1 /* Using Modified Sparse Row (MSR) storage. 2 See page 85, "Iterative Methods ..." by Saad. */ 3 4 /*$Id: sbaijfact.c,v 1.38 2000/10/31 16:06:00 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 #ifdef TEMP 191 for (k=0; k<mbs; k++){ 192 nzk = b->i[k+1] - b->i[k]; 193 printf("\n b->i[%d]: %d, nzk: %d\n",k,b->i[k],nzk); 194 jmin = b->i[k]; jmax = b->i[k+1]; 195 for (j=jmin; j<jmax; j++){ 196 printf(" %d,",b->j[j]); 197 } 198 } 199 #endif 200 PetscFunctionReturn(0); 201 } 202 203 #undef __FUNC__ 204 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N" 205 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B) 206 { 207 Mat C = *B; 208 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 209 IS isrow = b->row,isicol = b->icol; 210 int *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 211 int *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg; 212 int *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj; 213 MatScalar *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w; 214 215 PetscFunctionBegin; 216 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 217 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 218 rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 219 ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr); 220 /* generate work space needed by dense LU factorization */ 221 v_work = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work); 222 multiplier = v_work + bs; 223 v_pivots = (int*)(multiplier + bs2); 224 225 /* flops in while loop */ 226 bslog = 2*bs*bs2; 227 228 for (i=0; i<n; i++) { 229 nz = bi[i+1] - bi[i]; 230 ajtmp = bj + bi[i]; 231 for (j=0; j<nz; j++) { 232 ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 233 } 234 /* load in initial (unfactored row) */ 235 nz = ai[r[i]+1] - ai[r[i]]; 236 ajtmpold = aj + ai[r[i]]; 237 v = aa + bs2*ai[r[i]]; 238 for (j=0; j<nz; j++) { 239 ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr); 240 } 241 row = *ajtmp++; 242 while (row < i) { 243 pc = rtmp + bs2*row; 244 /* if (*pc) { */ 245 for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }} 246 if (flg) { 247 pv = ba + bs2*diag_offset[row]; 248 pj = bj + diag_offset[row] + 1; 249 Kernel_A_gets_A_times_B(bs,pc,pv,multiplier); 250 nz = bi[row+1] - diag_offset[row] - 1; 251 pv += bs2; 252 for (j=0; j<nz; j++) { 253 Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); 254 } 255 PLogFlops(bslog*(nz+1)-bs); 256 } 257 row = *ajtmp++; 258 } 259 /* finished row so stick it into b->a */ 260 pv = ba + bs2*bi[i]; 261 pj = bj + bi[i]; 262 nz = bi[i+1] - bi[i]; 263 for (j=0; j<nz; j++) { 264 ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr); 265 } 266 diag = diag_offset[i] - bi[i]; 267 /* invert diagonal block */ 268 w = pv + bs2*diag; 269 Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work); 270 } 271 272 ierr = PetscFree(rtmp);CHKERRQ(ierr); 273 ierr = PetscFree(v_work);CHKERRQ(ierr); 274 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 275 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 276 C->factor = FACTOR_LU; 277 C->assembled = PETSC_TRUE; 278 PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */ 279 PetscFunctionReturn(0); 280 } 281 282 /* 283 Version for when blocks are 7 by 7 284 */ 285 #undef __FUNC__ 286 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7" 287 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B) 288 { 289 Mat C = *B; 290 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 291 IS isrow = b->row,isicol = b->icol; 292 int *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 293 int *ajtmpold,*ajtmp,nz,row; 294 int *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj; 295 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 296 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 297 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; 298 MatScalar x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14; 299 MatScalar p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12; 300 MatScalar m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 301 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 302 MatScalar p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49; 303 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 304 MatScalar x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49; 305 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 306 MatScalar m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49; 307 MatScalar *ba = b->a,*aa = a->a; 308 309 PetscFunctionBegin; 310 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 311 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 312 rtmp = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 313 314 for (i=0; i<n; i++) { 315 nz = bi[i+1] - bi[i]; 316 ajtmp = bj + bi[i]; 317 for (j=0; j<nz; j++) { 318 x = rtmp+49*ajtmp[j]; 319 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 320 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 321 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 322 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 323 x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ; 324 x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ; 325 } 326 /* load in initial (unfactored row) */ 327 idx = r[i]; 328 nz = ai[idx+1] - ai[idx]; 329 ajtmpold = aj + ai[idx]; 330 v = aa + 49*ai[idx]; 331 for (j=0; j<nz; j++) { 332 x = rtmp+49*ic[ajtmpold[j]]; 333 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 334 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 335 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 336 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 337 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 338 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 339 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 340 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 341 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 342 x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39]; 343 x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43]; 344 x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47]; 345 x[48] = v[48]; 346 v += 49; 347 } 348 row = *ajtmp++; 349 while (row < i) { 350 pc = rtmp + 49*row; 351 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 352 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 353 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 354 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 355 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 356 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 357 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 358 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 359 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 360 p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39]; 361 p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43]; 362 p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47]; 363 p49 = pc[48]; 364 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 365 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 366 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 367 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 368 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 369 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 370 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 371 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 372 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || 373 p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || 374 p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || 375 p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || 376 p49 != 0.0) { 377 pv = ba + 49*diag_offset[row]; 378 pj = bj + diag_offset[row] + 1; 379 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 380 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 381 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 382 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 383 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 384 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 385 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 386 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 387 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 388 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 389 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 390 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 391 x49 = pv[48]; 392 pc[0] = m1 = p1*x1 + p8*x2 + p15*x3 + p22*x4 + p29*x5 + p36*x6 + p43*x7; 393 pc[1] = m2 = p2*x1 + p9*x2 + p16*x3 + p23*x4 + p30*x5 + p37*x6 + p44*x7; 394 pc[2] = m3 = p3*x1 + p10*x2 + p17*x3 + p24*x4 + p31*x5 + p38*x6 + p45*x7; 395 pc[3] = m4 = p4*x1 + p11*x2 + p18*x3 + p25*x4 + p32*x5 + p39*x6 + p46*x7; 396 pc[4] = m5 = p5*x1 + p12*x2 + p19*x3 + p26*x4 + p33*x5 + p40*x6 + p47*x7; 397 pc[5] = m6 = p6*x1 + p13*x2 + p20*x3 + p27*x4 + p34*x5 + p41*x6 + p48*x7; 398 pc[6] = m7 = p7*x1 + p14*x2 + p21*x3 + p28*x4 + p35*x5 + p42*x6 + p49*x7; 399 400 pc[7] = m8 = p1*x8 + p8*x9 + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14; 401 pc[8] = m9 = p2*x8 + p9*x9 + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14; 402 pc[9] = m10 = p3*x8 + p10*x9 + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14; 403 pc[10] = m11 = p4*x8 + p11*x9 + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14; 404 pc[11] = m12 = p5*x8 + p12*x9 + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14; 405 pc[12] = m13 = p6*x8 + p13*x9 + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14; 406 pc[13] = m14 = p7*x8 + p14*x9 + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14; 407 408 pc[14] = m15 = p1*x15 + p8*x16 + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21; 409 pc[15] = m16 = p2*x15 + p9*x16 + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21; 410 pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21; 411 pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21; 412 pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21; 413 pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21; 414 pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21; 415 416 pc[21] = m22 = p1*x22 + p8*x23 + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28; 417 pc[22] = m23 = p2*x22 + p9*x23 + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28; 418 pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28; 419 pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28; 420 pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28; 421 pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28; 422 pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28; 423 424 pc[28] = m29 = p1*x29 + p8*x30 + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35; 425 pc[29] = m30 = p2*x29 + p9*x30 + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35; 426 pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35; 427 pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35; 428 pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35; 429 pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35; 430 pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35; 431 432 pc[35] = m36 = p1*x36 + p8*x37 + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42; 433 pc[36] = m37 = p2*x36 + p9*x37 + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42; 434 pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42; 435 pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42; 436 pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42; 437 pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42; 438 pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42; 439 440 pc[42] = m43 = p1*x43 + p8*x44 + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49; 441 pc[43] = m44 = p2*x43 + p9*x44 + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49; 442 pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49; 443 pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49; 444 pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49; 445 pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49; 446 pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49; 447 448 nz = bi[row+1] - diag_offset[row] - 1; 449 pv += 49; 450 for (j=0; j<nz; j++) { 451 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 452 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 453 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 454 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 455 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 456 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 457 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 458 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 459 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 460 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 461 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 462 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 463 x49 = pv[48]; 464 x = rtmp + 49*pj[j]; 465 x[0] -= m1*x1 + m8*x2 + m15*x3 + m22*x4 + m29*x5 + m36*x6 + m43*x7; 466 x[1] -= m2*x1 + m9*x2 + m16*x3 + m23*x4 + m30*x5 + m37*x6 + m44*x7; 467 x[2] -= m3*x1 + m10*x2 + m17*x3 + m24*x4 + m31*x5 + m38*x6 + m45*x7; 468 x[3] -= m4*x1 + m11*x2 + m18*x3 + m25*x4 + m32*x5 + m39*x6 + m46*x7; 469 x[4] -= m5*x1 + m12*x2 + m19*x3 + m26*x4 + m33*x5 + m40*x6 + m47*x7; 470 x[5] -= m6*x1 + m13*x2 + m20*x3 + m27*x4 + m34*x5 + m41*x6 + m48*x7; 471 x[6] -= m7*x1 + m14*x2 + m21*x3 + m28*x4 + m35*x5 + m42*x6 + m49*x7; 472 473 x[7] -= m1*x8 + m8*x9 + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14; 474 x[8] -= m2*x8 + m9*x9 + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14; 