Actual source code: baijfact11.c

      1: /*
      2:     Factorization code for BAIJ format.
      3: */
      4: #include <../src/mat/impls/baij/seq/baij.h>
      5: #include <petsc/private/kernels/blockinvert.h>

      7: /*
      8:       Version for when blocks are 4 by 4
      9: */
     10: PetscErrorCode MatILUFactorNumeric_SeqBAIJ_4_inplace(Mat C, Mat A, const MatFactorInfo *info)
     11: {
     12:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
     13:   IS              isrow = b->row, isicol = b->icol;
     14:   const PetscInt *r, *ic;
     15:   PetscInt        i, j, n = a->mbs, *bi = b->i, *bj = b->j;
     16:   PetscInt       *ajtmpold, *ajtmp, nz, row;
     17:   const PetscInt *diag_offset;
     18:   PetscInt        idx, *ai = a->i, *aj = a->j, *pj;
     19:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
     20:   MatScalar       p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
     21:   MatScalar       p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
     22:   MatScalar       p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
     23:   MatScalar       m13, m14, m15, m16;
     24:   MatScalar      *ba = b->a, *aa = a->a;
     25:   PetscBool       pivotinblocks = b->pivotinblocks;
     26:   PetscReal       shift         = info->shiftamount;
     27:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

     29:   PetscFunctionBegin;
     30:   /* Since A is C and C is labeled as a factored matrix we need to lie to MatGetDiagonalMarkers_SeqBAIJ() to get it to compute the diagonals */
     31:   A->factortype = MAT_FACTOR_NONE;
     32:   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, &diag_offset, NULL));
     33:   A->factortype = MAT_FACTOR_ILU;
     34:   PetscCall(ISGetIndices(isrow, &r));
     35:   PetscCall(ISGetIndices(isicol, &ic));
     36:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
     37:   allowzeropivot = PetscNot(A->erroriffailure);

     39:   for (i = 0; i < n; i++) {
     40:     nz    = bi[i + 1] - bi[i];
     41:     ajtmp = bj + bi[i];
     42:     for (j = 0; j < nz; j++) {
     43:       x    = rtmp + 16 * ajtmp[j];
     44:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
     45:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
     46:     }
     47:     /* load in initial (unfactored row) */
     48:     idx      = r[i];
     49:     nz       = ai[idx + 1] - ai[idx];
     50:     ajtmpold = aj + ai[idx];
     51:     v        = aa + 16 * ai[idx];
     52:     for (j = 0; j < nz; j++) {
     53:       x     = rtmp + 16 * ic[ajtmpold[j]];
     54:       x[0]  = v[0];
     55:       x[1]  = v[1];
     56:       x[2]  = v[2];
     57:       x[3]  = v[3];
     58:       x[4]  = v[4];
     59:       x[5]  = v[5];
     60:       x[6]  = v[6];
     61:       x[7]  = v[7];
     62:       x[8]  = v[8];
     63:       x[9]  = v[9];
     64:       x[10] = v[10];
     65:       x[11] = v[11];
     66:       x[12] = v[12];
     67:       x[13] = v[13];
     68:       x[14] = v[14];
     69:       x[15] = v[15];
     70:       v += 16;
     71:     }
     72:     row = *ajtmp++;
     73:     while (row < i) {
     74:       pc  = rtmp + 16 * row;
     75:       p1  = pc[0];
     76:       p2  = pc[1];
     77:       p3  = pc[2];
     78:       p4  = pc[3];
     79:       p5  = pc[4];
     80:       p6  = pc[5];
     81:       p7  = pc[6];
     82:       p8  = pc[7];
     83:       p9  = pc[8];
     84:       p10 = pc[9];
     85:       p11 = pc[10];
     86:       p12 = pc[11];
     87:       p13 = pc[12];
     88:       p14 = pc[13];
     89:       p15 = pc[14];
     90:       p16 = pc[15];
     91:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0) {
     92:         pv    = ba + 16 * diag_offset[row];
     93:         pj    = bj + diag_offset[row] + 1;
     94:         x1    = pv[0];
     95:         x2    = pv[1];
     96:         x3    = pv[2];
     97:         x4    = pv[3];
     98:         x5    = pv[4];
     99:         x6    = pv[5];
    100:         x7    = pv[6];
    101:         x8    = pv[7];
    102:         x9    = pv[8];
    103:         x10   = pv[9];
    104:         x11   = pv[10];
    105:         x12   = pv[11];
    106:         x13   = pv[12];
    107:         x14   = pv[13];
    108:         x15   = pv[14];
    109:         x16   = pv[15];
    110:         pc[0] = m1 = p1 * x1 + p5 * x2 + p9 * x3 + p13 * x4;
    111:         pc[1] = m2 = p2 * x1 + p6 * x2 + p10 * x3 + p14 * x4;
    112:         pc[2] = m3 = p3 * x1 + p7 * x2 + p11 * x3 + p15 * x4;
    113:         pc[3] = m4 = p4 * x1 + p8 * x2 + p12 * x3 + p16 * x4;

