1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.46 2000/11/05 20:01:21 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,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 printf("called FactorNumeric_SeqSBAIJ_7_NaturalOrdering\n"); 699 /* initialization */ 700 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 701 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 702 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 703 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 704 for (i=0; i<mbs; i++) { 705 jl[i] = mbs; il[0] = 0; 706 } 707 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 708 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 709 710 ai = a->i; aj = a->j; aa = a->a; 711 712 /* for each row k */ 713 for (k = 0; k<mbs; k++){ 714 715 /*initialize k-th row with elements nonzero in row k of A */ 716 jmin = ai[k]; jmax = ai[k+1]; 717 if (jmin < jmax) { 718 ap = aa + jmin*49; 719 for (j = jmin; j < jmax; j++){ 720 vj = aj[j]; /* block col. index */ 721 wp = w + vj*49; 722 for (i=0; i<49; i++) *wp++ = *ap++; 723 } 724 } 725 726 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 727 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 728 i = jl[k]; /* first row to be added to k_th row */ 729 730 while (i < mbs){ 731 nexti = jl[i]; /* next row to be added to k_th row */ 732 733 /* compute multiplier */ 734 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 735 736 /* uik = -inv(Di)*U_bar(i,k) */ 737 d = ba + i*49; 738 u = ba + ili*49; 739 740 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]); 741 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]); 742 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]); 743 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]); 744 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]); 745 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]); 746 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]); 747 748 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]); 749 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]); 750 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]); 751 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]); 752 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]); 753 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]); 754 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]); 755 756 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]); 757 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]); 758 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]); 759 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]); 760 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]); 761 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]); 762 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]); 763 764 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]); 765 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]); 766 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]); 767 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]); 768 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]); 769 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]); 770 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]); 771 772 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]); 773 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]); 774 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]); 775 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]); 776 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]); 777 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]); 778 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]); 779 780 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]); 781 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]); 782 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]); 783 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]); 784 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]); 785 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]); 786 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]); 787 788 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]); 789 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]); 790 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]); 791 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]); 792 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]); 793 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]); 794 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]); 795 796 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 797 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]; 798 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]; 799 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]; 800 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]; 801 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]; 802 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]; 803 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]; 804 805 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]; 806 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]; 807 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]; 808 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]; 809 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]; 810 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]; 811 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]; 812 813 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]; 814 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]; 815 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]; 816 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]; 817 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]; 818 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]; 819 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]; 820 821 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]; 822 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]; 823 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]; 824 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]; 825 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]; 826 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]; 827 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]; 828 829 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]; 830 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]; 831 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]; 832 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]; 833 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]; 834 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]; 835 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]; 836 837 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]; 838 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]; 839 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]; 840 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]; 841 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]; 842 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]; 843 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]; 844 845 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]; 846 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]; 847 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]; 848 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]; 849 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]; 850 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]; 851 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]; 852 853 /* update -U(i,k) */ 854 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 855 856 /* add multiple of row i to k-th row ... */ 857 jmin = ili + 1; jmax = bi[i+1]; 858 if (jmin < jmax){ 859 for (j=jmin; j<jmax; j++) { 860 /* w += -U(i,k)^T * U_bar(i,j) */ 861 wp = w + bj[j]*49; 862 u = ba + j*49; 863 864 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]; 865 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]; 866 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]; 867 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]; 868 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]; 869 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]; 870 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]; 871 872 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]; 873 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]; 874 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]; 875 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]; 876 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]; 877 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]; 878 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]; 879 880 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]; 881 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]; 882 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]; 883 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]; 884 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]; 885 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]; 886 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]; 887 888 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]; 889 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]; 890 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]; 891 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]; 892 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]; 893 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]; 894 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]; 895 896 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]; 897 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]; 898 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]; 899 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]; 900 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]; 901 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]; 902 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]; 903 904 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]; 905 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]; 906 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]; 907 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]; 908 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]; 909 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]; 910 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]; 911 912 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]; 913 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]; 914 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]; 915 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]; 916 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]; 917 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]; 918 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]; 919 } 920 921 /* ... add i to row list for next nonzero entry */ 922 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 923 j = bj[jmin]; 924 jl[i] = jl[j]; jl[j] = i; /* update jl */ 925 } 926 i = nexti; 927 } 928 929 /* save nonzero entries in k-th row of U ... */ 930 931 /* invert diagonal block */ 932 d = ba+k*49; 933 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 934 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 935 936 jmin = bi[k]; jmax = bi[k+1]; 937 if (jmin < jmax) { 938 for (j=jmin; j<jmax; j++){ 939 vj = bj[j]; /* block col. index of U */ 940 u = ba + j*49; 941 wp = w + vj*49; 942 for (k1=0; k1<49; k1++){ 943 *u++ = *wp; 944 *wp++ = 0.0; 945 } 946 } 947 948 /* ... add k to row list for first nonzero entry in k-th row */ 949 il[k] = jmin; 950 i = bj[jmin]; 