Actual source code: sbaijfact.c
petsc-3.5.4 2015-05-23
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: PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*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: /* There are bugs for reordeing. Needs further work.
430: MatReordering for sbaij cannot be efficient. User should use aij formt! */
431: a->permute = PETSC_TRUE;
433: MatReorderingSeqSBAIJ(A,perm);
434: ai = a->inew; aj = a->jnew;
435: }
436: ISGetIndices(perm,&rip);
438: /* initialization */
439: PetscMalloc1((mbs+1),&ui);
440: ui[0] = 0;
442: /* jl: linked list for storing indices of the pivot rows
443: il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
444: PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
445: for (i=0; i<mbs; i++) {
446: jl[i] = mbs; il[i] = 0;
447: }
449: /* create and initialize a linked list for storing column indices of the active row k */
450: nlnk = mbs + 1;
451: PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);
453: /* initial FreeSpace size is fill*(ai[mbs]+1) */
454: PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+1)),&free_space);
455: current_space = free_space;
457: for (k=0; k<mbs; k++) { /* for each active row k */
458: /* initialize lnk by the column indices of row rip[k] of A */
459: nzk = 0;
460: ncols = ai[rip[k]+1] - ai[rip[k]];
461: for (j=0; j<ncols; j++) {
462: i = *(aj + ai[rip[k]] + j);
463: cols[j] = rip[i];
464: }
465: PetscLLAdd(ncols,cols,mbs,nlnk,lnk,lnkbt);
466: nzk += nlnk;
468: /* update lnk by computing fill-in for each pivot row to be merged in */
469: prow = jl[k]; /* 1st pivot row */
471: while (prow < k) {
472: nextprow = jl[prow];
473: /* merge prow into k-th row */
474: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
475: jmax = ui[prow+1];
476: ncols = jmax-jmin;
477: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
478: PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
479: nzk += nlnk;
481: /* update il and jl for prow */
482: if (jmin < jmax) {
483: il[prow] = jmin;
485: j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
486: }
487: prow = nextprow;
488: }
490: /* if free space is not available, make more free space */
491: if (current_space->local_remaining<nzk) {
492: i = mbs - k + 1; /* num of unfactored rows */
493: i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
494: PetscFreeSpaceGet(i,¤t_space);
495: reallocs++;
496: }
498: /* copy data into free space, then initialize lnk */
499: PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);
501: /* add the k-th row into il and jl */
502: if (nzk-1 > 0) {
503: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
504: jl[k] = jl[i]; jl[i] = k;
505: il[k] = ui[k] + 1;
506: }
507: ui_ptr[k] = current_space->array;
509: current_space->array += nzk;
510: current_space->local_used += nzk;
511: current_space->local_remaining -= nzk;
513: ui[k+1] = ui[k] + nzk;
514: }
516: ISRestoreIndices(perm,&rip);
517: PetscFree4(ui_ptr,il,jl,cols);
519: /* destroy list of free space and other temporary array(s) */
520: PetscMalloc1((ui[mbs]+1),&uj);
521: PetscFreeSpaceContiguous(&free_space,uj);
522: PetscLLDestroy(lnk,lnkbt);
524: /* put together the new matrix in MATSEQSBAIJ format */
525: MatSeqSBAIJSetPreallocation_SeqSBAIJ(fact,bs,MAT_SKIP_ALLOCATION,NULL);
527: b = (Mat_SeqSBAIJ*)fact->data;
528: b->singlemalloc = PETSC_FALSE;
529: b->free_a = PETSC_TRUE;
530: b->free_ij = PETSC_TRUE;
532: PetscMalloc1((ui[mbs]+1),&b->a);
534: b->j = uj;
535: b->i = ui;
536: b->diag = 0;
537: b->ilen = 0;
538: b->imax = 0;
539: b->row = perm;
541: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
543: PetscObjectReference((PetscObject)perm);
544: b->icol = perm;
545: PetscObjectReference((PetscObject)perm);
546: PetscMalloc1((mbs+1),&b->solve_work);
547: PetscLogObjectMemory((PetscObject)fact,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
548: b->maxnz = b->nz = ui[mbs];
550: fact->info.factor_mallocs = reallocs;
551: fact->info.fill_ratio_given = fill;
552: if (ai[mbs] != 0) {
553: fact->info.fill_ratio_needed = ((PetscReal)ui[mbs])/ai[mbs];
554: } else {
555: fact->info.fill_ratio_needed = 0.0;
556: }
557: #if defined(PETSC_USE_INFO)
558: if (ai[mbs] != 0) {
559: PetscReal af = fact->info.fill_ratio_needed;
560: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
561: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
562: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
563: } else {
564: PetscInfo(A,"Empty matrix.\n");
565: }
566: #endif
567: MatSeqSBAIJSetNumericFactorization_inplace(fact,perm_identity);
568: return(0);
569: }
573: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
