xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact4.c (revision e2df7a95c5ea77c899beea10ff9effd6061e7c8f)
1 #define PETSCMAT_DLL
2 
3 #include "src/mat/impls/sbaij/seq/sbaij.h"
4 #include "src/inline/ilu.h"
5 
6 /*
7       Version for when blocks are 3 by 3 Using natural ordering
8 */
9 #undef __FUNCT__
10 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
11 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,MatFactorInfo *info,Mat *B)
12 {
13   Mat            C = *B;
14   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
15   PetscErrorCode ierr;
16   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
17   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
18   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
19   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
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 
34   ai   = a->i; aj = a->j; aa = a->a;
35 
36   /* for each row k */
37   for (k = 0; k<mbs; k++){
38 
39     /*initialize k-th row with elements nonzero in row k of A */
40     jmin = ai[k]; jmax = ai[k+1];
41     if (jmin < jmax) {
42       ap = aa + jmin*9;
43       for (j = jmin; j < jmax; j++){
44         vj = aj[j];         /* block col. index */
45         rtmp_ptr = rtmp + vj*9;
46         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
47       }
48     }
49 
50     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
51     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
52     i = jl[k]; /* first row to be added to k_th row  */
53 
54     while (i < mbs){
55       nexti = jl[i]; /* next row to be added to k_th row */
56 
57       /* compute multiplier */
58       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
59 
60       /* uik = -inv(Di)*U_bar(i,k) */
61       diag = ba + i*9;
62       u    = ba + ili*9;
63 
64       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
65       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
66       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
67 
68       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
69       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
70       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
71 
72       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
73       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
74       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
75 
76       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
77       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
78       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
79       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
80 
81       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
82       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
83       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
84 
85       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
86       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
87       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
88 
89       /* update -U(i,k) */
90       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
91 
92       /* add multiple of row i to k-th row ... */
93       jmin = ili + 1; jmax = bi[i+1];
94       if (jmin < jmax){
95         for (j=jmin; j<jmax; j++) {
96           /* rtmp += -U(i,k)^T * U_bar(i,j) */
97           rtmp_ptr = rtmp + bj[j]*9;
98           u = ba + j*9;
99           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
100           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
101           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
102 
103           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
104           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
105           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
106 
107           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
108           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
109           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
110         }
111 
112         /* ... add i to row list for next nonzero entry */
113         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
114         j     = bj[jmin];
115         jl[i] = jl[j]; jl[j] = i; /* update jl */
116       }
117       i = nexti;
118     }
119 
120     /* save nonzero entries in k-th row of U ... */
121 
122     /* invert diagonal block */
123     diag = ba+k*9;
124     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
125     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
126 
127     jmin = bi[k]; jmax = bi[k+1];
128     if (jmin < jmax) {
129       for (j=jmin; j<jmax; j++){
130          vj = bj[j];           /* block col. index of U */
131          u   = ba + j*9;
132          rtmp_ptr = rtmp + vj*9;
133          for (k1=0; k1<9; k1++){
134            *u++        = *rtmp_ptr;
135            *rtmp_ptr++ = 0.0;
136          }
137       }
138 
139       /* ... add k to row list for first nonzero entry in k-th row */
140       il[k] = jmin;
141       i     = bj[jmin];
142       jl[k] = jl[i]; jl[i] = k;
143     }
144   }
145 
146   ierr = PetscFree(rtmp);CHKERRQ(ierr);
147   ierr = PetscFree(il);CHKERRQ(ierr);
148   ierr = PetscFree(dk);CHKERRQ(ierr);
149 
150   C->factor    = FACTOR_CHOLESKY;
151   C->assembled = PETSC_TRUE;
152   C->preallocated = PETSC_TRUE;
153   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
154   PetscFunctionReturn(0);
155 }
156