1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.44 2000/11/03 18:01:19 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 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 378 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 379 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 380 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 381 for (i=0; i<mbs; i++) { 382 jl[i] = mbs; il[0] = 0; 383 } 384 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 385 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 386 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 387 388 /* check permutation */ 389 if (!a->permute){ 390 ai = a->i; aj = a->j; aa = a->a; 391 } else { 392 ai = a->inew; aj = a->jnew; 393 aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 394 ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 395 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 396 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 397 398 for (i=0; i<mbs; i++){ 399 jmin = ai[i]; jmax = ai[i+1]; 400 for (j=jmin; j<jmax; j++){ 401 while (a2anew[j] != j){ 402 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 403 for (k1=0; k1<49; k1++){ 404 dk[k1] = aa[k*49+k1]; 405 aa[k*49+k1] = aa[j*49+k1]; 406 aa[j*49+k1] = dk[k1]; 407 } 408 } 409 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 410 if (i > aj[j]){ 411 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 412 ap = aa + j*49; /* ptr to the beginning of j-th block of aa */ 413 for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 414 for (k=0; k<7; k++){ /* j-th block of aa <- dk^T */ 415 for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1]; 416 } 417 } 418 } 419 } 420 ierr = PetscFree(a2anew);CHKERRA(ierr); 421 } 422 423 /* for each row k */ 424 for (k = 0; k<mbs; k++){ 425 426 /*initialize k-th row with elements nonzero in row perm(k) of A */ 427 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 428 if (jmin < jmax) { 429 ap = aa + jmin*49; 430 for (j = jmin; j < jmax; j++){ 431 vj = perm_ptr[aj[j]]; /* block col. index */ 432 wp = w + vj*49; 433 for (i=0; i<49; i++) *wp++ = *ap++; 434 } 435 } 436 437 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 438 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 439 i = jl[k]; /* first row to be added to k_th row */ 440 441 while (i < mbs){ 442 nexti = jl[i]; /* next row to be added to k_th row */ 443 444 /* compute multiplier */ 445 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 446 447 /* uik = -inv(Di)*U_bar(i,k) */ 448 d = ba + i*49; 449 u = ba + ili*49; 450 451 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]); 452 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]); 453 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]); 454 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]); 455 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]); 456 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]); 457 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]); 458 459 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]); 460 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]); 461 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]); 462 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]); 463 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]); 464 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]); 465 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]); 466 467 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]); 468 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]); 469 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]); 470 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]); 471 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]); 472 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]); 473 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]); 474 475 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]); 476 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]); 477 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]); 478 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]); 479 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]); 480 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]); 481 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]); 482 483 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]); 484 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]); 485 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]); 486 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]); 487 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]); 488 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]); 489 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]); 490 491 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]); 492 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]); 493 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]); 494 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]); 495 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]); 496 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]); 497 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]); 498 499 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]); 500 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]); 501 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]); 502 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]); 503 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]); 504 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]); 505 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]); 506 507 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 508 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]; 509 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]; 510 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]; 511 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]; 512 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]; 513 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]; 514 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]; 515 516 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]; 517 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]; 518 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]; 519 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]; 520 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]; 521 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]; 522 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]; 523 524 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]; 525 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]; 526 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]; 527 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]; 528 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]; 529 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]; 530 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]; 531 532 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]; 533 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]; 534 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]; 535 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]; 536 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]; 537 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]; 538 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]; 539 540 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]; 541 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]; 542 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]; 543 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]; 544 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]; 545 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]; 546 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]; 547 548 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]; 549 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]; 550 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]; 551 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]; 552 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]; 553 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]; 554 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]; 555 556 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]; 557 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]; 558 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]; 559 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]; 560 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]; 561 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]; 562 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]; 563 564 /* update -U(i,k) */ 565 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 566 567 /* add multiple of row i to k-th row ... */ 568 jmin = ili + 1; jmax = bi[i+1]; 569 if (jmin < jmax){ 570 for (j=jmin; j<jmax; j++) { 571 /* w += -U(i,k)^T * U_bar(i,j) */ 572 wp = w + bj[j]*49; 573 u = ba + j*49; 574 575 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]; 576 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]; 577 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]; 578 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]; 579 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]; 580 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]; 581 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]; 582 583 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]; 584 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]; 585 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]; 586 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]; 587 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]; 588 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]; 589 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]; 590 591 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]; 592 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]; 593 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]; 594 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]; 595 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]; 596 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]; 597 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]; 598 599 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]; 600 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]; 601 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]; 602 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]; 603 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]; 604 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]; 605 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]; 606 607 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]; 608 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]; 609 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]; 610 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]; 611 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]; 612 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]; 613 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]; 614 615 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]; 616 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]; 617 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]; 618 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]; 619 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]; 620 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]; 621 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]; 622 623 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]; 624 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]; 625 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]; 626 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]; 627 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]; 628 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]; 629 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]; 630 } 631 632 /* ... add i to row list for next nonzero entry */ 633 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 634 j = bj[jmin]; 635 jl[i] = jl[j]; jl[j] = i; /* update jl */ 636 } 637 i = nexti; 638 } 639 640 /* save nonzero entries in k-th row of U ... */ 641 642 /* invert diagonal block */ 643 d = ba+k*49; 644 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 645 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 646 647 jmin = bi[k]; jmax = bi[k+1]; 648 if (jmin < jmax) { 649 for (j=jmin; j<jmax; j++){ 650 vj = bj[j]; /* block col. index of U */ 651 u = ba + j*49; 652 wp = w + vj*49; 653 for (k1=0; k1<49; k1++){ 654 *u++ = *wp; 655 *wp++ = 0.0; 656 } 657 } 658 659 /* ... add k to row list for first nonzero entry in k-th row */ 660 il[k] = jmin; 661 i = bj[jmin]; 662 jl[k] = jl[i]; jl[i] = k; 663 } 664 } 665 666 ierr = PetscFree(w);CHKERRQ(ierr); 667 ierr = PetscFree(il);CHKERRQ(ierr); 668 ierr = PetscFree(jl);CHKERRQ(ierr); 669 ierr = PetscFree(dk);CHKERRQ(ierr); 670 ierr = PetscFree(uik);CHKERRQ(ierr); 671 if (a->permute){ 672 ierr = PetscFree(aa);CHKERRQ(ierr); 673 } 674 675 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 676 C->factor = FACTOR_CHOLESKY; 677 C->assembled = PETSC_TRUE; 678 C->preallocated = PETSC_TRUE; 679 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 680 PetscFunctionReturn(0); 681 } 682 683 /* 684 Version for when blocks are 7 by 7 Using natural ordering 685 */ 686 #undef __FUNC__ 687 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering" 688 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B) 689 { 690 Mat C = *B; 691 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 692 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 693 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 694 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 695 MatScalar *u,*d,*w,*wp; 696 697 PetscFunctionBegin; 698 /* initialization */ 699 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 700 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 701 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 702 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 703 for (i=0; i<mbs; i++) { 704 jl[i] = mbs; il[0] = 0; 705 } 706 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 707 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 708 709 ai = a->i; aj = a->j; aa = a->a; 710 711 /* for each row k */ 712 for (k = 0; k<mbs; k++){ 713 714 /*initialize k-th row with elements nonzero in row k of A */ 715 jmin = ai[k]; jmax = ai[k+1]; 716 if (jmin < jmax) { 717 ap = aa + jmin*49; 718 for (j = jmin; j < jmax; j++){ 719 vj = aj[j]; /* block col. index */ 720 wp = w + vj*49; 721 for (i=0; i<49; i++) *wp++ = *ap++; 722 } 723 } 724 725 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 726 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 727 i = jl[k]; /* first row to be added to k_th row */ 728 729 while (i < mbs){ 730 nexti = jl[i]; /* next row to be added to k_th row */ 731 732 /* compute multiplier */ 733 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 734 735 /* uik = -inv(Di)*U_bar(i,k) */ 736 d = ba + i*49; 737 u = ba + ili*49; 738 739 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]); 740 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]); 741 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]); 742 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]); 743 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]); 744 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]); 745 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]); 746 747 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]); 748 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]); 749 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]); 750 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]); 751 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]); 752 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]); 753 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]); 754 755 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]); 756 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]); 757 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]); 758 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]); 759 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]); 760 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]); 761 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]); 762 763 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]); 764 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]); 765 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]); 766 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]); 767 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]); 768 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]); 769 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]); 770 771 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]); 772 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]); 773 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]); 774 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]); 775 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]); 776 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]); 777 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]); 778 779 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]); 780 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]); 781 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]); 782 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]); 783 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]); 784 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]); 785 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]); 786 787 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]); 788 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]); 789 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]); 790 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]); 791 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]); 792 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]); 793 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]); 794 795 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 796 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]; 797 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]; 798 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]; 799 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]; 800 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]; 801 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]; 802 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]; 803 804 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]; 805 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]; 806 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]; 807 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]; 808 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]; 809 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]; 810 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]; 811 812 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]; 813 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]; 814 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]; 815 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]; 816 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]; 817 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]; 818 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]; 819 820 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]; 821 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]; 822 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]; 823 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]; 824 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]; 825 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]; 826 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]; 827 828 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]; 829 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]; 830 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]; 831 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]; 832 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]; 833 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]; 834 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]; 835 836 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]; 837 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]; 838 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]; 839 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]; 840 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]; 841 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]; 842 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]; 843 844 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]; 845 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]; 846 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]; 847 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]; 848 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]; 849 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]; 850 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]; 851 852 /* update -U(i,k) */ 853 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 854 855 /* add multiple of row i to k-th row ... */ 856 jmin = ili + 1; jmax = bi[i+1]; 857 if (jmin < jmax){ 858 for (j=jmin; j<jmax; j++) { 859 /* w += -U(i,k)^T * U_bar(i,j) */ 860 wp = w + bj[j]*49; 861 u = ba + j*49; 862 863 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]; 864 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]; 865 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]; 866 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]; 867 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]; 868 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]; 869 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]; 870 871 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]; 872 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]; 873 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]; 874 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]; 875 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]; 876 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]; 877 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]; 878 879 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]; 880 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]; 881 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]; 882 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]; 883 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]; 884 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]; 885 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]; 886 887 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]; 888 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]; 889 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]; 890 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]; 891 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]; 892 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]; 893 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]; 894 895 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]; 896 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]; 897 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]; 898 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]; 899 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]; 900 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]; 901 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]; 902 903 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]; 904 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]; 905 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]; 906 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]; 907 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]; 908 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]; 909 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]; 910 911 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]; 912 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]; 913 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]; 914 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]; 915 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]; 916 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]; 917 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]; 918 } 919 920 /* ... add i to row list for next nonzero entry */ 921 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 922 j = bj[jmin]; 923 jl[i] = jl[j]; jl[j] = i; /* update jl */ 924 } 925 i = nexti; 926 } 927 928 /* save nonzero entries in k-th row of U ... */ 929 930 /* invert diagonal block */ 931 d = ba+k*49; 932 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 933 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 934 935 jmin = bi[k]; jmax = bi[k+1]; 936 if (jmin < jmax) { 937 for (j=jmin; j<jmax; j++){ 938 vj = bj[j]; /* block col. index of U */ 939 u = ba + j*49; 940 wp = w + vj*49; 941 for (k1=0; k1<49; k1++){ 942 *u++ = *wp; 943 *wp++ = 0.0; 944 } 945 } 946 947 /* ... add k to row list for first nonzero entry in k-th row */ 948 il[k] = jmin; 949 i = bj[jmin]; 950 jl[k] = jl[i]; jl[i] = k; 951 } 952 } 953 954 ierr = PetscFree(w);CHKERRQ(ierr); 955 ierr = PetscFree(il);CHKERRQ(ierr); 956 ierr = PetscFree(jl);CHKERRQ(ierr); 957 ierr = PetscFree(dk);CHKERRQ(ierr); 958 ierr = PetscFree(uik);CHKERRQ(ierr); 959 960 C->factor = FACTOR_CHOLESKY; 961 C->assembled = PETSC_TRUE; 962 C->preallocated = PETSC_TRUE; 963 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 964 PetscFunctionReturn(0); 965 } 966 967 /* Version for when blocks are 6 by 6 */ 968 #undef __FUNC__ 969 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 970 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 971 { 972 Mat C = *B; 973 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 974 IS perm = b->row; 975 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 976 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 977 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 978 MatScalar *u,*d,*w,*wp; 979 980 PetscFunctionBegin; 981 /* initialization */ 982 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 983 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 984 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 985 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 986 for (i=0; i<mbs; i++) { 987 jl[i] = mbs; il[0] = 0; 988 } 989 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 