Actual source code: baijfact13.c
petsc-3.3-p7 2013-05-11
2: /*
3: Factorization code for BAIJ format.
4: */
5: #include <../src/mat/impls/baij/seq/baij.h>
6: #include <../src/mat/blockinvert.h>
8: /*
9: Version for when blocks are 3 by 3
10: */
13: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
14: {
15: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
16: IS isrow = b->row,isicol = b->icol;
18: const PetscInt *r,*ic;
19: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
20: PetscInt *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
21: PetscInt *diag_offset = b->diag,idx,*pj;
22: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
23: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
24: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
25: MatScalar *ba = b->a,*aa = a->a;
26: PetscReal shift = info->shiftamount;
29: ISGetIndices(isrow,&r);
30: ISGetIndices(isicol,&ic);
31: PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);
33: for (i=0; i<n; i++) {
34: nz = bi[i+1] - bi[i];
35: ajtmp = bj + bi[i];
36: for (j=0; j<nz; j++) {
37: x = rtmp + 9*ajtmp[j];
38: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
39: }
40: /* load in initial (unfactored row) */
41: idx = r[i];
42: nz = ai[idx+1] - ai[idx];
43: ajtmpold = aj + ai[idx];
44: v = aa + 9*ai[idx];
45: for (j=0; j<nz; j++) {
46: x = rtmp + 9*ic[ajtmpold[j]];
47: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
48: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
49: v += 9;
50: }
51: row = *ajtmp++;
52: while (row < i) {
53: pc = rtmp + 9*row;
54: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
55: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
56: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
57: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
58: pv = ba + 9*diag_offset[row];
59: pj = bj + diag_offset[row] + 1;
60: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
61: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
62: pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
63: pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
64: pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
66: pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
67: pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
68: pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
70: pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
71: pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
72: pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
73: nz = bi[row+1] - diag_offset[row] - 1;
74: pv += 9;
75: for (j=0; j<nz; j++) {
76: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
77: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
78: x = rtmp + 9*pj[j];
79: x[0] -= m1*x1 + m4*x2 + m7*x3;
80: x[1] -= m2*x1 + m5*x2 + m8*x3;
81: x[2] -= m3*x1 + m6*x2 + m9*x3;
82:
83: x[3] -= m1*x4 + m4*x5 + m7*x6;
84: x[4] -= m2*x4 + m5*x5 + m8*x6;
85: x[5] -= m3*x4 + m6*x5 + m9*x6;
87: x[6] -= m1*x7 + m4*x8 + m7*x9;
88: x[7] -= m2*x7 + m5*x8 + m8*x9;
89: x[8] -= m3*x7 + m6*x8 + m9*x9;
90: pv += 9;
91: }
92: PetscLogFlops(54.0*nz+36.0);
93: }
94: row = *ajtmp++;
95: }
96: /* finished row so stick it into b->a */
97: pv = ba + 9*bi[i];
98: pj = bj + bi[i];
99: nz = bi[i+1] - bi[i];
100: for (j=0; j<nz; j++) {
101: x = rtmp + 9*pj[j];
102: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
103: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
104: pv += 9;
105: }
106: /* invert diagonal block */
107: w = ba + 9*diag_offset[i];
108: PetscKernel_A_gets_inverse_A_3(w,shift);
109: }
111: PetscFree(rtmp);
112: ISRestoreIndices(isicol,&ic);
113: ISRestoreIndices(isrow,&r);
114: C->ops->solve = MatSolve_SeqBAIJ_3_inplace;
115: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
116: C->assembled = PETSC_TRUE;
117: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
118: return(0);
119: }
121: /* MatLUFactorNumeric_SeqBAIJ_3 -
122: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
123: PetscKernel_A_gets_A_times_B()
124: PetscKernel_A_gets_A_minus_B_times_C()
125: PetscKernel_A_gets_inverse_A()
126: */
129: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
130: {
131: Mat C=B;
132: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
133: IS isrow = b->row,isicol = b->icol;
135: const PetscInt *r,*ic;
136: PetscInt i,j,k,nz,nzL,row;
137: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
138: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
