Actual source code: baijfact.c
petsc-3.13.6 2020-09-29
2: /*
3: Factorization code for BAIJ format.
4: */
5: #include <../src/mat/impls/baij/seq/baij.h>
6: #include <petsc/private/kernels/blockinvert.h>
8: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo *info)
9: {
10: Mat C =B;
11: Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
12: IS isrow = b->row,isicol = b->icol;
14: const PetscInt *r,*ic;
15: PetscInt i,j,k,nz,nzL,row,*pj;
16: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
17: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
18: MatScalar *rtmp,*pc,*mwork,*pv;
19: MatScalar *aa=a->a,*v;
20: PetscInt flg;
21: PetscReal shift = info->shiftamount;
22: PetscBool allowzeropivot,zeropivotdetected;
25: ISGetIndices(isrow,&r);
26: ISGetIndices(isicol,&ic);
27: allowzeropivot = PetscNot(A->erroriffailure);
29: /* generate work space needed by the factorization */
30: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
31: PetscArrayzero(rtmp,bs2*n);
33: for (i=0; i<n; i++) {
34: /* zero rtmp */
35: /* L part */
36: nz = bi[i+1] - bi[i];
37: bjtmp = bj + bi[i];
38: for (j=0; j<nz; j++) {
39: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
40: }
42: /* U part */
43: nz = bdiag[i] - bdiag[i+1];
44: bjtmp = bj + bdiag[i+1]+1;
45: for (j=0; j<nz; j++) {
46: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
47: }
49: /* load in initial (unfactored row) */
50: nz = ai[r[i]+1] - ai[r[i]];
51: ajtmp = aj + ai[r[i]];
52: v = aa + bs2*ai[r[i]];
53: for (j=0; j<nz; j++) {
54: PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
55: }
57: /* elimination */
58: bjtmp = bj + bi[i];
59: nzL = bi[i+1] - bi[i];
60: for (k=0; k < nzL; k++) {
61: row = bjtmp[k];
62: pc = rtmp + bs2*row;
63: for (flg=0,j=0; j<bs2; j++) {
64: if (pc[j] != (PetscScalar)0.0) {
65: flg = 1;
66: break;
67: }
68: }
69: if (flg) {
70: pv = b->a + bs2*bdiag[row];
71: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
72: PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);
74: pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
75: pv = b->a + bs2*(bdiag[row+1]+1);
76: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
77: for (j=0; j<nz; j++) {
78: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
79: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
80: v = rtmp + 4*pj[j];
81: PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
82: pv += 4;
83: }
84: PetscLogFlops(16.0*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
85: }
86: }
88: /* finished row so stick it into b->a */
89: /* L part */
90: pv = b->a + bs2*bi[i];
91: pj = b->j + bi[i];
92: nz = bi[i+1] - bi[i];
93: for (j=0; j<nz; j++) {
94: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
95: }
97: /* Mark diagonal and invert diagonal for simplier triangular solves */
98: pv = b->a + bs2*bdiag[i];
99: pj = b->j + bdiag[i];
100: PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
101: PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
102: if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
104: /* U part */
105: pv = b->a + bs2*(bdiag[i+1]+1);
106: pj = b->j + bdiag[i+1]+1;
107: nz = bdiag[i] - bdiag[i+1] - 1;
108: for (j=0; j<nz; j++) {
109: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
110: }
111: }
113: PetscFree2(rtmp,mwork);
114: ISRestoreIndices(isicol,&ic);
115: ISRestoreIndices(isrow,&r);
117: C->ops->solve = MatSolve_SeqBAIJ_2;
118: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2;
119: C->assembled = PETSC_TRUE;
121: PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
122: return(0);
123: }
125: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
126: {
127: Mat C =B;
128: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
130: PetscInt i,j,k,nz,nzL,row,*pj;
131: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
132: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
133: MatScalar *rtmp,*pc,*mwork,*pv;
134: MatScalar *aa=a->a,*v;
135: PetscInt flg;
136: PetscReal shift = info->shiftamount;
137: PetscBool allowzeropivot,zeropivotdetected;
140: allowzeropivot = PetscNot(A->erroriffailure);
142: /* generate work space needed by the factorization */
143: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
144: PetscArrayzero(rtmp,bs2*n);
146: for (i=0; i<n; i++) {
147: /* zero rtmp */
148: /* L part */
149: nz = bi[i+1] - bi[i];
150: bjtmp = bj + bi[i];
151: for (j=0; j<nz; j++) {
152: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
153: }
155: /* U part */
156: nz = bdiag[i] - bdiag[i+1];
157: bjtmp = bj + bdiag[i+1]+1;
158: for (j=0; j<nz; j++) {
159: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
160: }
162: /* load in initial (unfactored row) */
163: nz = ai[i+1] - ai[i];
164: ajtmp = aj + ai[i];
165: v = aa + bs2*ai[i];
166: for (j=0; j<nz; j++) {
167: PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
168: }
170: /* elimination */
171: bjtmp = bj + bi[i];
172: nzL = bi[i+1] - bi[i];
173: for (k=0; k < nzL; k++) {
174: row = bjtmp[k];
175: pc = rtmp + bs2*row;
176: for (flg=0,j=0; j<bs2; j++) {
177: if (pc[j]!=(PetscScalar)0.0) {
178: flg = 1;
179: break;
180: }
181: }
182: if (flg) {
183: pv = b->a + bs2*bdiag[row];
184: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
185: PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);
187: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
188: pv = b->a + bs2*(bdiag[row+1]+1);
189: nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
190: for (j=0; j<nz; j++) {
191: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
192: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
193: v = rtmp + 4*pj[j];
194: PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
195: pv += 4;
196: }
197: PetscLogFlops(16.0*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
198: }
199: }
201: /* finished row so stick it into b->a */
202: /* L part */
203: pv = b->a + bs2*bi[i];
204: pj = b->j + bi[i];
205: nz = bi[i+1] - bi[i];
206: for (j=0; j<nz; j++) {
207: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
208: }
210: /* Mark diagonal and invert diagonal for simplier triangular solves */
211: pv = b->a + bs2*bdiag[i];
212: pj = b->j + bdiag[i];
213: PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
214: PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
215: if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
217: /* U part */
218: /*
219: pv = b->a + bs2*bi[2*n-i];
220: pj = b->j + bi[2*n-i];
