xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact3.c (revision 6abefa4f446b2ea91915da4e25ea0defa83db48e)
1 #define PETSCMAT_DLL
2 
3 #include "../src/mat/impls/sbaij/seq/sbaij.h"
4 #include "../src/mat/blockinvert.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->shiftamount;
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 = PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
26   for (i=0; i<mbs; i++) {
27     jl[i] = mbs; il[0] = 0;
28   }
29   ierr = PetscMalloc2(9,MatScalar,&dk,9,MatScalar,&uik);CHKERRQ(ierr);
30   ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
31 
32   /* check permutation */
33   if (!a->permute){
34     ai = a->i; aj = a->j; aa = a->a;
35   } else {
36     ai   = a->inew; aj = a->jnew;
37     ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr);
38     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
39     ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr);
40     ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr);
41 
42     for (i=0; i<mbs; i++){
43       jmin = ai[i]; jmax = ai[i+1];
44       for (j=jmin; j<jmax; j++){
45         while (a2anew[j] != j){
46           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
47           for (k1=0; k1<9; k1++){
48             dk[k1]       = aa[k*9+k1];
49             aa[k*9+k1] = aa[j*9+k1];
50             aa[j*9+k1] = dk[k1];
51           }
52         }
53         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
54         if (i > aj[j]){
55           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
56           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
57           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
58           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
59             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
60           }
61         }
62       }
63     }
64     ierr = PetscFree(a2anew);CHKERRQ(ierr);
65   }
66 
67   /* for each row k */
68   for (k = 0; k<mbs; k++){
69 
70     /*initialize k-th row with elements nonzero in row perm(k) of A */
71     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
72     if (jmin < jmax) {
73       ap = aa + jmin*9;
74       for (j = jmin; j < jmax; j++){
75         vj = perm_ptr[aj[j]];         /* block col. index */
76         rtmp_ptr = rtmp + vj*9;
77         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
78       }
79     }
80 
81     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
82     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
83     i = jl[k]; /* first row to be added to k_th row  */
84 
85     while (i < mbs){
86       nexti = jl[i]; /* next row to be added to k_th row */
87 
88       /* compute multiplier */
89       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
90 
91       /* uik = -inv(Di)*U_bar(i,k) */
92       diag = ba + i*9;
93       u    = ba + ili*9;
94 
95       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
96       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
97       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
98 
99       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
100       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
101       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
102 
103       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
104       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
105       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
106 
107       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
108       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
109       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
110       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
111 
112       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
113       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
114       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
115 
116       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
117       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
118       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
119 
120       ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr);
121 
122       /* update -U(i,k) */
123       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
124 
125       /* add multiple of row i to k-th row ... */
126       jmin = ili + 1; jmax = bi[i+1];
127       if (jmin < jmax){
128         for (j=jmin; j<jmax; j++) {
129           /* rtmp += -U(i,k)^T * U_bar(i,j) */
130           rtmp_ptr = rtmp + bj[j]*9;
131           u = ba + j*9;
132           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
133           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
134           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
135 
136           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
137           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
138           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
139 
140           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
141           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
142           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
143         }
144         ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr);
145 
146         /* ... add i to row list for next nonzero entry */
147         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
148         j     = bj[jmin];
149         jl[i] = jl[j]; jl[j] = i; /* update jl */
150       }
151       i = nexti;
152     }
153 
154     /* save nonzero entries in k-th row of U ... */
155 
156     /* invert diagonal block */
157     diag = ba+k*9;
158     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
159     ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
160 
161     jmin = bi[k]; jmax = bi[k+1];
162     if (jmin < jmax) {
163       for (j=jmin; j<jmax; j++){
164          vj = bj[j];           /* block col. index of U */
165          u   = ba + j*9;
166          rtmp_ptr = rtmp + vj*9;
167          for (k1=0; k1<9; k1++){
168            *u++        = *rtmp_ptr;
169            *rtmp_ptr++ = 0.0;
170          }
171       }
172 
173       /* ... add k to row list for first nonzero entry in k-th row */
174       il[k] = jmin;
175       i     = bj[jmin];
176       jl[k] = jl[i]; jl[i] = k;
177     }
178   }
179 
180   ierr = PetscFree(rtmp);CHKERRQ(ierr);
181   ierr = PetscFree2(il,jl);CHKERRQ(ierr);
182   ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
183   if (a->permute){
184     ierr = PetscFree(aa);CHKERRQ(ierr);
185   }
186 
187   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
188   C->ops->solve          = MatSolve_SeqSBAIJ_3_inplace;
189   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
190   C->assembled = PETSC_TRUE;
191   C->preallocated = PETSC_TRUE;
192   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
193   PetscFunctionReturn(0);
194 }
195