1 #ifdef PETSC_RCS_HEADER 2 static char vcid[] = "$Id: baijfact2.c,v 1.12 1998/10/08 17:55:25 bsmith Exp bsmith $"; 3 #endif 4 /* 5 Factorization code for BAIJ format. 6 */ 7 8 #include "src/mat/impls/baij/seq/baij.h" 9 #include "src/vec/vecimpl.h" 10 #include "src/inline/ilu.h" 11 12 /* ----------------------------------------------------------- */ 13 #undef __FUNC__ 14 #define __FUNC__ "MatSolve_SeqBAIJ_N" 15 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx) 16 { 17 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 18 IS iscol=a->col,isrow=a->row; 19 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j; 20 int nz,bs=a->bs,bs2=a->bs2,*rout,*cout; 21 Scalar *aa=a->a,*sum; 22 Scalar *x,*b,*lsum,*tmp,*v; 23 24 PetscFunctionBegin; 25 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 26 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 27 tmp = a->solve_work; 28 29 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 30 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 31 32 /* forward solve the lower triangular */ 33 PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar)); 34 for ( i=1; i<n; i++ ) { 35 v = aa + bs2*ai[i]; 36 vi = aj + ai[i]; 37 nz = a->diag[i] - ai[i]; 38 sum = tmp + bs*i; 39 PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar)); 40 while (nz--) { 41 Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++)); 42 v += bs2; 43 } 44 } 45 /* backward solve the upper triangular */ 46 lsum = a->solve_work + a->n; 47 for ( i=n-1; i>=0; i-- ){ 48 v = aa + bs2*(a->diag[i] + 1); 49 vi = aj + a->diag[i] + 1; 50 nz = ai[i+1] - a->diag[i] - 1; 51 PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar)); 52 while (nz--) { 53 Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++)); 54 v += bs2; 55 } 56 Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs); 57 PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar)); 58 } 59 60 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 61 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 62 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 63 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 64 PLogFlops(2*(a->bs2)*(a->nz) - a->n); 65 PetscFunctionReturn(0); 66 } 67 68 #undef __FUNC__ 69 #define __FUNC__ "MatSolve_SeqBAIJ_7" 70 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx) 71 { 72 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 73 IS iscol=a->col,isrow=a->row; 74 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 75 int *diag = a->diag; 76 Scalar *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7; 77 Scalar *x,*b,*tmp,*v; 78 79 PetscFunctionBegin; 80 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 81 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 82 tmp = a->solve_work; 83 84 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 85 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 86 87 /* forward solve the lower triangular */ 88 idx = 7*(*r++); 89 tmp[0] = b[idx]; tmp[1] = b[1+idx]; 90 tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx]; 91 tmp[5] = b[5+idx]; tmp[6] = b[6+idx]; 92 93 for ( i=1; i<n; i++ ) { 94 v = aa + 49*ai[i]; 95 vi = aj + ai[i]; 96 nz = diag[i] - ai[i]; 97 idx = 7*(*r++); 98 sum1 = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx]; 99 sum5 = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx]; 100 while (nz--) { 101 idx = 7*(*vi++); 102 x1 = tmp[idx]; x2 = tmp[1+idx];x3 = tmp[2+idx]; 103 x4 = tmp[3+idx];x5 = tmp[4+idx]; 104 x6 = tmp[5+idx];x7 = tmp[6+idx]; 105 sum1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 106 sum2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 107 sum3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 108 sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 109 sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 110 sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 111 sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 112 v += 49; 113 } 114 idx = 7*i; 115 tmp[idx] = sum1;tmp[1+idx] = sum2; 116 tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5; 117 tmp[5+idx] = sum6;tmp[6+idx] = sum7; 118 } 119 /* backward solve the upper triangular */ 120 for ( i=n-1; i>=0; i-- ){ 121 v = aa + 49*diag[i] + 49; 122 vi = aj + diag[i] + 1; 123 nz = ai[i+1] - diag[i] - 1; 124 idt = 7*i; 125 sum1 = tmp[idt]; sum2 = tmp[1+idt]; 126 sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt]; 127 sum6 = tmp[5+idt];sum7 = tmp[6+idt]; 128 while (nz--) { 129 idx = 7*(*vi++); 130 x1 = tmp[idx]; x2 = tmp[1+idx]; 131 x3 = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx]; 132 x6 = tmp[5+idx]; x7 = tmp[6+idx]; 133 sum1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 134 