951 jl[k] = jl[i]; jl[i] = k; 952 } 953 } 954 955 ierr = PetscFree(w);CHKERRQ(ierr); 956 ierr = PetscFree(il);CHKERRQ(ierr); 957 ierr = PetscFree(jl);CHKERRQ(ierr); 958 ierr = PetscFree(dk);CHKERRQ(ierr); 959 ierr = PetscFree(uik);CHKERRQ(ierr); 960 961 C->factor = FACTOR_CHOLESKY; 962 C->assembled = PETSC_TRUE; 963 C->preallocated = PETSC_TRUE; 964 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 965 PetscFunctionReturn(0); 966 } 967 968 /* Version for when blocks are 6 by 6 */ 969 #undef __FUNC__ 970 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 971 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 972 { 973 Mat C = *B; 974 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 975 IS perm = b->row; 976 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 977 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 978 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 979 MatScalar *u,*d,*w,*wp; 980 981 PetscFunctionBegin; 982 /* initialization */ 983 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 984 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 985 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 986 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 987 for (i=0; i<mbs; i++) { 988 jl[i] = mbs; il[0] = 0; 989 } 990 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 991 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 992 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 993 994 /* check permutation */ 995 if (!a->permute){ 996 ai = a->i; aj = a->j; aa = a->a; 997 } else { 998 ai = a->inew; aj = a->jnew; 999 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1000 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1001 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1002 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1003 1004 for (i=0; i<mbs; i++){ 1005 jmin = ai[i]; jmax = ai[i+1]; 1006 for (j=jmin; j<jmax; j++){ 1007 while (a2anew[j] != j){ 1008 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1009 for (k1=0; k1<36; k1++){ 1010 dk[k1] = aa[k*36+k1]; 1011 aa[k*36+k1] = aa[j*36+k1]; 1012 aa[j*36+k1] = dk[k1]; 1013 } 1014 } 1015 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1016 if (i > aj[j]){ 1017 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1018 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 1019 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1020 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 1021 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 1022 } 1023 } 1024 } 1025 } 1026 ierr = PetscFree(a2anew);CHKERRA(ierr); 1027 } 1028 1029 /* for each row k */ 1030 for (k = 0; k<mbs; k++){ 1031 1032 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1033 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1034 if (jmin < jmax) { 1035 ap = aa + jmin*36; 1036 for (j = jmin; j < jmax; j++){ 1037 vj = perm_ptr[aj[j]]; /* block col. index */ 1038 wp = w + vj*36; 1039 for (i=0; i<36; i++) *wp++ = *ap++; 1040 } 1041 } 1042 1043 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1044 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1045 i = jl[k]; /* first row to be added to k_th row */ 1046 1047 while (i < mbs){ 1048 nexti = jl[i]; /* next row to be added to k_th row */ 1049 1050 /* compute multiplier */ 1051 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1052 1053 /* uik = -inv(Di)*U_bar(i,k) */ 1054 d = ba + i*36; 1055 u = ba + ili*36; 1056 1057 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]); 1058 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]); 1059 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]); 1060 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]); 1061 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]); 1062 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]); 1063 1064 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]); 1065 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]); 1066 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]); 1067 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]); 1068 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]); 1069 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]); 1070 1071 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]); 1072 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]); 1073 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]); 1074 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]); 1075 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]); 1076 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]); 1077 1078 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]); 1079 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]); 1080 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]); 1081 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]); 1082 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]); 1083 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]); 1084 1085 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]); 1086 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]); 1087 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]); 1088 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]); 1089 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]); 1090 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]); 1091 1092 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]); 1093 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]); 1094 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]); 1095 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]); 1096 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]); 1097 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]); 1098 1099 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1100 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]; 1101 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]; 1102 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]; 1103 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]; 1104 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]; 1105 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]; 1106 1107 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]; 1108 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]; 1109 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]; 1110 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]; 1111 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]; 1112 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]; 1113 1114 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]; 1115 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]; 1116 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]; 1117 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]; 1118 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]; 1119 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]; 1120 1121 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]; 1122 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]; 1123 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]; 1124 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]; 1125 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]; 1126 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]; 1127 1128 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]; 1129 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]; 1130 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]; 1131 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]; 1132 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]; 1133 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]; 1134 1135 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]; 1136 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]; 1137 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]; 1138 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]; 1139 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]; 1140 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]; 1141 1142 /* update -U(i,k) */ 1143 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1144 1145 /* add multiple of row i to k-th row ... */ 1146 jmin = ili + 1; jmax = bi[i+1]; 1147 if (jmin < jmax){ 1148 for (j=jmin; j<jmax; j++) { 1149 /* w += -U(i,k)^T * U_bar(i,j) */ 1150 wp = w + bj[j]*36; 1151 u = ba + j*36; 1152 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]; 1153 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]; 1154 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]; 1155 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]; 1156 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]; 1157 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]; 1158 1159 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]; 1160 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]; 1161 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]; 1162 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]; 1163 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]; 1164 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]; 1165 1166 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]; 1167 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]; 1168 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]; 1169 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]; 1170 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]; 1171 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]; 1172 1173 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]; 1174 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]; 1175 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]; 1176 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]; 1177 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]; 1178 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]; 1179 1180 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]; 1181 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]; 1182 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]; 1183 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]; 1184 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]; 1185 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]; 1186 1187 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]; 1188 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]; 1189 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]; 1190 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]; 1191 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]; 1192 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]; 1193 } 1194 1195 /* ... add i to row list for next nonzero entry */ 1196 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1197 j = bj[jmin]; 1198 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1199 } 1200 i = nexti; 1201 } 1202 1203 /* save nonzero entries in k-th row of U ... */ 1204 1205 /* invert diagonal block */ 1206 d = ba+k*36; 1207 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1208 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1209 1210 jmin = bi[k]; jmax = bi[k+1]; 1211 if (jmin < jmax) { 1212 for (j=jmin; j<jmax; j++){ 1213 vj = bj[j]; /* block col. index of U */ 1214 u = ba + j*36; 1215 wp = w + vj*36; 1216 for (k1=0; k1<36; k1++){ 1217 *u++ = *wp; 1218 *wp++ = 0.0; 1219 } 1220 } 1221 1222 /* ... add k to row list for first nonzero entry in k-th row */ 1223 il[k] = jmin; 1224 i = bj[jmin]; 1225 jl[k] = jl[i]; jl[i] = k; 1226 } 1227 } 1228 1229 ierr = PetscFree(w);CHKERRQ(ierr); 1230 ierr = PetscFree(il);CHKERRQ(ierr); 1231 ierr = PetscFree(jl);CHKERRQ(ierr); 1232 ierr = PetscFree(dk);CHKERRQ(ierr); 1233 ierr = PetscFree(uik);CHKERRQ(ierr); 1234 if (a->permute){ 1235 