1
2 /*
3 Factorization code for BAIJ format.
4 */
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <petsc/private/kernels/blockinvert.h>
7
MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo * info)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;
13 PetscErrorCode ierr;
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;
23
24 PetscFunctionBegin;
25 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
26 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
27 allowzeropivot = PetscNot(A->erroriffailure);
28
29 /* generate work space needed by the factorization */
30 ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
31 ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr);
32
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 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
40 }
41
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 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
47 }
48
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 ierr = PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);CHKERRQ(ierr);
55 }
56
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 ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr);
73
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 ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr);
82 pv += 4;
83 }
84 ierr = PetscLogFlops(16.0*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
85 }
86 }
87
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 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
95 }
96
97 /* Mark diagonal and invert diagonal for simplier triangular solves */
98 pv = b->a + bs2*bdiag[i];
99 pj = b->j + bdiag[i];
100 ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr);
101 ierr = PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
102 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
103
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 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
110 }
111 }
112
113 ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
114 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
115 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
116
117 C->ops->solve = MatSolve_SeqBAIJ_2;
118 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2;
119 C->assembled = PETSC_TRUE;
120
121 ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
122 PetscFunctionReturn(0);
123 }
124
MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo * info)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;
129 PetscErrorCode ierr;
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;
138
139 PetscFunctionBegin;
140 allowzeropivot = PetscNot(A->erroriffailure);
141
142 /* generate work space needed by the factorization */
143 ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
144 ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr);
145
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 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
153 }
154
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 ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
160 }
161
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 ierr = PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);CHKERRQ(ierr);
168 }
169
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 ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr);
186
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 ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr);
195 pv += 4;
196 }
197 ierr = PetscLogFlops(16.0*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
198 }
199 }
200
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 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
208 }
209
210 /* Mark diagonal and invert diagonal for simplier triangular solves */
211 pv = b->a + bs2*bdiag[i];
212 pj = b->j + bdiag[i];
213 ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr);
214 ierr = PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
215 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
216
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 ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
228 }
229 }
230 ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
231
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;
237
238 ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
239 PetscFunctionReturn(0);
240 }
241
MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo * info)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;
247 PetscErrorCode ierr;
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;
257
258 PetscFunctionBegin;
259 allowzeropivot = PetscNot(A->erroriffailure);
260 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
261 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
262 ierr = PetscMalloc1(4*(n+1),&rtmp);CHKERRQ(ierr);
263
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 ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr);
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 ierr = PetscKernel_A_gets_inverse_A_2(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
319 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
320 }
321
322 ierr = PetscFree(rtmp);CHKERRQ(ierr);
323 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
324 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
325
326 C->ops->solve = MatSolve_SeqBAIJ_2_inplace;
327 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
328 C->assembled = PETSC_TRUE;
329
330 ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
331 PetscFunctionReturn(0);
332 }
333 /*
334 Version for when blocks are 2 by 2 Using natural ordering
335 */
MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo * info)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;
339 PetscErrorCode ierr;
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;
348
349 PetscFunctionBegin;
350 allowzeropivot = PetscNot(A->erroriffailure);
351 ierr = PetscMalloc1(4*(n+1),&rtmp);CHKERRQ(ierr);
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 ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr);
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 ierr = PetscKernel_A_gets_inverse_A_2(w,shift, allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
413 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
414 }
415
416 ierr = PetscFree(rtmp);CHKERRQ(ierr);
