1 /*$Id: baijfact2.c,v 1.30 1999/10/24 14:02:28 bsmith Exp bsmith $*/ 2 /* 3 Factorization code for BAIJ format. 4 */ 5 6 #include "src/mat/impls/baij/seq/baij.h" 7 #include "src/vec/vecimpl.h" 8 #include "src/inline/ilu.h" 9 #include "src/inline/dot.h" 10 11 #undef __FUNC__ 12 #define __FUNC__ "MatSolveTrans_SeqBAIJ_1_NaturalOrdering" 13 int MatSolveTrans_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx) 14 { 15 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 16 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz; 17 int *diag = a->diag; 18 MatScalar *aa=a->a,*v; 19 Scalar s1,*x,*b; 20 21 PetscFunctionBegin; 22 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 23 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 24 25 /* forward solve the U^T */ 26 for ( i=0; i<n; i++ ) { 27 28 v = aa + diag[i]; 29 /* multiply by the inverse of the block diagonal */ 30 s1 = (*v++)*b[i]; 31 vi = aj + diag[i] + 1; 32 nz = ai[i+1] - diag[i] - 1; 33 while (nz--) { 34 x[*vi++] -= (*v++)*s1; 35 } 36 x[i] = s1; 37 } 38 /* backward solve the L^T */ 39 for ( i=n-1; i>=0; i-- ){ 40 v = aa + diag[i] - 1; 41 vi = aj + diag[i] - 1; 42 nz = diag[i] - ai[i]; 43 s1 = x[i]; 44 while (nz--) { 45 x[*vi--] -= (*v--)*s1; 46 } 47 } 48 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 49 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 50 PLogFlops(2*(a->nz) - a->n); 51 PetscFunctionReturn(0); 52 } 53 54 #undef __FUNC__ 55 #define __FUNC__ "MatSolveTrans_SeqBAIJ_2_NaturalOrdering" 56 int MatSolveTrans_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx) 57 { 58 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 59 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 60 int *diag = a->diag,oidx; 61 MatScalar *aa=a->a,*v; 62 Scalar s1,s2,x1,x2; 63 Scalar *x,*b; 64 65 PetscFunctionBegin; 66 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 67 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 68 69 /* forward solve the U^T */ 70 idx = 0; 71 for ( i=0; i<n; i++ ) { 72 73 v = aa + 4*diag[i]; 74 /* multiply by the inverse of the block diagonal */ 75 x1 = b[idx]; x2 = b[1+idx]; 76 s1 = v[0]*x1 + v[1]*x2; 77 s2 = v[2]*x1 + v[3]*x2; 78 v += 4; 79 80 vi = aj + diag[i] + 1; 81 nz = ai[i+1] - diag[i] - 1; 82 while (nz--) { 83 oidx = 2*(*vi++); 84 x[oidx] -= v[0]*s1 + v[1]*s2; 85 x[oidx+1] -= v[2]*s1 + v[3]*s2; 86 v += 4; 87 } 88 x[idx] = s1;x[1+idx] = s2; 89 idx += 2; 90 } 91 /* backward solve the L^T */ 92 for ( i=n-1; i>=0; i-- ){ 93 v = aa + 4*diag[i] - 4; 94 vi = aj + diag[i] - 1; 95 nz = diag[i] - ai[i]; 96 idt = 2*i; 97 s1 = x[idt]; s2 = x[1+idt]; 98 while (nz--) { 99 idx = 2*(*vi--); 100 x[idx] -= v[0]*s1 + v[1]*s2; 101 x[idx+1] -= v[2]*s1 + v[3]*s2; 102 v -= 4; 103 } 104 } 105 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 106 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 107 PLogFlops(2*4*(a->nz) - 2*a->n); 108 PetscFunctionReturn(0); 109 } 110 111 #undef __FUNC__ 112 #define __FUNC__ "MatSolveTrans_SeqBAIJ_3_NaturalOrdering" 113 int MatSolveTrans_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx) 114 { 115 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 116 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 117 int *diag = a->diag,oidx; 118 MatScalar *aa=a->a,*v; 119 Scalar s1,s2,s3,x1,x2,x3; 120 Scalar *x,*b; 121 122 PetscFunctionBegin; 123 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 124 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 125 126 /* forward solve the U^T */ 127 idx = 0; 128 for ( i=0; i<n; i++ ) { 129 130 v = aa + 9*diag[i]; 131 /* multiply by the inverse of the block diagonal */ 132 x1 = b[idx]; x2 = b[1+idx]; x3 = b[2+idx]; 133 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3; 134 s2 = v[3]*x1 + v[4]*x2 + v[5]*x3; 135 s3 = v[6]*x1 + v[7]*x2 + v[8]*x3; 136 v += 9; 137 138 vi = aj + diag[i] + 1; 139 nz = ai[i+1] - diag[i] - 1; 140 while (nz--) { 141 oidx = 3*(*vi++); 142 x[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3; 143 x[oidx+1] -= v[3]*s1 + v[4]*s2 + v[5]*s3; 144 x[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3; 145 v += 9; 146 } 147 x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3; 148 idx += 3; 149 } 150 /* backward solve the L^T */ 151 for ( i=n-1; i>=0; i-- ){ 152 v = aa + 9*diag[i] - 9; 153 vi = aj + diag[i] - 1; 154 nz = diag[i] - ai[i]; 155 idt = 3*i; 156 s1 = x[idt]; s2 = x[1+idt]; s3 = x[2+idt]; 157 while (nz--) { 158 idx = 3*(*vi--); 159 x[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3; 160 x[idx+1] -= v[3]*s1 + v[4]*s2 + v[5]*s3; 161 x[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3; 162 v -= 9; 163 } 164 } 165 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 166 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 167 PLogFlops(2*9*(a->nz) - 3*a->n); 168 PetscFunctionReturn(0); 169 } 170 171 #undef __FUNC__ 172 #define __FUNC__ "MatSolveTrans_SeqBAIJ_4_NaturalOrdering" 173 int MatSolveTrans_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx) 174 { 175 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 176 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 177 int *diag = a->diag,oidx; 178 MatScalar *aa=a->a,*v; 179 Scalar s1,s2,s3,s4,x1,x2,x3,x4; 180 Scalar *x,*b; 181 182 PetscFunctionBegin; 183 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 184 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 185 186 /* forward solve the U^T */ 187 idx = 0; 188 for ( i=0; i<n; i++ ) { 189 190 v = aa + 16*diag[i]; 191 /* multiply by the inverse of the block diagonal */ 192 x1 = b[idx]; x2 = b[1+idx]; x3 = b[2+idx]; x4 = b[3+idx]; 193 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4; 194 s2 = v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4; 195 s3 = v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4; 196 s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4; 197 v += 16; 198 199 vi = aj + diag[i] + 1; 200 nz = ai[i+1] - diag[i] - 1; 201 while (nz--) { 202 oidx = 4*(*vi++); 203 x[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4; 204 x[oidx+1] -= v[4]*s1 + v[5]*s2 + v[6]*s3 + v[7]*s4; 205 x[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4; 206 x[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4; 207 v += 16; 208 } 209 x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; 210 idx += 4; 211 } 212 /* backward solve the L^T */ 213 for ( i=n-1; i>=0; i-- ){ 214 v = aa + 16*diag[i] - 16; 215 vi = aj + diag[i] - 1; 216 nz = diag[i] - ai[i]; 217 idt = 4*i; 218 s1 = x[idt]; s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; 219 while (nz--) { 220 idx = 4*(*vi--); 221 x[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4; 222 x[idx+1] -= v[4]*s1 + v[5]*s2 + v[6]*s3 + v[7]*s4; 223 x[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4; 224 x[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4; 225 v -= 16; 226 } 227 } 228 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 229 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 230 PLogFlops(2*16*(a->nz) - 4*a->n); 231 PetscFunctionReturn(0); 232 } 233 234 #undef __FUNC__ 235 #define __FUNC__ "MatSolveTrans_SeqBAIJ_5_NaturalOrdering" 236 int MatSolveTrans_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx) 237 { 238 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 239 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 240 int *diag = a->diag,oidx; 241 MatScalar *aa=a->a,*v; 242 Scalar s1,s2,s3,s4,s5,x1,x2,x3,x4,x5; 243 Scalar *x,*b; 244 245 PetscFunctionBegin; 246 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 247 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 248 249 /* forward solve the U^T */ 250 idx = 0; 251 for ( i=0; i<n; i++ ) { 252 253 v = aa + 25*diag[i]; 254 /* multiply by the inverse of the block diagonal */ 255 x1 = b[idx]; x2 = b[1+idx]; x3 = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx]; 256 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5; 257 s2 = v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5; 258 s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5; 259 s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5; 260 s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5; 261 v += 25; 262 263 vi = aj + diag[i] + 1; 264 nz = ai[i+1] - diag[i] - 1; 265 while (nz--) { 266 oidx = 5*(*vi++); 267 x[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5; 268 x[oidx+1] -= v[5]*s1 + v[6]*s2 + v[7]*s3 + v[8]*s4 + v[9]*s5; 269 x[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5; 270 x[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5; 271 x[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5; 272 v += 25; 273 } 274 x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5; 275 idx += 5; 276 } 277 /* backward solve the L^T */ 278 for ( i=n-1; i>=0; i-- ){ 279 v = aa + 25*diag[i] - 25; 280 vi = aj + diag[i] - 1; 281 nz = diag[i] - ai[i]; 282 idt = 5*i; 283 s1 = x[idt]; s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt]; 284 while (nz--) { 285 idx = 5*(*vi--); 286 x[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5; 287 x[idx+1] -= v[5]*s1 + v[6]*s2 + v[7]*s3 + v[8]*s4 + v[9]*s5; 288 x[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5; 289 x[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5; 290 x[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5; 291 v -= 25; 292 } 293 } 294 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 295 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 296 PLogFlops(2*25*(a->nz) - 5*a->n); 297 PetscFunctionReturn(0); 298 } 299 300 #undef __FUNC__ 301 #define __FUNC__ "MatSolveTrans_SeqBAIJ_6_NaturalOrdering" 302 int MatSolveTrans_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx) 303 { 304 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 305 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 306 int *diag = a->diag,oidx; 307 MatScalar *aa=a->a,*v; 308 Scalar s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6; 309 Scalar *x,*b; 310 311 PetscFunctionBegin; 312 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 313 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 314 315 /* forward solve the U^T */ 316 idx = 0; 317 for ( i=0; i<n; i++ ) { 318 319 v = aa + 36*diag[i]; 320 /* multiply by the inverse of the block diagonal */ 321 x1 = b[idx]; x2 = b[1+idx]; x3 = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx]; 322 x6 = b[5+idx]; 323 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5 + v[5]*x6; 324 s2 = v[6]*x1 + v[7]*x2 + v[8]*x3 + v[9]*x4 + v[10]*x5 + v[11]*x6; 325 s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6; 326 s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6; 327 s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6; 328 