221: nz = bi[2*n-i+1] - bi[2*n-i] - 1;
222: */
223: pv = b->a + bs2*(bdiag[i+1]+1);
224: pj = b->j + bdiag[i+1]+1;
225: nz = bdiag[i] - bdiag[i+1] - 1;
226: for (j=0; j<nz; j++) {
227: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
228: }
229: }
230: PetscFree2(rtmp,mwork);
232: C->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering;
233: C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_2_NaturalOrdering;
234: C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_2_NaturalOrdering;
235: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering;
236: C->assembled = PETSC_TRUE;
238: PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
239: return(0);
240: }
242: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info)
243: {
244: Mat C = B;
245: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
246: IS isrow = b->row,isicol = b->icol;
248: const PetscInt *r,*ic;
249: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
250: PetscInt *ajtmpold,*ajtmp,nz,row;
251: PetscInt *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
252: MatScalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
253: MatScalar p1,p2,p3,p4;
254: MatScalar *ba = b->a,*aa = a->a;
255: PetscReal shift = info->shiftamount;
256: PetscBool allowzeropivot,zeropivotdetected;
259: allowzeropivot = PetscNot(A->erroriffailure);
260: ISGetIndices(isrow,&r);
261: ISGetIndices(isicol,&ic);
262: PetscMalloc1(4*(n+1),&rtmp);
264: for (i=0; i<n; i++) {
265: nz = bi[i+1] - bi[i];
266: ajtmp = bj + bi[i];
267: for (j=0; j<nz; j++) {
268: x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
269: }
270: /* load in initial (unfactored row) */
271: idx = r[i];
272: nz = ai[idx+1] - ai[idx];
273: ajtmpold = aj + ai[idx];
274: v = aa + 4*ai[idx];
275: for (j=0; j<nz; j++) {
276: x = rtmp+4*ic[ajtmpold[j]];
277: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
278: v += 4;
279: }
280: row = *ajtmp++;
281: while (row < i) {
282: pc = rtmp + 4*row;
283: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
284: if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
285: pv = ba + 4*diag_offset[row];
286: pj = bj + diag_offset[row] + 1;
287: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
288: pc[0] = m1 = p1*x1 + p3*x2;
289: pc[1] = m2 = p2*x1 + p4*x2;
290: pc[2] = m3 = p1*x3 + p3*x4;
291: pc[3] = m4 = p2*x3 + p4*x4;
292: nz = bi[row+1] - diag_offset[row] - 1;
293: pv += 4;
294: for (j=0; j<nz; j++) {
295: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
296: x = rtmp + 4*pj[j];
297: x[0] -= m1*x1 + m3*x2;
298: x[1] -= m2*x1 + m4*x2;
299: x[2] -= m1*x3 + m3*x4;
300: x[3] -= m2*x3 + m4*x4;
301: pv += 4;
302: }
303: PetscLogFlops(16.0*nz+12.0);
304: }
305: row = *ajtmp++;
306: }
307: /* finished row so stick it into b->a */
308: pv = ba + 4*bi[i];
309: pj = bj + bi[i];
310: nz = bi[i+1] - bi[i];
311: for (j=0; j<nz; j++) {
312: x = rtmp+4*pj[j];
313: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
314: pv += 4;
315: }
316: /* invert diagonal block */
317: w = ba + 4*diag_offset[i];
318: PetscKernel_A_gets_inverse_A_2(w,shift,allowzeropivot,&zeropivotdetected);
319: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
320: }
322: PetscFree(rtmp);
323: ISRestoreIndices(isicol,&ic);
324: ISRestoreIndices(isrow,&r);
326: C->ops->solve = MatSolve_SeqBAIJ_2_inplace;
327: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
328: C->assembled = PETSC_TRUE;
330: PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
331: return(0);
332: }
333: /*
334: Version for when blocks are 2 by 2 Using natural ordering
335: */
336: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
337: {
338: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
340: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
341: PetscInt *ajtmpold,*ajtmp,nz,row;
342: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
343: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
344: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
345: MatScalar *ba = b->a,*aa = a->a;
346: PetscReal shift = info->shiftamount;
347: PetscBool allowzeropivot,zeropivotdetected;
350: allowzeropivot = PetscNot(A->erroriffailure);
351: PetscMalloc1(4*(n+1),&rtmp);
352: for (i=0; i<n; i++) {
353: nz = bi[i+1] - bi[i];
354: ajtmp = bj + bi[i];
355: for (j=0; j<nz; j++) {
356: x = rtmp+4*ajtmp[j];
357: x[0] = x[1] = x[2] = x[3] = 0.0;
358: }
359: /* load in initial (unfactored row) */
360: nz = ai[i+1] - ai[i];
361: ajtmpold = aj + ai[i];
362: v = aa + 4*ai[i];
363: for (j=0; j<nz; j++) {
364: x = rtmp+4*ajtmpold[j];
365: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
366: v += 4;
367: }
368: row = *ajtmp++;
369: while (row < i) {
370: pc = rtmp + 4*row;
371: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
372: if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
373: pv = ba + 4*diag_offset[row];
374: pj = bj + diag_offset[row] + 1;
375: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
376: pc[0] = m1 = p1*x1 + p3*x2;
377: pc[1] = m2 = p2*x1 + p4*x2;
378: pc[2] = m3 = p1*x3 + p3*x4;
379: pc[3] = m4 = p2*x3 + p4*x4;
380: nz = bi[row+1] - diag_offset[row] - 1;
381: pv += 4;
382: for (j=0; j<nz; j++) {
383: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
384: x = rtmp + 4*pj[j];
385: x[0] -= m1*x1 + m3*x2;
386: x[1] -= m2*x1 + m4*x2;
387: x[2] -= m1*x3 + m3*x4;
388: x[3] -= m2*x3 + m4*x4;
389: pv += 4;
390: }
391: PetscLogFlops(16.0*nz+12.0);
392: }
393: row = *ajtmp++;
394: }
395: /* finished row so stick it into b->a */
396: pv = ba + 4*bi[i];
397: pj = bj + bi[i];
398: nz = bi[i+1] - bi[i];
399: for (j=0; j<nz; j++) {
400: x = rtmp+4*pj[j];
401: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
402: /*
403: printf(" col %d:",pj[j]);
404: PetscInt j1;
405: for (j1=0; j1<4; j1++) printf(" %g,",*(pv+j1));
406: printf("\n");
407: */
408: pv += 4;
409: }
410: /* invert diagonal block */
411: w = ba + 4*diag_offset[i];
412: PetscKernel_A_gets_inverse_A_2(w,shift, allowzeropivot,&zeropivotdetected);
413: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
414: }
416: PetscFree(rtmp);
418: C->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
419: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
420: C->assembled = PETSC_TRUE;
422: PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
423: return(0);
424: }
426: /* ----------------------------------------------------------- */
427: /*
428: Version for when blocks are 1 by 1.
