1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.40 2000/11/01 16:46:00 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 /* initialization */ 211 printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n"); 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 #ifdef OLD 362 Mat C = *B; 363 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 364 IS isrow = b->row,isicol = b->icol; 365 int *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 366 int *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg; 367 int *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj; 368 MatScalar *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w; 369 370 PetscFunctionBegin; 371 printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n"); 372 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 373 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 374 rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 375 ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr); 376 /* generate work space needed by dense LU factorization */ 377 v_work = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work); 378 multiplier = v_work + bs; 379 v_pivots = (int*)(multiplier + bs2); 380 381 /* flops in while loop */ 382 bslog = 2*bs*bs2; 383 384 for (i=0; i<n; i++) { 385 nz = bi[i+1] - bi[i]; 386 ajtmp = bj + bi[i]; 387 for (j=0; j<nz; j++) { 388 ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 389 } 390 /* load in initial (unfactored row) */ 391 nz = ai[r[i]+1] - ai[r[i]]; 392 ajtmpold = aj + ai[r[i]]; 393 v = aa + bs2*ai[r[i]]; 394 for (j=0; j<nz; j++) { 395 ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr); 396 } 397 row = *ajtmp++; 398 while (row < i) { 399 pc = rtmp + bs2*row; 400 /* if (*pc) { */ 401 for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }} 402 if (flg) { 403 pv = ba + bs2*diag_offset[row]; 404 pj = bj + diag_offset[row] + 1; 405 Kernel_A_gets_A_times_B(bs,pc,pv,multiplier); 406 nz = bi[row+1] - diag_offset[row] - 1; 407 pv += bs2; 408 for (j=0; j<nz; j++) { 409 Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); 410 } 411 PLogFlops(bslog*(nz+1)-bs); 412 } 413 row = *ajtmp++; 414 } 415 /* finished row so stick it into b->a */ 416 pv = ba + bs2*bi[i]; 417 pj = bj + bi[i]; 418 nz = bi[i+1] - bi[i]; 419 for (j=0; j<nz; j++) { 420 ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 421 } 422 diag = diag_offset[i] - bi[i]; 423 /* invert diagonal block */ 424 w = pv + bs2*diag; 425 Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work); 426 } 427 428 ierr = PetscFree(rtmp);CHKERRQ(ierr); 429 ierr = PetscFree(v_work);CHKERRQ(ierr); 430 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 431 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 432 C->factor = FACTOR_LU; 433 C->assembled = PETSC_TRUE; 434 #endif 435 436 /* Version for when blocks are 7 by 7 */ 437 #undef __FUNC__ 438 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7" 439 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B) 440 { 441 Mat C = *B; 442 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 443 IS perm = b->row; 444 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 445 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 446 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 447 MatScalar *u,*d,*w,*wp; 448 449 PetscFunctionBegin; 450 /* initialization */ 451 printf("called MatCholeskyFactorNumeric_SeqSBAIJ_7 \n"); 452 w = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w); 453 ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr); 454 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 455 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 456 for (i=0; i<mbs; i++) { 457 jl[i] = mbs; il[0] = 0; 458 } 459 dk = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk); 460 uik = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik); 461 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 462 463 /* check permutation */ 464 if (!a->permute){ 465 ai = a->i; aj = a->j; aa = a->a; 466 } else { 467 ai = a->inew; aj = a->jnew; 468 aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 469 ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 470 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 471 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 472 473 for (i=0; i<mbs; i++){ 474 jmin = ai[i]; jmax = ai[i+1]; 475 for (j=jmin; j<jmax; j++){ 476 while (a2anew[j] != j){ 477 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 478 for (k1=0; k1<49; k1++){ 479 dk[k1] = aa[k*49+k1]; 480 aa[k*49+k1] = aa[j*49+k1]; 481 aa[j*49+k1] = dk[k1]; 482 } 483 } 484 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 485 if (i > aj[j]){ 486 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 487 ap = aa + j*49; /* ptr to the beginning of j-th block of aa */ 488 for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 489 for (k=0; k<7; k++){ /* j-th block of aa <- dk^T */ 490 for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1]; 491 } 492 } 493 } 494 } 495 ierr = PetscFree(a2anew);CHKERRA(ierr); 496 } 497 498 /* for each row k */ 499 for (k = 0; k<mbs; k++){ 500 501 /*initialize k-th row with elements nonzero in row perm(k) of A */ 502 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 503 if (jmin < jmax) { 504 ap = aa + jmin*49; 505 for (j = jmin; j < jmax; j++){ 506 vj = perm_ptr[aj[j]]; /* block col. index */ 507 wp = w + vj*49; 508 for (i=0; i<49; i++) *wp++ = *ap++; 509 } 510 } 511 512 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 513 ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr); 514 i = jl[k]; /* first row to be added to k_th row */ 515 516 while (i < mbs){ 517 nexti = jl[i]; /* next row to be added to k_th row */ 518 519 /* compute multiplier */ 520 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 521 522 /* uik = -inv(Di)*U_bar(i,k) */ 523 d = ba + i*49; 524 u = ba + ili*49; 525 526 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]); 527 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]); 528 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]); 529 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]); 530 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]); 531 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]); 532 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]); 533 534 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]); 535 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]); 536 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]); 537 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]); 538 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]); 539 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]); 540 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]); 541 542 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]); 543 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]); 544 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]); 545 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]); 546 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]); 547 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]); 548 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]); 549 550 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]); 551 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]); 552 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]); 553 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]); 554 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]); 555 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]); 556 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]); 557 558 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]); 559 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]); 560 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]); 561 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]); 562 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]); 563 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]); 564 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]); 565 566 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]); 567 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]); 568 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]); 569 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]); 570 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]); 571 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]); 572 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]); 573 574 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]); 575 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]); 576 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]); 577 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]); 578 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]); 579 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]); 580 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]); 581 582 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 583 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]; 584 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]; 585 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]; 586 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]; 587 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]; 588 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]; 589 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]; 590 591 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]; 592 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]; 593 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]; 594 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]; 595 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]; 596 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]; 597 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]; 598 599 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]; 600 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]; 601 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]; 602 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]; 603 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]; 604 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]; 605 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]; 606 607 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]; 608 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]; 609 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]; 610 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]; 611 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]; 612 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]; 613 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]; 614 615 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]; 616 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]; 617 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]; 618 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]; 619 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]; 620 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]; 621 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]; 622 623 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]; 624 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]; 625 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]; 626 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]; 627 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]; 628 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]; 629 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]; 630 631 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]; 632 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]; 633 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]; 634 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]; 635 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]; 636 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]; 637 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]; 638 639 /* update -U(i,k) */ 640 ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr); 641 642 /* add multiple of row i to k-th row ... */ 643 jmin = ili + 1; jmax = bi[i+1]; 644 if (jmin < jmax){ 645 for (j=jmin; j<jmax; j++) { 646 /* w += -U(i,k)^T * U_bar(i,j) */ 647 wp = w + bj[j]*49; 648 u = ba + j*49; 649 650 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]; 651 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]; 652 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]; 653 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]; 654 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]; 655 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]; 656 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]; 657 658 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]; 659 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]; 660 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]; 661 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]; 662 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]; 663 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]; 664 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]; 665 666 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]; 667 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]; 668 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]; 669 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]; 