139: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
140: PetscInt flg;
141: PetscReal shift = info->shiftamount;
144: ISGetIndices(isrow,&r);
145: ISGetIndices(isicol,&ic);
147: /* generate work space needed by the factorization */
148: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
149: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
151: for (i=0; i<n; i++){
152: /* zero rtmp */
153: /* L part */
154: nz = bi[i+1] - bi[i];
155: bjtmp = bj + bi[i];
156: for (j=0; j<nz; j++){
157: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
158: }
160: /* U part */
161: nz = bdiag[i] - bdiag[i+1];
162: bjtmp = bj + bdiag[i+1]+1;
163: for (j=0; j<nz; j++){
164: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
165: }
166:
167: /* load in initial (unfactored row) */
168: nz = ai[r[i]+1] - ai[r[i]];
169: ajtmp = aj + ai[r[i]];
170: v = aa + bs2*ai[r[i]];
171: for (j=0; j<nz; j++) {
172: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
173: }
175: /* elimination */
176: bjtmp = bj + bi[i];
177: nzL = bi[i+1] - bi[i];
178: for(k = 0;k < nzL;k++){
179: row = bjtmp[k];
180: pc = rtmp + bs2*row;
181: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
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_3(pc,pv,mwork);
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 + bs2*pj[j];
194: PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
195: pv += bs2;
196: }
197: PetscLogFlops(54*nz+45); /* 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: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
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: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
214: /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
215: PetscKernel_A_gets_inverse_A_3(pv,shift);
216:
217: /* U part */
218: pj = b->j + bdiag[i+1] + 1;
219: pv = b->a + bs2*(bdiag[i+1]+1);
220: nz = bdiag[i] - bdiag[i+1] - 1;
221: for (j=0; j<nz; j++){
222: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
223: }
224: }
226: PetscFree2(rtmp,mwork);
227: ISRestoreIndices(isicol,&ic);
228: ISRestoreIndices(isrow,&r);
229: C->ops->solve = MatSolve_SeqBAIJ_3;
230: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
232: C->assembled = PETSC_TRUE;
233: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
234: return(0);
235: }
239: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
240: {
241: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
243: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
244: PetscInt *ajtmpold,*ajtmp,nz,row;
245: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
246: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
247: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
248: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
249: MatScalar *ba = b->a,*aa = a->a;
250: PetscReal shift = info->shiftamount;
253: PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);
255: for (i=0; i<n; i++) {
256: nz = bi[i+1] - bi[i];
257: ajtmp = bj + bi[i];
258: for (j=0; j<nz; j++) {
259: x = rtmp+9*ajtmp[j];
260: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
261: }
262: /* load in initial (unfactored row) */
263: nz = ai[i+1] - ai[i];
264: ajtmpold = aj + ai[i];
265: v = aa + 9*ai[i];
266: for (j=0; j<nz; j++) {
267: x = rtmp+9*ajtmpold[j];
268: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
269: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
270: v += 9;
271: }
272: row = *ajtmp++;
273: while (row < i) {
274: pc = rtmp + 9*row;
275: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
276: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
277: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
278: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
279: pv = ba + 9*diag_offset[row];
280: pj = bj + diag_offset[row] + 1;
281: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
282: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
283: pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
284: pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
285: pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
287: pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
288: pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
289: pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
291: pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
292: pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
293: pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
295: nz = bi[row+1] - diag_offset[row] - 1;
296: pv += 9;