    115:         pc[4] = m5 = p1 * x5 + p5 * x6 + p9 * x7 + p13 * x8;
    116:         pc[5] = m6 = p2 * x5 + p6 * x6 + p10 * x7 + p14 * x8;
    117:         pc[6] = m7 = p3 * x5 + p7 * x6 + p11 * x7 + p15 * x8;
    118:         pc[7] = m8 = p4 * x5 + p8 * x6 + p12 * x7 + p16 * x8;

    120:         pc[8] = m9 = p1 * x9 + p5 * x10 + p9 * x11 + p13 * x12;
    121:         pc[9] = m10 = p2 * x9 + p6 * x10 + p10 * x11 + p14 * x12;
    122:         pc[10] = m11 = p3 * x9 + p7 * x10 + p11 * x11 + p15 * x12;
    123:         pc[11] = m12 = p4 * x9 + p8 * x10 + p12 * x11 + p16 * x12;

    125:         pc[12] = m13 = p1 * x13 + p5 * x14 + p9 * x15 + p13 * x16;
    126:         pc[13] = m14 = p2 * x13 + p6 * x14 + p10 * x15 + p14 * x16;
    127:         pc[14] = m15 = p3 * x13 + p7 * x14 + p11 * x15 + p15 * x16;
    128:         pc[15] = m16 = p4 * x13 + p8 * x14 + p12 * x15 + p16 * x16;

    130:         nz = bi[row + 1] - diag_offset[row] - 1;
    131:         pv += 16;
    132:         for (j = 0; j < nz; j++) {
    133:           x1  = pv[0];
    134:           x2  = pv[1];
    135:           x3  = pv[2];
    136:           x4  = pv[3];
    137:           x5  = pv[4];
    138:           x6  = pv[5];
    139:           x7  = pv[6];
    140:           x8  = pv[7];
    141:           x9  = pv[8];
    142:           x10 = pv[9];
    143:           x11 = pv[10];
    144:           x12 = pv[11];
    145:           x13 = pv[12];
    146:           x14 = pv[13];
    147:           x15 = pv[14];
    148:           x16 = pv[15];
    149:           x   = rtmp + 16 * pj[j];
    150:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
    151:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
    152:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
    153:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

    155:           x[4] -= m1 * x5 + m5 * x6 + m9 * x7 + m13 * x8;
    156:           x[5] -= m2 * x5 + m6 * x6 + m10 * x7 + m14 * x8;
    157:           x[6] -= m3 * x5 + m7 * x6 + m11 * x7 + m15 * x8;
    158:           x[7] -= m4 * x5 + m8 * x6 + m12 * x7 + m16 * x8;

    160:           x[8] -= m1 * x9 + m5 * x10 + m9 * x11 + m13 * x12;
    161:           x[9] -= m2 * x9 + m6 * x10 + m10 * x11 + m14 * x12;
    162:           x[10] -= m3 * x9 + m7 * x10 + m11 * x11 + m15 * x12;
    163:           x[11] -= m4 * x9 + m8 * x10 + m12 * x11 + m16 * x12;

    165:           x[12] -= m1 * x13 + m5 * x14 + m9 * x15 + m13 * x16;
    166:           x[13] -= m2 * x13 + m6 * x14 + m10 * x15 + m14 * x16;
    167:           x[14] -= m3 * x13 + m7 * x14 + m11 * x15 + m15 * x16;
    168:           x[15] -= m4 * x13 + m8 * x14 + m12 * x15 + m16 * x16;