s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6; 329 v += 36; 330 331 vi = aj + diag[i] + 1; 332 nz = ai[i+1] - diag[i] - 1; 333 while (nz--) { 334 oidx = 6*(*vi++); 335 x[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6; 336 x[oidx+1] -= v[6]*s1 + v[7]*s2 + v[8]*s3 + v[9]*s4 + v[10]*s5 + v[11]*s6; 337 x[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6; 338 x[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6; 339 x[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6; 340 x[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6; 341 v += 36; 342 } 343 x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5; 344 x[5+idx] = s6; 345 idx += 6; 346 } 347 /* backward solve the L^T */ 348 for ( i=n-1; i>=0; i-- ){ 349 v = aa + 36*diag[i] - 36; 350 vi = aj + diag[i] - 1; 351 nz = diag[i] - ai[i]; 352 idt = 6*i; 353 s1 = x[idt]; s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt]; 354 s6 = x[5+idt]; 355 while (nz--) { 356 idx = 6*(*vi--); 357 x[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6; 358 x[idx+1] -= v[6]*s1 + v[7]*s2 + v[8]*s3 + v[9]*s4 + v[10]*s5 + v[11]*s6; 359 x[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6; 360 x[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6; 361 x[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6; 362 x[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6; 363 v -= 36; 364 } 365 } 366 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 367 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 368 PLogFlops(2*36*(a->nz) - 6*a->n); 369 PetscFunctionReturn(0); 370 } 371 372 #undef __FUNC__ 373 #define __FUNC__ "MatSolveTrans_SeqBAIJ_7_NaturalOrdering" 374 int MatSolveTrans_SeqBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx) 375 { 376 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 377 int ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 378 int *diag = a->diag,oidx; 379 MatScalar *aa=a->a,*v; 380 Scalar s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7; 381 Scalar *x,*b; 382 383 PetscFunctionBegin; 384 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 385 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 386 387 /* forward solve the U^T */ 388 idx = 0; 389 for ( i=0; i<n; i++ ) { 390 391 v = aa + 49*diag[i]; 392 /* multiply by the inverse of the block diagonal */ 393 x1 = b[idx]; x2 = b[1+idx]; x3 = b[2+idx]; x4 = b[3+idx]; x5 = b[4+idx]; 394 x6 = b[5+idx]; x7 = b[6+idx]; 395 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5 + v[5]*x6 + v[6]*x7; 396 s2 = v[7]*x1 + v[8]*x2 + v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7; 397 s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7; 398 s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7; 399 s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7; 400 s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7; 401 s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7; 402 v += 49; 403 404 vi = aj + diag[i] + 1; 405 nz = ai[i+1] - diag[i] - 1; 406 while (nz--) { 407 oidx = 7*(*vi++); 408 x[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6 + v[6]*s7; 409 x[oidx+1] -= v[7]*s1 + v[8]*s2 + v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7; 410 x[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7; 411 x[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7; 412 x[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7; 413 x[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7; 414 x[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7; 415 v += 49; 416 } 417 x[idx] = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5; 418 x[5+idx] = s6;x[6+idx] = s7; 419 idx += 7; 420 } 421 /* backward solve the L^T */ 422 for ( i=n-1; i>=0; i-- ){ 423 v = aa + 49*diag[i] - 49; 424 vi = aj + diag[i] - 1; 425 nz = diag[i] - ai[i]; 426 idt = 7*i; 427 s1 = x[idt]; s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt]; 428 s6 = x[5+idt];s7 = x[6+idt]; 429 while (nz--) { 430 idx = 7*(*vi--); 431 x[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6 + v[6]*s7; 432 x[idx+1] -= v[7]*s1 + v[8]*s2 + v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7; 433 x[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7; 434 x[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7; 435 x[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7; 436 x[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7; 437 x[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7; 438 v -= 49; 439 } 440 } 441 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 442 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 443 PLogFlops(2*49*(a->nz) - 7*a->n); 444 PetscFunctionReturn(0); 445 } 446 447 /*---------------------------------------------------------------------------------------------*/ 448 #undef __FUNC__ 449 #define __FUNC__ "MatSolveTrans_SeqBAIJ_1" 450 int MatSolveTrans_SeqBAIJ_1(Mat A,Vec bb,Vec xx) 451 { 452 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 453 IS iscol=a->col,isrow=a->row; 454 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout; 455 int *diag = a->diag; 456 MatScalar *aa=a->a,*v; 457 Scalar s1,*x,*b,*t; 458 459 PetscFunctionBegin; 460 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 461 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 462 t = a->solve_work; 463 464 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 465 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 466 467 /* copy the b into temp work space according to permutation */ 468 for ( i=0; i<n; i++ ) { 469 t[i] = b[c[i]]; 470 } 471 472 /* forward solve the U^T */ 473 for ( i=0; i<n; i++ ) { 474 475 v = aa + diag[i]; 476 /* multiply by the inverse of the block diagonal */ 477 s1 = (*v++)*t[i]; 478 vi = aj + diag[i] + 1; 479 nz = ai[i+1] - diag[i] - 1; 480 while (nz--) { 481 t[*vi++] -= (*v++)*s1; 482 } 483 t[i] = s1; 484 } 485 /* backward solve the L^T */ 486 for ( i=n-1; i>=0; i-- ){ 487 v = aa + diag[i] - 1; 488 vi = aj + diag[i] - 1; 489 nz = diag[i] - ai[i]; 490 s1 = t[i]; 491 while (nz--) { 492 t[*vi--] -= (*v--)*s1; 493 } 494 } 495 496 /* copy t into x according to permutation */ 497 for ( i=0; i<n; i++ ) { 498 x[r[i]] = t[i]; 499 } 500 501 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 502 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 503 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 504 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 505 PLogFlops(2*(a->nz) - a->n); 506 PetscFunctionReturn(0); 507 } 508 509 #undef __FUNC__ 510 #define __FUNC__ "MatSolveTrans_SeqBAIJ_2" 511 int MatSolveTrans_SeqBAIJ_2(Mat A,Vec bb,Vec xx) 512 { 513 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 514 IS iscol=a->col,isrow=a->row; 515 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 516 int *diag = a->diag,ii,ic,ir,oidx; 517 MatScalar *aa=a->a,*v; 518 Scalar s1,s2,x1,x2; 519 Scalar *x,*b,*t; 520 521 PetscFunctionBegin; 522 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 523 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 524 t = a->solve_work; 525 526 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 527 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 528 529 /* copy the b into temp work space according to permutation */ 530 ii = 0; 531 for ( i=0; i<n; i++ ) { 532 ic = 2*c[i]; 533 t[ii] = b[ic]; 534 t[ii+1] = b[ic+1]; 535 ii += 2; 536 } 537 538 /* forward solve the U^T */ 539 idx = 0; 540 for ( i=0; i<n; i++ ) { 541 542 v = aa + 4*diag[i]; 543 /* multiply by the inverse of the block diagonal */ 544 x1 = t[idx]; x2 = t[1+idx]; 545 s1 = v[0]*x1 + v[1]*x2; 546 s2 = v[2]*x1 + v[3]*x2; 547 v += 4; 548 549 vi = aj + diag[i] + 1; 550 nz = ai[i+1] - diag[i] - 1; 551 while (nz--) { 552 oidx = 2*(*vi++); 553 t[oidx] -= v[0]*s1 + v[1]*s2; 554 t[oidx+1] -= v[2]*s1 + v[3]*s2; 555 v += 4; 556 } 557 t[idx] = s1;t[1+idx] = s2; 558 idx += 2; 559 } 560 /* backward solve the L^T */ 561 for ( i=n-1; i>=0; i-- ){ 562 v = aa + 4*diag[i] - 4; 563 vi = aj + diag[i] - 1; 564 nz = diag[i] - ai[i]; 565 idt = 2*i; 566 s1 = t[idt]; s2 = t[1+idt]; 567 while (nz--) { 568 idx = 2*(*vi--); 569 t[idx] -= v[0]*s1 + v[1]*s2; 570 t[idx+1] -= v[2]*s1 + v[3]*s2; 571 v -= 4; 572 } 573 } 574 575 /* copy t into x according to permutation */ 576 ii = 0; 577 for ( i=0; i<n; i++ ) { 578 ir = 2*r[i]; 579 x[ir] = t[ii]; 580 x[ir+1] = t[ii+1]; 581 ii += 2; 582 } 583 584 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 585 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 586 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 587 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 588 PLogFlops(2*4*(a->nz) - 2*a->n); 589 PetscFunctionReturn(0); 590 } 591 592 #undef __FUNC__ 593 #define __FUNC__ "MatSolveTrans_SeqBAIJ_3" 594 int MatSolveTrans_SeqBAIJ_3(Mat A,Vec bb,Vec xx) 595 { 596 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 597 IS iscol=a->col,isrow=a->row; 598 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 599 int *diag = a->diag,ii,ic,ir,oidx; 600 MatScalar *aa=a->a,*v; 601 Scalar s1,s2,s3,x1,x2,x3; 602 Scalar *x,*b,*t; 603 604 PetscFunctionBegin; 605 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 606 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 607 t = a->solve_work; 608 609 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 610 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 611 612 /* copy the b into temp work space according to permutation */ 613 ii = 0; 614 for ( i=0; i<n; i++ ) { 615 ic = 3*c[i]; 616 t[ii] = b[ic]; 617 t[ii+1] = b[ic+1]; 618 t[ii+2] = b[ic+2]; 619 ii += 3; 620 } 621 622 /* forward solve the U^T */ 623 idx = 0; 624 for ( i=0; i<n; i++ ) { 625 626 v = aa + 9*diag[i]; 627 /* multiply by the inverse of the block diagonal */ 628 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; 629 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3; 630 s2 = v[3]*x1 + v[4]*x2 + v[5]*x3; 631 s3 = v[6]*x1 + v[7]*x2 + v[8]*x3; 632 v += 9; 633 634 vi = aj + diag[i] + 1; 635 nz = ai[i+1] - diag[i] - 1; 636 while (nz--) { 637 oidx = 3*(*vi++); 638 t[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3; 639 t[oidx+1] -= v[3]*s1 + v[4]*s2 + v[5]*s3; 640 t[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3; 641 v += 9; 642 } 643 t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3; 644 idx += 3; 645 } 646 /* backward solve the L^T */ 647 for ( i=n-1; i>=0; i-- ){ 648 v = aa + 9*diag[i] - 9; 649 vi = aj + diag[i] - 1; 650 nz = diag[i] - ai[i]; 651 idt = 3*i; 652 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt]; 653 while (nz--) { 654 idx = 3*(*vi--); 655 t[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3; 656 t[idx+1] -= v[3]*s1 + v[4]*s2 + v[5]*s3; 657 t[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3; 658 v -= 9; 