ierr = PetscFree(aa);CHKERRQ(ierr); 1236 } 1237 1238 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1239 C->factor = FACTOR_CHOLESKY; 1240 C->assembled = PETSC_TRUE; 1241 C->preallocated = PETSC_TRUE; 1242 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1243 PetscFunctionReturn(0); 1244 } 1245 1246 /* 1247 Version for when blocks are 6 by 6 Using natural ordering 1248 */ 1249 #undef __FUNC__ 1250 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1251 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1252 { 1253 Mat C = *B; 1254 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1255 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1256 int *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1257 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1258 MatScalar *u,*d,*w,*wp; 1259 1260 PetscFunctionBegin; 1261 printf("called FactorNumeric_SeqSBAIJ_6_NaturalOrdering\n"); 1262 /* initialization */ 1263 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 1264 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1265 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1266 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1267 for (i=0; i<mbs; i++) { 1268 jl[i] = mbs; il[0] = 0; 1269 } 1270 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 1271 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 1272 1273 ai = a->i; aj = a->j; aa = a->a; 1274 1275 /* for each row k */ 1276 for (k = 0; k<mbs; k++){ 1277 1278 /*initialize k-th row with elements nonzero in row k of A */ 1279 jmin = ai[k]; jmax = ai[k+1]; 1280 if (jmin < jmax) { 1281 ap = aa + jmin*36; 1282 for (j = jmin; j < jmax; j++){ 1283 vj = aj[j]; /* block col. index */ 1284 wp = w + vj*36; 1285 for (i=0; i<36; i++) *wp++ = *ap++; 1286 } 1287 } 1288 1289 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1290 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1291 i = jl[k]; /* first row to be added to k_th row */ 1292 1293 while (i < mbs){ 1294 nexti = jl[i]; /* next row to be added to k_th row */ 1295 1296 /* compute multiplier */ 1297 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1298 1299 /* uik = -inv(Di)*U_bar(i,k) */ 1300 d = ba + i*36; 1301 u = ba + ili*36; 1302 1303 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]); 1304 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]); 1305 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]); 1306 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]); 1307 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]); 1308 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]); 1309 1310 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]); 1311 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]); 1312 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]); 1313 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]); 1314 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]); 1315 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]); 1316 1317 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]); 1318 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]); 1319 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]); 1320 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]); 1321 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]); 1322 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]); 1323 1324 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]); 1325 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]); 1326 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]); 1327 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]); 1328 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]); 1329 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]); 1330 1331 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]); 1332 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]); 1333 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]); 1334 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]); 1335 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]); 1336 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]); 1337 1338 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]); 1339 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]); 1340 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]); 1341 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]); 1342 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]); 1343 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]); 1344 1345 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1346 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]; 1347 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]; 1348 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]; 1349 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]; 1350 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]; 1351 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]; 1352 1353 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]; 1354 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]; 1355 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]; 1356 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]; 1357 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]; 1358 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]; 1359 1360 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]; 1361 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]; 1362 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]; 1363 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]; 1364 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]; 1365 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]; 1366 1367 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]; 1368 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]; 1369 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]; 1370 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]; 1371 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]; 1372 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]; 1373 1374 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]; 1375 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]; 1376 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]; 1377 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]; 1378 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]; 1379 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]; 1380 1381 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]; 1382 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]; 1383 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]; 1384 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]; 1385 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]; 1386 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]; 1387 1388 /* update -U(i,k) */ 1389 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1390 1391 /* add multiple of row i to k-th row ... */ 1392 jmin = ili + 1; jmax = bi[i+1]; 1393 if (jmin < jmax){ 1394 for (j=jmin; j<jmax; j++) { 1395 /* w += -U(i,k)^T * U_bar(i,j) */ 1396 wp = w + bj[j]*36; 1397 u = ba + j*36; 1398 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]; 1399 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]; 1400 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]; 1401 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]; 1402 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]; 1403 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]; 1404 1405 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]; 1406 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]; 1407 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]; 1408 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]; 1409 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]; 1410 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]; 1411 1412 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]; 1413 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]; 1414 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]; 1415 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]; 1416 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]; 1417 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]; 1418 1419 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]; 1420 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]; 1421 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]; 1422 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]; 1423 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]; 1424 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]; 1425 1426 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]; 1427 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]; 1428 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]; 1429 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]; 1430 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]; 1431 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]; 1432 1433 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]; 1434 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]; 1435 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]; 1436 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]; 1437 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]; 1438 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]; 1439 } 1440 1441 /* ... add i to row list for next nonzero entry */ 1442 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1443 j = bj[jmin]; 1444 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1445 } 1446 i = nexti; 1447 } 1448 1449 /* save nonzero entries in k-th row of U ... */ 1450 1451 /* invert diagonal block */ 1452 d = ba+k*36; 1453 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1454 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1455 1456 jmin = bi[k]; jmax = bi[k+1]; 1457 if (jmin < jmax) { 1458 for (j=jmin; j<jmax; j++){ 1459 vj = bj[j]; /* block col. index of U */ 1460 u = ba + j*36; 1461 wp = w + vj*36; 1462 for (k1=0; k1<36; k1++){ 1463 *u++ = *wp; 1464 *wp++ = 0.0; 1465 } 1466 } 1467 1468 /* ... add k to row list for first nonzero entry in k-th row */ 1469 il[k] = jmin; 1470 i = bj[jmin]; 1471 jl[k] = jl[i]; jl[i] = k; 1472 } 1473 } 1474 1475 ierr = PetscFree(w);CHKERRQ(ierr); 1476 ierr = PetscFree(il);CHKERRQ(ierr); 1477 ierr = PetscFree(jl);CHKERRQ(ierr); 1478 ierr = PetscFree(dk);CHKERRQ(ierr); 1479 ierr = PetscFree(uik);CHKERRQ(ierr); 1480 1481 C->factor = FACTOR_CHOLESKY; 1482 C->assembled = PETSC_TRUE; 1483 C->preallocated = PETSC_TRUE; 1484 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1485 PetscFunctionReturn(0); 1486 } 1487 1488 /* Version for when blocks are 5 by 5 */ 1489 #undef __FUNC__ 1490 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1491 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1492 { 1493 Mat C = *B; 1494 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1495 IS perm = b->row; 1496 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1497 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1498 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1499 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1500 1501 PetscFunctionBegin; 1502 /* initialization */ 1503 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1504 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1505 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1506 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1507 for (i=0; i<mbs; i++) { 1508 jl[i] = mbs; il[0] = 0; 1509 } 1510 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1511 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1512 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1513 