Actual source code: baijfact13.c
1: #define PETSCMAT_DLL
3: /*
4: Factorization code for BAIJ format.
5: */
6: #include ../src/mat/impls/baij/seq/baij.h
7: #include ../src/mat/blockinvert.h
9: /*
10: Version for when blocks are 3 by 3
11: */
14: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
15: {
16: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
17: IS isrow = b->row,isicol = b->icol;
19: const PetscInt *r,*ic;
20: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
21: PetscInt *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
22: PetscInt *diag_offset = b->diag,idx,*pj;
23: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
24: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
25: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
26: MatScalar *ba = b->a,*aa = a->a;
27: PetscReal shift = info->shiftamount;
30: ISGetIndices(isrow,&r);
31: ISGetIndices(isicol,&ic);
32: PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);
34: for (i=0; i<n; i++) {
35: nz = bi[i+1] - bi[i];
36: ajtmp = bj + bi[i];
37: for (j=0; j<nz; j++) {
38: x = rtmp + 9*ajtmp[j];
39: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
40: }
41: /* load in initial (unfactored row) */
42: idx = r[i];
43: nz = ai[idx+1] - ai[idx];
44: ajtmpold = aj + ai[idx];
45: v = aa + 9*ai[idx];
46: for (j=0; j<nz; j++) {
47: x = rtmp + 9*ic[ajtmpold[j]];
48: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
49: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
50: v += 9;
51: }
52: row = *ajtmp++;
53: while (row < i) {
54: pc = rtmp + 9*row;
55: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
56: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
57: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
58: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
59: pv = ba + 9*diag_offset[row];
60: pj = bj + diag_offset[row] + 1;
61: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
62: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
63: pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
64: pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
65: pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
67: pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
68: pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
69: pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
71: pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
72: pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
73: pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
74: nz = bi[row+1] - diag_offset[row] - 1;
75: pv += 9;
76: for (j=0; j<nz; j++) {
77: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
78: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
79: x = rtmp + 9*pj[j];
80: x[0] -= m1*x1 + m4*x2 + m7*x3;
81: x[1] -= m2*x1 + m5*x2 + m8*x3;
82: x[2] -= m3*x1 + m6*x2 + m9*x3;
83:
84: x[3] -= m1*x4 + m4*x5 + m7*x6;
85: x[4] -= m2*x4 + m5*x5 + m8*x6;
86: x[5] -= m3*x4 + m6*x5 + m9*x6;
88: x[6] -= m1*x7 + m4*x8 + m7*x9;
89: x[7] -= m2*x7 + m5*x8 + m8*x9;
90: x[8] -= m3*x7 + m6*x8 + m9*x9;
91: pv += 9;
92: }
93: PetscLogFlops(54.0*nz+36.0);
94: }
95: row = *ajtmp++;
96: }
97: /* finished row so stick it into b->a */
98: pv = ba + 9*bi[i];
99: pj = bj + bi[i];
100: nz = bi[i+1] - bi[i];
101: for (j=0; j<nz; j++) {
102: x = rtmp + 9*pj[j];
103: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
104: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
105: pv += 9;
106: }
107: /* invert diagonal block */
108: w = ba + 9*diag_offset[i];
109: Kernel_A_gets_inverse_A_3(w,shift);
110: }
112: PetscFree(rtmp);
113: ISRestoreIndices(isicol,&ic);
114: ISRestoreIndices(isrow,&r);
115: C->ops->solve = MatSolve_SeqBAIJ_3_inplace;
116: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117: C->assembled = PETSC_TRUE;
118: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
119: return(0);
120: }
122: /* MatLUFactorNumeric_SeqBAIJ_3 -
123: copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
124: Kernel_A_gets_A_times_B()
125: Kernel_A_gets_A_minus_B_times_C()
126: Kernel_A_gets_inverse_A()
127: */
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,*ics;
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;
145: ISGetIndices(isrow,&r);
146: ISGetIndices(isicol,&ic);
148: /* generate work space needed by the factorization */
149: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
150: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
151: ics = ic;
153: for (i=0; i<n; i++){
154: /* zero rtmp */
155: /* L part */
156: nz = bi[i+1] - bi[i];
157: bjtmp = bj + bi[i];