    170:           pv += 16;
    171:         }
    172:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    173:       }
    174:       row = *ajtmp++;
    175:     }
    176:     /* finished row so stick it into b->a */
    177:     pv = ba + 16 * bi[i];
    178:     pj = bj + bi[i];
    179:     nz = bi[i + 1] - bi[i];
    180:     for (j = 0; j < nz; j++) {
    181:       x      = rtmp + 16 * pj[j];
    182:       pv[0]  = x[0];
    183:       pv[1]  = x[1];
    184:       pv[2]  = x[2];
    185:       pv[3]  = x[3];
    186:       pv[4]  = x[4];
    187:       pv[5]  = x[5];
    188:       pv[6]  = x[6];
    189:       pv[7]  = x[7];
    190:       pv[8]  = x[8];
    191:       pv[9]  = x[9];
    192:       pv[10] = x[10];
    193:       pv[11] = x[11];
    194:       pv[12] = x[12];
    195:       pv[13] = x[13];
    196:       pv[14] = x[14];
    197:       pv[15] = x[15];
    198:       pv += 16;
    199:     }
    200:     /* invert diagonal block */
    201:     w = ba + 16 * diag_offset[i];
    202:     if (pivotinblocks) {
    203:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    204:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    205:     } else {
    206:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    207:     }
    208:   }

    210:   PetscCall(PetscFree(rtmp));
    211:   PetscCall(ISRestoreIndices(isicol, &ic));
    212:   PetscCall(ISRestoreIndices(isrow, &r));

    214:   C->ops->solve          = MatSolve_SeqBAIJ_4_inplace;
    215:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_inplace;
    216:   C->assembled           = PETSC_TRUE;

    218:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
    219:   PetscFunctionReturn(PETSC_SUCCESS);
    220: }

    222: /* MatLUFactorNumeric_SeqBAIJ_4 -
    223:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    224:        PetscKernel_A_gets_A_times_B()
    225:        PetscKernel_A_gets_A_minus_B_times_C()
    226:        PetscKernel_A_gets_inverse_A()
    227: */

    229: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4(Mat B, Mat A, const MatFactorInfo *info)
    230: {
    231:   Mat             C = B;
    232:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    233:   IS              isrow = b->row, isicol = b->icol;
    234:   const PetscInt *r, *ic;
    235:   PetscInt        i, j, k, nz, nzL, row;
    236:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
    237:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
    238:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
    239:   PetscInt        flg;
    240:   PetscReal       shift;
    241:   PetscBool       allowzeropivot, zeropivotdetected;

    243:   PetscFunctionBegin;
    244:   allowzeropivot = PetscNot(A->erroriffailure);
    245:   PetscCall(ISGetIndices(isrow, &r));
    246:   PetscCall(ISGetIndices(isicol, &ic));

    248:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
    249:     shift = 0;
    250:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    251:     shift = info->shiftamount;
    252:   }

    254:   /* generate work space needed by the factorization */
    255:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
    256:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

    258:   for (i = 0; i < n; i++) {
    259:     /* zero rtmp */
    260:     /* L part */
    261:     nz    = bi[i + 1] - bi[i];
    262:     bjtmp = bj + bi[i];
    263:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    265:     /* U part */
    266:     nz    = bdiag[i] - bdiag[i + 1];
    267:     bjtmp = bj + bdiag[i + 1] + 1;
    268:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    270:     /* load in initial (unfactored row) */
    271:     nz    = ai[r[i] + 1] - ai[r[i]];
    272:     ajtmp = aj + ai[r[i]];
    273:     v     = aa + bs2 * ai[r[i]];
    274:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

    276:     /* elimination */
    277:     bjtmp = bj + bi[i];
    278:     nzL   = bi[i + 1] - bi[i];
    279:     for (k = 0; k < nzL; k++) {
    280:       row = bjtmp[k];
    281:       pc  = rtmp + bs2 * row;
    282:       for (flg = 0, j = 0; j < bs2; j++) {
    283:         if (pc[j] != 0.0) {
    284:           flg = 1;
    285:           break;
    286:         }
    287:       }
    288:       if (flg) {
    289:         pv = b->a + bs2 * bdiag[row];
    290:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    291:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

    293:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
    294:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
    295:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
    296:         for (j = 0; j < nz; j++) {
    297:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    298:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    299:           v = rtmp + bs2 * pj[j];
    300:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
    301:           pv += bs2;
    302:         }
    303:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    304:       }
    305:     }

