1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.39 2000/10/31 19:39:49 hzhang Exp hzhang $*/ 5 /* 6 Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP. 7 */ 8 #include "sbaij.h" 9 #include "src/mat/impls/baij/seq/baij.h" 10 #include "src/vec/vecimpl.h" 11 #include "src/inline/ilu.h" 12 #include "include/petscis.h" 13 14 #undef __FUNC__ 15 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ" 16 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS perm,PetscReal f,Mat *B) 17 { 18 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b; 19 int *rip,ierr,i,mbs = a->mbs,*ai,*aj; 20 int *jutmp,bs = a->bs,bs2=a->bs2; 21 int m,nzi,realloc = 0; 22 int *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd; 23 /* PetscTruth ident; */ 24 25 PetscFunctionBegin; 26 PetscValidHeaderSpecific(perm,IS_COOKIE); 27 if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 28 29 /* check whether perm is the identity mapping */ 30 /* 31 ierr = ISView(perm, VIEWER_STDOUT_SELF);CHKERRA(ierr); 32 ierr = ISIdentity(perm,&ident);CHKERRQ(ierr); 33 printf("ident = %d\n", ident); 34 */ 35 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 36 for (i=0; i<mbs; i++){ 37 if (rip[i] != i){ 38 a->permute = PETSC_TRUE; 39 /* printf("non-trivial perm\n"); */ 40 break; 41 } 42 } 43 44 if (!a->permute){ /* without permutation */ 45 ai = a->i; aj = a->j; 46 } else { /* non-trivial permutation */ 47 ierr = MatReorderingSeqSBAIJ(A, perm);CHKERRA(ierr); 48 ai = a->inew; aj = a->jnew; 49 } 50 51 /* initialization */ 52 /* Don't know how many column pointers are needed so estimate. 53 Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */ 54 iu = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu); 55 umax = (int)(f*ai[mbs] + 1); umax += mbs + 1; 56 ju = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju); 57 iu[0] = mbs+1; 58 juptr = mbs; 59 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 60 q = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q); 61 for (i=0; i<mbs; i++){ 62 jl[i] = mbs; q[i] = 0; 63 } 64 65 /* for each row k */ 66 for (k=0; k<mbs; k++){ 67 nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */ 68 q[k] = mbs; 69 /* initialize nonzero structure of k-th row to row rip[k] of A */ 70 jmin = ai[rip[k]]; 71 jmax = ai[rip[k]+1]; 72 for (j=jmin; j<jmax; j++){ 73 vj = rip[aj[j]]; /* col. value */ 74 if(vj > k){ 75 qm = k; 76 do { 77 m = qm; qm = q[m]; 78 } while(qm < vj); 79 if (qm == vj) { 80 printf(" error: duplicate entry in A\n"); break; 81 } 82 nzk++; 83 q[m] = vj; 84 q[vj] = qm; 85 } /* if(vj > k) */ 86 } /* for (j=jmin; j<jmax; j++) */ 87 88 /* modify nonzero structure of k-th row by computing fill-in 89 for each row i to be merged in */ 90 i = k; 91 i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */ 92 /* printf(" next pivot row i=%d\n",i); */ 93 while (i < mbs){ 94 /* merge row i into k-th row */ 95 nzi = iu[i+1] - (iu[i]+1); 96 jmin = iu[i] + 1; jmax = iu[i] + nzi; 97 qm = k; 98 for (j=jmin; j<jmax+1; j++){ 99 vj = ju[j]; 100 do { 101 m = qm; qm = q[m]; 102 } while (qm < vj); 103 if (qm != vj){ 104 nzk++; q[m] = vj; q[vj] = qm; qm = vj; 105 } 106 } 107 i = jl[i]; /* next pivot row */ 108 } 109 110 /* add k to row list for first nonzero element in k-th row */ 111 if (nzk > 0){ 112 i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */ 113 jl[k] = jl[i]; jl[i] = k; 114 } 115 iu[k+1] = iu[k] + nzk; /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/ 116 117 /* allocate more space to ju if needed */ 118 if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax); 119 /* estimate how much additional space we will need */ 120 /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */ 121 /* just double the memory each time */ 122 maxadd = umax; 123 if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2; 124 umax += maxadd; 125 126 /* allocate a longer ju */ 127 jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp); 128 ierr = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr); 129 ierr = PetscFree(ju);CHKERRQ(ierr); 130 ju = jutmp; 131 realloc++; /* count how many times we realloc */ 132 } 133 134 /* save nonzero structure of k-th row in ju */ 135 i=k; 136 jumin = juptr + 1; juptr += nzk; 137 for (j=jumin; j<juptr+1; j++){ 138 i=q[i]; 139 ju[j]=i; 140 } 141 } 142 143 if (ai[mbs] != 0) { 144 PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]); 145 PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af); 146 PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af); 147 PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af); 148 PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n"); 149 } else { 150 PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n"); 151 } 152 153 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 154 ierr = PetscFree(q);CHKERRQ(ierr); 155 ierr = PetscFree(jl);CHKERRQ(ierr); 156 157 /* put together the new matrix */ 158 ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr); 159 /* PLogObjectParent(*B,iperm); */ 160 b = (Mat_SeqSBAIJ*)(*B)->data; 161 ierr = PetscFree(b->imax);CHKERRQ(ierr); 162 b->singlemalloc = PETSC_FALSE; 163 /* the next line frees the default space generated by the Create() */ 164 ierr = PetscFree(b->a);CHKERRQ(ierr); 165 ierr = PetscFree(b->ilen);CHKERRQ(ierr); 166 b->a = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a); 167 b->j = ju; 168 b->i = iu; 169 b->diag = 0; 170 b->ilen = 0; 171 b->imax = 0; 172 b->row = perm; 173 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 174 b->icol = perm; 175 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 176 b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 177 /* In b structure: Free imax, ilen, old a, old j. 178 Allocate idnew, solve_work, new a, new j */ 179 PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar))); 180 b->s_maxnz = b->s_nz = iu[mbs]; 181 182 (*B)->factor = FACTOR_CHOLESKY; 183 (*B)->info.factor_mallocs = realloc; 184 (*B)->info.fill_ratio_given = f; 185 if (ai[mbs] != 0) { 186 (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]); 187 } else { 188 (*B)->info.fill_ratio_needed = 0.0; 189 } 190 191 PetscFunctionReturn(0); 192 } 193 194 #undef __FUNC__ 195 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N" 196 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B) 197 { 198 Mat C = *B; 199 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 200 IS isrow = b->row,isicol = b->icol; 201 int *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 202 int *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg; 203 int *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj; 204 MatScalar *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w; 205 206 PetscFunctionBegin; 207 printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n"); 208 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 209 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 210 rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 211 ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr); 212 /* generate work space needed by dense LU factorization */ 213 v_work = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work); 214 multiplier = v_work + bs; 215 v_pivots = (int*)(multiplier + bs2); 216 217 /* flops in while loop */ 218 bslog = 2*bs*bs2; 219 220 for (i=0; i<n; i++) { 221 nz = bi[i+1] - bi[i]; 222 ajtmp = bj + bi[i]; 223 for (j=0; j<nz; j++) { 224 ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 225 } 226 /* load in initial (unfactored row) */ 227 nz = ai[r[i]+1] - ai[r[i]]; 228 ajtmpold = aj + ai[r[i]]; 229 v = aa + bs2*ai[r[i]]; 230 for (j=0; j<nz; j++) { 231 ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr); 232 } 233 row = *ajtmp++; 234 while (row < i) { 235 pc = rtmp + bs2*row; 236 /* if (*pc) { */ 237 for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }} 238 if (flg) { 239 pv = ba + bs2*diag_offset[row]; 240 pj = bj + diag_offset[row] + 1; 241 Kernel_A_gets_A_times_B(bs,pc,pv,multiplier); 242 nz = bi[row+1] - diag_offset[row] - 1; 243 pv += bs2; 244 for (j=0; j<nz; j++) { 245 Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); 246 } 247 PLogFlops(bslog*(nz+1)-bs); 248 } 249 row = *ajtmp++; 250 } 251 /* finished row so stick it into b->a */ 252 pv = ba + bs2*bi[i]; 253 pj = bj + bi[i]; 254 nz = bi[i+1] - bi[i]; 255 for (j=0; j<nz; j++) { 256 ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 257 } 258 diag = diag_offset[i] - bi[i]; 259 /* invert diagonal block */ 260 w = pv + bs2*diag; 261 Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work); 262 } 263 264 ierr = PetscFree(rtmp);CHKERRQ(ierr); 265 ierr = PetscFree(v_work);CHKERRQ(ierr); 266 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 267 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 268 C->factor = FACTOR_LU; 269 C->assembled = PETSC_TRUE; 270 PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */ 271 PetscFunctionReturn(0); 272 } 273 274 /* Version for when blocks are 7 by 7 */ 275 #undef __FUNC__ 276 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7" 277 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B) 278 { 279 Mat C = *B; 280 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 281 IS perm = b->row; 282 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 283 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 284 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 285 MatScalar *u,*d,*w,*wp; 286 287 PetscFunctionBegin; 288 /* initialization */ 289 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 290 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 291 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 292 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 293 for (i=0; i<mbs; i++) { 294 jl[i] = mbs; il[0] = 0; 295 } 296 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 297 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 298 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 299 300 /* check permutation */ 301 if (!a->permute){ 302 ai = a->i; aj = a->j; aa = a->a; 303 } else { 304 ai = a->inew; aj = a->jnew; 305 aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 306 ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 307 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 308 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 309 310 for (i=0; i<mbs; i++){ 311 jmin = ai[i]; jmax = ai[i+1]; 312 for (j=jmin; j<jmax; j++){ 313 while (a2anew[j] != j){ 314 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 315 for (k1=0; k1<49; k1++){ 316 dk[k1] = aa[k*49+k1]; 317 aa[k*49+k1] = aa[j*49+k1]; 318 aa[j*49+k1] = dk[k1]; 319 } 320 } 321 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 322 if (i > aj[j]){ 323 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 324 ap = aa + j*49; /* ptr to the beginning of j-th block of aa */ 325 for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 326 for (k=0; k<7; k++){ /* j-th block of aa <- dk^T */ 327 for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1]; 328 } 329 } 330 } 331 } 332 ierr = PetscFree(a2anew);CHKERRA(ierr); 333 } 334 335 /* for each row k */ 336 for (k = 0; k<mbs; k++){ 337 338 /*initialize k-th row with elements nonzero in row perm(k) of A */ 339 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 340 if (jmin < jmax) { 341 ap = aa + jmin*49; 342 for (j = jmin; j < jmax; j++){ 343 vj = perm_ptr[aj[j]]; /* block col. index */ 344 wp = w + vj*49; 345 for (i=0; i<49; i++) *wp++ = *ap++; 346 } 347 } 348 349 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 350 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 351 i = jl[k]; /* first row to be added to k_th row */ 352 353 while (i < mbs){ 354 nexti = jl[i]; /* next row to be added to k_th row */ 355 356 /* compute multiplier */ 357 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 358 359 /* uik = -inv(Di)*U_bar(i,k) */ 360 d = ba + i*49; 361 u = ba + ili*49; 362 363 uik[0] = -(d[0]*u[0] + d[7]*u[1]+ d[14]*u[2]+ d[21]*u[3]+ d[28]*u[4]+ d[35]*u[5]+ d[42]*u[6]); 364 uik[1] = -(d[1]*u[0] + d[8]*u[1]+ d[15]*u[2]+ d[22]*u[3]+ d[29]*u[4]+ d[36]*u[5]+ d[43]*u[6]); 365 uik[2] = -(d[2]*u[0] + d[9]*u[1]+ d[16]*u[2]+ d[23]*u[3]+ d[30]*u[4]+ d[37]*u[5]+ d[44]*u[6]); 366 uik[3] = -(d[3]*u[0]+ d[10]*u[1]+ d[17]*u[2]+ d[24]*u[3]+ d[31]*u[4]+ d[38]*u[5]+ d[45]*u[6]); 367 uik[4] = -(d[4]*u[0]+ d[11]*u[1]+ d[18]*u[2]+ d[25]*u[3]+ d[32]*u[4]+ d[39]*u[5]+ d[46]*u[6]); 368 uik[5] = -(d[5]*u[0]+ d[12]*u[1]+ d[19]*u[2]+ d[26]*u[3]+ d[33]*u[4]+ d[40]*u[5]+ d[47]*u[6]); 369 uik[6] = -(d[6]*u[0]+ d[13]*u[1]+ d[20]*u[2]+ d[27]*u[3]+ d[34]*u[4]+ d[41]*u[5]+ d[48]*u[6]); 370 371 uik[7] = -(d[0]*u[7] + d[7]*u[8]+ d[14]*u[9]+ d[21]*u[10]+ d[28]*u[11]+ d[35]*u[12]+ d[42]*u[13]); 372 uik[8] = -(d[1]*u[7] + d[8]*u[8]+ d[15]*u[9]+ d[22]*u[10]+ d[29]*u[11]+ d[36]*u[12]+ d[43]*u[13]); 373 uik[9] = -(d[2]*u[7] + d[9]*u[8]+ d[16]*u[9]+ d[23]*u[10]+ d[30]*u[11]+ d[37]*u[12]+ d[44]*u[13]); 374 uik[10]= -(d[3]*u[7]+ d[10]*u[8]+ d[17]*u[9]+ d[24]*u[10]+ d[31]*u[11]+ d[38]*u[12]+ d[45]*u[13]); 375 uik[11]= -(d[4]*u[7]+ d[11]*u[8]+ d[18]*u[9]+ d[25]*u[10]+ d[32]*u[11]+ d[39]*u[12]+ d[46]*u[13]); 376 uik[12]= -(d[5]*u[7]+ d[12]*u[8]+ d[19]*u[9]+ d[26]*u[10]+ d[33]*u[11]+ d[40]*u[12]+ d[47]*u[13]); 377 uik[13]= -(d[6]*u[7]+ d[13]*u[8]+ d[20]*u[9]+ d[27]*u[10]+ d[34]*u[11]+ d[41]*u[12]+ d[48]*u[13]); 378 379 uik[14]= -(d[0]*u[14] + d[7]*u[15]+ d[14]*u[16]+ d[21]*u[17]+ d[28]*u[18]+ d[35]*u[19]+ d[42]*u[20]); 380 uik[15]= -(d[1]*u[14] + d[8]*u[15]+ d[15]*u[16]+ d[22]*u[17]+ d[29]*u[18]+ d[36]*u[19]+ d[43]*u[20]); 381 uik[16]= -(d[2]*u[14] + d[9]*u[15]+ d[16]*u[16]+ d[23]*u[17]+ d[30]*u[18]+ d[37]*u[19]+ d[44]*u[20]); 382 uik[17]= -(d[3]*u[14]+ d[10]*u[15]+ d[17]*u[16]+ d[24]*u[17]+ d[31]*u[18]+ d[38]*u[19]+ d[45]*u[20]); 383 uik[18]= -(d[4]*u[14]+ d[11]*u[15]+ d[18]*u[16]+ d[25]*u[17]+ d[32]*u[18]+ d[39]*u[19]+ d[46]*u[20]); 384 uik[19]= -(d[5]*u[14]+ d[12]*u[15]+ d[19]*u[16]+ d[26]*u[17]+ d[33]*u[18]+ d[40]*u[19]+ d[47]*u[20]); 385 uik[20]= -(d[6]*u[14]+ d[13]*u[15]+ d[20]*u[16]+ d[27]*u[17]+ d[34]*u[18]+ d[41]*u[19]+ d[48]*u[20]); 386 387 uik[21]= -(d[0]*u[21] + d[7]*u[22]+ d[14]*u[23]+ d[21]*u[24]+ d[28]*u[25]+ d[35]*u[26]+ d[42]*u[27]); 388 uik[22]= -(d[1]*u[21] + d[8]*u[22]+ d[15]*u[23]+ d[22]*u[24]+ d[29]*u[25]+ d[36]*u[26]+ d[43]*u[27]); 389 uik[23]= -(d[2]*u[21] + d[9]*u[22]+ d[16]*u[23]+ d[23]*u[24]+ d[30]*u[25]+ d[37]*u[26]+ d[44]*u[27]); 390 uik[24]= -(d[3]*u[21]+ d[10]*u[22]+ d[17]*u[23]+ d[24]*u[24]+ d[31]*u[25]+ d[38]*u[26]+ d[45]*u[27]); 391 uik[25]= -(d[4]*u[21]+ d[11]*u[22]+ d[18]*u[23]+ d[25]*u[24]+ d[32]*u[25]+ d[39]*u[26]+ d[46]*u[27]); 392 uik[26]= -(d[5]*u[21]+ d[12]*u[22]+ d[19]*u[23]+ d[26]*u[24]+ d[33]*u[25]+ d[40]*u[26]+ d[47]*u[27]); 393 uik[27]= -(d[6]*u[21]+ d[13]*u[22]+ d[20]*u[23]+ d[27]*u[24]+ d[34]*u[25]+ d[41]*u[26]+ d[48]*u[27]); 394 395 uik[28]= -(d[0]*u[28] + d[7]*u[29]+ d[14]*u[30]+ d[21]*u[31]+ d[28]*u[32]+ d[35]*u[33]+ d[42]*u[34]); 396 uik[29]= -(d[1]*u[28] + d[8]*u[29]+ d[15]*u[30]+ d[22]*u[31]+ d[29]*u[32]+ d[36]*u[33]+ d[43]*u[34]); 397 uik[30]= -(d[2]*u[28] + d[9]*u[29]+ d[16]*u[30]+ d[23]*u[31]+ d[30]*u[32]+ d[37]*u[33]+ d[44]*u[34]); 398 uik[31]= -(d[3]*u[28]+ d[10]*u[29]+ d[17]*u[30]+ d[24]*u[31]+ d[31]*u[32]+ d[38]*u[33]+ d[45]*u[34]); 399 uik[32]= -(d[4]*u[28]+ d[11]*u[29]+ d[18]*u[30]+ d[25]*u[31]+ d[32]*u[32]+ d[39]*u[33]+ d[46]*u[34]); 400 uik[33]= -(d[5]*u[28]+ d[12]*u[29]+ d[19]*u[30]+ d[26]*u[31]+ d[33]*u[32]+ d[40]*u[33]+ d[47]*u[34]); 401 uik[34]= -(d[6]*u[28]+ d[13]*u[29]+ d[20]*u[30]+ d[27]*u[31]+ d[34]*u[32]+ d[41]*u[33]+ d[48]*u[34]); 402 403 uik[35]= -(d[0]*u[35] + d[7]*u[36]+ d[14]*u[37]+ d[21]*u[38]+ d[28]*u[39]+ d[35]*u[40]+ d[42]*u[41]); 404 uik[36]= -(d[1]*u[35] + d[8]*u[36]+ d[15]*u[37]+ d[22]*u[38]+ d[29]*u[39]+ d[36]*u[40]+ d[43]*u[41]); 405 uik[37]= -(d[2]*u[35] + d[9]*u[36]+ d[16]*u[37]+ d[23]*u[38]+ d[30]*u[39]+ d[37]*u[40]+ d[44]*u[41]); 406 uik[38]= -(d[3]*u[35]+ d[10]*u[36]+ d[17]*u[37]+ d[24]*u[38]+ d[31]*u[39]+ d[38]*u[40]+ d[45]*u[41]); 407 uik[39]= -(d[4]*u[35]+ d[11]*u[36]+ d[18]*u[37]+ d[25]*u[38]+ d[32]*u[39]+ d[39]*u[40]+ d[46]*u[41]); 408 uik[40]= -(d[5]*u[35]+ d[12]*u[36]+ d[19]*u[37]+ d[26]*u[38]+ d[33]*u[39]+ d[40]*u[40]+ d[47]*u[41]); 409 uik[41]= -(d[6]*u[35]+ d[13]*u[36]+ d[20]*u[37]+ d[27]*u[38]+ d[34]*u[39]+ d[41]*u[40]+ d[48]*u[41]); 410 411 uik[42]= -(d[0]*u[42] + d[7]*u[43]+ d[14]*u[44]+ d[21]*u[45]+ d[28]*u[46]+ d[35]*u[47]+ d[42]*u[48]); 412 uik[43]= -(d[1]*u[42] + d[8]*u[43]+ d[15]*u[44]+ d[22]*u[45]+ d[29]*u[46]+ d[36]*u[47]+ d[43]*u[48]); 413 uik[44]= -(d[2]*u[42] + d[9]*u[43]+ d[16]*u[44]+ d[23]*u[45]+ d[30]*u[46]+ d[37]*u[47]+ d[44]*u[48]); 414 uik[45]= -(d[3]*u[42]+ d[10]*u[43]+ d[17]*u[44]+ d[24]*u[45]+ d[31]*u[46]+ d[38]*u[47]+ d[45]*u[48]); 415 uik[46]= -(d[4]*u[42]+ d[11]*u[43]+ d[18]*u[44]+ d[25]*u[45]+ d[32]*u[46]+ d[39]*u[47]+ d[46]*u[48]); 416 uik[47]= -(d[5]*u[42]+ d[12]*u[43]+ d[19]*u[44]+ d[26]*u[45]+ d[33]*u[46]+ d[40]*u[47]+ d[47]*u[48]); 417 uik[48]= -(d[6]*u[42]+ d[13]*u[43]+ d[20]*u[44]+ d[27]*u[45]+ d[34]*u[46]+ d[41]*u[47]+ d[48]*u[48]); 418 419 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 420 dk[0]+= uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6]; 421 dk[1]+= uik[7]*u[0] + uik[8]*u[1] + uik[9]*u[2]+ uik[10]*u[3]+ uik[11]*u[4]+ uik[12]*u[5]+ uik[13]*u[6]; 422 dk[2]+= uik[14]*u[0]+ uik[15]*u[1]+ uik[16]*u[2]+ uik[17]*u[3]+ uik[18]*u[4]+ uik[19]*u[5]+ uik[20]*u[6]; 423 dk[3]+= uik[21]*u[0]+ uik[22]*u[1]+ uik[23]*u[2]+ uik[24]*u[3]+ uik[25]*u[4]+ uik[26]*u[5]+ uik[27]*u[6]; 424 dk[4]+= uik[28]*u[0]+ uik[29]*u[1]+ uik[30]*u[2]+ uik[31]*u[3]+ uik[32]*u[4]+ uik[33]*u[5]+ uik[34]*u[6]; 425 dk[5]+= uik[35]*u[0]+ uik[36]*u[1]+ uik[37]*u[2]+ uik[38]*u[3]+ uik[39]*u[4]+ uik[40]*u[5]+ uik[41]*u[6]; 426 dk[6]+= uik[42]*u[0]+ uik[43]*u[1]+ uik[44]*u[2]+ uik[45]*u[3]+ uik[46]*u[4]+ uik[47]*u[5]+ uik[48]*u[6]; 427 428 dk[7]+= uik[0]*u[7] + uik[1]*u[8] + uik[2]*u[9] + uik[3]*u[10] + uik[4]*u[11] + uik[5]*u[12] + uik[6]*u[13]; 429 dk[8]+= uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]; 430 dk[9]+= uik[14]*u[7]+ uik[15]*u[8]+ uik[16]*u[9]+ uik[17]*u[10]+ uik[18]*u[11]+ uik[19]*u[12]+ uik[20]*u[13]; 431 dk[10]+=uik[21]*u[7]+ uik[22]*u[8]+ uik[23]*u[9]+ uik[24]*u[10]+ uik[25]*u[11]+ uik[26]*u[12]+ uik[27]*u[13]; 432 dk[11]+=uik[28]*u[7]+ uik[29]*u[8]+ uik[30]*u[9]+ uik[31]*u[10]+ uik[32]*u[11]+ uik[33]*u[12]+ uik[34]*u[13]; 433 dk[12]+=uik[35]*u[7]+ uik[36]*u[8]+ uik[37]*u[9]+ uik[38]*u[10]+ uik[39]*u[11]+ uik[40]*u[12]+ uik[41]*u[13]; 434 dk[13]+=uik[42]*u[7]+ uik[43]*u[8]+ uik[44]*u[9]+ uik[45]*u[10]+ uik[46]*u[11]+ uik[47]*u[12]+ uik[48]*u[13]; 435 436 dk[14]+= uik[0]*u[14] + uik[1]*u[15] + uik[2]*u[16] + uik[3]*u[17] + uik[4]*u[18] + uik[5]*u[19] + uik[6]*u[20]; 437 dk[15]+= uik[7]*u[14] + uik[8]*u[15] + uik[9]*u[16]+ uik[10]*u[17]+ uik[11]*u[18]+ uik[12]*u[19]+ uik[13]*u[20]; 438 dk[16]+= uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]; 439 dk[17]+= uik[21]*u[14]+ uik[22]*u[15]+ uik[23]*u[16]+ uik[24]*u[17]+ uik[25]*u[18]+ uik[26]*u[19]+ uik[27]*u[20]; 440 dk[18]+= uik[28]*u[14]+ uik[29]*u[15]+ uik[30]*u[16]+ uik[31]*u[17]+ uik[32]*u[18]+ uik[33]*u[19]+ uik[34]*u[20]; 441 dk[19]+= uik[35]*u[14]+ uik[36]*u[15]+ uik[37]*u[16]+ uik[38]*u[17]+ uik[39]*u[18]+ uik[40]*u[19]+ uik[41]*u[20]; 442 dk[20]+= uik[42]*u[14]+ uik[43]*u[15]+ uik[44]*u[16]+ uik[45]*u[17]+ uik[46]*u[18]+ uik[47]*u[19]+ uik[48]*u[20]; 443 444 dk[21]+= uik[0]*u[21] + uik[1]*u[22] + uik[2]*u[23] + uik[3]*u[24] + uik[4]*u[25] + uik[5]*u[26] + uik[6]*u[27]; 445 dk[22]+= uik[7]*u[21] + uik[8]*u[22] + uik[9]*u[23]+ uik[10]*u[24]+ uik[11]*u[25]+ uik[12]*u[26]+ uik[13]*u[27]; 446 dk[23]+= uik[14]*u[21]+ uik[15]*u[22]+ uik[16]*u[23]+ uik[17]*u[24]+ uik[18]*u[25]+ uik[19]*u[26]+ uik[20]*u[27]; 447 dk[24]+= uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]; 448 dk[25]+= uik[28]*u[21]+ uik[29]*u[22]+ uik[30]*u[23]+ uik[31]*u[24]+ uik[32]*u[25]+ uik[33]*u[26]+ uik[34]*u[27]; 449 dk[26]+= uik[35]*u[21]+ uik[36]*u[22]+ uik[37]*u[23]+ uik[38]*u[24]+ uik[39]*u[25]+ uik[40]*u[26]+ uik[41]*u[27]; 450 dk[27]+= uik[42]*u[21]+ uik[43]*u[22]+ uik[44]*u[23]+ uik[45]*u[24]+ uik[46]*u[25]+ uik[47]*u[26]+ uik[48]*u[27]; 451 452 dk[28]+= uik[0]*u[28] + uik[1]*u[29] + uik[2]*u[30] + uik[3]*u[31] + uik[4]*u[32] + uik[5]*u[33] + uik[6]*u[34]; 453 dk[29]+= uik[7]*u[28] + uik[8]*u[29] + uik[9]*u[30]+ uik[10]*u[31]+ uik[11]*u[32]+ uik[12]*u[33]+ uik[13]*u[34]; 454 dk[30]+= uik[14]*u[28]+ uik[15]*u[29]+ uik[16]*u[30]+ uik[17]*u[31]+ uik[18]*u[32]+ uik[19]*u[33]+ uik[20]*u[34]; 455 dk[31]+= uik[21]*u[28]+ uik[22]*u[29]+ uik[23]*u[30]+ uik[24]*u[31]+ uik[25]*u[32]+ uik[26]*u[33]+ uik[27]*u[34]; 456 dk[32]+= uik[28]*u[28]+ uik[29]*u[29]+ uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]; 457 dk[33]+= uik[35]*u[28]+ uik[36]*u[29]+ uik[37]*u[30]+ uik[38]*u[31]+ uik[39]*u[32]+ uik[40]*u[33]+ uik[41]*u[34]; 458 dk[34]+= uik[42]*u[28]+ uik[43]*u[29]+ uik[44]*u[30]+ uik[45]*u[31]+ uik[46]*u[32]+ uik[47]*u[33]+ uik[48]*u[34]; 459 460 dk[35]+= uik[0]*u[35] + uik[1]*u[36] + uik[2]*u[37] + uik[3]*u[38] + uik[4]*u[39] + uik[5]*u[40] + uik[6]*u[41]; 461 dk[36]+= uik[7]*u[35] + uik[8]*u[36] + uik[9]*u[37]+ uik[10]*u[38]+ uik[11]*u[39]+ uik[12]*u[40]+ uik[13]*u[41]; 462 dk[37]+= uik[14]*u[35]+ uik[15]*u[36]+ uik[16]*u[37]+ uik[17]*u[38]+ uik[18]*u[39]+ uik[19]*u[40]+ uik[20]*u[41]; 463 dk[38]+= uik[21]*u[35]+ uik[22]*u[36]+ uik[23]*u[37]+ uik[24]*u[38]+ uik[25]*u[39]+ uik[26]*u[40]+ uik[27]*u[41]; 464 dk[39]+= uik[28]*u[35]+ uik[29]*u[36]+ uik[30]*u[37]+ uik[31]*u[38]+ uik[32]*u[39]+ uik[33]*u[40]+ uik[34]*u[41]; 465 dk[40]+= uik[35]*u[35]+ uik[36]*u[36]+ uik[37]*u[37]+ uik[38]*u[38]+ uik[39]*u[39]+ uik[40]*u[40]+ uik[41]*u[41]; 466 dk[41]+= uik[42]*u[35]+ uik[43]*u[36]+ uik[44]*u[37]+ uik[45]*u[38]+ uik[46]*u[39]+ uik[47]*u[40]+ uik[48]*u[41]; 467 468 dk[42]+= uik[0]*u[42] + uik[1]*u[43] + uik[2]*u[44] + uik[3]*u[45] + uik[4]*u[46] + uik[5]*u[47] + uik[6]*u[48]; 469 dk[43]+= uik[7]*u[42] + uik[8]*u[43] + uik[9]*u[44]+ uik[10]*u[45]+ uik[11]*u[46]+ uik[12]*u[47]+ uik[13]*u[48]; 470 dk[44]+= uik[14]*u[42]+ uik[15]*u[43]+ uik[16]*u[44]+ uik[17]*u[45]+ uik[18]*u[46]+ uik[19]*u[47]+ uik[20]*u[48]; 471 dk[45]+= uik[21]*u[42]+ uik[22]*u[43]+ uik[23]*u[44]+ uik[24]*u[45]+ uik[25]*u[46]+ uik[26]*u[47]+ uik[27]*u[48]; 472 dk[46]+= uik[28]*u[42]+ uik[29]*u[43]+ uik[30]*u[44]+ uik[31]*u[45]+ uik[32]*u[46]+ uik[33]*u[47]+ uik[34]*u[48]; 473 dk[47]+= uik[35]*u[42]+ uik[36]*u[43]+ uik[37]*u[44]+ uik[38]*u[45]+ uik[39]*u[46]+ uik[40]*u[47]+ uik[41]*u[48]; 474 dk[48]+= uik[42]*u[42]+ uik[43]*u[43]+ uik[44]*u[44]+ uik[45]*u[45]+ uik[46]*u[46]+ uik[47]*u[47]+ uik[48]*u[48]; 475 476 /* update -U(i,k) */ 477 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 478 479 /* add multiple of row i to k-th row ... */ 480 jmin = ili + 1; jmax = bi[i+1]; 481 if (jmin < jmax){ 482 for (j=jmin; j<jmax; j++) { 483 /* w += -U(i,k)^T * U_bar(i,j) */ 484 wp = w + bj[j]*49; 485 u = ba + j*49; 486 487 wp[0]+= uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6]; 488 wp[1]+= uik[7]*u[0] + uik[8]*u[1] + uik[9]*u[2]+ uik[10]*u[3]+ uik[11]*u[4]+ uik[12]*u[5]+ uik[13]*u[6]; 489 wp[2]+= uik[14]*u[0]+ uik[15]*u[1]+ uik[16]*u[2]+ uik[17]*u[3]+ uik[18]*u[4]+ uik[19]*u[5]+ uik[20]*u[6]; 490 wp[3]+= uik[21]*u[0]+ uik[22]*u[1]+ uik[23]*u[2]+ uik[24]*u[3]+ uik[25]*u[4]+ uik[26]*u[5]+ uik[27]*u[6]; 491 wp[4]+= uik[28]*u[0]+ uik[29]*u[1]+ uik[30]*u[2]+ uik[31]*u[3]+ uik[32]*u[4]+ uik[33]*u[5]+ uik[34]*u[6]; 492 wp[5]+= uik[35]*u[0]+ uik[36]*u[1]+ uik[37]*u[2]+ uik[38]*u[3]+ uik[39]*u[4]+ uik[40]*u[5]+ uik[41]*u[6]; 493 wp[6]+= uik[42]*u[0]+ uik[43]*u[1]+ uik[44]*u[2]+ uik[45]*u[3]+ uik[46]*u[4]+ uik[47]*u[5]+ uik[48]*u[6]; 494 495 wp[7]+= uik[0]*u[7] + uik[1]*u[8] + uik[2]*u[9] + uik[3]*u[10] + uik[4]*u[11] + uik[5]*u[12] + uik[6]*u[13]; 496 wp[8]+= uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]; 497 wp[9]+= uik[14]*u[7]+ uik[15]*u[8]+ uik[16]*u[9]+ uik[17]*u[10]+ uik[18]*u[11]+ uik[19]*u[12]+ uik[20]*u[13]; 498 wp[10]+=uik[21]*u[7]+ uik[22]*u[8]+ uik[23]*u[9]+ uik[24]*u[10]+ uik[25]*u[11]+ uik[26]*u[12]+ uik[27]*u[13]; 499 wp[11]+=uik[28]*u[7]+ uik[29]*u[8]+ uik[30]*u[9]+ uik[31]*u[10]+ uik[32]*u[11]+ uik[33]*u[12]+ uik[34]*u[13]; 500 wp[12]+=uik[35]*u[7]+ uik[36]*u[8]+ uik[37]*u[9]+ uik[38]*u[10]+ uik[39]*u[11]+ uik[40]*u[12]+ uik[41]*u[13]; 501 wp[13]+=uik[42]*u[7]+ uik[43]*u[8]+ uik[44]*u[9]+ uik[45]*u[10]+ uik[46]*u[11]+ uik[47]*u[12]+ uik[48]*u[13]; 502 503 wp[14]+= uik[0]*u[14] + uik[1]*u[15] + uik[2]*u[16] + uik[3]*u[17] + uik[4]*u[18] + uik[5]*u[19] + uik[6]*u[20]; 504 wp[15]+= uik[7]*u[14] + uik[8]*u[15] + uik[9]*u[16]+ uik[10]*u[17]+ uik[11]*u[18]+ uik[12]*u[19]+ uik[13]*u[20]; 505 wp[16]+= uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]; 506 wp[17]+= uik[21]*u[14]+ uik[22]*u[15]+ uik[23]*u[16]+ uik[24]*u[17]+ uik[25]*u[18]+ uik[26]*u[19]+ uik[27]*u[20]; 507 wp[18]+= uik[28]*u[14]+ uik[29]*u[15]+ uik[30]*u[16]+ uik[31]*u[17]+ uik[32]*u[18]+ uik[33]*u[19]+ uik[34]*u[20]; 508 wp[19]+= uik[35]*u[14]+ uik[36]*u[15]+ uik[37]*u[16]+ uik[38]*u[17]+ uik[39]*u[18]+ uik[40]*u[19]+ uik[41]*u[20]; 509 wp[20]+= uik[42]*u[14]+ uik[43]*u[15]+ uik[44]*u[16]+ uik[45]*u[17]+ uik[46]*u[18]+ uik[47]*u[19]+ uik[48]*u[20]; 510 511 wp[21]+= uik[0]*u[21] + uik[1]*u[22] + uik[2]*u[23] + uik[3]*u[24] + uik[4]*u[25] + uik[5]*u[26] + uik[6]*u[27]; 512 wp[22]+= uik[7]*u[21] + uik[8]*u[22] + uik[9]*u[23]+ uik[10]*u[24]+ uik[11]*u[25]+ uik[12]*u[26]+ uik[13]*u[27]; 513 wp[23]+= uik[14]*u[21]+ uik[15]*u[22]+ uik[16]*u[23]+ uik[17]*u[24]+ uik[18]*u[25]+ uik[19]*u[26]+ uik[20]*u[27]; 514 wp[24]+= uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]; 515 wp[25]+= uik[28]*u[21]+ uik[29]*u[22]+ uik[30]*u[23]+ uik[31]*u[24]+ uik[32]*u[25]+ uik[33]*u[26]+ uik[34]*u[27]; 516 wp[26]+= uik[35]*u[21]+ uik[36]*u[22]+ uik[37]*u[23]+ uik[38]*u[24]+ uik[39]*u[25]+ uik[40]*u[26]+ uik[41]*u[27]; 517 wp[27]+= uik[42]*u[21]+ uik[43]*u[22]+ uik[44]*u[23]+ uik[45]*u[24]+ uik[46]*u[25]+ uik[47]*u[26]+ uik[48]*u[27]; 518 519 wp[28]+= uik[0]*u[28] + uik[1]*u[29] + uik[2]*u[30] + uik[3]*u[31] + uik[4]*u[32] + uik[5]*u[33] + uik[6]*u[34]; 520 wp[29]+= uik[7]*u[28] + uik[8]*u[29] + uik[9]*u[30]+ uik[10]*u[31]+ uik[11]*u[32]+ uik[12]*u[33]+ uik[13]*u[34]; 521 wp[30]+= uik[14]*u[28]+ uik[15]*u[29]+ uik[16]*u[30]+ uik[17]*u[31]+ uik[18]*u[32]+ uik[19]*u[33]+ uik[20]*u[34]; 522 wp[31]+= uik[21]*u[28]+ uik[22]*u[29]+ uik[23]*u[30]+ uik[24]*u[31]+ uik[25]*u[32]+ uik[26]*u[33]+ uik[27]*u[34]; 523 wp[32]+= uik[28]*u[28]+ uik[29]*u[29]+ uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]; 524 wp[33]+= uik[35]*u[28]+ uik[36]*u[29]+ uik[37]*u[30]+ uik[38]*u[31]+ uik[39]*u[32]+ uik[40]*u[33]+ uik[41]*u[34]; 525 wp[34]+= uik[42]*u[28]+ uik[43]*u[29]+ uik[44]*u[30]+ uik[45]*u[31]+ uik[46]*u[32]+ uik[47]*u[33]+ uik[48]*u[34]; 526 527 wp[35]+= uik[0]*u[35] + uik[1]*u[36] + uik[2]*u[37] + uik[3]*u[38] + uik[4]*u[39] + uik[5]*u[40] + uik[6]*u[41]; 528 wp[36]+= uik[7]*u[35] + uik[8]*u[36] + uik[9]*u[37]+ uik[10]*u[38]+ uik[11]*u[39]+ uik[12]*u[40]+ uik[13]*u[41]; 529 wp[37]+= uik[14]*u[35]+ uik[15]*u[36]+ uik[16]*u[37]+ uik[17]*u[38]+ uik[18]*u[39]+ uik[19]*u[40]+ uik[20]*u[41]; 530 wp[38]+= uik[21]*u[35]+ uik[22]*u[36]+ uik[23]*u[37]+ uik[24]*u[38]+ uik[25]*u[39]+ uik[26]*u[40]+ uik[27]*u[41]; 531 wp[39]+= uik[28]*u[35]+ uik[29]*u[36]+ uik[30]*u[37]+ uik[31]*u[38]+ uik[32]*u[39]+ uik[33]*u[40]+ uik[34]*u[41]; 532 wp[40]+= uik[35]*u[35]+ uik[36]*u[36]+ uik[37]*u[37]+ uik[38]*u[38]+ uik[39]*u[39]+ uik[40]*u[40]+ uik[41]*u[41]; 533 wp[41]+= uik[42]*u[35]+ uik[43]*u[36]+ uik[44]*u[37]+ uik[45]*u[38]+ uik[46]*u[39]+ uik[47]*u[40]+ uik[48]*u[41]; 534 535 wp[42]+= uik[0]*u[42] + uik[1]*u[43] + uik[2]*u[44] + uik[3]*u[45] + uik[4]*u[46] + uik[5]*u[47] + uik[6]*u[48]; 536 wp[43]+= uik[7]*u[42] + uik[8]*u[43] + uik[9]*u[44]+ uik[10]*u[45]+ uik[11]*u[46]+ uik[12]*u[47]+ uik[13]*u[48]; 537 wp[44]+= uik[14]*u[42]+ uik[15]*u[43]+ uik[16]*u[44]+ uik[17]*u[45]+ uik[18]*u[46]+ uik[19]*u[47]+ uik[20]*u[48]; 538 wp[45]+= uik[21]*u[42]+ uik[22]*u[43]+ uik[23]*u[44]+ uik[24]*u[45]+ uik[25]*u[46]+ uik[26]*u[47]+ uik[27]*u[48]; 539 wp[46]+= uik[28]*u[42]+ uik[29]*u[43]+ uik[30]*u[44]+ uik[31]*u[45]+ uik[32]*u[46]+ uik[33]*u[47]+ uik[34]*u[48]; 540 wp[47]+= uik[35]*u[42]+ uik[36]*u[43]+ uik[37]*u[44]+ uik[38]*u[45]+ uik[39]*u[46]+ uik[40]*u[47]+ uik[41]*u[48]; 541 wp[48]+= uik[42]*u[42]+ uik[43]*u[43]+ uik[44]*u[44]+ uik[45]*u[45]+ uik[46]*u[46]+ uik[47]*u[47]+ uik[48]*u[48]; 542 } 543 544 /* ... add i to row list for next nonzero entry */ 545 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 546 j = bj[jmin]; 547 jl[i] = jl[j]; jl[j] = i; /* update jl */ 548 } 549 i = nexti; 550 } 551 552 /* save nonzero entries in k-th row of U ... */ 553 554 /* invert diagonal block */ 555 d = ba+k*49; 556 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 557 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 558 559 jmin = bi[k]; jmax = bi[k+1]; 560 if (jmin < jmax) { 561 for (j=jmin; j<jmax; j++){ 562 vj = bj[j]; /* block col. index of U */ 563 u = ba + j*49; 564 wp = w + vj*49; 565 for (k1=0; k1<49; k1++){ 566 *u++ = *wp; 567 *wp++ = 0.0; 568 } 569 } 570 571 /* ... add k to row list for first nonzero entry in k-th row */ 572 il[k] = jmin; 573 i = bj[jmin]; 574 jl[k] = jl[i]; jl[i] = k; 575 } 576 } 577 578 ierr = PetscFree(w);CHKERRQ(ierr); 579 ierr = PetscFree(il);CHKERRQ(ierr); 580 ierr = PetscFree(jl);CHKERRQ(ierr); 581 ierr = PetscFree(dk);CHKERRQ(ierr); 582 ierr = PetscFree(uik);CHKERRQ(ierr); 583 if (a->permute){ 584 ierr = PetscFree(aa);CHKERRQ(ierr); 585 } 586 587 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 588 C->factor = FACTOR_CHOLESKY; 589 C->assembled = PETSC_TRUE; 590 C->preallocated = PETSC_TRUE; 591 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 592 PetscFunctionReturn(0); 593 } 594 595 /* 596 Version for when blocks are 7 by 7 Using natural ordering 597 */ 598 #undef __FUNC__ 599 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering" 600 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B) 601 { 602 Mat C = *B; 603 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 604 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 605 int *ajtmpold,*ajtmp,nz,row; 606 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 607 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 608 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 609 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 610 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 611 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 612 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 613 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 614 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 615 MatScalar p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49; 616 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 617 MatScalar x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49; 618 