sum2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 135 sum3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 136 sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 137 sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 138 sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 139 sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 140 v += 49; 141 } 142 idc = 7*(*c--); 143 v = aa + 49*diag[i]; 144 x[idc] = tmp[idt] = v[0]*sum1+v[7]*sum2+v[14]*sum3+ 145 v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7; 146 x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+ 147 v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7; 148 x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+ 149 v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7; 150 x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+ 151 v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7; 152 x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+ 153 v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7; 154 x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+ 155 v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7; 156 x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+ 157 v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7; 158 } 159 160 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 161 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 162 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 163 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 164 PLogFlops(2*49*(a->nz) - a->n); 165 PetscFunctionReturn(0); 166 } 167 168 #undef __FUNC__ 169 #define __FUNC__ "MatSolve_SeqBAIJ_5" 170 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx) 171 { 172 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 173 IS iscol=a->col,isrow=a->row; 174 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 175 int *diag = a->diag; 176 Scalar *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5; 177 Scalar *x,*b,*tmp,*v; 178 179 PetscFunctionBegin; 180 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 181 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 182 tmp = a->solve_work; 183 184 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 185 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 186 187 /* forward solve the lower triangular */ 188 idx = 5*(*r++); 189 tmp[0] = b[idx]; tmp[1] = b[1+idx]; 190 tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx]; 191 for ( i=1; i<n; i++ ) { 192 v = aa + 25*ai[i]; 193 vi = aj + ai[i]; 194 nz = diag[i] - ai[i]; 195 idx = 5*(*r++); 196 sum1 = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx]; 197 sum5 = b[4+idx]; 198 while (nz--) { 199 idx = 5*(*vi++); 200 x1 = tmp[idx]; x2 = tmp[1+idx];x3 = tmp[2+idx]; 201 x4 = tmp[3+idx];x5 = tmp[4+idx]; 202 sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 203 sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 204 sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 205 sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 206 sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 207 v += 25; 208 } 209 idx = 5*i; 210 tmp[idx] = sum1;tmp[1+idx] = sum2; 211 tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5; 212 } 213 /* backward solve the upper triangular */ 214 for ( i=n-1; i>=0; i-- ){ 215 v = aa + 25*diag[i] + 25; 216 vi = aj + diag[i] + 1; 217 nz = ai[i+1] - diag[i] - 1; 218 idt = 5*i; 219 sum1 = tmp[idt]; sum2 = tmp[1+idt]; 220 sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt]; 221 while (nz--) { 222 idx = 5*(*vi++); 223 x1 = tmp[idx]; x2 = tmp[1+idx]; 224 x3 = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx]; 225 sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 226 sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 227 sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 228 sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 229 sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 230 v += 25; 231 } 232 idc = 5*(*c--); 233 v = aa + 25*diag[i]; 234 x[idc] = tmp[idt] = v[0]*sum1+v[5]*sum2+v[10]*sum3+ 235 v[15]*sum4+v[20]*sum5; 236 x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+ 237 v[16]*sum4+v[21]*sum5; 238 x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+ 239 v[17]*sum4+v[22]*sum5; 240 x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+ 241 v[18]*sum4+v[23]*sum5; 242 x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+ 243 v[19]*sum4+v[24]*sum5; 244 } 245 246 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 247 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 248 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 249 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 250 