670 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]; 671 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]; 672 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]; 673 674 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]; 675 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]; 676 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]; 677 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]; 678 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]; 679 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]; 680 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]; 681 682 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]; 683 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]; 684 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]; 685 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]; 686 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]; 687 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]; 688 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]; 689 690 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]; 691 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]; 692 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]; 693 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]; 694 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]; 695 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]; 696 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]; 697 698 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]; 699 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]; 700 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]; 701 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]; 702 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]; 703 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]; 704 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]; 705 } 706 707 /* ... add i to row list for next nonzero entry */ 708 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 709 j = bj[jmin]; 710 jl[i] = jl[j]; jl[j] = i; /* update jl */ 711 } 712 i = nexti; 713 } 714 715 /* save nonzero entries in k-th row of U ... */ 716 717 /* invert diagonal block */ 718 d = ba+k*49; 719 ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr); 720 ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr); 721 722 jmin = bi[k]; jmax = bi[k+1]; 723 if (jmin < jmax) { 724 for (j=jmin; j<jmax; j++){ 725 vj = bj[j]; /* block col. index of U */ 726 u = ba + j*49; 727 wp = w + vj*49; 728 for (k1=0; k1<49; k1++){ 729 *u++ = *wp; 730 *wp++ = 0.0; 731 } 732 } 733 734 /* ... add k to row list for first nonzero entry in k-th row */ 735 il[k] = jmin; 736 i = bj[jmin]; 737 jl[k] = jl[i]; jl[i] = k; 738 } 739 } 740 741 ierr = PetscFree(w);CHKERRQ(ierr); 742 ierr = PetscFree(il);CHKERRQ(ierr); 743 ierr = PetscFree(jl);CHKERRQ(ierr); 744 ierr = PetscFree(dk);CHKERRQ(ierr); 745 ierr = PetscFree(uik);CHKERRQ(ierr); 746 if (a->permute){ 747 ierr = PetscFree(aa);CHKERRQ(ierr); 748 } 749 750 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 751 C->factor = FACTOR_CHOLESKY; 752 C->assembled = PETSC_TRUE; 753 C->preallocated = PETSC_TRUE; 754 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 755 PetscFunctionReturn(0); 756 } 757 758 /* 759 Version for when blocks are 7 by 7 Using natural ordering 760 */ 761 #undef __FUNC__ 762 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering" 763 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B) 764 { 765 Mat C = *B; 766 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 767 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 768 int *ajtmpold,*ajtmp,nz,row; 769 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 770 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 771 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 772 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 773 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 774 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 775 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 776 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 777 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 778 MatScalar p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49; 779 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 780 MatScalar x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49; 781 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 782 MatScalar m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49; 783 MatScalar *ba = b->a,*aa = a->a; 784 785 PetscFunctionBegin; 786 rtmp = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 787 for (i=0; i<n; i++) { 788 nz = bi[i+1] - bi[i]; 789 ajtmp = bj + bi[i]; 790 for (j=0; j<nz; j++) { 791 x = rtmp+49*ajtmp[j]; 792 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 793 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 794 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 795 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 796 x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ; 797 x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ; 798 } 799 /* load in initial (unfactored row) */ 800 nz = ai[i+1] - ai[i]; 801 ajtmpold = aj + ai[i]; 802 v = aa + 49*ai[i]; 803 for (j=0; j<nz; j++) { 804 x = rtmp+49*ajtmpold[j]; 805 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 806 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 807 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 808 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 809 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 810 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 811 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 812 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 813 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 814 x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39]; 815 x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43]; 816 x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47]; 817 x[48] = v[48]; 818 v += 49; 819 } 820 row = *ajtmp++; 821 while (row < i) { 822 pc = rtmp + 49*row; 823 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 824 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 825 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 826 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 827 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 828 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 829 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 830 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 831 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 832 p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39]; 833 p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43]; 834 p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47]; 835 p49 = pc[48]; 836 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 837 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 838 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 839 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 840 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 841 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 842 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 843 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 844 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || 845 p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || 846 p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || 847 p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || 848 p49 != 0.0) { 849 pv = ba + 49*diag_offset[row]; 850 pj = bj + diag_offset[row] + 1; 851 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 852 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 853 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 854 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 855 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 856 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 857 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 858 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 859 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 860 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 861 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 862 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 863 x49 = pv[48]; 864 pc[0] = m1 = p1*x1 + p8*x2 + p15*x3 + p22*x4 + p29*x5 + p36*x6 + p43*x7; 865 pc[1] = m2 = p2*x1 + p9*x2 + p16*x3 + p23*x4 + p30*x5 + p37*x6 + p44*x7; 866 pc[2] = m3 = p3*x1 + p10*x2 + p17*x3 + p24*x4 + p31*x5 + p38*x6 + p45*x7; 867 pc[3] = m4 = p4*x1 + p11*x2 + p18*x3 + p25*x4 + p32*x5 + p39*x6 + p46*x7; 868 pc[4] = m5 = p5*x1 + p12*x2 + p19*x3 + p26*x4 + p33*x5 + p40*x6 + p47*x7; 869 pc[5] = m6 = p6*x1 + p13*x2 + p20*x3 + p27*x4 + p34*x5 + p41*x6 + p48*x7; 870 pc[6] = m7 = p7*x1 + p14*x2 + p21*x3 + p28*x4 + p35*x5 + p42*x6 + p49*x7; 871 872 pc[7] = m8 = p1*x8 + p8*x9 + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14; 873 pc[8] = m9 = p2*x8 + p9*x9 + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14; 874 pc[9] = m10 = p3*x8 + p10*x9 + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14; 875 pc[10] = m11 = p4*x8 + p11*x9 + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14; 876 pc[11] = m12 = p5*x8 + p12*x9 + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14; 877 pc[12] = m13 = p6*x8 + p13*x9 + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14; 878 pc[13] = m14 = p7*x8 + p14*x9 + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14; 879 880 pc[14] = m15 = p1*x15 + p8*x16 + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21; 881 pc[15] = m16 = p2*x15 + p9*x16 + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21; 882 pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21; 883 pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21; 884 pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21; 885 pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21; 886 pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21; 887 888 pc[21] = m22 = p1*x22 + p8*x23 + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28; 889 pc[22] = m23 = p2*x22 + p9*x23 + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28; 890 pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28; 891 pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28; 892 pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28; 893 pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28; 894 pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28; 895 896 pc[28] = m29 = p1*x29 + p8*x30 + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35; 897 pc[29] = m30 = p2*x29 + p9*x30 + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35; 898 pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35; 899 pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35; 900 pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35; 901 pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35; 902 pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35; 903 904 pc[35] = m36 = p1*x36 + p8*x37 + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42; 905 pc[36] = m37 = p2*x36 + p9*x37 + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42; 906 pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42; 907 pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42; 908 pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42; 909 pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42; 910 pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42; 911 912 pc[42] = m43 = p1*x43 + p8*x44 + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49; 913 pc[43] = m44 = p2*x43 + p9*x44 + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49; 914 pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49; 915 pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49; 916 pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49; 917 pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49; 918 pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49; 919 920 nz = bi[row+1] - diag_offset[row] - 1; 921 pv += 49; 922 for (j=0; j<nz; j++) { 923 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 924 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 925 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 926 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 927 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 928 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 929 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 930 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 931 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 932 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 933 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 934 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 935 x49 = pv[48]; 936 x = rtmp + 49*pj[j]; 937 x[0] -= m1*x1 + m8*x2 + m15*x3 + m22*x4 + m29*x5 + m36*x6 + m43*x7; 938 x[1] -= m2*x1 + m9*x2 + m16*x3 + m23*x4 + m30*x5 + m37*x6 + m44*x7; 939 x[2] -= m3*x1 + m10*x2 + m17*x3 + m24*x4 + m31*x5 + m38*x6 + m45*x7; 940 x[3] -= m4*x1 + m11*x2 + m18*x3 + m25*x4 + m32*x5 + m39*x6 + m46*x7; 941 x[4] -= m5*x1 + m12*x2 + m19*x3 + m26*x4 + m33*x5 + m40*x6 + m47*x7; 942 x[5] -= m6*x1 + m13*x2 + m20*x3 + m27*x4 + m34*x5 + m41*x6 + m48*x7; 943 x[6] -= m7*x1 + m14*x2 + m21*x3 + m28*x4 + m35*x5 + m42*x6 + m49*x7; 944 945 x[7] -= m1*x8 + m8*x9 + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14; 946 x[8] -= m2*x8 + m9*x9 + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14; 947 x[9] -= m3*x8 + m10*x9 + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14; 948 x[10] -= m4*x8 + m11*x9 + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14; 949 x[11] -= m5*x8 + m12*x9 + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14; 950 x[12] -= m6*x8 + m13*x9 + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14; 951 x[13] -= m7*x8 + m14*x9 + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14; 952 953 x[14] -= m1*x15 + m8*x16 + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21; 954 x[15] -= m2*x15 + m9*x16 + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21; 955 x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21; 956 x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21; 957 x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21; 958 x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21; 959 x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21; 960 961 x[21] -= m1*x22 + m8*x23 + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28; 962 x[22] -= m2*x22 + m9*x23 + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28; 963 x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28; 964 x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28; 965 x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28; 966 x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28; 967 x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28; 968 969 x[28] -= m1*x29 + m8*x30 + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35; 970 x[29] -= m2*x29 + m9*x30 + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35; 971 x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35; 972 x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35; 973 x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35; 974 x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35; 975 x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35; 976 977 x[35] -= m1*x36 + m8*x37 + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42; 978 x[36] -= m2*x36 + m9*x37 + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42; 979 x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42; 980 x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42; 981 x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42; 982 x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42; 983 x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42; 984 985 x[42] -= m1*x43 + m8*x44 + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49; 986 x[43] -= m2*x43 + m9*x44 + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49; 987 x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49; 988 x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49; 989 x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49; 990 x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49; 991 x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49; 992 pv += 49; 993 } 994 PLogFlops(686*nz+637); 995 } 996 row = *ajtmp++; 997 } 998 /* finished row so stick it into b->a */ 999 pv = ba + 49*bi[i]; 1000 pj = bj + bi[i]; 1001 nz = bi[i+1] - bi[i]; 1002 for (j=0; j<nz; j++) { 1003 x = rtmp+49*pj[j]; 1004 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1005 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 1006 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 1007 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1008 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 1009 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 1010 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 1011 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 1012 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 1013 pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39]; 1014 pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43]; 1015 pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47]; 1016 pv[48] = x[48]; 1017 pv += 49; 1018 } 1019 /* invert diagonal block */ 1020 w = ba + 49*diag_offset[i]; 1021 ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr); 1022 } 1023 1024 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1025 C->factor = FACTOR_LU; 1026 C->assembled = PETSC_TRUE; 1027 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 1028 PetscFunctionReturn(0); 1029 } 1030 1031 /* Version for when blocks are 6 by 6 */ 1032 #undef __FUNC__ 1033 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 1034 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 1035 { 1036 Mat C = *B; 1037 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1038 IS perm = b->row; 1039 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1040 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1041 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1042 MatScalar *u,*d,*w,*wp; 1043 1044 PetscFunctionBegin; 1045 /* initialization */ 1046 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 1047 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1048 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1049 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1050 for (i=0; i<mbs; i++) { 1051 jl[i] = mbs; il[0] = 0; 1052 } 1053 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 1054 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 1055 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1056 1057 /* check permutation */ 1058 if (!a->permute){ 1059 ai = a->i; aj = a->j; aa = a->a; 1060 } else { 1061 ai = a->inew; aj = a->jnew; 1062 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1063 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1064 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1065 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1066 1067 for (i=0; i<mbs; i++){ 1068 jmin = ai[i]; jmax = ai[i+1]; 1069 for (j=jmin; j<jmax; j++){ 1070 while (a2anew[j] != j){ 1071 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1072 for (k1=0; k1<36; k1++){ 1073 dk[k1] = aa[k*36+k1]; 1074 aa[k*36+k1] = aa[j*36+k1]; 1075 aa[j*36+k1] = dk[k1]; 1076 } 1077 } 1078 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1079 if (i > aj[j]){ 1080 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1081 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 1082 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1083 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 1084 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 1085 } 1086 } 1087 } 1088 } 1089 ierr = PetscFree(a2anew);CHKERRA(ierr); 1090 } 1091 1092 /* for each row k */ 1093 for (k = 0; k<mbs; k++){ 1094 1095 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1096 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1097 if (jmin < jmax) { 1098 ap = aa + jmin*36; 1099 for (j = jmin; j < jmax; j++){ 1100 vj = perm_ptr[aj[j]]; /* block col. index */ 1101 wp = w + vj*36; 1102 for (i=0; i<36; i++) *wp++ = *ap++; 1103 } 1104 } 1105 1106 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1107 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 1108 i = jl[k]; /* first row to be added to k_th row */ 1109 1110 while (i < mbs){ 1111 nexti = jl[i]; /* next row to be added to k_th row */ 1112 1113 /* compute multiplier */ 1114 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1115 1116 /* uik = -inv(Di)*U_bar(i,k) */ 1117 d = ba + i*36; 1118 u = ba + ili*36; 1119 1120 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]); 1121 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]); 1122 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]); 1123 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]); 1124 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]); 1125 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]); 1126 1127 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]); 1128 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]); 1129 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]); 1130 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]); 1131 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]); 1132 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]); 1133 1134 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]); 1135 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]); 1136 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]); 1137 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]); 1138 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]); 1139 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]); 1140 1141 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]); 1142 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]); 1143 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]); 1144 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]); 1145 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]); 1146 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]); 1147 1148 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]); 1149 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]); 1150 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]); 1151 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]); 1152 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]); 1153 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]); 1154 1155 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]); 1156 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]); 1157 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]); 1158 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]); 1159 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]); 1160 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]); 1161 1162 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1163 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]; 1164 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]; 1165 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]; 1166 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]; 1167 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]; 1168 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]; 1169 1170 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]; 1171 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]; 1172 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]; 1173 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]; 1174 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]; 1175 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]; 1176 1177 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]; 1178 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]; 1179 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]; 1180 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]; 1181 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]; 1182 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]; 1183 1184 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]; 1185 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]; 1186 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]; 1187 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]; 1188 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]; 1189 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]; 1190 1191 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]; 1192 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]; 1193 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]; 1194 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]; 1195 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]; 1196 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]; 1197 1198 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]; 1199 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]; 1200 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]; 1201 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]; 1202 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]; 1203 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]; 1204 1205 /* update -U(i,k) */ 1206 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1207 1208 /* add multiple of row i to k-th row ... */ 1209 jmin = ili + 1; jmax = bi[i+1]; 1210 if (jmin < jmax){ 1211 for (j=jmin; j<jmax; j++) { 1212 /* w += -U(i,k)^T * U_bar(i,j) */ 1213 wp = w + bj[j]*36; 1214 u = ba + j*36; 1215 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]; 1216 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]; 1217 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]; 1218 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]; 1219 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]; 1220 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]; 1221 1222 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]; 1223 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]; 1224 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]; 1225 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]; 1226 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]; 1227 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]; 1228 1229 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]; 1230 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]; 1231 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]; 1232 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]; 