659 } 660 } 661 662 /* copy t into x according to permutation */ 663 ii = 0; 664 for ( i=0; i<n; i++ ) { 665 ir = 3*r[i]; 666 x[ir] = t[ii]; 667 x[ir+1] = t[ii+1]; 668 x[ir+2] = t[ii+2]; 669 ii += 3; 670 } 671 672 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 673 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 674 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 675 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 676 PLogFlops(2*9*(a->nz) - 3*a->n); 677 PetscFunctionReturn(0); 678 } 679 680 #undef __FUNC__ 681 #define __FUNC__ "MatSolveTrans_SeqBAIJ_4" 682 int MatSolveTrans_SeqBAIJ_4(Mat A,Vec bb,Vec xx) 683 { 684 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 685 IS iscol=a->col,isrow=a->row; 686 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 687 int *diag = a->diag,ii,ic,ir,oidx; 688 MatScalar *aa=a->a,*v; 689 Scalar s1,s2,s3,s4,x1,x2,x3,x4; 690 Scalar *x,*b,*t; 691 692 PetscFunctionBegin; 693 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 694 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 695 t = a->solve_work; 696 697 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 698 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 699 700 /* copy the b into temp work space according to permutation */ 701 ii = 0; 702 for ( i=0; i<n; i++ ) { 703 ic = 4*c[i]; 704 t[ii] = b[ic]; 705 t[ii+1] = b[ic+1]; 706 t[ii+2] = b[ic+2]; 707 t[ii+3] = b[ic+3]; 708 ii += 4; 709 } 710 711 /* forward solve the U^T */ 712 idx = 0; 713 for ( i=0; i<n; i++ ) { 714 715 v = aa + 16*diag[i]; 716 /* multiply by the inverse of the block diagonal */ 717 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; x4 = t[3+idx]; 718 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4; 719 s2 = v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4; 720 s3 = v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4; 721 s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4; 722 v += 16; 723 724 vi = aj + diag[i] + 1; 725 nz = ai[i+1] - diag[i] - 1; 726 while (nz--) { 727 oidx = 4*(*vi++); 728 t[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4; 729 t[oidx+1] -= v[4]*s1 + v[5]*s2 + v[6]*s3 + v[7]*s4; 730 t[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4; 731 t[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4; 732 v += 16; 733 } 734 t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; 735 idx += 4; 736 } 737 /* backward solve the L^T */ 738 for ( i=n-1; i>=0; i-- ){ 739 v = aa + 16*diag[i] - 16; 740 vi = aj + diag[i] - 1; 741 nz = diag[i] - ai[i]; 742 idt = 4*i; 743 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; 744 while (nz--) { 745 idx = 4*(*vi--); 746 t[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4; 747 t[idx+1] -= v[4]*s1 + v[5]*s2 + v[6]*s3 + v[7]*s4; 748 t[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4; 749 t[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4; 750 v -= 16; 751 } 752 } 753 754 /* copy t into x according to permutation */ 755 ii = 0; 756 for ( i=0; i<n; i++ ) { 757 ir = 4*r[i]; 758 x[ir] = t[ii]; 759 x[ir+1] = t[ii+1]; 760 x[ir+2] = t[ii+2]; 761 x[ir+3] = t[ii+3]; 762 ii += 4; 763 } 764 765 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 766 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 767 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 768 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 769 PLogFlops(2*16*(a->nz) - 4*a->n); 770 PetscFunctionReturn(0); 771 } 772 773 #undef __FUNC__ 774 #define __FUNC__ "MatSolveTrans_SeqBAIJ_5" 775 int MatSolveTrans_SeqBAIJ_5(Mat A,Vec bb,Vec xx) 776 { 777 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 778 IS iscol=a->col,isrow=a->row; 779 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 780 int *diag = a->diag,ii,ic,ir,oidx; 781 MatScalar *aa=a->a,*v; 782 Scalar s1,s2,s3,s4,s5,x1,x2,x3,x4,x5; 783 Scalar *x,*b,*t; 784 785 PetscFunctionBegin; 786 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 787 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 788 t = a->solve_work; 789 790 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 791 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 792 793 /* copy the b into temp work space according to permutation */ 794 ii = 0; 795 for ( i=0; i<n; i++ ) { 796 ic = 5*c[i]; 797 t[ii] = b[ic]; 798 t[ii+1] = b[ic+1]; 799 t[ii+2] = b[ic+2]; 800 t[ii+3] = b[ic+3]; 801 t[ii+4] = b[ic+4]; 802 ii += 5; 803 } 804 805 /* forward solve the U^T */ 806 idx = 0; 807 for ( i=0; i<n; i++ ) { 808 809 v = aa + 25*diag[i]; 810 /* multiply by the inverse of the block diagonal */ 811 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx]; 812 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5; 813 s2 = v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5; 814 s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5; 815 s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5; 816 s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5; 817 v += 25; 818 819 vi = aj + diag[i] + 1; 820 nz = ai[i+1] - diag[i] - 1; 821 while (nz--) { 822 oidx = 5*(*vi++); 823 t[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5; 824 t[oidx+1] -= v[5]*s1 + v[6]*s2 + v[7]*s3 + v[8]*s4 + v[9]*s5; 825 t[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5; 826 t[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5; 827 t[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5; 828 v += 25; 829 } 830 t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5; 831 idx += 5; 832 } 833 /* backward solve the L^T */ 834 for ( i=n-1; i>=0; i-- ){ 835 v = aa + 25*diag[i] - 25; 836 vi = aj + diag[i] - 1; 837 nz = diag[i] - ai[i]; 838 idt = 5*i; 839 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt]; 840 while (nz--) { 841 idx = 5*(*vi--); 842 t[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5; 843 t[idx+1] -= v[5]*s1 + v[6]*s2 + v[7]*s3 + v[8]*s4 + v[9]*s5; 844 t[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5; 845 t[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5; 846 t[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5; 847 v -= 25; 848 } 849 } 850 851 /* copy t into x according to permutation */ 852 ii = 0; 853 for ( i=0; i<n; i++ ) { 854 ir = 5*r[i]; 855 x[ir] = t[ii]; 856 x[ir+1] = t[ii+1]; 857 x[ir+2] = t[ii+2]; 858 x[ir+3] = t[ii+3]; 859 x[ir+4] = t[ii+4]; 860 ii += 5; 861 } 862 863 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 864 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 865 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 866 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 867 PLogFlops(2*25*(a->nz) - 5*a->n); 868 PetscFunctionReturn(0); 869 } 870 871 #undef __FUNC__ 872 #define __FUNC__ "MatSolveTrans_SeqBAIJ_6" 873 int MatSolveTrans_SeqBAIJ_6(Mat A,Vec bb,Vec xx) 874 { 875 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 876 IS iscol=a->col,isrow=a->row; 877 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 878 int *diag = a->diag,ii,ic,ir,oidx; 879 MatScalar *aa=a->a,*v; 880 Scalar s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6; 881 Scalar *x,*b,*t; 882 883 PetscFunctionBegin; 884 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 885 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 886 t = a->solve_work; 887 888 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 889 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 890 891 /* copy the b into temp work space according to permutation */ 892 ii = 0; 893 for ( i=0; i<n; i++ ) { 894 ic = 6*c[i]; 895 t[ii] = b[ic]; 896 t[ii+1] = b[ic+1]; 897 t[ii+2] = b[ic+2]; 898 t[ii+3] = b[ic+3]; 899 t[ii+4] = b[ic+4]; 900 t[ii+5] = b[ic+5]; 901 ii += 6; 902 } 903 904 /* forward solve the U^T */ 905 idx = 0; 906 for ( i=0; i<n; i++ ) { 907 908 v = aa + 36*diag[i]; 909 /* multiply by the inverse of the block diagonal */ 910 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx]; 911 x6 = t[5+idx]; 912 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5 + v[5]*x6; 913 s2 = v[6]*x1 + v[7]*x2 + v[8]*x3 + v[9]*x4 + v[10]*x5 + v[11]*x6; 914 s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6; 915 s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6; 916 s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6; 917 s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6; 918 v += 36; 919 920 vi = aj + diag[i] + 1; 921 nz = ai[i+1] - diag[i] - 1; 922 while (nz--) { 923 oidx = 6*(*vi++); 924 t[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6; 925 t[oidx+1] -= v[6]*s1 + v[7]*s2 + v[8]*s3 + v[9]*s4 + v[10]*s5 + v[11]*s6; 926 t[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6; 927 t[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6; 928 t[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6; 929 t[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6; 930 v += 36; 931 } 932 t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5; 933 t[5+idx] = s6; 934 idx += 6; 935 } 936 /* backward solve the L^T */ 937 for ( i=n-1; i>=0; i-- ){ 938 v = aa + 36*diag[i] - 36; 939 vi = aj + diag[i] - 1; 940 nz = diag[i] - ai[i]; 941 idt = 6*i; 942 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt]; 943 s6 = t[5+idt]; 944 while (nz--) { 945 idx = 6*(*vi--); 946 t[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6; 947 t[idx+1] -= v[6]*s1 + v[7]*s2 + v[8]*s3 + v[9]*s4 + v[10]*s5 + v[11]*s6; 948 t[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6; 949 t[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6; 950 t[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6; 951 t[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6; 952 v -= 36; 953 } 954 } 955 956 /* copy t into x according to permutation */ 957 ii = 0; 958 for ( i=0; i<n; i++ ) { 959 ir = 6*r[i]; 960 x[ir] = t[ii]; 961 x[ir+1] = t[ii+1]; 962 x[ir+2] = t[ii+2]; 963 x[ir+3] = t[ii+3]; 964 x[ir+4] = t[ii+4]; 965 x[ir+5] = t[ii+5]; 966 ii += 6; 967 } 968 969 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 970 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 971 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 972 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 973 PLogFlops(2*36*(a->nz) - 6*a->n); 974 PetscFunctionReturn(0); 975 } 976 977 #undef __FUNC__ 978 #define __FUNC__ "MatSolveTrans_SeqBAIJ_7" 979 int MatSolveTrans_SeqBAIJ_7(Mat A,Vec bb,Vec xx) 980 { 981 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 982 IS iscol=a->col,isrow=a->row; 983 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,*rout,*cout; 984 int *diag = a->diag,ii,ic,ir,oidx; 985 MatScalar *aa=a->a,*v; 986 Scalar s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7; 987 Scalar *x,*b,*t; 988 989 PetscFunctionBegin; 990 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 991 