1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.42 2000/11/02 20:48:29 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_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 200 IS perm = b->row; 201 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 202 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 203 int bs=a->bs,bs2 = a->bs2; 204 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 205 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 206 MatScalar *W,*work; 207 int *pivots; 208 209 PetscFunctionBegin; 210 211 /* initialization */ 212 rtmp = (MatScalar*)PetscMalloc(bs2*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 213 ierr = PetscMemzero(rtmp,bs2*mbs*sizeof(MatScalar));CHKERRQ(ierr); 214 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 215 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 216 for (i=0; i<mbs; i++) { 217 jl[i] = mbs; il[0] = 0; 218 } 219 dk = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(dk); 220 uik = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(uik); 221 W = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(W); 222 work = (MatScalar*)PetscMalloc(bs*sizeof(MatScalar));CHKPTRQ(work); 223 pivots= (int*)PetscMalloc(bs*sizeof(int));CHKPTRQ(pivots); 224 225 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 226 227 /* check permutation */ 228 if (!a->permute){ 229 ai = a->i; aj = a->j; aa = a->a; 230 } else { 231 ai = a->inew; aj = a->jnew; 232 aa = (MatScalar*)PetscMalloc(bs2*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 233 ierr = PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 234 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 235 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 236 237 for (i=0; i<mbs; i++){ 238 jmin = ai[i]; jmax = ai[i+1]; 239 for (j=jmin; j<jmax; j++){ 240 while (a2anew[j] != j){ 241 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 242 for (k1=0; k1<bs2; k1++){ 243 dk[k1] = aa[k*bs2+k1]; 244 aa[k*bs2+k1] = aa[j*bs2+k1]; 245 aa[j*bs2+k1] = dk[k1]; 246 } 247 } 248 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 249 if (i > aj[j]){ 250 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 251 ap = aa + j*bs2; /* ptr to the beginning of j-th block of aa */ 252 for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 253 for (k=0; k<bs; k++){ /* j-th block of aa <- dk^T */ 254 for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1]; 255 } 256 } 257 } 258 } 259 ierr = PetscFree(a2anew);CHKERRA(ierr); 260 } 261 262 /* for each row k */ 263 for (k = 0; k<mbs; k++){ 264 265 /*initialize k-th row with elements nonzero in row perm(k) of A */ 266 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 267 if (jmin < jmax) { 268 ap = aa + jmin*bs2; 269 for (j = jmin; j < jmax; j++){ 270 vj = perm_ptr[aj[j]]; /* block col. index */ 271 rtmp_ptr = rtmp + vj*bs2; 272 for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++; 273 } 274 } 275 276 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 277 ierr = PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));CHKERRQ(ierr); 278 i = jl[k]; /* first row to be added to k_th row */ 279 280 while (i < mbs){ 281 nexti = jl[i]; /* next row to be added to k_th row */ 282 283 /* compute multiplier */ 284 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 285 286 /* uik = -inv(Di)*U_bar(i,k) */ 287 diag = ba + i*bs2; 288 u = ba + ili*bs2; 289 ierr = PetscMemzero(uik,bs2*sizeof(MatScalar));CHKERRQ(ierr); 290 Kernel_A_gets_A_minus_B_times_C(bs,uik,diag,u); 291 292 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 293 Kernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u); 294 295 /* update -U(i,k) */ 296 ierr = PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));CHKERRQ(ierr); 297 298 /* add multiple of row i to k-th row ... */ 299 jmin = ili + 1; jmax = bi[i+1]; 300 if (jmin < jmax){ 301 for (j=jmin; j<jmax; j++) { 302 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 303 rtmp_ptr = rtmp + bj[j]*bs2; 304 u = ba + j*bs2; 305 Kernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u); 306 } 307 308 /* ... add i to row list for next nonzero entry */ 309 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 310 j = bj[jmin]; 311 jl[i] = jl[j]; jl[j] = i; /* update jl */ 312 } 313 i = nexti; 314 } 315 316 /* save nonzero entries in k-th row of U ... */ 317 318 /* invert diagonal block */ 319 diag = ba+k*bs2; 320 ierr = PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));CHKERRQ(ierr); 321 Kernel_A_gets_inverse_A(bs,diag,pivots,work); 322 323 jmin = bi[k]; jmax = bi[k+1]; 324 if (jmin < jmax) { 325 for (j=jmin; j<jmax; j++){ 326 vj = bj[j]; /* block col. index of U */ 327 u = ba + j*bs2; 328 rtmp_ptr = rtmp + vj*bs2; 329 for (k1=0; k1<bs2; k1++){ 330 *u++ = *rtmp_ptr; 331 *rtmp_ptr++ = 0.0; 332 } 333 } 334 335 /* ... add k to row list for first nonzero entry in k-th row */ 336 il[k] = jmin; 337 i = bj[jmin]; 338 jl[k] = jl[i]; jl[i] = k; 339 } 340 } 341 342 ierr = PetscFree(rtmp);CHKERRQ(ierr); 343 ierr = PetscFree(il);CHKERRQ(ierr); 344 ierr = PetscFree(jl);CHKERRQ(ierr); 345 ierr = PetscFree(dk);CHKERRQ(ierr); 346 ierr = PetscFree(uik);CHKERRQ(ierr); 347 ierr = PetscFree(W);CHKERRQ(ierr); 348 ierr = PetscFree(work);CHKERRQ(ierr); 349 ierr = PetscFree(pivots);CHKERRQ(ierr); 350 if (a->permute){ 351 ierr = PetscFree(aa);CHKERRQ(ierr); 352 } 353 354 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 355 C->factor = FACTOR_CHOLESKY; 356 C->assembled = PETSC_TRUE; 357 C->preallocated = PETSC_TRUE; 358 PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */ 359 PetscFunctionReturn(0); 360 } 361 362 /* Version for when blocks are 7 by 7 */ 363 #undef __FUNC__ 364 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7" 365 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B) 366 { 367 Mat C = *B; 368 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 369 IS perm = b->row; 370 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 371 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 372 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 373 MatScalar *u,*d,*w,*wp; 374 375 PetscFunctionBegin; 376 /* initialization */ 377 printf("called MatCholeskyFactorNumeric_SeqSBAIJ_7 \n"); 378 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 379 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 380 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 381 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 382 for (i=0; i<mbs; i++) { 383 jl[i] = mbs; il[0] = 0; 384 } 385 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 386 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 387 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 388 389 /* check permutation */ 390 if (!a->permute){ 391 ai = a->i; aj = a->j; aa = a->a; 392 } else { 393 ai = a->inew; aj = a->jnew; 394 aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 395 ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 396 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 397 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 398 399 for (i=0; i<mbs; i++){ 400 jmin = ai[i]; jmax = ai[i+1]; 401 for (j=jmin; j<jmax; j++){ 402 while (a2anew[j] != j){ 403 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 404 for (k1=0; k1<49; k1++){ 405 dk[k1] = aa[k*49+k1]; 406 aa[k*49+k1] = aa[j*49+k1]; 407 aa[j*49+k1] = dk[k1]; 408 } 409 } 410 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 411 if (i > aj[j]){ 412 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 413 ap = aa + j*49; /* ptr to the beginning of j-th block of aa */ 414 for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 415 for (k=0; k<7; k++){ /* j-th block of aa <- dk^T */ 416 for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1]; 417 } 418 } 419 } 420 } 421 ierr = PetscFree(a2anew);CHKERRA(ierr); 422 } 423 424 /* for each row k */ 425 for (k = 0; k<mbs; k++){ 426 427 /*initialize k-th row with elements nonzero in row perm(k) of A */ 428 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 429 if (jmin < jmax) { 430 ap = aa + jmin*49; 431 for (j = jmin; j < jmax; j++){ 432 vj = perm_ptr[aj[j]]; /* block col. index */ 433 wp = w + vj*49; 434 for (i=0; i<49; i++) *wp++ = *ap++; 435 } 436 } 437 438 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 439 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 440 i = jl[k]; /* first row to be added to k_th row */ 441 442 while (i < mbs){ 443 nexti = jl[i]; /* next row to be added to k_th row */ 444 445 /* compute multiplier */ 446 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 447 448 /* uik = -inv(Di)*U_bar(i,k) */ 449 d = ba + i*49; 450 u = ba + ili*49; 451 452 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]); 453 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]); 454 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]); 455 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]); 456 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]); 457 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]); 458 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]); 459 460 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]); 461 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]); 462 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]); 463 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]); 464 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]); 465 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]); 466 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]); 467 468 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]); 469 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]); 470 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]); 471 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]); 472 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]); 473 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]); 474 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]); 475 476 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]); 477 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]); 478 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]); 479 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]); 480 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]); 481 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]); 482 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]); 483 484 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]); 485 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]); 486 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]); 487 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]); 488 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]); 489 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]); 490 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]); 491 492 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]); 493 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]); 494 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]); 495 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]); 496 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]); 497 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]); 498 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]); 499 500 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]); 501 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]); 502 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]); 503 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]); 504 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]); 505 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]); 506 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]); 507 508 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 509 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]; 510 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]; 511 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]; 512 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]; 513 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]; 514 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]; 515 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]; 516 517 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]; 518 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]; 519 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]; 520 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]; 521 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]; 522 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]; 523 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]; 524 525 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]; 526 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]; 527 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]; 528 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]; 529 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]; 530 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]; 531 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]; 532 533 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]; 534 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]; 535 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]; 536 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]; 537 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]; 538 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]; 539 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]; 540 541 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]; 542 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]; 543 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]; 544 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]; 545 