990 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 991 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 992 993 /* check permutation */ 994 if (!a->permute){ 995 ai = a->i; aj = a->j; aa = a->a; 996 } else { 997 ai = a->inew; aj = a->jnew; 998 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 999 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1000 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1001 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1002 1003 for (i=0; i<mbs; i++){ 1004 jmin = ai[i]; jmax = ai[i+1]; 1005 for (j=jmin; j<jmax; j++){ 1006 while (a2anew[j] != j){ 1007 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1008 for (k1=0; k1<36; k1++){ 1009 dk[k1] = aa[k*36+k1]; 1010 aa[k*36+k1] = aa[j*36+k1]; 1011 aa[j*36+k1] = dk[k1]; 1012 } 1013 } 1014 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1015 if (i > aj[j]){ 1016 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1017 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 1018 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1019 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 1020 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 1021 } 1022 } 1023 } 1024 } 1025 ierr = PetscFree(a2anew);CHKERRA(ierr); 1026 } 1027 1028 /* for each row k */ 1029 for (k = 0; k<mbs; k++){ 1030 1031 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1032 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1033 if (jmin < jmax) { 1034 ap = aa + jmin*36; 1035 for (j = jmin; j < jmax; j++){ 1036 vj = perm_ptr[aj[j]]; /* block col. index */ 1037 wp = w + vj*36; 1038 for (i=0; i<36; i++) *wp++ = *ap++; 1039 } 1040 } 1041 1042 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1043 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1044 i = jl[k]; /* first row to be added to k_th row */ 1045 1046 while (i < mbs){ 1047 nexti = jl[i]; /* next row to be added to k_th row */ 1048 1049 /* compute multiplier */ 1050 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1051 1052 /* uik = -inv(Di)*U_bar(i,k) */ 1053 d = ba + i*36; 1054 u = ba + ili*36; 1055 1056 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]); 1057 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]); 1058 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]); 1059 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]); 1060 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]); 1061 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]); 1062 1063 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]); 1064 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]); 1065 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]); 1066 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]); 1067 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]); 1068 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]); 1069 1070 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]); 1071 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]); 1072 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]); 1073 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]); 1074 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]); 1075 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]); 1076 1077 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]); 1078 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]); 1079 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]); 1080 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]); 1081 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]); 1082 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]); 1083 1084 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]); 1085 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]); 1086 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]); 1087 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]); 1088 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]); 1089 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]); 1090 1091 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]); 1092 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]); 1093 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]); 1094 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]); 1095 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]); 1096 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]); 1097 1098 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1099 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]; 1100 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]; 1101 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]; 1102 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]; 1103 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]; 1104 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]; 1105 1106 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]; 1107 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]; 1108 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]; 1109 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]; 1110 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]; 1111 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]; 1112 1113 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]; 1114 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]; 1115 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]; 1116 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]; 1117 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]; 1118 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]; 1119 1120 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]; 1121 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]; 1122 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]; 1123 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]; 1124 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]; 1125 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]; 1126 1127 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]; 1128 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]; 1129 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]; 1130 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]; 1131 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]; 1132 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]; 1133 1134 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]; 1135 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]; 1136 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]; 1137 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]; 1138 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]; 1139 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]; 1140 1141 /* update -U(i,k) */ 1142 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1143 1144 /* add multiple of row i to k-th row ... */ 1145 jmin = ili + 1; jmax = bi[i+1]; 1146 if (jmin < jmax){ 1147 for (j=jmin; j<jmax; j++) { 1148 /* w += -U(i,k)^T * U_bar(i,j) */ 1149 wp = w + bj[j]*36; 1150 u = ba + j*36; 1151 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]; 1152 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]; 1153 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]; 1154 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]; 1155 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]; 1156 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]; 1157 1158 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]; 1159 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]; 1160 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]; 1161 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]; 1162 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]; 1163 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]; 1164 1165 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]; 1166 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]; 1167 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]; 1168 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]; 1169 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]; 1170 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]; 1171 1172 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]; 1173 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]; 1174 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]; 1175 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]; 1176 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]; 1177 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]; 1178 1179 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]; 1180 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]; 1181 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]; 1182 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]; 1183 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]; 1184 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]; 1185 1186 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]; 1187 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]; 1188 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]; 1189 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]; 1190 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]; 1191 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]; 1192 } 1193 1194 /* ... add i to row list for next nonzero entry */ 1195 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1196 j = bj[jmin]; 1197 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1198 } 1199 i = nexti; 1200 } 1201 1202 /* save nonzero entries in k-th row of U ... */ 1203 1204 /* invert diagonal block */ 1205 d = ba+k*36; 1206 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1207 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1208 1209 jmin = bi[k]; jmax = bi[k+1]; 1210 if (jmin < jmax) { 1211 for (j=jmin; j<jmax; j++){ 1212 vj = bj[j]; /* block col. index of U */ 1213 u = ba + j*36; 1214 wp = w + vj*36; 1215 for (k1=0; k1<36; k1++){ 1216 *u++ = *wp; 1217 *wp++ = 0.0; 1218 } 1219 } 1220 1221 /* ... add k to row list for first nonzero entry in k-th row */ 1222 il[k] = jmin; 1223 i = bj[jmin]; 1224 jl[k] = jl[i]; jl[i] = k; 1225 } 1226 } 1227 1228 ierr = PetscFree(w);CHKERRQ(ierr); 1229 ierr = PetscFree(il);CHKERRQ(ierr); 1230 ierr = PetscFree(jl);CHKERRQ(ierr); 1231 ierr = PetscFree(dk);CHKERRQ(ierr); 1232 ierr = PetscFree(uik);CHKERRQ(ierr); 1233 if (a->permute){ 1234 ierr = PetscFree(aa);CHKERRQ(ierr); 1235 } 1236 1237 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1238 C->factor = FACTOR_CHOLESKY; 1239 C->assembled = PETSC_TRUE; 1240 C->preallocated = PETSC_TRUE; 1241 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1242 PetscFunctionReturn(0); 1243 } 1244 1245 /* 1246 Version for when blocks are 6 by 6 Using natural ordering 1247 */ 1248 #undef __FUNC__ 1249 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1250 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1251 { 1252 Mat C = *B; 1253 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1254 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1255 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1256 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1257 MatScalar *u,*d,*w,*wp; 1258 1259 PetscFunctionBegin; 1260 /* initialization */ 1261 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 1262 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1263 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1264 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1265 for (i=0; i<mbs; i++) { 1266 jl[i] = mbs; il[0] = 0; 1267 } 1268 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 1269 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 1270 1271 ai = a->i; aj = a->j; aa = a->a; 1272 1273 /* for each row k */ 1274 for (k = 0; k<mbs; k++){ 1275 1276 /*initialize k-th row with elements nonzero in row k of A */ 1277 jmin = ai[k]; jmax = ai[k+1]; 1278 if (jmin < jmax) { 1279 ap = aa + jmin*36; 1280 for (j = jmin; j < jmax; j++){ 1281 vj = aj[j]; /* block col. index */ 1282 wp = w + vj*36; 1283 for (i=0; i<36; i++) *wp++ = *ap++; 1284 } 1285 } 1286 1287 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1288 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1289 i = jl[k]; /* first row to be added to k_th row */ 1290 1291 while (i < mbs){ 1292 nexti = jl[i]; /* next row to be added to k_th row */ 1293 1294 /* compute multiplier */ 1295 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1296 1297 /* uik = -inv(Di)*U_bar(i,k) */ 1298 d = ba + i*36; 1299 u = ba + ili*36; 1300 1301 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]); 1302 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]); 1303 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]); 1304 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]); 1305 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]); 1306 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]); 1307 1308 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]); 1309 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]); 1310 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]); 1311 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]); 1312 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]); 1313 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]); 1314 1315 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]); 