Actual source code: baijfact13.c
petsc-3.14.6 2021-03-30
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: /*
9: Version for when blocks are 3 by 3
10: */
11: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
12: {
13: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
14: IS isrow = b->row,isicol = b->icol;
16: const PetscInt *r,*ic;
17: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
18: PetscInt *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
19: PetscInt *diag_offset = b->diag,idx,*pj;
20: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
21: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
22: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
23: MatScalar *ba = b->a,*aa = a->a;
24: PetscReal shift = info->shiftamount;
25: PetscBool allowzeropivot,zeropivotdetected;
28: ISGetIndices(isrow,&r);
29: ISGetIndices(isicol,&ic);
30: PetscMalloc1(9*(n+1),&rtmp);
31: allowzeropivot = PetscNot(A->erroriffailure);
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;
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,allowzeropivot,&zeropivotdetected);
109: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
110: }
112: PetscFree(rtmp);
113: ISRestoreIndices(isicol,&ic);
114: ISRestoreIndices(isrow,&r);
116: C->ops->solve = MatSolve_SeqBAIJ_3_inplace;
117: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
118: C->assembled = PETSC_TRUE;
120: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
121: return(0);
122: }
124: /* MatLUFactorNumeric_SeqBAIJ_3 -
125: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
126: PetscKernel_A_gets_A_times_B()
127: PetscKernel_A_gets_A_minus_B_times_C()
128: PetscKernel_A_gets_inverse_A()
129: */
130: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
131: {
132: Mat C =B;
133: Mat_SeqBAIJ *a =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
134: IS isrow = b->row,isicol = b->icol;
136: const PetscInt *r,*ic;
137: PetscInt i,j,k,nz,nzL,row;
138: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
139: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
140: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
141: PetscInt flg;
142: PetscReal shift = info->shiftamount;
143: PetscBool allowzeropivot,zeropivotdetected;
146: ISGetIndices(isrow,&r);
147: ISGetIndices(isicol,&ic);
148: allowzeropivot = PetscNot(A->erroriffailure);
150: /* generate work space needed by the factorization */
151: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
152: PetscArrayzero(rtmp,bs2*n);
154: for (i=0; i<n; i++) {
155: /* zero rtmp */
156: /* L part */
157: nz = bi[i+1] - bi[i];
158: bjtmp = bj + bi[i];
159: for (j=0; j<nz; j++) {
160: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
161: }
163: /* U part */
164: nz = bdiag[i] - bdiag[i+1];
165: bjtmp = bj + bdiag[i+1]+1;
166: for (j=0; j<nz; j++) {
167: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
168: }
170: /* load in initial (unfactored row) */
171: nz = ai[r[i]+1] - ai[r[i]];
172: ajtmp = aj + ai[r[i]];
173: v = aa + bs2*ai[r[i]];
174: for (j=0; j<nz; j++) {
175: PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
176: }
178: /* elimination */
179: bjtmp = bj + bi[i];
180: nzL = bi[i+1] - bi[i];
181: for (k = 0; k < nzL; k++) {
182: row = bjtmp[k];
183: pc = rtmp + bs2*row;
184: for (flg=0,j=0; j<bs2; j++) {
185: if (pc[j]!=0.0) {
186: flg = 1;
187: break;
188: }
189: }
190: if (flg) {
191: pv = b->a + bs2*bdiag[row];
192: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
193: PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);
195: pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
196: pv = b->a + bs2*(bdiag[row+1]+1);
197: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
198: for (j=0; j<nz; j++) {
199: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
200: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
201: v = rtmp + bs2*pj[j];
202: PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
203: pv += bs2;
204: }
205: PetscLogFlops(54.0*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
206: }
207: }
209: /* finished row so stick it into b->a */
210: /* L part */
211: pv = b->a + bs2*bi[i];
212: pj = b->j + bi[i];
213: nz = bi[i+1] - bi[i];
214: for (j=0; j<nz; j++) {
215: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
216: }
218: /* Mark diagonal and invert diagonal for simplier triangular solves */
219: pv = b->a + bs2*bdiag[i];
220: pj = b->j + bdiag[i];
221: PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
222: PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
223: if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
225: /* U part */
226: pj = b->j + bdiag[i+1] + 1;
227: pv = b->a + bs2*(bdiag[i+1]+1);
228: nz = bdiag[i] - bdiag[i+1] - 1;
229: for (j=0; j<nz; j++) {
230: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
231: }
232: }
234: PetscFree2(rtmp,mwork);
235: ISRestoreIndices(isicol,&ic);
236: ISRestoreIndices(isrow,&r);
238: C->ops->solve = MatSolve_SeqBAIJ_3;
239: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
240: C->assembled = PETSC_TRUE;
242: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
243: return(0);
244: }
246: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
247: {
248: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
250: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
251: PetscInt *ajtmpold,*ajtmp,nz,row;
252: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
253: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
254: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
255: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
256: MatScalar *ba = b->a,*aa = a->a;
257: PetscReal shift = info->shiftamount;
258: PetscBool allowzeropivot,zeropivotdetected;
261: PetscMalloc1(9*(n+1),&rtmp);
262: allowzeropivot = PetscNot(A->erroriffailure);
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+9*ajtmp[j];
269: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
270: }
271: /* load in initial (unfactored row) */
272: nz = ai[i+1] - ai[i];
273: ajtmpold = aj + ai[i];
274: v = aa + 9*ai[i];
275: for (j=0; j<nz; j++) {