PLogFlops(2*25*(a->nz) - a->n); 251 PetscFunctionReturn(0); 252 } 253 254 #undef __FUNC__ 255 #define __FUNC__ "MatSolve_SeqBAIJ_4" 256 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx) 257 { 258 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 259 IS iscol=a->col,isrow=a->row; 260 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 261 int *diag = a->diag; 262 Scalar *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4; 263 Scalar *x,*b,*tmp,*v; 264 265 PetscFunctionBegin; 266 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 267 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 268 tmp = a->solve_work; 269 270 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 271 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 272 273 /* forward solve the lower triangular */ 274 idx = 4*(*r++); 275 tmp[0] = b[idx]; tmp[1] = b[1+idx]; 276 tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; 277 for ( i=1; i<n; i++ ) { 278 v = aa + 16*ai[i]; 279 vi = aj + ai[i]; 280 nz = diag[i] - ai[i]; 281 idx = 4*(*r++); 282 sum1 = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx]; 283 while (nz--) { 284 idx = 4*(*vi++); 285 x1 = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx]; 286 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 287 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 288 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 289 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 290 v += 16; 291 } 292 idx = 4*i; 293 tmp[idx] = sum1;tmp[1+idx] = sum2; 294 tmp[2+idx] = sum3;tmp[3+idx] = sum4; 295 } 296 /* backward solve the upper triangular */ 297 for ( i=n-1; i>=0; i-- ){ 298 v = aa + 16*diag[i] + 16; 299 vi = aj + diag[i] + 1; 300 nz = ai[i+1] - diag[i] - 1; 301 idt = 4*i; 302 sum1 = tmp[idt]; sum2 = tmp[1+idt]; 303 sum3 = tmp[2+idt];sum4 = tmp[3+idt]; 304 while (nz--) { 305 idx = 4*(*vi++); 306 x1 = tmp[idx]; x2 = tmp[1+idx]; 307 x3 = tmp[2+idx]; x4 = tmp[3+idx]; 308 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 309 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 310 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 311 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 312 v += 16; 313 } 314 idc = 4*(*c--); 315 v = aa + 16*diag[i]; 316 x[idc] = tmp[idt] = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4; 317 x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4; 318 x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4; 319 x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4; 320 } 321 322 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 323 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 324 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 325 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 326 PLogFlops(2*16*(a->nz) - a->n); 327 PetscFunctionReturn(0); 328 } 329 330 /* 331 Special case where the matrix was ILU(0) factored in the natural 332 ordering. This eliminates the need for the column and row permutation. 333 */ 334 #undef __FUNC__ 335 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering" 336 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx) 337 { 338 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 339 int n=a->mbs,*ai=a->i,*aj=a->j; 340 int ierr,*diag = a->diag; 341 Scalar *aa=a->a; 342 Scalar *x,*b; 343 344 PetscFunctionBegin; 345 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 346 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 347 348 /*#undef USE_FORTRAN_KERNEL_SOLVEBAIJ 349 #define USE_FORTRAN_KERNEL_SOLVEBAIJ */ 350 351 #if defined(USE_FORTRAN_KERNEL_SOLVEBAIJBLAS) 352 { 353 static Scalar w[2000]; /* very BAD need to fix */ 354 fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w); 355 } 356 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJ) 357 { 358 static Scalar w[2000]; /* very BAD need to fix */ 359 fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w); 360 } 361 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL) 362 fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b); 363 #else 364 { 365 Scalar sum1,sum2,sum3,sum4,x1,x2,x3,x4,*v; 366 int jdx,idt,idx,nz,*vi,i; 367 368 /* forward solve the lower triangular */ 369 idx = 0; 370 x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3]; 371 for ( i=1; i<n; i++ ) { 372 v = aa + 16*ai[i]; 373 vi = aj + ai[i]; 374 nz = diag[i] - ai[i]; 375 idx += 4; 376 sum1 = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx]; 377 while (nz--) { 378 jdx = 4*(*vi++); 379 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx]; 380 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 381 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 382 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 