1233 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]; 1234 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]; 1235 1236 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]; 1237 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]; 1238 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]; 1239 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]; 1240 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]; 1241 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]; 1242 1243 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]; 1244 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]; 1245 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]; 1246 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]; 1247 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]; 1248 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]; 1249 1250 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]; 1251 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]; 1252 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]; 1253 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]; 1254 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]; 1255 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]; 1256 } 1257 1258 /* ... add i to row list for next nonzero entry */ 1259 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1260 j = bj[jmin]; 1261 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1262 } 1263 i = nexti; 1264 } 1265 1266 /* save nonzero entries in k-th row of U ... */ 1267 1268 /* invert diagonal block */ 1269 d = ba+k*36; 1270 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1271 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1272 1273 jmin = bi[k]; jmax = bi[k+1]; 1274 if (jmin < jmax) { 1275 for (j=jmin; j<jmax; j++){ 1276 vj = bj[j]; /* block col. index of U */ 1277 u = ba + j*36; 1278 wp = w + vj*36; 1279 for (k1=0; k1<36; k1++){ 1280 *u++ = *wp; 1281 *wp++ = 0.0; 1282 } 1283 } 1284 1285 /* ... add k to row list for first nonzero entry in k-th row */ 1286 il[k] = jmin; 1287 i = bj[jmin]; 1288 jl[k] = jl[i]; jl[i] = k; 1289 } 1290 } 1291 1292 ierr = PetscFree(w);CHKERRQ(ierr); 1293 ierr = PetscFree(il);CHKERRQ(ierr); 1294 ierr = PetscFree(jl);CHKERRQ(ierr); 1295 ierr = PetscFree(dk);CHKERRQ(ierr); 1296 ierr = PetscFree(uik);CHKERRQ(ierr); 1297 if (a->permute){ 1298 ierr = PetscFree(aa);CHKERRQ(ierr); 1299 } 1300 1301 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1302 C->factor = FACTOR_CHOLESKY; 1303 C->assembled = PETSC_TRUE; 1304 C->preallocated = PETSC_TRUE; 1305 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1306 PetscFunctionReturn(0); 1307 } 1308 1309 /* 1310 Version for when blocks are 6 by 6 Using natural ordering 1311 */ 1312 #undef __FUNC__ 1313 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1314 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1315 { 1316 Mat C = *B; 1317 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1318 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1319 int *ajtmpold,*ajtmp,nz,row; 1320 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1321 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1322 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1323 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1324 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1325 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1326 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1327 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1328 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 1329 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 1330 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 1331 MatScalar *ba = b->a,*aa = a->a; 1332 1333 PetscFunctionBegin; 1334 rtmp = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1335 for (i=0; i<n; i++) { 1336 nz = bi[i+1] - bi[i]; 1337 ajtmp = bj + bi[i]; 1338 for (j=0; j<nz; j++) { 1339 x = rtmp+36*ajtmp[j]; 1340 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1341 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 1342 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 1343 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 1344 x[34] = x[35] = 0.0 ; 1345 } 1346 /* load in initial (unfactored row) */ 1347 nz = ai[i+1] - ai[i]; 1348 ajtmpold = aj + ai[i]; 1349 v = aa + 36*ai[i]; 1350 for (j=0; j<nz; j++) { 1351 x = rtmp+36*ajtmpold[j]; 1352 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1353 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 1354 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 1355 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 1356 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 1357 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1358 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 1359 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 1360 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 1361 v += 36; 1362 } 1363 row = *ajtmp++; 1364 while (row < i) { 1365 pc = rtmp + 36*row; 1366 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1367 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 1368 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 1369 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 1370 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 1371 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 1372 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 1373 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 1374 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 1375 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 1376 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 1377 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 1378 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 1379 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 1380 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 1381 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 1382 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 1383 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) { 1384 pv = ba + 36*diag_offset[row]; 1385 pj = bj + diag_offset[row] + 1; 1386 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1387 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1388 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1389 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1390 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1391 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1392 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1393 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1394 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1395 pc[0] = m1 = p1*x1 + p7*x2 + p13*x3 + p19*x4 + p25*x5 + p31*x6; 1396 pc[1] = m2 = p2*x1 + p8*x2 + p14*x3 + p20*x4 + p26*x5 + p32*x6; 1397 pc[2] = m3 = p3*x1 + p9*x2 + p15*x3 + p21*x4 + p27*x5 + p33*x6; 1398 pc[3] = m4 = p4*x1 + p10*x2 + p16*x3 + p22*x4 + p28*x5 + p34*x6; 1399 pc[4] = m5 = p5*x1 + p11*x2 + p17*x3 + p23*x4 + p29*x5 + p35*x6; 1400 pc[5] = m6 = p6*x1 + p12*x2 + p18*x3 + p24*x4 + p30*x5 + p36*x6; 1401 1402 pc[6] = m7 = p1*x7 + p7*x8 + p13*x9 + p19*x10 + p25*x11 + p31*x12; 1403 pc[7] = m8 = p2*x7 + p8*x8 + p14*x9 + p20*x10 + p26*x11 + p32*x12; 1404 pc[8] = m9 = p3*x7 + p9*x8 + p15*x9 + p21*x10 + p27*x11 + p33*x12; 1405 pc[9] = m10 = p4*x7 + p10*x8 + p16*x9 + p22*x10 + p28*x11 + p34*x12; 1406 pc[10] = m11 = p5*x7 + p11*x8 + p17*x9 + p23*x10 + p29*x11 + p35*x12; 1407 pc[11] = m12 = p6*x7 + p12*x8 + p18*x9 + p24*x10 + p30*x11 + p36*x12; 1408 1409 pc[12] = m13 = p1*x13 + p7*x14 + p13*x15 + p19*x16 + p25*x17 + p31*x18; 1410 pc[13] = m14 = p2*x13 + p8*x14 + p14*x15 + p20*x16 + p26*x17 + p32*x18; 1411 pc[14] = m15 = p3*x13 + p9*x14 + p15*x15 + p21*x16 + p27*x17 + p33*x18; 1412 pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18; 1413 pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18; 1414 pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18; 1415 1416 pc[18] = m19 = p1*x19 + p7*x20 + p13*x21 + p19*x22 + p25*x23 + p31*x24; 1417 pc[19] = m20 = p2*x19 + p8*x20 + p14*x21 + p20*x22 + p26*x23 + p32*x24; 1418 pc[20] = m21 = p3*x19 + p9*x20 + p15*x21 + p21*x22 + p27*x23 + p33*x24; 1419 pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24; 1420 pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24; 1421 pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24; 1422 1423 pc[24] = m25 = p1*x25 + p7*x26 + p13*x27 + p19*x28 + p25*x29 + p31*x30; 1424 pc[25] = m26 = p2*x25 + p8*x26 + p14*x27 + p20*x28 + p26*x29 + p32*x30; 1425 pc[26] = m27 = p3*x25 + p9*x26 + p15*x27 + p21*x28 + p27*x29 + p33*x30; 1426 pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30; 1427 pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30; 1428 pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30; 1429 1430 pc[30] = m31 = p1*x31 + p7*x32 + p13*x33 + p19*x34 + p25*x35 + p31*x36; 1431 pc[31] = m32 = p2*x31 + p8*x32 + p14*x33 + p20*x34 + p26*x35 + p32*x36; 1432 pc[32] = m33 = p3*x31 + p9*x32 + p15*x33 + p21*x34 + p27*x35 + p33*x36; 1433 pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36; 1434 pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36; 1435 pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36; 1436 1437 nz = bi[row+1] - diag_offset[row] - 1; 1438 pv += 36; 1439 for (j=0; j<nz; j++) { 1440 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1441 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1442 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1443 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1444 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1445 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1446 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1447 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1448 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1449 x = rtmp + 36*pj[j]; 1450 x[0] -= m1*x1 + m7*x2 + m13*x3 + m19*x4 + m25*x5 + m31*x6; 1451 x[1] -= m2*x1 + m8*x2 + m14*x3 + m20*x4 + m26*x5 + m32*x6; 1452 x[2] -= m3*x1 + m9*x2 + m15*x3 + m21*x4 + m27*x5 + m33*x6; 1453 x[3] -= m4*x1 + m10*x2 + m16*x3 + m22*x4 + m28*x5 + m34*x6; 1454 x[4] -= m5*x1 + m11*x2 + m17*x3 + m23*x4 + m29*x5 + m35*x6; 1455 x[5] -= m6*x1 + m12*x2 + m18*x3 + m24*x4 + m30*x5 + m36*x6; 1456 1457 x[6] -= m1*x7 + m7*x8 + m13*x9 + m19*x10 + m25*x11 + m31*x12; 1458 x[7] -= m2*x7 + m8*x8 + m14*x9 + m20*x10 + m26*x11 + m32*x12; 1459 x[8] -= m3*x7 + m9*x8 + m15*x9 + m21*x10 + m27*x11 + m33*x12; 1460 x[9] -= m4*x7 + m10*x8 + m16*x9 + m22*x10 + m28*x11 + m34*x12; 1461 x[10] -= m5*x7 + m11*x8 + m17*x9 + m23*x10 + m29*x11 + m35*x12; 1462 x[11] -= m6*x7 + m12*x8 + m18*x9 + m24*x10 + m30*x11 + m36*x12; 1463 1464 x[12] -= m1*x13 + m7*x14 + m13*x15 + m19*x16 + m25*x17 + m31*x18; 1465 x[13] -= m2*x13 + m8*x14 + m14*x15 + m20*x16 + m26*x17 + m32*x18; 1466 x[14] -= m3*x13 + m9*x14 + m15*x15 + m21*x16 + m27*x17 + m33*x18; 1467 x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18; 1468 x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18; 1469 x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18; 1470 1471 x[18] -= m1*x19 + m7*x20 + m13*x21 + m19*x22 + m25*x23 + m31*x24; 1472 x[19] -= m2*x19 + m8*x20 + m14*x21 + m20*x22 + m26*x23 + m32*x24; 1473 x[20] -= m3*x19 + m9*x20 + m15*x21 + m21*x22 + m27*x23 + m33*x24; 1474 x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24; 1475 x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24; 1476 x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24; 1477 1478 x[24] -= m1*x25 + m7*x26 + m13*x27 + m19*x28 + m25*x29 + m31*x30; 1479 x[25] -= m2*x25 + m8*x26 + m14*x27 + m20*x28 + m26*x29 + m32*x30; 1480 x[26] -= m3*x25 + m9*x26 + m15*x27 + m21*x28 + m27*x29 + m33*x30; 1481 x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30; 1482 x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30; 1483 x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30; 1484 1485 x[30] -= m1*x31 + m7*x32 + m13*x33 + m19*x34 + m25*x35 + m31*x36; 1486 x[31] -= m2*x31 + m8*x32 + m14*x33 + m20*x34 + m26*x35 + m32*x36; 1487 x[32] -= m3*x31 + m9*x32 + m15*x33 + m21*x34 + m27*x35 + m33*x36; 1488 x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36; 1489 x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36; 1490 x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36; 1491 1492 pv += 36; 1493 } 1494 PLogFlops(432*nz+396); 1495 } 1496 row = *ajtmp++; 1497 } 1498 /* finished row so stick it into b->a */ 1499 pv = ba + 36*bi[i]; 1500 pj = bj + bi[i]; 1501 nz = bi[i+1] - bi[i]; 1502 for (j=0; j<nz; j++) { 1503 x = rtmp+36*pj[j]; 1504 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1505 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 1506 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 1507 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1508 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 1509 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 1510 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 1511 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 1512 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 1513 pv += 36; 1514 } 1515 /* invert diagonal block */ 1516 w = ba + 36*diag_offset[i]; 1517 ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr); 1518 } 1519 1520 