bs*bs2;
770: /* for each row k */
771: for (k = 0; k<mbs; k++) {
773: /*initialize k-th row with elements nonzero in row k of A */
774: jmin = ai[k]; jmax = ai[k+1];
775: ap = aa + jmin*bs2;
776: for (j = jmin; j < jmax; j++) {
777: vj = aj[j]; /* block col. index */
778: rtmp_ptr = rtmp + vj*bs2;
779: for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
780: }
782: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
783: PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
784: i = jl[k]; /* first row to be added to k_th row */
786: while (i < k) {
787: nexti = jl[i]; /* next row to be added to k_th row */
789: /* compute multiplier */
790: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
792: /* uik = -inv(Di)*U_bar(i,k) */
793: diag = ba + i*bs2;
794: u = ba + ili*bs2;
795: PetscMemzero(uik,bs2*sizeof(MatScalar));
796: PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);
798: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
799: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
800: PetscLogFlops(bslog*2.0);
802: /* update -U(i,k) */
803: PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));
805: /* add multiple of row i to k-th row ... */
806: jmin = ili + 1; jmax = bi[i+1];
807: if (jmin < jmax) {
808: for (j=jmin; j<jmax; j++) {
809: /* rtmp += -U(i,k)^T * U_bar(i,j) */
810: rtmp_ptr = rtmp + bj[j]*bs2;
811: u = ba + j*bs2;
812: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
813: }
814: PetscLogFlops(bslog*(jmax-jmin));
816: /* ... add i to row list for next nonzero entry */
817: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
818: j = bj[jmin];
819: jl[i] = jl[j]; jl[j] = i; /* update jl */
820: }
821: i = nexti;
822: }
824: /* save nonzero entries in k-th row of U ... */
826: /* invert diagonal block */
827: diag = ba+k*bs2;
828: PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
829: PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);
831: jmin = bi[k]; jmax = bi[k+1];
832: if (jmin < jmax) {
833: for (j=jmin; j<jmax; j++) {
834: vj = bj[j]; /* block col. index of U */
835: u = ba + j*bs2;
836: rtmp_ptr = rtmp + vj*bs2;
837: for (k1=0; k1<bs2; k1++) {
838: *u++ = *rtmp_ptr;
839: *rtmp_ptr++ = 0.0;
840: }
841: }
843: /* ... add k to row list for first nonzero entry in k-th row */
844: il[k] = jmin;
845: i = bj[jmin];
846: jl[k] = jl[i]; jl[i] = k;
847: }
848: }
850: PetscFree(rtmp);
851: PetscFree2(il,jl);
852: PetscFree3(dk,uik,work);
853: PetscFree(pivots);
855: C->ops->solve = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
856: C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
857: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
858: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
859: C->assembled = PETSC_TRUE;
860: C->preallocated = PETSC_TRUE;
862: PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
863: return(0);
864: }
866: /*
867: Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
868: Version for blocks 2 by 2.
869: */
872: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat C,Mat A,const MatFactorInfo *info)
873: {
874: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
875: IS perm = b->row;
877: const PetscInt *ai,*aj,*perm_ptr;
878: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
879: PetscInt *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
880: MatScalar *ba = b->a,*aa,*ap;
881: MatScalar *u,*diag,*rtmp,*rtmp_ptr,dk[4],uik[4];
882: PetscReal shift = info->shiftamount;
885: /* initialization */
886: /* il and jl record the first nonzero element in each row of the accessing
887: window U(0:k, k:mbs-1).