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 619 MatScalar m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49; 620 MatScalar *ba = b->a,*aa = a->a; 621 622 PetscFunctionBegin; 623 rtmp = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 624 for (i=0; i<n; i++) { 625 nz = bi[i+1] - bi[i]; 626 ajtmp = bj + bi[i]; 627 for (j=0; j<nz; j++) { 628 x = rtmp+49*ajtmp[j]; 629 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 630 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 631 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 632 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 633 x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ; 634 x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ; 635 } 636 /* load in initial (unfactored row) */ 637 nz = ai[i+1] - ai[i]; 638 ajtmpold = aj + ai[i]; 639 v = aa + 49*ai[i]; 640 for (j=0; j<nz; j++) { 641 x = rtmp+49*ajtmpold[j]; 642 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 643 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 644 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 645 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 646 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 647 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 648 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 649 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 650 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 651 x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39]; 652 x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43]; 653 x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47]; 654 x[48] = v[48]; 655 v += 49; 656 } 657 row = *ajtmp++; 658 while (row < i) { 659 pc = rtmp + 49*row; 660 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 661 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 662 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 663 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 664 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 665 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 666 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 667 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 668 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 669 p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39]; 670 p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43]; 671 p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47]; 672 p49 = pc[48]; 673 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 674 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 675 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 676 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 677 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 678 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 679 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 680 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 681 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || 682 p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || 683 p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || 684 p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || 685 p49 != 0.0) { 686 pv = ba + 49*diag_offset[row]; 687 pj = bj + diag_offset[row] + 1; 688 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 689 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 690 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 691 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 692 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 693 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 694 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 695 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 696 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 697 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 698 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 699 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 700 x49 = pv[48]; 701 pc[0] = m1 = p1*x1 + p8*x2 + p15*x3 + p22*x4 + p29*x5 + p36*x6 + p43*x7; 702 pc[1] = m2 = p2*x1 + p9*x2 + p16*x3 + p23*x4 + p30*x5 + p37*x6 + p44*x7; 703 pc[2] = m3 = p3*x1 + p10*x2 + p17*x3 + p24*x4 + p31*x5 + p38*x6 + p45*x7; 704 pc[3] = m4 = p4*x1 + p11*x2 + p18*x3 + p25*x4 + p32*x5 + p39*x6 + p46*x7; 705 pc[4] = m5 = p5*x1 + p12*x2 + p19*x3 + p26*x4 + p33*x5 + p40*x6 + p47*x7; 706 pc[5] = m6 = p6*x1 + p13*x2 + p20*x3 + p27*x4 + p34*x5 + p41*x6 + p48*x7; 707 pc[6] = m7 = p7*x1 + p14*x2 + p21*x3 + p28*x4 + p35*x5 + p42*x6 + p49*x7; 708 709 pc[7] = m8 = p1*x8 + p8*x9 + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14; 710 pc[8] = m9 = p2*x8 + p9*x9 + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14; 711 pc[9] = m10 = p3*x8 + p10*x9 + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14; 712 pc[10] = m11 = p4*x8 + p11*x9 + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14; 713 pc[11] = m12 = p5*x8 + p12*x9 + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14; 714 pc[12] = m13 = p6*x8 + p13*x9 + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14; 715 pc[13] = m14 = p7*x8 + p14*x9 + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14; 716 717 pc[14] = m15 = p1*x15 + p8*x16 + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21; 718 pc[15] = m16 = p2*x15 + p9*x16 + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21; 719 pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21; 720 pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21; 721 pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21; 722 pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21; 723 pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21; 724 725 pc[21] = m22 = p1*x22 + p8*x23 + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28; 726 pc[22] = m23 = p2*x22 + p9*x23 + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28; 727 pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28; 728 pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28; 729 pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28; 730 pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28; 731 pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28; 732 733 pc[28] = m29 = p1*x29 + p8*x30 + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35; 734 pc[29] = m30 = p2*x29 + p9*x30 + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35; 735 pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35; 736 pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35; 737 pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35; 738 pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35; 739 pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35; 740 741 pc[35] = m36 = p1*x36 + p8*x37 + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42; 742 pc[36] = m37 = p2*x36 + p9*x37 + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42; 743 pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42; 744 pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42; 745 pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42; 746 pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42; 747 pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42; 748 749 pc[42] = m43 = p1*x43 + p8*x44 + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49; 750 pc[43] = m44 = p2*x43 + p9*x44 + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49; 751 pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49; 752 pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49; 753 pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49; 754 pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49; 755 pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49; 756 757 nz = bi[row+1] - diag_offset[row] - 1; 758 pv += 49; 759 for (j=0; j<nz; j++) { 760 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 761 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 762 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 763 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 764 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 765 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 766 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 767 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 768 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 769 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 770 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 771 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 772 x49 = pv[48]; 773 x = rtmp + 49*pj[j]; 774 x[0] -= m1*x1 + m8*x2 + m15*x3 + m22*x4 + m29*x5 + m36*x6 + m43*x7; 775 x[1] -= m2*x1 + m9*x2 + m16*x3 + m23*x4 + m30*x5 + m37*x6 + m44*x7; 776 x[2] -= m3*x1 + m10*x2 + m17*x3 + m24*x4 + m31*x5 + m38*x6 + m45*x7; 777 x[3] -= m4*x1 + m11*x2 + m18*x3 + m25*x4 + m32*x5 + m39*x6 + m46*x7; 778 x[4] -= m5*x1 + m12*x2 + m19*x3 + m26*x4 + m33*x5 + m40*x6 + m47*x7; 779 x[5] -= m6*x1 + m13*x2 + m20*x3 + m27*x4 + m34*x5 + m41*x6 + m48*x7; 780 x[6] -= m7*x1 + m14*x2 + m21*x3 + m28*x4 + m35*x5 + m42*x6 + m49*x7; 781 782 x[7] -= m1*x8 + m8*x9 + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14; 783 x[8] -= m2*x8 + m9*x9 + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14; 784 x[9] -= m3*x8 + m10*x9 + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14; 785 x[10] -= m4*x8 + m11*x9 + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14; 786 x[11] -= m5*x8 + m12*x9 + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14; 787 x[12] -= m6*x8 + m13*x9 + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14; 788 x[13] -= m7*x8 + m14*x9 + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14; 789 790 x[14] -= m1*x15 + m8*x16 + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21; 791 x[15] -= m2*x15 + m9*x16 + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21; 792 x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21; 793 x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21; 794 x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21; 795 x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21; 796 x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21; 797 798 x[21] -= m1*x22 + m8*x23 + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28; 799 x[22] -= m2*x22 + m9*x23 + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28; 800 x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28; 801 x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28; 802 x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28; 803 x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28; 804 x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28; 805 806 x[28] -= m1*x29 + m8*x30 + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35; 807 x[29] -= m2*x29 + m9*x30 + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35; 808 x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35; 809 x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35; 810 x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35; 811 x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35; 812 x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35; 813 814 x[35] -= m1*x36 + m8*x37 + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42; 815 x[36] -= m2*x36 + m9*x37 + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42; 816 x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42; 817 x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42; 818 x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42; 819 x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42; 820 x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42; 821 822 x[42] -= m1*x43 + m8*x44 + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49; 823 x[43] -= m2*x43 + m9*x44 + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49; 824 x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49; 825 x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49; 826 x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49; 827 x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49; 828 x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49; 829 pv += 49; 830 } 831 PLogFlops(686*nz+637); 832 } 833 row = *ajtmp++; 834 } 835 /* finished row so stick it into b->a */ 836 pv = ba + 49*bi[i]; 837 pj = bj + bi[i]; 838 nz = bi[i+1] - bi[i]; 839 for (j=0; j<nz; j++) { 840 x = rtmp+49*pj[j]; 841 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 842 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 843 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 844 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 845 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 846 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 847 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 848 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 849 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 850 pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39]; 851 pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43]; 852 pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47]; 853 pv[48] = x[48]; 854 pv += 49; 855 } 856 /* invert diagonal block */ 857 w = ba + 49*diag_offset[i]; 858 ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr); 859 } 860 861 ierr = PetscFree(rtmp);CHKERRQ(ierr); 862 C->factor = FACTOR_LU; 863 C->assembled = PETSC_TRUE; 864 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 865 PetscFunctionReturn(0); 866 } 867 868 /* Version for when blocks are 6 by 6 */ 869 #undef __FUNC__ 870 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 871 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 872 { 873 Mat C = *B; 874 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 875 IS perm = b->row; 876 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 877 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 878 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 879 MatScalar *u,*d,*w,*wp; 880 881 PetscFunctionBegin; 882 /* initialization */ 883 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 884 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 885 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 886 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 887 for (i=0; i<mbs; i++) { 888 jl[i] = mbs; il[0] = 0; 889 } 890 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 891 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 892 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 893 894 /* check permutation */ 895 if (!a->permute){ 896 ai = a->i; aj = a->j; aa = a->a; 897 } else { 898 ai = a->inew; aj = a->jnew; 899 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 900 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 901 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 902 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 903 904 for (i=0; i<mbs; i++){ 905 jmin = ai[i]; jmax = ai[i+1]; 906 for (j=jmin; j<jmax; j++){ 907 while (a2anew[j] != j){ 908 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 909 for (k1=0; k1<36; k1++){ 910 dk[k1] = aa[k*36+k1]; 911 aa[k*36+k1] = aa[j*36+k1]; 912 aa[j*36+k1] = dk[k1]; 913 } 914 } 915 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 916 if (i > aj[j]){ 917 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 918 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 919 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 920 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 921 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 922 } 923 } 924 } 925 } 926 ierr = PetscFree(a2anew);CHKERRA(ierr); 927 } 928 929 /* for each row k */ 930 for (k = 0; k<mbs; k++){ 931 932 /*initialize k-th row with elements nonzero in row perm(k) of A */ 933 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 934 if (jmin < jmax) { 935 ap = aa + jmin*36; 936 for (j = jmin; j < jmax; j++){ 937 vj = perm_ptr[aj[j]]; /* block col. index */ 938 wp = w + vj*36; 939 for (i=0; i<36; i++) *wp++ = *ap++; 940 } 941 } 942 943 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 944 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 945 i = jl[k]; /* first row to be added to k_th row */ 946 947 while (i < mbs){ 948 nexti = jl[i]; /* next row to be added to k_th row */ 949 950 /* compute multiplier */ 951 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 952 953 /* uik = -inv(Di)*U_bar(i,k) */ 954 d = ba + i*36; 955 u = ba + ili*36; 956 957 uik[0] = -(d[0]*u[0] + d[6]*u[1] + d[12]*u[2] + d[18]*u[3] + d[24]*u[4] + d[30]*u[5]); 958 uik[1] = -(d[1]*u[0] + d[7]*u[1] + d[13]*u[2] + d[19]*u[3] + d[25]*u[4] + d[31]*u[5]); 959 uik[2] = -(d[2]*u[0] + d[8]*u[1] + d[14]*u[2] + d[20]*u[3] + d[26]*u[4] + d[32]*u[5]); 960 uik[3] = -(d[3]*u[0] + d[9]*u[1] + d[15]*u[2] + d[21]*u[3] + d[27]*u[4] + d[33]*u[5]); 961 uik[4] = -(d[4]*u[0]+ d[10]*u[1] + d[16]*u[2] + d[22]*u[3] + d[28]*u[4] + d[34]*u[5]); 962 uik[5] = -(d[5]*u[0]+ d[11]*u[1] + d[17]*u[2] + d[23]*u[3] + d[29]*u[4] + d[35]*u[5]); 963 964 uik[6] = -(d[0]*u[6] + d[6]*u[7] + d[12]*u[8] + d[18]*u[9] + d[24]*u[10] + d[30]*u[11]); 965 uik[7] = -(d[1]*u[6] + d[7]*u[7] + d[13]*u[8] + d[19]*u[9] + d[25]*u[10] + d[31]*u[11]); 966 uik[8] = -(d[2]*u[6] + d[8]*u[7] + d[14]*u[8] + d[20]*u[9] + d[26]*u[10] + d[32]*u[11]); 967 uik[9] = -(d[3]*u[6] + d[9]*u[7] + d[15]*u[8] + d[21]*u[9] + d[27]*u[10] + d[33]*u[11]); 968 uik[10]= -(d[4]*u[6]+ d[10]*u[7] + d[16]*u[8] + d[22]*u[9] + d[28]*u[10] + d[34]*u[11]); 969 uik[11]= -(d[5]*u[6]+ d[11]*u[7] + d[17]*u[8] + d[23]*u[9] + d[29]*u[10] + d[35]*u[11]); 970 971 uik[12] = -(d[0]*u[12] + d[6]*u[13] + d[12]*u[14] + d[18]*u[15] + d[24]*u[16] + d[30]*u[17]); 972 uik[13] = -(d[1]*u[12] + d[7]*u[13] + d[13]*u[14] + d[19]*u[15] + d[25]*u[16] + d[31]*u[17]); 973 uik[14] = -(d[2]*u[12] + d[8]*u[13] + d[14]*u[14] + d[20]*u[15] + d[26]*u[16] + d[32]*u[17]); 974 uik[15] = -(d[3]*u[12] + d[9]*u[13] + d[15]*u[14] + d[21]*u[15] + d[27]*u[16] + d[33]*u[17]); 975 uik[16] = -(d[4]*u[12]+ d[10]*u[13] + d[16]*u[14] + d[22]*u[15] + d[28]*u[16] + d[34]*u[17]); 976 uik[17] = -(d[5]*u[12]+ d[11]*u[13] + d[17]*u[14] + d[23]*u[15] + d[29]*u[16] + d[35]*u[17]); 977 978 uik[18] = -(d[0]*u[18] + d[6]*u[19] + d[12]*u[20] + d[18]*u[21] + d[24]*u[22] + d[30]*u[23]); 979 uik[19] = -(d[1]*u[18] + d[7]*u[19] + d[13]*u[20] + d[19]*u[21] + d[25]*u[22] + d[31]*u[23]); 980 uik[20] = -(d[2]*u[18] + d[8]*u[19] + d[14]*u[20] + d[20]*u[21] + d[26]*u[22] + d[32]*u[23]); 981 uik[21] = -(d[3]*u[18] + d[9]*u[19] + d[15]*u[20] + d[21]*u[21] + d[27]*u[22] + d[33]*u[23]); 982 uik[22] = -(d[4]*u[18]+ d[10]*u[19] + d[16]*u[20] + d[22]*u[21] + d[28]*u[22] + d[34]*u[23]); 983 uik[23] = -(d[5]*u[18]+ d[11]*u[19] + d[17]*u[20] + d[23]*u[21] + d[29]*u[22] + d[35]*u[23]); 984 985 uik[24] = -(d[0]*u[24] + d[6]*u[25] + d[12]*u[26] + d[18]*u[27] + d[24]*u[28] + d[30]*u[29]); 986 uik[25] = -(d[1]*u[24] + d[7]*u[25] + d[13]*u[26] + d[19]*u[27] + d[25]*u[28] + d[31]*u[29]); 987 uik[26] = -(d[2]*u[24] + d[8]*u[25] + d[14]*u[26] + d[20]*u[27] + d[26]*u[28] + d[32]*u[29]); 988 uik[27] = -(d[3]*u[24] + d[9]*u[25] + d[15]*u[26] + d[21]*u[27] + d[27]*u[28] + d[33]*u[29]); 989 uik[28] = -(d[4]*u[24]+ d[10]*u[25] + d[16]*u[26] + d[22]*u[27] + d[28]*u[28] + d[34]*u[29]); 990 uik[29] = -(d[5]*u[24]+ d[11]*u[25] + d[17]*u[26] + d[23]*u[27] + d[29]*u[28] + d[35]*u[29]); 991 992 uik[30] = -(d[0]*u[30] + d[6]*u[31] + d[12]*u[32] + d[18]*u[33] + d[24]*u[34] + d[30]*u[35]); 993 uik[31] = -(d[1]*u[30] + d[7]*u[31] + d[13]*u[32] + d[19]*u[33] + d[25]*u[34] + d[31]*u[35]); 994 uik[32] = -(d[2]*u[30] + d[8]*u[31] + d[14]*u[32] + d[20]*u[33] + d[26]*u[34] + d[32]*u[35]); 995 uik[33] = -(d[3]*u[30] + d[9]*u[31] + d[15]*u[32] + d[21]*u[33] + d[27]*u[34] + d[33]*u[35]); 996 uik[34] = -(d[4]*u[30]+ d[10]*u[31] + d[16]*u[32] + d[22]*u[33] + d[28]*u[34] + d[34]*u[35]); 997 uik[35] = -(d[5]*u[30]+ d[11]*u[31] + d[17]*u[32] + d[23]*u[33] + d[29]*u[34] + d[35]*u[35]); 998 999 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1000 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 1001 dk[1] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2] + uik[9]*u[3]+ uik[10]*u[4]+ uik[11]*u[5]; 1002 dk[2] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]+ uik[16]*u[4]+ uik[17]*u[5]; 1003 dk[3] += uik[18]*u[0]+ uik[19]*u[1]+ uik[20]*u[2]+ uik[21]*u[3]+ uik[22]*u[4]+ uik[23]*u[5]; 1004 dk[4] += uik[24]*u[0]+ uik[25]*u[1]+ uik[26]*u[2]+ uik[27]*u[3]+ uik[28]*u[4]+ uik[29]*u[5]; 1005 dk[5] += uik[30]*u[0]+ uik[31]*u[1]+ uik[32]*u[2]+ uik[33]*u[3]+ uik[34]*u[4]+ uik[35]*u[5]; 1006 1007 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8] + uik[3]*u[9] + uik[4]*u[10] + uik[5]*u[11]; 1008 dk[7] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]; 1009 dk[8] += uik[12]*u[6]+ uik[13]*u[7]+ uik[14]*u[8]+ uik[15]*u[9]+ uik[16]*u[10]+ uik[17]*u[11]; 1010 dk[9] += uik[18]*u[6]+ uik[19]*u[7]+ uik[20]*u[8]+ uik[21]*u[9]+ uik[22]*u[10]+ uik[23]*u[11]; 1011 dk[10]+= uik[24]*u[6]+ uik[25]*u[7]+ uik[26]*u[8]+ uik[27]*u[9]+ uik[28]*u[10]+ uik[29]*u[11]; 1012 dk[11]+= uik[30]*u[6]+ uik[31]*u[7]+ uik[32]*u[8]+ uik[33]*u[9]+ uik[34]*u[10]+ uik[35]*u[11]; 1013 1014 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15] + uik[4]*u[16] + uik[5]*u[17]; 1015 dk[13]+= uik[6]*u[12] + uik[7]*u[13] + uik[8]*u[14] + uik[9]*u[15]+ uik[10]*u[16]+ uik[11]*u[17]; 1016 dk[14]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]; 1017 dk[15]+= uik[18]*u[12]+ uik[19]*u[13]+ uik[20]*u[14]+ uik[21]*u[15]+ uik[22]*u[16]+ uik[23]*u[17]; 1018 dk[16]+= uik[24]*u[12]+ uik[25]*u[13]+ uik[26]*u[14]+ uik[27]*u[15]+ uik[28]*u[16]+ uik[29]*u[17]; 1019 dk[17]+= uik[30]*u[12]+ uik[31]*u[13]+ uik[32]*u[14]+ uik[33]*u[15]+ uik[34]*u[16]+ uik[35]*u[17]; 1020 1021 dk[18]+= uik[0]*u[18] + uik[1]*u[19] + uik[2]*u[20] + uik[3]*u[21] + uik[4]*u[22] + uik[5]*u[23]; 1022 dk[19]+= uik[6]*u[18] + uik[7]*u[19] + uik[8]*u[20] + uik[9]*u[21]+ uik[10]*u[22]+ uik[11]*u[23]; 1023 dk[20]+= uik[12]*u[18]+ uik[13]*u[19]+ uik[14]*u[20]+ uik[15]*u[21]+ uik[16]*u[22]+ uik[17]*u[23]; 1024 dk[21]+= uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]; 1025 dk[22]+= uik[24]*u[18]+ uik[25]*u[19]+ uik[26]*u[20]+ uik[27]*u[21]+ uik[28]*u[22]+ uik[29]*u[23]; 1026 dk[23]+= uik[30]*u[18]+ uik[31]*u[19]+ uik[32]*u[20]+ uik[33]*u[21]+ uik[34]*u[22]+ uik[35]*u[23]; 1027 1028 dk[24]+= uik[0]*u[24] + uik[1]*u[25] + uik[2]*u[26] + uik[3]*u[27] + uik[4]*u[28] + uik[5]*u[29]; 1029 dk[25]+= uik[6]*u[24] + uik[7]*u[25] + uik[8]*u[26] + uik[9]*u[27]+ uik[10]*u[28]+ uik[11]*u[29]; 1030 dk[26]+= uik[12]*u[24]+ uik[13]*u[25]+ uik[14]*u[26]+ uik[15]*u[27]+ uik[16]*u[28]+ uik[17]*u[29]; 1031 dk[27]+= uik[18]*u[24]+ uik[19]*u[25]+ uik[20]*u[26]+ uik[21]*u[27]+ uik[22]*u[28]+ uik[23]*u[29]; 1032 dk[28]+= uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]+ uik[28]*u[28]+ uik[29]*u[29]; 1033 dk[29]+= uik[30]*u[24]+ uik[31]*u[25]+ uik[32]*u[26]+ uik[33]*u[27]+ uik[34]*u[28]+ uik[35]*u[29]; 1034 1035 dk[30]+= uik[0]*u[30] + uik[1]*u[31] + uik[2]*u[32] + uik[3]*u[33] + uik[4]*u[34] + uik[5]*u[35]; 1036 dk[31]+= uik[6]*u[30] + uik[7]*u[31] + uik[8]*u[32] + uik[9]*u[33]+ uik[10]*u[34]+ uik[11]*u[35]; 1037 dk[32]+= uik[12]*u[30]+ uik[13]*u[31]+ uik[14]*u[32]+ uik[15]*u[33]+ uik[16]*u[34]+ uik[17]*u[35]; 1038 dk[33]+= uik[18]*u[30]+ uik[19]*u[31]+ uik[20]*u[32]+ uik[21]*u[33]+ uik[22]*u[34]+ uik[23]*u[35]; 1039 dk[34]+= uik[24]*u[30]+ uik[25]*u[31]+ uik[26]*u[32]+ uik[27]*u[33]+ uik[28]*u[34]+ uik[29]*u[35]; 1040 dk[35]+= uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]+ uik[35]*u[35]; 1041 1042 /* update -U(i,k) */ 1043 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1044 1045 /* add multiple of row i to k-th row ... */ 1046 jmin = ili + 1; jmax = bi[i+1]; 1047 if (jmin < jmax){ 1048 for (j=jmin; j<jmax; j++) { 1049 /* w += -U(i,k)^T * U_bar(i,j) */ 1050 wp = w + bj[j]*36; 1051 u = ba + j*36; 1052 wp[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 1053 wp[1] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2] + uik[9]*u[3]+ uik[10]*u[4]+ uik[11]*u[5]; 1054 wp[2] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]+ uik[16]*u[4]+ uik[17]*u[5]; 1055 wp[3] += uik[18]*u[0]+ uik[19]*u[1]+ uik[20]*u[2]+ uik[21]*u[3]+ uik[22]*u[4]+ uik[23]*u[5]; 1056 wp[4] += uik[24]*u[0]+ uik[25]*u[1]+ uik[26]*u[2]+ uik[27]*u[3]+ uik[28]*u[4]+ uik[29]*u[5]; 1057 wp[5] += uik[30]*u[0]+ uik[31]*u[1]+ uik[32]*u[2]+ uik[33]*u[3]+ uik[34]*u[4]+ uik[35]*u[5]; 1058 1059 wp[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8] + uik[3]*u[9] + uik[4]*u[10] + uik[5]*u[11]; 1060 wp[7] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]; 1061 wp[8] += uik[12]*u[6]+ uik[13]*u[7]+ uik[14]*u[8]+ uik[15]*u[9]+ uik[16]*u[10]+ uik[17]*u[11]; 1062 wp[9] += uik[18]*u[6]+ uik[19]*u[7]+ uik[20]*u[8]+ uik[21]*u[9]+ uik[22]*u[10]+ uik[23]*u[11]; 1063 wp[10]+= uik[24]*u[6]+ uik[25]*u[7]+ uik[26]*u[8]+ uik[27]*u[9]+ uik[28]*u[10]+ uik[29]*u[11]; 1064 wp[11]+= uik[30]*u[6]+ uik[31]*u[7]+ uik[32]*u[8]+ uik[33]*u[9]+ uik[34]*u[10]+ uik[35]*u[11]; 1065 1066 wp[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15] + uik[4]*u[16] + uik[5]*u[17]; 1067 wp[13]+= uik[6]*u[12] + uik[7]*u[13] + uik[8]*u[14] + uik[9]*u[15]+ uik[10]*u[16]+ uik[11]*u[17]; 1068 wp[14]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]; 1069 wp[15]+= uik[18]*u[12]+ uik[19]*u[13]+ uik[20]*u[14]+ uik[21]*u[15]+ uik[22]*u[16]+ uik[23]*u[17]; 1070 wp[16]+= uik[24]*u[12]+ uik[25]*u[13]+ uik[26]*u[14]+ uik[27]*u[15]+ uik[28]*u[16]+ uik[29]*u[17]; 1071 wp[17]+= uik[30]*u[12]+ uik[31]*u[13]+ uik[32]*u[14]+ uik[33]*u[15]+ uik[34]*u[16]+ uik[35]*u[17]; 1072 1073 wp[18]+= uik[0]*u[18] + uik[1]*u[19] + uik[2]*u[20] + uik[3]*u[21] + uik[4]*u[22] + uik[5]*u[23]; 1074 wp[19]+= uik[6]*u[18] + uik[7]*u[19] + uik[8]*u[20] + uik[9]*u[21]+ uik[10]*u[22]+ uik[11]*u[23]; 1075 wp[20]+= uik[12]*u[18]+ uik[13]*u[19]+ uik[14]*u[20]+ uik[15]*u[21]+ uik[16]*u[22]+ uik[17]*u[23]; 1076 wp[21]+= uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]; 1077 wp[22]+= uik[24]*u[18]+ uik[25]*u[19]+ uik[26]*u[20]+ uik[27]*u[21]+ uik[28]*u[22]+ uik[29]*u[23]; 1078 wp[23]+= uik[30]*u[18]+ uik[31]*u[19]+ uik[32]*u[20]+ uik[33]*u[21]+ uik[34]*u[22]+ uik[35]*u[23]; 1079 1080 wp[24]+= uik[0]*u[24] + uik[1]*u[25] + uik[2]*u[26] + uik[3]*u[27] + uik[4]*u[28] + uik[5]*u[29]; 1081 wp[25]+= uik[6]*u[24] + uik[7]*u[25] + uik[8]*u[26] + uik[9]*u[27]+ uik[10]*u[28]+ uik[11]*u[29]; 1082 wp[26]+= uik[12]*u[24]+ uik[13]*u[25]+ uik[14]*u[26]+ uik[15]*u[27]+ uik[16]*u[28]+ uik[17]*u[29]; 1083 wp[27]+= uik[18]*u[24]+ uik[19]*u[25]+ uik[20]*u[26]+ uik[21]*u[27]+ uik[22]*u[28]+ uik[23]*u[29]; 1084 wp[28]+= uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]+ uik[28]*u[28]+ uik[29]*u[29]; 1085 wp[29]+= uik[30]*u[24]+ uik[31]*u[25]+ uik[32]*u[26]+ uik[33]*u[27]+ uik[34]*u[28]+ uik[35]*u[29]; 1086 1087 wp[30]+= uik[0]*u[30] + uik[1]*u[31] + uik[2]*u[32] + uik[3]*u[33] + uik[4]*u[34] + uik[5]*u[35]; 1088 wp[31]+= uik[6]*u[30] + uik[7]*u[31] + uik[8]*u[32] + uik[9]*u[33]+ uik[10]*u[34]+ uik[11]*u[35]; 1089 wp[32]+= uik[12]*u[30]+ uik[13]*u[31]+ uik[14]*u[32]+ uik[15]*u[33]+ uik[16]*u[34]+ uik[17]*u[35]; 1090 wp[33]+= uik[18]*u[30]+ uik[19]*u[31]+ uik[20]*u[32]+ uik[21]*u[33]+ uik[22]*u[34]+ uik[23]*u[35]; 1091 wp[34]+= uik[24]*u[30]+ uik[25]*u[31]+ uik[26]*u[32]+ uik[27]*u[33]+ uik[28]*u[34]+ uik[29]*u[35]; 1092 wp[35]+= uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]+ uik[35]*u[35]; 1093 } 1094 1095 /* ... add i to row list for next nonzero entry */ 1096 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1097 j = bj[jmin]; 1098 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1099 } 1100 i = nexti; 1101 } 1102 1103 /* save nonzero entries in k-th row of U ... */ 1104 1105 /* invert diagonal block */ 1106 d = ba+k*36; 1107 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1108 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1109 1110 jmin = bi[k]; jmax = bi[k+1]; 1111 if (jmin < jmax) { 1112 for (j=jmin; j<jmax; j++){ 1113 vj = bj[j]; /* block col. index of U */ 1114 u = ba + j*36; 1115 wp = w + vj*36; 1116 for (k1=0; k1<36; k1++){ 1117 *u++ = *wp; 1118 *wp++ = 0.0; 1119 } 1120 } 1121 1122 /* ... add k to row list for first nonzero entry in k-th row */ 1123 il[k] = jmin; 1124 i = bj[jmin]; 1125 jl[k] = jl[i]; jl[i] = k; 1126 } 1127 } 1128 1129 ierr = PetscFree(w);CHKERRQ(ierr); 1130 ierr = PetscFree(il);CHKERRQ(ierr); 1131 ierr = PetscFree(jl);CHKERRQ(ierr); 1132 ierr = PetscFree(dk);CHKERRQ(ierr); 1133 ierr = PetscFree(uik);CHKERRQ(ierr); 1134 if (a->permute){ 1135 ierr = PetscFree(aa);CHKERRQ(ierr); 1136 } 1137 1138 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1139 C->factor = FACTOR_CHOLESKY; 1140 C->assembled = PETSC_TRUE; 1141 C->preallocated = PETSC_TRUE; 1142 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1143 PetscFunctionReturn(0); 1144 } 1145 1146 /* 1147 Version for when blocks are 6 by 6 Using natural ordering 1148 */ 1149 #undef __FUNC__ 1150 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1151 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1152 { 1153 Mat C = *B; 1154 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1155 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1156 int *ajtmpold,*ajtmp,nz,row; 1157 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1158 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1159 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1160 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1161 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1162 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1163 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1164 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1165 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 1166 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 1167 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 1168 MatScalar *ba = b->a,*aa = a->a; 1169 1170 PetscFunctionBegin; 1171 rtmp = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1172 for (i=0; i<n; i++) { 1173 nz = bi[i+1] - bi[i]; 1174 ajtmp = bj + bi[i]; 1175 for (j=0; j<nz; j++) { 1176 x = rtmp+36*ajtmp[j]; 1177 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1178 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 1179 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 1180 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 1181 x[34] = x[35] = 0.0 ; 1182 } 1183 /* load in initial (unfactored row) */ 1184 nz = ai[i+1] - ai[i]; 1185 ajtmpold = aj + ai[i]; 1186 v = aa + 36*ai[i]; 1187 for (j=0; j<nz; j++) { 1188 x = rtmp+36*ajtmpold[j]; 1189 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1190 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 1191 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 1192 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 1193 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 1194 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1195 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 1196 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 