429: */
430: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info)
431: {
432: Mat C =B;
433: Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
434: IS isrow = b->row,isicol = b->icol;
435: PetscErrorCode ierr;
436: const PetscInt *r,*ic,*ics;
437: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
438: PetscInt i,j,k,nz,nzL,row,*pj;
439: const PetscInt *ajtmp,*bjtmp;
440: MatScalar *rtmp,*pc,multiplier,*pv;
441: const MatScalar *aa=a->a,*v;
442: PetscBool row_identity,col_identity;
443: FactorShiftCtx sctx;
444: const PetscInt *ddiag;
445: PetscReal rs;
446: MatScalar d;
449: /* MatPivotSetUp(): initialize shift context sctx */
450: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
452: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
453: ddiag = a->diag;
454: sctx.shift_top = info->zeropivot;
455: for (i=0; i<n; i++) {
456: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
457: d = (aa)[ddiag[i]];
458: rs = -PetscAbsScalar(d) - PetscRealPart(d);
459: v = aa+ai[i];
460: nz = ai[i+1] - ai[i];
461: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
462: if (rs>sctx.shift_top) sctx.shift_top = rs;
463: }
464: sctx.shift_top *= 1.1;
465: sctx.nshift_max = 5;
466: sctx.shift_lo = 0.;
467: sctx.shift_hi = 1.;
468: }
470: ISGetIndices(isrow,&r);
471: ISGetIndices(isicol,&ic);
472: PetscMalloc1(n+1,&rtmp);
473: ics = ic;
475: do {
476: sctx.newshift = PETSC_FALSE;
477: for (i=0; i<n; i++) {
478: /* zero rtmp */
479: /* L part */
480: nz = bi[i+1] - bi[i];
481: bjtmp = bj + bi[i];
482: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
484: /* U part */
485: nz = bdiag[i]-bdiag[i+1];
486: bjtmp = bj + bdiag[i+1]+1;
487: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
489: /* load in initial (unfactored row) */
490: nz = ai[r[i]+1] - ai[r[i]];
491: ajtmp = aj + ai[r[i]];
492: v = aa + ai[r[i]];
493: for (j=0; j<nz; j++) rtmp[ics[ajtmp[j]]] = v[j];
495: /* ZeropivotApply() */
496: rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */
498: /* elimination */
499: bjtmp = bj + bi[i];
500: row = *bjtmp++;
501: nzL = bi[i+1] - bi[i];
502: for (k=0; k < nzL; k++) {
503: pc = rtmp + row;
504: if (*pc != (PetscScalar)0.0) {
505: pv = b->a + bdiag[row];
506: multiplier = *pc * (*pv);
507: *pc = multiplier;
509: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
510: pv = b->a + bdiag[row+1]+1;
511: nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
512: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
513: PetscLogFlops(2.0*nz);
514: }
515: row = *bjtmp++;
516: }
518: /* finished row so stick it into b->a */
519: rs = 0.0;
520: /* L part */
521: pv = b->a + bi[i];
522: pj = b->j + bi[i];
523: nz = bi[i+1] - bi[i];
524: for (j=0; j<nz; j++) {
525: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
526: }
528: /* U part */
529: pv = b->a + bdiag[i+1]+1;
530: pj = b->j + bdiag[i+1]+1;
531: nz = bdiag[i] - bdiag[i+1]-1;
532: for (j=0; j<nz; j++) {
533: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
534: }
536: sctx.rs = rs;
537: sctx.pv = rtmp[i];
538: MatPivotCheck(B,A,info,&sctx,i);
539: if (sctx.newshift) break; /* break for-loop */
540: rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */
542: /* Mark diagonal and invert diagonal for simplier triangular solves */
543: pv = b->a + bdiag[i];
544: *pv = (PetscScalar)1.0/rtmp[i];
546: } /* endof for (i=0; i<n; i++) { */
548: /* MatPivotRefine() */
549: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
550: /*
551: * if no shift in this attempt & shifting & started shifting & can refine,
552: * then try lower shift
553: */
554: sctx.shift_hi = sctx.shift_fraction;
555: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
556: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
557: sctx.newshift = PETSC_TRUE;
558: sctx.nshift++;
559: }
560: } while (sctx.newshift);
562: PetscFree(rtmp);
563: ISRestoreIndices(isicol,&ic);
564: ISRestoreIndices(isrow,&r);
566: ISIdentity(isrow,&row_identity);
567: ISIdentity(isicol,&col_identity);
568: if (row_identity && col_identity) {
569: C->ops->solve = MatSolve_SeqBAIJ_1_NaturalOrdering;
570: C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_1_NaturalOrdering;
571: C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_1_NaturalOrdering;
572: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering;
573: } else {
574: C->ops->solve = MatSolve_SeqBAIJ_1;
575: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1;
576: }
577: C->assembled = PETSC_TRUE;
578: PetscLogFlops(C->cmap->n);
580: /* MatShiftView(A,info,&sctx) */
581: if (sctx.nshift) {
582: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
583: 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);
584: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
585: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
586: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
587: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
588: }
589: }
590: return(0);
591: }
593: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
594: {
595: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
596: IS isrow = b->row,isicol = b->icol;
598: const PetscInt *r,*ic;
599: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
600: PetscInt *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j;
601: PetscInt *diag_offset = b->diag,diag,*pj;
602: MatScalar *pv,*v,*rtmp,multiplier,*pc;
603: MatScalar *ba = b->a,*aa = a->a;
604: PetscBool row_identity, col_identity;
607: ISGetIndices(isrow,&r);
608: ISGetIndices(isicol,&ic);
609: PetscMalloc1(n+1,&rtmp);
611: for (i=0; i<n; i++) {
612: nz = bi[i+1] - bi[i];
613: ajtmp = bj + bi[i];
614: for (j=0; j<nz; j++) rtmp[ajtmp[j]] = 0.0;
616: /* load in initial (unfactored row) */
617: nz = ai[r[i]+1] - ai[r[i]];
618: ajtmpold = aj + ai[r[i]];
619: v = aa + ai[r[i]];
620: for (j=0; j<nz; j++) rtmp[ic[ajtmpold[j]]] = v[j];
622: row = *ajtmp++;
623: while (row < i) {
624: pc = rtmp + row;
625: if (*pc != 0.0) {
626: pv = ba + diag_offset[row];
627: pj = bj + diag_offset[row] + 1;
628: multiplier = *pc * *pv++;
629: *pc = multiplier;
630: nz = bi[row+1] - diag_offset[row] - 1;
631: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
632: PetscLogFlops(1.0+2.0*nz);
633: }
634: row = *ajtmp++;
635: }
636: /* finished row so stick it into b->a */
637: pv = ba + bi[i];
638: pj = bj + bi[i];
639: nz = bi[i+1] - bi[i];
640: for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
641: diag = diag_offset[i] - bi[i];
642: /* check pivot entry for current row */
643: if (pv[diag] == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot: row in original ordering %D in permuted ordering %D",r[i],i);
644: pv[diag] = 1.0/pv[diag];
645: }
647: PetscFree(rtmp);
648: ISRestoreIndices(isicol,&ic);