    307:     /* finished row so stick it into b->a */
    308:     /* L part */
    309:     pv = b->a + bs2 * bi[i];
    310:     pj = b->j + bi[i];
    311:     nz = bi[i + 1] - bi[i];
    312:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    314:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    315:     pv = b->a + bs2 * bdiag[i];
    316:     pj = b->j + bdiag[i];
    317:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    318:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
    319:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    321:     /* U part */
    322:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
    323:     pj = b->j + bdiag[i + 1] + 1;
    324:     nz = bdiag[i] - bdiag[i + 1] - 1;
    325:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
    326:   }

    328:   PetscCall(PetscFree2(rtmp, mwork));
    329:   PetscCall(ISRestoreIndices(isicol, &ic));
    330:   PetscCall(ISRestoreIndices(isrow, &r));

    332:   C->ops->solve          = MatSolve_SeqBAIJ_4;
    333:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
    334:   C->assembled           = PETSC_TRUE;

    336:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
    337:   PetscFunctionReturn(PETSC_SUCCESS);
    338: }

    340: PetscErrorCode MatILUFactorNumeric_SeqBAIJ_4_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
    341: {
    342:   /*
    343:     Default Version for when blocks are 4 by 4 Using natural ordering
    344: */
    345:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    346:   PetscInt        i, j, n = a->mbs, *bi = b->i, *bj = b->j;
    347:   PetscInt       *ajtmpold, *ajtmp, nz, row;
    348:   const PetscInt *diag_offset;
    349:   PetscInt       *ai = a->i, *aj = a->j, *pj;
    350:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
    351:   MatScalar       p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
    352:   MatScalar       p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
    353:   MatScalar       p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
    354:   MatScalar       m13, m14, m15, m16;
    355:   MatScalar      *ba = b->a, *aa = a->a;
    356:   PetscBool       pivotinblocks = b->pivotinblocks;
    357:   PetscReal       shift         = info->shiftamount;
    358:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

    360:   PetscFunctionBegin;
    361:   /* Since A is C and C is labeled as a factored matrix we need to lie to MatGetDiagonalMarkers_SeqBAIJ() to get it to compute the diagonals */
    362:   A->factortype = MAT_FACTOR_NONE;
    363:   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, &diag_offset, NULL));
    364:   A->factortype  = MAT_FACTOR_ILU;
    365:   allowzeropivot = PetscNot(A->erroriffailure);
    366:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));

    368:   for (i = 0; i < n; i++) {
    369:     nz    = bi[i + 1] - bi[i];
    370:     ajtmp = bj + bi[i];
    371:     for (j = 0; j < nz; j++) {
    372:       x    = rtmp + 16 * ajtmp[j];
    373:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
    374:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
    375:     }
    376:     /* load in initial (unfactored row) */
    377:     nz       = ai[i + 1] - ai[i];
    378:     ajtmpold = aj + ai[i];
    379:     v        = aa + 16 * ai[i];
    380:     for (j = 0; j < nz; j++) {
    381:       x     = rtmp + 16 * ajtmpold[j];
    382:       x[0]  = v[0];
    383:       x[1]  = v[1];
    384:       x[2]  = v[2];
    385:       x[3]  = v[3];
    386:       x[4]  = v[4];
    387:       x[5]  = v[5];
    388:       x[6]  = v[6];
    389:       x[7]  = v[7];
    390:       x[8]  = v[8];
    391:       x[9]  = v[9];
    392:       x[10] = v[10];
    393:       x[11] = v[11];
    394:       x[12] = v[12];
    395:       x[13] = v[13];
    396:       x[14] = v[14];
    397:       x[15] = v[15];
    398:       v += 16;
    399:     }
    400:     row = *ajtmp++;
    401:     while (row < i) {
    402:       pc  = rtmp + 16 * row;
    403:       p1  = pc[0];
    404:       p2  = pc[1];
    405:       p3  = pc[2];
    406:       p4  = pc[3];
    407:       p5  = pc[4];
    408:       p6  = pc[5];
    409:       p7  = pc[6];
    410:       p8  = pc[7];
    411:       p9  = pc[8];
    412:       p10 = pc[9];
    413:       p11 = pc[10];
    414:       p12 = pc[11];
    415:       p13 = pc[12];
    416:       p14 = pc[13];
    417:       p15 = pc[14];
    418:       p16 = pc[15];
    419:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0) {
    420:         pv    = ba + 16 * diag_offset[row];
    421:         pj    = bj + diag_offset[row] + 1;
    422:         x1    = pv[0];
    423:         x2    = pv[1];
    424:         x3    = pv[2];
    425:         x4    = pv[3];
    426:         x5    = pv[4];
    427:         x6    = pv[5];
    428:         x7    = pv[6];
    429:         x8    = pv[7];
    430:         x9    = pv[8];
    431:         x10   = pv[9];
    432:         x11   = pv[10];
    433:         x12   = pv[11];
    434:         x13   = pv[12];
    435:         x14   = pv[13];
    436:         x15   = pv[14];
    437:         x16   = pv[15];
    438:         pc[0] = m1 = p1 * x1 + p5 * x2 + p9 * x3 + p13 * x4;
    439:         pc[1] = m2 = p2 * x1 + p6 * x2 + p10 * x3 + p14 * x4;
    440:         pc[2] = m3 = p3 * x1 + p7 * x2 + p11 * x3 + p15 * x4;
    441:         pc[3] = m4 = p4 * x1 + p8 * x2 + p12 * x3 + p16 * x4;

