xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact3.c (revision 7d6bfa3b9d7db0ccd4cc481237114ca8dbb0dbff)
1 #define PETSCMAT_DLL
2 
3 #include "../src/mat/impls/sbaij/seq/sbaij.h"
4 #include "../src/inline/ilu.h"
5 
6 /* Version for when blocks are 3 by 3  */
7 #undef __FUNCT__
8 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
9 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C,Mat A,const MatFactorInfo *info)
10 {
11   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
12   IS             perm = b->row;
13   PetscErrorCode ierr;
14   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
15   PetscInt       *a2anew,i,j,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
16   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
17   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
18   PetscReal      shift = info->shiftinblocks;
19 
20   PetscFunctionBegin;
21 
22   /* initialization */
23   ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
24   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
25   ierr = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr);
26   jl   = il + mbs;
27   for (i=0; i<mbs; i++) {
28     jl[i] = mbs; il[0] = 0;
29   }
30   ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr);
31   uik  = dk + 9;
32   ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
33 
34   /* check permutation */
35   if (!a->permute){
36     ai = a->i; aj = a->j; aa = a->a;
37   } else {
38     ai   = a->inew; aj = a->jnew;
39     ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr);
40     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
41     ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr);
42     ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr);
43 
44     for (i=0; i<mbs; i++){
45       jmin = ai[i]; jmax = ai[i+1];
46       for (j=jmin; j<jmax; j++){
47         while (a2anew[j] != j){
48           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
49           for (k1=0; k1<9; k1++){
50             dk[k1]       = aa[k*9+k1];
51             aa[k*9+k1] = aa[j*9+k1];
52             aa[j*9+k1] = dk[k1];
53           }
54         }
55         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
56         if (i > aj[j]){
57           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
58           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
59           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
60           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
61             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
62           }
63         }
64       }
65     }
66     ierr = PetscFree(a2anew);CHKERRQ(ierr);
67   }
68 
69   /* for each row k */
70   for (k = 0; k<mbs; k++){
71 
72     /*initialize k-th row with elements nonzero in row perm(k) of A */
73     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
74     if (jmin < jmax) {
75       ap = aa + jmin*9;
76       for (j = jmin; j < jmax; j++){
77         vj = perm_ptr[aj[j]];         /* block col. index */
78         rtmp_ptr = rtmp + vj*9;
79         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
80       }
81     }
82 
83     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
84     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
85     i = jl[k]; /* first row to be added to k_th row  */
86 
87     while (i < mbs){
88       nexti = jl[i]; /* next row to be added to k_th row */
89 
90       /* compute multiplier */
91       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
92 
93       /* uik = -inv(Di)*U_bar(i,k) */
94       diag = ba + i*9;
95       u    = ba + ili*9;
96 
97       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
98       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
99       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
100 
101       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
102       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
103       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
104 
105       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
106       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
107       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
108 
109       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
110       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
111       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
112       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
113 
114       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
115       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
116       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
117 
118       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
119       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
120       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
121 
122       ierr = PetscLogFlops(27*4);CHKERRQ(ierr);
123 
124       /* update -U(i,k) */
125       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
126 
127       /* add multiple of row i to k-th row ... */
128       jmin = ili + 1; jmax = bi[i+1];
129       if (jmin < jmax){
130         for (j=jmin; j<jmax; j++) {
131           /* rtmp += -U(i,k)^T * U_bar(i,j) */
132           rtmp_ptr = rtmp + bj[j]*9;
133           u = ba + j*9;
134           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
135           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
136           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
137 
138           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
139           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
140           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
141 
142           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
143           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
144           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
145         }
146         ierr = PetscLogFlops(2*27*(jmax-jmin));CHKERRQ(ierr);
147 
148         /* ... add i to row list for next nonzero entry */
149         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
150         j     = bj[jmin];
151         jl[i] = jl[j]; jl[j] = i; /* update jl */
152       }
153       i = nexti;
154     }
155 
156     /* save nonzero entries in k-th row of U ... */
157 
158     /* invert diagonal block */
159     diag = ba+k*9;
160     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
161     ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
162 
163     jmin = bi[k]; jmax = bi[k+1];
164     if (jmin < jmax) {
165       for (j=jmin; j<jmax; j++){
166          vj = bj[j];           /* block col. index of U */
167          u   = ba + j*9;
168          rtmp_ptr = rtmp + vj*9;
169          for (k1=0; k1<9; k1++){
170            *u++        = *rtmp_ptr;
171            *rtmp_ptr++ = 0.0;
172          }
173       }
174 
175       /* ... add k to row list for first nonzero entry in k-th row */
176       il[k] = jmin;
177       i     = bj[jmin];
178       jl[k] = jl[i]; jl[i] = k;
179     }
180   }
181 
182   ierr = PetscFree(rtmp);CHKERRQ(ierr);
183   ierr = PetscFree(il);CHKERRQ(ierr);
184   ierr = PetscFree(dk);CHKERRQ(ierr);
185   if (a->permute){
186     ierr = PetscFree(aa);CHKERRQ(ierr);
187   }
188 
189   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
190   C->ops->solve          = MatSolve_SeqSBAIJ_3;
191   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3;
192   C->assembled = PETSC_TRUE;
193   C->preallocated = PETSC_TRUE;
194   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
195   PetscFunctionReturn(0);
196 }
197