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1521 C->factor = FACTOR_LU; 1522 C->assembled = PETSC_TRUE; 1523 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1524 PetscFunctionReturn(0); 1525 } 1526 1527 /* Version for when blocks are 5 by 5 */ 1528 #undef __FUNC__ 1529 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1530 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1531 { 1532 Mat C = *B; 1533 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1534 IS perm = b->row; 1535 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1536 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1537 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1538 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1539 1540 PetscFunctionBegin; 1541 /* initialization */ 1542 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1543 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1544 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1545 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1546 for (i=0; i<mbs; i++) { 1547 jl[i] = mbs; il[0] = 0; 1548 } 1549 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1550 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1551 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1552 1553 /* check permutation */ 1554 if (!a->permute){ 1555 ai = a->i; aj = a->j; aa = a->a; 1556 } else { 1557 ai = a->inew; aj = a->jnew; 1558 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1559 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1560 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1561 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1562 1563 for (i=0; i<mbs; i++){ 1564 jmin = ai[i]; jmax = ai[i+1]; 1565 for (j=jmin; j<jmax; j++){ 1566 while (a2anew[j] != j){ 1567 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1568 for (k1=0; k1<25; k1++){ 1569 dk[k1] = aa[k*25+k1]; 1570 aa[k*25+k1] = aa[j*25+k1]; 1571 aa[j*25+k1] = dk[k1]; 1572 } 1573 } 1574 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1575 if (i > aj[j]){ 1576 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1577 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1578 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1579 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1580 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1581 } 1582 } 1583 } 1584 } 1585 ierr = PetscFree(a2anew);CHKERRA(ierr); 1586 } 1587 1588 /* for each row k */ 1589 for (k = 0; k<mbs; k++){ 1590 1591 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1592 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1593 if (jmin < jmax) { 1594 ap = aa + jmin*25; 1595 for (j = jmin; j < jmax; j++){ 1596 vj = perm_ptr[aj[j]]; /* block col. index */ 1597 rtmp_ptr = rtmp + vj*25; 1598 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1599 } 1600 } 1601 1602 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1603 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1604 i = jl[k]; /* first row to be added to k_th row */ 1605 1606 while (i < mbs){ 1607 nexti = jl[i]; /* next row to be added to k_th row */ 1608 1609 /* compute multiplier */ 1610 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1611 1612 /* uik = -inv(Di)*U_bar(i,k) */ 1613 d = ba + i*25; 1614 u = ba + ili*25; 1615 1616 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1617 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1618 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1619 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1620 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1621 1622 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1623 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1624 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1625 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1626 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1627 1628 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1629 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1630 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1631 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1632 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1633 1634 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1635 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1636 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1637 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1638 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1639 1640 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1641 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1642 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1643 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1644 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1645 1646 1647 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1648 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1649 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1650 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1651 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1652 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1653 1654 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1655 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1656 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1657 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1658 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1659 1660 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1661 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1662 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1663 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1664 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1665 1666 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1667 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1668 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1669 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1670 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1671 1672 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1673 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1674 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1675 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1676 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1677 1678 /* update -U(i,k) */ 1679 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1680 1681 /* add multiple of row i to k-th row ... */ 1682 jmin = ili + 1; jmax = bi[i+1]; 1683 if (jmin < jmax){ 1684 for (j=jmin; j<jmax; j++) { 1685 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1686 rtmp_ptr = rtmp + bj[j]*25; 1687 u = ba + j*25; 1688 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1689 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1690 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1691 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1692 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1693 1694 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1695 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1696 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1697 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1698 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1699 1700 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1701 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1702 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1703 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1704 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1705 1706 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1707 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1708 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1709 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1710 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1711 1712 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1713 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1714 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1715 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1716 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1717 } 1718 1719 /* ... add i to row list for next nonzero entry */ 1720 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1721 j = bj[jmin]; 1722 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1723 } 1724 i = nexti; 1725 } 1726 1727 /* save nonzero entries in k-th row of U ... */ 1728 1729 /* invert diagonal block */ 1730 d = ba+k*25; 1731 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1732 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1733 1734 jmin = bi[k]; jmax = bi[k+1]; 1735 if (jmin < jmax) { 1736 for (j=jmin; j<jmax; j++){ 1737 vj = bj[j]; /* block col. index of U */ 1738 u = ba + j*25; 1739 rtmp_ptr = rtmp + vj*25; 1740 for (k1=0; k1<25; k1++){ 1741 *u++ = *rtmp_ptr; 1742 *rtmp_ptr++ = 0.0; 1743 } 1744 } 1745 1746 /* ... add k to row list for first nonzero entry in k-th row */ 1747 il[k] = jmin; 1748 i = bj[jmin]; 1749 jl[k] = jl[i]; jl[i] = k; 1750 } 1751 } 1752 1753 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1754 ierr = PetscFree(il);CHKERRQ(ierr); 1755 ierr = PetscFree(jl);CHKERRQ(ierr); 1756 ierr = PetscFree(dk);CHKERRQ(ierr); 1757 ierr = PetscFree(uik);CHKERRQ(ierr); 1758 if (a->permute){ 1759 ierr = PetscFree(aa);CHKERRQ(ierr); 1760 } 1761 1762 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1763 C->factor = FACTOR_CHOLESKY; 1764 C->assembled = PETSC_TRUE; 1765 C->preallocated = PETSC_TRUE; 1766 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1767 PetscFunctionReturn(0); 1768 } 1769 1770 /* 1771 Version for when blocks are 5 by 5 Using natural ordering 1772 */ 1773 #undef __FUNC__ 1774 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1775 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1776 { 1777 Mat C = *B; 1778 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1779 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1780 int *ajtmpold,*ajtmp,nz,row; 1781 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1782 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1783 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1784 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1785 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1786 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1787 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1788 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1789 MatScalar *ba = b->a,*aa = a->a; 1790 1791 PetscFunctionBegin; 1792 rtmp = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1793 for (i=0; i<n; i++) { 1794 nz = bi[i+1] - bi[i]; 1795 ajtmp = bj + bi[i]; 1796 for (j=0; j<nz; j++) { 1797 x = rtmp+25*ajtmp[j]; 1798 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1799 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1800 x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 1801 } 1802 /* load in initial (unfactored row) */ 1803 nz = ai[i+1] - ai[i]; 1804 ajtmpold = aj + ai[i]; 1805 v = aa + 25*ai[i]; 1806 for (j=0; j<nz; j++) { 1807 x = rtmp+25*ajtmpold[j]; 1808 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1809 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1810 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1811 x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; 1812 x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1813 x[24] = v[24]; 1814 v += 25; 1815 } 1816 row = *ajtmp++; 1817 while (row < i) { 1818 pc = rtmp + 25*row; 1819 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1820 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1821 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1822 p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; 1823 p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; 1824 p24 = pc[23]; p25 = pc[24]; 1825 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1826 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1827 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1828 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 1829 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 1830 pv = ba + 25*diag_offset[row]; 1831 pj = bj + diag_offset[row] + 1; 1832 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1833 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1834 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1835 x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; 1836 x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1837 x25 = pv[24]; 1838 pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5; 1839 pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5; 1840 pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5; 1841 pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5; 1842 pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5; 1843 1844 pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10; 1845 pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10; 1846 pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10; 1847 pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10; 1848 pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10; 1849 1850 pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15; 1851 pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15; 1852 pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15; 1853 pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15; 