1197 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 1198 v += 36; 1199 } 1200 row = *ajtmp++; 1201 while (row < i) { 1202 pc = rtmp + 36*row; 1203 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1204 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 1205 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 1206 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 1207 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 1208 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 1209 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 1210 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 1211 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 1212 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 1213 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 1214 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 1215 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 1216 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 1217 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 1218 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 1219 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 1220 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) { 1221 pv = ba + 36*diag_offset[row]; 1222 pj = bj + diag_offset[row] + 1; 1223 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1224 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1225 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1226 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1227 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1228 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1229 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1230 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1231 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1232 pc[0] = m1 = p1*x1 + p7*x2 + p13*x3 + p19*x4 + p25*x5 + p31*x6; 1233 pc[1] = m2 = p2*x1 + p8*x2 + p14*x3 + p20*x4 + p26*x5 + p32*x6; 1234 pc[2] = m3 = p3*x1 + p9*x2 + p15*x3 + p21*x4 + p27*x5 + p33*x6; 1235 pc[3] = m4 = p4*x1 + p10*x2 + p16*x3 + p22*x4 + p28*x5 + p34*x6; 1236 pc[4] = m5 = p5*x1 + p11*x2 + p17*x3 + p23*x4 + p29*x5 + p35*x6; 1237 pc[5] = m6 = p6*x1 + p12*x2 + p18*x3 + p24*x4 + p30*x5 + p36*x6; 1238 1239 pc[6] = m7 = p1*x7 + p7*x8 + p13*x9 + p19*x10 + p25*x11 + p31*x12; 1240 pc[7] = m8 = p2*x7 + p8*x8 + p14*x9 + p20*x10 + p26*x11 + p32*x12; 1241 pc[8] = m9 = p3*x7 + p9*x8 + p15*x9 + p21*x10 + p27*x11 + p33*x12; 1242 pc[9] = m10 = p4*x7 + p10*x8 + p16*x9 + p22*x10 + p28*x11 + p34*x12; 1243 pc[10] = m11 = p5*x7 + p11*x8 + p17*x9 + p23*x10 + p29*x11 + p35*x12; 1244 pc[11] = m12 = p6*x7 + p12*x8 + p18*x9 + p24*x10 + p30*x11 + p36*x12; 1245 1246 pc[12] = m13 = p1*x13 + p7*x14 + p13*x15 + p19*x16 + p25*x17 + p31*x18; 1247 pc[13] = m14 = p2*x13 + p8*x14 + p14*x15 + p20*x16 + p26*x17 + p32*x18; 1248 pc[14] = m15 = p3*x13 + p9*x14 + p15*x15 + p21*x16 + p27*x17 + p33*x18; 1249 pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18; 1250 pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18; 1251 pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18; 1252 1253 pc[18] = m19 = p1*x19 + p7*x20 + p13*x21 + p19*x22 + p25*x23 + p31*x24; 1254 pc[19] = m20 = p2*x19 + p8*x20 + p14*x21 + p20*x22 + p26*x23 + p32*x24; 1255 pc[20] = m21 = p3*x19 + p9*x20 + p15*x21 + p21*x22 + p27*x23 + p33*x24; 1256 pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24; 1257 pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24; 1258 pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24; 1259 1260 pc[24] = m25 = p1*x25 + p7*x26 + p13*x27 + p19*x28 + p25*x29 + p31*x30; 1261 pc[25] = m26 = p2*x25 + p8*x26 + p14*x27 + p20*x28 + p26*x29 + p32*x30; 1262 pc[26] = m27 = p3*x25 + p9*x26 + p15*x27 + p21*x28 + p27*x29 + p33*x30; 1263 pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30; 1264 pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30; 1265 pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30; 1266 1267 pc[30] = m31 = p1*x31 + p7*x32 + p13*x33 + p19*x34 + p25*x35 + p31*x36; 1268 pc[31] = m32 = p2*x31 + p8*x32 + p14*x33 + p20*x34 + p26*x35 + p32*x36; 1269 pc[32] = m33 = p3*x31 + p9*x32 + p15*x33 + p21*x34 + p27*x35 + p33*x36; 1270 pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36; 1271 pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36; 1272 pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36; 1273 1274 nz = bi[row+1] - diag_offset[row] - 1; 1275 pv += 36; 1276 for (j=0; j<nz; j++) { 1277 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1278 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1279 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1280 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1281 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1282 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1283 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1284 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1285 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1286 x = rtmp + 36*pj[j]; 1287 x[0] -= m1*x1 + m7*x2 + m13*x3 + m19*x4 + m25*x5 + m31*x6; 1288 x[1] -= m2*x1 + m8*x2 + m14*x3 + m20*x4 + m26*x5 + m32*x6; 1289 x[2] -= m3*x1 + m9*x2 + m15*x3 + m21*x4 + m27*x5 + m33*x6; 1290 x[3] -= m4*x1 + m10*x2 + m16*x3 + m22*x4 + m28*x5 + m34*x6; 1291 x[4] -= m5*x1 + m11*x2 + m17*x3 + m23*x4 + m29*x5 + m35*x6; 1292 x[5] -= m6*x1 + m12*x2 + m18*x3 + m24*x4 + m30*x5 + m36*x6; 1293 1294 x[6] -= m1*x7 + m7*x8 + m13*x9 + m19*x10 + m25*x11 + m31*x12; 1295 x[7] -= m2*x7 + m8*x8 + m14*x9 + m20*x10 + m26*x11 + m32*x12; 1296 x[8] -= m3*x7 + m9*x8 + m15*x9 + m21*x10 + m27*x11 + m33*x12; 1297 x[9] -= m4*x7 + m10*x8 + m16*x9 + m22*x10 + m28*x11 + m34*x12; 1298 x[10] -= m5*x7 + m11*x8 + m17*x9 + m23*x10 + m29*x11 + m35*x12; 1299 x[11] -= m6*x7 + m12*x8 + m18*x9 + m24*x10 + m30*x11 + m36*x12; 1300 1301 x[12] -= m1*x13 + m7*x14 + m13*x15 + m19*x16 + m25*x17 + m31*x18; 1302 x[13] -= m2*x13 + m8*x14 + m14*x15 + m20*x16 + m26*x17 + m32*x18; 1303 x[14] -= m3*x13 + m9*x14 + m15*x15 + m21*x16 + m27*x17 + m33*x18; 1304 x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18; 1305 x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18; 1306 x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18; 1307 1308 x[18] -= m1*x19 + m7*x20 + m13*x21 + m19*x22 + m25*x23 + m31*x24; 1309 x[19] -= m2*x19 + m8*x20 + m14*x21 + m20*x22 + m26*x23 + m32*x24; 1310 x[20] -= m3*x19 + m9*x20 + m15*x21 + m21*x22 + m27*x23 + m33*x24; 1311 x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24; 1312 x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24; 1313 x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24; 1314 1315 x[24] -= m1*x25 + m7*x26 + m13*x27 + m19*x28 + m25*x29 + m31*x30; 1316 x[25] -= m2*x25 + m8*x26 + m14*x27 + m20*x28 + m26*x29 + m32*x30; 1317 x[26] -= m3*x25 + m9*x26 + m15*x27 + m21*x28 + m27*x29 + m33*x30; 1318 x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30; 1319 x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30; 1320 x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30; 1321 1322 x[30] -= m1*x31 + m7*x32 + m13*x33 + m19*x34 + m25*x35 + m31*x36; 1323 x[31] -= m2*x31 + m8*x32 + m14*x33 + m20*x34 + m26*x35 + m32*x36; 1324 x[32] -= m3*x31 + m9*x32 + m15*x33 + m21*x34 + m27*x35 + m33*x36; 1325 x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36; 1326 x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36; 1327 x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36; 1328 1329 pv += 36; 1330 } 1331 PLogFlops(432*nz+396); 1332 } 1333 row = *ajtmp++; 1334 } 1335 /* finished row so stick it into b->a */ 1336 pv = ba + 36*bi[i]; 1337 pj = bj + bi[i]; 1338 nz = bi[i+1] - bi[i]; 1339 for (j=0; j<nz; j++) { 1340 x = rtmp+36*pj[j]; 1341 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1342 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 1343 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 1344 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1345 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 1346 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 1347 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 1348 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 1349 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 1350 pv += 36; 1351 } 1352 /* invert diagonal block */ 1353 w = ba + 36*diag_offset[i]; 1354 ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr); 1355 } 1356 1357 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1358 C->factor = FACTOR_LU; 1359 C->assembled = PETSC_TRUE; 1360 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1361 PetscFunctionReturn(0); 1362 } 1363 1364 /* Version for when blocks are 5 by 5 */ 1365 #undef __FUNC__ 1366 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1367 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1368 { 1369 Mat C = *B; 1370 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1371 IS perm = b->row; 1372 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1373 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1374 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1375 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1376 1377 PetscFunctionBegin; 1378 /* initialization */ 1379 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1380 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1381 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1382 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1383 for (i=0; i<mbs; i++) { 1384 jl[i] = mbs; il[0] = 0; 1385 } 1386 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1387 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1388 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1389 1390 /* check permutation */ 1391 if (!a->permute){ 1392 ai = a->i; aj = a->j; aa = a->a; 1393 } else { 1394 ai = a->inew; aj = a->jnew; 1395 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1396 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1397 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1398 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1399 1400 for (i=0; i<mbs; i++){ 1401 jmin = ai[i]; jmax = ai[i+1]; 1402 for (j=jmin; j<jmax; j++){ 1403 while (a2anew[j] != j){ 1404 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1405 for (k1=0; k1<25; k1++){ 1406 dk[k1] = aa[k*25+k1]; 1407 aa[k*25+k1] = aa[j*25+k1]; 1408 aa[j*25+k1] = dk[k1]; 1409 } 1410 } 1411 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1412 if (i > aj[j]){ 1413 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1414 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1415 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1416 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1417 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1418 } 1419 } 1420 } 1421 } 1422 ierr = PetscFree(a2anew);CHKERRA(ierr); 1423 } 1424 1425 /* for each row k */ 1426 for (k = 0; k<mbs; k++){ 1427 1428 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1429 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1430 if (jmin < jmax) { 1431 ap = aa + jmin*25; 1432 for (j = jmin; j < jmax; j++){ 1433 vj = perm_ptr[aj[j]]; /* block col. index */ 1434 rtmp_ptr = rtmp + vj*25; 1435 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1436 } 1437 } 1438 1439 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1440 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1441 i = jl[k]; /* first row to be added to k_th row */ 1442 1443 while (i < mbs){ 1444 nexti = jl[i]; /* next row to be added to k_th row */ 1445 1446 /* compute multiplier */ 1447 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1448 1449 /* uik = -inv(Di)*U_bar(i,k) */ 1450 d = ba + i*25; 1451 u = ba + ili*25; 1452 1453 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1454 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1455 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1456 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1457 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1458 1459 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1460 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1461 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1462 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1463 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1464 1465 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1466 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1467 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1468 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1469 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1470 1471 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1472 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1473 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1474 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1475 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1476 1477 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1478 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1479 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1480 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1481 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1482 1483 1484 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1485 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1486 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1487 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1488 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1489 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1490 1491 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1492 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1493 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1494 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1495 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1496 1497 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1498 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1499 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1500 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1501 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1502 1503 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1504 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1505 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1506 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1507 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1508 1509 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1510 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1511 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1512 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1513 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1514 1515 /* update -U(i,k) */ 1516 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1517 1518 /* add multiple of row i to k-th row ... */ 1519 jmin = ili + 1; jmax = bi[i+1]; 1520 if (jmin < jmax){ 1521 for (j=jmin; j<jmax; j++) { 1522 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1523 rtmp_ptr = rtmp + bj[j]*25; 1524 u = ba + j*25; 1525 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1526 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1527 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1528 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1529 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1530 1531 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1532 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1533 