Actual source code: baijfact9.c


  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: /*
 10:       Version for when blocks are 5 by 5
 11: */
 12: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C,Mat A,const MatFactorInfo *info)
 13: {
 14:   Mat_SeqBAIJ     *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
 15:   IS              isrow = b->row,isicol = b->icol;
 16:   const PetscInt  *r,*ic,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
 17:   PetscInt        i,j,n = a->mbs,nz,row,idx,ipvt[5];
 18:   const PetscInt  *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
 19:   MatScalar       *w,*pv,*rtmp,*x,*pc;
 20:   const MatScalar *v,*aa = a->a;
 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,x10,x11,x12,x13,x14,x15,x16;
 23:   MatScalar       x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
 24:   MatScalar       p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
 25:   MatScalar       m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
 26:   MatScalar       *ba   = b->a,work[25];
 27:   PetscReal       shift = info->shiftamount;
 28:   PetscBool       allowzeropivot,zeropivotdetected;

 30:   allowzeropivot = PetscNot(A->erroriffailure);
 31:   ISGetIndices(isrow,&r);
 32:   ISGetIndices(isicol,&ic);
 33:   PetscMalloc1(25*(n+1),&rtmp);

 35: #define PETSC_USE_MEMZERO 1
 36: #define PETSC_USE_MEMCPY 1

 38:   for (i=0; i<n; i++) {
 39:     nz    = bi[i+1] - bi[i];
 40:     ajtmp = bj + bi[i];
 41:     for  (j=0; j<nz; j++) {
 42: #if defined(PETSC_USE_MEMZERO)
 43:       PetscArrayzero(rtmp+25*ajtmp[j],25);
 44: #else
 45:       x     = rtmp+25*ajtmp[j];
 46:       x[0]  = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
 47:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
 48:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
 49: #endif
 50:     }
 51:     /* load in initial (unfactored row) */
 52:     idx      = r[i];
 53:     nz       = ai[idx+1] - ai[idx];
 54:     ajtmpold = aj + ai[idx];
 55:     v        = aa + 25*ai[idx];
 56:     for (j=0; j<nz; j++) {
 57: #if defined(PETSC_USE_MEMCPY)
 58:       PetscArraycpy(rtmp+25*ic[ajtmpold[j]],v,25);
 59: #else
 60:       x     = rtmp+25*ic[ajtmpold[j]];
 61:       x[0]  = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
 62:       x[4]  = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
 63:       x[9]  = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
 64:       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
 65:       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
 66:       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
 67: #endif
 68:       v += 25;
 69:     }
 70:     row = *ajtmp++;
 71:     while (row < i) {
 72:       pc  = rtmp + 25*row;
 73:       p1  = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
 74:       p5  = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
 75:       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
 76:       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
 77:       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
 78:       p25 = pc[24];
 79:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
 80:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
 81:           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
 82:           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
 83:           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
 84:           p24 != 0.0 || p25 != 0.0) {
 85:         pv    = ba + 25*diag_offset[row];
 86:         pj    = bj + diag_offset[row] + 1;
 87:         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
 88:         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
 89:         x10   = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
 90:         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
 91:         x19   = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
 92:         x23   = pv[22]; x24 = pv[23]; x25 = pv[24];
 93:         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
 94:         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
 95:         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
 96:         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
 97:         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;

 99:         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
100:         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
101:         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
102:         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
103:         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;

105:         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
106:         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
107:         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
108:         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
109:         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;

111:         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
112:         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
113:         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
114:         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
115:         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;

117:         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
118:         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
119:         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
120:         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
121:         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;

123:         nz  = bi[row+1] - diag_offset[row] - 1;
124:         pv += 25;
125:         for (j=0; j<nz; j++) {
126:           x1    = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
127:           x5    = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
128:           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
129:           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
130:           x18   = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
131:           x22   = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
132:           x     = rtmp + 25*pj[j];
133:           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
134:           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
135:           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
136:           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
137:           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;

139:           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
140:           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
141:           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
142:           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
143:           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;

145:           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
146:           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
147:           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
148:           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
149:           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;