297: for (j=0; j<nz; j++) {
298: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
299: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
300: x = rtmp + 9*pj[j];
301: x[0] -= m1*x1 + m4*x2 + m7*x3;
302: x[1] -= m2*x1 + m5*x2 + m8*x3;
303: x[2] -= m3*x1 + m6*x2 + m9*x3;
304:
305: x[3] -= m1*x4 + m4*x5 + m7*x6;
306: x[4] -= m2*x4 + m5*x5 + m8*x6;
307: x[5] -= m3*x4 + m6*x5 + m9*x6;
309: x[6] -= m1*x7 + m4*x8 + m7*x9;
310: x[7] -= m2*x7 + m5*x8 + m8*x9;
311: x[8] -= m3*x7 + m6*x8 + m9*x9;
312: pv += 9;
313: }
314: PetscLogFlops(54.0*nz+36.0);
315: }
316: row = *ajtmp++;
317: }
318: /* finished row so stick it into b->a */
319: pv = ba + 9*bi[i];
320: pj = bj + bi[i];
321: nz = bi[i+1] - bi[i];
322: for (j=0; j<nz; j++) {
323: x = rtmp+9*pj[j];
324: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
325: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
326: pv += 9;
327: }
328: /* invert diagonal block */
329: w = ba + 9*diag_offset[i];
330: PetscKernel_A_gets_inverse_A_3(w,shift);
331: }
333: PetscFree(rtmp);
334: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
335: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
336: C->assembled = PETSC_TRUE;
337: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
338: return(0);
339: }
341: /*
342: MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
343: copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
344: */
347: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
348: {
349: Mat C=B;
350: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
352: PetscInt i,j,k,nz,nzL,row;
353: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
354: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
355: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
356: PetscInt flg;
357: PetscReal shift = info->shiftamount;
360: /* generate work space needed by the factorization */
361: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
362: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
364: for (i=0; i<n; i++){
365: /* zero rtmp */
366: /* L part */
367: nz = bi[i+1] - bi[i];
368: bjtmp = bj + bi[i];
369: for (j=0; j<nz; j++){
370: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
371: }
373: /* U part */
374: nz = bdiag[i] - bdiag[i+1];
375: bjtmp = bj + bdiag[i+1] + 1;
376: for (j=0; j<nz; j++){
377: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
378: }
379:
380: /* load in initial (unfactored row) */
381: nz = ai[i+1] - ai[i];
382: ajtmp = aj + ai[i];
383: v = aa + bs2*ai[i];
384: for (j=0; j<nz; j++) {
385: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
386: }
388: /* elimination */
389: bjtmp = bj + bi[i];
390: nzL = bi[i+1] - bi[i];
391: for(k=0;k<nzL;k++){
392: row = bjtmp[k];
393: pc = rtmp + bs2*row;
394: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
395: if (flg) {
396: pv = b->a + bs2*bdiag[row];
397: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
398: PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);
399:
400: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
401: pv = b->a + bs2*(bdiag[row+1]+1);
402: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
403: for (j=0; j<nz; j++) {
404: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
405: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
406: v = rtmp + bs2*pj[j];
407: PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
408: pv += bs2;
409: }
410: PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
411: }
412: }
414: /* finished row so stick it into b->a */
415: /* L part */
416: pv = b->a + bs2*bi[i] ;
417: pj = b->j + bi[i] ;
418: nz = bi[i+1] - bi[i];
419: for (j=0; j<nz; j++) {
420: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
421: }
423: /* Mark diagonal and invert diagonal for simplier triangular solves */
424: pv = b->a + bs2*bdiag[i];
425: pj = b->j + bdiag[i];
426: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
427: /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
428: PetscKernel_A_gets_inverse_A_3(pv,shift);
429:
430: /* U part */
431: pv = b->a + bs2*(bdiag[i+1]+1);
432: pj = b->j + bdiag[i+1]+1;
433: nz = bdiag[i] - bdiag[i+1] - 1;
434: for (j=0; j<nz; j++){
435: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
436: }
437: }
438: PetscFree2(rtmp,mwork);
439: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering;
440: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
441: C->assembled = PETSC_TRUE;
442: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
443: return(0);
444: }