1316 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]); 1317 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]); 1318 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]); 1319 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]); 1320 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]); 1321 1322 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]); 1323 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]); 1324 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]); 1325 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]); 1326 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]); 1327 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]); 1328 1329 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]); 1330 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]); 1331 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]); 1332 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]); 1333 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]); 1334 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]); 1335 1336 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]); 1337 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]); 1338 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]); 1339 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]); 1340 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]); 1341 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]); 1342 1343 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1344 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]; 1345 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]; 1346 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]; 1347 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]; 1348 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]; 1349 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]; 1350 1351 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]; 1352 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]; 1353 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]; 1354 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]; 1355 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]; 1356 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]; 1357 1358 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]; 1359 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]; 1360 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]; 1361 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]; 1362 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]; 1363 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]; 1364 1365 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]; 1366 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]; 1367 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]; 1368 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]; 1369 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]; 1370 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]; 1371 1372 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]; 1373 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]; 1374 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]; 1375 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]; 1376 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]; 1377 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]; 1378 1379 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]; 1380 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]; 1381 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]; 1382 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]; 1383 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]; 1384 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]; 1385 1386 /* update -U(i,k) */ 1387 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1388 1389 /* add multiple of row i to k-th row ... */ 1390 jmin = ili + 1; jmax = bi[i+1]; 1391 if (jmin < jmax){ 1392 for (j=jmin; j<jmax; j++) { 1393 /* w += -U(i,k)^T * U_bar(i,j) */ 1394 wp = w + bj[j]*36; 1395 u = ba + j*36; 1396 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]; 1397 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]; 1398 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]; 1399 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]; 1400 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]; 1401 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]; 1402 1403 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]; 1404 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]; 1405 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]; 1406 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]; 1407 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]; 1408 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]; 1409 1410 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]; 1411 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]; 1412 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]; 1413 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]; 1414 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]; 1415 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]; 1416 1417 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]; 1418 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]; 1419 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]; 1420 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]; 1421 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]; 1422 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]; 1423 1424 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]; 1425 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]; 1426 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]; 1427 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]; 1428 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]; 1429 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]; 1430 1431 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]; 1432 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]; 1433 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]; 1434 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]; 1435 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]; 1436 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]; 1437 } 1438 1439 /* ... add i to row list for next nonzero entry */ 1440 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1441 j = bj[jmin]; 1442 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1443 } 1444 i = nexti; 1445 } 1446 1447 /* save nonzero entries in k-th row of U ... */ 1448 1449 /* invert diagonal block */ 1450 d = ba+k*36; 1451 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1452 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1453 1454 jmin = bi[k]; jmax = bi[k+1]; 1455 if (jmin < jmax) { 1456 for (j=jmin; j<jmax; j++){ 1457 vj = bj[j]; /* block col. index of U */ 1458 u = ba + j*36; 1459 wp = w + vj*36; 1460 for (k1=0; k1<36; k1++){ 1461 *u++ = *wp; 1462 *wp++ = 0.0; 1463 } 1464 } 1465 1466 /* ... add k to row list for first nonzero entry in k-th row */ 1467 il[k] = jmin; 1468 i = bj[jmin]; 1469 jl[k] = jl[i]; jl[i] = k; 1470 } 1471 } 1472 1473 ierr = PetscFree(w);CHKERRQ(ierr); 1474 ierr = PetscFree(il);CHKERRQ(ierr); 1475 ierr = PetscFree(jl);CHKERRQ(ierr); 1476 ierr = PetscFree(dk);CHKERRQ(ierr); 1477 ierr = PetscFree(uik);CHKERRQ(ierr); 1478 1479 C->factor = FACTOR_CHOLESKY; 1480 C->assembled = PETSC_TRUE; 1481 C->preallocated = PETSC_TRUE; 1482 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1483 PetscFunctionReturn(0); 1484 } 1485 1486 /* Version for when blocks are 5 by 5 */ 1487 #undef __FUNC__ 1488 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1489 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1490 { 1491 Mat C = *B; 1492 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1493 IS perm = b->row; 1494 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1495 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1496 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1497 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1498 1499 PetscFunctionBegin; 1500 /* initialization */ 1501 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1502 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1503 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1504 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1505 for (i=0; i<mbs; i++) { 1506 jl[i] = mbs; il[0] = 0; 1507 } 1508 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1509 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1510 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1511 1512 /* check permutation */ 1513 if (!a->permute){ 1514 ai = a->i; aj = a->j; aa = a->a; 1515 } else { 1516 ai = a->inew; aj = a->jnew; 1517 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1518 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1519 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1520 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1521 1522 for (i=0; i<mbs; i++){ 1523 jmin = ai[i]; jmax = ai[i+1]; 1524 for (j=jmin; j<jmax; j++){ 1525 while (a2anew[j] != j){ 1526 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1527 for (k1=0; k1<25; k1++){ 1528 dk[k1] = aa[k*25+k1]; 1529 aa[k*25+k1] = aa[j*25+k1]; 1530 aa[j*25+k1] = dk[k1]; 1531 } 1532 } 1533 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1534 if (i > aj[j]){ 1535 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1536 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1537 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1538 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1539 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1540 } 1541 } 1542 } 1543 } 1544 ierr = PetscFree(a2anew);CHKERRA(ierr); 1545 } 1546 1547 /* for each row k */ 1548 for (k = 0; k<mbs; k++){ 1549 1550 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1551 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1552 if (jmin < jmax) { 1553 ap = aa + jmin*25; 1554 for (j = jmin; j < jmax; j++){ 1555 vj = perm_ptr[aj[j]]; /* block col. index */ 1556 rtmp_ptr = rtmp + vj*25; 1557 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1558 } 1559 } 1560 1561 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1562 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1563 i = jl[k]; /* first row to be added to k_th row */ 1564 1565 while (i < mbs){ 1566 nexti = jl[i]; /* next row to be added to k_th row */ 1567 1568 /* compute multiplier */ 1569 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1570 1571 /* uik = -inv(Di)*U_bar(i,k) */ 1572 d = ba + i*25; 1573 u = ba + ili*25; 1574 1575 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1576 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1577 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1578 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1579 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1580 1581 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1582 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1583 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1584 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1585 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1586 1587 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1588 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1589 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1590 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1591 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1592 1593 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1594 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1595 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1596 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1597 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1598 1599 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1600 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1601 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1602 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1603 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1604 1605 1606 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1607 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1608 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1609 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1610 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1611 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1612 1613 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1614 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1615 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1616 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1617 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1618 1619 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1620 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1621 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1622 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1623 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1624 1625 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1626 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1627 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1628 