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 992 t = a->solve_work; 993 994 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 995 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 996 997 /* copy the b into temp work space according to permutation */ 998 ii = 0; 999 for ( i=0; i<n; i++ ) { 1000 ic = 7*c[i]; 1001 t[ii] = b[ic]; 1002 t[ii+1] = b[ic+1]; 1003 t[ii+2] = b[ic+2]; 1004 t[ii+3] = b[ic+3]; 1005 t[ii+4] = b[ic+4]; 1006 t[ii+5] = b[ic+5]; 1007 t[ii+6] = b[ic+6]; 1008 ii += 7; 1009 } 1010 1011 /* forward solve the U^T */ 1012 idx = 0; 1013 for ( i=0; i<n; i++ ) { 1014 1015 v = aa + 49*diag[i]; 1016 /* multiply by the inverse of the block diagonal */ 1017 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx]; 1018 x6 = t[5+idx]; x7 = t[6+idx]; 1019 s1 = v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5 + v[5]*x6 + v[6]*x7; 1020 s2 = v[7]*x1 + v[8]*x2 + v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7; 1021 s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7; 1022 s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7; 1023 s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7; 1024 s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7; 1025 s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7; 1026 v += 49; 1027 1028 vi = aj + diag[i] + 1; 1029 nz = ai[i+1] - diag[i] - 1; 1030 while (nz--) { 1031 oidx = 7*(*vi++); 1032 t[oidx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6 + v[6]*s7; 1033 t[oidx+1] -= v[7]*s1 + v[8]*s2 + v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7; 1034 t[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7; 1035 t[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7; 1036 t[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7; 1037 t[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7; 1038 t[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7; 1039 v += 49; 1040 } 1041 t[idx] = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5; 1042 t[5+idx] = s6;t[6+idx] = s7; 1043 idx += 7; 1044 } 1045 /* backward solve the L^T */ 1046 for ( i=n-1; i>=0; i-- ){ 1047 v = aa + 49*diag[i] - 49; 1048 vi = aj + diag[i] - 1; 1049 nz = diag[i] - ai[i]; 1050 idt = 7*i; 1051 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt]; 1052 s6 = t[5+idt];s7 = t[6+idt]; 1053 while (nz--) { 1054 idx = 7*(*vi--); 1055 t[idx] -= v[0]*s1 + v[1]*s2 + v[2]*s3 + v[3]*s4 + v[4]*s5 + v[5]*s6 + v[6]*s7; 1056 t[idx+1] -= v[7]*s1 + v[8]*s2 + v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7; 1057 t[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7; 1058 t[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7; 1059 t[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7; 1060 t[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7; 1061 t[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7; 1062 v -= 49; 1063 } 1064 } 1065 1066 /* copy t into x according to permutation */ 1067 ii = 0; 1068 for ( i=0; i<n; i++ ) { 1069 ir = 7*r[i]; 1070 x[ir] = t[ii]; 1071 x[ir+1] = t[ii+1]; 1072 x[ir+2] = t[ii+2]; 1073 x[ir+3] = t[ii+3]; 1074 x[ir+4] = t[ii+4]; 1075 x[ir+5] = t[ii+5]; 1076 x[ir+6] = t[ii+6]; 1077 ii += 7; 1078 } 1079 1080 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1081 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1082 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1083 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1084 PLogFlops(2*49*(a->nz) - 7*a->n); 1085 PetscFunctionReturn(0); 1086 } 1087 1088 /* ----------------------------------------------------------- */ 1089 #undef __FUNC__ 1090 #define __FUNC__ "MatSolve_SeqBAIJ_N" 1091 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx) 1092 { 1093 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1094 IS iscol=a->col,isrow=a->row; 1095 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j; 1096 int nz,bs=a->bs,bs2=a->bs2,*rout,*cout; 1097 MatScalar *aa=a->a,*v; 1098 Scalar *x,*b,*s,*t,*ls; 1099 1100 PetscFunctionBegin; 1101 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1102 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1103 t = a->solve_work; 1104 1105 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1106 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1107 1108 /* forward solve the lower triangular */ 1109 ierr = PetscMemcpy(t,b+bs*(*r++),bs*sizeof(Scalar));CHKERRQ(ierr); 1110 for ( i=1; i<n; i++ ) { 1111 v = aa + bs2*ai[i]; 1112 vi = aj + ai[i]; 1113 nz = a->diag[i] - ai[i]; 1114 s = t + bs*i; 1115 ierr = PetscMemcpy(s,b+bs*(*r++),bs*sizeof(Scalar));CHKERRQ(ierr); 1116 while (nz--) { 1117 Kernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*(*vi++)); 1118 v += bs2; 1119 } 1120 } 1121 /* backward solve the upper triangular */ 1122 ls = a->solve_work + a->n; 1123 for ( i=n-1; i>=0; i-- ){ 1124 v = aa + bs2*(a->diag[i] + 1); 1125 vi = aj + a->diag[i] + 1; 1126 nz = ai[i+1] - a->diag[i] - 1; 1127 ierr = PetscMemcpy(ls,t+i*bs,bs*sizeof(Scalar));CHKERRQ(ierr); 1128 while (nz--) { 1129 Kernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*(*vi++)); 1130 v += bs2; 1131 } 1132 Kernel_w_gets_A_times_v(bs,ls,aa+bs2*a->diag[i],t+i*bs); 1133 ierr = PetscMemcpy(x + bs*(*c--),t+i*bs,bs*sizeof(Scalar));CHKERRQ(ierr); 1134 } 1135 1136 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1137 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1138 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1139 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1140 PLogFlops(2*(a->bs2)*(a->nz) - a->bs*a->n); 1141 PetscFunctionReturn(0); 1142 } 1143 1144 #undef __FUNC__ 1145 #define __FUNC__ "MatSolve_SeqBAIJ_7" 1146 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx) 1147 { 1148 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1149 IS iscol=a->col,isrow=a->row; 1150 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1151 int *diag = a->diag; 1152 MatScalar *aa=a->a,*v; 1153 Scalar s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7; 1154 Scalar *x,*b,*t; 1155 1156 PetscFunctionBegin; 1157 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1158 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1159 t = a->solve_work; 1160 1161 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1162 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1163 1164 /* forward solve the lower triangular */ 1165 idx = 7*(*r++); 1166 t[0] = b[idx]; t[1] = b[1+idx]; 1167 t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx]; 1168 t[5] = b[5+idx]; t[6] = b[6+idx]; 1169 1170 for ( i=1; i<n; i++ ) { 1171 v = aa + 49*ai[i]; 1172 vi = aj + ai[i]; 1173 nz = diag[i] - ai[i]; 1174 idx = 7*(*r++); 1175 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx]; 1176 s5 = b[4+idx];s6 = b[5+idx];s7 = b[6+idx]; 1177 while (nz--) { 1178 idx = 7*(*vi++); 1179 x1 = t[idx]; x2 = t[1+idx];x3 = t[2+idx]; 1180 x4 = t[3+idx];x5 = t[4+idx]; 1181 x6 = t[5+idx];x7 = t[6+idx]; 1182 s1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 1183 s2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 1184 s3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 1185 s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 1186 s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 1187 s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 1188 s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 1189 v += 49; 1190 } 1191 idx = 7*i; 1192 t[idx] = s1;t[1+idx] = s2; 1193 t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5; 1194 t[5+idx] = s6;t[6+idx] = s7; 1195 } 1196 /* backward solve the upper triangular */ 1197 for ( i=n-1; i>=0; i-- ){ 1198 v = aa + 49*diag[i] + 49; 1199 vi = aj + diag[i] + 1; 1200 nz = ai[i+1] - diag[i] - 1; 1201 idt = 7*i; 1202 s1 = t[idt]; s2 = t[1+idt]; 1203 s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt]; 1204 s6 = t[5+idt];s7 = t[6+idt]; 1205 while (nz--) { 1206 idx = 7*(*vi++); 1207 x1 = t[idx]; x2 = t[1+idx]; 1208 x3 = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx]; 1209 x6 = t[5+idx]; x7 = t[6+idx]; 1210 s1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 1211 s2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 1212 s3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 1213 s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 1214 s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 1215 s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 1216 s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 1217 v += 49; 1218 } 1219 idc = 7*(*c--); 1220 v = aa + 49*diag[i]; 1221 x[idc] = t[idt] = v[0]*s1+v[7]*s2+v[14]*s3+ 1222 v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7; 1223 x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+ 1224 v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7; 1225 x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+ 1226 v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7; 1227 x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+ 1228 v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7; 1229 x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+ 1230 v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7; 1231 x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+ 1232 v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7; 1233 x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+ 1234 v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7; 1235 } 1236 1237 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1238 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1239 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1240 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1241 PLogFlops(2*49*(a->nz) - 7*a->n); 1242 PetscFunctionReturn(0); 1243 } 1244 1245 #undef __FUNC__ 1246 #define __FUNC__ "MatSolve_SeqBAIJ_7_NaturalOrdering" 1247 int MatSolve_SeqBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx) 1248 { 1249 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1250 int i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 1251 int ierr,*diag = a->diag,jdx; 1252 MatScalar *aa=a->a,*v; 1253 Scalar *x,*b,s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7; 1254 1255 PetscFunctionBegin; 1256 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1257 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1258 /* forward solve the lower triangular */ 1259 idx = 0; 1260 x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; 1261 x[3] = b[3+idx]; x[4] = b[4+idx]; x[5] = b[5+idx]; 1262 x[6] = b[6+idx]; 1263 for ( i=1; i<n; i++ ) { 1264 v = aa + 49*ai[i]; 1265 vi = aj + ai[i]; 1266 nz = diag[i] - ai[i]; 1267 idx = 7*i; 1268 s1 = b[idx]; s2 = b[1+idx]; s3 = b[2+idx]; 1269 s4 = b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx]; 1270 s7 = b[6+idx]; 1271 while (nz--) { 1272 jdx = 