xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact3.c (revision a4efd8ea4bb0600a5aef92b2c23cbfa314827193)
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 A,MatFactorInfo *info,Mat *B)
10 {
11   Mat            C = *B;
12   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
13   IS             perm = b->row;
14   PetscErrorCode ierr;
15   PetscInt       *perm_ptr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
16   PetscInt       *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
17   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
18   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
19   PetscReal      shift = info->shiftinblocks;
20 
21   PetscFunctionBegin;
22 
23   /* initialization */
24   ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
25   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
26   ierr = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr);
27   jl   = il + mbs;
28   for (i=0; i<mbs; i++) {
29     jl[i] = mbs; il[0] = 0;
30   }
31   ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr);
32   uik  = dk + 9;
33   ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
34 
35   /* check permutation */
36   if (!a->permute){
37     ai = a->i; aj = a->j; aa = a->a;
38   } else {
39     ai   = a->inew; aj = a->jnew;
40     ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr);
41     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
42     ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr);
43     ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr);
44 
45     for (i=0; i<mbs; i++){
46       jmin = ai[i]; jmax = ai[i+1];
47       for (j=jmin; j<jmax; j++){
48         while (a2anew[j] != j){
49           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
50           for (k1=0; k1<9; k1++){
51             dk[k1]       = aa[k*9+k1];
52             aa[k*9+k1] = aa[j*9+k1];
53             aa[j*9+k1] = dk[k1];
54           }
55         }
56         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
57         if (i > aj[j]){
58           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
59           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
60           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
61           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
62             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
63           }
64         }
65       }
66     }
67     ierr = PetscFree(a2anew);CHKERRQ(ierr);
68   }
69 
70   /* for each row k */
71   for (k = 0; k<mbs; k++){
72 
73     /*initialize k-th row with elements nonzero in row perm(k) of A */
74     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
75     if (jmin < jmax) {
76       ap = aa + jmin*9;
77       for (j = jmin; j < jmax; j++){
78         vj = perm_ptr[aj[j]];         /* block col. index */
79         rtmp_ptr = rtmp + vj*9;
80         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
81       }
82     }
83 
84     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
85     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
86     i = jl[k]; /* first row to be added to k_th row  */
87 
88     while (i < mbs){
89       nexti = jl[i]; /* next row to be added to k_th row */
90 
91       /* compute multiplier */
92       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
93 
94       /* uik = -inv(Di)*U_bar(i,k) */
95       diag = ba + i*9;
96       u    = ba + ili*9;
97 
98       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
99       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
100       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
101 
102       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
103       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
104       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
105 
106       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
107       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
108       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
109 
110       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
111       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
112       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
113       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
114 
115       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
116       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
117       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
118 
119       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
120       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
121       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
122 
123       ierr = PetscLogFlops(27*4);CHKERRQ(ierr);
124 
125       /* update -U(i,k) */
126       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
127 
128       /* add multiple of row i to k-th row ... */
129       jmin = ili + 1; jmax = bi[i+1];
130       if (jmin < jmax){
131         for (j=jmin; j<jmax; j++) {
132           /* rtmp += -U(i,k)^T * U_bar(i,j) */
133           rtmp_ptr = rtmp + bj[j]*9;
134           u = ba + j*9;
135           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
136           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
137           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
138 
139           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
140           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
141           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
142 
143           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
144           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
145           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
146         }
147         ierr = PetscLogFlops(2*27*(jmax-jmin));CHKERRQ(ierr);
148 
149         /* ... add i to row list for next nonzero entry */
150         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
151         j     = bj[jmin];
152         jl[i] = jl[j]; jl[j] = i; /* update jl */
153       }
154       i = nexti;
155     }
156 
157     /* save nonzero entries in k-th row of U ... */
158 
159     /* invert diagonal block */
160     diag = ba+k*9;
161     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
162     ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
163 
164     jmin = bi[k]; jmax = bi[k+1];
165     if (jmin < jmax) {
166       for (j=jmin; j<jmax; j++){
167          vj = bj[j];           /* block col. index of U */
168          u   = ba + j*9;
169          rtmp_ptr = rtmp + vj*9;
170          for (k1=0; k1<9; k1++){
171            *u++        = *rtmp_ptr;
172            *rtmp_ptr++ = 0.0;
173          }
174       }
175 
176       /* ... add k to row list for first nonzero entry in k-th row */
177       il[k] = jmin;
178       i     = bj[jmin];
179       jl[k] = jl[i]; jl[i] = k;
180     }
181   }
182 
183   ierr = PetscFree(rtmp);CHKERRQ(ierr);
184   ierr = PetscFree(il);CHKERRQ(ierr);
185   ierr = PetscFree(dk);CHKERRQ(ierr);
186   if (a->permute){
187     ierr = PetscFree(aa);CHKERRQ(ierr);
188   }
189 
190   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
191   C->ops->solve          = MatSolve_SeqSBAIJ_3;
192   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3;
193   C->assembled = PETSC_TRUE;
194   C->preallocated = PETSC_TRUE;
195   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
196   PetscFunctionReturn(0);
197 }
198