417
418 C->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
419 C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
420 C->assembled = PETSC_TRUE;
421
422 ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
423 PetscFunctionReturn(0);
424 }
425
426 /* ----------------------------------------------------------- */
427 /*
428 Version for when blocks are 1 by 1.
429 */
MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo * info)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;
447
448 PetscFunctionBegin;
449 /* MatPivotSetUp(): initialize shift context sctx */
450 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
451
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 }
469
470 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
471 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
472 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr);
473 ics = ic;
474
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;
483
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;
488
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];
494
495 /* ZeropivotApply() */
496 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */
497
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;
508
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 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
514 }
515 row = *bjtmp++;
516 }
517
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 }
527
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 }
535
536 sctx.rs = rs;
537 sctx.pv = rtmp[i];
538 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr);
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 */
541
542 /* Mark diagonal and invert diagonal for simplier triangular solves */
543 pv = b->a + bdiag[i];
544 *pv = (PetscScalar)1.0/rtmp[i];
545
546 } /* endof for (i=0; i<n; i++) { */
547
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);
561
562 ierr = PetscFree(rtmp);CHKERRQ(ierr);
563 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
564 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
565
566 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
567 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
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 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
579
580 /* MatShiftView(A,info,&sctx) */
581 if (sctx.nshift) {
582 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
583 ierr = 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);CHKERRQ(ierr);
584 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
585 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr);
586 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
587 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr);
588 }
589 }
590 PetscFunctionReturn(0);
591 }
592
MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo * info)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;
597 PetscErrorCode ierr;
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;
605
606 PetscFunctionBegin;
607 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
608 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
609 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr);
610
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;
615
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];
621
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 ierr = PetscLogFlops(1.0+2.0*nz);CHKERRQ(ierr);
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 }
646
647 ierr = PetscFree(rtmp);CHKERRQ(ierr);
648 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
649 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
650 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
651 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
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 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
661 PetscFunctionReturn(0);
662 }
663
MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat * B)664 PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
665 {
666 PetscInt n = A->rmap->n;
667 PetscErrorCode ierr;
668
669 PetscFunctionBegin;
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 ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
674 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
675 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
676 ierr = MatSetType(*B,MATSEQBAIJ);CHKERRQ(ierr);
677
678 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqBAIJ;
679 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ;
680 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
681 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
682 ierr = MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
683
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;
688 (*B)->useordering = PETSC_TRUE;
689
690 ierr = PetscFree((*B)->solvertype);CHKERRQ(ierr);
691 ierr = PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);CHKERRQ(ierr);
692 PetscFunctionReturn(0);
693 }
694
695 /* ----------------------------------------------------------- */
MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo * info)696 PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
697 {
698 PetscErrorCode ierr;
699 Mat C;
700
701 PetscFunctionBegin;
702 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
703 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
704 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
705
706 A->ops->solve = C->ops->solve;
707 A->ops->solvetranspose = C->ops->solvetranspose;
708
709 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr);
710 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqBAIJ*)(A->data))->icol);CHKERRQ(ierr);
711 PetscFunctionReturn(0);
712 }
713
714 #include <../src/mat/impls/sbaij/seq/sbaij.h>
MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo * info)715 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