649: ISRestoreIndices(isrow,&r);
650: ISIdentity(isrow,&row_identity);
651: ISIdentity(isicol,&col_identity);
652: if (row_identity && col_identity) {
653: C->ops->solve = MatSolve_SeqBAIJ_1_NaturalOrdering_inplace;
654: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace;
655: } else {
656: C->ops->solve = MatSolve_SeqBAIJ_1_inplace;
657: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_inplace;
658: }
659: C->assembled = PETSC_TRUE;
660: PetscLogFlops(C->cmap->n);
661: return(0);
662: }
664: PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
665: {
666: PetscInt n = A->rmap->n;
670: #if defined(PETSC_USE_COMPLEX)
671: if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported");
672: #endif
673: MatCreate(PetscObjectComm((PetscObject)A),B);
674: MatSetSizes(*B,n,n,n,n);
675: if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
676: MatSetType(*B,MATSEQBAIJ);
678: (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqBAIJ;
679: (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ;
680: } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
681: MatSetType(*B,MATSEQSBAIJ);
682: MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,NULL);
684: (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqBAIJ;
685: (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqBAIJ;
686: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
687: (*B)->factortype = ftype;
689: PetscFree((*B)->solvertype);
690: PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);
691: return(0);
692: }
694: /* ----------------------------------------------------------- */
695: PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
696: {
698: Mat C;
701: MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);
702: MatLUFactorSymbolic(C,A,row,col,info);
703: MatLUFactorNumeric(C,A,info);
705: A->ops->solve = C->ops->solve;
706: A->ops->solvetranspose = C->ops->solvetranspose;
708: MatHeaderMerge(A,&C);
709: PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqBAIJ*)(A->data))->icol);
710: return(0);
711: }
713: #include <../src/mat/impls/sbaij/seq/sbaij.h>
714: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
715: {
717: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
718: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
719: IS ip=b->row;
720: const PetscInt *rip;
721: PetscInt i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol;
722: PetscInt *ai=a->i,*aj=a->j;
723: PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
724: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
725: PetscReal rs;
726: FactorShiftCtx sctx;
729: if (bs > 1) { /* convert A to a SBAIJ matrix and apply Cholesky factorization from it */
730: if (!a->sbaijMat) {
731: MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
732: }
733: (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);
734: MatDestroy(&a->sbaijMat);
735: return(0);
736: }
738: /* MatPivotSetUp(): initialize shift context sctx */
739: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
741: ISGetIndices(ip,&rip);
742: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);
744: sctx.shift_amount = 0.;
745: sctx.nshift = 0;
746: do {
747: sctx.newshift = PETSC_FALSE;
748: for (i=0; i<mbs; i++) {
749: rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
750: }
752: for (k = 0; k<mbs; k++) {
753: bval = ba + bi[k];
754: /* initialize k-th row by the perm[k]-th row of A */
755: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
756: for (j = jmin; j < jmax; j++) {
757: col = rip[aj[j]];
758: if (col >= k) { /* only take upper triangular entry */
759: rtmp[col] = aa[j];
760: *bval++ = 0.0; /* for in-place factorization */
761: }
762: }
764: /* shift the diagonal of the matrix */
765: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
767: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
768: dk = rtmp[k];
769: i = jl[k]; /* first row to be added to k_th row */
771: while (i < k) {
772: nexti = jl[i]; /* next row to be added to k_th row */
774: /* compute multiplier, update diag(k) and U(i,k) */
775: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
776: uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
777: dk += uikdi*ba[ili];
778: ba[ili] = uikdi; /* -U(i,k) */
780: /* add multiple of row i to k-th row */
781: jmin = ili + 1; jmax = bi[i+1];
782: if (jmin < jmax) {
783: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
784: /* update il and jl for row i */
785: il[i] = jmin;
786: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
787: }
788: i = nexti;
789: }
791: /* shift the diagonals when zero pivot is detected */
792: /* compute rs=sum of abs(off-diagonal) */
793: rs = 0.0;
794: jmin = bi[k]+1;
795: nz = bi[k+1] - jmin;
796: if (nz) {
797: bcol = bj + jmin;
798: while (nz--) {
799: rs += PetscAbsScalar(rtmp[*bcol]);
800: bcol++;
801: }
802: }
804: sctx.rs = rs;
805: sctx.pv = dk;
806: MatPivotCheck(C,A,info,&sctx,k);
807: if (sctx.newshift) break;
808: dk = sctx.pv;
810: /* copy data into U(k,:) */
811: ba[bi[k]] = 1.0/dk; /* U(k,k) */
812: jmin = bi[k]+1; jmax = bi[k+1];
813: if (jmin < jmax) {
814: for (j=jmin; j<jmax; j++) {
815: col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
816: }
817: /* add the k-th row into il and jl */
818: il[k] = jmin;
819: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
820: }
821: }
822: } while (sctx.newshift);
823: PetscFree3(rtmp,il,jl);
825: ISRestoreIndices(ip,&rip);
827: C->assembled = PETSC_TRUE;
828: C->preallocated = PETSC_TRUE;
830: PetscLogFlops(C->rmap->N);
831: if (sctx.nshift) {
832: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
833: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
834: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
835: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
836: }
837: }
838: return(0);
839: }
841: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
842: {
843: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
844: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
846: PetscInt i,j,am=a->mbs;
847: PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
848: PetscInt k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
849: MatScalar *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
850: PetscReal rs;
851: FactorShiftCtx sctx;
854: /* MatPivotSetUp(): initialize shift context sctx */
855: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
857: PetscMalloc3(am,&rtmp,am,&il,am,&jl);
859: do {
860: sctx.newshift = PETSC_FALSE;
861: for (i=0; i<am; i++) {
862: rtmp[i] = 0.0; jl[i] = am; il[0] = 0;
863: }
865: for (k = 0; k<am; k++) {
866: /* initialize k-th row with elements nonzero in row perm(k) of A */
867: nz = ai[k+1] - ai[k];
868: acol = aj + ai[k];
869: aval = aa + ai[k];
870: bval = ba + bi[k];
