1 #ifdef PETSC_RCS_HEADER 2 static char vcid[] = "$Id: baijfact2.c,v 1.13 1998/10/08 17:59:44 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 #if defined(USE_FORTRAN_KERNEL_SOLVEBAIJBLAS) 349 { 350 static Scalar w[2000]; /* very BAD need to fix */ 351 fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w); 352 } 353 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJ) 354 { 355 static Scalar w[2000]; /* very BAD need to fix */ 356 fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w); 357 } 358 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL) 359 fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b); 360 #else 361 { 362 Scalar sum1,sum2,sum3,sum4,x1,x2,x3,x4,*v; 363 int jdx,idt,idx,nz,*vi,i; 364 365 /* forward solve the lower triangular */ 366 idx = 0; 367 x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3]; 368 for ( i=1; i<n; i++ ) { 369 v = aa + 16*ai[i]; 370 vi = aj + ai[i]; 371 nz = diag[i] - ai[i]; 372 idx += 4; 373 sum1 = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx]; 374 while (nz--) { 375 jdx = 4*(*vi++); 376 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx]; 377 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 378 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 379 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 380 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 381 v += 16; 382 } 383 x[idx] = sum1; 384 x[1+idx] = sum2; 385 x[2+idx] = sum3; 386 x[3+idx] = sum4; 387 } 388 /* backward solve the upper triangular */ 389 for ( i=n-1; i>=0; i-- ){ 390 v = aa + 16*diag[i] + 16; 391 vi = aj + diag[i] + 1; 392 nz = ai[i+1] - diag[i] - 1; 393 idt = 4*i; 394 sum1 = x[idt]; sum2 = x[1+idt]; 395 sum3 = x[2+idt];sum4 = x[3+idt]; 396 while (nz--) { 397 idx = 4*(*vi++); 398 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; x4 = x[3+idx]; 399 sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 400 sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 401 sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 402 sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 403 v += 16; 404 } 405 v = aa + 16*diag[i]; 406 x[idt] = v[0]*sum1 + v[4]*sum2 + v[8]*sum3 + v[12]*sum4; 407 x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3 + v[13]*sum4; 408 x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4; 409 x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4; 410 } 411 } 412 #endif 413 414 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 415 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 416 PLogFlops(2*16*(a->nz) - a->n); 417 PetscFunctionReturn(0); 418 } 419 420 421 #undef __FUNC__ 422 #define __FUNC__ "MatSolve_SeqBAIJ_3" 423 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx) 424 { 425 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 426 IS iscol=a->col,isrow=a->row; 427 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 428 int *diag = a->diag; 429 Scalar *aa=a->a,sum1,sum2,sum3,x1,x2,x3; 430 Scalar *x,*b,*tmp,*v; 431 432 PetscFunctionBegin; 433 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 434 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 435 tmp = a->solve_work; 436 437 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 438 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 439 440 /* forward solve the lower triangular */ 441 idx = 3*(*r++); 442 tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx]; 443 for ( i=1; i<n; i++ ) { 444 v = aa + 9*ai[i]; 445 vi = aj + ai[i]; 446 nz = diag[i] - ai[i]; 447 idx = 3*(*r++); 448 sum1 = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx]; 449 while (nz--) { 450 idx = 3*(*vi++); 451 x1 = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx]; 452 sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 453 sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 454 sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 455 v += 9; 456 } 457 idx = 3*i; 458 tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3; 459 } 460 /* backward solve the upper triangular */ 461 for ( i=n-1; i>=0; i-- ){ 462 v = aa + 9*diag[i] + 9; 463 vi = aj + diag[i] + 1; 464 nz = ai[i+1] - diag[i] - 1; 465 idt = 3*i; 466 sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt]; 467 while (nz--) { 468 idx = 3*(*vi++); 469 x1 = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx]; 470 sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 471 sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 472 sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 473 v += 9; 474 } 475 idc = 3*(*c--); 476 v = aa + 9*diag[i]; 477 x[idc] = tmp[idt] = v[0]*sum1 + v[3]*sum2 + v[6]*sum3; 478 x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3; 479 x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3; 480 } 481 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 482 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 483 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 484 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 485 PLogFlops(2*9*(a->nz) - a->n); 486 PetscFunctionReturn(0); 487 } 488 489 #undef __FUNC__ 490 #define __FUNC__ "MatSolve_SeqBAIJ_2" 