574: {
575: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
576: IS perm = b->row;
578: const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
579: PetscInt i,j;
580: PetscInt *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
581: PetscInt bs =A->rmap->bs,bs2 = a->bs2,bslog = 0;
582: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
583: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
584: MatScalar *work;
585: PetscInt *pivots;
588: /* initialization */
589: PetscCalloc1(bs2*mbs,&rtmp);
590: PetscMalloc2(mbs,&il,mbs,&jl);
591: for (i=0; i<mbs; i++) {
592: jl[i] = mbs; il[0] = 0;
593: }
594: PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
595: PetscMalloc1(bs,&pivots);
597: ISGetIndices(perm,&perm_ptr);
599: /* check permutation */
600: if (!a->permute) {
601: ai = a->i; aj = a->j; aa = a->a;
602: } else {
603: ai = a->inew; aj = a->jnew;
604: PetscMalloc1(bs2*ai[mbs],&aa);
605: PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));
606: PetscMalloc1(ai[mbs],&a2anew);
607: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
609: /* flops in while loop */
610: bslog = 2*bs*bs2;
612: for (i=0; i<mbs; i++) {
613: jmin = ai[i]; jmax = ai[i+1];
614: for (j=jmin; j<jmax; j++) {
615: while (a2anew[j] != j) {
616: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
617: for (k1=0; k1<bs2; k1++) {
618: dk[k1] = aa[k*bs2+k1];
619: aa[k*bs2+k1] = aa[j*bs2+k1];
620: aa[j*bs2+k1] = dk[k1];
621: }
622: }
623: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
624: if (i > aj[j]) {
625: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
626: ap = aa + j*bs2; /* ptr to the beginning of j-th block of aa */
627: for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
628: for (k=0; k<bs; k++) { /* j-th block of aa <- dk^T */
629: for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1];
630: }
631: }
632: }
633: }
634: PetscFree(a2anew);
635: }
637: /* for each row k */
638: for (k = 0; k<mbs; k++) {
640: /*initialize k-th row with elements nonzero in row perm(k) of A */
641: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
643: ap = aa + jmin*bs2;
644: for (j = jmin; j < jmax; j++) {
645: vj = perm_ptr[aj[j]]; /* block col. index */
646: rtmp_ptr = rtmp + vj*bs2;
647: for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
648: }
650: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
651: PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
652: i = jl[k]; /* first row to be added to k_th row */
654: while (i < k) {
655: nexti = jl[i]; /* next row to be added to k_th row */
657: /* compute multiplier */
658: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
660: /* uik = -inv(Di)*U_bar(i,k) */
661: diag = ba + i*bs2;
662: u = ba + ili*bs2;
663: PetscMemzero(uik,bs2*sizeof(MatScalar));
664: PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);
666: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
667: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
668: PetscLogFlops(bslog*2.0);
670: /* update -U(i,k) */
671: PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));
673: /* add multiple of row i to k-th row ... */
674: jmin = ili + 1; jmax = bi[i+1];
675: if (jmin < jmax) {
676: for (j=jmin; j<jmax; j++) {
677: /* rtmp += -U(i,k)^T * U_bar(i,j) */
678: rtmp_ptr = rtmp + bj[j]*bs2;
679: u = ba + j*bs2;
680: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
681: }
682: PetscLogFlops(bslog*(jmax-jmin));
684: /* ... add i to row list for next nonzero entry */
685: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
686: j = bj[jmin];
687: jl[i] = jl[j]; jl[j] = i; /* update jl */
688: }
689: i = nexti;
690: }
692: /* save nonzero entries in k-th row of U ... */
694: /* invert diagonal block */
695: diag = ba+k*bs2;
696: PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
697: PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);
699: jmin = bi[k]; jmax = bi[k+1];
700: if (jmin < jmax) {
701: for (j=jmin; j<jmax; j++) {
702: vj = bj[j]; /* block col. index of U */
703: u = ba + j*bs2;
704: rtmp_ptr = rtmp + vj*bs2;
705: for (k1=0; k1<bs2; k1++) {
706: *u++ = *rtmp_ptr;
707: *rtmp_ptr++ = 0.0;
708: }
709: }
711: /* ... add k to row list for first nonzero entry in k-th row */
712: il[k] = jmin;
713: i = bj[jmin];
714: jl[k] = jl[i]; jl[i] = k;
715: }
716: }
718: PetscFree(rtmp);
719: PetscFree2(il,jl);
720: PetscFree3(dk,uik,work);
721: PetscFree(pivots);
722: if (a->permute) {
723: PetscFree(aa);
724: }
726: ISRestoreIndices(perm,&perm_ptr);
728: C->ops->solve = MatSolve_SeqSBAIJ_N_inplace;
729: C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_inplace;
730: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_N_inplace;
