Date: 2025-03-29T05:58:33+00:00

Actual source code: baijsolvtran3.c

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

      4: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_inplace(Mat A, Vec bb, Vec xx)
      5: {
      6:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
      7:   IS                 iscol = a->col, isrow = a->row;
      8:   const PetscInt    *r, *c, *rout, *cout;
      9:   const PetscInt    *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
     10:   PetscInt           i, nz, idx, idt, ii, ic, ir, oidx;
     11:   const MatScalar   *aa = a->a, *v;
     12:   PetscScalar        s1, s2, s3, x1, x2, x3, *x, *t;
     13:   const PetscScalar *b;

     15:   PetscFunctionBegin;
     16:   PetscCall(VecGetArrayRead(bb, &b));
     17:   PetscCall(VecGetArray(xx, &x));
     18:   t = a->solve_work;

     20:   PetscCall(ISGetIndices(isrow, &rout));
     21:   r = rout;
     22:   PetscCall(ISGetIndices(iscol, &cout));
     23:   c = cout;

     25:   /* copy the b into temp work space according to permutation */
     26:   ii = 0;
     27:   for (i = 0; i < n; i++) {
     28:     ic        = 3 * c[i];
     29:     t[ii]     = b[ic];
     30:     t[ii + 1] = b[ic + 1];
     31:     t[ii + 2] = b[ic + 2];
     32:     ii += 3;
     33:   }

     35:   /* forward solve the U^T */
     36:   idx = 0;
     37:   for (i = 0; i < n; i++) {
     38:     v = aa + 9 * diag[i];
     39:     /* multiply by the inverse of the block diagonal */
     40:     x1 = t[idx];
     41:     x2 = t[1 + idx];
     42:     x3 = t[2 + idx];
     43:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
     44:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
     45:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
     46:     v += 9;

     48:     vi = aj + diag[i] + 1;
     49:     nz = ai[i + 1] - diag[i] - 1;
     50:     while (nz--) {
     51:       oidx = 3 * (*vi++);
     52:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
     53:       t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
     54:       t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
     55:       v += 9;
     56:     }
     57:     t[idx]     = s1;
     58:     t[1 + idx] = s2;
     59:     t[2 + idx] = s3;
     60:     idx += 3;
     61:   }
     62:   /* backward solve the L^T */
     63:   for (i = n - 1; i >= 0; i--) {
     64:     v   = aa + 9 * diag[i] - 9;
     65:     vi  = aj + diag[i] - 1;
     66:     nz  = diag[i] - ai[i];
     67:     idt = 3 * i;
     68:     s1  = t[idt];
     69:     s2  = t[1 + idt];
     70:     s3  = t[2 + idt];
     71:     while (nz--) {
     72:       idx = 3 * (*vi--);
     73:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
     74:       t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
     75:       t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
     76:       v -= 9;
     77:     }
     78:   }

     80:   /* copy t into x according to permutation */
     81:   ii = 0;
     82:   for (i = 0; i < n; i++) {
     83:     ir        = 3 * r[i];
     84:     x[ir]     = t[ii];
     85:     x[ir + 1] = t[ii + 1];
     86:     x[ir + 2] = t[ii + 2];
     87:     ii += 3;
     88:   }

     90:   PetscCall(ISRestoreIndices(isrow, &rout));
     91:   PetscCall(ISRestoreIndices(iscol, &cout));
     92:   PetscCall(VecRestoreArrayRead(bb, &b));
     93:   PetscCall(VecRestoreArray(xx, &x));
     94:   PetscCall(PetscLogFlops(2.0 * 9 * (a->nz) - 3.0 * A->cmap->n));
     95:   PetscFunctionReturn(PETSC_SUCCESS);
     96: }

     98: PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A, Vec bb, Vec xx)
     99: {
    100:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
    101:   IS                 iscol = a->col, isrow = a->row;
    102:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
    103:   const PetscInt    *r, *c, *rout, *cout;
    104:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
    105:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
    106:   const MatScalar   *aa = a->a, *v;
    107:   PetscScalar        s1, s2, s3, x1, x2, x3, *x, *t;
    108:   const PetscScalar *b;

    110:   PetscFunctionBegin;
    111:   PetscCall(VecGetArrayRead(bb, &b));
    112:   PetscCall(VecGetArray(xx, &x));
    113:   t = a->solve_work;

    115:   PetscCall(ISGetIndices(isrow, &rout));
    116:   r = rout;
    117:   PetscCall(ISGetIndices(iscol, &cout));
    118:   c = cout;

    120:   /* copy b into temp work space according to permutation */
    121:   for (i = 0; i < n; i++) {
    122:     ii        = bs * i;
    123:     ic        = bs * c[i];
    124:     t[ii]     = b[ic];
    125:     t[ii + 1] = b[ic + 1];
    126:     t[ii + 2] = b[ic + 2];
    127:   }

    129:   /* forward solve the U^T */
    130:   idx = 0;
    131:   for (i = 0; i < n; i++) {
    132:     v = aa + bs2 * diag[i];
    133:     /* multiply by the inverse of the block diagonal */
    134:     x1 = t[idx];
    135:     x2 = t[1 + idx];
    136:     x3 = t[2 + idx];
    137:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
    138:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
    139:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
    140:     v -= bs2;

    142:     vi = aj + diag[i] - 1;
    143:     nz = diag[i] - diag[i + 1] - 1;
    144:     for (j = 0; j > -nz; j--) {
    145:       oidx = bs * vi[j];
    146:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
    147:       t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
    148:       t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
    149:       v -= bs2;
    150:     }
    151:     t[idx]     = s1;
    152:     t[1 + idx] = s2;
    153:     t[2 + idx] = s3;
    154:     idx += bs;
    155:   }
    156:   /* backward solve the L^T */
    157:   for (i = n - 1; i >= 0; i--) {
    158:     v   = aa + bs2 * ai[i];
    159:     vi  = aj + ai[i];
    160:     nz  = ai[i + 1] - ai[i];
    161:     idt = bs * i;
    162:     s1  = t[idt];
    163:     s2  = t[1 + idt];
    164:     s3  = t[2 + idt];
    165:     for (j = 0; j < nz; j++) {
    166:       idx = bs * vi[j];
    167:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
    168:       t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
    169:       t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
    170:       v += bs2;
    171:     }
    172:   }

    174:   /* copy t into x according to permutation */
    175:   for (i = 0; i < n; i++) {
    176:     ii        = bs * i;
    177:     ir        = bs * r[i];
    178:     x[ir]     = t[ii];
    179:     x[ir + 1] = t[ii + 1];
    180:     x[ir + 2] = t[ii + 2];
    181:   }

    183:   PetscCall(ISRestoreIndices(isrow, &rout));
    184:   PetscCall(ISRestoreIndices(iscol, &cout));
    185:   PetscCall(VecRestoreArrayRead(bb, &b));
    186:   PetscCall(VecRestoreArray(xx, &x));
    187:   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
    188:   PetscFunctionReturn(PETSC_SUCCESS);
    189: }