716 {
717 PetscErrorCode ierr;
718 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
719 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
720 IS ip=b->row;
721 const PetscInt *rip;
722 PetscInt i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol;
723 PetscInt *ai=a->i,*aj=a->j;
724 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
725 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
726 PetscReal rs;
727 FactorShiftCtx sctx;
728
729 PetscFunctionBegin;
730 if (bs > 1) { /* convert A to a SBAIJ matrix and apply Cholesky factorization from it */
731 if (!a->sbaijMat) {
732 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
733 }
734 ierr = (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);CHKERRQ(ierr);
735 ierr = MatDestroy(&a->sbaijMat);CHKERRQ(ierr);
736 PetscFunctionReturn(0);
737 }
738
739 /* MatPivotSetUp(): initialize shift context sctx */
740 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
741
742 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr);
743 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr);
744
745 sctx.shift_amount = 0.;
746 sctx.nshift = 0;
747 do {
748 sctx.newshift = PETSC_FALSE;
749 for (i=0; i<mbs; i++) {
750 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
751 }
752
753 for (k = 0; k<mbs; k++) {
754 bval = ba + bi[k];
755 /* initialize k-th row by the perm[k]-th row of A */
756 jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
757 for (j = jmin; j < jmax; j++) {
758 col = rip[aj[j]];
759 if (col >= k) { /* only take upper triangular entry */
760 rtmp[col] = aa[j];
761 *bval++ = 0.0; /* for in-place factorization */
762 }
763 }
764
765 /* shift the diagonal of the matrix */
766 if (sctx.nshift) rtmp[k] += sctx.shift_amount;
767
768 /* modify k-th row by adding in those rows i with U(i,k)!=0 */
769 dk = rtmp[k];
770 i = jl[k]; /* first row to be added to k_th row */
771
772 while (i < k) {
773 nexti = jl[i]; /* next row to be added to k_th row */
774
775 /* compute multiplier, update diag(k) and U(i,k) */
776 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
777 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
778 dk += uikdi*ba[ili];
779 ba[ili] = uikdi; /* -U(i,k) */
780
781 /* add multiple of row i to k-th row */
782 jmin = ili + 1; jmax = bi[i+1];
783 if (jmin < jmax) {
784 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
785 /* update il and jl for row i */
786 il[i] = jmin;
787 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
788 }
789 i = nexti;
790 }
791
792 /* shift the diagonals when zero pivot is detected */
793 /* compute rs=sum of abs(off-diagonal) */
794 rs = 0.0;
795 jmin = bi[k]+1;
796 nz = bi[k+1] - jmin;
797 if (nz) {
798 bcol = bj + jmin;
799 while (nz--) {
800 rs += PetscAbsScalar(rtmp[*bcol]);
801 bcol++;
802 }
803 }
804
805 sctx.rs = rs;
806 sctx.pv = dk;
807 ierr = MatPivotCheck(C,A,info,&sctx,k);CHKERRQ(ierr);
808 if (sctx.newshift) break;
809 dk = sctx.pv;
810
811 /* copy data into U(k,:) */
812 ba[bi[k]] = 1.0/dk; /* U(k,k) */
813 jmin = bi[k]+1; jmax = bi[k+1];
814 if (jmin < jmax) {
815 for (j=jmin; j<jmax; j++) {
816 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
817 }
818 /* add the k-th row into il and jl */
819 il[k] = jmin;
820 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
821 }
822 }
823 } while (sctx.newshift);
824 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
825
826 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
827
828 C->assembled = PETSC_TRUE;
829 C->preallocated = PETSC_TRUE;
830
831 ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr);
832 if (sctx.nshift) {
833 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
834 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr);
835 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
836 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr);
837 }
838 }
839 PetscFunctionReturn(0);
840 }
841
MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo * info)842 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
843 {
844 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
845 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
846 PetscErrorCode ierr;
847 PetscInt i,j,am=a->mbs;
848 PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
849 PetscInt k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
850 MatScalar *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
851 PetscReal rs;
852 FactorShiftCtx sctx;
853
854 PetscFunctionBegin;
855 /* MatPivotSetUp(): initialize shift context sctx */
856 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
857
858 ierr = PetscMalloc3(am,&rtmp,am,&il,am,&jl);CHKERRQ(ierr);
859
860 do {
861 sctx.newshift = PETSC_FALSE;
862 for (i=0; i<am; i++) {
863 rtmp[i] = 0.0; jl[i] = am; il[0] = 0;
864 }
865
866 for (k = 0; k<am; k++) {
867 /* initialize k-th row with elements nonzero in row perm(k) of A */
868 nz = ai[k+1] - ai[k];
869 acol = aj + ai[k];
870 aval = aa + ai[k];
871 bval = ba + bi[k];
872 while (nz--) {
873 if (*acol < k) { /* skip lower triangular entries */
874 acol++; aval++;
875 } else {
876 rtmp[*acol++] = *aval++;
877 *bval++ = 0.0; /* for in-place factorization */
878 }
879 }
880
881 /* shift the diagonal of the matrix */
882 if (sctx.nshift) rtmp[k] += sctx.shift_amount;
883
884 /* modify k-th row by adding in those rows i with U(i,k)!=0 */
885 dk = rtmp[k];
886 i = jl[k]; /* first row to be added to k_th row */
887
888 while (i < k) {
889 nexti = jl[i]; /* next row to be added to k_th row */
890 /* compute multiplier, update D(k) and U(i,k) */
891 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
892 uikdi = -ba[ili]*ba[bi[i]];
893 dk += uikdi*ba[ili];
894 ba[ili] = uikdi; /* -U(i,k) */
895
896 /* add multiple of row i to k-th row ... */
897 jmin = ili + 1;