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1534 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1535 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1536 1537 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1538 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1539 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1540 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1541 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1542 1543 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1544 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1545 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1546 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1547 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1548 1549 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1550 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1551 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1552 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1553 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1554 } 1555 1556 /* ... add i to row list for next nonzero entry */ 1557 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1558 j = bj[jmin]; 1559 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1560 } 1561 i = nexti; 1562 } 1563 1564 /* save nonzero entries in k-th row of U ... */ 1565 1566 /* invert diagonal block */ 1567 d = ba+k*25; 1568 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1569 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1570 1571 jmin = bi[k]; jmax = bi[k+1]; 1572 if (jmin < jmax) { 1573 for (j=jmin; j<jmax; j++){ 1574 vj = bj[j]; /* block col. index of U */ 1575 u = ba + j*25; 1576 rtmp_ptr = rtmp + vj*25; 1577 for (k1=0; k1<25; k1++){ 1578 *u++ = *rtmp_ptr; 1579 *rtmp_ptr++ = 0.0; 1580 } 1581 } 1582 1583 /* ... add k to row list for first nonzero entry in k-th row */ 1584 il[k] = jmin; 1585 i = bj[jmin]; 1586 jl[k] = jl[i]; jl[i] = k; 1587 } 1588 } 1589 1590 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1591 ierr = PetscFree(il);CHKERRQ(ierr); 1592 ierr = PetscFree(jl);CHKERRQ(ierr); 1593 ierr = PetscFree(dk);CHKERRQ(ierr); 1594 ierr = PetscFree(uik);CHKERRQ(ierr); 1595 if (a->permute){ 1596 ierr = PetscFree(aa);CHKERRQ(ierr); 1597 } 1598 1599 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1600 C->factor = FACTOR_CHOLESKY; 1601 C->assembled = PETSC_TRUE; 1602 C->preallocated = PETSC_TRUE; 1603 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1604 PetscFunctionReturn(0); 1605 } 1606 1607 /* 1608 Version for when blocks are 5 by 5 Using natural ordering 1609 */ 1610 #undef __FUNC__ 1611 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1612 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1613 { 1614 Mat C = *B; 1615 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1616 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1617 int *ajtmpold,*ajtmp,nz,row; 1618 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1619 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1620 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1621 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1622 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1623 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1624 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1625 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1626 MatScalar *ba = b->a,*aa = a->a; 1627 1628 PetscFunctionBegin; 1629 rtmp = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1630 for (i=0; i<n; i++) { 1631 nz = bi[i+1] - bi[i]; 1632 ajtmp = bj + bi[i]; 1633 for (j=0; j<nz; j++) { 1634 x = rtmp+25*ajtmp[j]; 1635 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1636 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1637 x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 1638 } 1639 /* load in initial (unfactored row) */ 1640 nz = ai[i+1] - ai[i]; 1641 ajtmpold = aj + ai[i]; 1642 v = aa + 25*ai[i]; 1643 for (j=0; j<nz; j++) { 1644 x = rtmp+25*ajtmpold[j]; 1645 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1646 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1647 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1648 x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; 1649 x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1650 x[24] = v[24]; 1651 v += 25; 1652 } 1653 row = *ajtmp++; 1654 while (row < i) { 1655 pc = rtmp + 25*row; 1656 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1657 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1658 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1659 p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; 1660 p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; 1661 p24 = pc[23]; p25 = pc[24]; 1662 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1663 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1664 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1665 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 1666 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 1667 pv = ba + 25*diag_offset[row]; 1668 pj = bj + diag_offset[row] + 1; 1669 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1670 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1671 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1672 x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; 1673 x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1674 x25 = pv[24]; 1675 pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5; 1676 pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5; 1677 pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5; 1678 pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5; 1679 pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5; 1680 1681 pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10; 1682 pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10; 1683 pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10; 1684 pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10; 1685 pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10; 1686 1687 pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15; 1688 pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15; 1689 pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15; 1690 pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15; 1691 pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15; 1692 1693 pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20; 1694 pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20; 1695 pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20; 1696 pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20; 1697 pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20; 1698 1699 pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25; 1700 pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25; 1701 pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25; 1702 pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25; 1703 pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25; 1704 1705 nz = bi[row+1] - diag_offset[row] - 1; 1706 pv += 25; 1707 for (j=0; j<nz; j++) { 1708 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1709 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1710 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1711 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; 1712 x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; 1713 x24 = pv[23]; x25 = pv[24]; 1714 x = rtmp + 25*pj[j]; 1715 x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5; 1716 x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5; 1717 x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5; 1718 x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5; 1719 x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5; 1720 1721 x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10; 1722 x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10; 1723 x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10; 1724 x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10; 1725 x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10; 1726 1727 x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15; 1728 x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15; 1729 x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15; 1730 x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15; 1731 x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15; 1732 1733 x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20; 1734 x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20; 1735 x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20; 1736 x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20; 1737 x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20; 1738 1739 x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25; 1740 x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25; 1741 x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25; 1742 x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25; 1743 x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25; 1744 pv += 25; 1745 } 1746 PLogFlops(250*nz+225); 1747 } 1748 row = *ajtmp++; 1749 } 1750 /* finished row so stick it into b->a */ 1751 pv = ba + 25*bi[i]; 1752 pj = bj + bi[i]; 1753 nz = bi[i+1] - bi[i]; 1754 for (j=0; j<nz; j++) { 1755 x = rtmp+25*pj[j]; 1756 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1757 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1758 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1759 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17]; 1760 pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; 1761 pv[23] = x[23]; pv[24] = x[24]; 1762 pv += 25; 1763 } 1764 /* invert diagonal block */ 1765 w = ba + 25*diag_offset[i]; 1766 ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr); 1767 } 1768 1769 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1770 C->factor = FACTOR_LU; 1771 C->assembled = PETSC_TRUE; 1772 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1773 PetscFunctionReturn(0); 1774 } 1775 1776 /* 1777 Version for when blocks are 4 by 4 Using natural ordering 1778 */ 1779 #undef __FUNC__ 1780 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1781 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1782 { 1783 Mat C = *B; 1784 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1785 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1786 int *ajtmpold,*ajtmp,nz,row; 1787 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1788 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1789 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 1790 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; 1791 MatScalar p10,p11,p12,p13,p14,p15,p16,m10,m11,m12; 1792 MatScalar m13,m14,m15,m16; 1793 MatScalar *ba = b->a,*aa = a->a; 1794 1795 PetscFunctionBegin; 1796 rtmp = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1797 1798 for (i=0; i<n; i++) { 1799 nz = bi[i+1] - bi[i]; 1800 ajtmp = bj + bi[i]; 1801 for (j=0; j<nz; j++) { 1802 x = rtmp+16*ajtmp[j]; 1803 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1804 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1805 } 1806 /* load in initial (unfactored row) */ 1807 nz = ai[i+1] - ai[i]; 1808 ajtmpold = aj + ai[i]; 1809 v = aa + 16*ai[i]; 1810 for (j=0; j<nz; j++) { 1811 x = rtmp+16*ajtmpold[j]; 1812 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1813 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1814 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1815 x[14] = v[14]; x[15] = v[15]; 1816 v += 16; 1817 } 1818 row = *ajtmp++; 1819 while (row < i) { 1820 pc = rtmp + 16*row; 1821 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1822 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1823 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1824 p15 = pc[14]; p16 = pc[15]; 1825 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1826 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1827 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1828 || p16 != 0.0) { 1829 pv = ba + 16*diag_offset[row]; 1830 pj = bj + diag_offset[row] + 1; 1831 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1832 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1833 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1834 x15 = pv[14]; x16 = pv[15]; 1835 pc[0] = m1 = p1*x1 + p5*x2 + p9*x3 + p13*x4; 1836 pc[1] = m2 = p2*x1 + p6*x2 + p10*x3 + p14*x4; 1837 pc[2] = m3 = p3*x1 + p7*x2 + p11*x3 + p15*x4; 1838 pc[3] = m4 = p4*x1 + p8*x2 + p12*x3 + p16*x4; 1839 1840 pc[4] = m5 = p1*x5 + p5*x6 + p9*x7 + p13*x8; 1841 pc[5] = m6 = p2*x5 + p6*x6 + p10*x7 + p14*x8; 1842 pc[6] = m7 = p3*x5 + p7*x6 + p11*x7 + p15*x8; 1843 pc[7] = m8 = p4*x5 + p8*x6 + p12*x7 + p16*x8; 1844 1845 pc[8] = m9 = p1*x9 + p5*x10 + p9*x11 + p13*x12; 1846 pc[9] = m10 = p2*x9 + p6*x10 + p10*x11 + p14*x12; 1847 pc[10] = m11 = p3*x9 + p7*x10 + p11*x11 + p15*x12; 1848 pc[11] = m12 = p4*x9 + p8*x10 + p12*x11 + p16*x12; 1849 1850 pc[12] = m13 = p1*x13 + p5*x14 + p9*x15 + p13*x16; 1851 pc[13] = m14 = p2*x13 + p6*x14 + p10*x15 + p14*x16; 1852 pc[14] = m15 = p3*x13 + p7*x14 + p11*x15 + p15*x16; 1853 pc[15] = m16 = p4*x13 + p8*x14 + p12*x15 + p16*x16; 1854 1855 nz = bi[row+1] - diag_offset[row] - 1; 1856 pv += 16; 1857 for (j=0; j<nz; j++) { 1858 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1859 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1860 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1861 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1862 x = rtmp + 16*pj[j]; 1863 x[0] -= m1*x1 + m5*x2 + m9*x3 + m13*x4; 1864 x[1] -= m2*x1 + m6*x2 + m10*x3 + m14*x4; 1865 x[2] -= m3*x1 + m7*x2 + m11*x3 + m15*x4; 1866 x[3] -= m4*x1 + m8*x2 + m12*x3 + m16*x4; 1867 1868 x[4] -= m1*x5 + m5*x6 + m9*x7 + m13*x8; 1869 x[5] -= m2*x5 + m6*x6 + m10*x7 + m14*x8; 1870 x[6] -= m3*x5 + m7*x6 + m11*x7 + m15*x8; 1871 x[7] -= m4*x5 + m8*x6 + m12*x7 + m16*x8; 1872 1873 x[8] -= m1*x9 + m5*x10 + m9*x11 + m13*x12; 1874 x[9] -= m2*x9 + m6*x10 + m10*x11 + m14*x12; 1875 x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12; 1876 x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12; 1877 1878 x[12] -= m1*x13 + m5*x14 + m9*x15 + m13*x16; 1879 x[13] -= m2*x13 + m6*x14 + m10*x15 + m14*x16; 1880 x[14] -= m3*x13 + m7*x14 + m11*x15 + m15*x16; 1881 x[15] -= m4*x13 + m8*x14 + m12*x15 + m16*x16; 1882 1883 pv += 16; 1884 } 1885 PLogFlops(128*nz+112); 1886 } 1887 row = *ajtmp++; 1888 } 1889 /* finished row so stick it into b->a */ 1890 pv = ba + 16*bi[i]; 1891 pj = bj + bi[i]; 1892 nz = bi[i+1] - bi[i]; 1893 for (j=0; j<nz; j++) { 1894 x = rtmp+16*pj[j]; 1895 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1896 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1897 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1898 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1899 pv += 16; 1900 } 1901 /* invert diagonal block */ 1902 w = ba + 16*diag_offset[i]; 1903 ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr); 1904 } 1905 1906 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1907 C->factor = FACTOR_LU; 1908 C->assembled = PETSC_TRUE; 1909 C->preallocated = PETSC_TRUE; 1910 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 1911 PetscFunctionReturn(0); 1912 } 1913 1914 /* Version for when blocks are 4 by 4 */ 1915 #undef __FUNC__ 1916 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 1917 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 1918 { 1919 Mat C = *B; 1920 