158: for (j=0; j<nz; j++){
159: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
160: }
162: /* U part */
163: nz = bdiag[i] - bdiag[i+1];
164: bjtmp = bj + bdiag[i+1]+1;
165: for (j=0; j<nz; j++){
166: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
167: }
168:
169: /* load in initial (unfactored row) */
170: nz = ai[r[i]+1] - ai[r[i]];
171: ajtmp = aj + ai[r[i]];
172: v = aa + bs2*ai[r[i]];
173: for (j=0; j<nz; j++) {
174: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
175: }
177: /* elimination */
178: bjtmp = bj + bi[i];
179: nzL = bi[i+1] - bi[i];
180: for(k = 0;k < nzL;k++){
181: row = bjtmp[k];
182: pc = rtmp + bs2*row;
183: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
184: if (flg) {
185: pv = b->a + bs2*bdiag[row];
186: /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
187: Kernel_A_gets_A_times_B_3(pc,pv,mwork);
188:
189: pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
190: pv = b->a + bs2*(bdiag[row+1]+1);
191: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
192: for (j=0; j<nz; j++) {
193: /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
194: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
195: v = rtmp + bs2*pj[j];
196: Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
197: pv += bs2;
198: }
199: PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
200: }
201: }
203: /* finished row so stick it into b->a */
204: /* L part */
205: pv = b->a + bs2*bi[i] ;
206: pj = b->j + bi[i] ;
207: nz = bi[i+1] - bi[i];
208: for (j=0; j<nz; j++) {
209: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
210: }
212: /* Mark diagonal and invert diagonal for simplier triangular solves */
213: pv = b->a + bs2*bdiag[i];
214: pj = b->j + bdiag[i];
215: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
216: /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
217: Kernel_A_gets_inverse_A_3(pv,shift);
218:
219: /* U part */
220: pj = b->j + bdiag[i+1] + 1;
221: pv = b->a + bs2*(bdiag[i+1]+1);
222: nz = bdiag[i] - bdiag[i+1] - 1;
223: for (j=0; j<nz; j++){
224: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
225: }
226: }
228: PetscFree2(rtmp,mwork);
229: ISRestoreIndices(isicol,&ic);
230: ISRestoreIndices(isrow,&r);
231: C->ops->solve = MatSolve_SeqBAIJ_3;
232: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
234: C->assembled = PETSC_TRUE;
235: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
236: return(0);
237: }
241: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
242: {
243: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
245: PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
246: PetscInt *ajtmpold,*ajtmp,nz,row;
247: PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
248: MatScalar *pv,*v,*rtmp,*pc,*w,*x;
249: MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
250: MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
251: MatScalar *ba = b->a,*aa = a->a;
252: PetscReal shift = info->shiftamount;
255: PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);
257: for (i=0; i<n; i++) {
258: nz = bi[i+1] - bi[i];
259: ajtmp = bj + bi[i];
260: for (j=0; j<nz; j++) {
261: x = rtmp+9*ajtmp[j];
262: x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
263: }
264: /* load in initial (unfactored row) */
265: nz = ai[i+1] - ai[i];
266: ajtmpold = aj + ai[i];
267: v = aa + 9*ai[i];
268: for (j=0; j<nz; j++) {
269: x = rtmp+9*ajtmpold[j];
270: x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
271: x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
272: v += 9;
273: }
274: row = *ajtmp++;
275: while (row < i) {
276: pc = rtmp + 9*row;
277: p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
278: p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
279: if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
280: p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
281: pv = ba + 9*diag_offset[row];
282: pj = bj + diag_offset[row] + 1;
283: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
284: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
285: pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
286: pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
287: pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
289: pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
290: pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
291: pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
293: pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
294: pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
295: pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