276: x = rtmp+9*ajtmpold[j];
277: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
278: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
279: v += 9;
280: }
281: row = *ajtmp++;
282: while (row < i) {
283: pc = rtmp + 9*row;
284: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
285: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
286: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
287: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
288: pv = ba + 9*diag_offset[row];
289: pj = bj + diag_offset[row] + 1;
290: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
291: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
292: pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
293: pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
294: pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
296: pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
297: pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
298: pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
300: pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
301: pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
302: pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
304: nz = bi[row+1] - diag_offset[row] - 1;
305: pv += 9;
306: for (j=0; j<nz; j++) {
307: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
308: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
309: x = rtmp + 9*pj[j];
310: x[0] -= m1*x1 + m4*x2 + m7*x3;
311: x[1] -= m2*x1 + m5*x2 + m8*x3;
312: x[2] -= m3*x1 + m6*x2 + m9*x3;
314: x[3] -= m1*x4 + m4*x5 + m7*x6;
315: x[4] -= m2*x4 + m5*x5 + m8*x6;
316: x[5] -= m3*x4 + m6*x5 + m9*x6;
318: x[6] -= m1*x7 + m4*x8 + m7*x9;
319: x[7] -= m2*x7 + m5*x8 + m8*x9;
320: x[8] -= m3*x7 + m6*x8 + m9*x9;
321: pv += 9;
322: }
323: PetscLogFlops(54.0*nz+36.0);
324: }
325: row = *ajtmp++;
326: }
327: /* finished row so stick it into b->a */
328: pv = ba + 9*bi[i];
329: pj = bj + bi[i];
330: nz = bi[i+1] - bi[i];
331: for (j=0; j<nz; j++) {
332: x = rtmp+9*pj[j];
333: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
334: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
335: pv += 9;
336: }
337: /* invert diagonal block */
338: w = ba + 9*diag_offset[i];
339: PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);
340: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
341: }
343: PetscFree(rtmp);
345: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
346: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
347: C->assembled = PETSC_TRUE;
349: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
350: return(0);
351: }
353: /*
354: MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
355: copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
356: */
357: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
358: {
359: Mat C =B;
360: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
362: PetscInt i,j,k,nz,nzL,row;
363: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
364: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
365: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
366: PetscInt flg;
367: PetscReal shift = info->shiftamount;
368: PetscBool allowzeropivot,zeropivotdetected;
371: allowzeropivot = PetscNot(A->erroriffailure);
373: /* generate work space needed by the factorization */
374: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
375: PetscArrayzero(rtmp,bs2*n);
377: for (i=0; i<n; i++) {
378: /* zero rtmp */
379: /* L part */
380: nz = bi[i+1] - bi[i];
381: bjtmp = bj + bi[i];
382: for (j=0; j<nz; j++) {
383: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
384: }
386: /* U part */
387: nz = bdiag[i] - bdiag[i+1];
388: bjtmp = bj + bdiag[i+1] + 1;
389: for (j=0; j<nz; j++) {
390: PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
391: }
393: /* load in initial (unfactored row) */
394: nz = ai[i+1] - ai[i];
395: ajtmp = aj + ai[i];
396: v = aa + bs2*ai[i];
397: for (j=0; j<nz; j++) {
398: PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
399: }
401: /* elimination */
402: bjtmp = bj + bi[i];
403: nzL = bi[i+1] - bi[i];
404: for (k=0; k<nzL; k++) {
405: row = bjtmp[k];
406: pc = rtmp + bs2*row;
407: for (flg=0,j=0; j<bs2; j++) {
408: if (pc[j]!=0.0) {
409: flg = 1;
410: break;
411: }
412: }
413: if (flg) {
414: pv = b->a + bs2*bdiag[row];
415: /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
416: PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);
418: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
419: pv = b->a + bs2*(bdiag[row+1]+1);
420: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
421: for (j=0; j<nz; j++) {
422: /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
423: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
424: v = rtmp + bs2*pj[j];
425: PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
426: pv += bs2;
427: }
428: PetscLogFlops(54.0*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
429: }
430: }
432: /* finished row so stick it into b->a */
433: /* L part */
434: pv = b->a + bs2*bi[i];
435: pj = b->j + bi[i];
436: nz = bi[i+1] - bi[i];
437: for (j=0; j<nz; j++) {
438: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
439: }
441: /* Mark diagonal and invert diagonal for simplier triangular solves */
442: pv = b->a + bs2*bdiag[i];
443: pj = b->j + bdiag[i];
444: PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
445: PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
446: if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
448: /* U part */
449: pv = b->a + bs2*(bdiag[i+1]+1);
450: pj = b->j + bdiag[i+1]+1;
451: nz = bdiag[i] - bdiag[i+1] - 1;
452: for (j=0; j<nz; j++) {
453: PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
454: }
455: }
456: PetscFree2(rtmp,mwork);
458: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering;
459: C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
460: C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
461: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
462: C->assembled = PETSC_TRUE;
464: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
465: return(0);
466: }