731: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_N_inplace;
733: C->assembled = PETSC_TRUE;
734: C->preallocated = PETSC_TRUE;
736: PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
737: return(0);
738: }
742: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
743: {
744: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
746: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
747: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
748: PetscInt bs =A->rmap->bs,bs2 = a->bs2,bslog;
749: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
750: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
751: MatScalar *work;
752: PetscInt *pivots;
755: PetscCalloc1(bs2*mbs,&rtmp);
756: PetscMalloc2(mbs,&il,mbs,&jl);
757: for (i=0; i<mbs; i++) {
758: jl[i] = mbs; il[0] = 0;
759: }
760: PetscMalloc3(bs2,&dk,bs2,&uik,bs,&work);
761: PetscMalloc1(bs,&pivots);
763: ai = a->i; aj = a->j; aa = a->a;
765: /* flops in while loop */
766: bslog = 2*bs*bs2;
768: /* for each row k */
769: for (k = 0; k<mbs; k++) {
771: /*initialize k-th row with elements nonzero in row k of A */
772: jmin = ai[k]; jmax = ai[k+1];
773: ap = aa + jmin*bs2;
774: for (j = jmin; j < jmax; j++) {
775: vj = aj[j]; /* block col. index */
776: rtmp_ptr = rtmp + vj*bs2;
777: for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
778: }
780: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
781: PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));
782: i = jl[k]; /* first row to be added to k_th row */
784: while (i < k) {
785: nexti = jl[i]; /* next row to be added to k_th row */
787: /* compute multiplier */
788: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
790: /* uik = -inv(Di)*U_bar(i,k) */
791: diag = ba + i*bs2;
792: u = ba + ili*bs2;
793: PetscMemzero(uik,bs2*sizeof(MatScalar));
794: PetscKernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);
796: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
797: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
798: PetscLogFlops(bslog*2.0);
800: /* update -U(i,k) */
801: PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));
803: /* add multiple of row i to k-th row ... */
804: jmin = ili + 1; jmax = bi[i+1];
805: if (jmin < jmax) {
806: for (j=jmin; j<jmax; j++) {
807: /* rtmp += -U(i,k)^T * U_bar(i,j) */
808: rtmp_ptr = rtmp + bj[j]*bs2;
809: u = ba + j*bs2;
810: PetscKernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
811: }
812: PetscLogFlops(bslog*(jmax-jmin));
814: /* ... add i to row list for next nonzero entry */
815: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
816: j = bj[jmin];
817: jl[i] = jl[j]; jl[j] = i; /* update jl */
818: }
819: i = nexti;
820: }
822: /* save nonzero entries in k-th row of U ... */
824: /* invert diagonal block */
825: diag = ba+k*bs2;
826: PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));
827: PetscKernel_A_gets_inverse_A(bs,diag,pivots,work);
829: jmin = bi[k]; jmax = bi[k+1];
830: if (jmin < jmax) {
831: for (j=jmin; j<jmax; j++) {
832: vj = bj[j]; /* block col. index of U */
833: u = ba + j*bs2;
834: rtmp_ptr = rtmp + vj*bs2;
835: for (k1=0; k1<bs2; k1++) {
836: *u++ = *rtmp_ptr;
837: *rtmp_ptr++ = 0.0;
838: }
839: }
841: /* ... add k to row list for first nonzero entry in k-th row */
842: il[k] = jmin;
843: i = bj[jmin];
844: jl[k] = jl[i]; jl[i] = k;
845: }
846: }
848: PetscFree(rtmp);
849: PetscFree2(il,jl);
850: PetscFree3(dk,uik,work);
851: PetscFree(pivots);
853: C->ops->solve = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
854: C->ops->solvetranspose = MatSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
855: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
856: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_N_NaturalOrdering_inplace;
857: C->assembled = PETSC_TRUE;
858: C->preallocated = PETSC_TRUE;
860: PetscLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
861: return(0);
862: }
864: /*
865: Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
866: Version for blocks 2 by 2.
867: */
870: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat C,Mat A,const MatFactorInfo *info)
871: {
872: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
873: IS perm = b->row;
875: const PetscInt *ai,*aj,*perm_ptr;
876: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
877: PetscInt *a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
878: MatScalar *ba = b->a,*aa,*ap;
879: MatScalar *u,*diag,*rtmp,*rtmp_ptr,dk[4],uik[4];
880: PetscReal shift = info->shiftamount;
883: /* initialization */
884: /* il and jl record the first nonzero element in each row of the accessing
885: window U(0:k, k:mbs-1).