475 x[9] -= m3*x8 + m10*x9 + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14; 476 x[10] -= m4*x8 + m11*x9 + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14; 477 x[11] -= m5*x8 + m12*x9 + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14; 478 x[12] -= m6*x8 + m13*x9 + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14; 479 x[13] -= m7*x8 + m14*x9 + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14; 480 481 x[14] -= m1*x15 + m8*x16 + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21; 482 x[15] -= m2*x15 + m9*x16 + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21; 483 x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21; 484 x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21; 485 x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21; 486 x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21; 487 x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21; 488 489 x[21] -= m1*x22 + m8*x23 + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28; 490 x[22] -= m2*x22 + m9*x23 + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28; 491 x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28; 492 x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28; 493 x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28; 494 x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28; 495 x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28; 496 497 x[28] -= m1*x29 + m8*x30 + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35; 498 x[29] -= m2*x29 + m9*x30 + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35; 499 x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35; 500 x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35; 501 x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35; 502 x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35; 503 x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35; 504 505 x[35] -= m1*x36 + m8*x37 + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42; 506 x[36] -= m2*x36 + m9*x37 + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42; 507 x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42; 508 x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42; 509 x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42; 510 x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42; 511 x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42; 512 513 x[42] -= m1*x43 + m8*x44 + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49; 514 x[43] -= m2*x43 + m9*x44 + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49; 515 x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49; 516 x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49; 517 x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49; 518 x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49; 519 x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49; 520 pv += 49; 521 } 522 PLogFlops(686*nz+637); 523 } 524 row = *ajtmp++; 525 } 526 /* finished row so stick it into b->a */ 527 pv = ba + 49*bi[i]; 528 pj = bj + bi[i]; 529 nz = bi[i+1] - bi[i]; 530 for (j=0; j<nz; j++) { 531 x = rtmp+49*pj[j]; 532 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 533 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 534 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 535 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 536 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 537 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 538 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 539 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 540 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 541 pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39]; 542 pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43]; 543 pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47]; 544 pv[48] = x[48]; 545 pv += 49; 546 } 547 /* invert diagonal block */ 548 w = ba + 49*diag_offset[i]; 549 ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr); 550 } 551 552 ierr = PetscFree(rtmp);CHKERRQ(ierr); 553 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 554 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 555 C->factor = FACTOR_LU; 556 C->assembled = PETSC_TRUE; 557 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 558 PetscFunctionReturn(0); 559 } 560 561 /* 562 Version for when blocks are 7 by 7 Using natural ordering 563 */ 564 #undef __FUNC__ 565 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering" 566 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B) 567 { 568 Mat C = *B; 569 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 570 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 571 int *ajtmpold,*ajtmp,nz,row; 572 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 573 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 574 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 575 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 576 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 577 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 578 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 579 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 580 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 581 MatScalar p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49; 582 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 583 MatScalar x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49; 584 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 585 MatScalar m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49; 586 MatScalar *ba = b->a,*aa = a->a; 587 588 PetscFunctionBegin; 589 rtmp = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 590 for (i=0; i<n; i++) { 591 nz = bi[i+1] - bi[i]; 592 ajtmp = bj + bi[i]; 593 for (j=0; j<nz; j++) { 594 x = rtmp+49*ajtmp[j]; 595 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 596 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 597 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 598 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 599 x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ; 600 x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ; 601 } 602 /* load in initial (unfactored row) */ 603 nz = ai[i+1] - ai[i]; 604 ajtmpold = aj + ai[i]; 605 v = aa + 49*ai[i]; 606 for (j=0; j<nz; j++) { 607 x = rtmp+49*ajtmpold[j]; 608 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 609 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 610 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 611 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 612 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 613 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 614 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 615 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 616 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 617 x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39]; 618 x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43]; 619 x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47]; 620 x[48] = v[48]; 621 v += 49; 622 } 623 row = *ajtmp++; 624 while (row < i) { 625 pc = rtmp + 49*row; 626 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 627 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 628 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 629 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 630 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 631 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 632 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 633 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 634 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 635 p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39]; 636 p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43]; 637 p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47]; 638 p49 = pc[48]; 639 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 640 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 641 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 642 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 643 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 644 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 645 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 646 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 647 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || 648 p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || 649 p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || 650 p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || 651 p49 != 0.0) { 652 pv = ba + 49*diag_offset[row]; 653 pj = bj + diag_offset[row] + 1; 654 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 655 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 656 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 657 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 658 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 659 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 660 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 661 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 662 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 663 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 664 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 665 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 666 x49 = pv[48]; 667 pc[0] = m1 = p1*x1 + p8*x2 + p15*x3 + p22*x4 + p29*x5 + p36*x6 + p43*x7; 668 pc[1] = m2 = p2*x1 + p9*x2 + p16*x3 + p23*x4 + p30*x5 + p37*x6 + p44*x7; 669 pc[2] = m3 = p3*x1 + p10*x2 + p17*x3 + p24*x4 + p31*x5 + p38*x6 + p45*x7; 670 pc[3] = m4 = p4*x1 + p11*x2 + p18*x3 + p25*x4 + p32*x5 + p39*x6 + p46*x7; 671 pc[4] = m5 = p5*x1 + p12*x2 + p19*x3 + p26*x4 + p33*x5 + p40*x6 + p47*x7; 672 pc[5] = m6 = p6*x1 + p13*x2 + p20*x3 + p27*x4 + p34*x5 + p41*x6 + p48*x7; 673 pc[6] = m7 = p7*x1 + p14*x2 + p21*x3 + p28*x4 + p35*x5 + p42*x6 + p49*x7; 674 675 pc[7] = m8 = p1*x8 + p8*x9 + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14; 676 pc[8] = m9 = p2*x8 + p9*x9 + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14; 677 pc[9] = m10 = p3*x8 + p10*x9 + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14; 678 pc[10] = m11 = p4*x8 + p11*x9 + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14; 679 pc[11] = m12 = p5*x8 + p12*x9 + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14; 680 pc[12] = m13 = p6*x8 + p13*x9 + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14; 681 pc[13] = m14 = p7*x8 + p14*x9 + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14; 682 683 pc[14] = m15 = p1*x15 + p8*x16 + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21; 684 pc[15] = m16 = p2*x15 + p9*x16 + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21; 685 pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21; 686 pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21; 687 pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21; 688 pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21; 689 pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21; 690 691 pc[21] = m22 = p1*x22 + p8*x23 + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28; 692 pc[22] = m23 = p2*x22 + p9*x23 + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28; 693 pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28; 694 pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28; 695 pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28; 696 pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28; 697 pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28; 698 699 pc[28] = m29 = p1*x29 + p8*x30 + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35; 700 pc[29] = m30 = p2*x29 + p9*x30 + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35; 701 pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35; 702 pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35; 703 pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35; 704 pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35; 705 pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35; 706 707 pc[35] = m36 = p1*x36 + p8*x37 + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42; 708 pc[36] = m37 = p2*x36 + p9*x37 + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42; 709 pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42; 710 pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42; 711 pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42; 712 pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42; 713 pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42; 714 715 pc[42] = m43 = p1*x43 + p8*x44 + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49; 716 pc[43] = m44 = p2*x43 + p9*x44 + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49; 717 pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49; 718 pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49; 719 pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49; 720 pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49; 721 pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49; 722 723 nz = bi[row+1] - diag_offset[row] - 1; 724 pv += 49; 725 for (j=0; j<nz; j++) { 726 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 727 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 728 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 729 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 730 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 731 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 732 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 733 