1854 pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15; 1855 1856 pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20; 1857 pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20; 1858 pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20; 1859 pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20; 1860 pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20; 1861 1862 pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25; 1863 pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25; 1864 pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25; 1865 pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25; 1866 pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25; 1867 1868 nz = bi[row+1] - diag_offset[row] - 1; 1869 pv += 25; 1870 for (j=0; j<nz; j++) { 1871 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1872 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1873 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1874 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; 1875 x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; 1876 x24 = pv[23]; x25 = pv[24]; 1877 x = rtmp + 25*pj[j]; 1878 x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5; 1879 x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5; 1880 x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5; 1881 x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5; 1882 x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5; 1883 1884 x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10; 1885 x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10; 1886 x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10; 1887 x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10; 1888 x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10; 1889 1890 x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15; 1891 x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15; 1892 x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15; 1893 x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15; 1894 x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15; 1895 1896 x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20; 1897 x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20; 1898 x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20; 1899 x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20; 1900 x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20; 1901 1902 x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25; 1903 x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25; 1904 x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25; 1905 x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25; 1906 x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25; 1907 pv += 25; 1908 } 1909 PLogFlops(250*nz+225); 1910 } 1911 row = *ajtmp++; 1912 } 1913 /* finished row so stick it into b->a */ 1914 pv = ba + 25*bi[i]; 1915 pj = bj + bi[i]; 1916 nz = bi[i+1] - bi[i]; 1917 for (j=0; j<nz; j++) { 1918 x = rtmp+25*pj[j]; 1919 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1920 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1921 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1922 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17]; 1923 pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; 1924 pv[23] = x[23]; pv[24] = x[24]; 1925 pv += 25; 1926 } 1927 /* invert diagonal block */ 1928 w = ba + 25*diag_offset[i]; 1929 ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr); 1930 } 1931 1932 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1933 C->factor = FACTOR_LU; 1934 C->assembled = PETSC_TRUE; 1935 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1936 PetscFunctionReturn(0); 1937 } 1938 1939 /* 1940 Version for when blocks are 4 by 4 Using natural ordering 1941 */ 1942 #undef __FUNC__ 1943 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1944 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1945 { 1946 Mat C = *B; 1947 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1948 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1949 int *ajtmpold,*ajtmp,nz,row; 1950 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1951 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1952 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 1953 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; 1954 MatScalar p10,p11,p12,p13,p14,p15,p16,m10,m11,m12; 1955 MatScalar m13,m14,m15,m16; 1956 MatScalar *ba = b->a,*aa = a->a; 1957 1958 PetscFunctionBegin; 1959 rtmp = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1960 1961 for (i=0; i<n; i++) { 1962 nz = bi[i+1] - bi[i]; 1963 ajtmp = bj + bi[i]; 1964 for (j=0; j<nz; j++) { 1965 x = rtmp+16*ajtmp[j]; 1966 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1967 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1968 } 1969 /* load in initial (unfactored row) */ 1970 nz = ai[i+1] - ai[i]; 1971 ajtmpold = aj + ai[i]; 1972 v = aa + 16*ai[i]; 1973 for (j=0; j<nz; j++) { 1974 x = rtmp+16*ajtmpold[j]; 1975 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1976 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1977 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1978 x[14] = v[14]; x[15] = v[15]; 1979 v += 16; 1980 } 1981 row = *ajtmp++; 1982 while (row < i) { 1983 pc = rtmp + 16*row; 1984 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1985 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1986 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1987 p15 = pc[14]; p16 = pc[15]; 1988 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1989 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1990 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1991 || p16 != 0.0) { 1992 pv = ba + 16*diag_offset[row]; 1993 pj = bj + diag_offset[row] + 1; 1994 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1995 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1996 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1997 x15 = pv[14]; x16 = pv[15]; 1998 pc[0] = m1 = p1*x1 + p5*x2 + p9*x3 + p13*x4; 1999 pc[1] = m2 = p2*x1 + p6*x2 + p10*x3 + p14*x4; 2000 pc[2] = m3 = p3*x1 + p7*x2 + p11*x3 + p15*x4; 2001 pc[3] = m4 = p4*x1 + p8*x2 + p12*x3 + p16*x4; 2002 2003 pc[4] = m5 = p1*x5 + p5*x6 + p9*x7 + p13*x8; 2004 pc[5] = m6 = p2*x5 + p6*x6 + p10*x7 + p14*x8; 2005 pc[6] = m7 = p3*x5 + p7*x6 + p11*x7 + p15*x8; 2006 pc[7] = m8 = p4*x5 + p8*x6 + p12*x7 + p16*x8; 2007 2008 pc[8] = m9 = p1*x9 + p5*x10 + p9*x11 + p13*x12; 2009 pc[9] = m10 = p2*x9 + p6*x10 + p10*x11 + p14*x12; 2010 pc[10] = m11 = p3*x9 + p7*x10 + p11*x11 + p15*x12; 2011 pc[11] = m12 = p4*x9 + p8*x10 + p12*x11 + p16*x12; 2012 2013 pc[12] = m13 = p1*x13 + p5*x14 + p9*x15 + p13*x16; 2014 pc[13] = m14 = p2*x13 + p6*x14 + p10*x15 + p14*x16; 2015 pc[14] = m15 = p3*x13 + p7*x14 + p11*x15 + p15*x16; 2016 pc[15] = m16 = p4*x13 + p8*x14 + p12*x15 + p16*x16; 2017 2018 nz = bi[row+1] - diag_offset[row] - 1; 2019 pv += 16; 2020 for (j=0; j<nz; j++) { 2021 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2022 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2023 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 2024 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 2025 x = rtmp + 16*pj[j]; 2026 x[0] -= m1*x1 + m5*x2 + m9*x3 + m13*x4; 2027 x[1] -= m2*x1 + m6*x2 + m10*x3 + m14*x4; 2028 x[2] -= m3*x1 + m7*x2 + m11*x3 + m15*x4; 2029 x[3] -= m4*x1 + m8*x2 + m12*x3 + m16*x4; 2030 2031 x[4] -= m1*x5 + m5*x6 + m9*x7 + m13*x8; 2032 x[5] -= m2*x5 + m6*x6 + m10*x7 + m14*x8; 2033 x[6] -= m3*x5 + m7*x6 + m11*x7 + m15*x8; 2034 x[7] -= m4*x5 + m8*x6 + m12*x7 + m16*x8; 2035 2036 x[8] -= m1*x9 + m5*x10 + m9*x11 + m13*x12; 2037 x[9] -= m2*x9 + m6*x10 + m10*x11 + m14*x12; 2038 x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12; 2039 x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12; 2040 2041 x[12] -= m1*x13 + m5*x14 + m9*x15 + m13*x16; 2042 x[13] -= m2*x13 + m6*x14 + m10*x15 + m14*x16; 2043 x[14] -= m3*x13 + m7*x14 + m11*x15 + m15*x16; 2044 x[15] -= m4*x13 + m8*x14 + m12*x15 + m16*x16; 2045 2046 pv += 16; 2047 } 2048 PLogFlops(128*nz+112); 2049 } 2050 row = *ajtmp++; 2051 } 2052 /* finished row so stick it into b->a */ 2053 pv = ba + 16*bi[i]; 2054 pj = bj + bi[i]; 2055 nz = bi[i+1] - bi[i]; 2056 for (j=0; j<nz; j++) { 2057 x = rtmp+16*pj[j]; 2058 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2059 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 2060 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 2061 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 2062 pv += 16; 2063 } 2064 /* invert diagonal block */ 2065 w = ba + 16*diag_offset[i]; 2066 ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr); 2067 } 2068 2069 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2070 C->factor = FACTOR_LU; 2071 C->assembled = PETSC_TRUE; 2072 C->preallocated = PETSC_TRUE; 2073 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2074 PetscFunctionReturn(0); 2075 } 2076 2077 /* Version for when blocks are 4 by 4 */ 2078 #undef __FUNC__ 2079 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 2080 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 2081 { 2082 Mat C = *B; 2083 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2084 IS perm = b->row; 2085 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2086 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2087 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2088 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2089 2090 PetscFunctionBegin; 2091 /* initialization */ 2092 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2093 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2094 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2095 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2096 for (i=0; i<mbs; i++) { 2097 jl[i] = mbs; il[0] = 0; 2098 } 2099 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 2100 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 2101 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2102 2103 /* check permutation */ 2104 if (!a->permute){ 2105 ai = a->i; aj = a->j; aa = a->a; 2106 } else { 2107 ai = a->inew; aj = a->jnew; 2108 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2109 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2110 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2111 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2112 2113 for (i=0; i<mbs; i++){ 2114 jmin = ai[i]; jmax = ai[i+1]; 2115 for (j=jmin; j<jmax; j++){ 2116 while (a2anew[j] != j){ 2117 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2118 for (k1=0; k1<16; k1++){ 2119 dk[k1] = aa[k*16+k1]; 2120 aa[k*16+k1] = aa[j*16+k1]; 2121 aa[j*16+k1] = dk[k1]; 2122 } 2123 } 2124 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2125 if (i > aj[j]){ 2126 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2127 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 2128 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2129 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 2130 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 2131 } 2132 } 2133 } 2134 } 2135 ierr = PetscFree(a2anew);CHKERRA(ierr); 2136 } 2137 2138 /* for each row k */ 2139 for (k = 0; k<mbs; k++){ 2140 2141 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2142 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2143 if (jmin < jmax) { 2144 ap = aa + jmin*16; 2145 for (j = jmin; j < jmax; j++){ 2146 vj = perm_ptr[aj[j]]; /* block col. index */ 2147 rtmp_ptr = rtmp + vj*16; 2148 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 2149 } 2150 } 2151 2152 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2153 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 2154 i = jl[k]; /* first row to be added to k_th row */ 2155 2156 while (i < mbs){ 2157 nexti = jl[i]; /* next row to be added to k_th row */ 2158 2159 /* compute multiplier */ 2160 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2161 2162 /* uik = -inv(Di)*U_bar(i,k) */ 2163 diag = ba + i*16; 2164 u = ba + ili*16; 2165 2166 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 2167 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 2168 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 2169 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 2170 2171 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 2172 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 2173 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 2174 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 2175 2176 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 2177 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 2178 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 2179 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 2180 2181 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 2182 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 2183 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 2184 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 2185 2186 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2187 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2188 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2189 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2190 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2191 2192 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2193 