xref: /petsc/src/mat/impls/baij/seq/baijsolvnat3.c (revision 503c0ea9b45bcfbcebbb1ea5341243bbc69f0bea)
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   const PetscInt    *diag = a->diag,*vi;
13   const MatScalar   *aa   =a->a,*v;
14   PetscScalar       *x,s1,s2,s3,x1,x2,x3;
15   const PetscScalar *b;
16   PetscInt          jdx,idt,idx,nz,i;
17 
18   PetscFunctionBegin;
19   PetscCall(VecGetArrayRead(bb,&b));
20   PetscCall(VecGetArray(xx,&x));
21 
22   /* forward solve the lower triangular */
23   idx  = 0;
24   x[0] = b[0]; x[1] = b[1]; x[2] = b[2];
25   for (i=1; i<n; i++) {
26     v    =  aa      + 9*ai[i];
27     vi   =  aj      + ai[i];
28     nz   =  diag[i] - ai[i];
29     idx +=  3;
30     s1   =  b[idx];s2 = b[1+idx];s3 = b[2+idx];
31     while (nz--) {
32       jdx = 3*(*vi++);
33       x1  = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];
34       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
35       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
36       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
37       v  += 9;
38     }
39     x[idx]   = s1;
40     x[1+idx] = s2;
41     x[2+idx] = s3;
42   }
43   /* backward solve the upper triangular */
44   for (i=n-1; i>=0; i--) {
45     v   = aa + 9*diag[i] + 9;
46     vi  = aj + diag[i] + 1;
47     nz  = ai[i+1] - diag[i] - 1;
48     idt = 3*i;
49     s1  = x[idt];  s2 = x[1+idt];
50     s3  = x[2+idt];
51     while (nz--) {
52       idx = 3*(*vi++);
53       x1  = x[idx];   x2 = x[1+idx];x3    = x[2+idx];
54       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
55       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
56       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
57       v  += 9;
58     }
59     v        = aa +  9*diag[i];
60     x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
61     x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
62     x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
63   }
64 
65   PetscCall(VecRestoreArrayRead(bb,&b));
66   PetscCall(VecRestoreArray(xx,&x));
67   PetscCall(PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n));
68   PetscFunctionReturn(0);
69 }
70 
71 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
72 {
73   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
74   const PetscInt    n  =a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
75   PetscInt          i,k,nz,idx,jdx,idt;
76   const PetscInt    bs = A->rmap->bs,bs2 = a->bs2;
77   const MatScalar   *aa=a->a,*v;
78   PetscScalar       *x;
79   const PetscScalar *b;
80   PetscScalar       s1,s2,s3,x1,x2,x3;
81 
82   PetscFunctionBegin;
83   PetscCall(VecGetArrayRead(bb,&b));
84   PetscCall(VecGetArray(xx,&x));
85   /* forward solve the lower triangular */
86   idx  = 0;
87   x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];
88   for (i=1; i<n; i++) {
89     v   = aa + bs2*ai[i];
90     vi  = aj + ai[i];
91     nz  = ai[i+1] - ai[i];
92     idx = bs*i;
93     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];
94     for (k=0; k<nz; k++) {
95       jdx = bs*vi[k];
96       x1  = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];
97       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
98       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
99       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
100 
101       v +=  bs2;
102     }
103 
104     x[idx]   = s1;
105     x[1+idx] = s2;
106     x[2+idx] = s3;
107   }
108 
109   /* backward solve the upper triangular */
110   for (i=n-1; i>=0; i--) {
111     v   = aa + bs2*(adiag[i+1]+1);
112     vi  = aj + adiag[i+1]+1;
113     nz  = adiag[i] - adiag[i+1]-1;
114     idt = bs*i;
115     s1  = x[idt];  s2 = x[1+idt];s3 = x[2+idt];
116 
117     for (k=0; k<nz; k++) {
118       idx = bs*vi[k];
119       x1  = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
120       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
121       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
122       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
123 
124       v +=  bs2;
125     }
126     /* x = inv_diagonal*x */
127     x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
128     x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
129     x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
130 
131   }
132 
133   PetscCall(VecRestoreArrayRead(bb,&b));
134   PetscCall(VecRestoreArray(xx,&x));
135   PetscCall(PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n));
136   PetscFunctionReturn(0);
137 }
138 
139 PetscErrorCode MatForwardSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
140 {
141   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
142   const PetscInt    n  =a->mbs,*vi,*ai=a->i,*aj=a->j;
143   PetscInt          i,k,nz,idx,jdx;
144   const PetscInt    bs = A->rmap->bs,bs2 = a->bs2;
145   const MatScalar   *aa=a->a,*v;
146   PetscScalar       *x;
147   const PetscScalar *b;
148   PetscScalar       s1,s2,s3,x1,x2,x3;
149 
150   PetscFunctionBegin;
151   PetscCall(VecGetArrayRead(bb,&b));
152   PetscCall(VecGetArray(xx,&x));
153   /* forward solve the lower triangular */
154   idx  = 0;
155   x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];
156   for (i=1; i<n; i++) {
157     v   = aa + bs2*ai[i];
158     vi  = aj + ai[i];
159     nz  = ai[i+1] - ai[i];
160     idx = bs*i;
161     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];
162     for (k=0; k<nz; k++) {
163       jdx = bs*vi[k];
164       x1  = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];
165       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
166       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
167       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
168 
169       v +=  bs2;
170     }
171 
172     x[idx]   = s1;
173     x[1+idx] = s2;
174     x[2+idx] = s3;
175   }
176 
177   PetscCall(VecRestoreArrayRead(bb,&b));
178   PetscCall(VecRestoreArray(xx,&x));
179   PetscCall(PetscLogFlops(1.0*bs2*(a->nz) - bs*A->cmap->n));
180   PetscFunctionReturn(0);
181 }
182 
183 PetscErrorCode MatBackwardSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
184 {
185   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
186   const PetscInt    n  =a->mbs,*vi,*aj=a->j,*adiag=a->diag;
187   PetscInt          i,k,nz,idx,idt;
188   const PetscInt    bs = A->rmap->bs,bs2 = a->bs2;
189   const MatScalar   *aa=a->a,*v;
190   PetscScalar       *x;
191   const PetscScalar *b;
192   PetscScalar       s1,s2,s3,x1,x2,x3;
193 
194   PetscFunctionBegin;
195   PetscCall(VecGetArrayRead(bb,&b));
196   PetscCall(VecGetArray(xx,&x));
197 
198   /* backward solve the upper triangular */
199   for (i=n-1; i>=0; i--) {
200     v   = aa + bs2*(adiag[i+1]+1);
201     vi  = aj + adiag[i+1]+1;
202     nz  = adiag[i] - adiag[i+1]-1;
203     idt = bs*i;
204     s1  = b[idt];  s2 = b[1+idt];s3 = b[2+idt];
205 
206     for (k=0; k<nz; k++) {
207       idx = bs*vi[k];
208       x1  = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
209       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
210       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
211       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
212 
213       v +=  bs2;
214     }
215     /* x = inv_diagonal*x */
216     x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
217     x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
218     x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
219 
220   }
221 
222   PetscCall(VecRestoreArrayRead(bb,&b));
223   PetscCall(VecRestoreArray(xx,&x));
224   PetscCall(PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n));
225   PetscFunctionReturn(0);
226 }
227