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 734 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 735 x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39]; 736 x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43]; 737 x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47]; 738 x49 = pv[48]; 739 x = rtmp + 49*pj[j]; 740 x[0] -= m1*x1 + m8*x2 + m15*x3 + m22*x4 + m29*x5 + m36*x6 + m43*x7; 741 x[1] -= m2*x1 + m9*x2 + m16*x3 + m23*x4 + m30*x5 + m37*x6 + m44*x7; 742 x[2] -= m3*x1 + m10*x2 + m17*x3 + m24*x4 + m31*x5 + m38*x6 + m45*x7; 743 x[3] -= m4*x1 + m11*x2 + m18*x3 + m25*x4 + m32*x5 + m39*x6 + m46*x7; 744 x[4] -= m5*x1 + m12*x2 + m19*x3 + m26*x4 + m33*x5 + m40*x6 + m47*x7; 745 x[5] -= m6*x1 + m13*x2 + m20*x3 + m27*x4 + m34*x5 + m41*x6 + m48*x7; 746 x[6] -= m7*x1 + m14*x2 + m21*x3 + m28*x4 + m35*x5 + m42*x6 + m49*x7; 747 748 x[7] -= m1*x8 + m8*x9 + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14; 749 x[8] -= m2*x8 + m9*x9 + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14; 750 x[9] -= m3*x8 + m10*x9 + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14; 751 x[10] -= m4*x8 + m11*x9 + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14; 752 x[11] -= m5*x8 + m12*x9 + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14; 753 x[12] -= m6*x8 + m13*x9 + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14; 754 x[13] -= m7*x8 + m14*x9 + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14; 755 756 x[14] -= m1*x15 + m8*x16 + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21; 757 x[15] -= m2*x15 + m9*x16 + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21; 758 x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21; 759 x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21; 760 x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21; 761 x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21; 762 x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21; 763 764 x[21] -= m1*x22 + m8*x23 + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28; 765 x[22] -= m2*x22 + m9*x23 + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28; 766 x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28; 767 x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28; 768 x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28; 769 x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28; 770 x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28; 771 772 x[28] -= m1*x29 + m8*x30 + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35; 773 x[29] -= m2*x29 + m9*x30 + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35; 774 x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35; 775 x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35; 776 x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35; 777 x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35; 778 x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35; 779 780 x[35] -= m1*x36 + m8*x37 + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42; 781 x[36] -= m2*x36 + m9*x37 + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42; 782 x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42; 783 x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42; 784 x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42; 785 x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42; 786 x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42; 787 788 x[42] -= m1*x43 + m8*x44 + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49; 789 x[43] -= m2*x43 + m9*x44 + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49; 790 x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49; 791 x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49; 792 x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49; 793 x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49; 794 x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49; 795 pv += 49; 796 } 797 PLogFlops(686*nz+637); 798 } 799 row = *ajtmp++; 800 } 801 /* finished row so stick it into b->a */ 802 pv = ba + 49*bi[i]; 803 pj = bj + bi[i]; 804 nz = bi[i+1] - bi[i]; 805 for (j=0; j<nz; j++) { 806 x = rtmp+49*pj[j]; 807 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 808 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 809 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 810 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 811 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 812 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 813 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 814 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 815 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 816 pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39]; 817 pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43]; 818 pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47]; 819 pv[48] = x[48]; 820 pv += 49; 821 } 822 /* invert diagonal block */ 823 w = ba + 49*diag_offset[i]; 824 ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr); 825 } 826 827 ierr = PetscFree(rtmp);CHKERRQ(ierr); 828 C->factor = FACTOR_LU; 829 C->assembled = PETSC_TRUE; 830 PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */ 831 PetscFunctionReturn(0); 832 } 833 834 /* Version for when blocks are 6 by 6 */ 835 #undef __FUNC__ 836 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6" 837 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B) 838 { 839 Mat C = *B; 840 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 841 IS perm = b->row; 842 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 843 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 844 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 845 MatScalar *u,*d,*w,*wp; 846 847 PetscFunctionBegin; 848 /* initialization */ 849 w = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w); 850 ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr); 851 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 852 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 853 for (i=0; i<mbs; i++) { 854 jl[i] = mbs; il[0] = 0; 855 } 856 dk = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk); 857 uik = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik); 858 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 859 860 /* check permutation */ 861 if (!a->permute){ 862 ai = a->i; aj = a->j; aa = a->a; 863 } else { 864 ai = a->inew; aj = a->jnew; 865 aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 866 ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 867 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 868 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 869 870 for (i=0; i<mbs; i++){ 871 jmin = ai[i]; jmax = ai[i+1]; 872 for (j=jmin; j<jmax; j++){ 873 while (a2anew[j] != j){ 874 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 875 for (k1=0; k1<36; k1++){ 876 dk[k1] = aa[k*36+k1]; 877 aa[k*36+k1] = aa[j*36+k1]; 878 aa[j*36+k1] = dk[k1]; 879 } 880 } 881 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 882 if (i > aj[j]){ 883 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 884 ap = aa + j*36; /* ptr to the beginning of j-th block of aa */ 885 for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 886 for (k=0; k<6; k++){ /* j-th block of aa <- dk^T */ 887 for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1]; 888 } 889 } 890 } 891 } 892 ierr = PetscFree(a2anew);CHKERRA(ierr); 893 } 894 895 /* for each row k */ 896 for (k = 0; k<mbs; k++){ 897 898 /*initialize k-th row with elements nonzero in row perm(k) of A */ 899 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 900 if (jmin < jmax) { 901 ap = aa + jmin*36; 902 for (j = jmin; j < jmax; j++){ 903 vj = perm_ptr[aj[j]]; /* block col. index */ 904 wp = w + vj*36; 905 for (i=0; i<36; i++) *wp++ = *ap++; 906 } 907 } 908 909 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 910 ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr); 911 i = jl[k]; /* first row to be added to k_th row */ 912 913 while (i < mbs){ 914 nexti = jl[i]; /* next row to be added to k_th row */ 915 916 /* compute multiplier */ 917 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 918 919 /* uik = -inv(Di)*U_bar(i,k) */ 920 d = ba + i*36; 921 u = ba + ili*36; 922 923 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]); 924 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]); 925 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]); 926 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]); 927 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]); 928 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]); 929 930 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]); 931 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]); 932 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]); 933 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]); 934 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]); 935 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]); 936 937 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]); 938 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]); 939 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]); 940 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]); 941 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]); 942 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]); 943 944 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]); 945 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]); 946 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]); 947 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]); 948 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]); 949 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]); 950 951 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]); 952 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]); 953 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]); 954 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]); 955 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]); 956 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]); 957 958 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]); 959 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]); 960 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]); 961 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]); 962 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]); 963 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]); 964 965 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 966 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]; 967 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]; 968 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]; 969 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]; 970 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]; 971 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]; 972 973 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]; 974 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]; 975 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]; 976 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]; 977 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]; 978 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]; 979 980 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]; 981 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]; 982 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]; 983 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]; 984 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]; 985 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]; 986 987 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]; 988 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]; 989 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]; 990 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]; 991 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]; 992 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]; 993 994 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]; 995 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]; 996 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]; 997 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]; 998 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]; 999 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]; 1000 1001 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]; 1002 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]; 1003 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]; 1004 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]; 1005 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]; 1006 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]; 1007 1008 /* update -U(i,k) */ 1009 ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr); 1010 1011 /* add multiple of row i to k-th row ... */ 1012 jmin = ili + 1; jmax = bi[i+1]; 1013 if (jmin < jmax){ 1014 for (j=jmin; j<jmax; j++) { 1015 /* w += -U(i,k)^T * U_bar(i,j) */ 1016 wp = w + bj[j]*36; 1017 u = ba + j*36; 1018 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]; 1019 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]; 1020 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]; 1021 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]; 1022 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]; 1023 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]; 1024 1025 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]; 1026 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]; 1027 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]; 1028 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]; 