898 nz = bi[i+1] - jmin;
899 if (nz > 0) {
900 bcol = bj + jmin;
901 bval = ba + jmin;
902 while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
903 /* update il and jl for i-th row */
904 il[i] = jmin;
905 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
906 }
907 i = nexti;
908 }
909
910 /* shift the diagonals when zero pivot is detected */
911 /* compute rs=sum of abs(off-diagonal) */
912 rs = 0.0;
913 jmin = bi[k]+1;
914 nz = bi[k+1] - jmin;
915 if (nz) {
916 bcol = bj + jmin;
917 while (nz--) {
918 rs += PetscAbsScalar(rtmp[*bcol]);
919 bcol++;
920 }
921 }
922
923 sctx.rs = rs;
924 sctx.pv = dk;
925 ierr = MatPivotCheck(C,A,info,&sctx,k);CHKERRQ(ierr);
926 if (sctx.newshift) break; /* sctx.shift_amount is updated */
927 dk = sctx.pv;
928
929 /* copy data into U(k,:) */
930 ba[bi[k]] = 1.0/dk;
931 jmin = bi[k]+1;
932 nz = bi[k+1] - jmin;
933 if (nz) {
934 bcol = bj + jmin;
935 bval = ba + jmin;
936 while (nz--) {
937 *bval++ = rtmp[*bcol];
938 rtmp[*bcol++] = 0.0;
939 }
940 /* add k-th row into il and jl */
941 il[k] = jmin;
942 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
943 }
944 }
945 } while (sctx.newshift);
946 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
947
948 C->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
949 C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
950 C->assembled = PETSC_TRUE;
951 C->preallocated = PETSC_TRUE;
952
953 ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr);
954 if (sctx.nshift) {
955 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
956 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr);
957 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
958 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr);
959 }
960 }
961 PetscFunctionReturn(0);
962 }
963
964 #include <petscbt.h>
965 #include <../src/mat/utils/freespace.h>
MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo * info)966 PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
967 {
968 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
969 Mat_SeqSBAIJ *b;
970 Mat B;
971 PetscErrorCode ierr;
972 PetscBool perm_identity,missing;
973 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui;
974 const PetscInt *rip;
975 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
976 PetscInt nlnk,*lnk,*lnk_lvl=NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr;
977 PetscReal fill =info->fill,levels=info->levels;
978 PetscFreeSpaceList free_space =NULL,current_space=NULL;
979 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
980 PetscBT lnkbt;
981
982 PetscFunctionBegin;
983 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
984 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
985
986 if (bs > 1) {
987 if (!a->sbaijMat) {
988 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
989 }
990 (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */
991
992 ierr = MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr);
993 PetscFunctionReturn(0);
994 }
995
996 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
997 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
998
999 /* special case that simply copies fill pattern */
1000 if (!levels && perm_identity) {
1001 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr);
1002 for (i=0; i<am; i++) ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */
1003 B = fact;
1004 ierr = MatSeqSBAIJSetPreallocation(B,1,0,ui);CHKERRQ(ierr);
1005
1006
1007 b = (Mat_SeqSBAIJ*)B->data;
1008 uj = b->j;
1009 for (i=0; i<am; i++) {
1010 aj = a->j + a->diag[i];
1011 for (j=0; j<ui[i]; j++) *uj++ = *aj++;
1012 b->ilen[i] = ui[i];
1013 }
1014 ierr = PetscFree(ui);CHKERRQ(ierr);
1015
1016 B->factortype = MAT_FACTOR_NONE;
1017
1018 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1019 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1020 B->factortype = MAT_FACTOR_ICC;
1021
1022 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1023 PetscFunctionReturn(0);
1024 }
1025
1026 /* initialization */
1027 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr);
1028 ui[0] = 0;
1029 ierr = PetscMalloc1(2*am+1,&cols_lvl);CHKERRQ(ierr);
1030
1031 /* jl: linked list for storing indices of the pivot rows
1032 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1033 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);CHKERRQ(ierr);
1034 for (i=0; i<am; i++) {
1035 jl[i] = am; il[i] = 0;
1036 }
1037
1038 /* create and initialize a linked list for storing column indices of the active row k */
1039 nlnk = am + 1;
1040 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1041
1042 /* initial FreeSpace size is fill*(ai[am]+am)/2 */
1043 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);CHKERRQ(ierr);
1044
1045 current_space = free_space;
1046
1047 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);CHKERRQ(ierr);
1048 current_space_lvl = free_space_lvl;
1049
1050 for (k=0; k<am; k++) { /* for each active row k */
1051 /* initialize lnk by the column indices of row rip[k] of A */
1052 nzk = 0;
1053 ncols = ai[rip[k]+1] - ai[rip[k]];
1054 ncols_upper = 0;
1055 cols = cols_lvl + am;
1056 for (j=0; j<ncols; j++) {
1057 i = rip[*(aj + ai[rip[k]] + j)];
1058 if (i >= k) { /* only take upper triangular entry */
1059 cols[ncols_upper] = i;
1060 cols_lvl[ncols_upper] = -1; /* initialize level for nonzero entries */
1061 ncols_upper++;
1062 }
1063 }
1064 ierr = PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1065 nzk += nlnk;
1066
1067 /* update lnk by computing fill-in for each pivot row to be merged in */
1068 prow = jl[k]; /* 1st pivot row */
1069
1070 while (prow < k) {
1071 nextprow = jl[prow];
1072
1073 /* merge prow into k-th row */
1074 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
1075 jmax = ui[prow+1];
1076 ncols = jmax-jmin;
1077 i = jmin - ui[prow];