1514 /* check permutation */ 1515 if (!a->permute){ 1516 ai = a->i; aj = a->j; aa = a->a; 1517 } else { 1518 ai = a->inew; aj = a->jnew; 1519 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1520 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1521 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1522 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1523 1524 for (i=0; i<mbs; i++){ 1525 jmin = ai[i]; jmax = ai[i+1]; 1526 for (j=jmin; j<jmax; j++){ 1527 while (a2anew[j] != j){ 1528 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1529 for (k1=0; k1<25; k1++){ 1530 dk[k1] = aa[k*25+k1]; 1531 aa[k*25+k1] = aa[j*25+k1]; 1532 aa[j*25+k1] = dk[k1]; 1533 } 1534 } 1535 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1536 if (i > aj[j]){ 1537 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1538 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1539 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1540 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1541 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1542 } 1543 } 1544 } 1545 } 1546 ierr = PetscFree(a2anew);CHKERRA(ierr); 1547 } 1548 1549 /* for each row k */ 1550 for (k = 0; k<mbs; k++){ 1551 1552 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1553 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1554 if (jmin < jmax) { 1555 ap = aa + jmin*25; 1556 for (j = jmin; j < jmax; j++){ 1557 vj = perm_ptr[aj[j]]; /* block col. index */ 1558 rtmp_ptr = rtmp + vj*25; 1559 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1560 } 1561 } 1562 1563 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1564 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1565 i = jl[k]; /* first row to be added to k_th row */ 1566 1567 while (i < mbs){ 1568 nexti = jl[i]; /* next row to be added to k_th row */ 1569 1570 /* compute multiplier */ 1571 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1572 1573 /* uik = -inv(Di)*U_bar(i,k) */ 1574 d = ba + i*25; 1575 u = ba + ili*25; 1576 1577 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1578 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1579 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1580 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1581 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1582 1583 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1584 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1585 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1586 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1587 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1588 1589 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1590 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1591 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1592 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1593 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1594 1595 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1596 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1597 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1598 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1599 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1600 1601 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1602 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1603 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1604 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1605 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1606 1607 1608 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1609 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1610 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1611 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1612 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1613 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1614 1615 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1616 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1617 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1618 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1619 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1620 1621 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1622 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1623 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1624 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1625 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1626 1627 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1628 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1629 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1630 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1631 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1632 1633 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1634 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1635 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1636 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1637 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1638 1639 /* update -U(i,k) */ 1640 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1641 1642 /* add multiple of row i to k-th row ... */ 1643 jmin = ili + 1; jmax = bi[i+1]; 1644 if (jmin < jmax){ 1645 for (j=jmin; j<jmax; j++) { 1646 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1647 rtmp_ptr = rtmp + bj[j]*25; 1648 u = ba + j*25; 1649 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1650 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1651 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1652 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1653 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1654 1655 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1656 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1657 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1658 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1659 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1660 1661 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1662 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1663 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1664 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1665 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1666 1667 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1668 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1669 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1670 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1671 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1672 1673 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1674 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1675 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1676 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1677 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1678 } 1679 1680 /* ... add i to row list for next nonzero entry */ 1681 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1682 j = bj[jmin]; 1683 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1684 } 1685 i = nexti; 1686 } 1687 1688 /* save nonzero entries in k-th row of U ... */ 1689 1690 /* invert diagonal block */ 1691 d = ba+k*25; 1692 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1693 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1694 1695 jmin = bi[k]; jmax = bi[k+1]; 1696 if (jmin < jmax) { 1697 for (j=jmin; j<jmax; j++){ 1698 vj = bj[j]; /* block col. index of U */ 1699 u = ba + j*25; 1700 rtmp_ptr = rtmp + vj*25; 1701 for (k1=0; k1<25; k1++){ 1702 *u++ = *rtmp_ptr; 1703 *rtmp_ptr++ = 0.0; 1704 } 1705 } 1706 1707 /* ... add k to row list for first nonzero entry in k-th row */ 1708 il[k] = jmin; 1709 i = bj[jmin]; 1710 jl[k] = jl[i]; jl[i] = k; 1711 } 1712 } 1713 1714 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1715 ierr = PetscFree(il);CHKERRQ(ierr); 1716 ierr = PetscFree(jl);CHKERRQ(ierr); 1717 ierr = PetscFree(dk);CHKERRQ(ierr); 1718 ierr = PetscFree(uik);CHKERRQ(ierr); 1719 if (a->permute){ 1720 ierr = PetscFree(aa);CHKERRQ(ierr); 1721 } 1722 1723 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1724 C->factor = FACTOR_CHOLESKY; 1725 C->assembled = PETSC_TRUE; 1726 C->preallocated = PETSC_TRUE; 1727 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1728 PetscFunctionReturn(0); 1729 } 1730 1731 /* 1732 Version for when blocks are 5 by 5 Using natural ordering 1733 */ 1734 #undef __FUNC__ 1735 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1736 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1737 { 1738 Mat C = *B; 1739 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1740 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1741 int *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1742 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1743 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1744 1745 PetscFunctionBegin; 1746 printf("called FactorNumeric_SeqSBAIJ_5_NaturalOrdering\n"); 1747 /* initialization */ 1748 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1749 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1750 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1751 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1752 for (i=0; i<mbs; i++) { 1753 jl[i] = mbs; il[0] = 0; 1754 } 1755 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1756 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1757 1758 ai = a->i; aj = a->j; aa = a->a; 1759 1760 /* for each row k */ 1761 for (k = 0; k<mbs; k++){ 1762 1763 /*initialize k-th row with elements nonzero in row k of A */ 1764 jmin = ai[k]; jmax = ai[k+1]; 1765 if (jmin < jmax) { 1766 ap = aa + jmin*25; 1767 for (j = jmin; j < jmax; j++){ 1768 vj = aj[j]; /* block col. index */ 1769 rtmp_ptr = rtmp + vj*25; 1770 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1771 } 1772 } 1773 1774 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1775 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1776 i = jl[k]; /* first row to be added to k_th row */ 1777 1778 while (i < mbs){ 1779 nexti = jl[i]; /* next row to be added to k_th row */ 1780 1781 /* compute multiplier */ 1782 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1783 1784 /* uik = -inv(Di)*U_bar(i,k) */ 1785 d = ba + i*25; 1786 u = ba + ili*25; 1787 1788 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1789 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1790 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1791 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1792 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1793 1794 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1795 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1796 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1797 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1798 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1799 1800 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1801 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1802 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1803 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1804 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1805 1806 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1807 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1808 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1809 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1810 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1811 1812 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1813 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1814 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1815 