888: jl: list of rows to be added to uneliminated rows
889: i>= k: jl(i) is the first row to be added to row i
890: i< k: jl(i) is the row following row i in some list of rows
891: jl(i) = mbs indicates the end of a list
892: il(i): points to the first nonzero element in columns k,...,mbs-1 of
893: row i of U */
894: PetscCalloc1(4*mbs,&rtmp);
895: PetscMalloc2(mbs,&il,mbs,&jl);
896: for (i=0; i<mbs; i++) {
897: jl[i] = mbs; il[0] = 0;
898: }
899: ISGetIndices(perm,&perm_ptr);
901: /* check permutation */
902: if (!a->permute) {
903: ai = a->i; aj = a->j; aa = a->a;
904: } else {
905: ai = a->inew; aj = a->jnew;
906: PetscMalloc1(4*ai[mbs],&aa);
907: PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));
908: PetscMalloc1(ai[mbs],&a2anew);
909: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
911: for (i=0; i<mbs; i++) {
912: jmin = ai[i]; jmax = ai[i+1];
913: for (j=jmin; j<jmax; j++) {
914: while (a2anew[j] != j) {
915: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
916: for (k1=0; k1<4; k1++) {
917: dk[k1] = aa[k*4+k1];
918: aa[k*4+k1] = aa[j*4+k1];
919: aa[j*4+k1] = dk[k1];
920: }
921: }
922: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
923: if (i > aj[j]) {
924: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
925: ap = aa + j*4; /* ptr to the beginning of the block */
926: dk[1] = ap[1]; /* swap ap[1] and ap[2] */
927: ap[1] = ap[2];
928: ap[2] = dk[1];
929: }
930: }
931: }
932: PetscFree(a2anew);
933: }
935: /* for each row k */
936: for (k = 0; k<mbs; k++) {
938: /*initialize k-th row with elements nonzero in row perm(k) of A */
939: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
940: ap = aa + jmin*4;
941: for (j = jmin; j < jmax; j++) {
942: vj = perm_ptr[aj[j]]; /* block col. index */
943: rtmp_ptr = rtmp + vj*4;
944: for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
945: }
947: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
948: PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
949: i = jl[k]; /* first row to be added to k_th row */
951: while (i < k) {
952: nexti = jl[i]; /* next row to be added to k_th row */
954: /* compute multiplier */
955: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
957: /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
958: diag = ba + i*4;
959: u = ba + ili*4;
960: uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
961: uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
962: uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
963: uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
965: /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
966: dk[0] += uik[0]*u[0] + uik[1]*u[1];
967: dk[1] += uik[2]*u[0] + uik[3]*u[1];
968: dk[2] += uik[0]*u[2] + uik[1]*u[3];
969: dk[3] += uik[2]*u[2] + uik[3]*u[3];
971: PetscLogFlops(16.0*2.0);
973: /* update -U(i,k): ba[ili] = uik */
974: PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));
976: /* add multiple of row i to k-th row ... */
977: jmin = ili + 1; jmax = bi[i+1];
978: if (jmin < jmax) {
979: for (j=jmin; j<jmax; j++) {
980: /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
981: rtmp_ptr = rtmp + bj[j]*4;
982: u = ba + j*4;
983: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
984: rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
985: rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
986: rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
987: }
988: PetscLogFlops(16.0*(jmax-jmin));
990: /* ... add i to row list for next nonzero entry */
991: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
992: j = bj[jmin];
993: jl[i] = jl[j]; jl[j] = i; /* update jl */
994: }
995: i = nexti;
996: }
998: /* save nonzero entries in k-th row of U ... */
1000: /* invert diagonal block */
1001: diag = ba+k*4;
1002: PetscMemcpy(diag,dk,4*sizeof(MatScalar));
1003: PetscKernel_A_gets_inverse_A_2(diag,shift);
1005: jmin = bi[k]; jmax = bi[k+1];
1006: if (jmin < jmax) {
1007: for (j=jmin; j<jmax; j++) {
1008: vj = bj[j]; /* block col. index of U */
1009: u = ba + j*4;
1010: rtmp_ptr = rtmp + vj*4;
1011: for (k1=0; k1<4; k1++) {
1012: *u++ = *rtmp_ptr;
1013: *rtmp_ptr++ = 0.0;
1014: }
1015: }
1017: /* ... add k to row list for first nonzero entry in k-th row */
1018: il[k] = jmin;
1019: i = bj[jmin];
1020: jl[k] = jl[i]; jl[i] = k;
1021: }
1022: }
1024: PetscFree(rtmp);
1025: PetscFree2(il,jl);
1026: if (a->permute) {
1027: PetscFree(aa);
1028: }
1029: ISRestoreIndices(perm,&perm_ptr);
1031: C->ops->solve = MatSolve_SeqSBAIJ_2_inplace;
1032: C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_inplace;
1033: C->assembled = PETSC_TRUE;
1034: C->preallocated = PETSC_TRUE;
1036: PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
1037: return(0);
1038: }
1040: /*
1041: Version for when blocks are 2 by 2 Using natural ordering
1042: */
1045: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
1046: {
1047: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
1049: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1050: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1051: MatScalar *ba = b->a,*aa,*ap,dk[8],uik[8];
1052: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
1053: PetscReal shift = info->shiftamount;
1056: /* initialization */
1057: /* il and jl record the first nonzero element in each row of the accessing
1058: window U(0:k, k:mbs-1).
