Actual source code: baijsolvtran2.c

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

      4: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_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, x1, x2, *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        = 2 * c[i];
     29:     t[ii]     = b[ic];
     30:     t[ii + 1] = b[ic + 1];
     31:     ii += 2;
     32:   }

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

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

     73:   /* copy t into x according to permutation */
     74:   ii = 0;
     75:   for (i = 0; i < n; i++) {
     76:     ir        = 2 * r[i];
     77:     x[ir]     = t[ii];
     78:     x[ir + 1] = t[ii + 1];
     79:     ii += 2;
     80:   }

     82:   PetscCall(ISRestoreIndices(isrow, &rout));
     83:   PetscCall(ISRestoreIndices(iscol, &cout));
     84:   PetscCall(VecRestoreArrayRead(bb, &b));
     85:   PetscCall(VecRestoreArray(xx, &x));
     86:   PetscCall(PetscLogFlops(2.0 * 4 * (a->nz) - 2.0 * A->cmap->n));
     87:   PetscFunctionReturn(PETSC_SUCCESS);
     88: }

     90: PetscErrorCode MatSolveTranspose_SeqBAIJ_2(Mat A, Vec bb, Vec xx)
     91: {
     92:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
     93:   IS                 iscol = a->col, isrow = a->row;
     94:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
     95:   const PetscInt    *r, *c, *rout, *cout;
     96:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
     97:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
     98:   const MatScalar   *aa = a->a, *v;
     99:   PetscScalar        s1, s2, x1, x2, *x, *t;
    100:   const PetscScalar *b;

    102:   PetscFunctionBegin;
    103:   PetscCall(VecGetArrayRead(bb, &b));
    104:   PetscCall(VecGetArray(xx, &x));
    105:   t = a->solve_work;

    107:   PetscCall(ISGetIndices(isrow, &rout));
    108:   r = rout;
    109:   PetscCall(ISGetIndices(iscol, &cout));
    110:   c = cout;

    112:   /* copy b into temp work space according to permutation */
    113:   for (i = 0; i < n; i++) {
    114:     ii        = bs * i;
    115:     ic        = bs * c[i];
    116:     t[ii]     = b[ic];
    117:     t[ii + 1] = b[ic + 1];
    118:   }

    120:   /* forward solve the U^T */
    121:   idx = 0;
    122:   for (i = 0; i < n; i++) {
    123:     v = aa + bs2 * diag[i];
    124:     /* multiply by the inverse of the block diagonal */
    125:     x1 = t[idx];
    126:     x2 = t[1 + idx];
    127:     s1 = v[0] * x1 + v[1] * x2;
    128:     s2 = v[2] * x1 + v[3] * x2;
    129:     v -= bs2;

    131:     vi = aj + diag[i] - 1;
    132:     nz = diag[i] - diag[i + 1] - 1;
    133:     for (j = 0; j > -nz; j--) {
    134:       oidx = bs * vi[j];
    135:       t[oidx] -= v[0] * s1 + v[1] * s2;
    136:       t[oidx + 1] -= v[2] * s1 + v[3] * s2;
    137:       v -= bs2;
    138:     }
    139:     t[idx]     = s1;
    140:     t[1 + idx] = s2;
    141:     idx += bs;
    142:   }
    143:   /* backward solve the L^T */
    144:   for (i = n - 1; i >= 0; i--) {
    145:     v   = aa + bs2 * ai[i];
    146:     vi  = aj + ai[i];
    147:     nz  = ai[i + 1] - ai[i];
    148:     idt = bs * i;
    149:     s1  = t[idt];
    150:     s2  = t[1 + idt];
    151:     for (j = 0; j < nz; j++) {
    152:       idx = bs * vi[j];
    153:       t[idx] -= v[0] * s1 + v[1] * s2;
    154:       t[idx + 1] -= v[2] * s1 + v[3] * s2;
    155:       v += bs2;
    156:     }
    157:   }

    159:   /* copy t into x according to permutation */
    160:   for (i = 0; i < n; i++) {
    161:     ii        = bs * i;
    162:     ir        = bs * r[i];
    163:     x[ir]     = t[ii];
    164:     x[ir + 1] = t[ii + 1];
    165:   }

    167:   PetscCall(ISRestoreIndices(isrow, &rout));
    168:   PetscCall(ISRestoreIndices(iscol, &cout));
    169:   PetscCall(VecRestoreArrayRead(bb, &b));
    170:   PetscCall(VecRestoreArray(xx, &x));
    171:   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
    172:   PetscFunctionReturn(PETSC_SUCCESS);
    173: }