1078 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
1079 for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
1080 ierr = PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1081 nzk += nlnk;
1082
1083 /* update il and jl for prow */
1084 if (jmin < jmax) {
1085 il[prow] = jmin;
1086
1087 j = *cols; jl[prow] = jl[j]; jl[j] = prow;
1088 }
1089 prow = nextprow;
1090 }
1091
1092 /* if free space is not available, make more free space */
1093 if (current_space->local_remaining<nzk) {
1094 i = am - k + 1; /* num of unfactored rows */
1095 i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1096 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr);
1097 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr);
1098 reallocs++;
1099 }
1100
1101 /* copy data into free_space and free_space_lvl, then initialize lnk */
1102 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1103
1104 /* add the k-th row into il and jl */
1105 if (nzk-1 > 0) {
1106 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
1107 jl[k] = jl[i]; jl[i] = k;
1108 il[k] = ui[k] + 1;
1109 }
1110 uj_ptr[k] = current_space->array;
1111 uj_lvl_ptr[k] = current_space_lvl->array;
1112
1113 current_space->array += nzk;
1114 current_space->local_used += nzk;
1115 current_space->local_remaining -= nzk;
1116
1117 current_space_lvl->array += nzk;
1118 current_space_lvl->local_used += nzk;
1119 current_space_lvl->local_remaining -= nzk;
1120
1121 ui[k+1] = ui[k] + nzk;
1122 }
1123
1124 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
1125 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);CHKERRQ(ierr);
1126 ierr = PetscFree(cols_lvl);CHKERRQ(ierr);
1127
1128 /* copy free_space into uj and free free_space; set uj in new datastructure; */
1129 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr);
1130 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
1131 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1132 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1133
1134 /* put together the new matrix in MATSEQSBAIJ format */
1135 B = fact;
1136 ierr = MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
1137
1138 b = (Mat_SeqSBAIJ*)B->data;
1139 b->singlemalloc = PETSC_FALSE;
1140 b->free_a = PETSC_TRUE;
1141 b->free_ij = PETSC_TRUE;
1142
1143 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr);
1144
1145 b->j = uj;
1146 b->i = ui;
1147 b->diag = NULL;
1148 b->ilen = NULL;
1149 b->imax = NULL;
1150 b->row = perm;
1151 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1152
1153 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1154
1155 b->icol = perm;
1156
1157 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1158 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr);
1159 ierr = PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1160
1161 b->maxnz = b->nz = ui[am];
1162
1163 B->info.factor_mallocs = reallocs;
1164 B->info.fill_ratio_given = fill;
1165 if (ai[am] != 0.) {
1166 /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
1167 B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
1168 } else {
1169 B->info.fill_ratio_needed = 0.0;
1170 }
1171 #if defined(PETSC_USE_INFO)
1172 if (ai[am] != 0) {
1173 PetscReal af = B->info.fill_ratio_needed;
1174 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr);
1175 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr);
1176 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr);
1177 } else {
1178 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
1179 }
1180 #endif
1181 if (perm_identity) {
1182 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1183 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1184 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1185 } else {
1186 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1187 }
1188 PetscFunctionReturn(0);
1189 }
1190
MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo * info)1191 PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1192 {
1193 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
1194 Mat_SeqSBAIJ *b;
1195 Mat B;
1196 PetscErrorCode ierr;
1197 PetscBool perm_identity,missing;
1198 PetscReal fill = info->fill;
1199 const PetscInt *rip;
1200 PetscInt i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
1201 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
1202 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
1203 PetscFreeSpaceList free_space=NULL,current_space=NULL;
1204 PetscBT lnkbt;
1205
1206 PetscFunctionBegin;
1207 if (bs > 1) { /* convert to seqsbaij */
1208 if (!a->sbaijMat) {
1209 ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
1210 }
1211 (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */
1212
1213 ierr = MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr);
1214 PetscFunctionReturn(0);
1215 }
1216
1217 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1218 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1219
1220 /* check whether perm is the identity mapping */
1221 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
1222 if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
1223 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
1224
1225 /* initialization */
1226 ierr = PetscMalloc1(mbs+1,&ui);CHKERRQ(ierr);
1227 ui[0] = 0;
1228
1229 /* jl: linked list for storing indices of the pivot rows
1230 il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
1231 ierr = PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);CHKERRQ(ierr);
1232 for (i=0; i<mbs; i++) {
1233 jl[i] = mbs; il[i] = 0;
1234 }
1235
1236 /* create and initialize a linked list for storing column indices of the active row k */
1237 nlnk = mbs + 1;
1238 ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1239
1240 /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
1241 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);CHKERRQ(ierr);
1242