383 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 384 v += 16; 385 } 386 x[idx] = sum1; 387 x[1+idx] = sum2; 388 x[2+idx] = sum3; 389 x[3+idx] = sum4; 390 } 391 /* backward solve the upper triangular */ 392 for ( i=n-1; i>=0; i-- ){ 393 v = aa + 16*diag[i] + 16; 394 vi = aj + diag[i] + 1; 395 nz = ai[i+1] - diag[i] - 1; 396 idt = 4*i; 397 sum1 = x[idt]; sum2 = x[1+idt]; 398 sum3 = x[2+idt];sum4 = x[3+idt]; 399 while (nz--) { 400 idx = 4*(*vi++); 401 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; x4 = x[3+idx]; 402 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 403 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 404 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 405 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 406 v += 16; 407 } 408 v = aa + 16*diag[i]; 409 x[idt] = v[0]*sum1 + v[4]*sum2 + v[8]*sum3 + v[12]*sum4; 410 x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3 + v[13]*sum4; 411 x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4; 412 x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4; 413 } 414 } 415 #endif 416 417 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 418 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 419 PLogFlops(2*16*(a->nz) - a->n); 420 PetscFunctionReturn(0); 421 } 422 423 424 #undef __FUNC__ 425 #define __FUNC__ "MatSolve_SeqBAIJ_3" 426 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx) 427 { 428 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 429 IS iscol=a->col,isrow=a->row; 430 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 431 int *diag = a->diag; 432 Scalar *aa=a->a,sum1,sum2,sum3,x1,x2,x3; 433 Scalar *x,*b,*tmp,*v; 434 435 PetscFunctionBegin; 436 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 437 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 438 tmp = a->solve_work; 439 440 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 441 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 442 443 /* forward solve the lower triangular */ 444 idx = 3*(*r++); 445 tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx]; 446 for ( i=1; i<n; i++ ) { 447 v = aa + 9*ai[i]; 448 vi = aj + ai[i]; 449 nz = diag[i] - ai[i]; 450 idx = 3*(*r++); 451 sum1 = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx]; 452 while (nz--) { 453 idx = 3*(*vi++); 454 x1 = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx]; 455 sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 456 sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 457 sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 458 v += 9; 459 } 460 idx = 3*i; 461 tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3; 462 } 463 /* backward solve the upper triangular */ 464 for ( i=n-1; i>=0; i-- ){ 465 v = aa + 9*diag[i] + 9; 466 vi = aj + diag[i] + 1; 467 nz = ai[i+1] - diag[i] - 1; 468 idt = 3*i; 469 sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt]; 470 while (nz--) { 471 idx = 3*(*vi++); 472 x1 = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx]; 473 sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 474 sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 475 sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 476 v += 9; 477 } 478 idc = 3*(*c--); 479 v = aa + 9*diag[i]; 480 x[idc] = tmp[idt] = v[0]*sum1 + v[3]*sum2 + v[6]*sum3; 481 x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3; 482 x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3; 483 } 484 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 485 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 486 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 487 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 488 PLogFlops(2*9*(a->nz) - a->n); 489 PetscFunctionReturn(0); 490 } 491 492 #undef __FUNC__ 493 #define __FUNC__ "MatSolve_SeqBAIJ_2" 494 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx) 495 { 496 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 497 IS iscol=a->col,isrow=a->row; 498 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 499 int *diag = a->diag; 500 Scalar *aa=a->a,sum1,sum2,x1,x2; 501 Scalar *x,*b,*tmp,*v; 502 503 PetscFunctionBegin; 504 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 505 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 506 tmp = a->solve_work; 507 508 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 509 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 510 511 /* forward solve the lower triangular */ 512 idx = 2*(*r++); 513 tmp[0] = b[idx]; tmp[1] = b[1+idx]; 514 for ( i=1; i<n; i++ ) { 515 v = aa + 4*ai[i]; 516 vi = aj + ai[i]; 517 nz = diag[i] - ai[i]; 518 idx = 2*(*r++); 519 sum1 = b[idx]; sum2 = b[1+idx]; 520 while (nz--) { 521 idx = 2*(*vi++); 522 x1 = tmp[idx]; x2 = tmp[1+idx]; 523 sum1 -= v[0]*x1 + v[2]*x2; 524 sum2 -= v[1]*x1 + v[3]*x2; 525 v += 4; 526 } 527 idx = 2*i; 528 tmp[idx] = sum1; tmp[1+idx] = sum2; 529 } 530 /* backward solve the upper triangular */ 531 for ( i=n-1; i>=0; i-- ){ 532 v = aa + 4*diag[i] + 4; 533 vi = aj + diag[i] + 1; 534 nz = ai[i+1] - diag[i] - 1; 535 idt = 2*i; 536 sum1 = tmp[idt]; sum2 = tmp[1+idt]; 537 while (nz--) { 538 idx = 2*(*vi++); 539 x1 = tmp[idx]; x2 = tmp[1+idx]; 540 sum1 -= v[0]*x1 + v[2]*x2; 541 sum2 -= v[1]*x1 + v[3]*x2; 542 v += 4; 543 } 544 idc = 2*(*c--); 545 v = aa + 4*diag[i]; 546 x[idc] = tmp[idt] = v[0]*sum1 + v[2]*sum2; 547 x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2; 548 } 549 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 550 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 551 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 552 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 553 PLogFlops(2*4*(a->nz) - a->n); 554 PetscFunctionReturn(0); 555 } 556 557 558 #undef __FUNC__ 559 #define __FUNC__ "MatSolve_SeqBAIJ_1" 560 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx) 561 { 562 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 563 IS iscol=a->col,isrow=a->row; 564 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout; 565 int *diag = a->diag; 566 Scalar *aa=a->a,sum1; 567 Scalar *x,*b,*tmp,*v; 568 569 PetscFunctionBegin; 570 if (!n) PetscFunctionReturn(0); 571 572 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 573 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 574 tmp = a->solve_work; 575 576 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 577 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 578 579 /* forward solve the lower triangular */ 580 tmp[0] = b[*r++]; 581 for ( i=1; i<n; i++ ) { 582 v = aa + ai[i]; 583 vi = aj + ai[i]; 584 nz = diag[i] - ai[i]; 585 sum1 = b[*r++]; 586 while (nz--) { 587 sum1 -= (*v++)*tmp[*vi++]; 588 } 589 tmp[i] = sum1; 590 } 591 /* backward solve the upper triangular */ 592 for ( i=n-1; i>=0; i-- ){ 593 v = aa + diag[i] + 1; 594 vi = aj + diag[i] + 1; 595 nz = ai[i+1] - diag[i] - 1; 596 sum1 = tmp[i]; 597 while (nz--) { 598 sum1 -= (*v++)*tmp[*vi++]; 599 } 600 x[*c--] = tmp[i] = aa[diag[i]]*sum1; 601 } 602 603 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 604 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 605 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 606 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 607 PLogFlops(2*1*(a->nz) - a->n); 608 PetscFunctionReturn(0); 609 } 610 611 extern int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat,Mat*); 612 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec); 613 /* ----------------------------------------------------------------*/ 614 /* 615 This code is virtually identical to MatILUFactorSymbolic_SeqAIJ 616 except that the data structure of Mat_SeqAIJ is slightly different. 617 Not a good example of code reuse. 618 */ 619 #undef __FUNC__ 620 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ" 621 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels, 622 Mat *fact) 623 { 624 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b; 625 IS isicol; 626 int *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j; 627 int *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev; 628 int *dloc, idx, row,m,fm, nzf, nzi,len, realloc = 0; 629 int incrlev,nnz,i,bs = a->bs,bs2 = a->bs2; 630 PetscTruth col_identity, row_identity; 631 632 PetscFunctionBegin; 633 ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr); 634 635 /* special case that simply copies fill pattern */ 636 PetscValidHeaderSpecific(isrow,IS_COOKIE); 637 PetscValidHeaderSpecific(iscol,IS_COOKIE); 638 ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity); 639 if (levels == 0 && row_identity && col_identity) { 640 ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact); CHKERRQ(ierr); 641 (*fact)->factor = FACTOR_LU; 642 b = (Mat_SeqBAIJ *) (*fact)->data; 643 if (!b->diag) { 644 ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr); 645 } 646 b->row = isrow; 647 b->col = iscol; 648 b->icol = isicol; 649 b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 650 /* 651 Blocksize 4 has a special faster solver for ILU(0) factorization 652 with natural ordering 653 */ 654 if (b->bs == 4) { 655 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering; 656 (*fact)->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering; 657 } 658 PetscFunctionReturn(0); 659 } 660 661 ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr); 662 ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr); 