1029 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]; 1030 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]; 1031 1032 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]; 1033 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]; 1034 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]; 1035 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]; 1036 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]; 1037 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]; 1038 1039 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]; 1040 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]; 1041 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]; 1042 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]; 1043 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]; 1044 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]; 1045 1046 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]; 1047 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]; 1048 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]; 1049 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]; 1050 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]; 1051 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]; 1052 1053 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]; 1054 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]; 1055 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]; 1056 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]; 1057 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]; 1058 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]; 1059 } 1060 1061 /* ... add i to row list for next nonzero entry */ 1062 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1063 j = bj[jmin]; 1064 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1065 } 1066 i = nexti; 1067 } 1068 1069 /* save nonzero entries in k-th row of U ... */ 1070 1071 /* invert diagonal block */ 1072 d = ba+k*36; 1073 ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr); 1074 ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr); 1075 1076 jmin = bi[k]; jmax = bi[k+1]; 1077 if (jmin < jmax) { 1078 for (j=jmin; j<jmax; j++){ 1079 vj = bj[j]; /* block col. index of U */ 1080 u = ba + j*36; 1081 wp = w + vj*36; 1082 for (k1=0; k1<36; k1++){ 1083 *u++ = *wp; 1084 *wp++ = 0.0; 1085 } 1086 } 1087 1088 /* ... add k to row list for first nonzero entry in k-th row */ 1089 il[k] = jmin; 1090 i = bj[jmin]; 1091 jl[k] = jl[i]; jl[i] = k; 1092 } 1093 } 1094 1095 ierr = PetscFree(w);CHKERRQ(ierr); 1096 ierr = PetscFree(il);CHKERRQ(ierr); 1097 ierr = PetscFree(jl);CHKERRQ(ierr); 1098 ierr = PetscFree(dk);CHKERRQ(ierr); 1099 ierr = PetscFree(uik);CHKERRQ(ierr); 1100 if (a->permute){ 1101 ierr = PetscFree(aa);CHKERRQ(ierr); 1102 } 1103 1104 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1105 C->factor = FACTOR_CHOLESKY; 1106 C->assembled = PETSC_TRUE; 1107 C->preallocated = PETSC_TRUE; 1108 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1109 PetscFunctionReturn(0); 1110 } 1111 1112 /* 1113 Version for when blocks are 6 by 6 Using natural ordering 1114 */ 1115 #undef __FUNC__ 1116 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering" 1117 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B) 1118 { 1119 Mat C = *B; 1120 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1121 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1122 int *ajtmpold,*ajtmp,nz,row; 1123 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1124 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1125 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1126 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1127 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1128 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1129 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1130 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1131 MatScalar p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36; 1132 MatScalar x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36; 1133 MatScalar m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36; 1134 MatScalar *ba = b->a,*aa = a->a; 1135 1136 PetscFunctionBegin; 1137 rtmp = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1138 for (i=0; i<n; i++) { 1139 nz = bi[i+1] - bi[i]; 1140 ajtmp = bj + bi[i]; 1141 for (j=0; j<nz; j++) { 1142 x = rtmp+36*ajtmp[j]; 1143 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1144 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0; 1145 x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ; 1146 x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ; 1147 x[34] = x[35] = 0.0 ; 1148 } 1149 /* load in initial (unfactored row) */ 1150 nz = ai[i+1] - ai[i]; 1151 ajtmpold = aj + ai[i]; 1152 v = aa + 36*ai[i]; 1153 for (j=0; j<nz; j++) { 1154 x = rtmp+36*ajtmpold[j]; 1155 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1156 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; 1157 x[8] = v[8]; x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; 1158 x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15]; 1159 x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19]; 1160 x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1161 x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27]; 1162 x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31]; 1163 x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35]; 1164 v += 36; 1165 } 1166 row = *ajtmp++; 1167 while (row < i) { 1168 pc = rtmp + 36*row; 1169 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1170 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; 1171 p9 = pc[8]; p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; 1172 p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15]; 1173 p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19]; 1174 p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23]; 1175 p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27]; 1176 p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31]; 1177 p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35]; 1178 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || 1179 p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || 1180 p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || 1181 p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || 1182 p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || 1183 p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || 1184 p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || 1185 p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || 1186 p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) { 1187 pv = ba + 36*diag_offset[row]; 1188 pj = bj + diag_offset[row] + 1; 1189 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1190 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1191 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1192 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1193 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1194 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1195 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1196 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1197 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1198 pc[0] = m1 = p1*x1 + p7*x2 + p13*x3 + p19*x4 + p25*x5 + p31*x6; 1199 pc[1] = m2 = p2*x1 + p8*x2 + p14*x3 + p20*x4 + p26*x5 + p32*x6; 1200 pc[2] = m3 = p3*x1 + p9*x2 + p15*x3 + p21*x4 + p27*x5 + p33*x6; 1201 pc[3] = m4 = p4*x1 + p10*x2 + p16*x3 + p22*x4 + p28*x5 + p34*x6; 1202 pc[4] = m5 = p5*x1 + p11*x2 + p17*x3 + p23*x4 + p29*x5 + p35*x6; 1203 pc[5] = m6 = p6*x1 + p12*x2 + p18*x3 + p24*x4 + p30*x5 + p36*x6; 1204 1205 pc[6] = m7 = p1*x7 + p7*x8 + p13*x9 + p19*x10 + p25*x11 + p31*x12; 1206 pc[7] = m8 = p2*x7 + p8*x8 + p14*x9 + p20*x10 + p26*x11 + p32*x12; 1207 pc[8] = m9 = p3*x7 + p9*x8 + p15*x9 + p21*x10 + p27*x11 + p33*x12; 1208 pc[9] = m10 = p4*x7 + p10*x8 + p16*x9 + p22*x10 + p28*x11 + p34*x12; 1209 pc[10] = m11 = p5*x7 + p11*x8 + p17*x9 + p23*x10 + p29*x11 + p35*x12; 1210 pc[11] = m12 = p6*x7 + p12*x8 + p18*x9 + p24*x10 + p30*x11 + p36*x12; 1211 1212 pc[12] = m13 = p1*x13 + p7*x14 + p13*x15 + p19*x16 + p25*x17 + p31*x18; 1213 pc[13] = m14 = p2*x13 + p8*x14 + p14*x15 + p20*x16 + p26*x17 + p32*x18; 1214 pc[14] = m15 = p3*x13 + p9*x14 + p15*x15 + p21*x16 + p27*x17 + p33*x18; 1215 pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18; 1216 pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18; 1217 pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18; 1218 1219 pc[18] = m19 = p1*x19 + p7*x20 + p13*x21 + p19*x22 + p25*x23 + p31*x24; 1220 pc[19] = m20 = p2*x19 + p8*x20 + p14*x21 + p20*x22 + p26*x23 + p32*x24; 1221 pc[20] = m21 = p3*x19 + p9*x20 + p15*x21 + p21*x22 + p27*x23 + p33*x24; 1222 pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24; 1223 pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24; 1224 pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24; 1225 1226 pc[24] = m25 = p1*x25 + p7*x26 + p13*x27 + p19*x28 + p25*x29 + p31*x30; 1227 pc[25] = m26 = p2*x25 + p8*x26 + p14*x27 + p20*x28 + p26*x29 + p32*x30; 1228 pc[26] = m27 = p3*x25 + p9*x26 + p15*x27 + p21*x28 + p27*x29 + p33*x30; 1229 pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30; 1230 pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30; 1231 pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30; 1232 1233 pc[30] = m31 = p1*x31 + p7*x32 + p13*x33 + p19*x34 + p25*x35 + p31*x36; 1234 pc[31] = m32 = p2*x31 + p8*x32 + p14*x33 + p20*x34 + p26*x35 + p32*x36; 1235 pc[32] = m33 = p3*x31 + p9*x32 + p15*x33 + p21*x34 + p27*x35 + p33*x36; 1236 pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36; 1237 pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36; 1238 pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36; 1239 1240 nz = bi[row+1] - diag_offset[row] - 1; 1241 pv += 36; 1242 for (j=0; j<nz; j++) { 1243 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1244 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; 1245 x9 = pv[8]; x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; 1246 x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1247 x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19]; 1248 x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1249 x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27]; 1250 x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31]; 1251 x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35]; 1252 x = rtmp + 36*pj[j]; 1253 x[0] -= m1*x1 + m7*x2 + m13*x3 + m19*x4 + m25*x5 + m31*x6; 1254 x[1] -= m2*x1 + m8*x2 + m14*x3 + m20*x4 + m26*x5 + m32*x6; 1255 x[2] -= m3*x1 + m9*x2 + m15*x3 + m21*x4 + m27*x5 + m33*x6; 1256 x[3] -= m4*x1 + m10*x2 + m16*x3 + m22*x4 + m28*x5 + m34*x6; 1257 x[4] -= m5*x1 + m11*x2 + m17*x3 + m23*x4 + m29*x5 + m35*x6; 1258 x[5] -= m6*x1 + m12*x2 + m18*x3 + m24*x4 + m30*x5 + m36*x6; 1259 1260 x[6] -= m1*x7 + m7*x8 + m13*x9 + m19*x10 + m25*x11 + m31*x12; 1261 x[7] -= m2*x7 + m8*x8 + m14*x9 + m20*x10 + m26*x11 + m32*x12; 1262 x[8] -= m3*x7 + m9*x8 + m15*x9 + m21*x10 + m27*x11 + m33*x12; 1263 x[9] -= m4*x7 + m10*x8 + m16*x9 + m22*x10 + m28*x11 + m34*x12; 1264 x[10] -= m5*x7 + m11*x8 + m17*x9 + m23*x10 + m29*x11 + m35*x12; 1265 x[11] -= m6*x7 + m12*x8 + m18*x9 + m24*x10 + m30*x11 + m36*x12; 1266 1267 x[12] -= m1*x13 + m7*x14 + m13*x15 + m19*x16 + m25*x17 + m31*x18; 1268 x[13] -= m2*x13 + m8*x14 + m14*x15 + m20*x16 + m26*x17 + m32*x18; 1269 x[14] -= m3*x13 + m9*x14 + m15*x15 + m21*x16 + m27*x17 + m33*x18; 1270 x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18; 1271 x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18; 1272 x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18; 1273 1274 x[18] -= m1*x19 + m7*x20 + m13*x21 + m19*x22 + m25*x23 + m31*x24; 1275 x[19] -= m2*x19 + m8*x20 + m14*x21 + m20*x22 + m26*x23 + m32*x24; 1276 x[20] -= m3*x19 + m9*x20 + m15*x21 + m21*x22 + m27*x23 + m33*x24; 1277 x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24; 1278 x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24; 1279 x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24; 1280 1281 x[24] -= m1*x25 + m7*x26 + m13*x27 + m19*x28 + m25*x29 + m31*x30; 1282 x[25] -= m2*x25 + m8*x26 + m14*x27 + m20*x28 + m26*x29 + m32*x30; 1283 x[26] -= m3*x25 + m9*x26 + m15*x27 + m21*x28 + m27*x29 + m33*x30; 1284 x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30; 1285 x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30; 1286 x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30; 1287 1288 x[30] -= m1*x31 + m7*x32 + m13*x33 + m19*x34 + m25*x35 + m31*x36; 1289 x[31] -= m2*x31 + m8*x32 + m14*x33 + m20*x34 + m26*x35 + m32*x36; 1290 x[32] -= m3*x31 + m9*x32 + m15*x33 + m21*x34 + m27*x35 + m33*x36; 1291 x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36; 1292 x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36; 1293 x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36; 1294 1295 pv += 36; 1296 } 1297 PLogFlops(432*nz+396); 1298 } 1299 row = *ajtmp++; 1300 } 1301 /* finished row so stick it into b->a */ 1302 pv = ba + 36*bi[i]; 1303 pj = bj + bi[i]; 1304 nz = bi[i+1] - bi[i]; 1305 for (j=0; j<nz; j++) { 1306 x = rtmp+36*pj[j]; 1307 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1308 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; 1309 pv[8] = x[8]; pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; 1310 pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1311 pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; 1312 pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; 1313 pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27]; 