Actual source code: baijsolvnat2.c
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_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;
17: VecGetArrayRead(bb,&b);
18: VecGetArray(xx,&x);
20: /* forward solve the lower triangular */
21: idx = 0;
22: x[0] = b[0]; x[1] = b[1];
23: for (i=1; i<n; i++) {
24: v = aa + 4*ai[i];
25: vi = aj + ai[i];
26: nz = diag[i] - ai[i];
27: idx += 2;
28: s1 = b[idx];s2 = b[1+idx];
29: while (nz--) {
30: jdx = 2*(*vi++);
31: x1 = x[jdx];x2 = x[1+jdx];
32: s1 -= v[0]*x1 + v[2]*x2;
33: s2 -= v[1]*x1 + v[3]*x2;
34: v += 4;
35: }
36: x[idx] = s1;
37: x[1+idx] = s2;
38: }
39: /* backward solve the upper triangular */
40: for (i=n-1; i>=0; i--) {
41: v = aa + 4*diag[i] + 4;
42: vi = aj + diag[i] + 1;
43: nz = ai[i+1] - diag[i] - 1;
44: idt = 2*i;
45: s1 = x[idt]; s2 = x[1+idt];
46: while (nz--) {
47: idx = 2*(*vi++);
48: x1 = x[idx]; x2 = x[1+idx];
49: s1 -= v[0]*x1 + v[2]*x2;
50: s2 -= v[1]*x1 + v[3]*x2;
51: v += 4;
52: }
53: v = aa + 4*diag[i];
54: x[idt] = v[0]*s1 + v[2]*s2;
55: x[1+idt] = v[1]*s1 + v[3]*s2;
56: }
58: VecRestoreArrayRead(bb,&b);
59: VecRestoreArray(xx,&x);
60: PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);
61: return 0;
62: }
64: PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
65: {
66: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
67: const PetscInt n = a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
68: PetscInt i,k,nz,idx,idt,jdx;
69: const MatScalar *aa=a->a,*v;
70: PetscScalar *x,s1,s2,x1,x2;
71: const PetscScalar *b;
73: VecGetArrayRead(bb,&b);
74: VecGetArray(xx,&x);
75: /* forward solve the lower triangular */
76: idx = 0;
77: x[0] = b[idx]; x[1] = b[1+idx];
78: for (i=1; i<n; i++) {
79: v = aa + 4*ai[i];
80: vi = aj + ai[i];
81: nz = ai[i+1] - ai[i];
82: idx = 2*i;
83: s1 = b[idx];s2 = b[1+idx];
84: PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
85: PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
86: for (k=0; k<nz; k++) {
87: jdx = 2*vi[k];
88: x1 = x[jdx];x2 = x[1+jdx];
89: s1 -= v[0]*x1 + v[2]*x2;
90: s2 -= v[1]*x1 + v[3]*x2;
91: v += 4;
92: }
93: x[idx] = s1;
94: x[1+idx] = s2;
95: }
97: /* backward solve the upper triangular */
98: for (i=n-1; i>=0; i--) {
99: v = aa + 4*(adiag[i+1]+1);
100: vi = aj + adiag[i+1]+1;
101: nz = adiag[i] - adiag[i+1]-1;
102: idt = 2*i;
103: s1 = x[idt]; s2 = x[1+idt];
104: PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
105: PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
106: for (k=0; k<nz; k++) {
107: idx = 2*vi[k];
108: x1 = x[idx]; x2 = x[1+idx];
109: s1 -= v[0]*x1 + v[2]*x2;
110: s2 -= v[1]*x1 + v[3]*x2;
111: v += 4;
112: }
113: /* x = inv_diagonal*x */
114: x[idt] = v[0]*s1 + v[2]*s2;
115: x[1+idt] = v[1]*s1 + v[3]*s2;
116: }
118: VecRestoreArrayRead(bb,&b);
119: VecRestoreArray(xx,&x);
120: PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);
121: return 0;
122: }
124: PetscErrorCode MatForwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
125: {
126: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
127: const PetscInt n = a->mbs,*vi,*ai=a->i,*aj=a->j;
128: PetscInt i,k,nz,idx,jdx;
129: const MatScalar *aa=a->a,*v;
130: PetscScalar *x,s1,s2,x1,x2;
131: const PetscScalar *b;
133: VecGetArrayRead(bb,&b);
134: VecGetArray(xx,&x);
135: /* forward solve the lower triangular */
136: idx = 0;
137: x[0] = b[idx]; x[1] = b[1+idx];
138: for (i=1; i<n; i++) {
139: v = aa + 4*ai[i];
140: vi = aj + ai[i];
141: nz = ai[i+1] - ai[i];
142: idx = 2*i;
143: s1 = b[idx];s2 = b[1+idx];
144: PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
145: PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
146: for (k=0; k<nz; k++) {
147: jdx = 2*vi[k];
148: x1 = x[jdx];x2 = x[1+jdx];
149: s1 -= v[0]*x1 + v[2]*x2;
150: s2 -= v[1]*x1 + v[3]*x2;
151: v += 4;
152: }
153: x[idx] = s1;
154: x[1+idx] = s2;
155: }
157: VecRestoreArrayRead(bb,&b);
158: VecRestoreArray(xx,&x);
159: PetscLogFlops(4.0*(a->nz) - A->cmap->n);
160: return 0;
161: }
163: PetscErrorCode MatBackwardSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
164: {
165: Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
166: const PetscInt n = a->mbs,*vi,*aj=a->j,*adiag=a->diag;
167: PetscInt i,k,nz,idx,idt;
168: const MatScalar *aa=a->a,*v;
169: PetscScalar *x,s1,s2,x1,x2;
170: const PetscScalar *b;
172: VecGetArrayRead(bb,&b);
173: VecGetArray(xx,&x);
175: /* backward solve the upper triangular */
176: for (i=n-1; i>=0; i--) {
177: v = aa + 4*(adiag[i+1]+1);
178: vi = aj + adiag[i+1]+1;
179: nz = adiag[i] - adiag[i+1]-1;
180: idt = 2*i;
181: s1 = b[idt]; s2 = b[1+idt];
182: PetscPrefetchBlock(vi+nz,nz,0,PETSC_PREFETCH_HINT_NTA);
183: PetscPrefetchBlock(v+4*nz,4*nz,0,PETSC_PREFETCH_HINT_NTA);
184: for (k=0; k<nz; k++) {
185: idx = 2*vi[k];
186: x1 = x[idx]; x2 = x[1+idx];
187: s1 -= v[0]*x1 + v[2]*x2;
188: s2 -= v[1]*x1 + v[3]*x2;
189: v += 4;
190: }
191: /* x = inv_diagonal*x */
192: x[idt] = v[0]*s1 + v[2]*s2;
193: x[1+idt] = v[1]*s1 + v[3]*s2;
194: }
196: VecRestoreArrayRead(bb,&b);
197: VecRestoreArray(xx,&x);
198: PetscLogFlops(4.0*a->nz - A->cmap->n);
199: return 0;
200: }