151:           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
152:           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
153:           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
154:           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
155:           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;

157:           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
158:           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
159:           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
160:           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
161:           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;

163:           pv += 25;
164:         }
165:         PetscLogFlops(250.0*nz+225.0);
166:       }
167:       row = *ajtmp++;
168:     }
169:     /* finished row so stick it into b->a */
170:     pv = ba + 25*bi[i];
171:     pj = bj + bi[i];
172:     nz = bi[i+1] - bi[i];
173:     for (j=0; j<nz; j++) {
174: #if defined(PETSC_USE_MEMCPY)
175:       PetscArraycpy(pv,rtmp+25*pj[j],25);
176: #else
177:       x      = rtmp+25*pj[j];
178:       pv[0]  = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
179:       pv[4]  = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
180:       pv[9]  = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
181:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
182:       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
183:       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
184: #endif
185:       pv += 25;
186:     }
187:     /* invert diagonal block */
188:     w    = ba + 25*diag_offset[i];
189:     PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
190:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
191:   }

193:   PetscFree(rtmp);
194:   ISRestoreIndices(isicol,&ic);
195:   ISRestoreIndices(isrow,&r);

197:   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
198:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
199:   C->assembled           = PETSC_TRUE;

201:   PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
202:   return 0;
203: }

205: /* MatLUFactorNumeric_SeqBAIJ_5 -
206:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
207:        PetscKernel_A_gets_A_times_B()
208:        PetscKernel_A_gets_A_minus_B_times_C()
209:        PetscKernel_A_gets_inverse_A()
210: */

212: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
213: {
214:   Mat            C     =B;
215:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
216:   IS             isrow = b->row,isicol = b->icol;
217:   const PetscInt *r,*ic;
218:   PetscInt       i,j,k,nz,nzL,row;
219:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
220:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
221:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
222:   PetscInt       flg,ipvt[5];
223:   PetscReal      shift = info->shiftamount;
224:   PetscBool      allowzeropivot,zeropivotdetected;

226:   allowzeropivot = PetscNot(A->erroriffailure);
227:   ISGetIndices(isrow,&r);
228:   ISGetIndices(isicol,&ic);

230:   /* generate work space needed by the factorization */
231:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
232:   PetscArrayzero(rtmp,bs2*n);

234:   for (i=0; i<n; i++) {
235:     /* zero rtmp */
236:     /* L part */
237:     nz    = bi[i+1] - bi[i];
238:     bjtmp = bj + bi[i];
239:     for  (j=0; j<nz; j++) {
240:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
241:     }

243:     /* U part */
244:     nz    = bdiag[i] - bdiag[i+1];
245:     bjtmp = bj + bdiag[i+1]+1;
246:     for  (j=0; j<nz; j++) {
247:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
248:     }

250:     /* load in initial (unfactored row) */
251:     nz    = ai[r[i]+1] - ai[r[i]];
252:     ajtmp = aj + ai[r[i]];
253:     v     = aa + bs2*ai[r[i]];
254:     for (j=0; j<nz; j++) {
255:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
256:     }

258:     /* elimination */
259:     bjtmp = bj + bi[i];
260:     nzL   = bi[i+1] - bi[i];
261:     for (k=0; k < nzL; k++) {
262:       row = bjtmp[k];
263:       pc  = rtmp + bs2*row;
264:       for (flg=0,j=0; j<bs2; j++) {
265:         if (pc[j]!=0.0) {
266:           flg = 1;
267:           break;
268:         }
269:       }
270:       if (flg) {
271:         pv = b->a + bs2*bdiag[row];
272:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
273:         PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);

275:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
276:         pv = b->a + bs2*(bdiag[row+1]+1);
277:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
278:         for (j=0; j<nz; j++) {
279:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
280:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
281:           v    = rtmp + bs2*pj[j];
282:           PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);
283:           pv  += bs2;
284:         }
285:         PetscLogFlops(250.0*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
286:       }
287:     }