871: while (nz--) {
872: if (*acol < k) { /* skip lower triangular entries */
873: acol++; aval++;
874: } else {
875: rtmp[*acol++] = *aval++;
876: *bval++ = 0.0; /* for in-place factorization */
877: }
878: }
880: /* shift the diagonal of the matrix */
881: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
883: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
884: dk = rtmp[k];
885: i = jl[k]; /* first row to be added to k_th row */
887: while (i < k) {
888: nexti = jl[i]; /* next row to be added to k_th row */
889: /* compute multiplier, update D(k) and U(i,k) */
890: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
891: uikdi = -ba[ili]*ba[bi[i]];
892: dk += uikdi*ba[ili];
893: ba[ili] = uikdi; /* -U(i,k) */
895: /* add multiple of row i to k-th row ... */
896: jmin = ili + 1;
897: nz = bi[i+1] - jmin;
898: if (nz > 0) {
899: bcol = bj + jmin;
900: bval = ba + jmin;
901: while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
902: /* update il and jl for i-th row */
903: il[i] = jmin;
904: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
905: }
906: i = nexti;
907: }
909: /* shift the diagonals when zero pivot is detected */
910: /* compute rs=sum of abs(off-diagonal) */
911: rs = 0.0;
912: jmin = bi[k]+1;
913: nz = bi[k+1] - jmin;
914: if (nz) {
915: bcol = bj + jmin;
916: while (nz--) {
917: rs += PetscAbsScalar(rtmp[*bcol]);
918: bcol++;
919: }
920: }
922: sctx.rs = rs;
923: sctx.pv = dk;
924: MatPivotCheck(C,A,info,&sctx,k);
925: if (sctx.newshift) break; /* sctx.shift_amount is updated */
926: dk = sctx.pv;
928: /* copy data into U(k,:) */
929: ba[bi[k]] = 1.0/dk;
930: jmin = bi[k]+1;
931: nz = bi[k+1] - jmin;
932: if (nz) {
933: bcol = bj + jmin;
934: bval = ba + jmin;
935: while (nz--) {
936: *bval++ = rtmp[*bcol];
937: rtmp[*bcol++] = 0.0;
938: }
939: /* add k-th row into il and jl */
940: il[k] = jmin;
941: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
942: }
943: }
944: } while (sctx.newshift);
945: PetscFree3(rtmp,il,jl);
947: C->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
948: C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
949: C->assembled = PETSC_TRUE;
950: C->preallocated = PETSC_TRUE;
952: PetscLogFlops(C->rmap->N);
953: if (sctx.nshift) {
954: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
955: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
956: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
957: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
958: }
959: }
960: return(0);
961: }
963: #include <petscbt.h>
964: #include <../src/mat/utils/freespace.h>
965: PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
966: {
967: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
968: Mat_SeqSBAIJ *b;
969: Mat B;
970: PetscErrorCode ierr;
971: PetscBool perm_identity,missing;
972: PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui;
973: const PetscInt *rip;
974: PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
975: PetscInt nlnk,*lnk,*lnk_lvl=NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr;
976: PetscReal fill =info->fill,levels=info->levels;
977: PetscFreeSpaceList free_space =NULL,current_space=NULL;
978: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
979: PetscBT lnkbt;
982: MatMissingDiagonal(A,&missing,&i);
983: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
985: if (bs > 1) {
986: if (!a->sbaijMat) {
987: MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
988: }
989: (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */
991: MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);
992: return(0);
993: }
995: ISIdentity(perm,&perm_identity);
996: ISGetIndices(perm,&rip);
998: /* special case that simply copies fill pattern */
999: if (!levels && perm_identity) {
1000: PetscMalloc1(am+1,&ui);
1001: for (i=0; i<am; i++) ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */
1002: B = fact;
1003: MatSeqSBAIJSetPreallocation(B,1,0,ui);
1006: b = (Mat_SeqSBAIJ*)B->data;
1007: uj = b->j;
1008: for (i=0; i<am; i++) {
1009: aj = a->j + a->diag[i];
1010: for (j=0; j<ui[i]; j++) *uj++ = *aj++;
1011: b->ilen[i] = ui[i];
1012: }
1013: PetscFree(ui);
1015: B->factortype = MAT_FACTOR_NONE;
1017: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1018: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1019: B->factortype = MAT_FACTOR_ICC;
1021: B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1022: return(0);
1023: }
1025: /* initialization */
1026: PetscMalloc1(am+1,&ui);
1027: ui[0] = 0;
1028: PetscMalloc1(2*am+1,&cols_lvl);
1030: /* jl: linked list for storing indices of the pivot rows
1031: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1032: PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);
1033: for (i=0; i<am; i++) {
1034: jl[i] = am; il[i] = 0;
1035: }
1037: /* create and initialize a linked list for storing column indices of the active row k */
1038: nlnk = am + 1;
1039: PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);
1041: /* initial FreeSpace size is fill*(ai[am]+am)/2 */
1042: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);
1044: current_space = free_space;
1046: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);
1047: current_space_lvl = free_space_lvl;
1049: for (k=0; k<am; k++) { /* for each active row k */
1050: /* initialize lnk by the column indices of row rip[k] of A */
1051: nzk = 0;
1052: ncols = ai[rip[k]+1] - ai[rip[k]];
1053: ncols_upper = 0;
1054: cols = cols_lvl + am;
1055: for (j=0; j<ncols; j++) {
1056: i = rip[*(aj + ai[rip[k]] + j)];
1057: if (i >= k) { /* only take upper triangular entry */
1058: cols[ncols_upper] = i;
1059: cols_lvl[ncols_upper] = -1; /* initialize level for nonzero entries */
1060: ncols_upper++;
1061: }
1062: }
1063: PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
1064: nzk += nlnk;
1066: /* update lnk by computing fill-in for each pivot row to be merged in */
1067: prow = jl[k]; /* 1st pivot row */
1069: while (prow < k) {
1070: nextprow = jl[prow];
1072: /* merge prow into k-th row */
1073: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
1074: jmax = ui[prow+1];
1075: ncols = jmax-jmin;
1076: i = jmin - ui[prow];
1077: cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
1078: for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
1079: PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
1080: nzk += nlnk;
1082: /* update il and jl for prow */
1083: if (jmin < jmax) {
1084: il[prow] = jmin;
1086: j = *cols; jl[prow] = jl[j]; jl[j] = prow;
1087: }
1088: prow = nextprow;
1089: }
1091: /* if free space is not available, make more free space */
1092: if (current_space->local_remaining<nzk) {
1093: i = am - k + 1; /* num of unfactored rows */