1243 current_space = free_space;
1244
1245 for (k=0; k<mbs; k++) { /* for each active row k */
1246 /* initialize lnk by the column indices of row rip[k] of A */
1247 nzk = 0;
1248 ncols = ai[rip[k]+1] - ai[rip[k]];
1249 ncols_upper = 0;
1250 for (j=0; j<ncols; j++) {
1251 i = rip[*(aj + ai[rip[k]] + j)];
1252 if (i >= k) { /* only take upper triangular entry */
1253 cols[ncols_upper] = i;
1254 ncols_upper++;
1255 }
1256 }
1257 ierr = PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1258 nzk += nlnk;
1259
1260 /* update lnk by computing fill-in for each pivot row to be merged in */
1261 prow = jl[k]; /* 1st pivot row */
1262
1263 while (prow < k) {
1264 nextprow = jl[prow];
1265 /* merge prow into k-th row */
1266 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
1267 jmax = ui[prow+1];
1268 ncols = jmax-jmin;
1269 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
1270 ierr = PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1271 nzk += nlnk;
1272
1273 /* update il and jl for prow */
1274 if (jmin < jmax) {
1275 il[prow] = jmin;
1276 j = *uj_ptr;
1277 jl[prow] = jl[j];
1278 jl[j] = prow;
1279 }
1280 prow = nextprow;
1281 }
1282
1283 /* if free space is not available, make more free space */
1284 if (current_space->local_remaining<nzk) {
1285 i = mbs - k + 1; /* num of unfactored rows */
1286 i = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1287 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr);
1288 reallocs++;
1289 }
1290
1291 /* copy data into free space, then initialize lnk */
1292 ierr = PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
1293
1294 /* add the k-th row into il and jl */
1295 if (nzk-1 > 0) {
1296 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
1297 jl[k] = jl[i]; jl[i] = k;
1298 il[k] = ui[k] + 1;
1299 }
1300 ui_ptr[k] = current_space->array;
1301 current_space->array += nzk;
1302 current_space->local_used += nzk;
1303 current_space->local_remaining -= nzk;
1304
1305 ui[k+1] = ui[k] + nzk;
1306 }
1307
1308 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
1309 ierr = PetscFree4(ui_ptr,il,jl,cols);CHKERRQ(ierr);
1310
1311 /* copy free_space into uj and free free_space; set uj in new datastructure; */
1312 ierr = PetscMalloc1(ui[mbs]+1,&uj);CHKERRQ(ierr);
1313 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
1314 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1315
1316 /* put together the new matrix in MATSEQSBAIJ format */
1317 B = fact;
1318 ierr = MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
1319
1320 b = (Mat_SeqSBAIJ*)B->data;
1321 b->singlemalloc = PETSC_FALSE;
1322 b->free_a = PETSC_TRUE;
1323 b->free_ij = PETSC_TRUE;
1324
1325 ierr = PetscMalloc1(ui[mbs]+1,&b->a);CHKERRQ(ierr);
1326
1327 b->j = uj;
1328 b->i = ui;
1329 b->diag = NULL;
1330 b->ilen = NULL;
1331 b->imax = NULL;
1332 b->row = perm;
1333 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1334
1335 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1336 b->icol = perm;
1337 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1338 ierr = PetscMalloc1(mbs+1,&b->solve_work);CHKERRQ(ierr);
1339 ierr = PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1340 b->maxnz = b->nz = ui[mbs];
1341
1342 B->info.factor_mallocs = reallocs;
1343 B->info.fill_ratio_given = fill;
1344 if (ai[mbs] != 0.) {
1345 /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
1346 B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
1347 } else {
1348 B->info.fill_ratio_needed = 0.0;
1349 }
1350 #if defined(PETSC_USE_INFO)
1351 if (ai[mbs] != 0.) {
1352 PetscReal af = B->info.fill_ratio_needed;
1353 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr);
1354 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr);
1355 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr);
1356 } else {
1357 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
1358 }
1359 #endif
1360 if (perm_identity) {
1361 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1362 } else {
1363 B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1364 }
1365 PetscFunctionReturn(0);
1366 }
1367
MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)1368 PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
1369 {
1370 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data;
1371 PetscErrorCode ierr;
1372 const PetscInt *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1373 PetscInt i,k,n=a->mbs;
1374 PetscInt nz,bs=A->rmap->bs,bs2=a->bs2;
1375 const MatScalar *aa=a->a,*v;
1376 PetscScalar *x,*s,*t,*ls;
1377 const PetscScalar *b;
1378
1379 PetscFunctionBegin;
1380 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1381 ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1382 t = a->solve_work;
1383
1384 /* forward solve the lower triangular */
1385 ierr = PetscArraycpy(t,b,bs);CHKERRQ(ierr); /* copy 1st block of b to t */
1386
1387 for (i=1; i<n; i++) {
1388 v = aa + bs2*ai[i];
1389 vi = aj + ai[i];
1390 nz = ai[i+1] - ai[i];
1391 s = t + bs*i;
1392 ierr = PetscArraycpy(s,b+bs*i,bs);CHKERRQ(ierr); /* copy i_th block of b to t */
1393 for (k=0;k<nz;k++) {
1394 PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
1395 v += bs2;
1396 }
1397 }
1398
1399 /* backward solve the upper triangular */
1400 ls = a->solve_work + A->cmap->n;
1401 for (i=n-1; i>=0; i--) {
1402 v = aa + bs2*(adiag[i+1]+1);
1403 vi = aj + adiag[i+1]+1;
1404 nz = adiag[i] - adiag[i+1]-1;
1405 ierr = PetscArraycpy(ls,t+i*bs,bs);CHKERRQ(ierr);
1406 for (k=0; k<nz; k++) {
1407 PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
1408 v += bs2;
1409 }
1410 PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
1411 ierr = PetscArraycpy(x+i*bs,t+i*bs,bs);CHKERRQ(ierr);
1412 }
1413
1414 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1415 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1416 ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr);
