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_2_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 PetscErrorCode ierr; 13 const MatScalar *aa=a->a,*v; 14 PetscScalar *x,s1,s2,x1,x2; 15 const PetscScalar *b; 16 PetscInt jdx,idt,idx,nz,i; 17 18 PetscFunctionBegin; 19 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 20 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 21 22 /* forward solve the lower triangular */ 23 idx = 0; 24 x[0] = b[0]; x[1] = b[1]; 25 for (i=1; i<n; i++) { 26 v = aa + 4*ai[i]; 27 vi = aj + ai[i]; 28 nz = diag[i] - ai[i]; 29 idx += 2; 30 s1 = b[idx];s2 = b[1+idx]; 31 while (nz--) { 32 jdx = 2*(*vi++); 33 x1 = x[jdx];x2 = x[1+jdx]; 34 s1 -= v[0]*x1 + v[2]*x2; 35 s2 -= v[1]*x1 + v[3]*x2; 36 v += 4; 37 } 38 x[idx] = s1; 39 x[1+idx] = s2; 40 } 41 /* backward solve the upper triangular */ 42 for (i=n-1; i>=0; i--) { 43 v = aa + 4*diag[i] + 4; 44 vi = aj + diag[i] + 1; 45 nz = ai[i+1] - diag[i] - 1; 46 idt = 2*i; 47 s1 = x[idt]; s2 = x[1+idt]; 48 while (nz--) { 49 idx = 2*(*vi++); 50 x1 = x[idx]; x2 = x[1+idx]; 51 s1 -= v[0]*x1 + v[2]*x2; 52 s2 -= v[1]*x1 + v[3]*x2; 53 v += 4; 54 } 55 v = aa + 4*diag[i]; 56 x[idt] = v[0]*s1 + v[2]*s2; 57 x[1+idt] = v[1]*s1 + v[3]*s2; 58 } 59 60 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 61 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 62 ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr); 63 PetscFunctionReturn(0); 64 } 65 66 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx) 67 { 68 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 69 const PetscInt n = a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag; 70 PetscInt i,k,nz,idx,idt,jdx; 71 PetscErrorCode ierr; 72 const MatScalar *aa=a->a,*v; 73 PetscScalar *x,s1,s2,x1,x2; 74 const PetscScalar *b; 75 76 PetscFunctionBegin; 77 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 78 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 79 /* forward solve the lower triangular */ 80 idx = 0; 81 x[0] = b[idx]; x[1] = b[1+idx]; 82 for (i=1; i<n; i++) { 83 v = aa + 4*ai[i]; 84 vi = aj + ai[i]; 85 nz = ai[i+1] - ai[i]; 86 idx = 2*i; 87 s1 = b[idx];s2 = b[1+idx]; 88 PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA); 89 PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA); 90 for (k=0; k<nz; k++) { 91 jdx = 2*vi[k]; 92 x1 = x[jdx];x2 = x[1+jdx]; 93 s1 -= v[0]*x1 + v[2]*x2; 94 s2 -= v[1]*x1 + v[3]*x2; 95 v += 4; 96 } 97 x[idx] = s1; 98 x[1+idx] = s2; 99 } 100 101 /* backward solve the upper triangular */ 102 for (i=n-1; i>=0; i--) { 103 v = aa + 4*(adiag[i+1]+1); 104 vi = aj + adiag[i+1]+1; 105 nz = adiag[i] - adiag[i+1]-1; 106 idt = 2*i; 107 s1 = x[idt]; s2 = x[1+idt]; 108 PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA); 109 PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA); 110 for (k=0; k<nz; k++) { 111 idx = 2*vi[k]; 112 x1 = x[idx]; x2 = x[1+idx]; 113 s1 -= v[0]*x1 + v[2]*x2; 114 s2 -= v[1]*x1 + v[3]*x2; 115 v += 4; 116 } 117 /* x = inv_diagonal*x */ 118 x[idt] = v[0]*s1 + v[2]*s2; 119 x[1+idt] = v[1]*s1 + v[3]*s2; 120 } 121 122 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 123 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 124 ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr); 125 PetscFunctionReturn(0); 126 } 127 128 PetscErrorCode MatForwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx) 129 { 130 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 131 const PetscInt n = a->mbs,*vi,*ai=a->i,*aj=a->j; 132 PetscInt i,k,nz,idx,jdx; 133 PetscErrorCode ierr; 134 const MatScalar *aa=a->a,*v; 135 PetscScalar *x,s1,s2,x1,x2; 136 const PetscScalar *b; 137 138 PetscFunctionBegin; 139 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 140 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 141 /* forward solve the lower triangular */ 142 idx = 0; 143 x[0] = b[idx]; x[1] = b[1+idx]; 144 for (i=1; i<n; i++) { 145 v = aa + 4*ai[i]; 146 vi = aj + ai[i]; 147 nz = ai[i+1] - ai[i]; 148 idx = 2*i; 149 s1 = b[idx];s2 = b[1+idx]; 150 PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA); 151 PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA); 152 for (k=0; k<nz; k++) { 153 jdx = 2*vi[k]; 154 x1 = x[jdx];x2 = x[1+jdx]; 155 s1 -= v[0]*x1 + v[2]*x2; 156 s2 -= v[1]*x1 + v[3]*x2; 157 v += 4; 158 } 159 x[idx] = s1; 160 x[1+idx] = s2; 161 } 162 163 164 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 165 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 166 ierr = PetscLogFlops(4.0*(a->nz) - A->cmap->n);CHKERRQ(ierr); 167 PetscFunctionReturn(0); 168 } 169 170 PetscErrorCode MatBackwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx) 171 { 172 Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data; 173 const PetscInt n = a->mbs,*vi,*aj=a->j,*adiag=a->diag; 174 PetscInt i,k,nz,idx,idt; 175 PetscErrorCode ierr; 176 const MatScalar *aa=a->a,*v; 177 PetscScalar *x,s1,s2,x1,x2; 178 const PetscScalar *b; 179 180 PetscFunctionBegin; 181 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 182 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 183 184 /* backward solve the upper triangular */ 185 for (i=n-1; i>=0; i--) { 186 v = aa + 4*(adiag[i+1]+1); 187 vi = aj + adiag[i+1]+1; 188 nz = adiag[i] - adiag[i+1]-1; 189 idt = 2*i; 190 s1 = b[idt]; s2 = b[1+idt]; 191 PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA); 192 PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA); 193 for (k=0; k<nz; k++) { 194 idx = 2*vi[k]; 195 x1 = x[idx]; x2 = x[1+idx]; 196 s1 -= v[0]*x1 + v[2]*x2; 197 s2 -= v[1]*x1 + v[3]*x2; 198 v += 4; 199 } 200 /* x = inv_diagonal*x */ 201 x[idt] = v[0]*s1 + v[2]*s2; 202 x[1+idt] = v[1]*s1 + v[3]*s2; 203 } 204 205 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 206 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 207 ierr = PetscLogFlops(4.0*a->nz - A->cmap->n);CHKERRQ(ierr); 208 PetscFunctionReturn(0); 209 } 210