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2194 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2195 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2196 2197 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2198 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2199 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2200 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2201 2202 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2203 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2204 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2205 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2206 2207 /* update -U(i,k) */ 2208 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2209 2210 /* add multiple of row i to k-th row ... */ 2211 jmin = ili + 1; jmax = bi[i+1]; 2212 if (jmin < jmax){ 2213 for (j=jmin; j<jmax; j++) { 2214 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2215 rtmp_ptr = rtmp + bj[j]*16; 2216 u = ba + j*16; 2217 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2218 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2219 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2220 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2221 2222 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2223 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2224 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2225 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2226 2227 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2228 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2229 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2230 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2231 2232 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2233 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2234 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2235 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2236 } 2237 2238 /* ... add i to row list for next nonzero entry */ 2239 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2240 j = bj[jmin]; 2241 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2242 } 2243 i = nexti; 2244 } 2245 2246 /* save nonzero entries in k-th row of U ... */ 2247 2248 /* invert diagonal block */ 2249 diag = ba+k*16; 2250 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2251 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2252 2253 jmin = bi[k]; jmax = bi[k+1]; 2254 if (jmin < jmax) { 2255 for (j=jmin; j<jmax; j++){ 2256 vj = bj[j]; /* block col. index of U */ 2257 u = ba + j*16; 2258 rtmp_ptr = rtmp + vj*16; 2259 for (k1=0; k1<16; k1++){ 2260 *u++ = *rtmp_ptr; 2261 *rtmp_ptr++ = 0.0; 2262 } 2263 } 2264 2265 /* ... add k to row list for first nonzero entry in k-th row */ 2266 il[k] = jmin; 2267 i = bj[jmin]; 2268 jl[k] = jl[i]; jl[i] = k; 2269 } 2270 } 2271 2272 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2273 ierr = PetscFree(il);CHKERRQ(ierr); 2274 ierr = PetscFree(jl);CHKERRQ(ierr); 2275 ierr = PetscFree(dk);CHKERRQ(ierr); 2276 ierr = PetscFree(uik);CHKERRQ(ierr); 2277 if (a->permute){ 2278 ierr = PetscFree(aa);CHKERRQ(ierr); 2279 } 2280 2281 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2282 C->factor = FACTOR_CHOLESKY; 2283 C->assembled = PETSC_TRUE; 2284 C->preallocated = PETSC_TRUE; 2285 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2286 PetscFunctionReturn(0); 2287 } 2288 2289 /* Version for when blocks are 3 by 3 */ 2290 #undef __FUNC__ 2291 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2292 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2293 { 2294 Mat C = *B; 2295 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2296 IS perm = b->row; 2297 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2298 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2299 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2300 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2301 2302 PetscFunctionBegin; 2303 /* initialization */ 2304 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2305 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2306 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2307 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2308 for (i=0; i<mbs; i++) { 2309 jl[i] = mbs; il[0] = 0; 2310 } 2311 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2312 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2313 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2314 2315 /* check permutation */ 2316 if (!a->permute){ 2317 ai = a->i; aj = a->j; aa = a->a; 2318 } else { 2319 ai = a->inew; aj = a->jnew; 2320 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2321 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2322 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2323 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2324 2325 for (i=0; i<mbs; i++){ 2326 jmin = ai[i]; jmax = ai[i+1]; 2327 for (j=jmin; j<jmax; j++){ 2328 while (a2anew[j] != j){ 2329 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2330 for (k1=0; k1<9; k1++){ 2331 dk[k1] = aa[k*9+k1]; 2332 aa[k*9+k1] = aa[j*9+k1]; 2333 aa[j*9+k1] = dk[k1]; 2334 } 2335 } 2336 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2337 if (i > aj[j]){ 2338 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2339 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2340 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2341 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2342 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2343 } 2344 } 2345 } 2346 } 2347 ierr = PetscFree(a2anew);CHKERRA(ierr); 2348 } 2349 2350 /* for each row k */ 2351 for (k = 0; k<mbs; k++){ 2352 2353 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2354 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2355 if (jmin < jmax) { 2356 ap = aa + jmin*9; 2357 for (j = jmin; j < jmax; j++){ 2358 vj = perm_ptr[aj[j]]; /* block col. index */ 2359 rtmp_ptr = rtmp + vj*9; 2360 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2361 } 2362 } 2363 2364 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2365 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2366 i = jl[k]; /* first row to be added to k_th row */ 2367 2368 while (i < mbs){ 2369 nexti = jl[i]; /* next row to be added to k_th row */ 2370 2371 /* compute multiplier */ 2372 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2373 2374 /* uik = -inv(Di)*U_bar(i,k) */ 2375 diag = ba + i*9; 2376 u = ba + ili*9; 2377 2378 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2379 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2380 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2381 2382 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2383 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2384 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2385 2386 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2387 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2388 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2389 2390 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2391 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2392 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2393 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2394 2395 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2396 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2397 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2398 2399 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2400 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2401 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2402 2403 /* update -U(i,k) */ 2404 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2405 2406 /* add multiple of row i to k-th row ... */ 2407 jmin = ili + 1; jmax = bi[i+1]; 2408 if (jmin < jmax){ 2409 for (j=jmin; j<jmax; j++) { 2410 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2411 rtmp_ptr = rtmp + bj[j]*9; 2412 u = ba + j*9; 2413 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2414 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2415 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2416 2417 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2418 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2419 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2420 2421 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2422 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2423 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2424 } 2425 2426 /* ... add i to row list for next nonzero entry */ 2427 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2428 j = bj[jmin]; 2429 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2430 } 2431 i = nexti; 2432 } 2433 2434 /* save nonzero entries in k-th row of U ... */ 2435 2436 /* invert diagonal block */ 2437 diag = ba+k*9; 2438 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2439 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2440 2441 jmin = bi[k]; jmax = bi[k+1]; 2442 if (jmin < jmax) { 2443 for (j=jmin; j<jmax; j++){ 2444 vj = bj[j]; /* block col. index of U */ 2445 u = ba + j*9; 2446 rtmp_ptr = rtmp + vj*9; 2447 for (k1=0; k1<9; k1++){ 2448 *u++ = *rtmp_ptr; 2449 *rtmp_ptr++ = 0.0; 2450 } 2451 } 2452 2453 /* ... add k to row list for first nonzero entry in k-th row */ 2454 il[k] = jmin; 2455 i = bj[jmin]; 2456 jl[k] = jl[i]; jl[i] = k; 2457 } 2458 } 2459 2460 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2461 ierr = PetscFree(il);CHKERRQ(ierr); 2462 ierr = PetscFree(jl);CHKERRQ(ierr); 2463 ierr = PetscFree(dk);CHKERRQ(ierr); 2464 ierr = PetscFree(uik);CHKERRQ(ierr); 2465 if (a->permute){ 2466 ierr = PetscFree(aa);CHKERRQ(ierr); 2467 } 2468 2469 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2470 C->factor = FACTOR_CHOLESKY; 2471 C->assembled = PETSC_TRUE; 2472 C->preallocated = PETSC_TRUE; 2473 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2474 PetscFunctionReturn(0); 2475 } 2476 2477 /* 2478 Version for when blocks are 3 by 3 Using natural ordering 2479 */ 2480 #undef __FUNC__ 2481 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2482 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B) 2483 { 2484 Mat C = *B; 2485 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2486 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2487 int *ajtmpold,*ajtmp,nz,row; 2488 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2489 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2490 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 2491 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9; 2492 MatScalar *ba = b->a,*aa = a->a; 2493 2494 PetscFunctionBegin; 2495 rtmp = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2496 2497 for (i=0; i<n; i++) { 2498 nz = bi[i+1] - bi[i]; 2499 ajtmp = bj + bi[i]; 2500 for (j=0; j<nz; j++) { 2501 x = rtmp+9*ajtmp[j]; 2502 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0; 2503 } 2504 /* load in initial (unfactored row) */ 2505 nz = ai[i+1] - ai[i]; 2506 ajtmpold = aj + ai[i]; 2507 v = aa + 9*ai[i]; 2508 for (j=0; j<nz; j++) { 2509 x = rtmp+9*ajtmpold[j]; 2510 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2511 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 2512 v += 9; 2513 } 2514 row = *ajtmp++; 2515 while (row < i) { 2516 pc = rtmp + 9*row; 2517 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2518 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 2519 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 2520 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) { 2521 pv = ba + 9*diag_offset[row]; 2522 pj = bj + diag_offset[row] + 1; 2523 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2524 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2525 pc[0] = m1 = p1*x1 + p4*x2 + p7*x3; 2526 pc[1] = m2 = p2*x1 + p5*x2 + p8*x3; 2527 pc[2] = m3 = p3*x1 + p6*x2 + p9*x3; 2528 2529 pc[3] = m4 = p1*x4 + p4*x5 + p7*x6; 2530 pc[4] = m5 = p2*x4 + p5*x5 + p8*x6; 2531 pc[5] = m6 = p3*x4 + p6*x5 + p9*x6; 2532 2533 pc[6] = m7 = p1*x7 + p4*x8 + p7*x9; 2534 pc[7] = m8 = p2*x7 + p5*x8 + p8*x9; 2535 pc[8] = m9 = p3*x7 + p6*x8 + p9*x9; 2536 2537 nz = bi[row+1] - diag_offset[row] - 1; 2538 pv += 9; 2539 for (j=0; j<nz; j++) { 2540 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2541 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2542 x = rtmp + 9*pj[j]; 2543 x[0] -= m1*x1 + m4*x2 + m7*x3; 2544 x[1] -= m2*x1 + m5*x2 + m8*x3; 2545 x[2] -= m3*x1 + m6*x2 + m9*x3; 2546 2547 x[3] -= m1*x4 + m4*x5 + m7*x6; 2548 x[4] -= m2*x4 + m5*x5 + m8*x6; 2549 x[5] -= m3*x4 + m6*x5 + m9*x6; 2550 2551 x[6] -= m1*x7 + m4*x8 + m7*x9; 2552 x[7] -= m2*x7 + m5*x8 + m8*x9; 2553 x[8] -= m3*x7 + m6*x8 + m9*x9; 2554 pv += 9; 2555 } 2556 PLogFlops(54*nz+36); 2557 } 2558 row = *ajtmp++; 2559 } 2560 /* finished row so stick it into b->a */ 2561 pv = ba + 9*bi[i]; 2562 pj = bj + bi[i]; 2563 nz = bi[i+1] - bi[i]; 2564 for (j=0; j<nz; j++) { 2565 x = rtmp+9*pj[j]; 2566 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2567 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 2568 pv += 9; 2569 } 2570 /* invert diagonal block */ 2571 w = ba + 9*diag_offset[i]; 2572 ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr); 2573 } 2574 2575 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2576 C->factor = FACTOR_CHOLESKY; 2577 C->assembled = PETSC_TRUE; 2578 C->preallocated = PETSC_TRUE; 2579 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2580 PetscFunctionReturn(0); 2581 } 2582 2583 /* 2584 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2585 Version for blocks 2 by 2. 