7*(*vi++); 1273 x1 = x[jdx]; x2 = x[1+jdx]; x3 = x[2+jdx]; 1274 x4 = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx]; 1275 x7 = x[6+jdx]; 1276 s1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 1277 s2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 1278 s3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 1279 s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 1280 s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 1281 s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 1282 s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 1283 v += 49; 1284 } 1285 x[idx] = s1; 1286 x[1+idx] = s2; 1287 x[2+idx] = s3; 1288 x[3+idx] = s4; 1289 x[4+idx] = s5; 1290 x[5+idx] = s6; 1291 x[6+idx] = s7; 1292 } 1293 /* backward solve the upper triangular */ 1294 for ( i=n-1; i>=0; i-- ){ 1295 v = aa + 49*diag[i] + 49; 1296 vi = aj + diag[i] + 1; 1297 nz = ai[i+1] - diag[i] - 1; 1298 idt = 7*i; 1299 s1 = x[idt]; s2 = x[1+idt]; 1300 s3 = x[2+idt]; s4 = x[3+idt]; 1301 s5 = x[4+idt]; s6 = x[5+idt]; 1302 s7 = x[6+idt]; 1303 while (nz--) { 1304 idx = 7*(*vi++); 1305 x1 = x[idx]; x2 = x[1+idx]; x3 = x[2+idx]; 1306 x4 = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx]; 1307 x7 = x[6+idx]; 1308 s1 -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7; 1309 s2 -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7; 1310 s3 -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7; 1311 s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7; 1312 s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7; 1313 s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7; 1314 s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7; 1315 v += 49; 1316 } 1317 v = aa + 49*diag[i]; 1318 x[idt] = v[0]*s1 + v[7]*s2 + v[14]*s3 + v[21]*s4 1319 + v[28]*s5 + v[35]*s6 + v[42]*s7; 1320 x[1+idt] = v[1]*s1 + v[8]*s2 + v[15]*s3 + v[22]*s4 1321 + v[29]*s5 + v[36]*s6 + v[43]*s7; 1322 x[2+idt] = v[2]*s1 + v[9]*s2 + v[16]*s3 + v[23]*s4 1323 + v[30]*s5 + v[37]*s6 + v[44]*s7; 1324 x[3+idt] = v[3]*s1 + v[10]*s2 + v[17]*s3 + v[24]*s4 1325 + v[31]*s5 + v[38]*s6 + v[45]*s7; 1326 x[4+idt] = v[4]*s1 + v[11]*s2 + v[18]*s3 + v[25]*s4 1327 + v[32]*s5 + v[39]*s6 + v[46]*s7; 1328 x[5+idt] = v[5]*s1 + v[12]*s2 + v[19]*s3 + v[26]*s4 1329 + v[33]*s5 + v[40]*s6 + v[47]*s7; 1330 x[6+idt] = v[6]*s1 + v[13]*s2 + v[20]*s3 + v[27]*s4 1331 + v[34]*s5 + v[41]*s6 + v[48]*s7; 1332 } 1333 1334 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1335 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1336 PLogFlops(2*36*(a->nz) - 6*a->n); 1337 PetscFunctionReturn(0); 1338 } 1339 1340 #undef __FUNC__ 1341 #define __FUNC__ "MatSolve_SeqBAIJ_6" 1342 int MatSolve_SeqBAIJ_6(Mat A,Vec bb,Vec xx) 1343 { 1344 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1345 IS iscol=a->col,isrow=a->row; 1346 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1347 int *diag = a->diag; 1348 MatScalar *aa=a->a,*v; 1349 Scalar *x,*b,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t; 1350 1351 PetscFunctionBegin; 1352 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1353 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1354 t = a->solve_work; 1355 1356 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1357 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1358 1359 /* forward solve the lower triangular */ 1360 idx = 6*(*r++); 1361 t[0] = b[idx]; t[1] = b[1+idx]; 1362 t[2] = b[2+idx]; t[3] = b[3+idx]; 1363 t[4] = b[4+idx]; t[5] = b[5+idx]; 1364 for ( i=1; i<n; i++ ) { 1365 v = aa + 36*ai[i]; 1366 vi = aj + ai[i]; 1367 nz = diag[i] - ai[i]; 1368 idx = 6*(*r++); 1369 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx]; 1370 s5 = b[4+idx]; s6 = b[5+idx]; 1371 while (nz--) { 1372 idx = 6*(*vi++); 1373 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; 1374 x4 = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx]; 1375 s1 -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6; 1376 s2 -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6; 1377 s3 -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6; 1378 s4 -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6; 1379 s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6; 1380 s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6; 1381 v += 36; 1382 } 1383 idx = 6*i; 1384 t[idx] = s1;t[1+idx] = s2; 1385 t[2+idx] = s3;t[3+idx] = s4; 1386 t[4+idx] = s5;t[5+idx] = s6; 1387 } 1388 /* backward solve the upper triangular */ 1389 for ( i=n-1; i>=0; i-- ){ 1390 v = aa + 36*diag[i] + 36; 1391 vi = aj + diag[i] + 1; 1392 nz = ai[i+1] - diag[i] - 1; 1393 idt = 6*i; 1394 s1 = t[idt]; s2 = t[1+idt]; 1395 s3 = t[2+idt];s4 = t[3+idt]; 1396 s5 = t[4+idt];s6 = t[5+idt]; 1397 while (nz--) { 1398 idx = 6*(*vi++); 1399 x1 = t[idx]; x2 = t[1+idx]; 1400 x3 = t[2+idx]; x4 = t[3+idx]; 1401 x5 = t[4+idx]; x6 = t[5+idx]; 1402 s1 -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6; 1403 s2 -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6; 1404 s3 -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6; 1405 s4 -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6; 1406 s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6; 1407 s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6; 1408 v += 36; 1409 } 1410 idc = 6*(*c--); 1411 v = aa + 36*diag[i]; 1412 x[idc] = t[idt] = v[0]*s1+v[6]*s2+v[12]*s3+ 1413 v[18]*s4+v[24]*s5+v[30]*s6; 1414 x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+ 1415 v[19]*s4+v[25]*s5+v[31]*s6; 1416 x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+ 1417 v[20]*s4+v[26]*s5+v[32]*s6; 1418 x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+ 1419 v[21]*s4+v[27]*s5+v[33]*s6; 1420 x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+ 1421 v[22]*s4+v[28]*s5+v[34]*s6; 1422 x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+ 1423 v[23]*s4+v[29]*s5+v[35]*s6; 1424 } 1425 1426 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1427 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1428 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1429 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1430 PLogFlops(2*36*(a->nz) - 6*a->n); 1431 PetscFunctionReturn(0); 1432 } 1433 1434 #undef __FUNC__ 1435 #define __FUNC__ "MatSolve_SeqBAIJ_6_NaturalOrdering" 1436 int MatSolve_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx) 1437 { 1438 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1439 int i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 1440 int ierr,*diag = a->diag,jdx; 1441 MatScalar *aa=a->a,*v; 1442 Scalar *x,*b,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6; 1443 1444 PetscFunctionBegin; 1445 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1446 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1447 /* forward solve the lower triangular */ 1448 idx = 0; 1449 x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; 1450 x[3] = b[3+idx]; x[4] = b[4+idx]; x[5] = b[5+idx]; 1451 for ( i=1; i<n; i++ ) { 1452 v = aa + 36*ai[i]; 1453 vi = aj + ai[i]; 1454 nz = diag[i] - ai[i]; 1455 idx = 6*i; 1456 s1 = b[idx]; s2 = b[1+idx]; s3 = b[2+idx]; 1457 s4 = b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx]; 1458 while (nz--) { 1459 jdx = 6*(*vi++); 1460 x1 = x[jdx]; x2 = x[1+jdx]; x3 = x[2+jdx]; 1461 x4 = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx]; 1462 s1 -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6; 1463 s2 -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6; 1464 s3 -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6; 1465 s4 -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6; 1466 s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6; 1467 s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6; 1468 v += 36; 1469 } 1470 x[idx] = s1; 1471 x[1+idx] = s2; 1472 x[2+idx] = s3; 1473 x[3+idx] = s4; 1474 x[4+idx] = s5; 1475 x[5+idx] = s6; 1476 } 1477 /* backward solve the upper triangular */ 1478 for ( i=n-1; i>=0; i-- ){ 1479 v = aa + 36*diag[i] + 36; 1480 vi = aj + diag[i] + 1; 1481 nz = ai[i+1] - diag[i] - 1; 1482 idt = 6*i; 1483 s1 = x[idt]; s2 = x[1+idt]; 1484 s3 = x[2+idt]; s4 = x[3+idt]; 1485 s5 = x[4+idt]; s6 = x[5+idt]; 1486 while (nz--) { 1487 idx = 6*(*vi++); 1488 x1 = x[idx]; x2 = x[1+idx]; x3 = x[2+idx]; 1489 x4 = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx]; 1490 s1 -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6; 1491 s2 -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6; 1492 s3 -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6; 1493 s4 -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6; 1494 s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6; 1495 s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6; 1496 v += 36; 1497 } 1498 v = aa + 36*diag[i]; 1499 x[idt] = v[0]*s1 + v[6]*s2 + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6; 1500 x[1+idt] = v[1]*s1 + v[7]*s2 + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6; 1501 x[2+idt] = v[2]*s1 + v[8]*s2 + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6; 1502 x[3+idt] = v[3]*s1 + v[9]*s2 + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6; 1503 x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6; 1504 x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6; 1505 } 1506 1507 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1508 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1509 PLogFlops(2*36*(a->nz) - 6*a->n); 1510 PetscFunctionReturn(0); 1511 } 1512 1513 #undef __FUNC__ 1514 #define __FUNC__ "MatSolve_SeqBAIJ_5" 1515 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx) 1516 { 1517 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1518 IS iscol=a->col,isrow=a->row; 1519 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1520 int *diag = a->diag; 1521 MatScalar *aa=a->a,*v; 1522 Scalar *x,*b,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t; 1523 1524 PetscFunctionBegin; 1525 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1526 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1527 t = a->solve_work; 1528 1529 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1530 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1531 1532 /* forward solve the lower triangular */ 1533 idx = 5*(*r++); 1534 t[0] = b[idx]; t[1] = b[1+idx]; 1535 t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx]; 1536 for ( i=1; i<n; i++ ) { 1537 v = aa + 25*ai[i]; 1538 vi = aj + ai[i]; 1539 nz = diag[i] - ai[i]; 1540 idx = 5*(*r++); 1541 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx]; 1542 s5 = b[4+idx]; 1543 while (nz--) { 1544 idx = 5*(*vi++); 1545 x1 = t[idx]; x2 = t[1+idx];x3 = t[2+idx]; 1546 x4 = t[3+idx];x5 = t[4+idx]; 1547 s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 1548 