663 664 /* get new row pointers */ 665 ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew); 666 ainew[0] = 0; 667 /* don't know how many column pointers are needed so estimate */ 668 jmax = (int) (f*ai[n] + 1); 669 ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew); 670 /* ajfill is level of fill for each fill entry */ 671 ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill); 672 /* fill is a linked list of nonzeros in active row */ 673 fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill); 674 /* im is level for each filled value */ 675 im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im); 676 /* dloc is location of diagonal in factor */ 677 dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc); 678 dloc[0] = 0; 679 for ( prow=0; prow<n; prow++ ) { 680 /* first copy previous fill into linked list */ 681 nzf = nz = ai[r[prow]+1] - ai[r[prow]]; 682 if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix"); 683 xi = aj + ai[r[prow]]; 684 fill[n] = n; 685 while (nz--) { 686 fm = n; 687 idx = ic[*xi++]; 688 do { 689 m = fm; 690 fm = fill[m]; 691 } while (fm < idx); 692 fill[m] = idx; 693 fill[idx] = fm; 694 im[idx] = 0; 695 } 696 nzi = 0; 697 row = fill[n]; 698 while ( row < prow ) { 699 incrlev = im[row] + 1; 700 nz = dloc[row]; 701 xi = ajnew + ainew[row] + nz; 702 flev = ajfill + ainew[row] + nz + 1; 703 nnz = ainew[row+1] - ainew[row] - nz - 1; 704 if (*xi++ != row) { 705 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal"); 706 } 707 fm = row; 708 while (nnz-- > 0) { 709 idx = *xi++; 710 if (*flev + incrlev > levels) { 711 flev++; 712 continue; 713 } 714 do { 715 m = fm; 716 fm = fill[m]; 717 } while (fm < idx); 718 if (fm != idx) { 719 im[idx] = *flev + incrlev; 720 fill[m] = idx; 721 fill[idx] = fm; 722 fm = idx; 723 nzf++; 724 } else { 725 if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev; 726 } 727 flev++; 728 } 729 row = fill[row]; 730 nzi++; 731 } 732 /* copy new filled row into permanent storage */ 733 ainew[prow+1] = ainew[prow] + nzf; 734 if (ainew[prow+1] > jmax) { 735 736 /* estimate how much additional space we will need */ 737 /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */ 738 /* just double the memory each time */ 739 int maxadd = jmax; 740 /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */ 741 if (maxadd < nzf) maxadd = (n-prow)*(nzf+1); 742 jmax += maxadd; 743 744 /* allocate a longer ajnew and ajfill */ 745 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 746 PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int)); 747 PetscFree(ajnew); 748 ajnew = xi; 749 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 750 PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int)); 751 PetscFree(ajfill); 752 ajfill = xi; 753 realloc++; /* count how many reallocations are needed */ 754 } 755 xi = ajnew + ainew[prow]; 756 flev = ajfill + ainew[prow]; 757 dloc[prow] = nzi; 758 fm = fill[n]; 759 while (nzf--) { 760 *xi++ = fm; 761 *flev++ = im[fm]; 762 fm = fill[fm]; 763 } 764 } 765 PetscFree(ajfill); 766 ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr); 767 ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr); 768 PetscFree(fill); PetscFree(im); 769 770 { 771 double af = ((double)ainew[n])/((double)ai[n]); 772 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n", 773 realloc,f,af); 774 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af); 775 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af); 776 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n"); 777 } 778 779 /* put together the new matrix */ 780 ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr); 781 PLogObjectParent(*fact,isicol); 782 b = (Mat_SeqBAIJ *) (*fact)->data; 783 PetscFree(b->imax); 784 b->singlemalloc = 0; 785 len = bs2*ainew[n]*sizeof(Scalar); 786 /* the next line frees the default space generated by the Create() */ 787 PetscFree(b->a); PetscFree(b->ilen); 788 b->a = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a); 789 b->j = ajnew; 790 b->i = ainew; 791 for ( i=0; i<n; i++ ) dloc[i] += ainew[i]; 792 b->diag = dloc; 793 b->ilen = 0; 794 b->imax = 0; 795 b->row = isrow; 796 b->col = iscol; 797 b->icol = isicol; 798 b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 799 /* In b structure: Free imax, ilen, old a, old j. 800 Allocate dloc, solve_work, new a, new j */ 801 PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar)); 802 b->maxnz = b->nz = ainew[n]; 803 (*fact)->factor = FACTOR_LU; 804 805 (*fact)->info.factor_mallocs = realloc; 806 (*fact)->info.fill_ratio_given = f; 807 (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]); 808 809 PetscFunctionReturn(0); 810 } 811 812 813 814 815