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1816 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1817 1818 1819 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1820 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1821 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1822 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1823 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1824 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1825 1826 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1827 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1828 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1829 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1830 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1831 1832 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1833 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1834 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1835 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1836 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1837 1838 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1839 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1840 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1841 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1842 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1843 1844 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1845 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1846 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1847 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1848 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1849 1850 /* update -U(i,k) */ 1851 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1852 1853 /* add multiple of row i to k-th row ... */ 1854 jmin = ili + 1; jmax = bi[i+1]; 1855 if (jmin < jmax){ 1856 for (j=jmin; j<jmax; j++) { 1857 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1858 rtmp_ptr = rtmp + bj[j]*25; 1859 u = ba + j*25; 1860 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1861 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1862 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1863 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1864 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1865 1866 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1867 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1868 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1869 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1870 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1871 1872 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1873 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1874 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1875 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1876 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1877 1878 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1879 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1880 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1881 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1882 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1883 1884 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1885 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1886 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1887 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1888 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1889 } 1890 1891 /* ... add i to row list for next nonzero entry */ 1892 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1893 j = bj[jmin]; 1894 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1895 } 1896 i = nexti; 1897 } 1898 1899 /* save nonzero entries in k-th row of U ... */ 1900 1901 /* invert diagonal block */ 1902 d = ba+k*25; 1903 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1904 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1905 1906 jmin = bi[k]; jmax = bi[k+1]; 1907 if (jmin < jmax) { 1908 for (j=jmin; j<jmax; j++){ 1909 vj = bj[j]; /* block col. index of U */ 1910 u = ba + j*25; 1911 rtmp_ptr = rtmp + vj*25; 1912 for (k1=0; k1<25; k1++){ 1913 *u++ = *rtmp_ptr; 1914 *rtmp_ptr++ = 0.0; 1915 } 1916 } 1917 1918 /* ... add k to row list for first nonzero entry in k-th row */ 1919 il[k] = jmin; 1920 i = bj[jmin]; 1921 jl[k] = jl[i]; jl[i] = k; 1922 } 1923 } 1924 1925 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1926 ierr = PetscFree(il);CHKERRQ(ierr); 1927 ierr = PetscFree(jl);CHKERRQ(ierr); 1928 ierr = PetscFree(dk);CHKERRQ(ierr); 1929 ierr = PetscFree(uik);CHKERRQ(ierr); 1930 1931 C->factor = FACTOR_CHOLESKY; 1932 C->assembled = PETSC_TRUE; 1933 C->preallocated = PETSC_TRUE; 1934 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1935 PetscFunctionReturn(0); 1936 } 1937 1938 /* 1939 Version for when blocks are 4 by 4 Using natural ordering 1940 */ 1941 #undef __FUNC__ 1942 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1943 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1944 { 1945 Mat C = *B; 1946 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1947 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1948 int *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1949 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1950 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 1951 1952 PetscFunctionBegin; 1953 printf("called FactorNumeric_SeqSBAIJ_4_NaturalOrdering\n"); 1954 /* initialization */ 1955 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1956 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1957 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1958 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1959 for (i=0; i<mbs; i++) { 1960 jl[i] = mbs; il[0] = 0; 1961 } 1962 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 1963 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 1964 1965 ai = a->i; aj = a->j; aa = a->a; 1966 1967 /* for each row k */ 1968 for (k = 0; k<mbs; k++){ 1969 1970 /*initialize k-th row with elements nonzero in row k of A */ 1971 jmin = ai[k]; jmax = ai[k+1]; 1972 if (jmin < jmax) { 1973 ap = aa + jmin*16; 1974 for (j = jmin; j < jmax; j++){ 1975 vj = aj[j]; /* block col. index */ 1976 rtmp_ptr = rtmp + vj*16; 1977 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 1978 } 1979 } 1980 1981 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1982 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 1983 i = jl[k]; /* first row to be added to k_th row */ 1984 1985 while (i < mbs){ 1986 nexti = jl[i]; /* next row to be added to k_th row */ 1987 1988 /* compute multiplier */ 1989 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1990 1991 /* uik = -inv(Di)*U_bar(i,k) */ 1992 diag = ba + i*16; 1993 u = ba + ili*16; 1994 1995 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 1996 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 1997 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 1998 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 1999 2000 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2001 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2002 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2003 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2004 2005 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2006 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2007 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2008 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2009 2010 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2011 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2012 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2013 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2014 2015 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2016 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2017 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2018 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2019 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2020 2021 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2022 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2023 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2024 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2025 2026 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2027 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2028 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2029 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2030 2031 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2032 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2033 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2034 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2035 2036 /* update -U(i,k) */ 2037 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2038 2039 /* add multiple of row i to k-th row ... */ 2040 jmin = ili + 1; jmax = bi[i+1]; 2041 if (jmin < jmax){ 2042 for (j=jmin; j<jmax; j++) { 2043 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2044 rtmp_ptr = rtmp + bj[j]*16; 2045 u = ba + j*16; 2046 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2047 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2048 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2049 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2050 2051 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2052 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2053 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2054 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2055 2056 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2057 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2058 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2059 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2060 2061 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2062 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2063 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2064 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2065 } 2066 2067 /* ... add i to row list for next nonzero entry */ 2068 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2069 j = bj[jmin]; 2070 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2071 } 2072 i = nexti; 2073 } 2074 2075 /* save nonzero entries in k-th row of U ... */ 2076 2077 /* invert diagonal block */ 2078 diag = ba+k*16; 2079 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2080 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2081 2082 jmin = bi[k]; jmax = bi[k+1]; 2083 if (jmin < jmax) { 2084 for (j=jmin; j<jmax; j++){ 2085 vj = bj[j]; /* block col. index of U */ 2086 u = ba + j*16; 2087 rtmp_ptr = rtmp + vj*16; 2088 for (k1=0; k1<16; k1++){ 2089 *u++ = *rtmp_ptr; 2090 *rtmp_ptr++ = 0.0; 2091 } 2092 } 2093 2094 /* ... add k to row list for first nonzero entry in k-th row */ 2095 il[k] = jmin; 2096 i = bj[jmin]; 2097 jl[k] = jl[i]; jl[i] = k; 2098 } 2099 } 2100 2101 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2102 ierr = PetscFree(il);CHKERRQ(ierr); 2103 ierr = PetscFree(jl);CHKERRQ(ierr); 2104 ierr = PetscFree(dk);CHKERRQ(ierr); 2105 ierr = PetscFree(uik);CHKERRQ(ierr); 2106 2107 C->factor = FACTOR_CHOLESKY; 2108 C->assembled = PETSC_TRUE; 2109 C->preallocated = PETSC_TRUE; 2110 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2111 PetscFunctionReturn(0); 2112 } 2113 2114 /* Version for when blocks are 4 by 4 */ 2115 #undef __FUNC__ 2116 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 2117 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 2118 { 2119 Mat C = *B; 2120 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2121 IS perm = b->row; 2122 