Actual source code: baijsolvtrannat4.c

  1: #include <../src/mat/impls/baij/seq/baij.h>

  3: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
  4: {
  5:   Mat_SeqBAIJ     *a    = (Mat_SeqBAIJ *)A->data;
  6:   const PetscInt  *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
  7:   PetscInt         i, nz, idx, idt, oidx;
  8:   const MatScalar *aa = a->a, *v;
  9:   PetscScalar      s1, s2, s3, s4, x1, x2, x3, x4, *x;

 11:   VecCopy(bb, xx);
 12:   VecGetArray(xx, &x);

 14:   /* forward solve the U^T */
 15:   idx = 0;
 16:   for (i = 0; i < n; i++) {
 17:     v = aa + 16 * diag[i];
 18:     /* multiply by the inverse of the block diagonal */
 19:     x1 = x[idx];
 20:     x2 = x[1 + idx];
 21:     x3 = x[2 + idx];
 22:     x4 = x[3 + idx];
 23:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
 24:     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
 25:     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
 26:     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
 27:     v += 16;

 29:     vi = aj + diag[i] + 1;
 30:     nz = ai[i + 1] - diag[i] - 1;
 31:     while (nz--) {
 32:       oidx = 4 * (*vi++);
 33:       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
 34:       x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
 35:       x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
 36:       x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
 37:       v += 16;
 38:     }
 39:     x[idx]     = s1;
 40:     x[1 + idx] = s2;
 41:     x[2 + idx] = s3;
 42:     x[3 + idx] = s4;
 43:     idx += 4;
 44:   }
 45:   /* backward solve the L^T */
 46:   for (i = n - 1; i >= 0; i--) {
 47:     v   = aa + 16 * diag[i] - 16;
 48:     vi  = aj + diag[i] - 1;
 49:     nz  = diag[i] - ai[i];
 50:     idt = 4 * i;
 51:     s1  = x[idt];
 52:     s2  = x[1 + idt];
 53:     s3  = x[2 + idt];
 54:     s4  = x[3 + idt];
 55:     while (nz--) {
 56:       idx = 4 * (*vi--);
 57:       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
 58:       x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
 59:       x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
 60:       x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
 61:       v -= 16;
 62:     }
 63:   }
 64:   VecRestoreArray(xx, &x);
 65:   PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n);
 66:   return 0;
 67: }

 69: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering(Mat A, Vec bb, Vec xx)
 70: {
 71:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
 72:   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
 73:   PetscInt         nz, idx, idt, j, i, oidx;
 74:   const PetscInt   bs = A->rmap->bs, bs2 = a->bs2;
 75:   const MatScalar *aa = a->a, *v;
 76:   PetscScalar      s1, s2, s3, s4, x1, x2, x3, x4, *x;

 78:   VecCopy(bb, xx);
 79:   VecGetArray(xx, &x);

 81:   /* forward solve the U^T */
 82:   idx = 0;
 83:   for (i = 0; i < n; i++) {
 84:     v = aa + bs2 * diag[i];
 85:     /* multiply by the inverse of the block diagonal */
 86:     x1 = x[idx];
 87:     x2 = x[1 + idx];
 88:     x3 = x[2 + idx];
 89:     x4 = x[3 + idx];
 90:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
 91:     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
 92:     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
 93:     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
 94:     v -= bs2;

 96:     vi = aj + diag[i] - 1;
 97:     nz = diag[i] - diag[i + 1] - 1;
 98:     for (j = 0; j > -nz; j--) {
 99:       oidx = bs * vi[j];
100:       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
101:       x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
102:       x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
103:       x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
104:       v -= bs2;
105:     }
106:     x[idx]     = s1;
107:     x[1 + idx] = s2;
108:     x[2 + idx] = s3;
109:     x[3 + idx] = s4;
110:     idx += bs;
111:   }
112:   /* backward solve the L^T */
113:   for (i = n - 1; i >= 0; i--) {
114:     v   = aa + bs2 * ai[i];
115:     vi  = aj + ai[i];
116:     nz  = ai[i + 1] - ai[i];
117:     idt = bs * i;
118:     s1  = x[idt];
119:     s2  = x[1 + idt];
120:     s3  = x[2 + idt];
121:     s4  = x[3 + idt];
122:     for (j = 0; j < nz; j++) {
123:       idx = bs * vi[j];
124:       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
125:       x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
126:       x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
127:       x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
128:       v += bs2;
129:     }
130:   }
131:   VecRestoreArray(xx, &x);
132:   PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n);
133:   return 0;
134: }