289:     /* finished row so stick it into b->a */
290:     /* L part */
291:     pv = b->a + bs2*bi[i];
292:     pj = b->j + bi[i];
293:     nz = bi[i+1] - bi[i];
294:     for (j=0; j<nz; j++) {
295:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
296:     }

298:     /* Mark diagonal and invert diagonal for simpler triangular solves */
299:     pv   = b->a + bs2*bdiag[i];
300:     pj   = b->j + bdiag[i];
301:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
302:     PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
303:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

305:     /* U part */
306:     pv = b->a + bs2*(bdiag[i+1]+1);
307:     pj = b->j + bdiag[i+1]+1;
308:     nz = bdiag[i] - bdiag[i+1] - 1;
309:     for (j=0; j<nz; j++) {
310:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
311:     }
312:   }

314:   PetscFree2(rtmp,mwork);
315:   ISRestoreIndices(isicol,&ic);
316:   ISRestoreIndices(isrow,&r);

318:   C->ops->solve          = MatSolve_SeqBAIJ_5;
319:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
320:   C->assembled           = PETSC_TRUE;

322:   PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
323:   return 0;
324: }

326: /*
327:       Version for when blocks are 5 by 5 Using natural ordering
328: */
329: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
330: {
331:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
332:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
333:   PetscInt       *ajtmpold,*ajtmp,nz,row;
334:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
335:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
336:   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
337:   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
338:   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
339:   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
340:   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
341:   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
342:   MatScalar      *ba   = b->a,*aa = a->a,work[25];
343:   PetscReal      shift = info->shiftamount;
344:   PetscBool      allowzeropivot,zeropivotdetected;

346:   allowzeropivot = PetscNot(A->erroriffailure);
347:   PetscMalloc1(25*(n+1),&rtmp);
348:   for (i=0; i<n; i++) {
349:     nz    = bi[i+1] - bi[i];
350:     ajtmp = bj + bi[i];
351:     for  (j=0; j<nz; j++) {
352:       x     = rtmp+25*ajtmp[j];
353:       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
354:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
355:       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
356:     }
357:     /* load in initial (unfactored row) */
358:     nz       = ai[i+1] - ai[i];
359:     ajtmpold = aj + ai[i];
360:     v        = aa + 25*ai[i];
361:     for (j=0; j<nz; j++) {
362:       x     = rtmp+25*ajtmpold[j];
363:       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
364:       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
365:       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
366:       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
367:       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
368:       x[24] = v[24];
369:       v    += 25;
370:     }
371:     row = *ajtmp++;
372:     while (row < i) {
373:       pc  = rtmp + 25*row;
374:       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
375:       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
376:       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
377:       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
378:       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
379:       p24 = pc[23]; p25 = pc[24];
380:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
381:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
382:           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
383:           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
384:           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
385:         pv    = ba + 25*diag_offset[row];
386:         pj    = bj + diag_offset[row] + 1;
387:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
388:         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
389:         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
390:         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
391:         x20   = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
392:         x25   = pv[24];
393:         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
394:         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
395:         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
396:         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
397:         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;

399:         pc[5] = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
400:         pc[6] = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
401:         pc[7] = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
402:         pc[8] = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
403:         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;

405:         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
406:         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
407:         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
408:         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
409:         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;

411:         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
412:         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
413:         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
414:         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
415:         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;

417:         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
418:         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
419:         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
420:         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
421:         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;

423:         nz  = bi[row+1] - diag_offset[row] - 1;
424:         pv += 25;
425:         for (j=0; j<nz; j++) {
426:           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
427:           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
428:           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
429:           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
430:           x19   = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
431:           x24   = pv[23];  x25 = pv[24];
432:           x     = rtmp + 25*pj[j];
433:           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
434:           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
435:           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
436:           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
437:           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;

439:           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
440:           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
441:           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
442:           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
443:           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;

445:           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
446:           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
447:           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
448:           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
449:           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;

451:           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
452:           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
453:           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
454:           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
455:           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;