s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 1549 s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 1550 s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 1551 s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 1552 v += 25; 1553 } 1554 idx = 5*i; 1555 t[idx] = s1;t[1+idx] = s2; 1556 t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5; 1557 } 1558 /* backward solve the upper triangular */ 1559 for ( i=n-1; i>=0; i-- ){ 1560 v = aa + 25*diag[i] + 25; 1561 vi = aj + diag[i] + 1; 1562 nz = ai[i+1] - diag[i] - 1; 1563 idt = 5*i; 1564 s1 = t[idt]; s2 = t[1+idt]; 1565 s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt]; 1566 while (nz--) { 1567 idx = 5*(*vi++); 1568 x1 = t[idx]; x2 = t[1+idx]; 1569 x3 = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx]; 1570 s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 1571 s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 1572 s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 1573 s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 1574 s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 1575 v += 25; 1576 } 1577 idc = 5*(*c--); 1578 v = aa + 25*diag[i]; 1579 x[idc] = t[idt] = v[0]*s1+v[5]*s2+v[10]*s3+ 1580 v[15]*s4+v[20]*s5; 1581 x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+ 1582 v[16]*s4+v[21]*s5; 1583 x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+ 1584 v[17]*s4+v[22]*s5; 1585 x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+ 1586 v[18]*s4+v[23]*s5; 1587 x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+ 1588 v[19]*s4+v[24]*s5; 1589 } 1590 1591 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1592 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1593 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1594 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1595 PLogFlops(2*25*(a->nz) - 5*a->n); 1596 PetscFunctionReturn(0); 1597 } 1598 1599 #undef __FUNC__ 1600 #define __FUNC__ "MatSolve_SeqBAIJ_5_NaturalOrdering" 1601 int MatSolve_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx) 1602 { 1603 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1604 int i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt; 1605 int ierr,*diag = a->diag,jdx; 1606 MatScalar *aa=a->a,*v; 1607 Scalar *x,*b,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;; 1608 1609 PetscFunctionBegin; 1610 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1611 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1612 /* forward solve the lower triangular */ 1613 idx = 0; 1614 x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx]; 1615 for ( i=1; i<n; i++ ) { 1616 v = aa + 25*ai[i]; 1617 vi = aj + ai[i]; 1618 nz = diag[i] - ai[i]; 1619 idx = 5*i; 1620 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx]; 1621 while (nz--) { 1622 jdx = 5*(*vi++); 1623 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx]; 1624 s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 1625 s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 1626 s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 1627 s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 1628 s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 1629 v += 25; 1630 } 1631 x[idx] = s1; 1632 x[1+idx] = s2; 1633 x[2+idx] = s3; 1634 x[3+idx] = s4; 1635 x[4+idx] = s5; 1636 } 1637 /* backward solve the upper triangular */ 1638 for ( i=n-1; i>=0; i-- ){ 1639 v = aa + 25*diag[i] + 25; 1640 vi = aj + diag[i] + 1; 1641 nz = ai[i+1] - diag[i] - 1; 1642 idt = 5*i; 1643 s1 = x[idt]; s2 = x[1+idt]; 1644 s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt]; 1645 while (nz--) { 1646 idx = 5*(*vi++); 1647 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx]; 1648 s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5; 1649 s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5; 1650 s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5; 1651 s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5; 1652 s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5; 1653 v += 25; 1654 } 1655 v = aa + 25*diag[i]; 1656 x[idt] = v[0]*s1 + v[5]*s2 + v[10]*s3 + v[15]*s4 + v[20]*s5; 1657 x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3 + v[16]*s4 + v[21]*s5; 1658 x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3 + v[17]*s4 + v[22]*s5; 1659 x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3 + v[18]*s4 + v[23]*s5; 1660 x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3 + v[19]*s4 + v[24]*s5; 1661 } 1662 1663 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1664 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1665 PLogFlops(2*25*(a->nz) - 5*a->n); 1666 PetscFunctionReturn(0); 1667 } 1668 1669 #undef __FUNC__ 1670 #define __FUNC__ "MatSolve_SeqBAIJ_4" 1671 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx) 1672 { 1673 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1674 IS iscol=a->col,isrow=a->row; 1675 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1676 int *diag = a->diag; 1677 MatScalar *aa=a->a,*v; 1678 Scalar *x,*b,s1,s2,s3,s4,x1,x2,x3,x4,*t; 1679 1680 PetscFunctionBegin; 1681 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1682 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1683 t = a->solve_work; 1684 1685 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1686 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1687 1688 /* forward solve the lower triangular */ 1689 idx = 4*(*r++); 1690 t[0] = b[idx]; t[1] = b[1+idx]; 1691 t[2] = b[2+idx]; t[3] = b[3+idx]; 1692 for ( i=1; i<n; i++ ) { 1693 v = aa + 16*ai[i]; 1694 vi = aj + ai[i]; 1695 nz = diag[i] - ai[i]; 1696 idx = 4*(*r++); 1697 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx]; 1698 while (nz--) { 1699 idx = 4*(*vi++); 1700 x1 = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx]; 1701 s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 1702 s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 1703 s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 1704 s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 1705 v += 16; 1706 } 1707 idx = 4*i; 1708 t[idx] = s1;t[1+idx] = s2; 1709 t[2+idx] = s3;t[3+idx] = s4; 1710 } 1711 /* backward solve the upper triangular */ 1712 for ( i=n-1; i>=0; i-- ){ 1713 v = aa + 16*diag[i] + 16; 1714 vi = aj + diag[i] + 1; 1715 nz = ai[i+1] - diag[i] - 1; 1716 idt = 4*i; 1717 s1 = t[idt]; s2 = t[1+idt]; 1718 s3 = t[2+idt];s4 = t[3+idt]; 1719 while (nz--) { 1720 idx = 4*(*vi++); 1721 x1 = t[idx]; x2 = t[1+idx]; 1722 x3 = t[2+idx]; x4 = t[3+idx]; 1723 s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 1724 s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 1725 s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 1726 s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 1727 v += 16; 1728 } 1729 idc = 4*(*c--); 1730 v = aa + 16*diag[i]; 1731 x[idc] = t[idt] = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4; 1732 x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4; 1733 x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4; 1734 x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4; 1735 } 1736 1737 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1738 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1739 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1740 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1741 PLogFlops(2*16*(a->nz) - 4*a->n); 1742 PetscFunctionReturn(0); 1743 } 1744 1745 1746 /* 1747 Special case where the matrix was ILU(0) factored in the natural 1748 ordering. This eliminates the need for the column and row permutation. 1749 */ 1750 #undef __FUNC__ 1751 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering" 1752 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx) 1753 { 1754 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1755 int n=a->mbs,*ai=a->i,*aj=a->j; 1756 int ierr,*diag = a->diag; 1757 MatScalar *aa=a->a; 1758 Scalar *x,*b; 1759 1760 PetscFunctionBegin; 1761 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1762 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1763 1764 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJBLAS) 1765 { 1766 static Scalar w[2000]; /* very BAD need to fix */ 1767 fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w); 1768 } 1769 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJ) 1770 { 1771 static Scalar w[2000]; /* very BAD need to fix */ 1772 fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w); 1773 } 1774 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL) 1775 fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b); 1776 #else 1777 { 1778 Scalar s1,s2,s3,s4,x1,x2,x3,x4; 1779 MatScalar *v; 1780 int jdx,idt,idx,nz,*vi,i; 1781 1782 /* forward solve the lower triangular */ 1783 idx = 0; 1784 x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3]; 1785 for ( i=1; i<n; i++ ) { 1786 v = aa + 16*ai[i]; 1787 vi = aj + ai[i]; 1788 nz = diag[i] - ai[i]; 1789 idx += 4; 1790 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx]; 1791 while (nz--) { 1792 jdx = 4*(*vi++); 1793 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx]; 1794 s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 1795 s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 1796 s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 1797 s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 1798 v += 16; 1799 } 1800 x[idx] = s1; 1801 x[1+idx] = s2; 1802 x[2+idx] = s3; 1803 x[3+idx] = s4; 1804 } 1805 /* backward solve the upper triangular */ 1806 for ( i=n-1; i>=0; i-- ){ 1807 v = aa + 16*diag[i] + 16; 1808 vi = aj + diag[i] + 1; 1809 nz = ai[i+1] - diag[i] - 1; 1810 idt = 4*i; 1811 s1 = x[idt]; s2 = x[1+idt]; 1812 s3 = x[2+idt];s4 = x[3+idt]; 1813 while (nz--) { 1814 idx = 4*(*vi++); 1815 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; x4 = x[3+idx]; 1816 s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4; 1817 s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4; 1818 s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4; 1819 s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4; 1820 v += 16; 1821 } 1822 v = aa + 16*diag[i]; 1823 x[idt] = v[0]*s1 + v[4]*s2 + v[8]*s3 + v[12]*s4; 1824 x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3 + v[13]*s4; 1825 x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4; 1826 x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4; 1827 } 1828 } 1829 #endif 1830 1831 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1832 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1833 PLogFlops(2*16*(a->nz) - 4*a->n); 1834 PetscFunctionReturn(0); 1835 } 1836 1837 #undef __FUNC__ 1838 #define __FUNC__ "MatSolve_SeqBAIJ_3" 1839 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx) 1840 { 