1059: jl: list of rows to be added to uneliminated rows
1060: i>= k: jl(i) is the first row to be added to row i
1061: i< k: jl(i) is the row following row i in some list of rows
1062: jl(i) = mbs indicates the end of a list
1063: il(i): points to the first nonzero element in columns k,...,mbs-1 of
1064: row i of U */
1065: PetscCalloc1(4*mbs,&rtmp);
1066: PetscMalloc2(mbs,&il,mbs,&jl);
1067: for (i=0; i<mbs; i++) {
1068: jl[i] = mbs; il[0] = 0;
1069: }
1070: ai = a->i; aj = a->j; aa = a->a;
1072: /* for each row k */
1073: for (k = 0; k<mbs; k++) {
1075: /*initialize k-th row with elements nonzero in row k of A */
1076: jmin = ai[k]; jmax = ai[k+1];
1077: ap = aa + jmin*4;
1078: for (j = jmin; j < jmax; j++) {
1079: vj = aj[j]; /* block col. index */
1080: rtmp_ptr = rtmp + vj*4;
1081: for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
1082: }
1084: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1085: PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
1086: i = jl[k]; /* first row to be added to k_th row */
1088: while (i < k) {
1089: nexti = jl[i]; /* next row to be added to k_th row */
1091: /* compute multiplier */
1092: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1094: /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
1095: diag = ba + i*4;
1096: u = ba + ili*4;
1097: uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
1098: uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
1099: uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
1100: uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
1102: /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
1103: dk[0] += uik[0]*u[0] + uik[1]*u[1];
1104: dk[1] += uik[2]*u[0] + uik[3]*u[1];
1105: dk[2] += uik[0]*u[2] + uik[1]*u[3];
1106: dk[3] += uik[2]*u[2] + uik[3]*u[3];
1108: PetscLogFlops(16.0*2.0);
1110: /* update -U(i,k): ba[ili] = uik */
1111: PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));
1113: /* add multiple of row i to k-th row ... */
1114: jmin = ili + 1; jmax = bi[i+1];
1115: if (jmin < jmax) {
1116: for (j=jmin; j<jmax; j++) {
1117: /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
1118: rtmp_ptr = rtmp + bj[j]*4;
1119: u = ba + j*4;
1120: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
1121: rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
1122: rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
1123: rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
1124: }
1125: PetscLogFlops(16.0*(jmax-jmin));
1127: /* ... add i to row list for next nonzero entry */
1128: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
1129: j = bj[jmin];
1130: jl[i] = jl[j]; jl[j] = i; /* update jl */
1131: }
1132: i = nexti;
1133: }
1135: /* save nonzero entries in k-th row of U ... */
1137: /* invert diagonal block */
1138: diag = ba+k*4;
1139: PetscMemcpy(diag,dk,4*sizeof(MatScalar));
1140: PetscKernel_A_gets_inverse_A_2(diag,shift);
1142: jmin = bi[k]; jmax = bi[k+1];
1143: if (jmin < jmax) {
1144: for (j=jmin; j<jmax; j++) {
1145: vj = bj[j]; /* block col. index of U */
1146: u = ba + j*4;
1147: rtmp_ptr = rtmp + vj*4;
1148: for (k1=0; k1<4; k1++) {
1149: *u++ = *rtmp_ptr;
1150: *rtmp_ptr++ = 0.0;
1151: }
1152: }
1154: /* ... add k to row list for first nonzero entry in k-th row */
1155: il[k] = jmin;
1156: i = bj[jmin];
1157: jl[k] = jl[i]; jl[i] = k;
1158: }
1159: }
1161: PetscFree(rtmp);
1162: PetscFree2(il,jl);
1164: C->ops->solve = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1165: C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1166: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1167: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1168: C->assembled = PETSC_TRUE;
1169: C->preallocated = PETSC_TRUE;
1171: PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
1172: return(0);
1173: }
1175: /*
1176: Numeric U^T*D*U factorization for SBAIJ format.
1177: Version for blocks are 1 by 1.