1314 pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31]; 1315 pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35]; 1316 pv += 36; 1317 } 1318 /* invert diagonal block */ 1319 w = ba + 36*diag_offset[i]; 1320 ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr); 1321 } 1322 1323 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1324 C->factor = FACTOR_LU; 1325 C->assembled = PETSC_TRUE; 1326 PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */ 1327 PetscFunctionReturn(0); 1328 } 1329 1330 /* Version for when blocks are 5 by 5 */ 1331 #undef __FUNC__ 1332 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 1333 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B) 1334 { 1335 Mat C = *B; 1336 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1337 IS perm = b->row; 1338 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1339 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1340 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1341 MatScalar *u,*d,*rtmp,*rtmp_ptr; 1342 1343 PetscFunctionBegin; 1344 /* initialization */ 1345 rtmp = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1346 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1347 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1348 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1349 for (i=0; i<mbs; i++) { 1350 jl[i] = mbs; il[0] = 0; 1351 } 1352 dk = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk); 1353 uik = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik); 1354 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1355 1356 /* check permutation */ 1357 if (!a->permute){ 1358 ai = a->i; aj = a->j; aa = a->a; 1359 } else { 1360 ai = a->inew; aj = a->jnew; 1361 aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1362 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1363 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1364 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1365 1366 for (i=0; i<mbs; i++){ 1367 jmin = ai[i]; jmax = ai[i+1]; 1368 for (j=jmin; j<jmax; j++){ 1369 while (a2anew[j] != j){ 1370 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1371 for (k1=0; k1<25; k1++){ 1372 dk[k1] = aa[k*25+k1]; 1373 aa[k*25+k1] = aa[j*25+k1]; 1374 aa[j*25+k1] = dk[k1]; 1375 } 1376 } 1377 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1378 if (i > aj[j]){ 1379 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1380 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 1381 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1382 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 1383 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 1384 } 1385 } 1386 } 1387 } 1388 ierr = PetscFree(a2anew);CHKERRA(ierr); 1389 } 1390 1391 /* for each row k */ 1392 for (k = 0; k<mbs; k++){ 1393 1394 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1395 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1396 if (jmin < jmax) { 1397 ap = aa + jmin*25; 1398 for (j = jmin; j < jmax; j++){ 1399 vj = perm_ptr[aj[j]]; /* block col. index */ 1400 rtmp_ptr = rtmp + vj*25; 1401 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 1402 } 1403 } 1404 1405 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1406 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 1407 i = jl[k]; /* first row to be added to k_th row */ 1408 1409 while (i < mbs){ 1410 nexti = jl[i]; /* next row to be added to k_th row */ 1411 1412 /* compute multiplier */ 1413 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1414 1415 /* uik = -inv(Di)*U_bar(i,k) */ 1416 d = ba + i*25; 1417 u = ba + ili*25; 1418 1419 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 1420 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 1421 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 1422 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 1423 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 1424 1425 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 1426 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 1427 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 1428 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 1429 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 1430 1431 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 1432 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 1433 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 1434 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 1435 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 1436 1437 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 1438 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 1439 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 1440 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 1441 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 1442 1443 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 1444 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 1445 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 1446 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 1447 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 1448 1449 1450 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1451 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1452 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1453 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1454 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1455 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1456 1457 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1458 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1459 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1460 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1461 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1462 1463 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1464 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1465 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1466 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1467 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1468 1469 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1470 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1471 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1472 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1473 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1474 1475 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1476 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1477 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1478 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1479 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1480 1481 /* update -U(i,k) */ 1482 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 1483 1484 /* add multiple of row i to k-th row ... */ 1485 jmin = ili + 1; jmax = bi[i+1]; 1486 if (jmin < jmax){ 1487 for (j=jmin; j<jmax; j++) { 1488 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 1489 rtmp_ptr = rtmp + bj[j]*25; 1490 u = ba + j*25; 1491 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 1492 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 1493 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 1494 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 1495 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 1496 1497 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 1498 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 1499 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 1500 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 1501 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 1502 1503 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 1504 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 1505 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 1506 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 1507 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 1508 1509 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 1510 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 1511 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 1512 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 1513 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 1514 1515 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 1516 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 1517 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 1518 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 1519 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 1520 } 1521 1522 /* ... add i to row list for next nonzero entry */ 1523 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 1524 j = bj[jmin]; 1525 jl[i] = jl[j]; jl[j] = i; /* update jl */ 1526 } 1527 i = nexti; 1528 } 1529 1530 /* save nonzero entries in k-th row of U ... */ 1531 1532 /* invert diagonal block */ 1533 d = ba+k*25; 1534 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 1535 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 1536 1537 jmin = bi[k]; jmax = bi[k+1]; 1538 if (jmin < jmax) { 1539 for (j=jmin; j<jmax; j++){ 1540 vj = bj[j]; /* block col. index of U */ 1541 u = ba + j*25; 1542 rtmp_ptr = rtmp + vj*25; 1543 for (k1=0; k1<25; k1++){ 1544 *u++ = *rtmp_ptr; 1545 *rtmp_ptr++ = 0.0; 1546 } 1547 } 1548 1549 /* ... add k to row list for first nonzero entry in k-th row */ 1550 il[k] = jmin; 1551 i = bj[jmin]; 1552 jl[k] = jl[i]; jl[i] = k; 1553 } 1554 } 1555 1556 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1557 ierr = PetscFree(il);CHKERRQ(ierr); 1558 ierr = PetscFree(jl);CHKERRQ(ierr); 1559 ierr = PetscFree(dk);CHKERRQ(ierr); 1560 ierr = PetscFree(uik);CHKERRQ(ierr); 1561 if (a->permute){ 1562 ierr = PetscFree(aa);CHKERRQ(ierr); 1563 } 1564 1565 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 1566 C->factor = FACTOR_CHOLESKY; 1567 C->assembled = PETSC_TRUE; 1568 C->preallocated = PETSC_TRUE; 1569 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1570 PetscFunctionReturn(0); 1571 } 1572 1573 /* 1574 Version for when blocks are 5 by 5 Using natural ordering 1575 */ 1576 #undef __FUNC__ 1577 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 1578 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B) 1579 { 1580 Mat C = *B; 1581 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1582 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1583 int *ajtmpold,*ajtmp,nz,row; 1584 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1585 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1586 MatScalar x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; 1587 MatScalar x16,x17,x18,x19,x20,x21,x22,x23,x24,x25; 1588 MatScalar p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15; 1589 MatScalar p16,p17,p18,p19,p20,p21,p22,p23,p24,p25; 1590 MatScalar m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15; 1591 MatScalar m16,m17,m18,m19,m20,m21,m22,m23,m24,m25; 1592 MatScalar *ba = b->a,*aa = a->a; 1593 1594 PetscFunctionBegin; 1595 rtmp = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1596 for (i=0; i<n; i++) { 1597 nz = bi[i+1] - bi[i]; 1598 ajtmp = bj + bi[i]; 1599 for (j=0; j<nz; j++) { 1600 x = rtmp+25*ajtmp[j]; 1601 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1602 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1603 x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0; 1604 } 1605 /* load in initial (unfactored row) */ 1606 nz = ai[i+1] - ai[i]; 1607 ajtmpold = aj + ai[i]; 1608 v = aa + 25*ai[i]; 1609 for (j=0; j<nz; j++) { 1610 x = rtmp+25*ajtmpold[j]; 1611 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1612 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1613 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1614 x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; 1615 x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23]; 1616 x[24] = v[24]; 1617 v += 25; 1618 } 1619 row = *ajtmp++; 1620 while (row < i) { 1621 pc = rtmp + 25*row; 1622 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1623 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1624 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1625 p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; 1626 p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; 1627 p24 = pc[23]; p25 = pc[24]; 1628 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1629 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1630 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1631 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 1632 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) { 1633 pv = ba + 25*diag_offset[row]; 1634 pj = bj + diag_offset[row] + 1; 1635 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1636 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1637 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1638 x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; 1639 x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23]; 1640 x25 = pv[24]; 1641 pc[0] = m1 = p1*x1 + p6*x2 + p11*x3 + p16*x4 + p21*x5; 1642 pc[1] = m2 = p2*x1 + p7*x2 + p12*x3 + p17*x4 + p22*x5; 1643 pc[2] = m3 = p3*x1 + p8*x2 + p13*x3 + p18*x4 + p23*x5; 1644 pc[3] = m4 = p4*x1 + p9*x2 + p14*x3 + p19*x4 + p24*x5; 1645 pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5; 1646 1647 pc[5] = m6 = p1*x6 + p6*x7 + p11*x8 + p16*x9 + p21*x10; 1648 pc[6] = m7 = p2*x6 + p7*x7 + p12*x8 + p17*x9 + p22*x10; 1649 pc[7] = m8 = p3*x6 + p8*x7 + p13*x8 + p18*x9 + p23*x10; 1650 pc[8] = m9 = p4*x6 + p9*x7 + p14*x8 + p19*x9 + p24*x10; 1651 pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10; 1652 1653 pc[10] = m11 = p1*x11 + p6*x12 + p11*x13 + p16*x14 + p21*x15; 1654 pc[11] = m12 = p2*x11 + p7*x12 + p12*x13 + p17*x14 + p22*x15; 1655 pc[12] = m13 = p3*x11 + p8*x12 + p13*x13 + p18*x14 + p23*x15; 1656 pc[13] = m14 = p4*x11 + p9*x12 + p14*x13 + p19*x14 + p24*x15; 1657 pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15; 1658 1659 pc[15] = m16 = p1*x16 + p6*x17 + p11*x18 + p16*x19 + p21*x20; 1660 pc[16] = m17 = p2*x16 + p7*x17 + p12*x18 + p17*x19 + p22*x20; 1661 pc[17] = m18 = p3*x16 + p8*x17 + p13*x18 + p18*x19 + p23*x20; 1662 pc[18] = m19 = p4*x16 + p9*x17 + p14*x18 + p19*x19 + p24*x20; 1663 pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20; 1664 1665 pc[20] = m21 = p1*x21 + p6*x22 + p11*x23 + p16*x24 + p21*x25; 1666 pc[21] = m22 = p2*x21 + p7*x22 + p12*x23 + p17*x24 + p22*x25; 1667 pc[22] = m23 = p3*x21 + p8*x22 + p13*x23 + p18*x24 + p23*x25; 1668 pc[23] = m24 = p4*x21 + p9*x22 + p14*x23 + p19*x24 + p24*x25; 1669 pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25; 1670 1671 nz = bi[row+1] - diag_offset[row] - 1; 1672 pv += 25; 1673 for (j=0; j<nz; j++) { 1674 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1675 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1676 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1677 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; 1678 x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; 1679 x24 = pv[23]; x25 = pv[24]; 1680 x = rtmp + 25*pj[j]; 1681 x[0] -= m1*x1 + m6*x2 + m11*x3 + m16*x4 + m21*x5; 1682 x[1] -= m2*x1 + m7*x2 + m12*x3 + m17*x4 + m22*x5; 1683 x[2] -= m3*x1 + m8*x2 + m13*x3 + m18*x4 + m23*x5; 1684 x[3] -= m4*x1 + m9*x2 + m14*x3 + m19*x4 + m24*x5; 1685 x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5; 1686 1687 x[5] -= m1*x6 + m6*x7 + m11*x8 + m16*x9 + m21*x10; 1688 x[6] -= m2*x6 + m7*x7 + m12*x8 + m17*x9 + m22*x10; 1689 x[7] -= m3*x6 + m8*x7 + m13*x8 + m18*x9 + m23*x10; 1690 x[8] -= m4*x6 + m9*x7 + m14*x8 + m19*x9 + m24*x10; 1691 x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10; 1692 1693 x[10] -= m1*x11 + m6*x12 + m11*x13 + m16*x14 + m21*x15; 1694 x[11] -= m2*x11 + m7*x12 + m12*x13 + m17*x14 + m22*x15; 1695 x[12] -= m3*x11 + m8*x12 + m13*x13 + m18*x14 + m23*x15; 1696 x[13] -= m4*x11 + m9*x12 + m14*x13 + m19*x14 + m24*x15; 1697 x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15; 1698 1699 x[15] -= m1*x16 + m6*x17 + m11*x18 + m16*x19 + m21*x20; 1700 x[16] -= m2*x16 + m7*x17 + m12*x18 + m17*x19 + m22*x20; 1701 x[17] -= m3*x16 + m8*x17 + m13*x18 + m18*x19 + m23*x20; 1702 x[18] -= m4*x16 + m9*x17 + m14*x18 + m19*x19 + m24*x20; 1703 x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20; 1704 1705 x[20] -= m1*x21 + m6*x22 + m11*x23 + m16*x24 + m21*x25; 1706 x[21] -= m2*x21 + m7*x22 + m12*x23 + m17*x24 + m22*x25; 1707 x[22] -= m3*x21 + m8*x22 + m13*x23 + m18*x24 + m23*x25; 1708 x[23] -= m4*x21 + m9*x22 + m14*x23 + m19*x24 + m24*x25; 1709 x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25; 1710 pv += 25; 1711 } 1712 PLogFlops(250*nz+225); 1713 } 1714 row = *ajtmp++; 1715 } 1716 /* finished row so stick it into b->a */ 1717 pv = ba + 25*bi[i]; 1718 pj = bj + bi[i]; 1719 nz = bi[i+1] - bi[i]; 1720 for (j=0; j<nz; j++) { 1721 x = rtmp+25*pj[j]; 1722 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1723 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1724 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1725 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17]; 1726 pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; 1727 pv[23] = x[23]; pv[24] = x[24]; 1728 pv += 25; 1729 } 1730 /* invert diagonal block */ 1731 w = ba + 25*diag_offset[i]; 1732 ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr); 1733 } 1734 1735 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1736 C->factor = FACTOR_LU; 1737 C->assembled = PETSC_TRUE; 1738 PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 1739 PetscFunctionReturn(0); 1740 } 1741 1742 /* 1743 Version for when blocks are 4 by 4 Using natural ordering 1744 */ 1745 #undef __FUNC__ 1746 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 1747 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B) 1748 { 1749 Mat C = *B; 1750 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 1751 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 1752 int *ajtmpold,*ajtmp,nz,row; 1753 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 1754 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 1755 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 1756 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16; 1757 MatScalar p10,p11,p12,p13,p14,p15,p16,m10,m11,m12; 1758 MatScalar m13,m14,m15,m16; 1759 MatScalar *ba = b->a,*aa = a->a; 1760 1761 PetscFunctionBegin; 1762 rtmp = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 1763 1764 for (i=0; i<n; i++) { 1765 nz = bi[i+1] - bi[i]; 1766 ajtmp = bj + bi[i]; 1767 for (j=0; j<nz; j++) { 1768 x = rtmp+16*ajtmp[j]; 1769 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0; 1770 x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0; 1771 } 1772 /* load in initial (unfactored row) */ 1773 nz = ai[i+1] - ai[i]; 1774 ajtmpold = aj + ai[i]; 1775 v = aa + 16*ai[i]; 1776 for (j=0; j<nz; j++) { 1777 x = rtmp+16*ajtmpold[j]; 1778 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 1779 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 1780 x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13]; 1781 x[14] = v[14]; x[15] = v[15]; 1782 v += 16; 1783 } 1784 row = *ajtmp++; 1785 while (row < i) { 1786 pc = rtmp + 16*row; 1787 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 1788 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 1789 p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13]; 1790 p15 = pc[14]; p16 = pc[15]; 1791 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 1792 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || 1793 p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 1794 || p16 != 0.0) { 1795 pv = ba + 16*diag_offset[row]; 1796 pj = bj + diag_offset[row] + 1; 1797 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1798 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1799 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13]; 1800 x15 = pv[14]; x16 = pv[15]; 1801 pc[0] = m1 = p1*x1 + p5*x2 + p9*x3 + p13*x4; 1802 pc[1] = m2 = p2*x1 + p6*x2 + p10*x3 + p14*x4; 1803 pc[2] = m3 = p3*x1 + p7*x2 + p11*x3 + p15*x4; 1804 pc[3] = m4 = p4*x1 + p8*x2 + p12*x3 + p16*x4; 1805 1806 pc[4] = m5 = p1*x5 + p5*x6 + p9*x7 + p13*x8; 1807 pc[5] = m6 = p2*x5 + p6*x6 + p10*x7 + p14*x8; 1808 pc[6] = m7 = p3*x5 + p7*x6 + p11*x7 + p15*x8; 1809 pc[7] = m8 = p4*x5 + p8*x6 + p12*x7 + p16*x8; 1810 1811 pc[8] = m9 = p1*x9 + p5*x10 + p9*x11 + p13*x12; 1812 pc[9] = m10 = p2*x9 + p6*x10 + p10*x11 + p14*x12; 1813 pc[10] = m11 = p3*x9 + p7*x10 + p11*x11 + p15*x12; 1814 pc[11] = m12 = p4*x9 + p8*x10 + p12*x11 + p16*x12; 1815 1816 pc[12] = m13 = p1*x13 + p5*x14 + p9*x15 + p13*x16; 1817 pc[13] = m14 = p2*x13 + p6*x14 + p10*x15 + p14*x16; 1818 pc[14] = m15 = p3*x13 + p7*x14 + p11*x15 + p15*x16; 1819 pc[15] = m16 = p4*x13 + p8*x14 + p12*x15 + p16*x16; 1820 1821 nz = bi[row+1] - diag_offset[row] - 1; 1822 pv += 16; 1823 for (j=0; j<nz; j++) { 1824 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 1825 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 1826 x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; 1827 x14 = pv[13]; x15 = pv[14]; x16 = pv[15]; 1828 x = rtmp + 16*pj[j]; 1829 x[0] -= m1*x1 + m5*x2 + m9*x3 + m13*x4; 1830 x[1] -= m2*x1 + m6*x2 + m10*x3 + m14*x4; 1831 x[2] -= m3*x1 + m7*x2 + m11*x3 + m15*x4; 1832 x[3] -= m4*x1 + m8*x2 + m12*x3 + m16*x4; 1833 1834 x[4] -= m1*x5 + m5*x6 + m9*x7 + m13*x8; 1835 x[5] -= m2*x5 + m6*x6 + m10*x7 + m14*x8; 1836 x[6] -= m3*x5 + m7*x6 + m11*x7 + m15*x8; 1837 x[7] -= m4*x5 + m8*x6 + m12*x7 + m16*x8; 1838 1839 x[8] -= m1*x9 + m5*x10 + m9*x11 + m13*x12; 1840 x[9] -= m2*x9 + m6*x10 + m10*x11 + m14*x12; 1841 x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12; 1842 x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12; 1843 1844 x[12] -= m1*x13 + m5*x14 + m9*x15 + m13*x16; 1845 x[13] -= m2*x13 + m6*x14 + m10*x15 + m14*x16; 1846 x[14] -= m3*x13 + m7*x14 + m11*x15 + m15*x16; 1847 x[15] -= m4*x13 + m8*x14 + m12*x15 + m16*x16; 1848 1849 pv += 16; 1850 } 1851 PLogFlops(128*nz+112); 1852 } 1853 row = *ajtmp++; 1854 } 1855 /* finished row so stick it into b->a */ 1856 pv = ba + 16*bi[i]; 1857 pj = bj + bi[i]; 1858 nz = bi[i+1] - bi[i]; 1859 for (j=0; j<nz; j++) { 1860 x = rtmp+16*pj[j]; 1861 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 1862 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 1863 pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12]; 1864 pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; 1865 pv += 16; 1866 } 1867 /* invert diagonal block */ 1868 w = ba + 16*diag_offset[i]; 1869 ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr); 1870 } 1871 1872 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1873 C->factor = FACTOR_LU; 1874 C->assembled = PETSC_TRUE; 1875 C->preallocated = PETSC_TRUE; 1876 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 1877 PetscFunctionReturn(0); 1878 } 1879 1880 /* Version for when blocks are 4 by 4 */ 1881 #undef __FUNC__ 1882 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 1883 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 1884 { 1885 Mat C = *B; 1886 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 1887 IS perm = b->row; 1888 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 1889 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 1890 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 1891 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 1892 1893 PetscFunctionBegin; 1894 /* initialization */ 1895 rtmp = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 1896 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 1897 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 1898 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 1899 for (i=0; i<mbs; i++) { 1900 jl[i] = mbs; il[0] = 0; 1901 } 1902 dk = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk); 1903 uik = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik); 1904 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 1905 1906 /* check permutation */ 1907 if (!a->permute){ 1908 ai = a->i; aj = a->j; aa = a->a; 1909 } else { 1910 ai = a->inew; aj = a->jnew; 1911 aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 1912 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 1913 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 1914 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 1915 1916 for (i=0; i<mbs; i++){ 1917 jmin = ai[i]; jmax = ai[i+1]; 1918 for (j=jmin; j<jmax; j++){ 1919 while (a2anew[j] != j){ 1920 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 1921 for (k1=0; k1<16; k1++){ 1922 dk[k1] = aa[k*16+k1]; 1923 aa[k*16+k1] = aa[j*16+k1]; 1924 aa[j*16+k1] = dk[k1]; 1925 } 1926 } 1927 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 1928 if (i > aj[j]){ 1929 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 1930 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 1931 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 1932 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 1933 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 1934 } 1935 } 1936 } 1937 } 1938 ierr = PetscFree(a2anew);CHKERRA(ierr); 1939 } 1940 1941 /* for each row k */ 1942 for (k = 0; k<mbs; k++){ 1943 1944 /*initialize k-th row with elements nonzero in row perm(k) of A */ 1945 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 1946 if (jmin < jmax) { 1947 ap = aa + jmin*16; 1948 for (j = jmin; j < jmax; j++){ 1949 vj = perm_ptr[aj[j]]; /* block col. index */ 1950 rtmp_ptr = rtmp + vj*16; 1951 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 1952 } 1953 } 1954 1955 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 1956 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 1957 i = jl[k]; /* first row to be added to k_th row */ 1958 1959 while (i < mbs){ 1960 nexti = jl[i]; /* next row to be added to k_th row */ 1961 1962 /* compute multiplier */ 1963 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1964 1965 /* uik = -inv(Di)*U_bar(i,k) */ 1966 diag = ba + i*16; 1967 u = ba + ili*16; 1968 1969 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 1970 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 1971 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 1972 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 1973 1974 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 1975 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 1976 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 1977 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 1978 1979 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 1980 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 1981 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 1982 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 1983 1984 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 1985 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 1986 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 1987 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 1988 1989 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 1990 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 1991 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 1992 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 1993 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 1994 1995 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 1996 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 1997 