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2123 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2124 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2125 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2126 2127 PetscFunctionBegin; 2128 /* initialization */ 2129 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2130 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2131 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2132 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2133 for (i=0; i<mbs; i++) { 2134 jl[i] = mbs; il[0] = 0; 2135 } 2136 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 2137 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 2138 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2139 2140 /* check permutation */ 2141 if (!a->permute){ 2142 ai = a->i; aj = a->j; aa = a->a; 2143 } else { 2144 ai = a->inew; aj = a->jnew; 2145 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2146 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2147 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2148 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2149 2150 for (i=0; i<mbs; i++){ 2151 jmin = ai[i]; jmax = ai[i+1]; 2152 for (j=jmin; j<jmax; j++){ 2153 while (a2anew[j] != j){ 2154 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2155 for (k1=0; k1<16; k1++){ 2156 dk[k1] = aa[k*16+k1]; 2157 aa[k*16+k1] = aa[j*16+k1]; 2158 aa[j*16+k1] = dk[k1]; 2159 } 2160 } 2161 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2162 if (i > aj[j]){ 2163 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2164 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 2165 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2166 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 2167 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 2168 } 2169 } 2170 } 2171 } 2172 ierr = PetscFree(a2anew);CHKERRA(ierr); 2173 } 2174 2175 /* for each row k */ 2176 for (k = 0; k<mbs; k++){ 2177 2178 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2179 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2180 if (jmin < jmax) { 2181 ap = aa + jmin*16; 2182 for (j = jmin; j < jmax; j++){ 2183 vj = perm_ptr[aj[j]]; /* block col. index */ 2184 rtmp_ptr = rtmp + vj*16; 2185 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 2186 } 2187 } 2188 2189 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2190 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 2191 i = jl[k]; /* first row to be added to k_th row */ 2192 2193 while (i < mbs){ 2194 nexti = jl[i]; /* next row to be added to k_th row */ 2195 2196 /* compute multiplier */ 2197 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2198 2199 /* uik = -inv(Di)*U_bar(i,k) */ 2200 diag = ba + i*16; 2201 u = ba + ili*16; 2202 2203 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 2204 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 2205 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 2206 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 2207 2208 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2209 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2210 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2211 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2212 2213 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2214 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2215 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2216 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2217 2218 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2219 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2220 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2221 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2222 2223 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2224 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2225 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2226 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2227 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2228 2229 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2230 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2231 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2232 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2233 2234 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2235 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2236 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2237 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2238 2239 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2240 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2241 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2242 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2243 2244 /* update -U(i,k) */ 2245 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2246 2247 /* add multiple of row i to k-th row ... */ 2248 jmin = ili + 1; jmax = bi[i+1]; 2249 if (jmin < jmax){ 2250 for (j=jmin; j<jmax; j++) { 2251 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2252 rtmp_ptr = rtmp + bj[j]*16; 2253 u = ba + j*16; 2254 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2255 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2256 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2257 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2258 2259 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2260 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2261 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2262 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2263 2264 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2265 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2266 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2267 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2268 2269 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2270 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2271 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2272 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2273 } 2274 2275 /* ... add i to row list for next nonzero entry */ 2276 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2277 j = bj[jmin]; 2278 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2279 } 2280 i = nexti; 2281 } 2282 2283 /* save nonzero entries in k-th row of U ... */ 2284 2285 /* invert diagonal block */ 2286 diag = ba+k*16; 2287 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2288 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2289 2290 jmin = bi[k]; jmax = bi[k+1]; 2291 if (jmin < jmax) { 2292 for (j=jmin; j<jmax; j++){ 2293 vj = bj[j]; /* block col. index of U */ 2294 u = ba + j*16; 2295 rtmp_ptr = rtmp + vj*16; 2296 for (k1=0; k1<16; k1++){ 2297 *u++ = *rtmp_ptr; 2298 *rtmp_ptr++ = 0.0; 2299 } 2300 } 2301 2302 /* ... add k to row list for first nonzero entry in k-th row */ 2303 il[k] = jmin; 2304 i = bj[jmin]; 2305 jl[k] = jl[i]; jl[i] = k; 2306 } 2307 } 2308 2309 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2310 ierr = PetscFree(il);CHKERRQ(ierr); 2311 ierr = PetscFree(jl);CHKERRQ(ierr); 2312 ierr = PetscFree(dk);CHKERRQ(ierr); 2313 ierr = PetscFree(uik);CHKERRQ(ierr); 2314 if (a->permute){ 2315 ierr = PetscFree(aa);CHKERRQ(ierr); 2316 } 2317 2318 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2319 C->factor = FACTOR_CHOLESKY; 2320 C->assembled = PETSC_TRUE; 2321 C->preallocated = PETSC_TRUE; 2322 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2323 PetscFunctionReturn(0); 2324 } 2325 2326 /* Version for when blocks are 3 by 3 */ 2327 #undef __FUNC__ 2328 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2329 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2330 { 2331 Mat C = *B; 2332 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2333 IS perm = b->row; 2334 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2335 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2336 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2337 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2338 2339 PetscFunctionBegin; 2340 /* printf("called FactorNumeric_SeqSBAIJ_3\n"); */ 2341 /* initialization */ 2342 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2343 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2344 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2345 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2346 for (i=0; i<mbs; i++) { 2347 jl[i] = mbs; il[0] = 0; 2348 } 2349 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2350 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2351 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2352 2353 /* check permutation */ 2354 if (!a->permute){ 2355 ai = a->i; aj = a->j; aa = a->a; 2356 } else { 2357 ai = a->inew; aj = a->jnew; 2358 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2359 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2360 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2361 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2362 2363 for (i=0; i<mbs; i++){ 2364 jmin = ai[i]; jmax = ai[i+1]; 2365 for (j=jmin; j<jmax; j++){ 2366 while (a2anew[j] != j){ 2367 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2368 for (k1=0; k1<9; k1++){ 2369 dk[k1] = aa[k*9+k1]; 2370 aa[k*9+k1] = aa[j*9+k1]; 2371 aa[j*9+k1] = dk[k1]; 2372 } 2373 } 2374 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2375 if (i > aj[j]){ 2376 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2377 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2378 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2379 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2380 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2381 } 2382 } 2383 } 2384 } 2385 ierr = PetscFree(a2anew);CHKERRA(ierr); 2386 } 2387 2388 /* for each row k */ 2389 for (k = 0; k<mbs; k++){ 2390 2391 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2392 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2393 if (jmin < jmax) { 2394 ap = aa + jmin*9; 2395 for (j = jmin; j < jmax; j++){ 2396 vj = perm_ptr[aj[j]]; /* block col. index */ 2397 rtmp_ptr = rtmp + vj*9; 2398 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2399 } 2400 } 2401 2402 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2403 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2404 i = jl[k]; /* first row to be added to k_th row */ 2405 2406 while (i < mbs){ 2407 nexti = jl[i]; /* next row to be added to k_th row */ 2408 2409 /* compute multiplier */ 2410 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2411 2412 /* uik = -inv(Di)*U_bar(i,k) */ 2413 diag = ba + i*9; 2414 u = ba + ili*9; 2415 2416 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2417 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2418 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2419 2420 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2421 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2422 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2423 2424 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2425 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2426 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2427 2428 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2429 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2430 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2431 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2432 2433 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2434 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2435 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2436 2437 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2438 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2439 