1417 PetscFunctionReturn(0);
1418 }
1419
MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)1420 PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1421 {
1422 Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data;
1423 IS iscol=a->col,isrow=a->row;
1424 PetscErrorCode ierr;
1425 const PetscInt *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1426 PetscInt i,m,n=a->mbs;
1427 PetscInt nz,bs=A->rmap->bs,bs2=a->bs2;
1428 const MatScalar *aa=a->a,*v;
1429 PetscScalar *x,*s,*t,*ls;
1430 const PetscScalar *b;
1431
1432 PetscFunctionBegin;
1433 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1434 ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1435 t = a->solve_work;
1436
1437 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1438 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1439
1440 /* forward solve the lower triangular */
1441 ierr = PetscArraycpy(t,b+bs*r[0],bs);CHKERRQ(ierr);
1442 for (i=1; i<n; i++) {
1443 v = aa + bs2*ai[i];
1444 vi = aj + ai[i];
1445 nz = ai[i+1] - ai[i];
1446 s = t + bs*i;
1447 ierr = PetscArraycpy(s,b+bs*r[i],bs);CHKERRQ(ierr);
1448 for (m=0; m<nz; m++) {
1449 PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
1450 v += bs2;
1451 }
1452 }
1453
1454 /* backward solve the upper triangular */
1455 ls = a->solve_work + A->cmap->n;
1456 for (i=n-1; i>=0; i--) {
1457 v = aa + bs2*(adiag[i+1]+1);
1458 vi = aj + adiag[i+1]+1;
1459 nz = adiag[i] - adiag[i+1] - 1;
1460 ierr = PetscArraycpy(ls,t+i*bs,bs);CHKERRQ(ierr);
1461 for (m=0; m<nz; m++) {
1462 PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
1463 v += bs2;
1464 }
1465 PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
1466 ierr = PetscArraycpy(x + bs*c[i],t+i*bs,bs);CHKERRQ(ierr);
1467 }
1468 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1469 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1470 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1471 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1472 ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr);
1473 PetscFunctionReturn(0);
1474 }
1475
1476 /*
1477 For each block in an block array saves the largest absolute value in the block into another array
1478 */
MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar * blockarray,PetscReal * absarray)1479 static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
1480 {
1481 PetscErrorCode ierr;
1482 PetscInt i,j;
1483
1484 PetscFunctionBegin;
1485 ierr = PetscArrayzero(absarray,nbs+1);CHKERRQ(ierr);
1486 for (i=0; i<nbs; i++) {
1487 for (j=0; j<bs2; j++) {
1488 if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
1489 }
1490 }
1491 PetscFunctionReturn(0);
1492 }
1493
1494 /*
1495 This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
1496 */
MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo * info,Mat * fact)1497 PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
1498 {
1499 Mat B = *fact;
1500 Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b;
1501 IS isicol;
1502 PetscErrorCode ierr;
1503 const PetscInt *r,*ic;
1504 PetscInt i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
1505 PetscInt *bi,*bj,*bdiag;
1506
1507 PetscInt row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
1508 PetscInt nlnk,*lnk;
1509 PetscBT lnkbt;
1510 PetscBool row_identity,icol_identity;
1511 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
1512 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp;
1513
1514 PetscReal dt=info->dt; /* shift=info->shiftamount; */
1515 PetscInt nnz_max;
1516 PetscBool missing;
1517 PetscReal *vtmp_abs;
1518 MatScalar *v_work;
1519 PetscInt *v_pivots;
1520 PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;
1521
1522 PetscFunctionBegin;
1523 /* ------- symbolic factorization, can be reused ---------*/
1524 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1525 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1526 adiag=a->diag;
1527
1528 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1529
1530 /* bdiag is location of diagonal in factor */
1531 ierr = PetscMalloc1(mbs+1,&bdiag);CHKERRQ(ierr);
1532
1533 /* allocate row pointers bi */
1534 ierr = PetscMalloc1(2*mbs+2,&bi);CHKERRQ(ierr);
1535
1536 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
1537 dtcount = (PetscInt)info->dtcount;
1538 if (dtcount > mbs-1) dtcount = mbs-1;
1539 nnz_max = ai[mbs]+2*mbs*dtcount +2;
1540 /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
1541 ierr = PetscMalloc1(nnz_max,&bj);CHKERRQ(ierr);
1542 nnz_max = nnz_max*bs2;
1543 ierr = PetscMalloc1(nnz_max,&ba);CHKERRQ(ierr);
1544
1545 /* put together the new matrix */
1546 ierr = MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
1547 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr);
1548
1549 b = (Mat_SeqBAIJ*)(B)->data;
1550 b->free_a = PETSC_TRUE;
1551 b->free_ij = PETSC_TRUE;
1552 b->singlemalloc = PETSC_FALSE;
1553
1554 b->a = ba;
1555 b->j = bj;
1556 b->i = bi;
1557 b->diag = bdiag;
1558 b->ilen = NULL;
1559 b->imax = NULL;
1560 b->row = isrow;
1561 b->col = iscol;
1562
1563 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1564 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1565
1566 b->icol = isicol;
1567 ierr = PetscMalloc1(bs*(mbs+1),&b->solve_work);CHKERRQ(ierr);
1568 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1569 b->maxnz = nnz_max/bs2;
1570
1571 (B)->factortype = MAT_FACTOR_ILUDT;
1572 (B)->info.factor_mallocs = 0;
1573 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
1574 /* ------- end of symbolic factorization ---------*/
1575 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1576 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1577
1578 /* linked list for storing column indices of the active row */
1579 nlnk = mbs + 1;
1580 ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1581