886: jl: list of rows to be added to uneliminated rows
887: i>= k: jl(i) is the first row to be added to row i
888: i< k: jl(i) is the row following row i in some list of rows
889: jl(i) = mbs indicates the end of a list
890: il(i): points to the first nonzero element in columns k,...,mbs-1 of
891: row i of U */
892: PetscCalloc1(4*mbs,&rtmp);
893: PetscMalloc2(mbs,&il,mbs,&jl);
894: for (i=0; i<mbs; i++) {
895: jl[i] = mbs; il[0] = 0;
896: }
897: ISGetIndices(perm,&perm_ptr);
899: /* check permutation */
900: if (!a->permute) {
901: ai = a->i; aj = a->j; aa = a->a;
902: } else {
903: ai = a->inew; aj = a->jnew;
904: PetscMalloc1(4*ai[mbs],&aa);
905: PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));
906: PetscMalloc1(ai[mbs],&a2anew);
907: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
909: for (i=0; i<mbs; i++) {
910: jmin = ai[i]; jmax = ai[i+1];
911: for (j=jmin; j<jmax; j++) {
912: while (a2anew[j] != j) {
913: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
914: for (k1=0; k1<4; k1++) {
915: dk[k1] = aa[k*4+k1];
916: aa[k*4+k1] = aa[j*4+k1];
917: aa[j*4+k1] = dk[k1];
918: }
919: }
920: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
921: if (i > aj[j]) {
922: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
923: ap = aa + j*4; /* ptr to the beginning of the block */
924: dk[1] = ap[1]; /* swap ap[1] and ap[2] */
925: ap[1] = ap[2];
926: ap[2] = dk[1];
927: }
928: }
929: }
930: PetscFree(a2anew);
931: }
933: /* for each row k */
934: for (k = 0; k<mbs; k++) {
936: /*initialize k-th row with elements nonzero in row perm(k) of A */
937: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
938: ap = aa + jmin*4;
939: for (j = jmin; j < jmax; j++) {
940: vj = perm_ptr[aj[j]]; /* block col. index */
941: rtmp_ptr = rtmp + vj*4;
942: for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
943: }
945: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
946: PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
947: i = jl[k]; /* first row to be added to k_th row */
949: while (i < k) {
950: nexti = jl[i]; /* next row to be added to k_th row */
952: /* compute multiplier */
953: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
955: /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
956: diag = ba + i*4;
957: u = ba + ili*4;
958: uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
959: uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
960: uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
961: uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
963: /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
964: dk[0] += uik[0]*u[0] + uik[1]*u[1];
965: dk[1] += uik[2]*u[0] + uik[3]*u[1];
966: dk[2] += uik[0]*u[2] + uik[1]*u[3];
967: dk[3] += uik[2]*u[2] + uik[3]*u[3];
969: PetscLogFlops(16.0*2.0);
971: /* update -U(i,k): ba[ili] = uik */
972: PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));
974: /* add multiple of row i to k-th row ... */
975: jmin = ili + 1; jmax = bi[i+1];
976: if (jmin < jmax) {
977: for (j=jmin; j<jmax; j++) {
978: /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
979: rtmp_ptr = rtmp + bj[j]*4;
980: u = ba + j*4;
981: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
982: rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
983: rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
984: rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
985: }
986: PetscLogFlops(16.0*(jmax-jmin));
988: /* ... add i to row list for next nonzero entry */
989: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
990: j = bj[jmin];
991: jl[i] = jl[j]; jl[j] = i; /* update jl */
992: }
993: i = nexti;
994: }
996: /* save nonzero entries in k-th row of U ... */
998: /* invert diagonal block */
999: diag = ba+k*4;
1000: PetscMemcpy(diag,dk,4*sizeof(MatScalar));
1001: PetscKernel_A_gets_inverse_A_2(diag,shift);
1003: jmin = bi[k]; jmax = bi[k+1];
1004: if (jmin < jmax) {
1005: for (j=jmin; j<jmax; j++) {
1006: vj = bj[j]; /* block col. index of U */
1007: u = ba + j*4;
1008: rtmp_ptr = rtmp + vj*4;
1009: for (k1=0; k1<4; k1++) {
1010: *u++ = *rtmp_ptr;
1011: *rtmp_ptr++ = 0.0;
1012: }
1013: }
1015: /* ... add k to row list for first nonzero entry in k-th row */
1016: il[k] = jmin;
1017: i = bj[jmin];
1018: jl[k] = jl[i]; jl[i] = k;
1019: }
1020: }
1022: PetscFree(rtmp);
1023: PetscFree2(il,jl);
1024: if (a->permute) {
1025: PetscFree(aa);
1026: }
1027: ISRestoreIndices(perm,&perm_ptr);
1029: C->ops->solve = MatSolve_SeqSBAIJ_2_inplace;
1030: C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_inplace;
1031: C->assembled = PETSC_TRUE;
1032: C->preallocated = PETSC_TRUE;
1034: PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
1035: return(0);
1036: }
1038: /*
1039: Version for when blocks are 2 by 2 Using natural ordering
1040: */
1043: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
1044: {
1045: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
1047: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1048: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1049: MatScalar *ba = b->a,*aa,*ap,dk[8],uik[8];
1050: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
1051: PetscReal shift = info->shiftamount;
1054: /* initialization */
1055: /* il and jl record the first nonzero element in each row of the accessing
1056: window U(0:k, k:mbs-1).