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]; 546 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]; 547 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]; 548 549 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]; 550 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]; 551 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]; 552 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]; 553 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]; 554 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]; 555 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]; 556 557 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]; 558 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]; 559 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]; 560 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]; 561 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]; 562 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]; 563 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]; 564 565 /* update -U(i,k) */ 566 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 567 568 /* add multiple of row i to k-th row ... */ 569 jmin = ili + 1; jmax = bi[i+1]; 570 if (jmin < jmax){ 571 for (j=jmin; j<jmax; j++) { 572 /* w += -U(i,k)^T * U_bar(i,j) */ 573 wp = w + bj[j]*49; 574 u = ba + j*49; 575 576 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]; 577 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]; 578 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]; 579 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]; 580 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]; 581 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]; 582 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]; 583 584 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]; 585 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]; 586 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]; 587 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]; 588 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]; 589 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]; 590 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]; 591 592 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]; 593 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]; 594 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]; 595 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]; 596 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]; 597 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]; 598 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]; 599 600 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]; 601 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]; 602 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]; 603 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]; 604 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]; 605 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]; 606 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]; 607 608 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]; 609 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]; 610 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]; 611 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]; 612 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]; 613 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]; 614 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]; 615 616 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]; 617 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]; 618 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]; 619 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]; 620 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]; 621 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]; 622 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]; 623 624 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]; 625 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]; 626 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]; 627 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]; 628 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]; 629 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]; 630 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]; 631 } 632 633 /* ... add i to row list for next nonzero entry */ 634 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 635 j = bj[jmin]; 636 jl[i] = jl[j]; jl[j] = i; /* update jl */ 637 } 638 i = nexti; 639 } 640 641 /* save nonzero entries in k-th row of U ... */ 642 643 /* invert diagonal block */ 644 d = ba+k*49; 645 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 646 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 647 648 jmin = bi[k]; jmax = bi[k+1]; 649 if (jmin < jmax) { 650 for (j=jmin; j<jmax; j++){ 651 vj = bj[j]; /* block col. index of U */ 652 u = ba + j*49; 653 wp = w + vj*49; 654 for (k1=0; k1<49; k1++){ 655 *u++ = *wp; 656 *wp++ = 0.0; 657 } 658 } 659 660 /* ... add k to row list for first nonzero entry in k-th row */ 661 il[k] = jmin; 662 i = bj[jmin]; 663 jl[k] = jl[i]; jl[i] = k; 664 } 665 } 666 667 ierr = PetscFree(w);CHKERRQ(ierr); 668 ierr = PetscFree(il);CHKERRQ(ierr); 669 ierr = PetscFree(jl);CHKERRQ(ierr); 670 ierr = PetscFree(dk);CHKERRQ(ierr); 671 ierr = PetscFree(uik);CHKERRQ(ierr); 672 if (a->permute){ 673 ierr = PetscFree(aa);CHKERRQ(ierr); 674 } 675 676 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 677 C->factor = FACTOR_CHOLESKY; 678 C->assembled = PETSC_TRUE; 679 C->preallocated = PETSC_TRUE; 680 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 681 PetscFunctionReturn(0); 682 } 683 684 /* 685 Version for when blocks are 7 by 7 Using natural ordering 686 */ 687 #undef __FUNC__ 688 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering" 689 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B) 690 { 691 Mat C = *B; 692 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 693 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 694 int *ajtmpold,*ajtmp,nz,row; 695 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 696 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 697 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 698 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 699 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 700 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 701 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 702 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 703 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 704 MatScalar p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49; 705 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 706 MatScalar x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49; 707 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 708 MatScalar m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49; 709 MatScalar *ba = b->a,*aa = a->a; 710 711 PetscFunctionBegin; 712 rtmp = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 713 for (i=0; i<n; i++) { 714 nz = bi[i+1] - bi[i]; 715 ajtmp = bj + bi[i]; 716 for (j=0; j<nz; j++) { 717 x = rtmp+49*ajtmp[j]; 718 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 719 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 720 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 721 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 722 x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ; 723 x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ; 724 } 725 /* load in initial (unfactored row) */ 726 nz = ai[i+1] - ai[i]; 727 ajtmpold = aj + ai[i]; 728 v = aa + 49*ai[i]; 729 for (j=0; j<nz; j++) { 730 x = rtmp+49*ajtmpold[j]; 731 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 732 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 733 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 734 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 735 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 736 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 737 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 738 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 739 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 740 x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39]; 741 x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43]; 742 x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47]; 743 x[48] = v[48]; 744 v += 49; 745 } 746 row = *ajtmp++; 747 while (row < i) { 748 pc = rtmp + 49*row; 749 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 750 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 751 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 752 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 753 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 754 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 755 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 756 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 757 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 758 p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39]; 759 p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43]; 760 p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47]; 761 p49 = pc[48]; 762 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 763 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 764 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 765 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 766 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 767 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 768 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 769 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 770 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || 771 p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || 772 p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || 773 p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || 774 p49 != 0.0) { 775 pv = ba + 49*diag_offset[row]; 776 pj = bj + diag_offset[row] + 1; 777 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 778 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 779 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 780 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 781 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 782 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 783 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 784 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 785 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 786 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 787 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 788 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 789 x49 = pv[48]; 790 pc[0] = m1 = p1*x1 + p8*x2 + p15*x3 + p22*x4 + p29*x5 + p36*x6 + p43*x7; 791 pc[1] = m2 = p2*x1 + p9*x2 + p16*x3 + p23*x4 + p30*x5 + p37*x6 + p44*x7; 792 pc[2] = m3 = p3*x1 + p10*x2 + p17*x3 + p24*x4 + p31*x5 + p38*x6 + p45*x7; 793 pc[3] = m4 = p4*x1 + p11*x2 + p18*x3 + p25*x4 + p32*x5 + p39*x6 + p46*x7; 794 pc[4] = m5 = p5*x1 + p12*x2 + p19*x3 + p26*x4 + p33*x5 + p40*x6 + p47*x7; 795 pc[5] = m6 = p6*x1 + p13*x2 + p20*x3 + p27*x4 + p34*x5 + p41*x6 + p48*x7; 796 pc[6] = m7 = p7*x1 + p14*x2 + p21*x3 + p28*x4 + p35*x5 + p42*x6 + p49*x7; 797 798 pc[7] = m8 = p1*x8 + p8*x9 + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14; 799 pc[8] = m9 = p2*x8 + p9*x9 + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14; 800 pc[9] = m10 = p3*x8 + p10*x9 + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14; 801 pc[10] = m11 = p4*x8 + p11*x9 + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14; 802 pc[11] = m12 = p5*x8 + p12*x9 + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14; 803 pc[12] = m13 = p6*x8 + p13*x9 + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14; 804 pc[13] = m14 = p7*x8 + p14*x9 + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14; 805 806 pc[14] = m15 = p1*x15 + p8*x16 + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21; 807 pc[15] = m16 = p2*x15 + p9*x16 + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21; 808 pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21; 809 pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21; 810 pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21; 811 pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21; 812 pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21; 813 814 pc[21] = m22 = p1*x22 + p8*x23 + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28; 815 pc[22] = m23 = p2*x22 + p9*x23 + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28; 816 pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28; 817 pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28; 818 pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28; 819 pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28; 820 pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28; 821 822 pc[28] = m29 = p1*x29 + p8*x30 + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35; 823 pc[29] = m30 = p2*x29 + p9*x30 + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35; 824 pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35; 825 pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35; 826 pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35; 827 pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35; 828 pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35; 829 830 pc[35] = m36 = p1*x36 + p8*x37 + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42; 831 pc[36] = m37 = p2*x36 + p9*x37 + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42; 832 pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42; 