297: nz = bi[row+1] - diag_offset[row] - 1;
298: pv += 9;
299: for (j=0; j<nz; j++) {
300: x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
301: x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
302: x = rtmp + 9*pj[j];
303: x[0] -= m1*x1 + m4*x2 + m7*x3;
304: x[1] -= m2*x1 + m5*x2 + m8*x3;
305: x[2] -= m3*x1 + m6*x2 + m9*x3;
306:
307: x[3] -= m1*x4 + m4*x5 + m7*x6;
308: x[4] -= m2*x4 + m5*x5 + m8*x6;
309: x[5] -= m3*x4 + m6*x5 + m9*x6;
311: x[6] -= m1*x7 + m4*x8 + m7*x9;
312: x[7] -= m2*x7 + m5*x8 + m8*x9;
313: x[8] -= m3*x7 + m6*x8 + m9*x9;
314: pv += 9;
315: }
316: PetscLogFlops(54.0*nz+36.0);
317: }
318: row = *ajtmp++;
319: }
320: /* finished row so stick it into b->a */
321: pv = ba + 9*bi[i];
322: pj = bj + bi[i];
323: nz = bi[i+1] - bi[i];
324: for (j=0; j<nz; j++) {
325: x = rtmp+9*pj[j];
326: pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
327: pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
328: pv += 9;
329: }
330: /* invert diagonal block */
331: w = ba + 9*diag_offset[i];
332: Kernel_A_gets_inverse_A_3(w,shift);
333: }
335: PetscFree(rtmp);
336: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
337: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
338: C->assembled = PETSC_TRUE;
339: PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
340: return(0);
341: }
343: /*
344: MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
345: copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
346: */
349: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
350: {
351: Mat C=B;
352: Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
354: PetscInt i,j,k,nz,nzL,row;
355: const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
356: const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
357: MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
358: PetscInt flg;
359: PetscReal shift = info->shiftamount;
362: /* generate work space needed by the factorization */
363: PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
364: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
366: for (i=0; i<n; i++){
367: /* zero rtmp */
368: /* L part */
369: nz = bi[i+1] - bi[i];
370: bjtmp = bj + bi[i];
371: for (j=0; j<nz; j++){
372: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
373: }
375: /* U part */
376: nz = bdiag[i] - bdiag[i+1];
377: bjtmp = bj + bdiag[i+1] + 1;
378: for (j=0; j<nz; j++){
379: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
380: }
381:
382: /* load in initial (unfactored row) */
383: nz = ai[i+1] - ai[i];
384: ajtmp = aj + ai[i];
385: v = aa + bs2*ai[i];
386: for (j=0; j<nz; j++) {
387: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
388: }
390: /* elimination */
391: bjtmp = bj + bi[i];
392: nzL = bi[i+1] - bi[i];
393: for(k=0;k<nzL;k++){
394: row = bjtmp[k];
395: pc = rtmp + bs2*row;
396: for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
397: if (flg) {
398: pv = b->a + bs2*bdiag[row];
399: /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
400: Kernel_A_gets_A_times_B_3(pc,pv,mwork);
401:
402: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
403: pv = b->a + bs2*(bdiag[row+1]+1);
404: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
405: for (j=0; j<nz; j++) {
406: /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
407: /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
408: v = rtmp + bs2*pj[j];
409: Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
410: pv += bs2;
411: }
412: PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
413: }
414: }
416: /* finished row so stick it into b->a */
417: /* L part */
418: pv = b->a + bs2*bi[i] ;
419: pj = b->j + bi[i] ;
420: nz = bi[i+1] - bi[i];
421: for (j=0; j<nz; j++) {
422: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
423: }
425: /* Mark diagonal and invert diagonal for simplier triangular solves */
426: pv = b->a + bs2*bdiag[i];
427: pj = b->j + bdiag[i];
428: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
429: /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
430: Kernel_A_gets_inverse_A_3(pv,shift);
431:
432: /* U part */
433: pv = b->a + bs2*(bdiag[i+1]+1);
434: pj = b->j + bdiag[i+1]+1;
435: nz = bdiag[i] - bdiag[i+1] - 1;
436: for (j=0; j<nz; j++){
437: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
438: }
439: }
440: PetscFree2(rtmp,mwork);
441: C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering;
442: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
443: C->assembled = PETSC_TRUE;
444: PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
445: return(0);
446: }