1094: i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1095: PetscFreeSpaceGet(i,¤t_space);
1096: PetscFreeSpaceGet(i,¤t_space_lvl);
1097: reallocs++;
1098: }
1100: /* copy data into free_space and free_space_lvl, then initialize lnk */
1101: PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
1103: /* add the k-th row into il and jl */
1104: if (nzk-1 > 0) {
1105: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
1106: jl[k] = jl[i]; jl[i] = k;
1107: il[k] = ui[k] + 1;
1108: }
1109: uj_ptr[k] = current_space->array;
1110: uj_lvl_ptr[k] = current_space_lvl->array;
1112: current_space->array += nzk;
1113: current_space->local_used += nzk;
1114: current_space->local_remaining -= nzk;
1116: current_space_lvl->array += nzk;
1117: current_space_lvl->local_used += nzk;
1118: current_space_lvl->local_remaining -= nzk;
1120: ui[k+1] = ui[k] + nzk;
1121: }
1123: ISRestoreIndices(perm,&rip);
1124: PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);
1125: PetscFree(cols_lvl);
1127: /* copy free_space into uj and free free_space; set uj in new datastructure; */
1128: PetscMalloc1(ui[am]+1,&uj);
1129: PetscFreeSpaceContiguous(&free_space,uj);
1130: PetscIncompleteLLDestroy(lnk,lnkbt);
1131: PetscFreeSpaceDestroy(free_space_lvl);
1133: /* put together the new matrix in MATSEQSBAIJ format */
1134: B = fact;
1135: MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);
1137: b = (Mat_SeqSBAIJ*)B->data;
1138: b->singlemalloc = PETSC_FALSE;
1139: b->free_a = PETSC_TRUE;
1140: b->free_ij = PETSC_TRUE;
1142: PetscMalloc1(ui[am]+1,&b->a);
1144: b->j = uj;
1145: b->i = ui;
1146: b->diag = 0;
1147: b->ilen = 0;
1148: b->imax = 0;
1149: b->row = perm;
1150: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1152: PetscObjectReference((PetscObject)perm);
1154: b->icol = perm;
1156: PetscObjectReference((PetscObject)perm);
1157: PetscMalloc1(am+1,&b->solve_work);
1158: PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));
1160: b->maxnz = b->nz = ui[am];
1162: B->info.factor_mallocs = reallocs;
1163: B->info.fill_ratio_given = fill;
1164: if (ai[am] != 0.) {
1165: /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
1166: B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
1167: } else {
1168: B->info.fill_ratio_needed = 0.0;
1169: }
1170: #if defined(PETSC_USE_INFO)
1171: if (ai[am] != 0) {
1172: PetscReal af = B->info.fill_ratio_needed;
1173: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
1174: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
1175: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
1176: } else {
1177: PetscInfo(A,"Empty matrix\n");
1178: }
1179: #endif
1180: if (perm_identity) {
1181: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1182: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1183: B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1184: } else {
1185: (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1186: }
1187: return(0);
1188: }
1190: PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1191: {
1192: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
1193: Mat_SeqSBAIJ *b;
1194: Mat B;
1195: PetscErrorCode ierr;
1196: PetscBool perm_identity,missing;
1197: PetscReal fill = info->fill;
1198: const PetscInt *rip;
1199: PetscInt i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
1200: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
1201: PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
1202: PetscFreeSpaceList free_space=NULL,current_space=NULL;
1203: PetscBT lnkbt;
1206: if (bs > 1) { /* convert to seqsbaij */
1207: if (!a->sbaijMat) {
1208: MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
1209: }
1210: (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */
1212: MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);
1213: return(0);
1214: }
1216: MatMissingDiagonal(A,&missing,&i);
1217: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1219: /* check whether perm is the identity mapping */
1220: ISIdentity(perm,&perm_identity);
1221: if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
1222: ISGetIndices(perm,&rip);
1224: /* initialization */
1225: PetscMalloc1(mbs+1,&ui);
1226: ui[0] = 0;
1228: /* jl: linked list for storing indices of the pivot rows
1229: il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
1230: PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
1231: for (i=0; i<mbs; i++) {
1232: jl[i] = mbs; il[i] = 0;
1233: }
1235: /* create and initialize a linked list for storing column indices of the active row k */
1236: nlnk = mbs + 1;
1237: PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);
1239: /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
1240: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);
1242: current_space = free_space;
1244: for (k=0; k<mbs; k++) { /* for each active row k */
1245: /* initialize lnk by the column indices of row rip[k] of A */
1246: nzk = 0;
1247: ncols = ai[rip[k]+1] - ai[rip[k]];
1248: ncols_upper = 0;
1249: for (j=0; j<ncols; j++) {
1250: i = rip[*(aj + ai[rip[k]] + j)];
1251: if (i >= k) { /* only take upper triangular entry */
1252: cols[ncols_upper] = i;
1253: ncols_upper++;
1254: }
1255: }
1256: PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);
1257: nzk += nlnk;
1259: /* update lnk by computing fill-in for each pivot row to be merged in */
1260: prow = jl[k]; /* 1st pivot row */
1262: while (prow < k) {
1263: nextprow = jl[prow];
1264: /* merge prow into k-th row */
1265: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
1266: jmax = ui[prow+1];
1267: ncols = jmax-jmin;
1268: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
1269: PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
1270: nzk += nlnk;
1272: /* update il and jl for prow */
1273: if (jmin < jmax) {
1274: il[prow] = jmin;
1275: j = *uj_ptr;
1276: jl[prow] = jl[j];
1277: jl[j] = prow;
1278: }
1279: prow = nextprow;
1280: }
1282: /* if free space is not available, make more free space */
1283: if (current_space->local_remaining<nzk) {
1284: i = mbs - k + 1; /* num of unfactored rows */
1285: i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1286: PetscFreeSpaceGet(i,¤t_space);
1287: reallocs++;
1288: }
1290: /* copy data into free space, then initialize lnk */
1291: PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);
1293: /* add the k-th row into il and jl */
1294: if (nzk-1 > 0) {
1295: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
1296: jl[k] = jl[i]; jl[i] = k;
1297: il[k] = ui[k] + 1;
1298: }
1299: ui_ptr[k] = current_space->array;
1300: current_space->array += nzk;
1301: current_space->local_used += nzk;
1302: current_space->local_remaining -= nzk;
1304: ui[k+1] = ui[k] + nzk;
1305: }
1307: ISRestoreIndices(perm,&rip);
1308: PetscFree4(ui_ptr,il,jl,cols);