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2440 2441 /* update -U(i,k) */ 2442 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2443 2444 /* add multiple of row i to k-th row ... */ 2445 jmin = ili + 1; jmax = bi[i+1]; 2446 if (jmin < jmax){ 2447 for (j=jmin; j<jmax; j++) { 2448 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2449 rtmp_ptr = rtmp + bj[j]*9; 2450 u = ba + j*9; 2451 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2452 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2453 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2454 2455 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2456 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2457 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2458 2459 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2460 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2461 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2462 } 2463 2464 /* ... add i to row list for next nonzero entry */ 2465 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2466 j = bj[jmin]; 2467 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2468 } 2469 i = nexti; 2470 } 2471 2472 /* save nonzero entries in k-th row of U ... */ 2473 2474 /* invert diagonal block */ 2475 diag = ba+k*9; 2476 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2477 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2478 2479 jmin = bi[k]; jmax = bi[k+1]; 2480 if (jmin < jmax) { 2481 for (j=jmin; j<jmax; j++){ 2482 vj = bj[j]; /* block col. index of U */ 2483 u = ba + j*9; 2484 rtmp_ptr = rtmp + vj*9; 2485 for (k1=0; k1<9; k1++){ 2486 *u++ = *rtmp_ptr; 2487 *rtmp_ptr++ = 0.0; 2488 } 2489 } 2490 2491 /* ... add k to row list for first nonzero entry in k-th row */ 2492 il[k] = jmin; 2493 i = bj[jmin]; 2494 jl[k] = jl[i]; jl[i] = k; 2495 } 2496 } 2497 2498 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2499 ierr = PetscFree(il);CHKERRQ(ierr); 2500 ierr = PetscFree(jl);CHKERRQ(ierr); 2501 ierr = PetscFree(dk);CHKERRQ(ierr); 2502 ierr = PetscFree(uik);CHKERRQ(ierr); 2503 if (a->permute){ 2504 ierr = PetscFree(aa);CHKERRQ(ierr); 2505 } 2506 2507 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2508 C->factor = FACTOR_CHOLESKY; 2509 C->assembled = PETSC_TRUE; 2510 C->preallocated = PETSC_TRUE; 2511 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2512 PetscFunctionReturn(0); 2513 } 2514 2515 /* 2516 Version for when blocks are 3 by 3 Using natural ordering 2517 */ 2518 #undef __FUNC__ 2519 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2520 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B) 2521 { 2522 Mat C = *B; 2523 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2524 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2525 int *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2526 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2527 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2528 2529 PetscFunctionBegin; 2530 printf("called FactorNumeric_SeqSBAIJ_3_NaturalOrdering\n"); 2531 /* initialization */ 2532 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2533 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2534 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2535 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2536 for (i=0; i<mbs; i++) { 2537 jl[i] = mbs; il[0] = 0; 2538 } 2539 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2540 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2541 2542 ai = a->i; aj = a->j; aa = a->a; 2543 2544 /* for each row k */ 2545 for (k = 0; k<mbs; k++){ 2546 2547 /*initialize k-th row with elements nonzero in row k of A */ 2548 jmin = ai[k]; jmax = ai[k+1]; 2549 if (jmin < jmax) { 2550 ap = aa + jmin*9; 2551 for (j = jmin; j < jmax; j++){ 2552 vj = aj[j]; /* block col. index */ 2553 rtmp_ptr = rtmp + vj*9; 2554 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2555 } 2556 } 2557 2558 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2559 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2560 i = jl[k]; /* first row to be added to k_th row */ 2561 2562 while (i < mbs){ 2563 nexti = jl[i]; /* next row to be added to k_th row */ 2564 2565 /* compute multiplier */ 2566 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2567 2568 /* uik = -inv(Di)*U_bar(i,k) */ 2569 diag = ba + i*9; 2570 u = ba + ili*9; 2571 2572 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2573 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2574 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2575 2576 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2577 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2578 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2579 2580 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2581 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2582 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2583 2584 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2585 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2586 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2587 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2588 2589 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2590 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2591 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2592 2593 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2594 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2595 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2596 2597 /* update -U(i,k) */ 2598 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2599 2600 /* add multiple of row i to k-th row ... */ 2601 jmin = ili + 1; jmax = bi[i+1]; 2602 if (jmin < jmax){ 2603 for (j=jmin; j<jmax; j++) { 2604 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2605 rtmp_ptr = rtmp + bj[j]*9; 2606 u = ba + j*9; 2607 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2608 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2609 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2610 2611 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2612 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2613 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2614 2615 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2616 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2617 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2618 } 2619 2620 /* ... add i to row list for next nonzero entry */ 2621 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2622 j = bj[jmin]; 2623 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2624 } 2625 i = nexti; 2626 } 2627 2628 /* save nonzero entries in k-th row of U ... */ 2629 2630 /* invert diagonal block */ 2631 diag = ba+k*9; 2632 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2633 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2634 2635 jmin = bi[k]; jmax = bi[k+1]; 2636 if (jmin < jmax) { 2637 for (j=jmin; j<jmax; j++){ 2638 vj = bj[j]; /* block col. index of U */ 2639 u = ba + j*9; 2640 rtmp_ptr = rtmp + vj*9; 2641 for (k1=0; k1<9; k1++){ 2642 *u++ = *rtmp_ptr; 2643 *rtmp_ptr++ = 0.0; 2644 } 2645 } 2646 2647 /* ... add k to row list for first nonzero entry in k-th row */ 2648 il[k] = jmin; 2649 i = bj[jmin]; 2650 jl[k] = jl[i]; jl[i] = k; 2651 } 2652 } 2653 2654 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2655 ierr = PetscFree(il);CHKERRQ(ierr); 2656 ierr = PetscFree(jl);CHKERRQ(ierr); 2657 ierr = PetscFree(dk);CHKERRQ(ierr); 2658 ierr = PetscFree(uik);CHKERRQ(ierr); 2659 2660 C->factor = FACTOR_CHOLESKY; 2661 C->assembled = PETSC_TRUE; 2662 C->preallocated = PETSC_TRUE; 2663 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2664 PetscFunctionReturn(0); 2665 } 2666 2667 /* 2668 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2669 Version for blocks 2 by 2. 2670 */ 2671 #undef __FUNC__ 2672 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2673 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2674 { 2675 Mat C = *B; 2676 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2677 IS perm = b->row; 2678 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2679 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2680 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2681 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2682 2683 PetscFunctionBegin; 2684 /* printf("called FactorNumeric_SeqSBAIJ_2\n"); */ 2685 /* initialization */ 2686 /* il and jl record the first nonzero element in each row of the accessing 2687 window U(0:k, k:mbs-1). 2688 jl: list of rows to be added to uneliminated rows 2689 i>= k: jl(i) is the first row to be added to row i 2690 i< k: jl(i) is the row following row i in some list of rows 2691 jl(i) = mbs indicates the end of a list 2692 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2693 row i of U */ 2694 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2695 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2696 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2697 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2698 for (i=0; i<mbs; i++) { 2699 jl[i] = mbs; il[0] = 0; 2700 } 2701 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2702 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2703 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2704 2705 /* check permutation */ 2706 if (!a->permute){ 2707 ai = a->i; aj = a->j; aa = a->a; 2708 } else { 2709 ai = a->inew; aj = a->jnew; 2710 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2711 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2712 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2713 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2714 2715 for (i=0; i<mbs; i++){ 2716 jmin = ai[i]; jmax = ai[i+1]; 2717 for (j=jmin; j<jmax; j++){ 2718 while (a2anew[j] != j){ 2719 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2720 for (k1=0; k1<4; k1++){ 2721 dk[k1] = aa[k*4+k1]; 2722 aa[k*4+k1] = aa[j*4+k1]; 2723 aa[j*4+k1] = dk[k1]; 2724 } 2725 } 2726 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2727 if (i > aj[j]){ 2728 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2729 ap = aa + j*4; /* ptr to the beginning of the block */ 2730 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2731 ap[1] = ap[2]; 2732 ap[2] = dk[1]; 2733 } 2734 } 2735 } 2736 ierr = PetscFree(a2anew);CHKERRA(ierr); 2737 } 2738 2739 /* for each row k */ 2740 for (k = 0; k<mbs; k++){ 2741 2742 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2743 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2744 if (jmin < jmax) { 2745 ap = aa + jmin*4; 2746 for (j = jmin; j < jmax; j++){ 2747 vj = perm_ptr[aj[j]]; /* block col. index */ 2748 rtmp_ptr = rtmp + vj*4; 2749 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2750 } 2751 } 2752 2753 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2754 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2755 i = jl[k]; /* first row to be added to k_th row */ 2756 2757 while (i < mbs){ 2758 nexti = jl[i]; /* next row to be added to k_th row */ 2759 2760 /* compute multiplier */ 2761 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2762 2763 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2764 diag = ba + i*4; 2765 u = ba + ili*4; 2766 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2767 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2768 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2769 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2770 2771 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2772 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2773 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2774 