833 pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42; 834 pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42; 835 pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42; 836 pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42; 837 838 pc[42] = m43 = p1*x43 + p8*x44 + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49; 839 pc[43] = m44 = p2*x43 + p9*x44 + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49; 840 pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49; 841 pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49; 842 pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49; 843 pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49; 844 pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49; 845 846 nz = bi[row+1] - diag_offset[row] - 1; 847 pv += 49; 848 for (j=0; j<nz; j++) { 849 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 850 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 851 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 852 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 853 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 854 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 855 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 856 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 857 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 858 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 859 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 860 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 861 x49 = pv[48]; 862 x = rtmp + 49*pj[j]; 863 x[0] -= m1*x1 + m8*x2 + m15*x3 + m22*x4 + m29*x5 + m36*x6 + m43*x7; 864 x[1] -= m2*x1 + m9*x2 + m16*x3 + m23*x4 + m30*x5 + m37*x6 + m44*x7; 865 x[2] -= m3*x1 + m10*x2 + m17*x3 + m24*x4 + m31*x5 + m38*x6 + m45*x7; 866 x[3] -= m4*x1 + m11*x2 + m18*x3 + m25*x4 + m32*x5 + m39*x6 + m46*x7; 867 x[4] -= m5*x1 + m12*x2 + m19*x3 + m26*x4 + m33*x5 + m40*x6 + m47*x7; 868 x[5] -= m6*x1 + m13*x2 + m20*x3 + m27*x4 + m34*x5 + m41*x6 + m48*x7; 869 x[6] -= m7*x1 + m14*x2 + m21*x3 + m28*x4 + m35*x5 + m42*x6 + m49*x7; 870 871 x[7] -= m1*x8 + m8*x9 + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14; 872 x[8] -= m2*x8 + m9*x9 + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14; 873 x[9] -= m3*x8 + m10*x9 + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14; 874 x[10] -= m4*x8 + m11*x9 + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14; 875 x[11] -= m5*x8 + m12*x9 + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14; 876 x[12] -= m6*x8 + m13*x9 + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14; 877 x[13] -= m7*x8 + m14*x9 + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14; 878 879 x[14] -= m1*x15 + m8*x16 + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21; 880 x[15] -= m2*x15 + m9*x16 + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21; 881 x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21; 882 x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21; 883 x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21; 884 x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21; 885 x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21; 886 887 x[21] -= m1*x22 + m8*x23 + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28; 888 x[22] -= m2*x22 + m9*x23 + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28; 889 x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28; 890 x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28; 891 x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28; 892 x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28; 893 x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28; 894 895 x[28] -= m1*x29 + m8*x30 + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35; 896 x[29] -= m2*x29 + m9*x30 + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35; 897 x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35; 898 x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35; 899 x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35; 900 x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35; 901 x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35; 902 903 x[35] -= m1*x36 + m8*x37 + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42; 904 x[36] -= m2*x36 + m9*x37 + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42; 905 x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42; 906 x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42; 907 x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42; 908 x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42; 909 x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42; 910 911 x[42] -= m1*x43 + m8*x44 + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49; 912 x[43] -= m2*x43 + m9*x44 + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49; 913 x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49; 914 x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49; 915 x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49; 916 x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49; 917 x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49; 918 pv += 49; 919 } 920 PLogFlops(686*nz+637); 921 } 922 row = *ajtmp++; 923 } 924 /* finished row so stick it into b->a */ 925 pv = ba + 49*bi[i]; 926 pj = bj + bi[i]; 927 nz = bi[i+1] - bi[i]; 928 for (j=0; j<nz; j++) { 929 x = rtmp+49*pj[j]; 930 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 931 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 932 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 933 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 934 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 935 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 936 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 937 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 938 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 939 pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39]; 940 pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43]; 941 pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47]; 942 pv[48] = x[48]; 943 pv += 49; 944 } 945 /* invert diagonal block */ 946 w = ba + 49*diag_offset[i]; 947 ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr); 948 } 949 950 ierr = PetscFree(rtmp);CHKERRQ(ierr); 951 C->factor = FACTOR_LU; 952 C->assembled = PETSC_TRUE; 953 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 954 PetscFunctionReturn(0); 955 } 956 957 /* Version for when blocks are 6 by 6 */ 958 #undef __FUNC__ 959 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 960 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 961 { 962 Mat C = *B; 963 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 964 IS perm = b->row; 965 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 966 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 967 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 968 MatScalar *u,*d,*w,*wp; 969 970 PetscFunctionBegin; 971 /* initialization */ 972 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 973 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 974 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 975 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 976 for (i=0; i<mbs; i++) { 977 jl[i] = mbs; il[0] = 0; 978 } 979 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 980 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 981 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 982 983 /* check permutation */ 984 if (!a->permute){ 985 ai = a->i; aj = a->j; aa = a->a; 986 } else { 987 ai = a->inew; aj = a->jnew; 988 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 989 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 990 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 991 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 992 993 for (i=0; i<mbs; i++){ 994 jmin = ai[i]; jmax = ai[i+1]; 995 for (j=jmin; j<jmax; j++){ 996 while (a2anew[j] != j){ 997 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 998 for (k1=0; k1<36; k1++){ 999 dk[k1] = aa[k*36+k1]; 1000 aa[k*36+k1] = aa[j*36+k1]; 1001 aa[j*36+k1] = dk[k1]; 1002 } 1003 } 1004 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1005 if (i > aj[j]){ 1006 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1007 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 1008 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1009 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 1010 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 1011 } 1012 } 1013 } 1014 } 1015 ierr = PetscFree(a2anew);CHKERRA(ierr); 1016 } 1017 1018 /* for each row k */ 1019 for (k = 0; k<mbs; k++){ 1020 1021 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1022 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1023 if (jmin < jmax) { 1024 ap = aa + jmin*36; 1025 for (j = jmin; j < jmax; j++){ 1026 vj = perm_ptr[aj[j]]; /* block col. index */ 1027 wp = w + vj*36; 1028 for (i=0; i<36; i++) *wp++ = *ap++; 1029 } 1030 } 1031 1032 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1033 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1034 i = jl[k]; /* first row to be added to k_th row */ 1035 1036 while (i < mbs){ 1037 nexti = jl[i]; /* next row to be added to k_th row */ 1038 1039 /* compute multiplier */ 1040 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1041 1042 /* uik = -inv(Di)*U_bar(i,k) */ 1043 d = ba + i*36; 1044 u = ba + ili*36; 1045 1046 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]); 1047 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]); 1048 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]); 1049 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]); 1050 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]); 1051 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]); 1052 1053 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]); 1054 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]); 1055 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]); 1056 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]); 1057 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]); 1058 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]); 1059 1060 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]); 1061 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]); 1062 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]); 1063 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]); 1064 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]); 1065 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]); 1066 1067 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]); 1068 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]); 1069 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]); 1070 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]); 1071 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]); 1072 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]); 1073 1074 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]); 1075 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]); 1076 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]); 1077 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]); 1078 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]); 1079 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]); 1080 1081 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]); 1082 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]); 1083 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]); 1084 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]); 1085 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]); 1086 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]); 1087 1088 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1089 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]; 1090 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]; 1091 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]; 1092 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]; 1093 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]; 1094 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]; 1095 1096 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]; 1097 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]; 1098 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]; 1099 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]; 1100 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]; 1101 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]; 1102 1103 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]; 1104 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]; 1105 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]; 1106 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]; 1107 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]; 1108 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]; 1109 1110 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]; 1111 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]; 1112 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]; 1113 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]; 1114 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]; 1115 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]; 1116 1117 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]; 1118 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]; 1119 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]; 1120 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]; 1121 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]; 1122 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]; 1123 1124 