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 1998 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 1999 2000 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2001 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2002 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2003 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2004 2005 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2006 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2007 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2008 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2009 2010 /* update -U(i,k) */ 2011 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 2012 2013 /* add multiple of row i to k-th row ... */ 2014 jmin = ili + 1; jmax = bi[i+1]; 2015 if (jmin < jmax){ 2016 for (j=jmin; j<jmax; j++) { 2017 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2018 rtmp_ptr = rtmp + bj[j]*16; 2019 u = ba + j*16; 2020 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 2021 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 2022 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 2023 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 2024 2025 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 2026 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 2027 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 2028 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 2029 2030 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 2031 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 2032 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 2033 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 2034 2035 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 2036 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 2037 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 2038 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 2039 } 2040 2041 /* ... add i to row list for next nonzero entry */ 2042 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2043 j = bj[jmin]; 2044 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2045 } 2046 i = nexti; 2047 } 2048 2049 /* save nonzero entries in k-th row of U ... */ 2050 2051 /* invert diagonal block */ 2052 diag = ba+k*16; 2053 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 2054 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 2055 2056 jmin = bi[k]; jmax = bi[k+1]; 2057 if (jmin < jmax) { 2058 for (j=jmin; j<jmax; j++){ 2059 vj = bj[j]; /* block col. index of U */ 2060 u = ba + j*16; 2061 rtmp_ptr = rtmp + vj*16; 2062 for (k1=0; k1<16; k1++){ 2063 *u++ = *rtmp_ptr; 2064 *rtmp_ptr++ = 0.0; 2065 } 2066 } 2067 2068 /* ... add k to row list for first nonzero entry in k-th row */ 2069 il[k] = jmin; 2070 i = bj[jmin]; 2071 jl[k] = jl[i]; jl[i] = k; 2072 } 2073 } 2074 2075 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2076 ierr = PetscFree(il);CHKERRQ(ierr); 2077 ierr = PetscFree(jl);CHKERRQ(ierr); 2078 ierr = PetscFree(dk);CHKERRQ(ierr); 2079 ierr = PetscFree(uik);CHKERRQ(ierr); 2080 if (a->permute){ 2081 ierr = PetscFree(aa);CHKERRQ(ierr); 2082 } 2083 2084 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2085 C->factor = FACTOR_CHOLESKY; 2086 C->assembled = PETSC_TRUE; 2087 C->preallocated = PETSC_TRUE; 2088 PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 2089 PetscFunctionReturn(0); 2090 } 2091 2092 /* Version for when blocks are 3 by 3 */ 2093 #undef __FUNC__ 2094 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 2095 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 2096 { 2097 Mat C = *B; 2098 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2099 IS perm = b->row; 2100 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2101 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2102 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2103 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2104 2105 PetscFunctionBegin; 2106 /* initialization */ 2107 rtmp = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2108 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2109 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2110 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2111 for (i=0; i<mbs; i++) { 2112 jl[i] = mbs; il[0] = 0; 2113 } 2114 dk = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk); 2115 uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik); 2116 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2117 2118 /* check permutation */ 2119 if (!a->permute){ 2120 ai = a->i; aj = a->j; aa = a->a; 2121 } else { 2122 ai = a->inew; aj = a->jnew; 2123 aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2124 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2125 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2126 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2127 2128 for (i=0; i<mbs; i++){ 2129 jmin = ai[i]; jmax = ai[i+1]; 2130 for (j=jmin; j<jmax; j++){ 2131 while (a2anew[j] != j){ 2132 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2133 for (k1=0; k1<9; k1++){ 2134 dk[k1] = aa[k*9+k1]; 2135 aa[k*9+k1] = aa[j*9+k1]; 2136 aa[j*9+k1] = dk[k1]; 2137 } 2138 } 2139 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2140 if (i > aj[j]){ 2141 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2142 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 2143 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 2144 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 2145 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 2146 } 2147 } 2148 } 2149 } 2150 ierr = PetscFree(a2anew);CHKERRA(ierr); 2151 } 2152 2153 /* for each row k */ 2154 for (k = 0; k<mbs; k++){ 2155 2156 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2157 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2158 if (jmin < jmax) { 2159 ap = aa + jmin*9; 2160 for (j = jmin; j < jmax; j++){ 2161 vj = perm_ptr[aj[j]]; /* block col. index */ 2162 rtmp_ptr = rtmp + vj*9; 2163 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 2164 } 2165 } 2166 2167 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2168 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 2169 i = jl[k]; /* first row to be added to k_th row */ 2170 2171 while (i < mbs){ 2172 nexti = jl[i]; /* next row to be added to k_th row */ 2173 2174 /* compute multiplier */ 2175 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2176 2177 /* uik = -inv(Di)*U_bar(i,k) */ 2178 diag = ba + i*9; 2179 u = ba + ili*9; 2180 2181 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 2182 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 2183 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 2184 2185 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 2186 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 2187 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 2188 2189 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 2190 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 2191 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 2192 2193 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 2194 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2195 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2196 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2197 2198 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2199 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2200 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2201 2202 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2203 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2204 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2205 2206 /* update -U(i,k) */ 2207 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 2208 2209 /* add multiple of row i to k-th row ... */ 2210 jmin = ili + 1; jmax = bi[i+1]; 2211 if (jmin < jmax){ 2212 for (j=jmin; j<jmax; j++) { 2213 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 2214 rtmp_ptr = rtmp + bj[j]*9; 2215 u = ba + j*9; 2216 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 2217 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 2218 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 2219 2220 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 2221 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 2222 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 2223 2224 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 2225 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 2226 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 2227 } 2228 2229 /* ... add i to row list for next nonzero entry */ 2230 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2231 j = bj[jmin]; 2232 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2233 } 2234 i = nexti; 2235 } 2236 2237 /* save nonzero entries in k-th row of U ... */ 2238 2239 /* invert diagonal block */ 2240 diag = ba+k*9; 2241 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 2242 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 2243 2244 jmin = bi[k]; jmax = bi[k+1]; 2245 if (jmin < jmax) { 2246 for (j=jmin; j<jmax; j++){ 2247 vj = bj[j]; /* block col. index of U */ 2248 u = ba + j*9; 2249 rtmp_ptr = rtmp + vj*9; 2250 for (k1=0; k1<9; k1++){ 2251 *u++ = *rtmp_ptr; 2252 *rtmp_ptr++ = 0.0; 2253 } 2254 } 2255 2256 /* ... add k to row list for first nonzero entry in k-th row */ 2257 il[k] = jmin; 2258 i = bj[jmin]; 2259 jl[k] = jl[i]; jl[i] = k; 2260 } 2261 } 2262 2263 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2264 ierr = PetscFree(il);CHKERRQ(ierr); 2265 ierr = PetscFree(jl);CHKERRQ(ierr); 2266 ierr = PetscFree(dk);CHKERRQ(ierr); 2267 ierr = PetscFree(uik);CHKERRQ(ierr); 2268 if (a->permute){ 2269 ierr = PetscFree(aa);CHKERRQ(ierr); 2270 } 2271 2272 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2273 C->factor = FACTOR_CHOLESKY; 2274 C->assembled = PETSC_TRUE; 2275 C->preallocated = PETSC_TRUE; 2276 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2277 PetscFunctionReturn(0); 2278 } 2279 2280 /* 2281 Version for when blocks are 3 by 3 Using natural ordering 2282 */ 2283 #undef __FUNC__ 2284 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 2285 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B) 2286 { 2287 Mat C = *B; 2288 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2289 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2290 int *ajtmpold,*ajtmp,nz,row; 2291 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2292 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2293 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4; 2294 MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9; 2295 MatScalar *ba = b->a,*aa = a->a; 2296 2297 PetscFunctionBegin; 2298 rtmp = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2299 2300 for (i=0; i<n; i++) { 2301 nz = bi[i+1] - bi[i]; 2302 ajtmp = bj + bi[i]; 2303 for (j=0; j<nz; j++) { 2304 x = rtmp+9*ajtmp[j]; 2305 x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0; 2306 } 2307 /* load in initial (unfactored row) */ 2308 nz = ai[i+1] - ai[i]; 2309 ajtmpold = aj + ai[i]; 2310 v = aa + 9*ai[i]; 2311 for (j=0; j<nz; j++) { 2312 x = rtmp+9*ajtmpold[j]; 2313 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2314 x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8]; 2315 v += 9; 2316 } 2317 row = *ajtmp++; 2318 while (row < i) { 2319 pc = rtmp + 9*row; 2320 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2321 p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8]; 2322 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || 2323 p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) { 2324 pv = ba + 9*diag_offset[row]; 2325 pj = bj + diag_offset[row] + 1; 2326 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2327 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2328 pc[0] = m1 = p1*x1 + p4*x2 + p7*x3; 2329 pc[1] = m2 = p2*x1 + p5*x2 + p8*x3; 2330 pc[2] = m3 = p3*x1 + p6*x2 + p9*x3; 2331 2332 pc[3] = m4 = p1*x4 + p4*x5 + p7*x6; 2333 pc[4] = m5 = p2*x4 + p5*x5 + p8*x6; 2334 pc[5] = m6 = p3*x4 + p6*x5 + p9*x6; 2335 2336 pc[6] = m7 = p1*x7 + p4*x8 + p7*x9; 2337 pc[7] = m8 = p2*x7 + p5*x8 + p8*x9; 2338 pc[8] = m9 = p3*x7 + p6*x8 + p9*x9; 2339 2340 nz = bi[row+1] - diag_offset[row] - 1; 2341 pv += 9; 2342 for (j=0; j<nz; j++) { 2343 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2344 x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8]; 2345 x = rtmp + 9*pj[j]; 2346 x[0] -= m1*x1 + m4*x2 + m7*x3; 2347 x[1] -= m2*x1 + m5*x2 + m8*x3; 2348 x[2] -= m3*x1 + m6*x2 + m9*x3; 2349 2350 x[3] -= m1*x4 + m4*x5 + m7*x6; 2351 x[4] -= m2*x4 + m5*x5 + m8*x6; 2352 x[5] -= m3*x4 + m6*x5 + m9*x6; 2353 2354 x[6] -= m1*x7 + m4*x8 + m7*x9; 2355 x[7] -= m2*x7 + m5*x8 + m8*x9; 2356 x[8] -= m3*x7 + m6*x8 + m9*x9; 2357 pv += 9; 2358 } 2359 PLogFlops(54*nz+36); 2360 } 2361 row = *ajtmp++; 2362 } 2363 /* finished row so stick it into b->a */ 2364 pv = ba + 9*bi[i]; 2365 pj = bj + bi[i]; 2366 nz = bi[i+1] - bi[i]; 2367 for (j=0; j<nz; j++) { 2368 x = rtmp+9*pj[j]; 2369 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2370 pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8]; 2371 pv += 9; 2372 } 2373 /* invert diagonal block */ 2374 w = ba + 9*diag_offset[i]; 2375 ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr); 2376 } 2377 2378 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2379 C->factor = FACTOR_CHOLESKY; 2380 C->assembled = PETSC_TRUE; 2381 C->preallocated = PETSC_TRUE; 2382 PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 2383 PetscFunctionReturn(0); 2384 } 2385 2386 /* 2387 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2388 Version for blocks 2 by 2. 