1582 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
1583 ierr = PetscMalloc2(mbs,&im,mbs,&jtmp);CHKERRQ(ierr);
1584 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
1585 ierr = PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);CHKERRQ(ierr);
1586 ierr = PetscMalloc1(mbs+1,&vtmp_abs);CHKERRQ(ierr);
1587 ierr = PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);CHKERRQ(ierr);
1588
1589 allowzeropivot = PetscNot(A->erroriffailure);
1590 bi[0] = 0;
1591 bdiag[0] = (nnz_max/bs2)-1; /* location of diagonal in factor B */
1592 bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
1593 for (i=0; i<mbs; i++) {
1594 /* copy initial fill into linked list */
1595 nzi = ai[r[i]+1] - ai[r[i]];
1596 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);
1597 nzi_al = adiag[r[i]] - ai[r[i]];
1598 nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
1599
1600 /* load in initial unfactored row */
1601 ajtmp = aj + ai[r[i]];
1602 ierr = PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1603 ierr = PetscArrayzero(rtmp,mbs*bs2);CHKERRQ(ierr);
1604 aatmp = a->a + bs2*ai[r[i]];
1605 for (j=0; j<nzi; j++) {
1606 ierr = PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2);CHKERRQ(ierr);
1607 }
1608
1609 /* add pivot rows into linked list */
1610 row = lnk[mbs];
1611 while (row < i) {
1612 nzi_bl = bi[row+1] - bi[row] + 1;
1613 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
1614 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
1615 nzi += nlnk;
1616 row = lnk[row];
1617 }
1618
1619 /* copy data from lnk into jtmp, then initialize lnk */
1620 ierr = PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
1621
1622 /* numerical factorization */
1623 bjtmp = jtmp;
1624 row = *bjtmp++; /* 1st pivot row */
1625
1626 while (row < i) {
1627 pc = rtmp + bs2*row;
1628 pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
1629 PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
1630 ierr = MatBlockAbs_private(1,bs2,pc,vtmp_abs);CHKERRQ(ierr);
1631 if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
1632 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
1633 pv = ba + bs2*(bdiag[row+1] + 1);
1634 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
1635 for (j=0; j<nz; j++) {
1636 PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
1637 }
1638 /* ierr = PetscLogFlops(bslog*(nz+1.0)-bs);CHKERRQ(ierr); */
1639 }
1640 row = *bjtmp++;
1641 }
1642
1643 /* copy sparse rtmp into contiguous vtmp; separate L and U part */
1644 nzi_bl = 0; j = 0;
1645 while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
1646 ierr = PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);CHKERRQ(ierr);
1647 nzi_bl++; j++;
1648 }
1649 nzi_bu = nzi - nzi_bl -1;
1650
1651 while (j < nzi) { /* U-part */
1652 ierr = PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);CHKERRQ(ierr);
1653 j++;
1654 }
1655
1656 ierr = MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);CHKERRQ(ierr);
1657
1658 bjtmp = bj + bi[i];
1659 batmp = ba + bs2*bi[i];
1660 /* apply level dropping rule to L part */
1661 ncut = nzi_al + dtcount;
1662 if (ncut < nzi_bl) {
1663 ierr = PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);CHKERRQ(ierr);
1664 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
1665 } else {
1666 ncut = nzi_bl;
1667 }
1668 for (j=0; j<ncut; j++) {
1669 bjtmp[j] = jtmp[j];
1670 ierr = PetscArraycpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
1671 }
1672 bi[i+1] = bi[i] + ncut;
1673 nzi = ncut + 1;
1674
1675 /* apply level dropping rule to U part */
1676 ncut = nzi_au + dtcount;
1677 if (ncut < nzi_bu) {
1678 ierr = PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
1679 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
1680 } else {
1681 ncut = nzi_bu;
1682 }
1683 nzi += ncut;
1684
1685 /* mark bdiagonal */
1686 bdiag[i+1] = bdiag[i] - (ncut + 1);
1687 bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);
1688
1689 bjtmp = bj + bdiag[i];
1690 batmp = ba + bs2*bdiag[i];
1691 ierr = PetscArraycpy(batmp,rtmp+bs2*i,bs2);CHKERRQ(ierr);
1692 *bjtmp = i;
1693
1694 bjtmp = bj + bdiag[i+1]+1;
1695 batmp = ba + (bdiag[i+1]+1)*bs2;
1696
1697 for (k=0; k<ncut; k++) {
1698 bjtmp[k] = jtmp[nzi_bl+1+k];
1699 ierr = PetscArraycpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2);CHKERRQ(ierr);
1700 }
1701
1702 im[i] = nzi; /* used by PetscLLAddSortedLU() */
1703
1704 /* invert diagonal block for simplier triangular solves - add shift??? */
1705 batmp = ba + bs2*bdiag[i];
1706
1707 ierr = PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1708 if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1709 } /* for (i=0; i<mbs; i++) */
1710 ierr = PetscFree3(v_work,multiplier,v_pivots);CHKERRQ(ierr);
1711
1712 /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
1713 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
1715 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1716 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1717
1718 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1719
1720 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
1721 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
1722
1723 ierr = PetscLogFlops(bs2*B->cmap->n);CHKERRQ(ierr);
1724 b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];
1725
1726 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1727 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
1728 if (row_identity && icol_identity) {
1729 B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
1730 } else {
1731 B->ops->solve = MatSolve_SeqBAIJ_N;
1732 }
1733
1734 B->ops->solveadd = NULL;
1735 B->ops->solvetranspose = NULL;
1736 B->ops->solvetransposeadd = NULL;
1737 B->ops->matsolve = NULL;
1738 B->assembled = PETSC_TRUE;
1739 B->preallocated = PETSC_TRUE;
1740 PetscFunctionReturn(0);
1741 }
1742