1178: */
1181: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
1182: {
1183: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
1184: IS ip=b->row;
1186: const PetscInt *ai,*aj,*rip;
1187: PetscInt *a2anew,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j,*bcol;
1188: PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1189: MatScalar *rtmp,*ba=b->a,*bval,*aa,dk,uikdi;
1190: PetscReal rs;
1191: FactorShiftCtx sctx;
1194: /* MatPivotSetUp(): initialize shift context sctx */
1195: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1197: ISGetIndices(ip,&rip);
1198: if (!a->permute) {
1199: ai = a->i; aj = a->j; aa = a->a;
1200: } else {
1201: ai = a->inew; aj = a->jnew;
1202: nz = ai[mbs];
1203: PetscMalloc1(nz,&aa);
1204: a2anew = a->a2anew;
1205: bval = a->a;
1206: for (j=0; j<nz; j++) {
1207: aa[a2anew[j]] = *(bval++);
1208: }
1209: }
1211: /* initialization */
1212: /* il and jl record the first nonzero element in each row of the accessing
1213: window U(0:k, k:mbs-1).
1214: jl: list of rows to be added to uneliminated rows
1215: i>= k: jl(i) is the first row to be added to row i
1216: i< k: jl(i) is the row following row i in some list of rows
1217: jl(i) = mbs indicates the end of a list
1218: il(i): points to the first nonzero element in columns k,...,mbs-1 of
1219: row i of U */
1220: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);
1222: do {
1223: sctx.newshift = PETSC_FALSE;
1224: for (i=0; i<mbs; i++) {
1225: rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1226: }
1228: for (k = 0; k<mbs; k++) {
1229: /*initialize k-th row by the perm[k]-th row of A */
1230: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1231: bval = ba + bi[k];
1232: for (j = jmin; j < jmax; j++) {
1233: col = rip[aj[j]];
1234: rtmp[col] = aa[j];
1235: *bval++ = 0.0; /* for in-place factorization */
1236: }
1238: /* shift the diagonal of the matrix */
1239: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1241: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1242: dk = rtmp[k];
1243: i = jl[k]; /* first row to be added to k_th row */
1245: while (i < k) {
1246: nexti = jl[i]; /* next row to be added to k_th row */
1248: /* compute multiplier, update diag(k) and U(i,k) */
1249: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1250: uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
1251: dk += uikdi*ba[ili];
1252: ba[ili] = uikdi; /* -U(i,k) */
1254: /* add multiple of row i to k-th row */
1255: jmin = ili + 1; jmax = bi[i+1];
1256: if (jmin < jmax) {
1257: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1258: PetscLogFlops(2.0*(jmax-jmin));
1260: /* update il and jl for row i */
1261: il[i] = jmin;
1262: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1263: }
1264: i = nexti;
1265: }
1267: /* shift the diagonals when zero pivot is detected */
1268: /* compute rs=sum of abs(off-diagonal) */
1269: rs = 0.0;
1270: jmin = bi[k]+1;
1271: nz = bi[k+1] - jmin;
1272: if (nz) {
1273: bcol = bj + jmin;
1274: while (nz--) {
1275: rs += PetscAbsScalar(rtmp[*bcol]);
1276: bcol++;
1277: }
1278: }
1280: sctx.rs = rs;
1281: sctx.pv = dk;
1282: MatPivotCheck(A,info,&sctx,k);
1283: if (sctx.newshift) break; /* sctx.shift_amount is updated */
1284: dk = sctx.pv;
1286: /* copy data into U(k,:) */
1287: ba[bi[k]] = 1.0/dk; /* U(k,k) */
1288: jmin = bi[k]+1; jmax = bi[k+1];
1289: if (jmin < jmax) {
1290: for (j=jmin; j<jmax; j++) {
1291: col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
1292: }
1293: /* add the k-th row into il and jl */
1294: il[k] = jmin;
1295: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1296: }
1297: }
1298: } while (sctx.newshift);
1299: PetscFree3(rtmp,il,jl);
1300: if (a->permute) {PetscFree(aa);}
1302: ISRestoreIndices(ip,&rip);
1304: C->ops->solve = MatSolve_SeqSBAIJ_1_inplace;
1305: C->ops->solves = MatSolves_SeqSBAIJ_1_inplace;
1306: C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
1307: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace;
1308: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace;
1309: C->assembled = PETSC_TRUE;
1310: C->preallocated = PETSC_TRUE;
1312: PetscLogFlops(C->rmap->N);
1313: if (sctx.nshift) {
1314: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1315: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1316: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1317: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1318: }
1319: }
1320: return(0);
1321: }
1323: /*
1324: Version for when blocks are 1 by 1 Using natural ordering under new datastructure
1325: Modified from MatCholeskyFactorNumeric_SeqAIJ()
1326: */
1329: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
1330: {
1331: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data;
1332: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)B->data;
1334: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1335: PetscInt *ai=a->i,*aj=a->j,*ajtmp;
