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