1841 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1842 IS iscol=a->col,isrow=a->row; 1843 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1844 int *diag = a->diag; 1845 MatScalar *aa=a->a,*v; 1846 Scalar *x,*b,s1,s2,s3,x1,x2,x3,*t; 1847 1848 PetscFunctionBegin; 1849 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1850 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1851 t = a->solve_work; 1852 1853 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1854 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1855 1856 /* forward solve the lower triangular */ 1857 idx = 3*(*r++); 1858 t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx]; 1859 for ( i=1; i<n; i++ ) { 1860 v = aa + 9*ai[i]; 1861 vi = aj + ai[i]; 1862 nz = diag[i] - ai[i]; 1863 idx = 3*(*r++); 1864 s1 = b[idx]; s2 = b[1+idx]; s3 = b[2+idx]; 1865 while (nz--) { 1866 idx = 3*(*vi++); 1867 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; 1868 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 1869 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 1870 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 1871 v += 9; 1872 } 1873 idx = 3*i; 1874 t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3; 1875 } 1876 /* backward solve the upper triangular */ 1877 for ( i=n-1; i>=0; i-- ){ 1878 v = aa + 9*diag[i] + 9; 1879 vi = aj + diag[i] + 1; 1880 nz = ai[i+1] - diag[i] - 1; 1881 idt = 3*i; 1882 s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt]; 1883 while (nz--) { 1884 idx = 3*(*vi++); 1885 x1 = t[idx]; x2 = t[1+idx]; x3 = t[2+idx]; 1886 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 1887 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 1888 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 1889 v += 9; 1890 } 1891 idc = 3*(*c--); 1892 v = aa + 9*diag[i]; 1893 x[idc] = t[idt] = v[0]*s1 + v[3]*s2 + v[6]*s3; 1894 x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3; 1895 x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3; 1896 } 1897 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1898 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1899 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1900 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1901 PLogFlops(2*9*(a->nz) - 3*a->n); 1902 PetscFunctionReturn(0); 1903 } 1904 1905 /* 1906 Special case where the matrix was ILU(0) factored in the natural 1907 ordering. This eliminates the need for the column and row permutation. 1908 */ 1909 #undef __FUNC__ 1910 #define __FUNC__ "MatSolve_SeqBAIJ_3_NaturalOrdering" 1911 int MatSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx) 1912 { 1913 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 1914 int n=a->mbs,*ai=a->i,*aj=a->j; 1915 int ierr,*diag = a->diag; 1916 MatScalar *aa=a->a, *v; 1917 Scalar *x,*b,s1,s2,s3,x1,x2,x3; 1918 int jdx,idt,idx,nz,*vi,i; 1919 1920 PetscFunctionBegin; 1921 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1922 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1923 1924 1925 /* forward solve the lower triangular */ 1926 idx = 0; 1927 x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; 1928 for ( i=1; i<n; i++ ) { 1929 v = aa + 9*ai[i]; 1930 vi = aj + ai[i]; 1931 nz = diag[i] - ai[i]; 1932 idx += 3; 1933 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx]; 1934 while (nz--) { 1935 jdx = 3*(*vi++); 1936 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx]; 1937 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 1938 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 1939 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 1940 v += 9; 1941 } 1942 x[idx] = s1; 1943 x[1+idx] = s2; 1944 x[2+idx] = s3; 1945 } 1946 /* backward solve the upper triangular */ 1947 for ( i=n-1; i>=0; i-- ){ 1948 v = aa + 9*diag[i] + 9; 1949 vi = aj + diag[i] + 1; 1950 nz = ai[i+1] - diag[i] - 1; 1951 idt = 3*i; 1952 s1 = x[idt]; s2 = x[1+idt]; 1953 s3 = x[2+idt]; 1954 while (nz--) { 1955 idx = 3*(*vi++); 1956 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; 1957 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 1958 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 1959 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 1960 v += 9; 1961 } 1962 v = aa + 9*diag[i]; 1963 x[idt] = v[0]*s1 + v[3]*s2 + v[6]*s3; 1964 x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3; 1965 x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3; 1966 } 1967 1968 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1969 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1970 PLogFlops(2*9*(a->nz) - 3*a->n); 1971 PetscFunctionReturn(0); 1972 } 1973 1974 #undef __FUNC__ 1975 #define __FUNC__ "MatSolve_SeqBAIJ_2" 1976 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx) 1977 { 1978 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 1979 IS iscol=a->col,isrow=a->row; 1980 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout; 1981 int *diag = a->diag; 1982 MatScalar *aa=a->a,*v; 1983 Scalar *x,*b,s1,s2,x1,x2,*t; 1984 1985 PetscFunctionBegin; 1986 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1987 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1988 t = a->solve_work; 1989 1990 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1991 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1992 1993 /* forward solve the lower triangular */ 1994 idx = 2*(*r++); 1995 t[0] = b[idx]; t[1] = b[1+idx]; 1996 for ( i=1; i<n; i++ ) { 1997 v = aa + 4*ai[i]; 1998 vi = aj + ai[i]; 1999 nz = diag[i] - ai[i]; 2000 idx = 2*(*r++); 2001 s1 = b[idx]; s2 = b[1+idx]; 2002 while (nz--) { 2003 idx = 2*(*vi++); 2004 x1 = t[idx]; x2 = t[1+idx]; 2005 s1 -= v[0]*x1 + v[2]*x2; 2006 s2 -= v[1]*x1 + v[3]*x2; 2007 v += 4; 2008 } 2009 idx = 2*i; 2010 t[idx] = s1; t[1+idx] = s2; 2011 } 2012 /* backward solve the upper triangular */ 2013 for ( i=n-1; i>=0; i-- ){ 2014 v = aa + 4*diag[i] + 4; 2015 vi = aj + diag[i] + 1; 2016 nz = ai[i+1] - diag[i] - 1; 2017 idt = 2*i; 2018 s1 = t[idt]; s2 = t[1+idt]; 2019 while (nz--) { 2020 idx = 2*(*vi++); 2021 x1 = t[idx]; x2 = t[1+idx]; 2022 s1 -= v[0]*x1 + v[2]*x2; 2023 s2 -= v[1]*x1 + v[3]*x2; 2024 v += 4; 2025 } 2026 idc = 2*(*c--); 2027 v = aa + 4*diag[i]; 2028 x[idc] = t[idt] = v[0]*s1 + v[2]*s2; 2029 x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2; 2030 } 2031 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2032 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2033 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 2034 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2035 PLogFlops(2*4*(a->nz) - 2*a->n); 2036 PetscFunctionReturn(0); 2037 } 2038 2039 /* 2040 Special case where the matrix was ILU(0) factored in the natural 2041 ordering. This eliminates the need for the column and row permutation. 2042 */ 2043 #undef __FUNC__ 2044 #define __FUNC__ "MatSolve_SeqBAIJ_2_NaturalOrdering" 2045 int MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx) 2046 { 2047 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 2048 int n=a->mbs,*ai=a->i,*aj=a->j; 2049 int ierr,*diag = a->diag; 2050 MatScalar *aa=a->a,*v; 2051 Scalar *x,*b,s1,s2,x1,x2; 2052 int jdx,idt,idx,nz,*vi,i; 2053 2054 PetscFunctionBegin; 2055 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 2056 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2057 2058 /* forward solve the lower triangular */ 2059 idx = 0; 2060 x[0] = b[0]; x[1] = b[1]; 2061 for ( i=1; i<n; i++ ) { 2062 v = aa + 4*ai[i]; 2063 vi = aj + ai[i]; 2064 nz = diag[i] - ai[i]; 2065 idx += 2; 2066 s1 = b[idx];s2 = b[1+idx]; 2067 while (nz--) { 2068 jdx = 2*(*vi++); 2069 x1 = x[jdx];x2 = x[1+jdx]; 2070 s1 -= v[0]*x1 + v[2]*x2; 2071 s2 -= v[1]*x1 + v[3]*x2; 2072 v += 4; 2073 } 2074 x[idx] = s1; 2075 x[1+idx] = s2; 2076 } 2077 /* backward solve the upper triangular */ 2078 for ( i=n-1; i>=0; i-- ){ 2079 v = aa + 4*diag[i] + 4; 2080 vi = aj + diag[i] + 1; 2081 nz = ai[i+1] - diag[i] - 1; 2082 idt = 2*i; 2083 s1 = x[idt]; s2 = x[1+idt]; 2084 while (nz--) { 2085 idx = 2*(*vi++); 2086 x1 = x[idx]; x2 = x[1+idx]; 2087 s1 -= v[0]*x1 + v[2]*x2; 2088 s2 -= v[1]*x1 + v[3]*x2; 2089 v += 4; 2090 } 2091 v = aa + 4*diag[i]; 2092 x[idt] = v[0]*s1 + v[2]*s2; 2093 x[1+idt] = v[1]*s1 + v[3]*s2; 2094 } 2095 2096 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 2097 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2098 PLogFlops(2*4*(a->nz) - 2*a->n); 2099 PetscFunctionReturn(0); 2100 } 2101 2102 #undef __FUNC__ 2103 #define __FUNC__ "MatSolve_SeqBAIJ_1" 2104 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx) 2105 { 2106 Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data; 2107 IS iscol=a->col,isrow=a->row; 2108 int *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout; 2109 int *diag = a->diag; 2110 MatScalar *aa=a->a,*v; 2111 Scalar *x,*b,s1,*t; 2112 2113 PetscFunctionBegin; 2114 if (!n) PetscFunctionReturn(0); 2115 2116 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 2117 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2118 t = a->solve_work; 2119 2120 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 2121 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 2122 2123 /* forward solve the lower triangular */ 2124 t[0] = b[*r++]; 2125 for ( i=1; i<n; i++ ) { 2126 v = aa + ai[i]; 2127 vi = aj + ai[i]; 2128 nz = diag[i] - ai[i]; 2129 s1 = b[*r++]; 2130 while (nz--) { 2131 s1 -= (*v++)*t[*vi++]; 2132 } 2133 t[i] = s1; 2134 } 2135 /* backward solve the upper triangular */ 2136 for ( i=n-1; i>=0; i-- ){ 2137 v = aa + diag[i] + 1; 2138 vi = aj + diag[i] + 1; 2139 nz = ai[i+1] - diag[i] - 1; 2140 s1 = t[i]; 2141 while (nz--) { 2142 s1 -= (*v++)*t[*vi++]; 2143 } 2144 x[*c--] = t[i] = aa[diag[i]]*s1; 2145 } 2146 2147 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 2148 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 2149 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 2150 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2151 PLogFlops(2*1*(a->nz) - a->n); 2152 PetscFunctionReturn(0); 2153 } 2154 /* 2155 Special case where the matrix was ILU(0) factored in the natural 2156 ordering. This eliminates the need for the column and row permutation. 