2586 */ 2587 #undef __FUNC__ 2588 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2589 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2590 { 2591 Mat C = *B; 2592 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2593 IS perm = b->row; 2594 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2595 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2596 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2597 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2598 2599 PetscFunctionBegin; 2600 2601 /* initialization */ 2602 /* il and jl record the first nonzero element in each row of the accessing 2603 window U(0:k, k:mbs-1). 2604 jl: list of rows to be added to uneliminated rows 2605 i>= k: jl(i) is the first row to be added to row i 2606 i< k: jl(i) is the row following row i in some list of rows 2607 jl(i) = mbs indicates the end of a list 2608 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2609 row i of U */ 2610 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2611 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2612 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2613 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2614 for (i=0; i<mbs; i++) { 2615 jl[i] = mbs; il[0] = 0; 2616 } 2617 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2618 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2619 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2620 2621 /* check permutation */ 2622 if (!a->permute){ 2623 ai = a->i; aj = a->j; aa = a->a; 2624 } else { 2625 ai = a->inew; aj = a->jnew; 2626 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2627 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2628 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2629 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2630 2631 for (i=0; i<mbs; i++){ 2632 jmin = ai[i]; jmax = ai[i+1]; 2633 for (j=jmin; j<jmax; j++){ 2634 while (a2anew[j] != j){ 2635 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2636 for (k1=0; k1<4; k1++){ 2637 dk[k1] = aa[k*4+k1]; 2638 aa[k*4+k1] = aa[j*4+k1]; 2639 aa[j*4+k1] = dk[k1]; 2640 } 2641 } 2642 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2643 if (i > aj[j]){ 2644 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2645 ap = aa + j*4; /* ptr to the beginning of the block */ 2646 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2647 ap[1] = ap[2]; 2648 ap[2] = dk[1]; 2649 } 2650 } 2651 } 2652 ierr = PetscFree(a2anew);CHKERRA(ierr); 2653 } 2654 2655 /* for each row k */ 2656 for (k = 0; k<mbs; k++){ 2657 2658 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2659 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2660 if (jmin < jmax) { 2661 ap = aa + jmin*4; 2662 for (j = jmin; j < jmax; j++){ 2663 vj = perm_ptr[aj[j]]; /* block col. index */ 2664 rtmp_ptr = rtmp + vj*4; 2665 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2666 } 2667 } 2668 2669 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2670 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2671 i = jl[k]; /* first row to be added to k_th row */ 2672 2673 while (i < mbs){ 2674 nexti = jl[i]; /* next row to be added to k_th row */ 2675 2676 /* compute multiplier */ 2677 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2678 2679 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2680 diag = ba + i*4; 2681 u = ba + ili*4; 2682 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2683 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2684 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2685 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2686 2687 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2688 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2689 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2690 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2691 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2692 2693 /* update -U(i,k): ba[ili] = uik */ 2694 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2695 2696 /* add multiple of row i to k-th row ... */ 2697 jmin = ili + 1; jmax = bi[i+1]; 2698 if (jmin < jmax){ 2699 for (j=jmin; j<jmax; j++) { 2700 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2701 rtmp_ptr = rtmp + bj[j]*4; 2702 u = ba + j*4; 2703 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2704 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2705 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2706 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2707 } 2708 2709 /* ... add i to row list for next nonzero entry */ 2710 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2711 j = bj[jmin]; 2712 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2713 } 2714 i = nexti; 2715 } 2716 2717 /* save nonzero entries in k-th row of U ... */ 2718 2719 /* invert diagonal block */ 2720 diag = ba+k*4; 2721 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2722 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2723 2724 jmin = bi[k]; jmax = bi[k+1]; 2725 if (jmin < jmax) { 2726 for (j=jmin; j<jmax; j++){ 2727 vj = bj[j]; /* block col. index of U */ 2728 u = ba + j*4; 2729 rtmp_ptr = rtmp + vj*4; 2730 for (k1=0; k1<4; k1++){ 2731 *u++ = *rtmp_ptr; 2732 *rtmp_ptr++ = 0.0; 2733 } 2734 } 2735 2736 /* ... add k to row list for first nonzero entry in k-th row */ 2737 il[k] = jmin; 2738 i = bj[jmin]; 2739 jl[k] = jl[i]; jl[i] = k; 2740 } 2741 } 2742 2743 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2744 ierr = PetscFree(il);CHKERRQ(ierr); 2745 ierr = PetscFree(jl);CHKERRQ(ierr); 2746 ierr = PetscFree(dk);CHKERRQ(ierr); 2747 ierr = PetscFree(uik);CHKERRQ(ierr); 2748 if (a->permute) { 2749 ierr = PetscFree(aa);CHKERRQ(ierr); 2750 } 2751 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2752 C->factor = FACTOR_CHOLESKY; 2753 C->assembled = PETSC_TRUE; 2754 C->preallocated = PETSC_TRUE; 2755 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2756 PetscFunctionReturn(0); 2757 } 2758 2759 /* 2760 Version for when blocks are 2 by 2 Using natural ordering 2761 */ 2762 #undef __FUNC__ 2763 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2764 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2765 { 2766 Mat C = *B; 2767 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2768 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2769 int *ajtmpold,*ajtmp,nz,row; 2770 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2771 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2772 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4; 2773 MatScalar *ba = b->a,*aa = a->a; 2774 2775 PetscFunctionBegin; 2776 rtmp = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2777 2778 for (i=0; i<n; i++) { 2779 nz = bi[i+1] - bi[i]; 2780 ajtmp = bj + bi[i]; 2781 for (j=0; j<nz; j++) { 2782 x = rtmp+4*ajtmp[j]; 2783 x[0] = x[1] = x[2] = x[3] = 0.0; 2784 } 2785 /* load in initial (unfactored row) */ 2786 nz = ai[i+1] - ai[i]; 2787 ajtmpold = aj + ai[i]; 2788 v = aa + 4*ai[i]; 2789 for (j=0; j<nz; j++) { 2790 x = rtmp+4*ajtmpold[j]; 2791 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2792 v += 4; 2793 } 2794 row = *ajtmp++; 2795 while (row < i) { 2796 pc = rtmp + 4*row; 2797 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2798 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) { 2799 pv = ba + 4*diag_offset[row]; 2800 pj = bj + diag_offset[row] + 1; 2801 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2802 pc[0] = m1 = p1*x1 + p3*x2; 2803 pc[1] = m2 = p2*x1 + p4*x2; 2804 pc[2] = m3 = p1*x3 + p3*x4; 2805 pc[3] = m4 = p2*x3 + p4*x4; 2806 nz = bi[row+1] - diag_offset[row] - 1; 2807 pv += 4; 2808 for (j=0; j<nz; j++) { 2809 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2810 x = rtmp + 4*pj[j]; 2811 x[0] -= m1*x1 + m3*x2; 2812 x[1] -= m2*x1 + m4*x2; 2813 x[2] -= m1*x3 + m3*x4; 2814 x[3] -= m2*x3 + m4*x4; 2815 pv += 4; 2816 } 2817 PLogFlops(16*nz+12); 2818 } 2819 row = *ajtmp++; 2820 } 2821 /* finished row so stick it into b->a */ 2822 pv = ba + 4*bi[i]; 2823 pj = bj + bi[i]; 2824 nz = bi[i+1] - bi[i]; 2825 for (j=0; j<nz; j++) { 2826 x = rtmp+4*pj[j]; 2827 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2828 pv += 4; 2829 } 2830 /* invert diagonal block */ 2831 w = ba + 4*diag_offset[i]; 2832 ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr); 2833 } 2834 2835 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2836 C->factor = FACTOR_LU; 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 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2845 Version for blocks are 1 by 1. 2846 */ 2847 #undef __FUNC__ 2848 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2849 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2850 { 2851 Mat C = *B; 2852 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2853 IS ip = b->row; 2854 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2855 int *ai,*aj,*r; 2856 MatScalar *rtmp; 2857 MatScalar *ba = b->a,*aa,ak; 2858 MatScalar dk,uikdi; 2859 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2860 2861 PetscFunctionBegin; 2862 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2863 if (!a->permute){ 2864 ai = a->i; aj = a->j; aa = a->a; 2865 } else { 2866 ai = a->inew; aj = a->jnew; 2867 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2868 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2869 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 2870 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2871 2872 jmin = ai[0]; jmax = ai[mbs]; 2873 for (j=jmin; j<jmax; j++){ 2874 while (r[j] != j){ 2875 k = r[j]; r[j] = r[k]; r[k] = k; 2876 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 2877 } 2878 } 2879 ierr = PetscFree(r);CHKERRA(ierr); 2880 } 2881 2882 /* initialization */ 2883 /* il and jl record the first nonzero element in each row of the accessing 2884 window U(0:k, k:mbs-1). 2885 jl: list of rows to be added to uneliminated rows 2886 i>= k: jl(i) is the first row to be added to row i 2887 i< k: jl(i) is the row following row i in some list of rows 2888 jl(i) = mbs indicates the end of a list 2889 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2890 row i of U */ 2891 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2892 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2893 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2894 for (i=0; i<mbs; i++) { 2895 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2896 } 2897 2898 /* for each row k */ 2899 for (k = 0; k<mbs; k++){ 2900 2901 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2902 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2903 if (jmin < jmax) { 2904 for (j = jmin; j < jmax; j++){ 2905 vj = rip[aj[j]]; 2906 /* if (k <= vj)*/ rtmp[vj] = aa[j]; 2907 } 2908 } 2909 2910 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2911 dk = rtmp[k]; 2912 i = jl[k]; /* first row to be added to k_th row */ 2913 /* printf(" k=%d, pivot row = %d\n",k,i); */ 2914 2915 while (i < mbs){ 2916 nexti = jl[i]; /* next row to be added to k_th row */ 2917 2918 /* compute multiplier, update D(k) and U(i,k) */ 2919 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2920 uikdi = - ba[ili]*ba[i]; 2921 dk += uikdi*ba[ili]; 2922 ba[ili] = uikdi; /* -U(i,k) */ 2923 2924 /* add multiple of row i to k-th row ... */ 2925 jmin = ili + 1; jmax = bi[i+1]; 2926 if (jmin < jmax){ 2927 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2928 /* ... add i to row list for next nonzero entry */ 2929 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2930 j = bj[jmin]; 2931 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2932 } 2933 i = nexti; /* printf(" pivot row i=%d\n",i); */ 2934 } 2935 2936 /* check for zero pivot and save diagoanl element */ 2937 if (dk == 0.0){ 2938 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 2939 }else if (PetscRealPart(dk) < 0){ 2940 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 2941 } 2942 2943 /* save nonzero entries in k-th row of U ... */ 2944 ba[k] = 1.0/dk; 2945 jmin = bi[k]; jmax = bi[k+1]; 2946 if (jmin < jmax) { 2947 for (j=jmin; j<jmax; j++){ 2948 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 2949 } 2950 /* ... add k to row list for first nonzero entry in k-th row */ 2951 il[k] = jmin; 2952 i = bj[jmin]; 2953 jl[k] = jl[i]; jl[i] = k; 2954 } 2955 } 2956 2957 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2958 ierr = PetscFree(il);CHKERRQ(ierr); 2959 ierr = PetscFree(jl);CHKERRQ(ierr); 2960 if (a->permute){ 2961 ierr = PetscFree(aa);CHKERRQ(ierr); 2962 } 2963 2964 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2965 C->factor = FACTOR_CHOLESKY; 2966 C->assembled = PETSC_TRUE; 2967 C->preallocated = PETSC_TRUE; 2968 PLogFlops(b->mbs); 2969 PetscFunctionReturn(0); 2970 } 2971 2972 #undef __FUNC__ 2973 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 2974 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 2975 { 2976 int ierr; 2977 Mat C; 2978 2979 PetscFunctionBegin; 2980 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 2981 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 2982 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 2983 PetscFunctionReturn(0); 2984 } 2985 2986 2987