1057: jl: list of rows to be added to uneliminated rows
1058: i>= k: jl(i) is the first row to be added to row i
1059: i< k: jl(i) is the row following row i in some list of rows
1060: jl(i) = mbs indicates the end of a list
1061: il(i): points to the first nonzero element in columns k,...,mbs-1 of
1062: row i of U */
1063: PetscCalloc1(4*mbs,&rtmp);
1064: PetscMalloc2(mbs,&il,mbs,&jl);
1065: for (i=0; i<mbs; i++) {
1066: jl[i] = mbs; il[0] = 0;
1067: }
1068: ai = a->i; aj = a->j; aa = a->a;
1070: /* for each row k */
1071: for (k = 0; k<mbs; k++) {
1073: /*initialize k-th row with elements nonzero in row k of A */
1074: jmin = ai[k]; jmax = ai[k+1];
1075: ap = aa + jmin*4;
1076: for (j = jmin; j < jmax; j++) {
1077: vj = aj[j]; /* block col. index */
1078: rtmp_ptr = rtmp + vj*4;
1079: for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
1080: }
1082: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1083: PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));
1084: i = jl[k]; /* first row to be added to k_th row */
1086: while (i < k) {
1087: nexti = jl[i]; /* next row to be added to k_th row */
1089: /* compute multiplier */
1090: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1092: /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
1093: diag = ba + i*4;
1094: u = ba + ili*4;
1095: uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
1096: uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
1097: uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
1098: uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
1100: /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
1101: dk[0] += uik[0]*u[0] + uik[1]*u[1];
1102: dk[1] += uik[2]*u[0] + uik[3]*u[1];
1103: dk[2] += uik[0]*u[2] + uik[1]*u[3];
1104: dk[3] += uik[2]*u[2] + uik[3]*u[3];
1106: PetscLogFlops(16.0*2.0);
1108: /* update -U(i,k): ba[ili] = uik */
1109: PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));
1111: /* add multiple of row i to k-th row ... */
1112: jmin = ili + 1; jmax = bi[i+1];
1113: if (jmin < jmax) {
1114: for (j=jmin; j<jmax; j++) {
1115: /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
1116: rtmp_ptr = rtmp + bj[j]*4;
1117: u = ba + j*4;
1118: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
1119: rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
1120: rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
1121: rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
1122: }
1123: PetscLogFlops(16.0*(jmax-jmin));
1125: /* ... add i to row list for next nonzero entry */
1126: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
1127: j = bj[jmin];
1128: jl[i] = jl[j]; jl[j] = i; /* update jl */
1129: }
1130: i = nexti;
1131: }
1133: /* save nonzero entries in k-th row of U ... */
1135: /* invert diagonal block */
1136: diag = ba+k*4;
1137: PetscMemcpy(diag,dk,4*sizeof(MatScalar));
1138: PetscKernel_A_gets_inverse_A_2(diag,shift);
1140: jmin = bi[k]; jmax = bi[k+1];
1141: if (jmin < jmax) {
1142: for (j=jmin; j<jmax; j++) {
1143: vj = bj[j]; /* block col. index of U */
1144: u = ba + j*4;
1145: rtmp_ptr = rtmp + vj*4;
1146: for (k1=0; k1<4; k1++) {
1147: *u++ = *rtmp_ptr;
1148: *rtmp_ptr++ = 0.0;
1149: }
1150: }
1152: /* ... add k to row list for first nonzero entry in k-th row */
1153: il[k] = jmin;
1154: i = bj[jmin];
1155: jl[k] = jl[i]; jl[i] = k;
1156: }
1157: }
1159: PetscFree(rtmp);
1160: PetscFree2(il,jl);
1162: C->ops->solve = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1163: C->ops->solvetranspose = MatSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1164: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1165: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_2_NaturalOrdering_inplace;
1166: C->assembled = PETSC_TRUE;
1167: C->preallocated = PETSC_TRUE;
1169: PetscLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
1170: return(0);
1171: }
1173: /*
1174: Numeric U^T*D*U factorization for SBAIJ format.