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]; 1125 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]; 1126 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]; 1127 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]; 1128 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]; 1129 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]; 1130 1131 /* update -U(i,k) */ 1132 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1133 1134 /* add multiple of row i to k-th row ... */ 1135 jmin = ili + 1; jmax = bi[i+1]; 1136 if (jmin < jmax){ 1137 for (j=jmin; j<jmax; j++) { 1138 /* w += -U(i,k)^T * U_bar(i,j) */ 1139 wp = w + bj[j]*36; 1140 u = ba + j*36; 1141 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]; 1142 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]; 1143 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]; 1144 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]; 1145 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]; 1146 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]; 1147 1148 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]; 1149 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]; 1150 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]; 1151 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]; 1152 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]; 1153 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]; 1154 1155 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]; 1156 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]; 1157 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]; 1158 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]; 1159 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]; 1160 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]; 1161 1162 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]; 1163 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]; 1164 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]; 1165 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]; 1166 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]; 1167 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]; 1168 1169 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]; 1170 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]; 1171 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]; 1172 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]; 1173 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]; 1174 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]; 1175 1176 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]; 1177 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]; 1178 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]; 1179 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]; 1180 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]; 1181 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]; 1182 } 1183 1184 /* ... add i to row list for next nonzero entry */ 1185 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1186 j = bj[jmin]; 1187 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1188 } 1189 i = nexti; 1190 } 1191 1192 /* save nonzero entries in k-th row of U ... */ 1193 1194 /* invert diagonal block */ 1195 d = ba+k*36; 1196 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1197 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1198 1199 jmin = bi[k]; jmax = bi[k+1]; 1200 if (jmin < jmax) { 1201 for (j=jmin; j<jmax; j++){ 1202 vj = bj[j]; /* block col. index of U */ 1203 u = ba + j*36; 1204 wp = w + vj*36; 1205 for (k1=0; k1<36; k1++){ 1206 *u++ = *wp; 1207 *wp++ = 0.0; 1208 } 1209 } 1210 1211 /* ... add k to row list for first nonzero entry in k-th row */ 1212 il[k] = jmin; 1213 i = bj[jmin]; 1214 jl[k] = jl[i]; jl[i] = k; 1215 } 1216 } 1217 1218 ierr = PetscFree(w);CHKERRQ(ierr); 1219 ierr = PetscFree(il);CHKERRQ(ierr); 1220 ierr = PetscFree(jl);CHKERRQ(ierr); 1221 ierr = PetscFree(dk);CHKERRQ(ierr); 1222 ierr = PetscFree(uik);CHKERRQ(ierr); 1223 if (a->permute){ 1224 ierr = PetscFree(aa);CHKERRQ(ierr); 1225 } 1226 1227 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1228 C->factor = FACTOR_CHOLESKY; 1229 C->assembled = PETSC_TRUE; 1230 C->preallocated = PETSC_TRUE; 1231 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1232 PetscFunctionReturn(0); 1233 } 1234 1235 /* 1236 Version for when blocks are 6 by 6 Using natural ordering 1237 */ 1238 #undef __FUNC__ 1239 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1240 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1241 { 1242 Mat C = *B; 1243 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1244 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1245 int *ajtmpold,*ajtmp,nz,row; 1246 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1247 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1248 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1249 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1250 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1251 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1252 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1253 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1254 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 1255 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 1256 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 1257 MatScalar *ba = b->a,*aa = a->a; 1258 1259 PetscFunctionBegin; 1260 rtmp = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1261 for (i=0; i<n; i++) { 1262 nz = bi[i+1] - bi[i]; 1263 ajtmp = bj + bi[i]; 1264 for (j=0; j<nz; j++) { 1265 x = rtmp+36*ajtmp[j]; 1266 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1267 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 1268 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 1269 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 1270 x[34] = x[35] = 0.0 ; 1271 } 1272 /* load in initial (unfactored row) */ 1273 nz = ai[i+1] - ai[i]; 1274 ajtmpold = aj + ai[i]; 1275 v = aa + 36*ai[i]; 1276 for (j=0; j<nz; j++) { 1277 x = rtmp+36*ajtmpold[j]; 1278 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1279 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 1280 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 1281 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 1282 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 1283 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1284 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 1285 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 1286 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 1287 v += 36; 1288 } 1289 row = *ajtmp++; 1290 while (row < i) { 1291 pc = rtmp + 36*row; 1292 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1293 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 1294 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 1295 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 1296 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 1297 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 1298 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 1299 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 1300 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 1301 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 1302 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 1303 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 1304 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 1305 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 1306 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 1307 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 1308 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 1309 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) { 1310 pv = ba + 36*diag_offset[row]; 1311 pj = bj + diag_offset[row] + 1; 1312 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1313 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1314 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1315 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1316 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1317 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1318 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1319 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1320 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1321 pc[0] = m1 = p1*x1 + p7*x2 + p13*x3 + p19*x4 + p25*x5 + p31*x6; 1322 pc[1] = m2 = p2*x1 + p8*x2 + p14*x3 + p20*x4 + p26*x5 + p32*x6; 1323 pc[2] = m3 = p3*x1 + p9*x2 + p15*x3 + p21*x4 + p27*x5 + p33*x6; 1324 pc[3] = m4 = p4*x1 + p10*x2 + p16*x3 + p22*x4 + p28*x5 + p34*x6; 1325 pc[4] = m5 = p5*x1 + p11*x2 + p17*x3 + p23*x4 + p29*x5 + p35*x6; 1326 pc[5] = m6 = p6*x1 + p12*x2 + p18*x3 + p24*x4 + p30*x5 + p36*x6; 1327 1328 pc[6] = m7 = p1*x7 + p7*x8 + p13*x9 + p19*x10 + p25*x11 + p31*x12; 1329 pc[7] = m8 = p2*x7 + p8*x8 + p14*x9 + p20*x10 + p26*x11 + p32*x12; 1330 pc[8] = m9 = p3*x7 + p9*x8 + p15*x9 + p21*x10 + p27*x11 + p33*x12; 1331 pc[9] = m10 = p4*x7 + p10*x8 + p16*x9 + p22*x10 + p28*x11 + p34*x12; 1332 pc[10] = m11 = p5*x7 + p11*x8 + p17*x9 + p23*x10 + p29*x11 + p35*x12; 1333 pc[11] = m12 = p6*x7 + p12*x8 + p18*x9 + p24*x10 + p30*x11 + p36*x12; 1334 1335 pc[12] = m13 = p1*x13 + p7*x14 + p13*x15 + p19*x16 + p25*x17 + p31*x18; 1336 pc[13] = m14 = p2*x13 + p8*x14 + p14*x15 + p20*x16 + p26*x17 + p32*x18; 1337 pc[14] = m15 = p3*x13 + p9*x14 + p15*x15 + p21*x16 + p27*x17 + p33*x18; 1338 pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18; 1339 pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18; 1340 pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18; 1341 1342 pc[18] = m19 = p1*x19 + p7*x20 + p13*x21 + p19*x22 + p25*x23 + p31*x24; 1343 pc[19] = m20 = p2*x19 + p8*x20 + p14*x21 + p20*x22 + p26*x23 + p32*x24; 1344 pc[20] = m21 = p3*x19 + p9*x20 + p15*x21 + p21*x22 + p27*x23 + p33*x24; 1345 pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24; 1346 pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24; 1347 pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24; 1348 1349 pc[24] = m25 = p1*x25 + p7*x26 + p13*x27 + p19*x28 + p25*x29 + p31*x30; 1350 pc[25] = m26 = p2*x25 + p8*x26 + p14*x27 + p20*x28 + p26*x29 + p32*x30; 1351 pc[26] = m27 = p3*x25 + p9*x26 + p15*x27 + p21*x28 + p27*x29 + p33*x30; 1352 pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30; 1353 pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30; 1354 pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30; 1355 1356 pc[30] = m31 = p1*x31 + p7*x32 + p13*x33 + p19*x34 + p25*x35 + p31*x36; 1357 pc[31] = m32 = p2*x31 + p8*x32 + p14*x33 + p20*x34 + p26*x35 + p32*x36; 1358 pc[32] = m33 = p3*x31 + p9*x32 + p15*x33 + p21*x34 + p27*x35 + p33*x36; 1359 pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36; 1360 pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36; 1361 pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36; 1362 1363 nz = bi[row+1] - diag_offset[row] - 1; 1364 pv += 36; 1365 for (j=0; j<nz; j++) { 1366 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1367 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1368 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1369 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1370 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1371 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1372 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1373 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1374 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1375 x = rtmp + 36*pj[j]; 1376 x[0] -= m1*x1 + m7*x2 + m13*x3 + m19*x4 + m25*x5 + m31*x6; 1377 x[1] -= m2*x1 + m8*x2 + m14*x3 + m20*x4 + m26*x5 + m32*x6; 1378 x[2] -= m3*x1 + m9*x2 + m15*x3 + m21*x4 + m27*x5 + m33*x6; 1379 x[3] -= m4*x1 + m10*x2 + m16*x3 + m22*x4 + m28*x5 + m34*x6; 1380 x[4] -= m5*x1 + m11*x2 + m17*x3 + m23*x4 + m29*x5 + m35*x6; 1381 x[5] -= m6*x1 + m12*x2 + m18*x3 + m24*x4 + m30*x5 + m36*x6; 1382 1383 x[6] -= m1*x7 + m7*x8 + m13*x9 + m19*x10 + m25*x11 + m31*x12; 1384 x[7] -= m2*x7 + m8*x8 + m14*x9 + m20*x10 + m26*x11 + m32*x12; 1385 x[8] -= m3*x7 + m9*x8 + m15*x9 + m21*x10 + m27*x11 + m33*x12; 1386 x[9] -= m4*x7 + m10*x8 + m16*x9 + m22*x10 + m28*x11 + m34*x12; 1387 x[10] -= m5*x7 + m11*x8 + m17*x9 + m23*x10 + m29*x11 + m35*x12; 1388 x[11] -= m6*x7 + m12*x8 + m18*x9 + m24*x10 + m30*x11 + m36*x12; 1389 1390 x[12] -= m1*x13 + m7*x14 + m13*x15 + m19*x16 + m25*x17 + m31*x18; 1391 x[13] -= m2*x13 + m8*x14 + m14*x15 + m20*x16 + m26*x17 + m32*x18; 1392 x[14] -= m3*x13 + m9*x14 + m15*x15 + m21*x16 + m27*x17 + m33*x18; 1393 x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18; 1394 x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18; 1395 x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18; 1396 1397 x[18] -= m1*x19 + m7*x20 + m13*x21 + m19*x22 + m25*x23 + m31*x24; 1398 x[19] -= m2*x19 + m8*x20 + m14*x21 + m20*x22 + m26*x23 + m32*x24; 1399 x[20] -= m3*x19 + m9*x20 + m15*x21 + m21*x22 + m27*x23 + m33*x24; 1400 x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24; 1401 x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24; 1402 x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24; 1403 1404 x[24] -= m1*x25 + m7*x26 + m13*x27 + m19*x28 + m25*x29 + m31*x30; 1405 x[25] -= m2*x25 + m8*x26 + m14*x27 + m20*x28 + m26*x29 + m32*x30; 1406 x[26] -= m3*x25 + m9*x26 + m15*x27 + m21*x28 + m27*x29 + m33*x30; 1407 x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30; 1408 x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30; 1409 x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30; 1410 1411 x[30] -= m1*x31 + m7*x32 + m13*x33 + m19*x34 + m25*x35 + m31*x36; 1412 x[31] -= m2*x31 + m8*x32 + m14*x33 + m20*x34 + m26*x35 + m32*x36; 1413 x[32] -= m3*x31 + m9*x32 + m15*x33 + m21*x34 + m27*x35 + m33*x36; 1414 x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36; 1415 x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36; 1416 x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36; 1417 1418 pv += 36; 1419 } 1420 PLogFlops(432*nz+396); 1421 } 1422 row = *ajtmp++; 1423 } 1424 /* finished row so stick it into b->a */ 1425 pv = ba + 36*bi[i]; 1426 pj = bj + bi[i]; 1427 nz = bi[i+1] - bi[i]; 1428 for (j=0; j<nz; j++) { 1429 x = rtmp+36*pj[j]; 1430 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1431 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 1432 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 1433 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1434 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 1435 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 1436 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 1437 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 1438 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 1439 pv += 36; 1440 } 1441 /* invert diagonal block */ 1442 w = ba + 36*diag_offset[i]; 1443 ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr); 1444 } 1445 1446 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1447 C->factor = FACTOR_LU; 1448 C->assembled = PETSC_TRUE; 1449 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1450 PetscFunctionReturn(0); 1451 } 1452 1453 /* Version for when blocks are 5 by 5 */ 1454 #undef __FUNC__ 1455 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1456 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1457 { 1458 Mat C = *B; 1459 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1460 IS perm = b->row; 1461 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1462 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1463 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1464 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1465 1466 PetscFunctionBegin; 1467 /* initialization */ 1468 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1469 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1470 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1471 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1472 for (i=0; i<mbs; i++) { 1473 jl[i] = mbs; il[0] = 0; 1474 } 1475 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1476 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1477 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1478 1479 /* check permutation */ 1480 if (!a->permute){ 1481 ai = a->i; aj = a->j; aa = a->a; 1482 } else { 1483 ai = a->inew; aj = a->jnew; 1484 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1485 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1486 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1487 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1488 1489 for (i=0; i<mbs; i++){ 1490 jmin = ai[i]; jmax = ai[i+1]; 1491 for (j=jmin; j<jmax; j++){ 1492 while (a2anew[j] != j){ 1493 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1494 for (k1=0; k1<25; k1++){ 1495 dk[k1] = aa[k*25+k1]; 1496 aa[k*25+k1] = aa[j*25+k1]; 1497 aa[j*25+k1] = dk[k1]; 1498 } 1499 } 1500 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1501 if (i > aj[j]){ 1502 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1503 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1504 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1505 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1506 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1507 } 1508 } 1509 } 1510 } 1511 ierr = PetscFree(a2anew);CHKERRA(ierr); 1512 } 1513 1514 /* for each row k */ 1515 for (k = 0; k<mbs; k++){ 1516 1517 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1518 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1519 if (jmin < jmax) { 1520 ap = aa + jmin*25; 1521 for (j = jmin; j < jmax; j++){ 1522 vj = perm_ptr[aj[j]]; /* block col. index */ 1523 rtmp_ptr = rtmp + vj*25; 1524 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1525 } 1526 } 1527 1528 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1529 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1530 i = jl[k]; /* first row to be added to k_th row */ 1531 1532 while (i < mbs){ 1533 nexti = jl[i]; /* next row to be added to k_th row */ 1534 1535 /* compute multiplier */ 1536 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1537 1538 /* uik = -inv(Di)*U_bar(i,k) */ 1539 d = ba + i*25; 1540 u = ba + ili*25; 1541 1542 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1543 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1544 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1545 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1546 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1547 1548 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1549 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1550 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1551 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1552 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1553 1554 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1555 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1556 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1557 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1558 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1559 1560 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1561 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1562 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1563 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1564 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1565 1566 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1567 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1568 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1569 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1570 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1571 1572 1573 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1574 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1575 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1576 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1577 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1578 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1579 1580 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1581 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1582 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1583 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1584 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1585 1586 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1587 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1588 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1589 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1590 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1591 1592 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1593 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1594 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1595 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1596 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1597 1598 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1599 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1600 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1601 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1602 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1603 1604 /* update -U(i,k) */ 1605 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1606 1607 /* add multiple of row i to k-th row ... */ 1608 jmin = ili + 1; jmax = bi[i+1]; 1609 if (jmin < jmax){ 1610 for (j=jmin; j<jmax; j++) { 1611 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1612 rtmp_ptr = rtmp + bj[j]*25; 1613 u = ba + j*25; 1614 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1615 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1616 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1617 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1618 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1619 1620 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1621 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1622 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1623 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1624 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1625 1626 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1627 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1628 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1629 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1630 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1631 1632 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1633 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1634 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1635 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1636 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1637 1638 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1639 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1640 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1641 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1642 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1643 } 1644 1645 /* ... add i to row list for next nonzero entry */ 1646 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1647 j = bj[jmin]; 1648 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1649 } 1650 i = nexti; 1651 } 1652 1653 /* save nonzero entries in k-th row of U ... */ 1654 1655 /* invert diagonal block */ 1656 d = ba+k*25; 1657 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1658 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1659 1660 jmin = bi[k]; jmax = bi[k+1]; 1661 if (jmin < jmax) { 1662 for (j=jmin; j<jmax; j++){ 1663 vj = bj[j]; /* block col. index of U */ 1664 u = ba + j*25; 1665 rtmp_ptr = rtmp + vj*25; 1666 for (k1=0; k1<25; k1++){ 1667 *u++ = *rtmp_ptr; 1668 *rtmp_ptr++ = 0.0; 1669 } 1670 } 1671 1672 /* ... add k to row list for first nonzero entry in k-th row */ 1673 il[k] = jmin; 1674 i = bj[jmin]; 1675 jl[k] = jl[i]; jl[i] = k; 1676 } 1677 } 1678 1679 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1680 ierr = PetscFree(il);CHKERRQ(ierr); 1681 ierr = PetscFree(jl);CHKERRQ(ierr); 1682 ierr = PetscFree(dk);CHKERRQ(ierr); 1683 ierr = PetscFree(uik);CHKERRQ(ierr); 1684 if (a->permute){ 1685 ierr = PetscFree(aa);CHKERRQ(ierr); 1686 } 1687 1688 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1689 C->factor = FACTOR_CHOLESKY; 1690 C->assembled = PETSC_TRUE; 1691 C->preallocated = PETSC_TRUE; 1692 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1693 PetscFunctionReturn(0); 1694 } 1695 1696 /* 1697 Version for when blocks are 5 by 5 Using natural ordering 1698 */ 1699 #undef __FUNC__ 1700 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1701 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1702 { 1703 Mat C = *B; 1704 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1705 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1706 int *ajtmpold,*ajtmp,nz,row; 1707 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1708 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1709 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1710 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1711 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1712 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1713 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1714 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1715 MatScalar *ba = b->a,*aa = a->a; 1716 1717 PetscFunctionBegin; 1718 rtmp = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1719 for (i=0; i<n; i++) { 1720 nz = bi[i+1] - bi[i]; 1721 ajtmp = bj + bi[i]; 1722 for (j=0; j<nz; j++) { 1723 x = rtmp+25*ajtmp[j]; 1724 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1725 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1726 x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 1727 } 1728 /* load in initial (unfactored row) */ 1729 nz = ai[i+1] - ai[i]; 1730 ajtmpold = aj + ai[i]; 1731 v = aa + 25*ai[i]; 1732 for (j=0; j<nz; j++) { 1733 x = rtmp+25*ajtmpold[j]; 1734 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1735 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1736 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1737 x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; 1738 x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1739 x[24] = v[24]; 1740 v += 25; 1741 } 1742 row = *ajtmp++; 1743 while (row < i) { 1744 pc = rtmp + 25*row; 1745 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1746 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1747 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1748 p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; 1749 p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; 1750 p24 = pc[23]; p25 = pc[24]; 1751 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1752 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1753 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1754 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 1755 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 1756 pv = ba + 25*diag_offset[row]; 1757 pj = bj + diag_offset[row] + 1; 1758 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1759 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1760 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1761 x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; 1762 