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1921 IS perm = b->row; 1922 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1923 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1924 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1925 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 1926 1927 PetscFunctionBegin; 1928 /* initialization */ 1929 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1930 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1931 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1932 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1933 for (i=0; i<mbs; i++) { 1934 jl[i] = mbs; il[0] = 0; 1935 } 1936 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 1937 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 1938 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1939 1940 /* check permutation */ 1941 if (!a->permute){ 1942 ai = a->i; aj = a->j; aa = a->a; 1943 } else { 1944 ai = a->inew; aj = a->jnew; 1945 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1946 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1947 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1948 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1949 1950 for (i=0; i<mbs; i++){ 1951 jmin = ai[i]; jmax = ai[i+1]; 1952 for (j=jmin; j<jmax; j++){ 1953 while (a2anew[j] != j){ 1954 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1955 for (k1=0; k1<16; k1++){ 1956 dk[k1] = aa[k*16+k1]; 1957 aa[k*16+k1] = aa[j*16+k1]; 1958 aa[j*16+k1] = dk[k1]; 1959 } 1960 } 1961 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1962 if (i > aj[j]){ 1963 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1964 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 1965 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1966 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 1967 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 1968 } 1969 } 1970 } 1971 } 1972 ierr = PetscFree(a2anew);CHKERRA(ierr); 1973 } 1974 1975 /* for each row k */ 1976 for (k = 0; k<mbs; k++){ 1977 1978 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1979 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1980 if (jmin < jmax) { 1981 ap = aa + jmin*16; 1982 for (j = jmin; j < jmax; j++){ 1983 vj = perm_ptr[aj[j]]; /* block col. index */ 1984 rtmp_ptr = rtmp + vj*16; 1985 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 1986 } 1987 } 1988 1989 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1990 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 1991 i = jl[k]; /* first row to be added to k_th row */ 1992 1993 while (i < mbs){ 1994 nexti = jl[i]; /* next row to be added to k_th row */ 1995 1996 /* compute multiplier */ 1997 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1998 1999 /* uik = -inv(Di)*U_bar(i,k) */ 2000 diag = ba + i*16; 2001 u = ba + ili*16; 2002 2003 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 2004 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 2005 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 2006 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 2007 2008 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2009 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2010 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2011 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2012 2013 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2014 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2015 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2016 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2017 2018 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2019 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2020 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2021 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2022 2023 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2024 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2025 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2026 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2027 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2028 2029 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2030 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2031 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2032 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2033 2034 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2035 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2036 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2037 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2038 2039 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2040 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2041 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2042 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2043 2044 /* update -U(i,k) */ 2045 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2046 2047 /* add multiple of row i to k-th row ... */ 2048 jmin = ili + 1; jmax = bi[i+1]; 2049 if (jmin < jmax){ 2050 for (j=jmin; j<jmax; j++) { 2051 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2052 rtmp_ptr = rtmp + bj[j]*16; 2053 u = ba + j*16; 2054 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2055 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2056 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2057 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2058 2059 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2060 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2061 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2062 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2063 2064 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2065 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2066 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2067 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2068 2069 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2070 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2071 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2072 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2073 } 2074 2075 /* ... add i to row list for next nonzero entry */ 2076 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2077 j = bj[jmin]; 2078 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2079 } 2080 i = nexti; 2081 } 2082 2083 /* save nonzero entries in k-th row of U ... */ 2084 2085 /* invert diagonal block */ 2086 diag = ba+k*16; 2087 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2088 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2089 2090 jmin = bi[k]; jmax = bi[k+1]; 2091 if (jmin < jmax) { 2092 for (j=jmin; j<jmax; j++){ 2093 vj = bj[j]; /* block col. index of U */ 2094 u = ba + j*16; 2095 rtmp_ptr = rtmp + vj*16; 2096 for (k1=0; k1<16; k1++){ 2097 *u++ = *rtmp_ptr; 2098 *rtmp_ptr++ = 0.0; 2099 } 2100 } 2101 2102 /* ... add k to row list for first nonzero entry in k-th row */ 2103 il[k] = jmin; 2104 i = bj[jmin]; 2105 jl[k] = jl[i]; jl[i] = k; 2106 } 2107 } 2108 2109 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2110 ierr = PetscFree(il);CHKERRQ(ierr); 2111 ierr = PetscFree(jl);CHKERRQ(ierr); 2112 ierr = PetscFree(dk);CHKERRQ(ierr); 2113 ierr = PetscFree(uik);CHKERRQ(ierr); 2114 if (a->permute){ 2115 ierr = PetscFree(aa);CHKERRQ(ierr); 2116 } 2117 2118 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2119 C->factor = FACTOR_CHOLESKY; 2120 C->assembled = PETSC_TRUE; 2121 C->preallocated = PETSC_TRUE; 2122 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2123 PetscFunctionReturn(0); 2124 } 2125 2126 /* Version for when blocks are 3 by 3 */ 2127 #undef __FUNC__ 2128 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2129 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2130 { 2131 Mat C = *B; 2132 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2133 IS perm = b->row; 2134 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2135 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2136 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2137 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2138 2139 PetscFunctionBegin; 2140 /* initialization */ 2141 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2142 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2143 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2144 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2145 for (i=0; i<mbs; i++) { 2146 jl[i] = mbs; il[0] = 0; 2147 } 2148 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2149 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2150 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2151 2152 /* check permutation */ 2153 if (!a->permute){ 2154 ai = a->i; aj = a->j; aa = a->a; 2155 } else { 2156 ai = a->inew; aj = a->jnew; 2157 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2158 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2159 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2160 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2161 2162 for (i=0; i<mbs; i++){ 2163 jmin = ai[i]; jmax = ai[i+1]; 2164 for (j=jmin; j<jmax; j++){ 2165 while (a2anew[j] != j){ 2166 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2167 for (k1=0; k1<9; k1++){ 2168 dk[k1] = aa[k*9+k1]; 2169 aa[k*9+k1] = aa[j*9+k1]; 2170 aa[j*9+k1] = dk[k1]; 2171 } 2172 } 2173 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2174 if (i > aj[j]){ 2175 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2176 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2177 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2178 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2179 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2180 } 2181 } 2182 } 2183 } 2184 ierr = PetscFree(a2anew);CHKERRA(ierr); 2185 } 2186 2187 /* for each row k */ 2188 for (k = 0; k<mbs; k++){ 2189 2190 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2191 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2192 if (jmin < jmax) { 2193 ap = aa + jmin*9; 2194 for (j = jmin; j < jmax; j++){ 2195 vj = perm_ptr[aj[j]]; /* block col. index */ 2196 rtmp_ptr = rtmp + vj*9; 2197 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2198 } 2199 } 2200 2201 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2202 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2203 i = jl[k]; /* first row to be added to k_th row */ 2204 2205 while (i < mbs){ 2206 nexti = jl[i]; /* next row to be added to k_th row */ 2207 2208 /* compute multiplier */ 2209 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2210 2211 /* uik = -inv(Di)*U_bar(i,k) */ 2212 diag = ba + i*9; 2213 u = ba + ili*9; 2214 2215 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2216 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2217 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2218 2219 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2220 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2221 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2222 2223 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2224 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2225 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2226 2227 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2228 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2229 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2230 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2231 2232 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2233 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2234 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2235 2236 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2237 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2238 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2239 2240 /* update -U(i,k) */ 2241 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2242 2243 /* add multiple of row i to k-th row ... */ 2244 jmin = ili + 1; jmax = bi[i+1]; 2245 if (jmin < jmax){ 2246 for (j=jmin; j<jmax; j++) { 2247 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2248 rtmp_ptr = rtmp + bj[j]*9; 2249 u = ba + j*9; 2250 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2251 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2252 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2253 2254 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2255 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2256 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2257 2258 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2259 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2260 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2261 } 2262 2263 /* ... add i to row list for next nonzero entry */ 2264 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2265 j = bj[jmin]; 2266 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2267 } 2268 i = nexti; 2269 } 2270 2271 /* save nonzero entries in k-th row of U ... */ 2272 2273 /* invert diagonal block */ 2274 diag = ba+k*9; 2275 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2276 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2277 2278 jmin = bi[k]; jmax = bi[k+1]; 2279 if (jmin < jmax) { 2280 for (j=jmin; j<jmax; j++){ 2281 vj = bj[j]; /* block col. index of U */ 2282 u = ba + j*9; 2283 rtmp_ptr = rtmp + vj*9; 2284 for (k1=0; k1<9; k1++){ 2285 *u++ = *rtmp_ptr; 2286 *rtmp_ptr++ = 0.0; 2287 } 2288 } 2289 2290 /* ... add k to row list for first nonzero entry in k-th row */ 2291 il[k] = jmin; 2292 i = bj[jmin]; 2293 jl[k] = jl[i]; jl[i] = k; 2294 } 2295 } 2296 2297 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2298 ierr = PetscFree(il);CHKERRQ(ierr); 2299 ierr = PetscFree(jl);CHKERRQ(ierr); 2300 ierr = PetscFree(dk);CHKERRQ(ierr); 2301 ierr = PetscFree(uik);CHKERRQ(ierr); 2302 if (a->permute){ 2303 ierr = PetscFree(aa);CHKERRQ(ierr); 2304 } 2305 2306 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2307 C->factor = FACTOR_CHOLESKY; 2308 C->assembled = PETSC_TRUE; 2309 C->preallocated = PETSC_TRUE; 2310 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2311 PetscFunctionReturn(0); 2312 } 2313 2314 /* 2315 Version for when blocks are 3 by 3 Using natural ordering 2316 */ 2317 #undef __FUNC__ 2318 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2319 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B) 2320 { 2321 Mat C = *B; 2322 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2323 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2324 int *ajtmpold,*ajtmp,nz,row; 2325 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2326 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2327 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 2328 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9; 2329 MatScalar *ba = b->a,*aa = a->a; 2330 2331 PetscFunctionBegin; 2332 rtmp = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2333 2334 for (i=0; i<n; i++) { 2335 nz = bi[i+1] - bi[i]; 2336 ajtmp = bj + bi[i]; 2337 for (j=0; j<nz; j++) { 2338 x = rtmp+9*ajtmp[j]; 2339 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0; 2340 } 2341 /* load in initial (unfactored row) */ 2342 nz = ai[i+1] - ai[i]; 2343 ajtmpold = aj + ai[i]; 2344 v = aa + 9*ai[i]; 2345 for (j=0; j<nz; j++) { 2346 x = rtmp+9*ajtmpold[j]; 2347 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2348 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 2349 v += 9; 2350 } 2351 row = *ajtmp++; 2352 while (row < i) { 2353 pc = rtmp + 9*row; 2354 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2355 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 2356 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 2357 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) { 2358 pv = ba + 9*diag_offset[row]; 2359 pj = bj + diag_offset[row] + 1; 2360 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2361 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2362 pc[0] = m1 = p1*x1 + p4*x2 + p7*x3; 2363 pc[1] = m2 = p2*x1 + p5*x2 + p8*x3; 2364 pc[2] = m3 = p3*x1 + p6*x2 + p9*x3; 2365 2366 pc[3] = m4 = p1*x4 + p4*x5 + p7*x6; 2367 pc[4] = m5 = p2*x4 + p5*x5 + p8*x6; 2368 pc[5] = m6 = p3*x4 + p6*x5 + p9*x6; 2369 2370 pc[6] = m7 = p1*x7 + p4*x8 + p7*x9; 2371 pc[7] = m8 = p2*x7 + p5*x8 + p8*x9; 2372 pc[8] = m9 = p3*x7 + p6*x8 + p9*x9; 2373 2374 nz = bi[row+1] - diag_offset[row] - 1; 2375 pv += 9; 2376 for (j=0; j<nz; j++) { 2377 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2378 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2379 x = rtmp + 9*pj[j]; 2380 x[0] -= m1*x1 + m4*x2 + m7*x3; 2381 x[1] -= m2*x1 + m5*x2 + m8*x3; 2382 x[2] -= m3*x1 + m6*x2 + m9*x3; 2383 2384 x[3] -= m1*x4 + m4*x5 + m7*x6; 2385 x[4] -= m2*x4 + m5*x5 + m8*x6; 2386 x[5] -= m3*x4 + m6*x5 + m9*x6; 2387 2388 x[6] -= m1*x7 + m4*x8 + m7*x9; 2389 x[7] -= m2*x7 + m5*x8 + m8*x9; 2390 x[8] -= m3*x7 + m6*x8 + m9*x9; 2391 pv += 9; 2392 } 2393 PLogFlops(54*nz+36); 2394 } 2395 row = *ajtmp++; 2396 } 2397 /* finished row so stick it into b->a */ 2398 pv = ba + 9*bi[i]; 2399 pj = bj + bi[i]; 2400 nz = bi[i+1] - bi[i]; 2401 for (j=0; j<nz; j++) { 2402 x = rtmp+9*pj[j]; 2403 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2404 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 2405 pv += 9; 2406 } 2407 /* invert diagonal block */ 2408 w = ba + 9*diag_offset[i]; 2409 ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr); 2410 } 2411 2412 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2413 C->factor = FACTOR_CHOLESKY; 2414 C->assembled = PETSC_TRUE; 2415 C->preallocated = PETSC_TRUE; 2416 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2417 PetscFunctionReturn(0); 2418 } 2419 2420 /* 2421 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2422 Version for blocks 2 by 2. 