    443:         pc[4] = m5 = p1 * x5 + p5 * x6 + p9 * x7 + p13 * x8;
    444:         pc[5] = m6 = p2 * x5 + p6 * x6 + p10 * x7 + p14 * x8;
    445:         pc[6] = m7 = p3 * x5 + p7 * x6 + p11 * x7 + p15 * x8;
    446:         pc[7] = m8 = p4 * x5 + p8 * x6 + p12 * x7 + p16 * x8;

    448:         pc[8] = m9 = p1 * x9 + p5 * x10 + p9 * x11 + p13 * x12;
    449:         pc[9] = m10 = p2 * x9 + p6 * x10 + p10 * x11 + p14 * x12;
    450:         pc[10] = m11 = p3 * x9 + p7 * x10 + p11 * x11 + p15 * x12;
    451:         pc[11] = m12 = p4 * x9 + p8 * x10 + p12 * x11 + p16 * x12;

    453:         pc[12] = m13 = p1 * x13 + p5 * x14 + p9 * x15 + p13 * x16;
    454:         pc[13] = m14 = p2 * x13 + p6 * x14 + p10 * x15 + p14 * x16;
    455:         pc[14] = m15 = p3 * x13 + p7 * x14 + p11 * x15 + p15 * x16;
    456:         pc[15] = m16 = p4 * x13 + p8 * x14 + p12 * x15 + p16 * x16;
    457:         nz           = bi[row + 1] - diag_offset[row] - 1;
    458:         pv += 16;
    459:         for (j = 0; j < nz; j++) {
    460:           x1  = pv[0];
    461:           x2  = pv[1];
    462:           x3  = pv[2];
    463:           x4  = pv[3];
    464:           x5  = pv[4];
    465:           x6  = pv[5];
    466:           x7  = pv[6];
    467:           x8  = pv[7];
    468:           x9  = pv[8];
    469:           x10 = pv[9];
    470:           x11 = pv[10];
    471:           x12 = pv[11];
    472:           x13 = pv[12];
    473:           x14 = pv[13];
    474:           x15 = pv[14];
    475:           x16 = pv[15];
    476:           x   = rtmp + 16 * pj[j];
    477:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
    478:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
    479:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
    480:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

    482:           x[4] -= m1 * x5 + m5 * x6 + m9 * x7 + m13 * x8;
    483:           x[5] -= m2 * x5 + m6 * x6 + m10 * x7 + m14 * x8;
    484:           x[6] -= m3 * x5 + m7 * x6 + m11 * x7 + m15 * x8;
    485:           x[7] -= m4 * x5 + m8 * x6 + m12 * x7 + m16 * x8;

    487:           x[8] -= m1 * x9 + m5 * x10 + m9 * x11 + m13 * x12;
    488:           x[9] -= m2 * x9 + m6 * x10 + m10 * x11 + m14 * x12;
    489:           x[10] -= m3 * x9 + m7 * x10 + m11 * x11 + m15 * x12;
    490:           x[11] -= m4 * x9 + m8 * x10 + m12 * x11 + m16 * x12;

    492:           x[12] -= m1 * x13 + m5 * x14 + m9 * x15 + m13 * x16;
    493:           x[13] -= m2 * x13 + m6 * x14 + m10 * x15 + m14 * x16;
    494:           x[14] -= m3 * x13 + m7 * x14 + m11 * x15 + m15 * x16;
    495:           x[15] -= m4 * x13 + m8 * x14 + m12 * x15 + m16 * x16;