1175: Version for blocks are 1 by 1.
1176: */
1179: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
1180: {
1181: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
1182: IS ip=b->row;
1184: const PetscInt *ai,*aj,*rip;
1185: PetscInt *a2anew,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j,*bcol;
1186: PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
1187: MatScalar *rtmp,*ba=b->a,*bval,*aa,dk,uikdi;
1188: PetscReal rs;
1189: FactorShiftCtx sctx;
1192: /* MatPivotSetUp(): initialize shift context sctx */
1193: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1195: ISGetIndices(ip,&rip);
1196: if (!a->permute) {
1197: ai = a->i; aj = a->j; aa = a->a;
1198: } else {
1199: ai = a->inew; aj = a->jnew;
1200: nz = ai[mbs];
1201: PetscMalloc1(nz,&aa);
1202: a2anew = a->a2anew;
1203: bval = a->a;
1204: for (j=0; j<nz; j++) {
1205: aa[a2anew[j]] = *(bval++);
1206: }
1207: }
1209: /* initialization */
1210: /* il and jl record the first nonzero element in each row of the accessing
1211: window U(0:k, k:mbs-1).
1212: jl: list of rows to be added to uneliminated rows
1213: i>= k: jl(i) is the first row to be added to row i
1214: i< k: jl(i) is the row following row i in some list of rows
1215: jl(i) = mbs indicates the end of a list
1216: il(i): points to the first nonzero element in columns k,...,mbs-1 of
1217: row i of U */
1218: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);
1220: do {
1221: sctx.newshift = PETSC_FALSE;
1222: for (i=0; i<mbs; i++) {
1223: rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1224: }
1226: for (k = 0; k<mbs; k++) {
1227: /*initialize k-th row by the perm[k]-th row of A */
1228: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
1229: bval = ba + bi[k];
1230: for (j = jmin; j < jmax; j++) {
1231: col = rip[aj[j]];
1232: rtmp[col] = aa[j];
1233: *bval++ = 0.0; /* for in-place factorization */
1234: }
1236: /* shift the diagonal of the matrix */
1237: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1239: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1240: dk = rtmp[k];
1241: i = jl[k]; /* first row to be added to k_th row */
1243: while (i < k) {
1244: nexti = jl[i]; /* next row to be added to k_th row */
1246: /* compute multiplier, update diag(k) and U(i,k) */
1247: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1248: uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
1249: dk += uikdi*ba[ili];
1250: ba[ili] = uikdi; /* -U(i,k) */
1252: /* add multiple of row i to k-th row */
1253: jmin = ili + 1; jmax = bi[i+1];
1254: if (jmin < jmax) {
1255: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1256: PetscLogFlops(2.0*(jmax-jmin));
1258: /* update il and jl for row i */
1259: il[i] = jmin;
1260: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1261: }
1262: i = nexti;
1263: }
1265: /* shift the diagonals when zero pivot is detected */
1266: /* compute rs=sum of abs(off-diagonal) */
1267: rs = 0.0;
1268: jmin = bi[k]+1;
1269: nz = bi[k+1] - jmin;
1270: if (nz) {
1271: bcol = bj + jmin;
1272: while (nz--) {
1273: rs += PetscAbsScalar(rtmp[*bcol]);
1274: bcol++;
1275: }
1276: }
1278: sctx.rs = rs;
1279: sctx.pv = dk;
1280: MatPivotCheck(A,info,&sctx,k);
1281: if (sctx.newshift) break; /* sctx.shift_amount is updated */
1282: dk = sctx.pv;
1284: /* copy data into U(k,:) */
1285: ba[bi[k]] = 1.0/dk; /* U(k,k) */
1286: jmin = bi[k]+1; jmax = bi[k+1];
1287: if (jmin < jmax) {
1288: for (j=jmin; j<jmax; j++) {
1289: col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
1290: }
1291: /* add the k-th row into il and jl */
1292: il[k] = jmin;
1293: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1294: }
1295: }
1296: } while (sctx.newshift);
1297: PetscFree3(rtmp,il,jl);
1298: if (a->permute) {PetscFree(aa);}
1300: ISRestoreIndices(ip,&rip);
1302: C->ops->solve = MatSolve_SeqSBAIJ_1_inplace;
1303: C->ops->solves = MatSolves_SeqSBAIJ_1_inplace;
1304: C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
1305: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace;
1306: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace;
1307: C->assembled = PETSC_TRUE;
1308: C->preallocated = PETSC_TRUE;
1310: PetscLogFlops(C->rmap->N);
1311: if (sctx.nshift) {
1312: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1313: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1314: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1315: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1316: }
1317: }
1318: return(0);
1319: }
1321: /*
1322: Version for when blocks are 1 by 1 Using natural ordering under new datastructure
1323: Modified from MatCholeskyFactorNumeric_SeqAIJ()
1324: */
1327: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
1328: {
1329: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data;
1330: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)B->data;
1332: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