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2775 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2776 2777 /* update -U(i,k): ba[ili] = uik */ 2778 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2779 2780 /* add multiple of row i to k-th row ... */ 2781 jmin = ili + 1; jmax = bi[i+1]; 2782 if (jmin < jmax){ 2783 for (j=jmin; j<jmax; j++) { 2784 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2785 rtmp_ptr = rtmp + bj[j]*4; 2786 u = ba + j*4; 2787 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2788 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2789 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2790 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2791 } 2792 2793 /* ... add i to row list for next nonzero entry */ 2794 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2795 j = bj[jmin]; 2796 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2797 } 2798 i = nexti; 2799 } 2800 2801 /* save nonzero entries in k-th row of U ... */ 2802 2803 /* invert diagonal block */ 2804 diag = ba+k*4; 2805 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2806 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2807 2808 jmin = bi[k]; jmax = bi[k+1]; 2809 if (jmin < jmax) { 2810 for (j=jmin; j<jmax; j++){ 2811 vj = bj[j]; /* block col. index of U */ 2812 u = ba + j*4; 2813 rtmp_ptr = rtmp + vj*4; 2814 for (k1=0; k1<4; k1++){ 2815 *u++ = *rtmp_ptr; 2816 *rtmp_ptr++ = 0.0; 2817 } 2818 } 2819 2820 /* ... add k to row list for first nonzero entry in k-th row */ 2821 il[k] = jmin; 2822 i = bj[jmin]; 2823 jl[k] = jl[i]; jl[i] = k; 2824 } 2825 } 2826 2827 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2828 ierr = PetscFree(il);CHKERRQ(ierr); 2829 ierr = PetscFree(jl);CHKERRQ(ierr); 2830 ierr = PetscFree(dk);CHKERRQ(ierr); 2831 ierr = PetscFree(uik);CHKERRQ(ierr); 2832 if (a->permute) { 2833 ierr = PetscFree(aa);CHKERRQ(ierr); 2834 } 2835 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2836 C->factor = FACTOR_CHOLESKY; 2837 C->assembled = PETSC_TRUE; 2838 C->preallocated = PETSC_TRUE; 2839 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2840 PetscFunctionReturn(0); 2841 } 2842 2843 /* 2844 Version for when blocks are 2 by 2 Using natural ordering 2845 */ 2846 #undef __FUNC__ 2847 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2848 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2849 { 2850 Mat C = *B; 2851 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2852 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2853 int *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2854 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2855 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2856 2857 PetscFunctionBegin; 2858 printf("called FactorNumeric_SeqSBAIJ_2_NaturalOrdering\n"); 2859 /* initialization */ 2860 /* il and jl record the first nonzero element in each row of the accessing 2861 window U(0:k, k:mbs-1). 2862 jl: list of rows to be added to uneliminated rows 2863 i>= k: jl(i) is the first row to be added to row i 2864 i< k: jl(i) is the row following row i in some list of rows 2865 jl(i) = mbs indicates the end of a list 2866 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2867 row i of U */ 2868 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2869 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2870 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2871 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2872 for (i=0; i<mbs; i++) { 2873 jl[i] = mbs; il[0] = 0; 2874 } 2875 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2876 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2877 2878 ai = a->i; aj = a->j; aa = a->a; 2879 2880 /* for each row k */ 2881 for (k = 0; k<mbs; k++){ 2882 2883 /*initialize k-th row with elements nonzero in row k of A */ 2884 jmin = ai[k]; jmax = ai[k+1]; 2885 if (jmin < jmax) { 2886 ap = aa + jmin*4; 2887 for (j = jmin; j < jmax; j++){ 2888 vj = aj[j]; /* block col. index */ 2889 rtmp_ptr = rtmp + vj*4; 2890 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2891 } 2892 } 2893 2894 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2895 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2896 i = jl[k]; /* first row to be added to k_th row */ 2897 2898 while (i < mbs){ 2899 nexti = jl[i]; /* next row to be added to k_th row */ 2900 2901 /* compute multiplier */ 2902 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2903 2904 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2905 diag = ba + i*4; 2906 u = ba + ili*4; 2907 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2908 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2909 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2910 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2911 2912 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2913 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2914 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2915 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2916 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2917 2918 /* update -U(i,k): ba[ili] = uik */ 2919 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2920 2921 /* add multiple of row i to k-th row ... */ 2922 jmin = ili + 1; jmax = bi[i+1]; 2923 if (jmin < jmax){ 2924 for (j=jmin; j<jmax; j++) { 2925 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2926 rtmp_ptr = rtmp + bj[j]*4; 2927 u = ba + j*4; 2928 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2929 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2930 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2931 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2932 } 2933 2934 /* ... add i to row list for next nonzero entry */ 2935 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2936 j = bj[jmin]; 2937 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2938 } 2939 i = nexti; 2940 } 2941 2942 /* save nonzero entries in k-th row of U ... */ 2943 2944 /* invert diagonal block */ 2945 diag = ba+k*4; 2946 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2947 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2948 2949 jmin = bi[k]; jmax = bi[k+1]; 2950 if (jmin < jmax) { 2951 for (j=jmin; j<jmax; j++){ 2952 vj = bj[j]; /* block col. index of U */ 2953 u = ba + j*4; 2954 rtmp_ptr = rtmp + vj*4; 2955 for (k1=0; k1<4; k1++){ 2956 *u++ = *rtmp_ptr; 2957 *rtmp_ptr++ = 0.0; 2958 } 2959 } 2960 2961 /* ... add k to row list for first nonzero entry in k-th row */ 2962 il[k] = jmin; 2963 i = bj[jmin]; 2964 jl[k] = jl[i]; jl[i] = k; 2965 } 2966 } 2967 2968 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2969 ierr = PetscFree(il);CHKERRQ(ierr); 2970 ierr = PetscFree(jl);CHKERRQ(ierr); 2971 ierr = PetscFree(dk);CHKERRQ(ierr); 2972 ierr = PetscFree(uik);CHKERRQ(ierr); 2973 2974 C->factor = FACTOR_CHOLESKY; 2975 C->assembled = PETSC_TRUE; 2976 C->preallocated = PETSC_TRUE; 2977 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2978 PetscFunctionReturn(0); 2979 } 2980 2981 /* 2982 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2983 Version for blocks are 1 by 1. 2984 */ 2985 #undef __FUNC__ 2986 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2987 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2988 { 2989 Mat C = *B; 2990 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2991 IS ip = b->row; 2992 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2993 int *ai,*aj,*r; 2994 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2995 MatScalar *rtmp; 2996 MatScalar *ba = b->a,*aa,ak; 2997 MatScalar dk,uikdi; 2998 2999 PetscFunctionBegin; 3000 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 3001 if (!a->permute){ 3002 ai = a->i; aj = a->j; aa = a->a; 3003 } else { 3004 ai = a->inew; aj = a->jnew; 3005 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 3006 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 3007 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 3008 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 3009 3010 jmin = ai[0]; jmax = ai[mbs]; 3011 for (j=jmin; j<jmax; j++){ 3012 while (r[j] != j){ 3013 k = r[j]; r[j] = r[k]; r[k] = k; 3014 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 3015 } 3016 } 3017 ierr = PetscFree(r);CHKERRA(ierr); 3018 } 3019 3020 /* initialization */ 3021 /* il and jl record the first nonzero element in each row of the accessing 3022 window U(0:k, k:mbs-1). 3023 jl: list of rows to be added to uneliminated rows 3024 i>= k: jl(i) is the first row to be added to row i 3025 i< k: jl(i) is the row following row i in some list of rows 3026 jl(i) = mbs indicates the end of a list 3027 il(i): points to the first nonzero element in columns k,...,mbs-1 of 3028 row i of U */ 3029 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 3030 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 3031 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 3032 for (i=0; i<mbs; i++) { 3033 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 3034 } 3035 3036 /* for each row k */ 3037 for (k = 0; k<mbs; k++){ 3038 3039 /*initialize k-th row with elements nonzero in row perm(k) of A */ 3040 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 3041 if (jmin < jmax) { 3042 for (j = jmin; j < jmax; j++){ 3043 vj = rip[aj[j]]; 3044 rtmp[vj] = aa[j]; 3045 } 3046 } 3047 3048 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 3049 dk = rtmp[k]; 3050 i = jl[k]; /* first row to be added to k_th row */ 3051 3052 while (i < mbs){ 3053 nexti = jl[i]; /* next row to be added to k_th row */ 3054 3055 /* compute multiplier, update D(k) and U(i,k) */ 3056 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 3057 uikdi = - ba[ili]*ba[i]; 3058 dk += uikdi*ba[ili]; 3059 ba[ili] = uikdi; /* -U(i,k) */ 3060 3061 /* add multiple of row i to k-th row ... */ 3062 jmin = ili + 1; jmax = bi[i+1]; 3063 if (jmin < jmax){ 3064 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 3065 /* ... add i to row list for next nonzero entry */ 3066 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 3067 j = bj[jmin]; 3068 jl[i] = jl[j]; jl[j] = i; /* update jl */ 3069 } 3070 i = nexti; 3071 } 3072 3073 /* check for zero pivot and save diagoanl element */ 3074 if (dk == 0.0){ 3075 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 3076 }else if (PetscRealPart(dk) < 0){ 3077 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 3078 } 3079 3080 /* save nonzero entries in k-th row of U ... */ 3081 ba[k] = 1.0/dk; 3082 jmin = bi[k]; jmax = bi[k+1]; 3083 if (jmin < jmax) { 3084 for (j=jmin; j<jmax; j++){ 3085 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 3086 } 3087 /* ... add k to row list for first nonzero entry in k-th row */ 3088 il[k] = jmin; 3089 i = bj[jmin]; 3090 jl[k] = jl[i]; jl[i] = k; 3091 } 3092 } 3093 3094 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3095 ierr = PetscFree(il);CHKERRQ(ierr); 3096 ierr = PetscFree(jl);CHKERRQ(ierr); 3097 if (a->permute){ 3098 ierr = PetscFree(aa);CHKERRQ(ierr); 3099 } 3100 3101 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 3102 C->factor = FACTOR_CHOLESKY; 3103 C->assembled = PETSC_TRUE; 3104 C->preallocated = PETSC_TRUE; 3105 PLogFlops(b->mbs); 3106 PetscFunctionReturn(0); 3107 } 3108 3109 #undef __FUNC__ 3110 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 3111 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 3112 { 3113 int ierr; 3114 Mat C; 3115 3116 PetscFunctionBegin; 3117 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 3118 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 3119 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 3120 PetscFunctionReturn(0); 3121 } 3122 3123 3124