491 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx) 492 { 493 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 494 IS iscol=a->col,isrow=a->row; 495 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 496 int *diag = a->diag; 497 Scalar *aa=a->a,sum1,sum2,x1,x2; 498 Scalar *x,*b,*tmp,*v; 499 500 PetscFunctionBegin; 501 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 502 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 503 tmp = a->solve_work; 504 505 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 506 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 507 508 /* forward solve the lower triangular */ 509 idx = 2*(*r++); 510 tmp[0] = b[idx]; tmp[1] = b[1+idx]; 511 for ( i=1; i<n; i++ ) { 512 v = aa + 4*ai[i]; 513 vi = aj + ai[i]; 514 nz = diag[i] - ai[i]; 515 idx = 2*(*r++); 516 sum1 = b[idx]; sum2 = b[1+idx]; 517 while (nz--) { 518 idx = 2*(*vi++); 519 x1 = tmp[idx]; x2 = tmp[1+idx]; 520 sum1 -= v[0]*x1 + v[2]*x2; 521 sum2 -= v[1]*x1 + v[3]*x2; 522 v += 4; 523 } 524 idx = 2*i; 525 tmp[idx] = sum1; tmp[1+idx] = sum2; 526 } 527 /* backward solve the upper triangular */ 528 for ( i=n-1; i>=0; i-- ){ 529 v = aa + 4*diag[i] + 4; 530 vi = aj + diag[i] + 1; 531 nz = ai[i+1] - diag[i] - 1; 532 idt = 2*i; 533 sum1 = tmp[idt]; sum2 = tmp[1+idt]; 534 while (nz--) { 535 idx = 2*(*vi++); 536 x1 = tmp[idx]; x2 = tmp[1+idx]; 537 sum1 -= v[0]*x1 + v[2]*x2; 538 sum2 -= v[1]*x1 + v[3]*x2; 539 v += 4; 540 } 541 idc = 2*(*c--); 542 v = aa + 4*diag[i]; 543 x[idc] = tmp[idt] = v[0]*sum1 + v[2]*sum2; 544 x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2; 545 } 546 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 547 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 548 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 549 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 550 PLogFlops(2*4*(a->nz) - a->n); 551 PetscFunctionReturn(0); 552 } 553 554 555 #undef __FUNC__ 556 #define __FUNC__ "MatSolve_SeqBAIJ_1" 557 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx) 558 { 559 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 560 IS iscol=a->col,isrow=a->row; 561 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout; 562 int *diag = a->diag; 563 Scalar *aa=a->a,sum1; 564 Scalar *x,*b,*tmp,*v; 565 566 PetscFunctionBegin; 567 if (!n) PetscFunctionReturn(0); 568 569 ierr = VecGetArray(bb,&b); CHKERRQ(ierr); 570 ierr = VecGetArray(xx,&x); CHKERRQ(ierr); 571 tmp = a->solve_work; 572 573 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 574 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 575 576 /* forward solve the lower triangular */ 577 tmp[0] = b[*r++]; 578 for ( i=1; i<n; i++ ) { 579 v = aa + ai[i]; 580 vi = aj + ai[i]; 581 nz = diag[i] - ai[i]; 582 sum1 = b[*r++]; 583 while (nz--) { 584 sum1 -= (*v++)*tmp[*vi++]; 585 } 586 tmp[i] = sum1; 587 } 588 /* backward solve the upper triangular */ 589 for ( i=n-1; i>=0; i-- ){ 590 v = aa + diag[i] + 1; 591 vi = aj + diag[i] + 1; 592 nz = ai[i+1] - diag[i] - 1; 593 sum1 = tmp[i]; 594 while (nz--) { 595 sum1 -= (*v++)*tmp[*vi++]; 596 } 597 x[*c--] = tmp[i] = aa[diag[i]]*sum1; 598 } 599 600 ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr); 601 ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr); 602 ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr); 603 ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr); 604 PLogFlops(2*1*(a->nz) - a->n); 605 PetscFunctionReturn(0); 606 } 607 608 extern int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat,Mat*); 609 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec); 610 /* ----------------------------------------------------------------*/ 611 /* 612 This code is virtually identical to MatILUFactorSymbolic_SeqAIJ 613 except that the data structure of Mat_SeqAIJ is slightly different. 614 Not a good example of code reuse. 615 */ 616 #undef __FUNC__ 617 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ" 618 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels, 619 Mat *fact) 620 { 621 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b; 622 IS isicol; 623 int *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j; 624 int *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev; 625 int *dloc, idx, row,m,fm, nzf, nzi,len, realloc = 0; 626 int incrlev,nnz,i,bs = a->bs,bs2 = a->bs2; 627 PetscTruth col_identity, row_identity; 628 629 PetscFunctionBegin; 630 ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr); 631 632 /* special case that simply copies fill pattern */ 633 PetscValidHeaderSpecific(isrow,IS_COOKIE); 634 PetscValidHeaderSpecific(iscol,IS_COOKIE); 635 ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity); 636 if (levels == 0 && row_identity && col_identity) { 637 ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact); CHKERRQ(ierr); 638 (*fact)->factor = FACTOR_LU; 639 b = (Mat_SeqBAIJ *) (*fact)->data; 640 if (!b->diag) { 641 ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr); 642 } 643 b->row = isrow; 644 b->col = iscol; 645 b->icol = isicol; 646 b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 647 /* 