1333: PetscInt *ai=a->i,*aj=a->j,*ajtmp;
1334: PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
1335: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
1336: FactorShiftCtx sctx;
1337: PetscReal rs;
1338: MatScalar d,*v;
1341: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);
1343: /* MatPivotSetUp(): initialize shift context sctx */
1344: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1346: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
1347: sctx.shift_top = info->zeropivot;
1349: PetscMemzero(rtmp,mbs*sizeof(MatScalar));
1351: for (i=0; i<mbs; i++) {
1352: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1353: d = (aa)[a->diag[i]];
1354: rtmp[i] += -PetscRealPart(d); /* diagonal entry */
1355: ajtmp = aj + ai[i] + 1; /* exclude diagonal */
1356: v = aa + ai[i] + 1;
1357: nz = ai[i+1] - ai[i] - 1;
1358: for (j=0; j<nz; j++) {
1359: rtmp[i] += PetscAbsScalar(v[j]);
1360: rtmp[ajtmp[j]] += PetscAbsScalar(v[j]);
1361: }
1362: if (PetscRealPart(rtmp[i]) > sctx.shift_top) sctx.shift_top = PetscRealPart(rtmp[i]);
1363: }
1364: sctx.shift_top *= 1.1;
1365: sctx.nshift_max = 5;
1366: sctx.shift_lo = 0.;
1367: sctx.shift_hi = 1.;
1368: }
1370: /* allocate working arrays
1371: c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
1372: 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
1373: */
1374: do {
1375: sctx.newshift = PETSC_FALSE;
1377: for (i=0; i<mbs; i++) c2r[i] = mbs;
1378: if (mbs) il[0] = 0;
1380: for (k = 0; k<mbs; k++) {
1381: /* zero rtmp */
1382: nz = bi[k+1] - bi[k];
1383: bjtmp = bj + bi[k];
1384: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
1386: /* load in initial unfactored row */
1387: bval = ba + bi[k];
1388: jmin = ai[k]; jmax = ai[k+1];
1389: for (j = jmin; j < jmax; j++) {
1390: col = aj[j];
1391: rtmp[col] = aa[j];
1392: *bval++ = 0.0; /* for in-place factorization */
1393: }
1394: /* shift the diagonal of the matrix: ZeropivotApply() */
1395: rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */
1397: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1398: dk = rtmp[k];
1399: i = c2r[k]; /* first row to be added to k_th row */
1401: while (i < k) {
1402: nexti = c2r[i]; /* next row to be added to k_th row */
1404: /* compute multiplier, update diag(k) and U(i,k) */
1405: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1406: uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
1407: dk += uikdi*ba[ili]; /* update diag[k] */
1408: ba[ili] = uikdi; /* -U(i,k) */
1410: /* add multiple of row i to k-th row */
1411: jmin = ili + 1; jmax = bi[i+1];
1412: if (jmin < jmax) {
1413: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
1414: /* update il and c2r for row i */
1415: il[i] = jmin;
1416: j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
1417: }
1418: i = nexti;
1419: }
1421: /* copy data into U(k,:) */
1422: rs = 0.0;
1423: jmin = bi[k]; jmax = bi[k+1]-1;
1424: if (jmin < jmax) {
1425: for (j=jmin; j<jmax; j++) {
1426: col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
1427: }
1428: /* add the k-th row into il and c2r */
1429: il[k] = jmin;
1430: i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
1431: }
1433: sctx.rs = rs;
1434: sctx.pv = dk;
1435: MatPivotCheck(A,info,&sctx,k);
1436: if (sctx.newshift) break;
1437: dk = sctx.pv;
1439: ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
1440: }
1441: } while (sctx.newshift);
1443: PetscFree3(rtmp,il,c2r);
1445: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1446: B->ops->solves = MatSolves_SeqSBAIJ_1;
1447: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
1448: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
1449: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
1451: B->assembled = PETSC_TRUE;
1452: B->preallocated = PETSC_TRUE;
1454: PetscLogFlops(B->rmap->n);
1456: /* MatPivotView() */
1457: if (sctx.nshift) {
1458: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1459: 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);
1460: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1461: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1462: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
1463: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
1464: }
1465: }
1466: return(0);
1467: }
1471: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
1472: {
1473: Mat_SeqSBAIJ *a=(Mat_SeqSBAIJ*)A->data,*b=(Mat_SeqSBAIJ*)C->data;
1475: PetscInt i,j,mbs = a->mbs;
1476: PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
1477: PetscInt k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
1478: MatScalar *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
1479: PetscReal rs;
1480: FactorShiftCtx sctx;
1483: /* MatPivotSetUp(): initialize shift context sctx */
1484: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
1486: /* initialization */
1487: /* il and jl record the first nonzero element in each row of the accessing
1488: window U(0:k, k:mbs-1).