1310: /* copy free_space into uj and free free_space; set uj in new datastructure; */
1311: PetscMalloc1(ui[mbs]+1,&uj);
1312: PetscFreeSpaceContiguous(&free_space,uj);
1313: PetscLLDestroy(lnk,lnkbt);
1315: /* put together the new matrix in MATSEQSBAIJ format */
1316: B = fact;
1317: MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);
1319: b = (Mat_SeqSBAIJ*)B->data;
1320: b->singlemalloc = PETSC_FALSE;
1321: b->free_a = PETSC_TRUE;
1322: b->free_ij = PETSC_TRUE;
1324: PetscMalloc1(ui[mbs]+1,&b->a);
1326: b->j = uj;
1327: b->i = ui;
1328: b->diag = 0;
1329: b->ilen = 0;
1330: b->imax = 0;
1331: b->row = perm;
1332: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1334: PetscObjectReference((PetscObject)perm);
1335: b->icol = perm;
1336: PetscObjectReference((PetscObject)perm);
1337: PetscMalloc1(mbs+1,&b->solve_work);
1338: PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
1339: b->maxnz = b->nz = ui[mbs];
1341: B->info.factor_mallocs = reallocs;
1342: B->info.fill_ratio_given = fill;
1343: if (ai[mbs] != 0.) {
1344: /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
1345: B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
1346: } else {
1347: B->info.fill_ratio_needed = 0.0;
1348: }
1349: #if defined(PETSC_USE_INFO)
1350: if (ai[mbs] != 0.) {
1351: PetscReal af = B->info.fill_ratio_needed;
1352: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
1353: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
1354: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
1355: } else {
1356: PetscInfo(A,"Empty matrix\n");
1357: }
1358: #endif
1359: if (perm_identity) {
1360: B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1361: } else {
1362: B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1363: }
1364: return(0);
1365: }
1367: PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
1368: {
1369: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
1370: PetscErrorCode ierr;
1371: const PetscInt *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1372: PetscInt i,k,n=a->mbs;
1373: PetscInt nz,bs=A->rmap->bs,bs2=a->bs2;
1374: const MatScalar *aa=a->a,*v;
1375: PetscScalar *x,*s,*t,*ls;
1376: const PetscScalar *b;
1379: VecGetArrayRead(bb,&b);
1380: VecGetArray(xx,&x);
1381: t = a->solve_work;
1383: /* forward solve the lower triangular */
1384: PetscArraycpy(t,b,bs); /* copy 1st block of b to t */
1386: for (i=1; i<n; i++) {
1387: v = aa + bs2*ai[i];
1388: vi = aj + ai[i];
1389: nz = ai[i+1] - ai[i];
1390: s = t + bs*i;
1391: PetscArraycpy(s,b+bs*i,bs); /* copy i_th block of b to t */
1392: for (k=0;k<nz;k++) {
1393: PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
1394: v += bs2;
1395: }
1396: }
1398: /* backward solve the upper triangular */
1399: ls = a->solve_work + A->cmap->n;
1400: for (i=n-1; i>=0; i--) {
1401: v = aa + bs2*(adiag[i+1]+1);
1402: vi = aj + adiag[i+1]+1;
1403: nz = adiag[i] - adiag[i+1]-1;
1404: PetscArraycpy(ls,t+i*bs,bs);
1405: for (k=0; k<nz; k++) {
1406: PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
1407: v += bs2;
1408: }
1409: PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
1410: PetscArraycpy(x+i*bs,t+i*bs,bs);
1411: }
1413: VecRestoreArrayRead(bb,&b);
1414: VecRestoreArray(xx,&x);
1415: PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
1416: return(0);
1417: }
1419: PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1420: {
1421: Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data;
1422: IS iscol=a->col,isrow=a->row;
1423: PetscErrorCode ierr;
1424: const PetscInt *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1425: PetscInt i,m,n=a->mbs;
1426: PetscInt nz,bs=A->rmap->bs,bs2=a->bs2;
1427: const MatScalar *aa=a->a,*v;
1428: PetscScalar *x,*s,*t,*ls;
1429: const PetscScalar *b;
1432: VecGetArrayRead(bb,&b);
1433: VecGetArray(xx,&x);
1434: t = a->solve_work;
1436: ISGetIndices(isrow,&rout); r = rout;
1437: ISGetIndices(iscol,&cout); c = cout;
1439: /* forward solve the lower triangular */
1440: PetscArraycpy(t,b+bs*r[0],bs);
1441: for (i=1; i<n; i++) {
1442: v = aa + bs2*ai[i];
1443: vi = aj + ai[i];
1444: nz = ai[i+1] - ai[i];
1445: s = t + bs*i;
1446: PetscArraycpy(s,b+bs*r[i],bs);
1447: for (m=0; m<nz; m++) {
1448: PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
1449: v += bs2;
1450: }
1451: }
1453: /* backward solve the upper triangular */
1454: ls = a->solve_work + A->cmap->n;
1455: for (i=n-1; i>=0; i--) {
1456: v = aa + bs2*(adiag[i+1]+1);
1457: vi = aj + adiag[i+1]+1;
1458: nz = adiag[i] - adiag[i+1] - 1;
1459: PetscArraycpy(ls,t+i*bs,bs);
1460: for (m=0; m<nz; m++) {
1461: PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
1462: v += bs2;
1463: }
1464: PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
1465: PetscArraycpy(x + bs*c[i],t+i*bs,bs);
1466: }
1467: ISRestoreIndices(isrow,&rout);
1468: ISRestoreIndices(iscol,&cout);
1469: VecRestoreArrayRead(bb,&b);
1470: VecRestoreArray(xx,&x);
1471: PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
1472: return(0);
1473: }
1475: /*
1476: For each block in an block array saves the largest absolute value in the block into another array
1477: */
1478: static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
1479: {
1481: PetscInt i,j;
1484: PetscArrayzero(absarray,nbs+1);
1485: for (i=0; i<nbs; i++) {
1486: for (j=0; j<bs2; j++) {
1487: if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
1488: }
1489: }
1490: return(0);
1491: }
1493: /*
1494: This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
1495: */
1496: PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
1497: {
1498: Mat B = *fact;
1499: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b;
1500: IS isicol;
1502: const PetscInt *r,*ic;
1503: PetscInt i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
1504: PetscInt *bi,*bj,*bdiag;
1506: PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
1507: PetscInt nlnk,*lnk;
1508: PetscBT lnkbt;
1509: PetscBool row_identity,icol_identity;
1510: MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
1511: PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp;
1513: PetscReal dt=info->dt; /* shift=info->shiftamount; */
1514: PetscInt nnz_max;
1515: PetscBool missing;
1516: PetscReal *vtmp_abs;
1517: MatScalar *v_work;
1518: PetscInt *v_pivots;
1519: PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;
1522: /* ------- symbolic factorization, can be reused ---------*/
1523: MatMissingDiagonal(A,&missing,&i);
1524: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1525: adiag=a->diag;
1527: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1529: /* bdiag is location of diagonal in factor */
1530: PetscMalloc1(mbs+1,&bdiag);
1532: /* allocate row pointers bi */
1533: PetscMalloc1(2*mbs+2,&bi);