648 Blocksize 4 has a special faster solver for ILU(0) factorization 649 with natural ordering 650 */ 651 if (b->bs == 4) { 652 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering; 653 (*fact)->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering; 654 } 655 PetscFunctionReturn(0); 656 } 657 658 ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr); 659 ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr); 660 661 /* get new row pointers */ 662 ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew); 663 ainew[0] = 0; 664 /* don't know how many column pointers are needed so estimate */ 665 jmax = (int) (f*ai[n] + 1); 666 ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew); 667 /* ajfill is level of fill for each fill entry */ 668 ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill); 669 /* fill is a linked list of nonzeros in active row */ 670 fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill); 671 /* im is level for each filled value */ 672 im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im); 673 /* dloc is location of diagonal in factor */ 674 dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc); 675 dloc[0] = 0; 676 for ( prow=0; prow<n; prow++ ) { 677 /* first copy previous fill into linked list */ 678 nzf = nz = ai[r[prow]+1] - ai[r[prow]]; 679 if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix"); 680 xi = aj + ai[r[prow]]; 681 fill[n] = n; 682 while (nz--) { 683 fm = n; 684 idx = ic[*xi++]; 685 do { 686 m = fm; 687 fm = fill[m]; 688 } while (fm < idx); 689 fill[m] = idx; 690 fill[idx] = fm; 691 im[idx] = 0; 692 } 693 nzi = 0; 694 row = fill[n]; 695 while ( row < prow ) { 696 incrlev = im[row] + 1; 697 nz = dloc[row]; 698 xi = ajnew + ainew[row] + nz; 699 flev = ajfill + ainew[row] + nz + 1; 700 nnz = ainew[row+1] - ainew[row] - nz - 1; 701 if (*xi++ != row) { 702 SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal"); 703 } 704 fm = row; 705 while (nnz-- > 0) { 706 idx = *xi++; 707 if (*flev + incrlev > levels) { 708 flev++; 709 continue; 710 } 711 do { 712 m = fm; 713 fm = fill[m]; 714 } while (fm < idx); 715 if (fm != idx) { 716 im[idx] = *flev + incrlev; 717 fill[m] = idx; 718 fill[idx] = fm; 719 fm = idx; 720 nzf++; 721 } else { 722 if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev; 723 } 724 flev++; 725 } 726 row = fill[row]; 727 nzi++; 728 } 729 /* copy new filled row into permanent storage */ 730 ainew[prow+1] = ainew[prow] + nzf; 731 if (ainew[prow+1] > jmax) { 732 733 /* estimate how much additional space we will need */ 734 /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */ 735 /* just double the memory each time */ 736 int maxadd = jmax; 737 /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */ 738 if (maxadd < nzf) maxadd = (n-prow)*(nzf+1); 739 jmax += maxadd; 740 741 /* allocate a longer ajnew and ajfill */ 742 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 743 PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int)); 744 PetscFree(ajnew); 745 ajnew = xi; 746 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 747 PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int)); 748 PetscFree(ajfill); 749 ajfill = xi; 750 realloc++; /* count how many reallocations are needed */ 751 } 752 xi = ajnew + ainew[prow]; 753 flev = ajfill + ainew[prow]; 754 dloc[prow] = nzi; 755 fm = fill[n]; 756 while (nzf--) { 757 *xi++ = fm; 758 *flev++ = im[fm]; 759 fm = fill[fm]; 760 } 761 } 762 PetscFree(ajfill); 763 ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr); 764 ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr); 765 PetscFree(fill); PetscFree(im); 766 767 { 768 double af = ((double)ainew[n])/((double)ai[n]); 769 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n", 770 realloc,f,af); 771 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af); 772 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af); 773 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n"); 774 } 775 776 /* put together the new matrix */ 777 ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr); 778 PLogObjectParent(*fact,isicol); 779 b = (Mat_SeqBAIJ *) (*fact)->data; 780 PetscFree(b->imax); 781 b->singlemalloc = 0; 782 len = bs2*ainew[n]*sizeof(Scalar); 783 /* the next line frees the default space generated by the Create() */ 784 PetscFree(b->a); PetscFree(b->ilen); 785 b->a = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a); 786 b->j = ajnew; 787 b->i = ainew; 788 for ( i=0; i<n; i++ ) dloc[i] += ainew[i]; 789 b->diag = dloc; 790 b->ilen = 0; 791 b->imax = 0; 792 b->row = isrow; 793 b->col = iscol; 794 b->icol = isicol; 795 b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 796 /* In b structure: Free imax, ilen, old a, old j. 797 Allocate dloc, solve_work, new a, new j */ 798 PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar)); 799 b->maxnz = b->nz = ainew[n]; 800 (*fact)->factor = FACTOR_LU; 801 802 (*fact)->info.factor_mallocs = realloc; 803 (*fact)->info.fill_ratio_given = f; 804 (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]); 805 806 PetscFunctionReturn(0); 807 } 808 809 810 811 812