1489: jl: list of rows to be added to uneliminated rows
1490: i>= k: jl(i) is the first row to be added to row i
1491: i< k: jl(i) is the row following row i in some list of rows
1492: jl(i) = mbs indicates the end of a list
1493: il(i): points to the first nonzero element in U(i,k:mbs-1)
1494: */
1495: PetscMalloc1(mbs,&rtmp);
1496: PetscMalloc2(mbs,&il,mbs,&jl);
1498: do {
1499: sctx.newshift = PETSC_FALSE;
1500: for (i=0; i<mbs; i++) {
1501: rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
1502: }
1504: for (k = 0; k<mbs; k++) {
1505: /*initialize k-th row with elements nonzero in row perm(k) of A */
1506: nz = ai[k+1] - ai[k];
1507: acol = aj + ai[k];
1508: aval = aa + ai[k];
1509: bval = ba + bi[k];
1510: while (nz--) {
1511: rtmp[*acol++] = *aval++;
1512: *bval++ = 0.0; /* for in-place factorization */
1513: }
1515: /* shift the diagonal of the matrix */
1516: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
1518: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
1519: dk = rtmp[k];
1520: i = jl[k]; /* first row to be added to k_th row */
1522: while (i < k) {
1523: nexti = jl[i]; /* next row to be added to k_th row */
1524: /* compute multiplier, update D(k) and U(i,k) */
1525: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
1526: uikdi = -ba[ili]*ba[bi[i]];
1527: dk += uikdi*ba[ili];
1528: ba[ili] = uikdi; /* -U(i,k) */
1530: /* add multiple of row i to k-th row ... */
1531: jmin = ili + 1;
1532: nz = bi[i+1] - jmin;
1533: if (nz > 0) {
1534: bcol = bj + jmin;
1535: bval = ba + jmin;
1536: PetscLogFlops(2.0*nz);
1537: while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
1539: /* update il and jl for i-th row */
1540: il[i] = jmin;
1541: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
1542: }
1543: i = nexti;
1544: }
1546: /* shift the diagonals when zero pivot is detected */
1547: /* compute rs=sum of abs(off-diagonal) */
1548: rs = 0.0;
1549: jmin = bi[k]+1;
1550: nz = bi[k+1] - jmin;
1551: if (nz) {
1552: bcol = bj + jmin;
1553: while (nz--) {
1554: rs += PetscAbsScalar(rtmp[*bcol]);
1555: bcol++;
1556: }
1557: }
1559: sctx.rs = rs;
1560: sctx.pv = dk;
1561: MatPivotCheck(A,info,&sctx,k);
1562: if (sctx.newshift) break; /* sctx.shift_amount is updated */
1563: dk = sctx.pv;
1565: /* copy data into U(k,:) */
1566: ba[bi[k]] = 1.0/dk;
1567: jmin = bi[k]+1;
1568: nz = bi[k+1] - jmin;
1569: if (nz) {
1570: bcol = bj + jmin;
1571: bval = ba + jmin;
1572: while (nz--) {
1573: *bval++ = rtmp[*bcol];
1574: rtmp[*bcol++] = 0.0;
1575: }
1576: /* add k-th row into il and jl */
1577: il[k] = jmin;
1578: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
1579: }
1580: } /* end of for (k = 0; k<mbs; k++) */
1581: } while (sctx.newshift);
1582: PetscFree(rtmp);
1583: PetscFree2(il,jl);
1585: C->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1586: C->ops->solves = MatSolves_SeqSBAIJ_1_inplace;
1587: C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1588: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1589: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1591: C->assembled = PETSC_TRUE;
1592: C->preallocated = PETSC_TRUE;
1594: PetscLogFlops(C->rmap->N);
1595: if (sctx.nshift) {
1596: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1597: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1598: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1599: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
1600: }
1601: }
1602: return(0);
1603: }
1607: PetscErrorCode MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,const MatFactorInfo *info)
1608: {
1610: Mat C;
1613: MatGetFactor(A,"petsc",MAT_FACTOR_CHOLESKY,&C);
1614: MatCholeskyFactorSymbolic(C,A,perm,info);
1615: MatCholeskyFactorNumeric(C,A,info);
1617: A->ops->solve = C->ops->solve;
1618: A->ops->solvetranspose = C->ops->solvetranspose;
1620: MatHeaderMerge(A,C);
1621: return(0);
1622: }