1336: PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1337: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1338: FactorShiftCtx sctx;
1339: PetscReal rs;
1340: MatScalar d,*v;
1343: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);
1345: /* MatPivotSetUp(): initialize shift context sctx */
1346: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1348: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
1349: sctx.shift_top = info->zeropivot;
1351: PetscMemzero(rtmp,mbs*sizeof(MatScalar));
1353: for (i=0; i<mbs; i++) {
1354: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1355: d = (aa)[a->diag[i]];
1356: rtmp[i] += -PetscRealPart(d); /* diagonal entry */
1357: ajtmp = aj + ai[i] + 1; /* exclude diagonal */
1358: v = aa + ai[i] + 1;
1359: nz = ai[i+1] - ai[i] - 1;
1360: for (j=0; j<nz; j++) {
1361: rtmp[i] += PetscAbsScalar(v[j]);
1362: rtmp[ajtmp[j]] += PetscAbsScalar(v[j]);
1363: }
1364: if (PetscRealPart(rtmp[i]) > sctx.shift_top) sctx.shift_top = PetscRealPart(rtmp[i]);
1365: }
1366: sctx.shift_top *= 1.1;
1367: sctx.nshift_max = 5;
1368: sctx.shift_lo = 0.;
1369: sctx.shift_hi = 1.;
1370: }
1372: /* allocate working arrays
1373: c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1374: il: for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays
1375: */
1376: do {
1377: sctx.newshift = PETSC_FALSE;
1379: for (i=0; i<mbs; i++) c2r[i] = mbs;
1380: if (mbs) il[0] = 0;
1382: for (k = 0; k<mbs; k++) {
1383: /* zero rtmp */
1384: nz = bi[k+1] - bi[k];
1385: bjtmp = bj + bi[k];
1386: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1388: /* load in initial unfactored row */
1389: bval = ba + bi[k];
1390: jmin = ai[k]; jmax = ai[k+1];
1391: for (j = jmin; j < jmax; j++) {
1392: col = aj[j];
1393: rtmp[col] = aa[j];
1394: *bval++ = 0.0; /* for in-place factorization */
1395: }
1396: /* shift the diagonal of the matrix: ZeropivotApply() */
1397: rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */
1399: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1400: dk = rtmp[k];
1401: i = c2r[k]; /* first row to be added to k_th row */
1403: while (i < k) {
1404: nexti = c2r[i]; /* next row to be added to k_th row */
1406: /* compute multiplier, update diag(k) and U(i,k) */
1407: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1408: uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
1409: dk += uikdi*ba[ili]; /* update diag[k] */
1410: ba[ili] = uikdi; /* -U(i,k) */
1412: /* add multiple of row i to k-th row */
1413: jmin = ili + 1; jmax = bi[i+1];
1414: if (jmin < jmax) {
1415: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1416: /* update il and c2r for row i */
1417: il[i] = jmin;
1418: j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1419: }
1420: i = nexti;
1421: }
1423: /* copy data into U(k,:) */
1424: rs = 0.0;
1425: jmin = bi[k]; jmax = bi[k+1]-1;
1426: if (jmin < jmax) {
1427: for (j=jmin; j<jmax; j++) {
1428: col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
1429: }
1430: /* add the k-th row into il and c2r */
1431: il[k] = jmin;
1432: i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1433: }
1435: sctx.rs = rs;
1436: sctx.pv = dk;
1437: MatPivotCheck(A,info,&sctx,k);
1438: if (sctx.newshift) break;
1439: dk = sctx.pv;
1441: ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1442: }
1443: } while (sctx.newshift);
1445: PetscFree3(rtmp,il,c2r);
1447: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1448: B->ops->solves = MatSolves_SeqSBAIJ_1;
1449: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1450: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
1451: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
1453: B->assembled = PETSC_TRUE;
1454: B->preallocated = PETSC_TRUE;
1456: PetscLogFlops(B->rmap->n);
1458: /* MatPivotView() */
1459: if (sctx.nshift) {
1460: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1461: PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
1462: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1463: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1464: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
1465: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
1466: }
1467: }
1468: return(0);
1469: }
1473: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
1474: {
1475: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
1477: PetscInt i,j,mbs = a->mbs;
1478: PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
1479: PetscInt k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
1480: MatScalar *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
1481: PetscReal rs;
1482: FactorShiftCtx sctx;
1485: /* MatPivotSetUp(): initialize shift context sctx */
1486: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1488: /* initialization */
1489: /* il and jl record the first nonzero element in each row of the accessing
1490: window U(0:k, k:mbs-1).
