1 #include <../src/mat/impls/baij/seq/baij.h> 2 #include <petsc/private/kernels/blockinvert.h> 3 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_3_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 9 { 10 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 11 const PetscInt n =a->mbs,*ai=a->i,*aj=a->j; 12 PetscErrorCode ierr; 13 const PetscInt *diag = a->diag,*vi; 14 const MatScalar *aa =a->a,*v; 15 PetscScalar *x,s1,s2,s3,x1,x2,x3; 16 const PetscScalar *b; 17 PetscInt jdx,idt,idx,nz,i; 18 19 PetscFunctionBegin; 20 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 21 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 22 23 /* forward solve the lower triangular */ 24 idx = 0; 25 x[0] = b[0]; x[1] = b[1]; x[2] = b[2]; 26 for (i=1; i<n; i++) { 27 v = aa + 9*ai[i]; 28 vi = aj + ai[i]; 29 nz = diag[i] - ai[i]; 30 idx += 3; 31 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx]; 32 while (nz--) { 33 jdx = 3*(*vi++); 34 x1 = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx]; 35 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 36 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 37 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 38 v += 9; 39 } 40 x[idx] = s1; 41 x[1+idx] = s2; 42 x[2+idx] = s3; 43 } 44 /* backward solve the upper triangular */ 45 for (i=n-1; i>=0; i--) { 46 v = aa + 9*diag[i] + 9; 47 vi = aj + diag[i] + 1; 48 nz = ai[i+1] - diag[i] - 1; 49 idt = 3*i; 50 s1 = x[idt]; s2 = x[1+idt]; 51 s3 = x[2+idt]; 52 while (nz--) { 53 idx = 3*(*vi++); 54 x1 = x[idx]; x2 = x[1+idx];x3 = x[2+idx]; 55 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 56 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 57 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 58 v += 9; 59 } 60 v = aa + 9*diag[i]; 61 x[idt] = v[0]*s1 + v[3]*s2 + v[6]*s3; 62 x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3; 63 x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3; 64 } 65 66 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 67 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 68 ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr); 69 PetscFunctionReturn(0); 70 } 71 72 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx) 73 { 74 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 75 const PetscInt n =a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag; 76 PetscErrorCode ierr; 77 PetscInt i,k,nz,idx,jdx,idt; 78 const PetscInt bs = A->rmap->bs,bs2 = a->bs2; 79 const MatScalar *aa=a->a,*v; 80 PetscScalar *x; 81 const PetscScalar *b; 82 PetscScalar s1,s2,s3,x1,x2,x3; 83 84 PetscFunctionBegin; 85 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 86 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 87 /* forward solve the lower triangular */ 88 idx = 0; 89 x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx]; 90 for (i=1; i<n; i++) { 91 v = aa + bs2*ai[i]; 92 vi = aj + ai[i]; 93 nz = ai[i+1] - ai[i]; 94 idx = bs*i; 95 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx]; 96 for (k=0; k<nz; k++) { 97 jdx = bs*vi[k]; 98 x1 = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx]; 99 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 100 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 101 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 102 103 v += bs2; 104 } 105 106 x[idx] = s1; 107 x[1+idx] = s2; 108 x[2+idx] = s3; 109 } 110 111 /* backward solve the upper triangular */ 112 for (i=n-1; i>=0; i--) { 113 v = aa + bs2*(adiag[i+1]+1); 114 vi = aj + adiag[i+1]+1; 115 nz = adiag[i] - adiag[i+1]-1; 116 idt = bs*i; 117 s1 = x[idt]; s2 = x[1+idt];s3 = x[2+idt]; 118 119 for (k=0; k<nz; k++) { 120 idx = bs*vi[k]; 121 x1 = x[idx]; x2 = x[1+idx]; x3 = x[2+idx]; 122 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 123 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 124 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 125 126 v += bs2; 127 } 128 /* x = inv_diagonal*x */ 129 x[idt] = v[0]*s1 + v[3]*s2 + v[6]*s3; 130 x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3; 131 x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3; 132 133 } 134 135 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 136 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 137 ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr); 138 PetscFunctionReturn(0); 139 } 140 141 PetscErrorCode MatForwardSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx) 142 { 143 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 144 const PetscInt n =a->mbs,*vi,*ai=a->i,*aj=a->j; 145 PetscErrorCode ierr; 146 PetscInt i,k,nz,idx,jdx; 147 const PetscInt bs = A->rmap->bs,bs2 = a->bs2; 148 const MatScalar *aa=a->a,*v; 149 PetscScalar *x; 150 const PetscScalar *b; 151 PetscScalar s1,s2,s3,x1,x2,x3; 152 153 PetscFunctionBegin; 154 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 155 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 156 /* forward solve the lower triangular */ 157 idx = 0; 158 x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx]; 159 for (i=1; i<n; i++) { 160 v = aa + bs2*ai[i]; 161 vi = aj + ai[i]; 162 nz = ai[i+1] - ai[i]; 163 idx = bs*i; 164 s1 = b[idx];s2 = b[1+idx];s3 = b[2+idx]; 165 for (k=0; k<nz; k++) { 166 jdx = bs*vi[k]; 167 x1 = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx]; 168 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 169 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 170 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 171 172 v += bs2; 173 } 174 175 x[idx] = s1; 176 x[1+idx] = s2; 177 x[2+idx] = s3; 178 } 179 180 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 181 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 182 ierr = PetscLogFlops(1.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr); 183 PetscFunctionReturn(0); 184 } 185 186 PetscErrorCode MatBackwardSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx) 187 { 188 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 189 const PetscInt n =a->mbs,*vi,*aj=a->j,*adiag=a->diag; 190 PetscErrorCode ierr; 191 PetscInt i,k,nz,idx,idt; 192 const PetscInt bs = A->rmap->bs,bs2 = a->bs2; 193 const MatScalar *aa=a->a,*v; 194 PetscScalar *x; 195 const PetscScalar *b; 196 PetscScalar s1,s2,s3,x1,x2,x3; 197 198 PetscFunctionBegin; 199 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 200 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 201 202 /* backward solve the upper triangular */ 203 for (i=n-1; i>=0; i--) { 204 v = aa + bs2*(adiag[i+1]+1); 205 vi = aj + adiag[i+1]+1; 206 nz = adiag[i] - adiag[i+1]-1; 207 idt = bs*i; 208 s1 = b[idt]; s2 = b[1+idt];s3 = b[2+idt]; 209 210 for (k=0; k<nz; k++) { 211 idx = bs*vi[k]; 212 x1 = x[idx]; x2 = x[1+idx]; x3 = x[2+idx]; 213 s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3; 214 s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3; 215 s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3; 216 217 v += bs2; 218 } 219 /* x = inv_diagonal*x */ 220 x[idt] = v[0]*s1 + v[3]*s2 + v[6]*s3; 221 x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3; 222 x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3; 223 224 } 225 226 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 227 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 228 ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr); 229 PetscFunctionReturn(0); 230 } 231