2157 */ 2158 #undef __FUNC__ 2159 #define __FUNC__ "MatSolve_SeqBAIJ_1_NaturalOrdering" 2160 int MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx) 2161 { 2162 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 2163 int n=a->mbs,*ai=a->i,*aj=a->j; 2164 int ierr,*diag = a->diag; 2165 MatScalar *aa=a->a; 2166 Scalar *x,*b; 2167 Scalar s1,x1; 2168 MatScalar *v; 2169 int jdx,idt,idx,nz,*vi,i; 2170 2171 PetscFunctionBegin; 2172 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 2173 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2174 2175 /* forward solve the lower triangular */ 2176 idx = 0; 2177 x[0] = b[0]; 2178 for ( i=1; i<n; i++ ) { 2179 v = aa + ai[i]; 2180 vi = aj + ai[i]; 2181 nz = diag[i] - ai[i]; 2182 idx += 1; 2183 s1 = b[idx]; 2184 while (nz--) { 2185 jdx = *vi++; 2186 x1 = x[jdx]; 2187 s1 -= v[0]*x1; 2188 v += 1; 2189 } 2190 x[idx] = s1; 2191 } 2192 /* backward solve the upper triangular */ 2193 for ( i=n-1; i>=0; i-- ){ 2194 v = aa + diag[i] + 1; 2195 vi = aj + diag[i] + 1; 2196 nz = ai[i+1] - diag[i] - 1; 2197 idt = i; 2198 s1 = x[idt]; 2199 while (nz--) { 2200 idx = *vi++; 2201 x1 = x[idx]; 2202 s1 -= v[0]*x1; 2203 v += 1; 2204 } 2205 v = aa + diag[i]; 2206 x[idt] = v[0]*s1; 2207 } 2208 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 2209 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2210 PLogFlops(2*(a->nz) - a->n); 2211 PetscFunctionReturn(0); 2212 } 2213 2214 /* ----------------------------------------------------------------*/ 2215 /* 2216 This code is virtually identical to MatILUFactorSymbolic_SeqAIJ 2217 except that the data structure of Mat_SeqAIJ is slightly different. 2218 Not a good example of code reuse. 2219 */ 2220 extern int MatMissingDiag_SeqBAIJ(Mat); 2221 2222 #undef __FUNC__ 2223 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ" 2224 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,MatILUInfo *info,Mat *fact) 2225 { 2226 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b; 2227 IS isicol; 2228 int *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j; 2229 int *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev; 2230 int *dloc, idx, row,m,fm, nzf, nzi,len, realloc = 0, dcount = 0; 2231 int incrlev,nnz,i,bs = a->bs,bs2 = a->bs2, levels, diagonal_fill; 2232 PetscTruth col_identity, row_identity; 2233 double f; 2234 2235 PetscFunctionBegin; 2236 if (info) { 2237 f = info->fill; 2238 levels = (int) info->levels; 2239 diagonal_fill = (int) info->diagonal_fill; 2240 } else { 2241 f = 1.0; 2242 levels = 0; 2243 diagonal_fill = 0; 2244 } 2245 ierr = ISInvertPermutation(iscol,&isicol);CHKERRQ(ierr); 2246 2247 /* special case that simply copies fill pattern */ 2248 PetscValidHeaderSpecific(isrow,IS_COOKIE); 2249 PetscValidHeaderSpecific(iscol,IS_COOKIE); 2250 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2251 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 2252 if (levels == 0 && row_identity && col_identity) { 2253 ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact);CHKERRQ(ierr); 2254 (*fact)->factor = FACTOR_LU; 2255 b = (Mat_SeqBAIJ *) (*fact)->data; 2256 if (!b->diag) { 2257 ierr = MatMarkDiag_SeqBAIJ(*fact);CHKERRQ(ierr); 2258 } 2259 ierr = MatMissingDiag_SeqBAIJ(*fact);CHKERRQ(ierr); 2260 b->row = isrow; 2261 b->col = iscol; 2262 b->icol = isicol; 2263 b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 2264 /* 2265 Blocksize 2, 3, 4, 5, 6 and 7 have a special faster factorization/solver 2266 for ILU(0) factorization with natural ordering 2267 */ 2268 switch (b->bs) { 2269 case 2: 2270 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering; 2271 (*fact)->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering; 2272 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Using special in-place natural ordering factor and solve BS=2\n"); 2273 break; 2274 case 3: 2275 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering; 2276 (*fact)->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering; 2277 PLogInfo(A,"UMatILUFactorSymbolic_SeqBAIJ:sing special in-place natural ordering factor and solve BS=3\n"); 2278 break; 2279 case 4: 2280 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering; 2281 (*fact)->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering; 2282 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Using special in-place natural ordering factor and solve BS=4\n"); 2283 break; 2284 case 5: 2285 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering; 2286 (*fact)->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering; 2287 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Using special in-place natural ordering factor and solve BS=5\n"); 2288 break; 2289 case 6: 2290 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering; 2291 (*fact)->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering; 2292 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Using special in-place natural ordering factor and solve BS=6\n"); 2293 break; 2294 case 7: 2295 (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_7_NaturalOrdering; 2296 (*fact)->ops->solve = MatSolve_SeqBAIJ_7_NaturalOrdering; 2297 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Using special in-place natural ordering factor and solve BS=7\n"); 2298 break; 2299 } 2300 PetscFunctionReturn(0); 2301 } 2302 2303 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2304 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2305 2306 /* get new row pointers */ 2307 ainew = (int *) PetscMalloc( (n+1)*sizeof(int) );CHKPTRQ(ainew); 2308 ainew[0] = 0; 2309 /* don't know how many column pointers are needed so estimate */ 2310 jmax = (int) (f*ai[n] + 1); 2311 ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) );CHKPTRQ(ajnew); 2312 /* ajfill is level of fill for each fill entry */ 2313 ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) );CHKPTRQ(ajfill); 2314 /* fill is a linked list of nonzeros in active row */ 2315 fill = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(fill); 2316 /* im is level for each filled value */ 2317 im = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(im); 2318 /* dloc is location of diagonal in factor */ 2319 dloc = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(dloc); 2320 dloc[0] = 0; 2321 for ( prow=0; prow<n; prow++ ) { 2322 2323 /* copy prow into linked list */ 2324 nzf = nz = ai[r[prow]+1] - ai[r[prow]]; 2325 if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix"); 2326 xi = aj + ai[r[prow]]; 2327 fill[n] = n; 2328 fill[prow] = -1; /* marker for diagonal entry */ 2329 while (nz--) { 2330 fm = n; 2331 idx = ic[*xi++]; 2332 do { 2333 m = fm; 2334 fm = fill[m]; 2335 } while (fm < idx); 2336 fill[m] = idx; 2337 fill[idx] = fm; 2338 im[idx] = 0; 2339 } 2340 2341 /* make sure diagonal entry is included */ 2342 if (diagonal_fill && fill[prow] == -1) { 2343 fm = n; 2344 while (fill[fm] < prow) fm = fill[fm]; 2345 fill[prow] = fill[fm]; /* insert diagonal into linked list */ 2346 fill[fm] = prow; 2347 im[prow] = 0; 2348 nzf++; 2349 dcount++; 2350 } 2351 2352 nzi = 0; 2353 row = fill[n]; 2354 while ( row < prow ) { 2355 incrlev = im[row] + 1; 2356 nz = dloc[row]; 2357 xi = ajnew + ainew[row] + nz + 1; 2358 flev = ajfill + ainew[row] + nz + 1; 2359 nnz = ainew[row+1] - ainew[row] - nz - 1; 2360 fm = row; 2361 while (nnz-- > 0) { 2362 idx = *xi++; 2363 if (*flev + incrlev > levels) { 2364 flev++; 2365 continue; 2366 } 2367 do { 2368 m = fm; 2369 fm = fill[m]; 2370 } while (fm < idx); 2371 if (fm != idx) { 2372 im[idx] = *flev + incrlev; 2373 fill[m] = idx; 2374 fill[idx] = fm; 2375 fm = idx; 2376 nzf++; 2377 } else { 2378 if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev; 2379 } 2380 flev++; 2381 } 2382 row = fill[row]; 2383 nzi++; 2384 } 2385 /* copy new filled row into permanent storage */ 2386 ainew[prow+1] = ainew[prow] + nzf; 2387 if (ainew[prow+1] > jmax) { 2388 2389 /* estimate how much additional space we will need */ 2390 /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */ 2391 /* just double the memory each time */ 2392 int maxadd = jmax; 2393 /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */ 2394 if (maxadd < nzf) maxadd = (n-prow)*(nzf+1); 2395 jmax += maxadd; 2396 2397 /* allocate a longer ajnew and ajfill */ 2398 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 2399 ierr = PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));CHKERRQ(ierr); 2400 ierr = PetscFree(ajnew);CHKERRQ(ierr); 2401 ajnew = xi; 2402 xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi); 2403 ierr = PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));CHKERRQ(ierr); 2404 ierr = PetscFree(ajfill);CHKERRQ(ierr); 2405 ajfill = xi; 2406 realloc++; /* count how many reallocations are needed */ 2407 } 2408 xi = ajnew + ainew[prow]; 2409 flev = ajfill + ainew[prow]; 2410 dloc[prow] = nzi; 2411 fm = fill[n]; 2412 while (nzf--) { 2413 *xi++ = fm; 2414 *flev++ = im[fm]; 2415 fm = fill[fm]; 2416 } 2417 /* make sure row has diagonal entry */ 2418 if (ajnew[ainew[prow]+dloc[prow]] != prow) { 2419 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,1,"Row %d has missing diagonal in factored matrix\n\ 2420 try running with -pc_ilu_nonzeros_along_diagonal or -pc_ilu_diagonal_fill",prow); 2421 } 2422 } 2423 ierr = PetscFree(ajfill);CHKERRQ(ierr); 2424 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2425 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2426 ierr = PetscFree(fill);CHKERRQ(ierr); 2427 ierr = PetscFree(im);CHKERRQ(ierr); 2428 2429 { 2430 double af = ((double)ainew[n])/((double)ai[n]); 2431 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n", 2432 realloc,f,af); 2433 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af); 2434 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af); 2435 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n"); 2436 if (diagonal_fill) { 2437 PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Detected and replace %d missing diagonals",dcount); 2438 } 2439 } 2440 2441 /* put together the new matrix */ 2442 ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr); 2443 PLogObjectParent(*fact,isicol); 2444 b = (Mat_SeqBAIJ *) (*fact)->data; 2445 ierr = PetscFree(b->imax);CHKERRQ(ierr); 2446 b->singlemalloc = 0; 2447 len = bs2*ainew[n]*sizeof(MatScalar); 2448 /* the next line frees the default space generated by the Create() */ 2449 ierr = PetscFree(b->a);CHKERRQ(ierr); 2450 ierr = PetscFree(b->ilen);CHKERRQ(ierr); 2451 b->a = (MatScalar *) PetscMalloc( len );CHKPTRQ(b->a); 2452 b->j = ajnew; 2453 b->i = ainew; 2454 for ( i=0; i<n; i++ ) dloc[i] += ainew[i]; 2455 b->diag = dloc; 2456 b->ilen = 0; 2457 b->imax = 0; 2458 b->row = isrow; 2459 b->col = iscol; 2460 b->icol = isicol; 2461 b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work); 2462 /* In b structure: Free imax, ilen, old a, old j. 2463 Allocate dloc, solve_work, new a, new j */ 2464 PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar)); 2465 b->maxnz = b->nz = ainew[n]; 2466 (*fact)->factor = FACTOR_LU; 2467 2468 (*fact)->info.factor_mallocs = realloc; 2469 (*fact)->info.fill_ratio_given = f; 2470 (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]); 2471 2472 PetscFunctionReturn(0); 2473 } 2474 2475 2476 2477 2478