x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1763 x25 = pv[24]; 1764 pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5; 1765 pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5; 1766 pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5; 1767 pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5; 1768 pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5; 1769 1770 pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10; 1771 pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10; 1772 pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10; 1773 pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10; 1774 pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10; 1775 1776 pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15; 1777 pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15; 1778 pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15; 1779 pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15; 1780 pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15; 1781 1782 pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20; 1783 pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20; 1784 pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20; 1785 pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20; 1786 pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20; 1787 1788 pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25; 1789 pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25; 1790 pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25; 1791 pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25; 1792 pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25; 1793 1794 nz = bi[row+1] - diag_offset[row] - 1; 1795 pv += 25; 1796 for (j=0; j<nz; j++) { 1797 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1798 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1799 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1800 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; 1801 x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; 1802 x24 = pv[23]; x25 = pv[24]; 1803 x = rtmp + 25*pj[j]; 1804 x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5; 1805 x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5; 1806 x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5; 1807 x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5; 1808 x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5; 1809 1810 x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10; 1811 x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10; 1812 x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10; 1813 x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10; 1814 x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10; 1815 1816 x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15; 1817 x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15; 1818 x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15; 1819 x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15; 1820 x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15; 1821 1822 x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20; 1823 x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20; 1824 x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20; 1825 x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20; 1826 x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20; 1827 1828 x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25; 1829 x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25; 1830 x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25; 1831 x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25; 1832 x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25; 1833 pv += 25; 1834 } 1835 PLogFlops(250*nz+225); 1836 } 1837 row = *ajtmp++; 1838 } 1839 /* finished row so stick it into b->a */ 1840 pv = ba + 25*bi[i]; 1841 pj = bj + bi[i]; 1842 nz = bi[i+1] - bi[i]; 1843 for (j=0; j<nz; j++) { 1844 x = rtmp+25*pj[j]; 1845 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1846 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1847 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1848 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17]; 1849 pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; 1850 pv[23] = x[23]; pv[24] = x[24]; 1851 pv += 25; 1852 } 1853 /* invert diagonal block */ 1854 w = ba + 25*diag_offset[i]; 1855 ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr); 1856 } 1857 1858 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1859 C->factor = FACTOR_LU; 1860 C->assembled = PETSC_TRUE; 1861 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1862 PetscFunctionReturn(0); 1863 } 1864 1865 /* 1866 Version for when blocks are 4 by 4 Using natural ordering 1867 */ 1868 #undef __FUNC__ 1869 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1870 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1871 { 1872 Mat C = *B; 1873 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1874 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1875 int *ajtmpold,*ajtmp,nz,row; 1876 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1877 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1878 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 1879 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; 1880 MatScalar p10,p11,p12,p13,p14,p15,p16,m10,m11,m12; 1881 MatScalar m13,m14,m15,m16; 1882 MatScalar *ba = b->a,*aa = a->a; 1883 1884 PetscFunctionBegin; 1885 rtmp = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1886 1887 for (i=0; i<n; i++) { 1888 nz = bi[i+1] - bi[i]; 1889 ajtmp = bj + bi[i]; 1890 for (j=0; j<nz; j++) { 1891 x = rtmp+16*ajtmp[j]; 1892 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1893 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1894 } 1895 /* load in initial (unfactored row) */ 1896 nz = ai[i+1] - ai[i]; 1897 ajtmpold = aj + ai[i]; 1898 v = aa + 16*ai[i]; 1899 for (j=0; j<nz; j++) { 1900 x = rtmp+16*ajtmpold[j]; 1901 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1902 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1903 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1904 x[14] = v[14]; x[15] = v[15]; 1905 v += 16; 1906 } 1907 row = *ajtmp++; 1908 while (row < i) { 1909 pc = rtmp + 16*row; 1910 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1911 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1912 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1913 p15 = pc[14]; p16 = pc[15]; 1914 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1915 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1916 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1917 || p16 != 0.0) { 1918 pv = ba + 16*diag_offset[row]; 1919 pj = bj + diag_offset[row] + 1; 1920 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1921 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1922 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1923 x15 = pv[14]; x16 = pv[15]; 1924 pc[0] = m1 = p1*x1 + p5*x2 + p9*x3 + p13*x4; 1925 pc[1] = m2 = p2*x1 + p6*x2 + p10*x3 + p14*x4; 1926 pc[2] = m3 = p3*x1 + p7*x2 + p11*x3 + p15*x4; 1927 pc[3] = m4 = p4*x1 + p8*x2 + p12*x3 + p16*x4; 1928 1929 pc[4] = m5 = p1*x5 + p5*x6 + p9*x7 + p13*x8; 1930 pc[5] = m6 = p2*x5 + p6*x6 + p10*x7 + p14*x8; 1931 pc[6] = m7 = p3*x5 + p7*x6 + p11*x7 + p15*x8; 1932 pc[7] = m8 = p4*x5 + p8*x6 + p12*x7 + p16*x8; 1933 1934 pc[8] = m9 = p1*x9 + p5*x10 + p9*x11 + p13*x12; 1935 pc[9] = m10 = p2*x9 + p6*x10 + p10*x11 + p14*x12; 1936 pc[10] = m11 = p3*x9 + p7*x10 + p11*x11 + p15*x12; 1937 pc[11] = m12 = p4*x9 + p8*x10 + p12*x11 + p16*x12; 1938 1939 pc[12] = m13 = p1*x13 + p5*x14 + p9*x15 + p13*x16; 1940 pc[13] = m14 = p2*x13 + p6*x14 + p10*x15 + p14*x16; 1941 pc[14] = m15 = p3*x13 + p7*x14 + p11*x15 + p15*x16; 1942 pc[15] = m16 = p4*x13 + p8*x14 + p12*x15 + p16*x16; 1943 1944 nz = bi[row+1] - diag_offset[row] - 1; 1945 pv += 16; 1946 for (j=0; j<nz; j++) { 1947 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1948 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1949 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1950 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1951 x = rtmp + 16*pj[j]; 1952 x[0] -= m1*x1 + m5*x2 + m9*x3 + m13*x4; 1953 x[1] -= m2*x1 + m6*x2 + m10*x3 + m14*x4; 1954 x[2] -= m3*x1 + m7*x2 + m11*x3 + m15*x4; 1955 x[3] -= m4*x1 + m8*x2 + m12*x3 + m16*x4; 1956 1957 x[4] -= m1*x5 + m5*x6 + m9*x7 + m13*x8; 1958 x[5] -= m2*x5 + m6*x6 + m10*x7 + m14*x8; 1959 x[6] -= m3*x5 + m7*x6 + m11*x7 + m15*x8; 1960 x[7] -= m4*x5 + m8*x6 + m12*x7 + m16*x8; 1961 1962 x[8] -= m1*x9 + m5*x10 + m9*x11 + m13*x12; 1963 x[9] -= m2*x9 + m6*x10 + m10*x11 + m14*x12; 1964 x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12; 1965 x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12; 1966 1967 x[12] -= m1*x13 + m5*x14 + m9*x15 + m13*x16; 1968 x[13] -= m2*x13 + m6*x14 + m10*x15 + m14*x16; 1969 x[14] -= m3*x13 + m7*x14 + m11*x15 + m15*x16; 1970 x[15] -= m4*x13 + m8*x14 + m12*x15 + m16*x16; 1971 1972 pv += 16; 1973 } 1974 PLogFlops(128*nz+112); 1975 } 1976 row = *ajtmp++; 1977 } 1978 /* finished row so stick it into b->a */ 1979 pv = ba + 16*bi[i]; 1980 pj = bj + bi[i]; 1981 nz = bi[i+1] - bi[i]; 1982 for (j=0; j<nz; j++) { 1983 x = rtmp+16*pj[j]; 1984 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1985 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1986 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1987 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1988 pv += 16; 1989 } 1990 /* invert diagonal block */ 1991 w = ba + 16*diag_offset[i]; 1992 ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr); 1993 } 1994 1995 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1996 C->factor = FACTOR_LU; 1997 C->assembled = PETSC_TRUE; 1998 C->preallocated = PETSC_TRUE; 1999 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2000 PetscFunctionReturn(0); 2001 } 2002 2003 /* Version for when blocks are 4 by 4 */ 2004 #undef __FUNC__ 2005 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 2006 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 2007 { 2008 Mat C = *B; 2009 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2010 IS perm = b->row; 2011 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2012 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2013 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2014 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2015 2016 PetscFunctionBegin; 2017 /* initialization */ 2018 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2019 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2020 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2021 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2022 for (i=0; i<mbs; i++) { 2023 jl[i] = mbs; il[0] = 0; 2024 } 2025 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 2026 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 2027 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2028 2029 /* check permutation */ 2030 if (!a->permute){ 2031 ai = a->i; aj = a->j; aa = a->a; 2032 } else { 2033 ai = a->inew; aj = a->jnew; 2034 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2035 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2036 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2037 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2038 2039 for (i=0; i<mbs; i++){ 2040 jmin = ai[i]; jmax = ai[i+1]; 2041 for (j=jmin; j<jmax; j++){ 2042 while (a2anew[j] != j){ 2043 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2044 for (k1=0; k1<16; k1++){ 2045 dk[k1] = aa[k*16+k1]; 2046 aa[k*16+k1] = aa[j*16+k1]; 2047 aa[j*16+k1] = dk[k1]; 2048 } 2049 } 2050 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2051 if (i > aj[j]){ 2052 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2053 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 2054 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2055 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 2056 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 2057 } 2058 } 2059 } 2060 } 2061 ierr = PetscFree(a2anew);CHKERRA(ierr); 2062 } 2063 2064 /* for each row k */ 2065 for (k = 0; k<mbs; k++){ 2066 2067 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2068 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2069 if (jmin < jmax) { 2070 ap = aa + jmin*16; 2071 for (j = jmin; j < jmax; j++){ 2072 vj = perm_ptr[aj[j]]; /* block col. index */ 2073 rtmp_ptr = rtmp + vj*16; 2074 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 2075 } 2076 } 2077 2078 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2079 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 2080 i = jl[k]; /* first row to be added to k_th row */ 2081 2082 while (i < mbs){ 2083 nexti = jl[i]; /* next row to be added to k_th row */ 2084 2085 /* compute multiplier */ 2086 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2087 2088 /* uik = -inv(Di)*U_bar(i,k) */ 2089 diag = ba + i*16; 2090 u = ba + ili*16; 2091 2092 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 2093 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 2094 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 2095 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 2096 2097 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2098 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2099 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2100 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2101 2102 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2103 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2104 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2105 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2106 2107 