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1629 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1630 1631 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1632 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1633 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1634 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1635 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1636 1637 /* update -U(i,k) */ 1638 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1639 1640 /* add multiple of row i to k-th row ... */ 1641 jmin = ili + 1; jmax = bi[i+1]; 1642 if (jmin < jmax){ 1643 for (j=jmin; j<jmax; j++) { 1644 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1645 rtmp_ptr = rtmp + bj[j]*25; 1646 u = ba + j*25; 1647 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1648 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1649 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1650 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1651 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1652 1653 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1654 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1655 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1656 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1657 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1658 1659 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1660 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1661 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1662 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1663 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1664 1665 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1666 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1667 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1668 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1669 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1670 1671 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1672 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1673 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1674 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1675 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1676 } 1677 1678 /* ... add i to row list for next nonzero entry */ 1679 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1680 j = bj[jmin]; 1681 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1682 } 1683 i = nexti; 1684 } 1685 1686 /* save nonzero entries in k-th row of U ... */ 1687 1688 /* invert diagonal block */ 1689 d = ba+k*25; 1690 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1691 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1692 1693 jmin = bi[k]; jmax = bi[k+1]; 1694 if (jmin < jmax) { 1695 for (j=jmin; j<jmax; j++){ 1696 vj = bj[j]; /* block col. index of U */ 1697 u = ba + j*25; 1698 rtmp_ptr = rtmp + vj*25; 1699 for (k1=0; k1<25; k1++){ 1700 *u++ = *rtmp_ptr; 1701 *rtmp_ptr++ = 0.0; 1702 } 1703 } 1704 1705 /* ... add k to row list for first nonzero entry in k-th row */ 1706 il[k] = jmin; 1707 i = bj[jmin]; 1708 jl[k] = jl[i]; jl[i] = k; 1709 } 1710 } 1711 1712 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1713 ierr = PetscFree(il);CHKERRQ(ierr); 1714 ierr = PetscFree(jl);CHKERRQ(ierr); 1715 ierr = PetscFree(dk);CHKERRQ(ierr); 1716 ierr = PetscFree(uik);CHKERRQ(ierr); 1717 if (a->permute){ 1718 ierr = PetscFree(aa);CHKERRQ(ierr); 1719 } 1720 1721 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1722 C->factor = FACTOR_CHOLESKY; 1723 C->assembled = PETSC_TRUE; 1724 C->preallocated = PETSC_TRUE; 1725 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1726 PetscFunctionReturn(0); 1727 } 1728 1729 /* 1730 Version for when blocks are 5 by 5 Using natural ordering 1731 */ 1732 #undef __FUNC__ 1733 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1734 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1735 { 1736 Mat C = *B; 1737 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1738 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1739 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1740 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1741 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1742 1743 PetscFunctionBegin; 1744 /* initialization */ 1745 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1746 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1747 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1748 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1749 for (i=0; i<mbs; i++) { 1750 jl[i] = mbs; il[0] = 0; 1751 } 1752 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1753 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1754 1755 ai = a->i; aj = a->j; aa = a->a; 1756 1757 /* for each row k */ 1758 for (k = 0; k<mbs; k++){ 1759 1760 /*initialize k-th row with elements nonzero in row k of A */ 1761 jmin = ai[k]; jmax = ai[k+1]; 1762 if (jmin < jmax) { 1763 ap = aa + jmin*25; 1764 for (j = jmin; j < jmax; j++){ 1765 vj = aj[j]; /* block col. index */ 1766 rtmp_ptr = rtmp + vj*25; 1767 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1768 } 1769 } 1770 1771 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1772 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1773 i = jl[k]; /* first row to be added to k_th row */ 1774 1775 while (i < mbs){ 1776 nexti = jl[i]; /* next row to be added to k_th row */ 1777 1778 /* compute multiplier */ 1779 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1780 1781 /* uik = -inv(Di)*U_bar(i,k) */ 1782 d = ba + i*25; 1783 u = ba + ili*25; 1784 1785 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1786 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1787 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1788 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1789 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1790 1791 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1792 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1793 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1794 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1795 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1796 1797 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1798 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1799 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1800 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1801 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1802 1803 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1804 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1805 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1806 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1807 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1808 1809 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1810 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1811 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1812 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1813 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1814 1815 1816 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1817 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1818 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1819 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1820 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1821 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1822 1823 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1824 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1825 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1826 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1827 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1828 1829 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1830 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1831 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1832 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1833 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1834 1835 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1836 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1837 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1838 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1839 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1840 1841 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1842 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1843 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1844 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1845 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1846 1847 /* update -U(i,k) */ 1848 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1849 1850 /* add multiple of row i to k-th row ... */ 1851 jmin = ili + 1; jmax = bi[i+1]; 1852 if (jmin < jmax){ 1853 for (j=jmin; j<jmax; j++) { 1854 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1855 rtmp_ptr = rtmp + bj[j]*25; 1856 u = ba + j*25; 1857 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1858 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1859 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1860 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1861 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1862 1863 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1864 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1865 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1866 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1867 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1868 1869 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1870 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1871 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1872 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1873 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1874 1875 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1876 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1877 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1878 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1879 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1880 1881 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1882 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1883 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1884 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1885 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1886 } 1887 1888 /* ... add i to row list for next nonzero entry */ 1889 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1890 j = bj[jmin]; 1891 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1892 } 1893 i = nexti; 1894 } 1895 1896 /* save nonzero entries in k-th row of U ... */ 1897 1898 /* invert diagonal block */ 1899 d = ba+k*25; 1900 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1901 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1902 1903 jmin = bi[k]; jmax = bi[k+1]; 1904 if (jmin < jmax) { 1905 for (j=jmin; j<jmax; j++){ 1906 vj = bj[j]; /* block col. index of U */ 1907 u = ba + j*25; 1908 rtmp_ptr = rtmp + vj*25; 1909 for (k1=0; k1<25; k1++){ 1910 *u++ = *rtmp_ptr; 1911 *rtmp_ptr++ = 0.0; 1912 } 1913 } 1914 1915 /* ... add k to row list for first nonzero entry in k-th row */ 1916 il[k] = jmin; 1917 i = bj[jmin]; 1918 jl[k] = jl[i]; jl[i] = k; 1919 } 1920 } 1921 1922 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1923 ierr = PetscFree(il);CHKERRQ(ierr); 1924 ierr = PetscFree(jl);CHKERRQ(ierr); 1925 ierr = PetscFree(dk);CHKERRQ(ierr); 1926 ierr = PetscFree(uik);CHKERRQ(ierr); 1927 1928 C->factor = FACTOR_CHOLESKY; 1929 C->assembled = PETSC_TRUE; 1930 C->preallocated = PETSC_TRUE; 1931 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1932 PetscFunctionReturn(0); 1933 } 1934 1935 /* 1936 Version for when blocks are 4 by 4 Using natural ordering 1937 */ 1938 #undef __FUNC__ 1939 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1940 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1941 { 1942 Mat C = *B; 1943 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1944 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1945 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1946 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1947 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 1948 1949 PetscFunctionBegin; 1950 /* initialization */ 1951 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1952 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1953 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1954 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1955 for (i=0; i<mbs; i++) { 1956 jl[i] = mbs; il[0] = 0; 1957 } 1958 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 1959 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 1960 1961 ai = a->i; aj = a->j; aa = a->a; 1962 1963 /* for each row k */ 1964 for (k = 0; k<mbs; k++){ 1965 1966 /*initialize k-th row with elements nonzero in row k of A */ 1967 jmin = ai[k]; jmax = ai[k+1]; 1968 if (jmin < jmax) { 1969 ap = aa + jmin*16; 1970 for (j = jmin; j < jmax; j++){ 1971 vj = aj[j]; /* block col. index */ 1972 rtmp_ptr = rtmp + vj*16; 1973 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 1974 } 1975 } 1976 1977 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1978 