1491: jl: list of rows to be added to uneliminated rows
1492: i>= k: jl(i) is the first row to be added to row i
1493: i< k: jl(i) is the row following row i in some list of rows
1494: jl(i) = mbs indicates the end of a list
1495: il(i): points to the first nonzero element in U(i,k:mbs-1)
1496: */
1497: PetscMalloc1(mbs,&rtmp);
1498: PetscMalloc2(mbs,&il,mbs,&jl);
1500: do {
1501: sctx.newshift = PETSC_FALSE;
1502: for (i=0; i<mbs; i++) {
1503: rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1504: }
1506: for (k = 0; k<mbs; k++) {
1507: /*initialize k-th row with elements nonzero in row perm(k) of A */
1508: nz = ai[k+1] - ai[k];
1509: acol = aj + ai[k];
1510: aval = aa + ai[k];
1511: bval = ba + bi[k];
1512: while (nz--) {
1513: rtmp[*acol++] = *aval++;
1514: *bval++ = 0.0; /* for in-place factorization */
1515: }
1517: /* shift the diagonal of the matrix */
1518: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1520: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1521: dk = rtmp[k];
1522: i = jl[k]; /* first row to be added to k_th row */
1524: while (i < k) {
1525: nexti = jl[i]; /* next row to be added to k_th row */
1526: /* compute multiplier, update D(k) and U(i,k) */
1527: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1528: uikdi = -ba[ili]*ba[bi[i]];
1529: dk += uikdi*ba[ili];
1530: ba[ili] = uikdi; /* -U(i,k) */
1532: /* add multiple of row i to k-th row ... */
1533: jmin = ili + 1;
1534: nz = bi[i+1] - jmin;
1535: if (nz > 0) {
1536: bcol = bj + jmin;
1537: bval = ba + jmin;
1538: PetscLogFlops(2.0*nz);
1539: while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
1541: /* update il and jl for i-th row */
1542: il[i] = jmin;
1543: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1544: }
1545: i = nexti;
1546: }
1548: /* shift the diagonals when zero pivot is detected */
1549: /* compute rs=sum of abs(off-diagonal) */
1550: rs = 0.0;
1551: jmin = bi[k]+1;
1552: nz = bi[k+1] - jmin;
1553: if (nz) {
1554: bcol = bj + jmin;
1555: while (nz--) {
1556: rs += PetscAbsScalar(rtmp[*bcol]);
1557: bcol++;
1558: }
1559: }
1561: sctx.rs = rs;
1562: sctx.pv = dk;
1563: MatPivotCheck(A,info,&sctx,k);
1564: if (sctx.newshift) break; /* sctx.shift_amount is updated */
1565: dk = sctx.pv;
1567: /* copy data into U(k,:) */
1568: ba[bi[k]] = 1.0/dk;
1569: jmin = bi[k]+1;
1570: nz = bi[k+1] - jmin;
1571: if (nz) {
1572: bcol = bj + jmin;
1573: bval = ba + jmin;
1574: while (nz--) {
1575: *bval++ = rtmp[*bcol];
1576: rtmp[*bcol++] = 0.0;
1577: }
1578: /* add k-th row into il and jl */
1579: il[k] = jmin;
1580: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1581: }
1582: } /* end of for (k = 0; k<mbs; k++) */
1583: } while (sctx.newshift);
1584: PetscFree(rtmp);
1585: PetscFree2(il,jl);
1587: C->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1588: C->ops->solves = MatSolves_SeqSBAIJ_1_inplace;
1589: C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1590: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1591: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1593: C->assembled = PETSC_TRUE;
1594: C->preallocated = PETSC_TRUE;
1596: PetscLogFlops(C->rmap->N);
1597: if (sctx.nshift) {
1598: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1599: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1600: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1601: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1602: }
1603: }
1604: return(0);
1605: }
1609: PetscErrorCode MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,const MatFactorInfo *info)
1610: {
1612: Mat C;
1615: MatGetFactor(A,"petsc",MAT_FACTOR_CHOLESKY,&C);
1616: MatCholeskyFactorSymbolic(C,A,perm,info);
1617: MatCholeskyFactorNumeric(C,A,info);
1619: A->ops->solve = C->ops->solve;
1620: A->ops->solvetranspose = C->ops->solvetranspose;
1622: MatHeaderMerge(A,C);
1623: return(0);
1624: }