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2108 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2109 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2110 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2111 2112 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2113 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2114 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2115 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2116 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2117 2118 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2119 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2120 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2121 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2122 2123 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2124 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2125 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2126 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2127 2128 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2129 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2130 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2131 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2132 2133 /* update -U(i,k) */ 2134 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2135 2136 /* add multiple of row i to k-th row ... */ 2137 jmin = ili + 1; jmax = bi[i+1]; 2138 if (jmin < jmax){ 2139 for (j=jmin; j<jmax; j++) { 2140 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2141 rtmp_ptr = rtmp + bj[j]*16; 2142 u = ba + j*16; 2143 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2144 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2145 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2146 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2147 2148 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2149 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2150 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2151 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2152 2153 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2154 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2155 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2156 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2157 2158 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2159 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2160 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2161 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2162 } 2163 2164 /* ... add i to row list for next nonzero entry */ 2165 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2166 j = bj[jmin]; 2167 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2168 } 2169 i = nexti; 2170 } 2171 2172 /* save nonzero entries in k-th row of U ... */ 2173 2174 /* invert diagonal block */ 2175 diag = ba+k*16; 2176 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2177 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2178 2179 jmin = bi[k]; jmax = bi[k+1]; 2180 if (jmin < jmax) { 2181 for (j=jmin; j<jmax; j++){ 2182 vj = bj[j]; /* block col. index of U */ 2183 u = ba + j*16; 2184 rtmp_ptr = rtmp + vj*16; 2185 for (k1=0; k1<16; k1++){ 2186 *u++ = *rtmp_ptr; 2187 *rtmp_ptr++ = 0.0; 2188 } 2189 } 2190 2191 /* ... add k to row list for first nonzero entry in k-th row */ 2192 il[k] = jmin; 2193 i = bj[jmin]; 2194 jl[k] = jl[i]; jl[i] = k; 2195 } 2196 } 2197 2198 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2199 ierr = PetscFree(il);CHKERRQ(ierr); 2200 ierr = PetscFree(jl);CHKERRQ(ierr); 2201 ierr = PetscFree(dk);CHKERRQ(ierr); 2202 ierr = PetscFree(uik);CHKERRQ(ierr); 2203 if (a->permute){ 2204 ierr = PetscFree(aa);CHKERRQ(ierr); 2205 } 2206 2207 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2208 C->factor = FACTOR_CHOLESKY; 2209 C->assembled = PETSC_TRUE; 2210 C->preallocated = PETSC_TRUE; 2211 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2212 PetscFunctionReturn(0); 2213 } 2214 2215 /* Version for when blocks are 3 by 3 */ 2216 #undef __FUNC__ 2217 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2218 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2219 { 2220 Mat C = *B; 2221 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2222 IS perm = b->row; 2223 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2224 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2225 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2226 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2227 2228 PetscFunctionBegin; 2229 /* initialization */ 2230 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2231 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2232 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2233 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2234 for (i=0; i<mbs; i++) { 2235 jl[i] = mbs; il[0] = 0; 2236 } 2237 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2238 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2239 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2240 2241 /* check permutation */ 2242 if (!a->permute){ 2243 ai = a->i; aj = a->j; aa = a->a; 2244 } else { 2245 ai = a->inew; aj = a->jnew; 2246 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2247 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2248 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2249 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2250 2251 for (i=0; i<mbs; i++){ 2252 jmin = ai[i]; jmax = ai[i+1]; 2253 for (j=jmin; j<jmax; j++){ 2254 while (a2anew[j] != j){ 2255 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2256 for (k1=0; k1<9; k1++){ 2257 dk[k1] = aa[k*9+k1]; 2258 aa[k*9+k1] = aa[j*9+k1]; 2259 aa[j*9+k1] = dk[k1]; 2260 } 2261 } 2262 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2263 if (i > aj[j]){ 2264 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2265 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2266 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2267 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2268 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2269 } 2270 } 2271 } 2272 } 2273 ierr = PetscFree(a2anew);CHKERRA(ierr); 2274 } 2275 2276 /* for each row k */ 2277 for (k = 0; k<mbs; k++){ 2278 2279 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2280 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2281 if (jmin < jmax) { 2282 ap = aa + jmin*9; 2283 for (j = jmin; j < jmax; j++){ 2284 vj = perm_ptr[aj[j]]; /* block col. index */ 2285 rtmp_ptr = rtmp + vj*9; 2286 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2287 } 2288 } 2289 2290 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2291 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2292 i = jl[k]; /* first row to be added to k_th row */ 2293 2294 while (i < mbs){ 2295 nexti = jl[i]; /* next row to be added to k_th row */ 2296 2297 /* compute multiplier */ 2298 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2299 2300 /* uik = -inv(Di)*U_bar(i,k) */ 2301 diag = ba + i*9; 2302 u = ba + ili*9; 2303 2304 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2305 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2306 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2307 2308 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2309 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2310 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2311 2312 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2313 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2314 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2315 2316 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2317 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2318 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2319 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2320 2321 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2322 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2323 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2324 2325 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2326 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2327 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2328 2329 /* update -U(i,k) */ 2330 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2331 2332 /* add multiple of row i to k-th row ... */ 2333 jmin = ili + 1; jmax = bi[i+1]; 2334 if (jmin < jmax){ 2335 for (j=jmin; j<jmax; j++) { 2336 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2337 rtmp_ptr = rtmp + bj[j]*9; 2338 u = ba + j*9; 2339 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2340 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2341 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2342 2343 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2344 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2345 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2346 2347 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2348 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2349 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2350 } 2351 2352 /* ... add i to row list for next nonzero entry */ 2353 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2354 j = bj[jmin]; 2355 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2356 } 2357 i = nexti; 2358 } 2359 2360 /* save nonzero entries in k-th row of U ... */ 2361 2362 /* invert diagonal block */ 2363 diag = ba+k*9; 2364 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2365 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2366 2367 jmin = bi[k]; jmax = bi[k+1]; 2368 if (jmin < jmax) { 2369 for (j=jmin; j<jmax; j++){ 2370 vj = bj[j]; /* block col. index of U */ 2371 u = ba + j*9; 2372 rtmp_ptr = rtmp + vj*9; 2373 for (k1=0; k1<9; k1++){ 2374 *u++ = *rtmp_ptr; 2375 *rtmp_ptr++ = 0.0; 2376 } 2377 } 2378 2379 /* ... add k to row list for first nonzero entry in k-th row */ 2380 il[k] = jmin; 2381 i = bj[jmin]; 2382 jl[k] = jl[i]; jl[i] = k; 2383 } 2384 } 2385 2386 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2387 ierr = PetscFree(il);CHKERRQ(ierr); 2388 ierr = PetscFree(jl);CHKERRQ(ierr); 2389 ierr = PetscFree(dk);CHKERRQ(ierr); 2390 ierr = PetscFree(uik);CHKERRQ(ierr); 2391 if (a->permute){ 2392 ierr = PetscFree(aa);CHKERRQ(ierr); 2393 } 2394 2395 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2396 C->factor = FACTOR_CHOLESKY; 2397 C->assembled = PETSC_TRUE; 2398 C->preallocated = PETSC_TRUE; 2399 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2400 PetscFunctionReturn(0); 2401 } 2402 2403 /* 2404 Version for when blocks are 3 by 3 Using natural ordering 2405 */ 2406 #undef __FUNC__ 2407 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2408 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B) 2409 { 2410 Mat C = *B; 2411 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2412 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2413 int *ajtmpold,*ajtmp,nz,row; 2414 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2415 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2416 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 2417 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9; 2418 MatScalar *ba = b->a,*aa = a->a; 2419 2420 PetscFunctionBegin; 2421 rtmp = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2422 2423 for (i=0; i<n; i++) { 2424 nz = bi[i+1] - bi[i]; 2425 ajtmp = bj + bi[i]; 2426 for (j=0; j<nz; j++) { 2427 x = rtmp+9*ajtmp[j]; 2428 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0; 2429 } 2430 /* load in initial (unfactored row) */ 2431 nz = ai[i+1] - ai[i]; 2432 ajtmpold = aj + ai[i]; 2433 v = aa + 9*ai[i]; 2434 for (j=0; j<nz; j++) { 2435 x = rtmp+9*ajtmpold[j]; 2436 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2437 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 2438 v += 9; 2439 } 2440 row = *ajtmp++; 2441 while (row < i) { 2442 pc = rtmp + 9*row; 2443 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2444 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 2445 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 2446 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) { 2447 pv = ba + 9*diag_offset[row]; 2448 pj = bj + diag_offset[row] + 1; 2449 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2450 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2451 pc[0] = m1 = p1*x1 + p4*x2 + p7*x3; 2452 pc[1] = m2 = p2*x1 + p5*x2 + p8*x3; 2453 pc[2] = m3 = p3*x1 + p6*x2 + p9*x3; 2454 2455 pc[3] = m4 = p1*x4 + p4*x5 + p7*x6; 2456 pc[4] = m5 = p2*x4 + p5*x5 + p8*x6; 2457 pc[5] = m6 = p3*x4 + p6*x5 + p9*x6; 2458 2459 pc[6] = m7 = p1*x7 + p4*x8 + p7*x9; 2460 pc[7] = m8 = p2*x7 + p5*x8 + p8*x9; 2461 pc[8] = m9 = p3*x7 + p6*x8 + p9*x9; 2462 2463 nz = bi[row+1] - diag_offset[row] - 1; 2464 pv += 9; 2465 for (j=0; j<nz; j++) { 2466 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2467 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2468 x = rtmp + 9*pj[j]; 2469 x[0] -= m1*x1 + m4*x2 + m7*x3; 2470 x[1] -= m2*x1 + m5*x2 + m8*x3; 2471 x[2] -= m3*x1 + m6*x2 + m9*x3; 2472 2473 x[3] -= m1*x4 + m4*x5 + m7*x6; 2474 x[4] -= m2*x4 + m5*x5 + m8*x6; 2475 x[5] -= m3*x4 + m6*x5 + m9*x6; 2476 2477 x[6] -= m1*x7 + m4*x8 + m7*x9; 2478 x[7] -= m2*x7 + m5*x8 + m8*x9; 2479 x[8] -= m3*x7 + m6*x8 + m9*x9; 2480 pv += 9; 2481 } 2482 PLogFlops(54*nz+36); 2483 } 2484 row = *ajtmp++; 2485 } 2486 /* finished row so stick it into b->a */ 2487 pv = ba + 9*bi[i]; 2488 pj = bj + bi[i]; 2489 nz = bi[i+1] - bi[i]; 2490 for (j=0; j<nz; j++) { 2491 x = rtmp+9*pj[j]; 2492 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2493 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 2494 pv += 9; 2495 } 2496 /* invert diagonal block */ 2497 w = ba + 9*diag_offset[i]; 2498 ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr); 2499 } 2500 2501 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2502 C->factor = FACTOR_CHOLESKY; 2503 C->assembled = PETSC_TRUE; 2504 C->preallocated = PETSC_TRUE; 2505 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2506 PetscFunctionReturn(0); 2507 } 2508 2509 /* 2510 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2511 Version for blocks 2 by 2. 