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 1979 i = jl[k]; /* first row to be added to k_th row */ 1980 1981 while (i < mbs){ 1982 nexti = jl[i]; /* next row to be added to k_th row */ 1983 1984 /* compute multiplier */ 1985 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1986 1987 /* uik = -inv(Di)*U_bar(i,k) */ 1988 diag = ba + i*16; 1989 u = ba + ili*16; 1990 1991 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 1992 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 1993 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 1994 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 1995 1996 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 1997 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 1998 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 1999 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2000 2001 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2002 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2003 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2004 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2005 2006 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2007 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2008 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2009 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2010 2011 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2012 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2013 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2014 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2015 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2016 2017 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2018 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2019 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2020 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2021 2022 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2023 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2024 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2025 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2026 2027 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2028 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2029 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2030 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2031 2032 /* update -U(i,k) */ 2033 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2034 2035 /* add multiple of row i to k-th row ... */ 2036 jmin = ili + 1; jmax = bi[i+1]; 2037 if (jmin < jmax){ 2038 for (j=jmin; j<jmax; j++) { 2039 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2040 rtmp_ptr = rtmp + bj[j]*16; 2041 u = ba + j*16; 2042 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2043 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2044 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2045 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2046 2047 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2048 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2049 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2050 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2051 2052 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2053 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2054 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2055 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2056 2057 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2058 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2059 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2060 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2061 } 2062 2063 /* ... add i to row list for next nonzero entry */ 2064 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2065 j = bj[jmin]; 2066 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2067 } 2068 i = nexti; 2069 } 2070 2071 /* save nonzero entries in k-th row of U ... */ 2072 2073 /* invert diagonal block */ 2074 diag = ba+k*16; 2075 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2076 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2077 2078 jmin = bi[k]; jmax = bi[k+1]; 2079 if (jmin < jmax) { 2080 for (j=jmin; j<jmax; j++){ 2081 vj = bj[j]; /* block col. index of U */ 2082 u = ba + j*16; 2083 rtmp_ptr = rtmp + vj*16; 2084 for (k1=0; k1<16; k1++){ 2085 *u++ = *rtmp_ptr; 2086 *rtmp_ptr++ = 0.0; 2087 } 2088 } 2089 2090 /* ... add k to row list for first nonzero entry in k-th row */ 2091 il[k] = jmin; 2092 i = bj[jmin]; 2093 jl[k] = jl[i]; jl[i] = k; 2094 } 2095 } 2096 2097 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2098 ierr = PetscFree(il);CHKERRQ(ierr); 2099 ierr = PetscFree(jl);CHKERRQ(ierr); 2100 ierr = PetscFree(dk);CHKERRQ(ierr); 2101 ierr = PetscFree(uik);CHKERRQ(ierr); 2102 2103 C->factor = FACTOR_CHOLESKY; 2104 C->assembled = PETSC_TRUE; 2105 C->preallocated = PETSC_TRUE; 2106 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2107 PetscFunctionReturn(0); 2108 } 2109 2110 /* Version for when blocks are 4 by 4 */ 2111 #undef __FUNC__ 2112 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 2113 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 2114 { 2115 Mat C = *B; 2116 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2117 IS perm = b->row; 2118 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2119 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2120 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2121 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2122 2123 PetscFunctionBegin; 2124 /* initialization */ 2125 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2126 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2127 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2128 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2129 for (i=0; i<mbs; i++) { 2130 jl[i] = mbs; il[0] = 0; 2131 } 2132 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 2133 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 2134 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2135 2136 /* check permutation */ 2137 if (!a->permute){ 2138 ai = a->i; aj = a->j; aa = a->a; 2139 } else { 2140 ai = a->inew; aj = a->jnew; 2141 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2142 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2143 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2144 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2145 2146 for (i=0; i<mbs; i++){ 2147 jmin = ai[i]; jmax = ai[i+1]; 2148 for (j=jmin; j<jmax; j++){ 2149 while (a2anew[j] != j){ 2150 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2151 for (k1=0; k1<16; k1++){ 2152 dk[k1] = aa[k*16+k1]; 2153 aa[k*16+k1] = aa[j*16+k1]; 2154 aa[j*16+k1] = dk[k1]; 2155 } 2156 } 2157 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2158 if (i > aj[j]){ 2159 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2160 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 2161 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2162 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 2163 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 2164 } 2165 } 2166 } 2167 } 2168 ierr = PetscFree(a2anew);CHKERRA(ierr); 2169 } 2170 2171 /* for each row k */ 2172 for (k = 0; k<mbs; k++){ 2173 2174 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2175 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2176 if (jmin < jmax) { 2177 ap = aa + jmin*16; 2178 for (j = jmin; j < jmax; j++){ 2179 vj = perm_ptr[aj[j]]; /* block col. index */ 2180 rtmp_ptr = rtmp + vj*16; 2181 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 2182 } 2183 } 2184 2185 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2186 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 2187 i = jl[k]; /* first row to be added to k_th row */ 2188 2189 while (i < mbs){ 2190 nexti = jl[i]; /* next row to be added to k_th row */ 2191 2192 /* compute multiplier */ 2193 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2194 2195 /* uik = -inv(Di)*U_bar(i,k) */ 2196 diag = ba + i*16; 2197 u = ba + ili*16; 2198 2199 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 2200 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 2201 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 2202 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 2203 2204 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2205 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2206 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2207 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2208 2209 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2210 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2211 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2212 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2213 2214 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2215 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2216 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2217 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2218 2219 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2220 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2221 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2222 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2223 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2224 2225 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2226 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2227 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2228 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2229 2230 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2231 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2232 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2233 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2234 2235 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2236 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2237 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2238 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2239 2240 /* update -U(i,k) */ 2241 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2242 2243 /* add multiple of row i to k-th row ... */ 2244 jmin = ili + 1; jmax = bi[i+1]; 2245 if (jmin < jmax){ 2246 for (j=jmin; j<jmax; j++) { 2247 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2248 rtmp_ptr = rtmp + bj[j]*16; 2249 u = ba + j*16; 2250 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2251 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2252 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2253 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2254 2255 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2256 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2257 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2258 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2259 2260 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2261 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2262 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2263 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2264 2265 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2266 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2267 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2268 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2269 } 2270 2271 /* ... add i to row list for next nonzero entry */ 2272 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2273 j = bj[jmin]; 2274 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2275 } 2276 i = nexti; 2277 } 2278 2279 /* save nonzero entries in k-th row of U ... */ 2280 2281 /* invert diagonal block */ 2282 diag = ba+k*16; 2283 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2284 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2285 2286 jmin = bi[k]; jmax = bi[k+1]; 2287 if (jmin < jmax) { 2288 for (j=jmin; j<jmax; j++){ 2289 vj = bj[j]; /* block col. index of U */ 2290 u = ba + j*16; 2291 rtmp_ptr = rtmp + vj*16; 2292 for (k1=0; k1<16; k1++){ 2293 *u++ = *rtmp_ptr; 2294 *rtmp_ptr++ = 0.0; 2295 } 2296 } 2297 2298 /* ... add k to row list for first nonzero entry in k-th row */ 2299 il[k] = jmin; 2300 i = bj[jmin]; 2301 jl[k] = jl[i]; jl[i] = k; 2302 } 2303 } 2304 2305 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2306 ierr = PetscFree(il);CHKERRQ(ierr); 2307 ierr = PetscFree(jl);CHKERRQ(ierr); 2308 ierr = PetscFree(dk);CHKERRQ(ierr); 2309 ierr = PetscFree(uik);CHKERRQ(ierr); 2310 if (a->permute){ 2311 ierr = PetscFree(aa);CHKERRQ(ierr); 2312 } 2313 2314 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2315 C->factor = FACTOR_CHOLESKY; 2316 C->assembled = PETSC_TRUE; 2317 C->preallocated = PETSC_TRUE; 2318 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2319 PetscFunctionReturn(0); 2320 } 2321 2322 /* Version for when blocks are 3 by 3 */ 2323 #undef __FUNC__ 2324 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2325 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2326 { 2327 Mat C = *B; 2328 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2329 IS perm = b->row; 2330 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2331 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2332 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2333 