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

  4: /*
  5:       Special case where the matrix was ILU(0) factored in the natural
  6:    ordering. This eliminates the need for the column and row permutation.
  7: */
  8: PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
  9: {
 10:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
 11:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
 12:   const MatScalar   *aa = a->a, *v;
 13:   PetscScalar       *x;
 14:   const PetscScalar *b;
 15:   PetscScalar        s1, x1;
 16:   PetscInt           jdx, idt, idx, nz, i;

 18:   PetscFunctionBegin;
 19:   PetscCall(VecGetArrayRead(bb, &b));
 20:   PetscCall(VecGetArray(xx, &x));

 22:   /* forward solve the lower triangular */
 23:   idx  = 0;
 24:   x[0] = b[0];
 25:   for (i = 1; i < n; i++) {
 26:     v  = aa + ai[i];
 27:     vi = aj + ai[i];
 28:     nz = diag[i] - ai[i];
 29:     idx += 1;
 30:     s1 = b[idx];
 31:     while (nz--) {
 32:       jdx = *vi++;
 33:       x1  = x[jdx];
 34:       s1 -= v[0] * x1;
 35:       v += 1;
 36:     }
 37:     x[idx] = s1;
 38:   }
 39:   /* backward solve the upper triangular */
 40:   for (i = n - 1; i >= 0; i--) {
 41:     v   = aa + diag[i] + 1;
 42:     vi  = aj + diag[i] + 1;
 43:     nz  = ai[i + 1] - diag[i] - 1;
 44:     idt = i;
 45:     s1  = x[idt];
 46:     while (nz--) {
 47:       idx = *vi++;
 48:       x1  = x[idx];
 49:       s1 -= v[0] * x1;
 50:       v += 1;
 51:     }
 52:     v      = aa + diag[i];
 53:     x[idt] = v[0] * s1;
 54:   }
 55:   PetscCall(VecRestoreArrayRead(bb, &b));
 56:   PetscCall(VecRestoreArray(xx, &x));
 57:   PetscCall(PetscLogFlops(2.0 * (a->nz) - A->cmap->n));
 58:   PetscFunctionReturn(PETSC_SUCCESS);
 59: }

 61: PetscErrorCode MatForwardSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
 62: {
 63:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
 64:   const PetscInt     n = a->mbs, *ai = a->i, *aj = a->j, *vi;
 65:   PetscScalar       *x, sum;
 66:   const PetscScalar *b;
 67:   const MatScalar   *aa = a->a, *v;
 68:   PetscInt           i, nz;

 70:   PetscFunctionBegin;
 71:   if (!n) PetscFunctionReturn(PETSC_SUCCESS);

 73:   PetscCall(VecGetArrayRead(bb, &b));
 74:   PetscCall(VecGetArray(xx, &x));

 76:   /* forward solve the lower triangular */
 77:   x[0] = b[0];
 78:   v    = aa;
 79:   vi   = aj;
 80:   for (i = 1; i < n; i++) {
 81:     nz  = ai[i + 1] - ai[i];
 82:     sum = b[i];
 83:     PetscSparseDenseMinusDot(sum, x, v, vi, nz);
 84:     v += nz;
 85:     vi += nz;
 86:     x[i] = sum;
 87:   }
 88:   PetscCall(PetscLogFlops(a->nz - A->cmap->n));
 89:   PetscCall(VecRestoreArrayRead(bb, &b));
 90:   PetscCall(VecRestoreArray(xx, &x));
 91:   PetscFunctionReturn(PETSC_SUCCESS);
 92: }

 94: PetscErrorCode MatBackwardSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
 95: {
 96:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
 97:   const PetscInt     n = a->mbs, *aj = a->j, *adiag = a->diag, *vi;
 98:   PetscScalar       *x, sum;
 99:   const PetscScalar *b;
100:   const MatScalar   *aa = a->a, *v;
101:   PetscInt           i, nz;

103:   PetscFunctionBegin;
104:   if (!n) PetscFunctionReturn(PETSC_SUCCESS);

106:   PetscCall(VecGetArrayRead(bb, &b));
107:   PetscCall(VecGetArray(xx, &x));

109:   /* backward solve the upper triangular */
110:   for (i = n - 1; i >= 0; i--) {
111:     v   = aa + adiag[i + 1] + 1;
112:     vi  = aj + adiag[i + 1] + 1;
113:     nz  = adiag[i] - adiag[i + 1] - 1;
114:     sum = b[i];
115:     PetscSparseDenseMinusDot(sum, x, v, vi, nz);
116:     x[i] = sum * v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
117:   }

119:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
120:   PetscCall(VecRestoreArrayRead(bb, &b));
121:   PetscCall(VecRestoreArray(xx, &x));
122:   PetscFunctionReturn(PETSC_SUCCESS);
123: }

125: PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx)
126: {
127:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
128:   const PetscInt     n = a->mbs, *ai = a->i, *aj = a->j, *adiag = a->diag, *vi;
129:   PetscScalar       *x, sum;
130:   const PetscScalar *b;
131:   const MatScalar   *aa = a->a, *v;
132:   PetscInt           i, nz;

134:   PetscFunctionBegin;
135:   if (!n) PetscFunctionReturn(PETSC_SUCCESS);

137:   PetscCall(VecGetArrayRead(bb, &b));
138:   PetscCall(VecGetArray(xx, &x));

140:   /* forward solve the lower triangular */
141:   x[0] = b[0];
142:   v    = aa;
143:   vi   = aj;
144:   for (i = 1; i < n; i++) {
145:     nz  = ai[i + 1] - ai[i];
146:     sum = b[i];
147:     PetscSparseDenseMinusDot(sum, x, v, vi, nz);
148:     v += nz;
149:     vi += nz;
150:     x[i] = sum;
151:   }

153:   /* backward solve the upper triangular */
154:   for (i = n - 1; i >= 0; i--) {
155:     v   = aa + adiag[i + 1] + 1;
156:     vi  = aj + adiag[i + 1] + 1;
157:     nz  = adiag[i] - adiag[i + 1] - 1;
158:     sum = x[i];
159:     PetscSparseDenseMinusDot(sum, x, v, vi, nz);
160:     x[i] = sum * v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
161:   }

163:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
164:   PetscCall(VecRestoreArrayRead(bb, &b));
165:   PetscCall(VecRestoreArray(xx, &x));
166:   PetscFunctionReturn(PETSC_SUCCESS);
167: }