457:           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
458:           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
459:           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
460:           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
461:           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
462:           pv    += 25;
463:         }
464:         PetscLogFlops(250.0*nz+225.0);
465:       }
466:       row = *ajtmp++;
467:     }
468:     /* finished row so stick it into b->a */
469:     pv = ba + 25*bi[i];
470:     pj = bj + bi[i];
471:     nz = bi[i+1] - bi[i];
472:     for (j=0; j<nz; j++) {
473:       x      = rtmp+25*pj[j];
474:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
475:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
476:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
477:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
478:       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
479:       pv[23] = x[23]; pv[24] = x[24];
480:       pv    += 25;
481:     }
482:     /* invert diagonal block */
483:     w    = ba + 25*diag_offset[i];
484:     PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
485:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
486:   }

488:   PetscFree(rtmp);

490:   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
491:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
492:   C->assembled           = PETSC_TRUE;

494:   PetscLogFlops(1.333333333333*5*5*5*b->mbs); /* from inverting diagonal blocks */
495:   return 0;
496: }

498: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
499: {
500:   Mat            C =B;
501:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
502:   PetscInt       i,j,k,nz,nzL,row;
503:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
504:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
505:   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
506:   PetscInt       flg,ipvt[5];
507:   PetscReal      shift = info->shiftamount;
508:   PetscBool      allowzeropivot,zeropivotdetected;

510:   allowzeropivot = PetscNot(A->erroriffailure);

512:   /* generate work space needed by the factorization */
513:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
514:   PetscArrayzero(rtmp,bs2*n);

516:   for (i=0; i<n; i++) {
517:     /* zero rtmp */
518:     /* L part */
519:     nz    = bi[i+1] - bi[i];
520:     bjtmp = bj + bi[i];
521:     for  (j=0; j<nz; j++) {
522:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
523:     }

525:     /* U part */
526:     nz    = bdiag[i] - bdiag[i+1];
527:     bjtmp = bj + bdiag[i+1]+1;
528:     for  (j=0; j<nz; j++) {
529:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
530:     }

532:     /* load in initial (unfactored row) */
533:     nz    = ai[i+1] - ai[i];
534:     ajtmp = aj + ai[i];
535:     v     = aa + bs2*ai[i];
536:     for (j=0; j<nz; j++) {
537:       PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
538:     }

540:     /* elimination */
541:     bjtmp = bj + bi[i];
542:     nzL   = bi[i+1] - bi[i];
543:     for (k=0; k < nzL; k++) {
544:       row = bjtmp[k];
545:       pc  = rtmp + bs2*row;
546:       for (flg=0,j=0; j<bs2; j++) {
547:         if (pc[j]!=0.0) {
548:           flg = 1;
549:           break;
550:         }
551:       }
552:       if (flg) {
553:         pv = b->a + bs2*bdiag[row];
554:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
555:         PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);

557:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
558:         pv = b->a + bs2*(bdiag[row+1]+1);
559:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
560:         for (j=0; j<nz; j++) {
561:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
562:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
563:           vv   = rtmp + bs2*pj[j];
564:           PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);
565:           pv  += bs2;
566:         }
567:         PetscLogFlops(250.0*nz+225); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
568:       }
569:     }

571:     /* finished row so stick it into b->a */
572:     /* L part */
573:     pv = b->a + bs2*bi[i];
574:     pj = b->j + bi[i];
575:     nz = bi[i+1] - bi[i];
576:     for (j=0; j<nz; j++) {
577:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
578:     }

580:     /* Mark diagonal and invert diagonal for simpler triangular solves */
581:     pv   = b->a + bs2*bdiag[i];
582:     pj   = b->j + bdiag[i];
583:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
584:     PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
585:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

587:     /* U part */
588:     pv = b->a + bs2*(bdiag[i+1]+1);
589:     pj = b->j + bdiag[i+1]+1;
590:     nz = bdiag[i] - bdiag[i+1] - 1;
591:     for (j=0; j<nz; j++) {
592:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
593:     }
594:   }
595:   PetscFree2(rtmp,mwork);

597:   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
598:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
599:   C->assembled           = PETSC_TRUE;

601:   PetscLogFlops(1.333333333333*5*5*5*n); /* from inverting diagonal blocks */
602:   return 0;
603: }