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2334 2335 PetscFunctionBegin; 2336 /* initialization */ 2337 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2338 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2339 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2340 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2341 for (i=0; i<mbs; i++) { 2342 jl[i] = mbs; il[0] = 0; 2343 } 2344 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2345 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2346 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2347 2348 /* check permutation */ 2349 if (!a->permute){ 2350 ai = a->i; aj = a->j; aa = a->a; 2351 } else { 2352 ai = a->inew; aj = a->jnew; 2353 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2354 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2355 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2356 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2357 2358 for (i=0; i<mbs; i++){ 2359 jmin = ai[i]; jmax = ai[i+1]; 2360 for (j=jmin; j<jmax; j++){ 2361 while (a2anew[j] != j){ 2362 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2363 for (k1=0; k1<9; k1++){ 2364 dk[k1] = aa[k*9+k1]; 2365 aa[k*9+k1] = aa[j*9+k1]; 2366 aa[j*9+k1] = dk[k1]; 2367 } 2368 } 2369 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2370 if (i > aj[j]){ 2371 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2372 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2373 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2374 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2375 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2376 } 2377 } 2378 } 2379 } 2380 ierr = PetscFree(a2anew);CHKERRA(ierr); 2381 } 2382 2383 /* for each row k */ 2384 for (k = 0; k<mbs; k++){ 2385 2386 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2387 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2388 if (jmin < jmax) { 2389 ap = aa + jmin*9; 2390 for (j = jmin; j < jmax; j++){ 2391 vj = perm_ptr[aj[j]]; /* block col. index */ 2392 rtmp_ptr = rtmp + vj*9; 2393 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2394 } 2395 } 2396 2397 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2398 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2399 i = jl[k]; /* first row to be added to k_th row */ 2400 2401 while (i < mbs){ 2402 nexti = jl[i]; /* next row to be added to k_th row */ 2403 2404 /* compute multiplier */ 2405 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2406 2407 /* uik = -inv(Di)*U_bar(i,k) */ 2408 diag = ba + i*9; 2409 u = ba + ili*9; 2410 2411 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2412 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2413 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2414 2415 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2416 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2417 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2418 2419 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2420 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2421 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2422 2423 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2424 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2425 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2426 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2427 2428 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2429 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2430 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2431 2432 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2433 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2434 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2435 2436 /* update -U(i,k) */ 2437 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2438 2439 /* add multiple of row i to k-th row ... */ 2440 jmin = ili + 1; jmax = bi[i+1]; 2441 if (jmin < jmax){ 2442 for (j=jmin; j<jmax; j++) { 2443 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2444 rtmp_ptr = rtmp + bj[j]*9; 2445 u = ba + j*9; 2446 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2447 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2448 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2449 2450 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2451 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2452 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2453 2454 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2455 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2456 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2457 } 2458 2459 /* ... add i to row list for next nonzero entry */ 2460 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2461 j = bj[jmin]; 2462 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2463 } 2464 i = nexti; 2465 } 2466 2467 /* save nonzero entries in k-th row of U ... */ 2468 2469 /* invert diagonal block */ 2470 diag = ba+k*9; 2471 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2472 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2473 2474 jmin = bi[k]; jmax = bi[k+1]; 2475 if (jmin < jmax) { 2476 for (j=jmin; j<jmax; j++){ 2477 vj = bj[j]; /* block col. index of U */ 2478 u = ba + j*9; 2479 rtmp_ptr = rtmp + vj*9; 2480 for (k1=0; k1<9; k1++){ 2481 *u++ = *rtmp_ptr; 2482 *rtmp_ptr++ = 0.0; 2483 } 2484 } 2485 2486 /* ... add k to row list for first nonzero entry in k-th row */ 2487 il[k] = jmin; 2488 i = bj[jmin]; 2489 jl[k] = jl[i]; jl[i] = k; 2490 } 2491 } 2492 2493 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2494 ierr = PetscFree(il);CHKERRQ(ierr); 2495 ierr = PetscFree(jl);CHKERRQ(ierr); 2496 ierr = PetscFree(dk);CHKERRQ(ierr); 2497 ierr = PetscFree(uik);CHKERRQ(ierr); 2498 if (a->permute){ 2499 ierr = PetscFree(aa);CHKERRQ(ierr); 2500 } 2501 2502 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2503 C->factor = FACTOR_CHOLESKY; 2504 C->assembled = PETSC_TRUE; 2505 C->preallocated = PETSC_TRUE; 2506 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2507 PetscFunctionReturn(0); 2508 } 2509 2510 /* 2511 Version for when blocks are 3 by 3 Using natural ordering 2512 */ 2513 #undef __FUNC__ 2514 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2515 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(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 /* initialization */ 2527 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2528 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2529 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2530 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2531 for (i=0; i<mbs; i++) { 2532 jl[i] = mbs; il[0] = 0; 2533 } 2534 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2535 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2536 2537 ai = a->i; aj = a->j; aa = a->a; 2538 2539 /* for each row k */ 2540 for (k = 0; k<mbs; k++){ 2541 2542 /*initialize k-th row with elements nonzero in row k of A */ 2543 jmin = ai[k]; jmax = ai[k+1]; 2544 if (jmin < jmax) { 2545 ap = aa + jmin*9; 2546 for (j = jmin; j < jmax; j++){ 2547 vj = aj[j]; /* block col. index */ 2548 rtmp_ptr = rtmp + vj*9; 2549 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2550 } 2551 } 2552 2553 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2554 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2555 i = jl[k]; /* first row to be added to k_th row */ 2556 2557 while (i < mbs){ 2558 nexti = jl[i]; /* next row to be added to k_th row */ 2559 2560 /* compute multiplier */ 2561 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2562 2563 /* uik = -inv(Di)*U_bar(i,k) */ 2564 diag = ba + i*9; 2565 u = ba + ili*9; 2566 2567 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2568 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2569 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2570 2571 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2572 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2573 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2574 2575 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2576 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2577 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2578 2579 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2580 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2581 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2582 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2583 2584 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2585 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2586 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2587 2588 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2589 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2590 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2591 2592 /* update -U(i,k) */ 2593 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2594 2595 /* add multiple of row i to k-th row ... */ 2596 jmin = ili + 1; jmax = bi[i+1]; 2597 if (jmin < jmax){ 2598 for (j=jmin; j<jmax; j++) { 2599 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2600 rtmp_ptr = rtmp + bj[j]*9; 2601 u = ba + j*9; 2602 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2603 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2604 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2605 2606 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2607 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2608 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2609 2610 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2611 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2612 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2613 } 2614 2615 /* ... add i to row list for next nonzero entry */ 2616 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2617 j = bj[jmin]; 2618 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2619 } 2620 i = nexti; 2621 } 2622 2623 /* save nonzero entries in k-th row of U ... */ 2624 2625 /* invert diagonal block */ 2626 diag = ba+k*9; 2627 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2628 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2629 2630 jmin = bi[k]; jmax = bi[k+1]; 2631 if (jmin < jmax) { 2632 for (j=jmin; j<jmax; j++){ 2633 vj = bj[j]; /* block col. index of U */ 2634 u = ba + j*9; 2635 rtmp_ptr = rtmp + vj*9; 2636 for (k1=0; k1<9; k1++){ 2637 *u++ = *rtmp_ptr; 2638 *rtmp_ptr++ = 0.0; 2639 } 2640 } 2641 2642 /* ... add k to row list for first nonzero entry in k-th row */ 2643 il[k] = jmin; 2644 i = bj[jmin]; 2645 jl[k] = jl[i]; jl[i] = k; 2646 } 2647 } 2648 2649 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2650 ierr = PetscFree(il);CHKERRQ(ierr); 2651 ierr = PetscFree(jl);CHKERRQ(ierr); 2652 ierr = PetscFree(dk);CHKERRQ(ierr); 2653 ierr = PetscFree(uik);CHKERRQ(ierr); 2654 2655 C->factor = FACTOR_CHOLESKY; 2656 C->assembled = PETSC_TRUE; 2657 C->preallocated = PETSC_TRUE; 2658 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2659 PetscFunctionReturn(0); 2660 } 2661 2662 /* 2663 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2664 Version for blocks 2 by 2. 2665 */ 2666 #undef __FUNC__ 2667 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2668 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2669 { 2670 Mat C = *B; 2671 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2672 IS perm = b->row; 2673 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2674 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2675 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2676 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2677 2678 PetscFunctionBegin; 2679 /* printf("called Numeric_SeqSBAIJ_2\n"); */ 2680 /* initialization */ 2681 /* il and jl record the first nonzero element in each row of the accessing 2682 window U(0:k, k:mbs-1). 