2512 */ 2513 #undef __FUNC__ 2514 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2515 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2516 { 2517 Mat C = *B; 2518 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2519 IS perm = b->row; 2520 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2521 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2522 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2523 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2524 2525 PetscFunctionBegin; 2526 2527 /* initialization */ 2528 /* il and jl record the first nonzero element in each row of the accessing 2529 window U(0:k, k:mbs-1). 2530 jl: list of rows to be added to uneliminated rows 2531 i>= k: jl(i) is the first row to be added to row i 2532 i< k: jl(i) is the row following row i in some list of rows 2533 jl(i) = mbs indicates the end of a list 2534 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2535 row i of U */ 2536 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2537 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2538 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2539 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2540 for (i=0; i<mbs; i++) { 2541 jl[i] = mbs; il[0] = 0; 2542 } 2543 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2544 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2545 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2546 2547 /* check permutation */ 2548 if (!a->permute){ 2549 ai = a->i; aj = a->j; aa = a->a; 2550 } else { 2551 ai = a->inew; aj = a->jnew; 2552 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2553 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2554 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2555 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2556 2557 for (i=0; i<mbs; i++){ 2558 jmin = ai[i]; jmax = ai[i+1]; 2559 for (j=jmin; j<jmax; j++){ 2560 while (a2anew[j] != j){ 2561 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2562 for (k1=0; k1<4; k1++){ 2563 dk[k1] = aa[k*4+k1]; 2564 aa[k*4+k1] = aa[j*4+k1]; 2565 aa[j*4+k1] = dk[k1]; 2566 } 2567 } 2568 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2569 if (i > aj[j]){ 2570 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2571 ap = aa + j*4; /* ptr to the beginning of the block */ 2572 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2573 ap[1] = ap[2]; 2574 ap[2] = dk[1]; 2575 } 2576 } 2577 } 2578 ierr = PetscFree(a2anew);CHKERRA(ierr); 2579 } 2580 2581 /* for each row k */ 2582 for (k = 0; k<mbs; k++){ 2583 2584 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2585 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2586 if (jmin < jmax) { 2587 ap = aa + jmin*4; 2588 for (j = jmin; j < jmax; j++){ 2589 vj = perm_ptr[aj[j]]; /* block col. index */ 2590 rtmp_ptr = rtmp + vj*4; 2591 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2592 } 2593 } 2594 2595 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2596 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2597 i = jl[k]; /* first row to be added to k_th row */ 2598 2599 while (i < mbs){ 2600 nexti = jl[i]; /* next row to be added to k_th row */ 2601 2602 /* compute multiplier */ 2603 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2604 2605 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2606 diag = ba + i*4; 2607 u = ba + ili*4; 2608 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2609 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2610 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2611 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2612 2613 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2614 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2615 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2616 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2617 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2618 2619 /* update -U(i,k): ba[ili] = uik */ 2620 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2621 2622 /* add multiple of row i to k-th row ... */ 2623 jmin = ili + 1; jmax = bi[i+1]; 2624 if (jmin < jmax){ 2625 for (j=jmin; j<jmax; j++) { 2626 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2627 rtmp_ptr = rtmp + bj[j]*4; 2628 u = ba + j*4; 2629 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2630 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2631 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2632 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2633 } 2634 2635 /* ... add i to row list for next nonzero entry */ 2636 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2637 j = bj[jmin]; 2638 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2639 } 2640 i = nexti; 2641 } 2642 2643 /* save nonzero entries in k-th row of U ... */ 2644 2645 /* invert diagonal block */ 2646 diag = ba+k*4; 2647 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2648 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2649 2650 jmin = bi[k]; jmax = bi[k+1]; 2651 if (jmin < jmax) { 2652 for (j=jmin; j<jmax; j++){ 2653 vj = bj[j]; /* block col. index of U */ 2654 u = ba + j*4; 2655 rtmp_ptr = rtmp + vj*4; 2656 for (k1=0; k1<4; k1++){ 2657 *u++ = *rtmp_ptr; 2658 *rtmp_ptr++ = 0.0; 2659 } 2660 } 2661 2662 /* ... add k to row list for first nonzero entry in k-th row */ 2663 il[k] = jmin; 2664 i = bj[jmin]; 2665 jl[k] = jl[i]; jl[i] = k; 2666 } 2667 } 2668 2669 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2670 ierr = PetscFree(il);CHKERRQ(ierr); 2671 ierr = PetscFree(jl);CHKERRQ(ierr); 2672 ierr = PetscFree(dk);CHKERRQ(ierr); 2673 ierr = PetscFree(uik);CHKERRQ(ierr); 2674 if (a->permute) { 2675 ierr = PetscFree(aa);CHKERRQ(ierr); 2676 } 2677 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2678 C->factor = FACTOR_CHOLESKY; 2679 C->assembled = PETSC_TRUE; 2680 C->preallocated = PETSC_TRUE; 2681 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2682 PetscFunctionReturn(0); 2683 } 2684 2685 /* 2686 Version for when blocks are 2 by 2 Using natural ordering 2687 */ 2688 #undef __FUNC__ 2689 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2690 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2691 { 2692 Mat C = *B; 2693 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2694 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2695 int *ajtmpold,*ajtmp,nz,row; 2696 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2697 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2698 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4; 2699 MatScalar *ba = b->a,*aa = a->a; 2700 2701 PetscFunctionBegin; 2702 rtmp = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2703 2704 for (i=0; i<n; i++) { 2705 nz = bi[i+1] - bi[i]; 2706 ajtmp = bj + bi[i]; 2707 for (j=0; j<nz; j++) { 2708 x = rtmp+4*ajtmp[j]; 2709 x[0] = x[1] = x[2] = x[3] = 0.0; 2710 } 2711 /* load in initial (unfactored row) */ 2712 nz = ai[i+1] - ai[i]; 2713 ajtmpold = aj + ai[i]; 2714 v = aa + 4*ai[i]; 2715 for (j=0; j<nz; j++) { 2716 x = rtmp+4*ajtmpold[j]; 2717 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2718 v += 4; 2719 } 2720 row = *ajtmp++; 2721 while (row < i) { 2722 pc = rtmp + 4*row; 2723 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2724 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) { 2725 pv = ba + 4*diag_offset[row]; 2726 pj = bj + diag_offset[row] + 1; 2727 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2728 pc[0] = m1 = p1*x1 + p3*x2; 2729 pc[1] = m2 = p2*x1 + p4*x2; 2730 pc[2] = m3 = p1*x3 + p3*x4; 2731 pc[3] = m4 = p2*x3 + p4*x4; 2732 nz = bi[row+1] - diag_offset[row] - 1; 2733 pv += 4; 2734 for (j=0; j<nz; j++) { 2735 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2736 x = rtmp + 4*pj[j]; 2737 x[0] -= m1*x1 + m3*x2; 2738 x[1] -= m2*x1 + m4*x2; 2739 x[2] -= m1*x3 + m3*x4; 2740 x[3] -= m2*x3 + m4*x4; 2741 pv += 4; 2742 } 2743 PLogFlops(16*nz+12); 2744 } 2745 row = *ajtmp++; 2746 } 2747 /* finished row so stick it into b->a */ 2748 pv = ba + 4*bi[i]; 2749 pj = bj + bi[i]; 2750 nz = bi[i+1] - bi[i]; 2751 for (j=0; j<nz; j++) { 2752 x = rtmp+4*pj[j]; 2753 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2754 pv += 4; 2755 } 2756 /* invert diagonal block */ 2757 w = ba + 4*diag_offset[i]; 2758 ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr); 2759 } 2760 2761 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2762 C->factor = FACTOR_LU; 2763 C->assembled = PETSC_TRUE; 2764 C->preallocated = PETSC_TRUE; 2765 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2766 PetscFunctionReturn(0); 2767 } 2768 2769 /* 2770 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2771 Version for blocks are 1 by 1. 2772 */ 2773 #undef __FUNC__ 2774 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2775 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2776 { 2777 Mat C = *B; 2778 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2779 IS ip = b->row; 2780 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2781 int *ai,*aj,*r; 2782 MatScalar *rtmp; 2783 MatScalar *ba = b->a,*aa,ak; 2784 MatScalar dk,uikdi; 2785 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2786 2787 PetscFunctionBegin; 2788 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2789 if (!a->permute){ 2790 ai = a->i; aj = a->j; aa = a->a; 2791 } else { 2792 ai = a->inew; aj = a->jnew; 2793 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2794 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2795 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 2796 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2797 2798 jmin = ai[0]; jmax = ai[mbs]; 2799 for (j=jmin; j<jmax; j++){ 2800 while (r[j] != j){ 2801 k = r[j]; r[j] = r[k]; r[k] = k; 2802 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 2803 } 2804 } 2805 ierr = PetscFree(r);CHKERRA(ierr); 2806 } 2807 2808 /* initialization */ 2809 /* il and jl record the first nonzero element in each row of the accessing 2810 window U(0:k, k:mbs-1). 2811 jl: list of rows to be added to uneliminated rows 2812 i>= k: jl(i) is the first row to be added to row i 2813 i< k: jl(i) is the row following row i in some list of rows 2814 jl(i) = mbs indicates the end of a list 2815 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2816 row i of U */ 2817 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2818 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2819 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2820 for (i=0; i<mbs; i++) { 2821 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2822 } 2823 2824 /* for each row k */ 2825 for (k = 0; k<mbs; k++){ 2826 2827 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2828 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2829 if (jmin < jmax) { 2830 for (j = jmin; j < jmax; j++){ 2831 vj = rip[aj[j]]; 2832 /* if (k <= vj)*/ rtmp[vj] = aa[j]; 2833 } 2834 } 2835 2836 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2837 dk = rtmp[k]; 2838 i = jl[k]; /* first row to be added to k_th row */ 2839 /* printf(" k=%d, pivot row = %d\n",k,i); */ 2840 2841 while (i < mbs){ 2842 nexti = jl[i]; /* next row to be added to k_th row */ 2843 2844 /* compute multiplier, update D(k) and U(i,k) */ 2845 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2846 uikdi = - ba[ili]*ba[i]; 2847 dk += uikdi*ba[ili]; 2848 ba[ili] = uikdi; /* -U(i,k) */ 2849 2850 /* add multiple of row i to k-th row ... */ 2851 jmin = ili + 1; jmax = bi[i+1]; 2852 if (jmin < jmax){ 2853 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2854 /* ... add i to row list for next nonzero entry */ 2855 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2856 j = bj[jmin]; 2857 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2858 } 2859 i = nexti; /* printf(" pivot row i=%d\n",i); */ 2860 } 2861 2862 /* check for zero pivot and save diagoanl element */ 2863 if (dk == 0.0){ 2864 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 2865 }else if (PetscRealPart(dk) < 0){ 2866 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 2867 } 2868 2869 /* save nonzero entries in k-th row of U ... */ 2870 ba[k] = 1.0/dk; 2871 jmin = bi[k]; jmax = bi[k+1]; 2872 if (jmin < jmax) { 2873 for (j=jmin; j<jmax; j++){ 2874 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 2875 } 2876 /* ... add k to row list for first nonzero entry in k-th row */ 2877 il[k] = jmin; 2878 i = bj[jmin]; 2879 jl[k] = jl[i]; jl[i] = k; 2880 } 2881 } 2882 2883 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2884 ierr = PetscFree(il);CHKERRQ(ierr); 2885 ierr = PetscFree(jl);CHKERRQ(ierr); 2886 if (a->permute){ 2887 ierr = PetscFree(aa);CHKERRQ(ierr); 2888 } 2889 2890 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2891 C->factor = FACTOR_CHOLESKY; 2892 C->assembled = PETSC_TRUE; 2893 C->preallocated = PETSC_TRUE; 2894 PLogFlops(b->mbs); 2895 PetscFunctionReturn(0); 2896 } 2897 2898 #undef __FUNC__ 2899 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 2900 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 2901 { 2902 int ierr; 2903 Mat C; 2904 2905 PetscFunctionBegin; 2906 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 2907 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 2908 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 2909 PetscFunctionReturn(0); 2910 } 2911 2912 2913