    497:           pv += 16;
    498:         }
    499:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    500:       }
    501:       row = *ajtmp++;
    502:     }
    503:     /* finished row so stick it into b->a */
    504:     pv = ba + 16 * bi[i];
    505:     pj = bj + bi[i];
    506:     nz = bi[i + 1] - bi[i];
    507:     for (j = 0; j < nz; j++) {
    508:       x      = rtmp + 16 * pj[j];
    509:       pv[0]  = x[0];
    510:       pv[1]  = x[1];
    511:       pv[2]  = x[2];
    512:       pv[3]  = x[3];
    513:       pv[4]  = x[4];
    514:       pv[5]  = x[5];
    515:       pv[6]  = x[6];
    516:       pv[7]  = x[7];
    517:       pv[8]  = x[8];
    518:       pv[9]  = x[9];
    519:       pv[10] = x[10];
    520:       pv[11] = x[11];
    521:       pv[12] = x[12];
    522:       pv[13] = x[13];
    523:       pv[14] = x[14];
    524:       pv[15] = x[15];
    525:       pv += 16;
    526:     }
    527:     /* invert diagonal block */
    528:     w = ba + 16 * diag_offset[i];
    529:     if (pivotinblocks) {
    530:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    531:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    532:     } else {
    533:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    534:     }
    535:   }

    537:   PetscCall(PetscFree(rtmp));

    539:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
    540:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
    541:   C->assembled           = PETSC_TRUE;

    543:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
    544:   PetscFunctionReturn(PETSC_SUCCESS);
    545: }

    547: /*
    548:   MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering -
    549:     copied from MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace()
    550: */
    551: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
    552: {
    553:   Mat             C = B;
    554:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    555:   PetscInt        i, j, k, nz, nzL, row;
    556:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
    557:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
    558:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
    559:   PetscInt        flg;
    560:   PetscReal       shift;
    561:   PetscBool       allowzeropivot, zeropivotdetected;

    563:   PetscFunctionBegin;
    564:   allowzeropivot = PetscNot(A->erroriffailure);

    566:   /* generate work space needed by the factorization */
    567:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
    568:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

    570:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
    571:     shift = 0;
    572:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    573:     shift = info->shiftamount;
    574:   }

    576:   for (i = 0; i < n; i++) {
    577:     /* zero rtmp */
    578:     /* L part */
    579:     nz    = bi[i + 1] - bi[i];
    580:     bjtmp = bj + bi[i];
    581:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    583:     /* U part */
    584:     nz    = bdiag[i] - bdiag[i + 1];
    585:     bjtmp = bj + bdiag[i + 1] + 1;
    586:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    588:     /* load in initial (unfactored row) */
    589:     nz    = ai[i + 1] - ai[i];
    590:     ajtmp = aj + ai[i];
    591:     v     = aa + bs2 * ai[i];
    592:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

    594:     /* elimination */
    595:     bjtmp = bj + bi[i];
    596:     nzL   = bi[i + 1] - bi[i];
    597:     for (k = 0; k < nzL; k++) {
    598:       row = bjtmp[k];
    599:       pc  = rtmp + bs2 * row;
    600:       for (flg = 0, j = 0; j < bs2; j++) {
    601:         if (pc[j] != 0.0) {
    602:           flg = 1;
    603:           break;
    604:         }
    605:       }
    606:       if (flg) {
    607:         pv = b->a + bs2 * bdiag[row];
    608:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    609:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

    611:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
    612:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
    613:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
    614:         for (j = 0; j < nz; j++) {
    615:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    616:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    617:           v = rtmp + bs2 * pj[j];
    618:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
    619:           pv += bs2;
    620:         }
    621:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    622:       }
    623:     }

    625:     /* finished row so stick it into b->a */
    626:     /* L part */
    627:     pv = b->a + bs2 * bi[i];
    628:     pj = b->j + bi[i];
    629:     nz = bi[i + 1] - bi[i];
    630:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    632:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    633:     pv = b->a + bs2 * bdiag[i];
    634:     pj = b->j + bdiag[i];
    635:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    636:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
    637:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    639:     /* U part */
    640:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
    641:     pj = b->j + bdiag[i + 1] + 1;
    642:     nz = bdiag[i] - bdiag[i + 1] - 1;
    643:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
    644:   }
    645:   PetscCall(PetscFree2(rtmp, mwork));

    647:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
    648:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    649:   C->assembled           = PETSC_TRUE;

    651:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
    652:   PetscFunctionReturn(PETSC_SUCCESS);
    653: }