Actual source code: sbaijfact3.c

      1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
      2: #include <petsc/private/kernels/blockinvert.h>

      4: /* Version for when blocks are 3 by 3  */
      5: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C, Mat A, const MatFactorInfo *info)
      6: {
      7:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
      8:   IS              perm = b->row;
      9:   const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j;
     10:   PetscInt       *a2anew, i, j, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
     11:   MatScalar      *ba = b->a, *aa, *ap, *dk, *uik;
     12:   MatScalar      *u, *diag, *rtmp, *rtmp_ptr;
     13:   PetscReal       shift = info->shiftamount;
     14:   PetscBool       allowzeropivot, zeropivotdetected;

     16:   PetscFunctionBegin;
     17:   /* initialization */
     18:   allowzeropivot = PetscNot(A->erroriffailure);
     19:   PetscCall(PetscCalloc1(9 * mbs, &rtmp));
     20:   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
     21:   il[0] = 0;
     22:   for (i = 0; i < mbs; i++) jl[i] = mbs;

     24:   PetscCall(PetscMalloc2(9, &dk, 9, &uik));
     25:   PetscCall(ISGetIndices(perm, &perm_ptr));

     27:   /* check permutation */
     28:   if (!a->permute) {
     29:     ai = a->i;
     30:     aj = a->j;
     31:     aa = a->a;
     32:   } else {
     33:     ai = a->inew;
     34:     aj = a->jnew;
     35:     PetscCall(PetscMalloc1(9 * ai[mbs], &aa));
     36:     PetscCall(PetscArraycpy(aa, a->a, 9 * ai[mbs]));
     37:     PetscCall(PetscMalloc1(ai[mbs], &a2anew));
     38:     PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs]));

     40:     for (i = 0; i < mbs; i++) {
     41:       jmin = ai[i];
     42:       jmax = ai[i + 1];
     43:       for (j = jmin; j < jmax; j++) {
     44:         while (a2anew[j] != j) {
     45:           k         = a2anew[j];
     46:           a2anew[j] = a2anew[k];
     47:           a2anew[k] = k;
     48:           for (k1 = 0; k1 < 9; k1++) {
     49:             dk[k1]         = aa[k * 9 + k1];
     50:             aa[k * 9 + k1] = aa[j * 9 + k1];
     51:             aa[j * 9 + k1] = dk[k1];
     52:           }
     53:         }
     54:         /* transform column-oriented blocks that lie in the lower triangle to row-oriented blocks */
     55:         if (i > aj[j]) {
     56:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
     57:           ap = aa + j * 9;                       /* ptr to the beginning of j-th block of aa */
     58:           for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
     59:           for (k = 0; k < 3; k++) {              /* j-th block of aa <- dk^T */
     60:             for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * k1];
     61:           }
     62:         }
     63:       }
     64:     }
     65:     PetscCall(PetscFree(a2anew));
     66:   }

     68:   /* for each row k */
     69:   for (k = 0; k < mbs; k++) {
     70:     /*initialize k-th row with elements nonzero in row perm(k) of A */
     71:     jmin = ai[perm_ptr[k]];
     72:     jmax = ai[perm_ptr[k] + 1];
     73:     if (jmin < jmax) {
     74:       ap = aa + jmin * 9;
     75:       for (j = jmin; j < jmax; j++) {
     76:         vj       = perm_ptr[aj[j]]; /* block col. index */
     77:         rtmp_ptr = rtmp + vj * 9;
     78:         for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
     79:       }
     80:     }

     82:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
     83:     PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
     84:     i = jl[k]; /* first row to be added to k_th row  */

     86:     while (i < mbs) {
     87:       nexti = jl[i]; /* next row to be added to k_th row */

     89:       /* compute multiplier */
     90:       ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */

     92:       /* uik = -inv(Di)*U_bar(i,k) */
     93:       diag = ba + i * 9;
     94:       u    = ba + ili * 9;

     96:       uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
     97:       uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
     98:       uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);

    100:       uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
    101:       uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
    102:       uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);

    104:       uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
    105:       uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
    106:       uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);

    108:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
    109:       dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
    110:       dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
    111:       dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

    113:       dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
    114:       dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
    115:       dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

    117:       dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
    118:       dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
    119:       dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];

    121:       PetscCall(PetscLogFlops(27.0 * 4.0));

    123:       /* update -U(i,k) */
    124:       PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));

    126:       /* add multiple of row i to k-th row ... */
    127:       jmin = ili + 1;
    128:       jmax = bi[i + 1];
    129:       if (jmin < jmax) {
    130:         for (j = jmin; j < jmax; j++) {
    131:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
    132:           rtmp_ptr = rtmp + bj[j] * 9;
    133:           u        = ba + j * 9;
    134:           rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
    135:           rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
    136:           rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

    138:           rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
    139:           rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
    140:           rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

    142:           rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
    143:           rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
    144:           rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
    145:         }
    146:         PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin)));

    148:         /* ... add i to row list for next nonzero entry */
    149:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
    150:         j     = bj[jmin];
    151:         jl[i] = jl[j];
    152:         jl[j] = i; /* update jl */
    153:       }
    154:       i = nexti;
    155:     }

    157:     /* save nonzero entries in k-th row of U ... */

    159:     /* invert diagonal block */
    160:     diag = ba + k * 9;
    161:     PetscCall(PetscArraycpy(diag, dk, 9));
    162:     PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
    163:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    165:     jmin = bi[k];
    166:     jmax = bi[k + 1];
    167:     if (jmin < jmax) {
    168:       for (j = jmin; j < jmax; j++) {
    169:         vj       = bj[j]; /* block col. index of U */
    170:         u        = ba + j * 9;
    171:         rtmp_ptr = rtmp + vj * 9;
    172:         for (k1 = 0; k1 < 9; k1++) {
    173:           *u++        = *rtmp_ptr;
    174:           *rtmp_ptr++ = 0.0;
    175:         }
    176:       }

    178:       /* ... add k to row list for first nonzero entry in k-th row */
    179:       il[k] = jmin;
    180:       i     = bj[jmin];
    181:       jl[k] = jl[i];
    182:       jl[i] = k;
    183:     }
    184:   }

    186:   PetscCall(PetscFree(rtmp));
    187:   PetscCall(PetscFree2(il, jl));
    188:   PetscCall(PetscFree2(dk, uik));
    189:   if (a->permute) PetscCall(PetscFree(aa));

    191:   PetscCall(ISRestoreIndices(perm, &perm_ptr));

    193:   C->ops->solve          = MatSolve_SeqSBAIJ_3_inplace;
    194:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
    195:   C->assembled           = PETSC_TRUE;
    196:   C->preallocated        = PETSC_TRUE;

    198:   PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
    199:   PetscFunctionReturn(PETSC_SUCCESS);
    200: }