2423 */ 2424 #undef __FUNC__ 2425 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2426 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2427 { 2428 Mat C = *B; 2429 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2430 IS perm = b->row; 2431 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2432 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2433 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2434 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2435 2436 PetscFunctionBegin; 2437 2438 /* initialization */ 2439 /* il and jl record the first nonzero element in each row of the accessing 2440 window U(0:k, k:mbs-1). 2441 jl: list of rows to be added to uneliminated rows 2442 i>= k: jl(i) is the first row to be added to row i 2443 i< k: jl(i) is the row following row i in some list of rows 2444 jl(i) = mbs indicates the end of a list 2445 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2446 row i of U */ 2447 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2448 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2449 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2450 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2451 for (i=0; i<mbs; i++) { 2452 jl[i] = mbs; il[0] = 0; 2453 } 2454 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2455 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2456 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2457 2458 /* check permutation */ 2459 if (!a->permute){ 2460 ai = a->i; aj = a->j; aa = a->a; 2461 } else { 2462 ai = a->inew; aj = a->jnew; 2463 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2464 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2465 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2466 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2467 2468 for (i=0; i<mbs; i++){ 2469 jmin = ai[i]; jmax = ai[i+1]; 2470 for (j=jmin; j<jmax; j++){ 2471 while (a2anew[j] != j){ 2472 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2473 for (k1=0; k1<4; k1++){ 2474 dk[k1] = aa[k*4+k1]; 2475 aa[k*4+k1] = aa[j*4+k1]; 2476 aa[j*4+k1] = dk[k1]; 2477 } 2478 } 2479 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2480 if (i > aj[j]){ 2481 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2482 ap = aa + j*4; /* ptr to the beginning of the block */ 2483 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2484 ap[1] = ap[2]; 2485 ap[2] = dk[1]; 2486 } 2487 } 2488 } 2489 ierr = PetscFree(a2anew);CHKERRA(ierr); 2490 } 2491 2492 /* for each row k */ 2493 for (k = 0; k<mbs; k++){ 2494 2495 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2496 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2497 if (jmin < jmax) { 2498 ap = aa + jmin*4; 2499 for (j = jmin; j < jmax; j++){ 2500 vj = perm_ptr[aj[j]]; /* block col. index */ 2501 rtmp_ptr = rtmp + vj*4; 2502 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2503 } 2504 } 2505 2506 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2507 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2508 i = jl[k]; /* first row to be added to k_th row */ 2509 2510 while (i < mbs){ 2511 nexti = jl[i]; /* next row to be added to k_th row */ 2512 2513 /* compute multiplier */ 2514 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2515 2516 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2517 diag = ba + i*4; 2518 u = ba + ili*4; 2519 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2520 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2521 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2522 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2523 2524 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2525 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2526 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2527 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2528 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2529 2530 /* update -U(i,k): ba[ili] = uik */ 2531 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2532 2533 /* add multiple of row i to k-th row ... */ 2534 jmin = ili + 1; jmax = bi[i+1]; 2535 if (jmin < jmax){ 2536 for (j=jmin; j<jmax; j++) { 2537 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2538 rtmp_ptr = rtmp + bj[j]*4; 2539 u = ba + j*4; 2540 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2541 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2542 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2543 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2544 } 2545 2546 /* ... add i to row list for next nonzero entry */ 2547 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2548 j = bj[jmin]; 2549 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2550 } 2551 i = nexti; 2552 } 2553 2554 /* save nonzero entries in k-th row of U ... */ 2555 2556 /* invert diagonal block */ 2557 diag = ba+k*4; 2558 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2559 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2560 2561 jmin = bi[k]; jmax = bi[k+1]; 2562 if (jmin < jmax) { 2563 for (j=jmin; j<jmax; j++){ 2564 vj = bj[j]; /* block col. index of U */ 2565 u = ba + j*4; 2566 rtmp_ptr = rtmp + vj*4; 2567 for (k1=0; k1<4; k1++){ 2568 *u++ = *rtmp_ptr; 2569 *rtmp_ptr++ = 0.0; 2570 } 2571 } 2572 2573 /* ... add k to row list for first nonzero entry in k-th row */ 2574 il[k] = jmin; 2575 i = bj[jmin]; 2576 jl[k] = jl[i]; jl[i] = k; 2577 } 2578 } 2579 2580 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2581 ierr = PetscFree(il);CHKERRQ(ierr); 2582 ierr = PetscFree(jl);CHKERRQ(ierr); 2583 ierr = PetscFree(dk);CHKERRQ(ierr); 2584 ierr = PetscFree(uik);CHKERRQ(ierr); 2585 if (a->permute) { 2586 ierr = PetscFree(aa);CHKERRQ(ierr); 2587 } 2588 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2589 C->factor = FACTOR_CHOLESKY; 2590 C->assembled = PETSC_TRUE; 2591 C->preallocated = PETSC_TRUE; 2592 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2593 PetscFunctionReturn(0); 2594 } 2595 2596 /* 2597 Version for when blocks are 2 by 2 Using natural ordering 2598 */ 2599 #undef __FUNC__ 2600 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2601 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2602 { 2603 Mat C = *B; 2604 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2605 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2606 int *ajtmpold,*ajtmp,nz,row; 2607 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2608 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2609 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4; 2610 MatScalar *ba = b->a,*aa = a->a; 2611 2612 PetscFunctionBegin; 2613 rtmp = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2614 2615 for (i=0; i<n; i++) { 2616 nz = bi[i+1] - bi[i]; 2617 ajtmp = bj + bi[i]; 2618 for (j=0; j<nz; j++) { 2619 x = rtmp+4*ajtmp[j]; 2620 x[0] = x[1] = x[2] = x[3] = 0.0; 2621 } 2622 /* load in initial (unfactored row) */ 2623 nz = ai[i+1] - ai[i]; 2624 ajtmpold = aj + ai[i]; 2625 v = aa + 4*ai[i]; 2626 for (j=0; j<nz; j++) { 2627 x = rtmp+4*ajtmpold[j]; 2628 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2629 v += 4; 2630 } 2631 row = *ajtmp++; 2632 while (row < i) { 2633 pc = rtmp + 4*row; 2634 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2635 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) { 2636 pv = ba + 4*diag_offset[row]; 2637 pj = bj + diag_offset[row] + 1; 2638 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2639 pc[0] = m1 = p1*x1 + p3*x2; 2640 pc[1] = m2 = p2*x1 + p4*x2; 2641 pc[2] = m3 = p1*x3 + p3*x4; 2642 pc[3] = m4 = p2*x3 + p4*x4; 2643 nz = bi[row+1] - diag_offset[row] - 1; 2644 pv += 4; 2645 for (j=0; j<nz; j++) { 2646 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2647 x = rtmp + 4*pj[j]; 2648 x[0] -= m1*x1 + m3*x2; 2649 x[1] -= m2*x1 + m4*x2; 2650 x[2] -= m1*x3 + m3*x4; 2651 x[3] -= m2*x3 + m4*x4; 2652 pv += 4; 2653 } 2654 PLogFlops(16*nz+12); 2655 } 2656 row = *ajtmp++; 2657 } 2658 /* finished row so stick it into b->a */ 2659 pv = ba + 4*bi[i]; 2660 pj = bj + bi[i]; 2661 nz = bi[i+1] - bi[i]; 2662 for (j=0; j<nz; j++) { 2663 x = rtmp+4*pj[j]; 2664 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2665 pv += 4; 2666 } 2667 /* invert diagonal block */ 2668 w = ba + 4*diag_offset[i]; 2669 ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr); 2670 } 2671 2672 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2673 C->factor = FACTOR_LU; 2674 C->assembled = PETSC_TRUE; 2675 C->preallocated = PETSC_TRUE; 2676 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2677 PetscFunctionReturn(0); 2678 } 2679 2680 /* 2681 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2682 Version for blocks are 1 by 1. 2683 */ 2684 #undef __FUNC__ 2685 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2686 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2687 { 2688 Mat C = *B; 2689 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2690 IS ip = b->row; 2691 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2692 int *ai,*aj,*r; 2693 MatScalar *rtmp; 2694 MatScalar *ba = b->a,*aa,ak; 2695 MatScalar dk,uikdi; 2696 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2697 2698 PetscFunctionBegin; 2699 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2700 if (!a->permute){ 2701 ai = a->i; aj = a->j; aa = a->a; 2702 } else { 2703 ai = a->inew; aj = a->jnew; 2704 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2705 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2706 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 2707 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2708 2709 jmin = ai[0]; jmax = ai[mbs]; 2710 for (j=jmin; j<jmax; j++){ 2711 while (r[j] != j){ 2712 k = r[j]; r[j] = r[k]; r[k] = k; 2713 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 2714 } 2715 } 2716 ierr = PetscFree(r);CHKERRA(ierr); 2717 } 2718 2719 /* initialization */ 2720 /* il and jl record the first nonzero element in each row of the accessing 2721 window U(0:k, k:mbs-1). 2722 jl: list of rows to be added to uneliminated rows 2723 i>= k: jl(i) is the first row to be added to row i 2724 i< k: jl(i) is the row following row i in some list of rows 2725 jl(i) = mbs indicates the end of a list 2726 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2727 row i of U */ 2728 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2729 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2730 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2731 for (i=0; i<mbs; i++) { 2732 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2733 } 2734 2735 /* for each row k */ 2736 for (k = 0; k<mbs; k++){ 2737 2738 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2739 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2740 if (jmin < jmax) { 2741 for (j = jmin; j < jmax; j++){ 2742 vj = rip[aj[j]]; 2743 /* if (k <= vj)*/ rtmp[vj] = aa[j]; 2744 } 2745 } 2746 2747 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2748 dk = rtmp[k]; 2749 i = jl[k]; /* first row to be added to k_th row */ 2750 /* printf(" k=%d, pivot row = %d\n",k,i); */ 2751 2752 while (i < mbs){ 2753 nexti = jl[i]; /* next row to be added to k_th row */ 2754 2755 /* compute multiplier, update D(k) and U(i,k) */ 2756 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2757 uikdi = - ba[ili]*ba[i]; 2758 dk += uikdi*ba[ili]; 2759 ba[ili] = uikdi; /* -U(i,k) */ 2760 2761 /* add multiple of row i to k-th row ... */ 2762 jmin = ili + 1; jmax = bi[i+1]; 2763 if (jmin < jmax){ 2764 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2765 /* ... add i to row list for next nonzero entry */ 2766 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2767 j = bj[jmin]; 2768 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2769 } 2770 i = nexti; /* printf(" pivot row i=%d\n",i); */ 2771 } 2772 2773 /* check for zero pivot and save diagoanl element */ 2774 if (dk == 0.0){ 2775 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 2776 }else if (PetscRealPart(dk) < 0){ 2777 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 2778 } 2779 2780 /* save nonzero entries in k-th row of U ... */ 2781 ba[k] = 1.0/dk; 2782 jmin = bi[k]; jmax = bi[k+1]; 2783 if (jmin < jmax) { 2784 for (j=jmin; j<jmax; j++){ 2785 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 2786 } 2787 /* ... add k to row list for first nonzero entry in k-th row */ 2788 il[k] = jmin; 2789 i = bj[jmin]; 2790 jl[k] = jl[i]; jl[i] = k; 2791 } 2792 } 2793 2794 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2795 ierr = PetscFree(il);CHKERRQ(ierr); 2796 ierr = PetscFree(jl);CHKERRQ(ierr); 2797 if (a->permute){ 2798 ierr = PetscFree(aa);CHKERRQ(ierr); 2799 } 2800 2801 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2802 C->factor = FACTOR_CHOLESKY; 2803 C->assembled = PETSC_TRUE; 2804 C->preallocated = PETSC_TRUE; 2805 PLogFlops(b->mbs); 2806 PetscFunctionReturn(0); 2807 } 2808 2809 #undef __FUNC__ 2810 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 2811 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 2812 { 2813 int ierr; 2814 Mat C; 2815 2816 PetscFunctionBegin; 2817 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 2818 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 2819 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 2820 PetscFunctionReturn(0); 2821 } 2822 2823 2824