2683 jl: list of rows to be added to uneliminated rows 2684 i>= k: jl(i) is the first row to be added to row i 2685 i< k: jl(i) is the row following row i in some list of rows 2686 jl(i) = mbs indicates the end of a list 2687 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2688 row i of U */ 2689 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2690 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2691 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2692 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2693 for (i=0; i<mbs; i++) { 2694 jl[i] = mbs; il[0] = 0; 2695 } 2696 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2697 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2698 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2699 2700 /* check permutation */ 2701 if (!a->permute){ 2702 ai = a->i; aj = a->j; aa = a->a; 2703 } else { 2704 ai = a->inew; aj = a->jnew; 2705 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2706 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2707 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2708 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2709 2710 for (i=0; i<mbs; i++){ 2711 jmin = ai[i]; jmax = ai[i+1]; 2712 for (j=jmin; j<jmax; j++){ 2713 while (a2anew[j] != j){ 2714 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2715 for (k1=0; k1<4; k1++){ 2716 dk[k1] = aa[k*4+k1]; 2717 aa[k*4+k1] = aa[j*4+k1]; 2718 aa[j*4+k1] = dk[k1]; 2719 } 2720 } 2721 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2722 if (i > aj[j]){ 2723 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2724 ap = aa + j*4; /* ptr to the beginning of the block */ 2725 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2726 ap[1] = ap[2]; 2727 ap[2] = dk[1]; 2728 } 2729 } 2730 } 2731 ierr = PetscFree(a2anew);CHKERRA(ierr); 2732 } 2733 2734 /* for each row k */ 2735 for (k = 0; k<mbs; k++){ 2736 2737 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2738 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2739 if (jmin < jmax) { 2740 ap = aa + jmin*4; 2741 for (j = jmin; j < jmax; j++){ 2742 vj = perm_ptr[aj[j]]; /* block col. index */ 2743 rtmp_ptr = rtmp + vj*4; 2744 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2745 } 2746 } 2747 2748 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2749 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2750 i = jl[k]; /* first row to be added to k_th row */ 2751 2752 while (i < mbs){ 2753 nexti = jl[i]; /* next row to be added to k_th row */ 2754 2755 /* compute multiplier */ 2756 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2757 2758 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2759 diag = ba + i*4; 2760 u = ba + ili*4; 2761 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2762 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2763 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2764 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2765 2766 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2767 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2768 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2769 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2770 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2771 2772 /* update -U(i,k): ba[ili] = uik */ 2773 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2774 2775 /* add multiple of row i to k-th row ... */ 2776 jmin = ili + 1; jmax = bi[i+1]; 2777 if (jmin < jmax){ 2778 for (j=jmin; j<jmax; j++) { 2779 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2780 rtmp_ptr = rtmp + bj[j]*4; 2781 u = ba + j*4; 2782 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2783 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2784 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2785 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2786 } 2787 2788 /* ... add i to row list for next nonzero entry */ 2789 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2790 j = bj[jmin]; 2791 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2792 } 2793 i = nexti; 2794 } 2795 2796 /* save nonzero entries in k-th row of U ... */ 2797 2798 /* invert diagonal block */ 2799 diag = ba+k*4; 2800 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2801 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2802 2803 jmin = bi[k]; jmax = bi[k+1]; 2804 if (jmin < jmax) { 2805 for (j=jmin; j<jmax; j++){ 2806 vj = bj[j]; /* block col. index of U */ 2807 u = ba + j*4; 2808 rtmp_ptr = rtmp + vj*4; 2809 for (k1=0; k1<4; k1++){ 2810 *u++ = *rtmp_ptr; 2811 *rtmp_ptr++ = 0.0; 2812 } 2813 } 2814 2815 /* ... add k to row list for first nonzero entry in k-th row */ 2816 il[k] = jmin; 2817 i = bj[jmin]; 2818 jl[k] = jl[i]; jl[i] = k; 2819 } 2820 } 2821 2822 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2823 ierr = PetscFree(il);CHKERRQ(ierr); 2824 ierr = PetscFree(jl);CHKERRQ(ierr); 2825 ierr = PetscFree(dk);CHKERRQ(ierr); 2826 ierr = PetscFree(uik);CHKERRQ(ierr); 2827 if (a->permute) { 2828 ierr = PetscFree(aa);CHKERRQ(ierr); 2829 } 2830 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2831 C->factor = FACTOR_CHOLESKY; 2832 C->assembled = PETSC_TRUE; 2833 C->preallocated = PETSC_TRUE; 2834 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2835 PetscFunctionReturn(0); 2836 } 2837 2838 /* 2839 Version for when blocks are 2 by 2 Using natural ordering 2840 */ 2841 #undef __FUNC__ 2842 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2843 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2844 { 2845 Mat C = *B; 2846 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2847 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2848 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2849 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2850 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2851 2852 PetscFunctionBegin; 2853 /* printf("called Numeric_SeqSBAIJ_2_NaturalOrdering\n"); */ 2854 /* initialization */ 2855 /* il and jl record the first nonzero element in each row of the accessing 2856 window U(0:k, k:mbs-1). 2857 jl: list of rows to be added to uneliminated rows 2858 i>= k: jl(i) is the first row to be added to row i 2859 i< k: jl(i) is the row following row i in some list of rows 2860 jl(i) = mbs indicates the end of a list 2861 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2862 row i of U */ 2863 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2864 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2865 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2866 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2867 for (i=0; i<mbs; i++) { 2868 jl[i] = mbs; il[0] = 0; 2869 } 2870 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2871 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2872 2873 ai = a->i; aj = a->j; aa = a->a; 2874 2875 /* for each row k */ 2876 for (k = 0; k<mbs; k++){ 2877 2878 /*initialize k-th row with elements nonzero in row k of A */ 2879 jmin = ai[k]; jmax = ai[k+1]; 2880 if (jmin < jmax) { 2881 ap = aa + jmin*4; 2882 for (j = jmin; j < jmax; j++){ 2883 vj = aj[j]; /* block col. index */ 2884 rtmp_ptr = rtmp + vj*4; 2885 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2886 } 2887 } 2888 2889 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2890 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2891 i = jl[k]; /* first row to be added to k_th row */ 2892 2893 while (i < mbs){ 2894 nexti = jl[i]; /* next row to be added to k_th row */ 2895 2896 /* compute multiplier */ 2897 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2898 2899 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2900 diag = ba + i*4; 2901 u = ba + ili*4; 2902 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2903 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2904 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2905 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2906 2907 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2908 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2909 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2910 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2911 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2912 2913 /* update -U(i,k): ba[ili] = uik */ 2914 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2915 2916 /* add multiple of row i to k-th row ... */ 2917 jmin = ili + 1; jmax = bi[i+1]; 2918 if (jmin < jmax){ 2919 for (j=jmin; j<jmax; j++) { 2920 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2921 rtmp_ptr = rtmp + bj[j]*4; 2922 u = ba + j*4; 2923 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2924 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2925 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2926 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2927 } 2928 2929 /* ... add i to row list for next nonzero entry */ 2930 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2931 j = bj[jmin]; 2932 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2933 } 2934 i = nexti; 2935 } 2936 2937 /* save nonzero entries in k-th row of U ... */ 2938 2939 /* invert diagonal block */ 2940 diag = ba+k*4; 2941 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2942 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2943 2944 jmin = bi[k]; jmax = bi[k+1]; 2945 if (jmin < jmax) { 2946 for (j=jmin; j<jmax; j++){ 2947 vj = bj[j]; /* block col. index of U */ 2948 u = ba + j*4; 2949 rtmp_ptr = rtmp + vj*4; 2950 for (k1=0; k1<4; k1++){ 2951 *u++ = *rtmp_ptr; 2952 *rtmp_ptr++ = 0.0; 2953 } 2954 } 2955 2956 /* ... add k to row list for first nonzero entry in k-th row */ 2957 il[k] = jmin; 2958 i = bj[jmin]; 2959 jl[k] = jl[i]; jl[i] = k; 2960 } 2961 } 2962 2963 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2964 ierr = PetscFree(il);CHKERRQ(ierr); 2965 ierr = PetscFree(jl);CHKERRQ(ierr); 2966 ierr = PetscFree(dk);CHKERRQ(ierr); 2967 ierr = PetscFree(uik);CHKERRQ(ierr); 2968 2969 C->factor = FACTOR_CHOLESKY; 2970 C->assembled = PETSC_TRUE; 2971 C->preallocated = PETSC_TRUE; 2972 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2973 PetscFunctionReturn(0); 2974 } 2975 2976 /* 2977 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2978 Version for blocks are 1 by 1. 2979 */ 2980 #undef __FUNC__ 2981 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2982 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2983 { 2984 Mat C = *B; 2985 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2986 IS ip = b->row; 2987 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2988 int *ai,*aj,*r; 2989 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2990 MatScalar *rtmp; 2991 MatScalar *ba = b->a,*aa,ak; 2992 MatScalar dk,uikdi; 2993 2994 PetscFunctionBegin; 2995 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2996 if (!a->permute){ 2997 ai = a->i; aj = a->j; aa = a->a; 2998 } else { 2999 ai = a->inew; aj = a->jnew; 3000 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 3001 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 3002 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 3003 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 3004 3005 jmin = ai[0]; jmax = ai[mbs]; 3006 for (j=jmin; j<jmax; j++){ 3007 while (r[j] != j){ 3008 k = r[j]; r[j] = r[k]; r[k] = k; 3009 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 3010 } 3011 } 3012 ierr = PetscFree(r);CHKERRA(ierr); 3013 } 3014 3015 /* initialization */ 3016 /* il and jl record the first nonzero element in each row of the accessing 3017 window U(0:k, k:mbs-1). 3018 jl: list of rows to be added to uneliminated rows 3019 i>= k: jl(i) is the first row to be added to row i 3020 i< k: jl(i) is the row following row i in some list of rows 3021 jl(i) = mbs indicates the end of a list 3022 il(i): points to the first nonzero element in columns k,...,mbs-1 of 3023 row i of U */ 3024 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 3025 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 3026 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 3027 for (i=0; i<mbs; i++) { 3028 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 3029 } 3030 3031 /* for each row k */ 3032 for (k = 0; k<mbs; k++){ 3033 3034 /*initialize k-th row with elements nonzero in row perm(k) of A */ 3035 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 3036 if (jmin < jmax) { 3037 for (j = jmin; j < jmax; j++){ 3038 vj = rip[aj[j]]; 3039 rtmp[vj] = aa[j]; 3040 } 3041 } 3042 3043 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 3044 dk = rtmp[k]; 3045 i = jl[k]; /* first row to be added to k_th row */ 3046 3047 while (i < mbs){ 3048 nexti = jl[i]; /* next row to be added to k_th row */ 3049 3050 /* compute multiplier, update D(k) and U(i,k) */ 3051 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 3052 uikdi = - ba[ili]*ba[i]; 3053 dk += uikdi*ba[ili]; 3054 ba[ili] = uikdi; /* -U(i,k) */ 3055 3056 /* add multiple of row i to k-th row ... */ 3057 jmin = ili + 1; jmax = bi[i+1]; 3058 if (jmin < jmax){ 3059 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 3060 /* ... add i to row list for next nonzero entry */ 3061 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 3062 j = bj[jmin]; 3063 jl[i] = jl[j]; jl[j] = i; /* update jl */ 3064 } 3065 i = nexti; 3066 } 3067 3068 /* check for zero pivot and save diagoanl element */ 3069 if (dk == 0.0){ 3070 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 3071 }else if (PetscRealPart(dk) < 0){ 3072 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 3073 } 3074 3075 /* save nonzero entries in k-th row of U ... */ 3076 ba[k] = 1.0/dk; 3077 jmin = bi[k]; jmax = bi[k+1]; 3078 if (jmin < jmax) { 3079 for (j=jmin; j<jmax; j++){ 3080 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 3081 } 3082 /* ... add k to row list for first nonzero entry in k-th row */ 3083 il[k] = jmin; 3084 i = bj[jmin]; 3085 jl[k] = jl[i]; jl[i] = k; 3086 } 3087 } 3088 3089 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3090 ierr = PetscFree(il);CHKERRQ(ierr); 3091 ierr = PetscFree(jl);CHKERRQ(ierr); 3092 if (a->permute){ 3093 ierr = PetscFree(aa);CHKERRQ(ierr); 3094 } 3095 3096 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 3097 C->factor = FACTOR_CHOLESKY; 3098 C->assembled = PETSC_TRUE; 3099 C->preallocated = PETSC_TRUE; 3100 PLogFlops(b->mbs); 3101 PetscFunctionReturn(0); 3102 } 3103 3104 #undef __FUNC__ 3105 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 3106 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 3107 { 3108 int ierr; 3109 Mat C; 3110 3111 PetscFunctionBegin; 3112 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 3113 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 3114 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 3115 PetscFunctionReturn(0); 3116 } 3117 3118 3119