1535: /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
1536: dtcount = (PetscInt)info->dtcount;
1537: if (dtcount > mbs-1) dtcount = mbs-1;
1538: nnz_max = ai[mbs]+2*mbs*dtcount +2;
1539: /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
1540: PetscMalloc1(nnz_max,&bj);
1541: nnz_max = nnz_max*bs2;
1542: PetscMalloc1(nnz_max,&ba);
1544: /* put together the new matrix */
1545: MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);
1546: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
1548: b = (Mat_SeqBAIJ*)(B)->data;
1549: b->free_a = PETSC_TRUE;
1550: b->free_ij = PETSC_TRUE;
1551: b->singlemalloc = PETSC_FALSE;
1553: b->a = ba;
1554: b->j = bj;
1555: b->i = bi;
1556: b->diag = bdiag;
1557: b->ilen = 0;
1558: b->imax = 0;
1559: b->row = isrow;
1560: b->col = iscol;
1562: PetscObjectReference((PetscObject)isrow);
1563: PetscObjectReference((PetscObject)iscol);
1565: b->icol = isicol;
1566: PetscMalloc1(bs*(mbs+1),&b->solve_work);
1567: PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
1568: b->maxnz = nnz_max/bs2;
1570: (B)->factortype = MAT_FACTOR_ILUDT;
1571: (B)->info.factor_mallocs = 0;
1572: (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
1573: /* ------- end of symbolic factorization ---------*/
1574: ISGetIndices(isrow,&r);
1575: ISGetIndices(isicol,&ic);
1577: /* linked list for storing column indices of the active row */
1578: nlnk = mbs + 1;
1579: PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);
1581: /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
1582: PetscMalloc2(mbs,&im,mbs,&jtmp);
1583: /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
1584: PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);
1585: PetscMalloc1(mbs+1,&vtmp_abs);
1586: PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);
1588: allowzeropivot = PetscNot(A->erroriffailure);
1589: bi[0] = 0;
1590: bdiag[0] = (nnz_max/bs2)-1; /* location of diagonal in factor B */
1591: bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
1592: for (i=0; i<mbs; i++) {
1593: /* copy initial fill into linked list */
1594: nzi = ai[r[i]+1] - ai[r[i]];
1595: if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1596: nzi_al = adiag[r[i]] - ai[r[i]];
1597: nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
1599: /* load in initial unfactored row */
1600: ajtmp = aj + ai[r[i]];
1601: PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);
1602: PetscArrayzero(rtmp,mbs*bs2);
1603: aatmp = a->a + bs2*ai[r[i]];
1604: for (j=0; j<nzi; j++) {
1605: PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2);
1606: }
1608: /* add pivot rows into linked list */
1609: row = lnk[mbs];
1610: while (row < i) {
1611: nzi_bl = bi[row+1] - bi[row] + 1;
1612: bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
1613: PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
1614: nzi += nlnk;
1615: row = lnk[row];
1616: }
1618: /* copy data from lnk into jtmp, then initialize lnk */
1619: PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);
1621: /* numerical factorization */
1622: bjtmp = jtmp;
1623: row = *bjtmp++; /* 1st pivot row */
1625: while (row < i) {
1626: pc = rtmp + bs2*row;
1627: pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
1628: PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
1629: MatBlockAbs_private(1,bs2,pc,vtmp_abs);
1630: if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
1631: pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
1632: pv = ba + bs2*(bdiag[row+1] + 1);
1633: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
1634: for (j=0; j<nz; j++) {
1635: PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
1636: }
1637: /* PetscLogFlops(bslog*(nz+1.0)-bs); */
1638: }
1639: row = *bjtmp++;
1640: }
1642: /* copy sparse rtmp into contiguous vtmp; separate L and U part */
1643: nzi_bl = 0; j = 0;
1644: while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
1645: PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
1646: nzi_bl++; j++;
1647: }
1648: nzi_bu = nzi - nzi_bl -1;
1650: while (j < nzi) { /* U-part */
1651: PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
1652: j++;
1653: }
1655: MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);
1657: bjtmp = bj + bi[i];
1658: batmp = ba + bs2*bi[i];
1659: /* apply level dropping rule to L part */
1660: ncut = nzi_al + dtcount;
1661: if (ncut < nzi_bl) {
1662: PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);
1663: PetscSortIntWithScalarArray(ncut,jtmp,vtmp);
1664: } else {
1665: ncut = nzi_bl;
1666: }
1667: for (j=0; j<ncut; j++) {
1668: bjtmp[j] = jtmp[j];
1669: PetscArraycpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2);
1670: }
1671: bi[i+1] = bi[i] + ncut;
1672: nzi = ncut + 1;
1674: /* apply level dropping rule to U part */
1675: ncut = nzi_au + dtcount;
1676: if (ncut < nzi_bu) {
1677: PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);
1678: PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
1679: } else {
1680: ncut = nzi_bu;
1681: }
1682: nzi += ncut;
1684: /* mark bdiagonal */
1685: bdiag[i+1] = bdiag[i] - (ncut + 1);
1686: bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);
1688: bjtmp = bj + bdiag[i];
1689: batmp = ba + bs2*bdiag[i];
1690: PetscArraycpy(batmp,rtmp+bs2*i,bs2);
1691: *bjtmp = i;
1693: bjtmp = bj + bdiag[i+1]+1;
1694: batmp = ba + (bdiag[i+1]+1)*bs2;
1696: for (k=0; k<ncut; k++) {
1697: bjtmp[k] = jtmp[nzi_bl+1+k];
1698: PetscArraycpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2);
1699: }
1701: im[i] = nzi; /* used by PetscLLAddSortedLU() */
1703: /* invert diagonal block for simplier triangular solves - add shift??? */
1704: batmp = ba + bs2*bdiag[i];
1706: PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);
1707: if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1708: } /* for (i=0; i<mbs; i++) */
1709: PetscFree3(v_work,multiplier,v_pivots);
1711: /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
1712: if (bi[mbs] >= bdiag[mbs]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[mbs],bdiag[mbs]);
1714: ISRestoreIndices(isrow,&r);
1715: ISRestoreIndices(isicol,&ic);
1717: PetscLLDestroy(lnk,lnkbt);
1719: PetscFree2(im,jtmp);
1720: PetscFree2(rtmp,vtmp);
1722: PetscLogFlops(bs2*B->cmap->n);
1723: b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];
1725: ISIdentity(isrow,&row_identity);
1726: ISIdentity(isicol,&icol_identity);
1727: if (row_identity && icol_identity) {
1728: B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
1729: } else {
1730: B->ops->solve = MatSolve_SeqBAIJ_N;
1731: }
1733: B->ops->solveadd = 0;
1734: B->ops->solvetranspose = 0;
1735: B->ops->solvetransposeadd = 0;
1736: B->ops->matsolve = 0;
1737: B->assembled = PETSC_TRUE;
1738: B->preallocated = PETSC_TRUE;
1739: return(0);
1740: }