2389 */ 2390 #undef __FUNC__ 2391 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2" 2392 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B) 2393 { 2394 Mat C = *B; 2395 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2396 IS perm = b->row; 2397 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 2398 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 2399 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 2400 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 2401 2402 PetscFunctionBegin; 2403 2404 /* initialization */ 2405 /* il and jl record the first nonzero element in each row of the accessing 2406 window U(0:k, k:mbs-1). 2407 jl: list of rows to be added to uneliminated rows 2408 i>= k: jl(i) is the first row to be added to row i 2409 i< k: jl(i) is the row following row i in some list of rows 2410 jl(i) = mbs indicates the end of a list 2411 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2412 row i of U */ 2413 rtmp = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2414 ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr); 2415 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2416 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2417 for (i=0; i<mbs; i++) { 2418 jl[i] = mbs; il[0] = 0; 2419 } 2420 dk = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk); 2421 uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik); 2422 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 2423 2424 /* check permutation */ 2425 if (!a->permute){ 2426 ai = a->i; aj = a->j; aa = a->a; 2427 } else { 2428 ai = a->inew; aj = a->jnew; 2429 aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2430 ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2431 a2anew = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew); 2432 ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2433 2434 for (i=0; i<mbs; i++){ 2435 jmin = ai[i]; jmax = ai[i+1]; 2436 for (j=jmin; j<jmax; j++){ 2437 while (a2anew[j] != j){ 2438 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 2439 for (k1=0; k1<4; k1++){ 2440 dk[k1] = aa[k*4+k1]; 2441 aa[k*4+k1] = aa[j*4+k1]; 2442 aa[j*4+k1] = dk[k1]; 2443 } 2444 } 2445 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 2446 if (i > aj[j]){ 2447 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 2448 ap = aa + j*4; /* ptr to the beginning of the block */ 2449 dk[1] = ap[1]; /* swap ap[1] and ap[2] */ 2450 ap[1] = ap[2]; 2451 ap[2] = dk[1]; 2452 } 2453 } 2454 } 2455 ierr = PetscFree(a2anew);CHKERRA(ierr); 2456 } 2457 2458 /* for each row k */ 2459 for (k = 0; k<mbs; k++){ 2460 2461 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2462 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 2463 if (jmin < jmax) { 2464 ap = aa + jmin*4; 2465 for (j = jmin; j < jmax; j++){ 2466 vj = perm_ptr[aj[j]]; /* block col. index */ 2467 rtmp_ptr = rtmp + vj*4; 2468 for (i=0; i<4; i++) *rtmp_ptr++ = *ap++; 2469 } 2470 } 2471 2472 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2473 ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr); 2474 i = jl[k]; /* first row to be added to k_th row */ 2475 2476 while (i < mbs){ 2477 nexti = jl[i]; /* next row to be added to k_th row */ 2478 2479 /* compute multiplier */ 2480 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2481 2482 /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */ 2483 diag = ba + i*4; 2484 u = ba + ili*4; 2485 uik[0] = -(diag[0]*u[0] + diag[2]*u[1]); 2486 uik[1] = -(diag[1]*u[0] + diag[3]*u[1]); 2487 uik[2] = -(diag[0]*u[2] + diag[2]*u[3]); 2488 uik[3] = -(diag[1]*u[2] + diag[3]*u[3]); 2489 2490 /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */ 2491 dk[0] += uik[0]*u[0] + uik[1]*u[1]; 2492 dk[1] += uik[2]*u[0] + uik[3]*u[1]; 2493 dk[2] += uik[0]*u[2] + uik[1]*u[3]; 2494 dk[3] += uik[2]*u[2] + uik[3]*u[3]; 2495 2496 /* update -U(i,k): ba[ili] = uik */ 2497 ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr); 2498 2499 /* add multiple of row i to k-th row ... */ 2500 jmin = ili + 1; jmax = bi[i+1]; 2501 if (jmin < jmax){ 2502 for (j=jmin; j<jmax; j++) { 2503 /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */ 2504 rtmp_ptr = rtmp + bj[j]*4; 2505 u = ba + j*4; 2506 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1]; 2507 rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1]; 2508 rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3]; 2509 rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3]; 2510 } 2511 2512 /* ... add i to row list for next nonzero entry */ 2513 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2514 j = bj[jmin]; 2515 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2516 } 2517 i = nexti; 2518 } 2519 2520 /* save nonzero entries in k-th row of U ... */ 2521 2522 /* invert diagonal block */ 2523 diag = ba+k*4; 2524 ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr); 2525 ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr); 2526 2527 jmin = bi[k]; jmax = bi[k+1]; 2528 if (jmin < jmax) { 2529 for (j=jmin; j<jmax; j++){ 2530 vj = bj[j]; /* block col. index of U */ 2531 u = ba + j*4; 2532 rtmp_ptr = rtmp + vj*4; 2533 for (k1=0; k1<4; k1++){ 2534 *u++ = *rtmp_ptr; 2535 *rtmp_ptr++ = 0.0; 2536 } 2537 } 2538 2539 /* ... add k to row list for first nonzero entry in k-th row */ 2540 il[k] = jmin; 2541 i = bj[jmin]; 2542 jl[k] = jl[i]; jl[i] = k; 2543 } 2544 } 2545 2546 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2547 ierr = PetscFree(il);CHKERRQ(ierr); 2548 ierr = PetscFree(jl);CHKERRQ(ierr); 2549 ierr = PetscFree(dk);CHKERRQ(ierr); 2550 ierr = PetscFree(uik);CHKERRQ(ierr); 2551 if (a->permute){ 2552 ierr = PetscFree(aa);CHKERRQ(ierr); 2553 } 2554 2555 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 2556 C->factor = FACTOR_CHOLESKY; 2557 C->assembled = PETSC_TRUE; 2558 C->preallocated = PETSC_TRUE; 2559 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2560 PetscFunctionReturn(0); 2561 } 2562 2563 /* 2564 Version for when blocks are 2 by 2 Using natural ordering 2565 */ 2566 #undef __FUNC__ 2567 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering" 2568 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B) 2569 { 2570 Mat C = *B; 2571 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data; 2572 int ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j; 2573 int *ajtmpold,*ajtmp,nz,row; 2574 int *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj; 2575 MatScalar *pv,*v,*rtmp,*pc,*w,*x; 2576 MatScalar p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4; 2577 MatScalar *ba = b->a,*aa = a->a; 2578 2579 PetscFunctionBegin; 2580 rtmp = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp); 2581 2582 for (i=0; i<n; i++) { 2583 nz = bi[i+1] - bi[i]; 2584 ajtmp = bj + bi[i]; 2585 for (j=0; j<nz; j++) { 2586 x = rtmp+4*ajtmp[j]; 2587 x[0] = x[1] = x[2] = x[3] = 0.0; 2588 } 2589 /* load in initial (unfactored row) */ 2590 nz = ai[i+1] - ai[i]; 2591 ajtmpold = aj + ai[i]; 2592 v = aa + 4*ai[i]; 2593 for (j=0; j<nz; j++) { 2594 x = rtmp+4*ajtmpold[j]; 2595 x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3]; 2596 v += 4; 2597 } 2598 row = *ajtmp++; 2599 while (row < i) { 2600 pc = rtmp + 4*row; 2601 p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3]; 2602 if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) { 2603 pv = ba + 4*diag_offset[row]; 2604 pj = bj + diag_offset[row] + 1; 2605 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2606 pc[0] = m1 = p1*x1 + p3*x2; 2607 pc[1] = m2 = p2*x1 + p4*x2; 2608 pc[2] = m3 = p1*x3 + p3*x4; 2609 pc[3] = m4 = p2*x3 + p4*x4; 2610 nz = bi[row+1] - diag_offset[row] - 1; 2611 pv += 4; 2612 for (j=0; j<nz; j++) { 2613 x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3]; 2614 x = rtmp + 4*pj[j]; 2615 x[0] -= m1*x1 + m3*x2; 2616 x[1] -= m2*x1 + m4*x2; 2617 x[2] -= m1*x3 + m3*x4; 2618 x[3] -= m2*x3 + m4*x4; 2619 pv += 4; 2620 } 2621 PLogFlops(16*nz+12); 2622 } 2623 row = *ajtmp++; 2624 } 2625 /* finished row so stick it into b->a */ 2626 pv = ba + 4*bi[i]; 2627 pj = bj + bi[i]; 2628 nz = bi[i+1] - bi[i]; 2629 for (j=0; j<nz; j++) { 2630 x = rtmp+4*pj[j]; 2631 pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3]; 2632 pv += 4; 2633 } 2634 /* invert diagonal block */ 2635 w = ba + 4*diag_offset[i]; 2636 ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr); 2637 /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/ 2638 } 2639 2640 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2641 C->factor = FACTOR_LU; 2642 C->assembled = PETSC_TRUE; 2643 C->preallocated = PETSC_TRUE; 2644 PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */ 2645 PetscFunctionReturn(0); 2646 } 2647 2648 /* 2649 Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP. 2650 Version for blocks are 1 by 1. 2651 */ 2652 #undef __FUNC__ 2653 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1" 2654 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B) 2655 { 2656 Mat C = *B; 2657 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 2658 IS ip = b->row; 2659 int *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j; 2660 int *ai,*aj,*r; 2661 MatScalar *rtmp; 2662 MatScalar *ba = b->a,*aa,ak; 2663 MatScalar dk,uikdi; 2664 int k,jmin,jmax,*jl,*il,vj,nexti,ili; 2665 2666 PetscFunctionBegin; 2667 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2668 if (!a->permute){ 2669 ai = a->i; aj = a->j; aa = a->a; 2670 } else { 2671 ai = a->inew; aj = a->jnew; 2672 aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa); 2673 ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 2674 r = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r); 2675 ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 2676 2677 jmin = ai[0]; jmax = ai[mbs]; 2678 for (j=jmin; j<jmax; j++){ 2679 while (r[j] != j){ 2680 k = r[j]; r[j] = r[k]; r[k] = k; 2681 ak = aa[k]; aa[k] = aa[j]; aa[j] = ak; 2682 } 2683 } 2684 ierr = PetscFree(r);CHKERRA(ierr); 2685 } 2686 2687 /* initialization */ 2688 /* il and jl record the first nonzero element in each row of the accessing 2689 window U(0:k, k:mbs-1). 2690 jl: list of rows to be added to uneliminated rows 2691 i>= k: jl(i) is the first row to be added to row i 2692 i< k: jl(i) is the row following row i in some list of rows 2693 jl(i) = mbs indicates the end of a list 2694 il(i): points to the first nonzero element in columns k,...,mbs-1 of 2695 row i of U */ 2696 rtmp = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp); 2697 il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il); 2698 jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl); 2699 for (i=0; i<mbs; i++) { 2700 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2701 } 2702 2703 /* for each row k */ 2704 for (k = 0; k<mbs; k++){ 2705 2706 /*initialize k-th row with elements nonzero in row perm(k) of A */ 2707 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2708 if (jmin < jmax) { 2709 for (j = jmin; j < jmax; j++){ 2710 vj = rip[aj[j]]; 2711 /* if (k <= vj)*/ rtmp[vj] = aa[j]; 2712 } 2713 } 2714 2715 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 2716 dk = rtmp[k]; 2717 i = jl[k]; /* first row to be added to k_th row */ 2718 /* printf(" k=%d, pivot row = %d\n",k,i); */ 2719 2720 while (i < mbs){ 2721 nexti = jl[i]; /* next row to be added to k_th row */ 2722 2723 /* compute multiplier, update D(k) and U(i,k) */ 2724 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2725 uikdi = - ba[ili]*ba[i]; 2726 dk += uikdi*ba[ili]; 2727 ba[ili] = uikdi; /* -U(i,k) */ 2728 2729 /* add multiple of row i to k-th row ... */ 2730 jmin = ili + 1; jmax = bi[i+1]; 2731 if (jmin < jmax){ 2732 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2733 /* ... add i to row list for next nonzero entry */ 2734 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 2735 j = bj[jmin]; 2736 jl[i] = jl[j]; jl[j] = i; /* update jl */ 2737 } 2738 i = nexti; /* printf(" pivot row i=%d\n",i); */ 2739 } 2740 2741 /* check for zero pivot and save diagoanl element */ 2742 if (dk == 0.0){ 2743 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot"); 2744 }else if (PetscRealPart(dk) < 0){ 2745 ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk); 2746 } 2747 2748 /* save nonzero entries in k-th row of U ... */ 2749 ba[k] = 1.0/dk; 2750 jmin = bi[k]; jmax = bi[k+1]; 2751 if (jmin < jmax) { 2752 for (j=jmin; j<jmax; j++){ 2753 vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0; 2754 } 2755 /* ... add k to row list for first nonzero entry in k-th row */ 2756 il[k] = jmin; 2757 i = bj[jmin]; 2758 jl[k] = jl[i]; jl[i] = k; 2759 } 2760 } 2761 2762 ierr = PetscFree(rtmp);CHKERRQ(ierr); 2763 ierr = PetscFree(il);CHKERRQ(ierr); 2764 ierr = PetscFree(jl);CHKERRQ(ierr); 2765 if (a->permute){ 2766 ierr = PetscFree(aa);CHKERRQ(ierr); 2767 } 2768 2769 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2770 C->factor = FACTOR_CHOLESKY; 2771 C->assembled = PETSC_TRUE; 2772 C->preallocated = PETSC_TRUE; 2773 PLogFlops(b->mbs); 2774 #ifdef TEMP 2775 printf("in factnum_1\n"); 2776 for (k=0; k<mbs; k++){ 2777 i = b->i[k+1] - b->i[k]; 2778 printf("\n b->i[%d]: %d, nzk: %d, diag: %g\n",k,b->i[k],i,b->a[k]); 2779 jmin = b->i[k]; jmax = b->i[k+1]; 2780 for (j=jmin; j<jmax; j++){ 2781 printf(" %d %g, ",b->j[j],b->a[j]); 2782 } 2783 } 2784 #endif 2785 PetscFunctionReturn(0); 2786 } 2787 2788 #undef __FUNC__ 2789 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ" 2790 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f) 2791 { 2792 int ierr; 2793 Mat C; 2794 2795 PetscFunctionBegin; 2796 ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr); 2797 ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr); 2798 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 2799 PetscFunctionReturn(0); 2800 } 2801 2802 2803