xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact4.c (revision d44834fb5aa6ab55eaa2e18f09dfd00e40aa4639)
1 
2 #include "src/mat/impls/sbaij/seq/sbaij.h"
3 #include "src/inline/ilu.h"
4 
5 /*
6       Version for when blocks are 3 by 3 Using natural ordering
7 */
8 #undef __FUNCT__
9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
10 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
11 {
12   Mat            C = *B;
13   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
14   PetscErrorCode ierr;
15   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
16   PetscInt       *ai,*aj,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 
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 
33   ai   = a->i; aj = a->j; aa = a->a;
34 
35   /* for each row k */
36   for (k = 0; k<mbs; k++){
37 
38     /*initialize k-th row with elements nonzero in row k of A */
39     jmin = ai[k]; jmax = ai[k+1];
40     if (jmin < jmax) {
41       ap = aa + jmin*9;
42       for (j = jmin; j < jmax; j++){
43         vj = aj[j];         /* block col. index */
44         rtmp_ptr = rtmp + vj*9;
45         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
46       }
47     }
48 
49     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
50     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
51     i = jl[k]; /* first row to be added to k_th row  */
52 
53     while (i < mbs){
54       nexti = jl[i]; /* next row to be added to k_th row */
55 
56       /* compute multiplier */
57       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
58 
59       /* uik = -inv(Di)*U_bar(i,k) */
60       diag = ba + i*9;
61       u    = ba + ili*9;
62 
63       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
64       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
65       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
66 
67       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
68       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
69       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
70 
71       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
72       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
73       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
74 
75       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
76       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
77       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
78       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
79 
80       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
81       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
82       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
83 
84       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
85       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
86       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
87 
88       /* update -U(i,k) */
89       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
90 
91       /* add multiple of row i to k-th row ... */
92       jmin = ili + 1; jmax = bi[i+1];
93       if (jmin < jmax){
94         for (j=jmin; j<jmax; j++) {
95           /* rtmp += -U(i,k)^T * U_bar(i,j) */
96           rtmp_ptr = rtmp + bj[j]*9;
97           u = ba + j*9;
98           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
99           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
100           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
101 
102           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
103           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
104           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
105 
106           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
107           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
108           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
109         }
110 
111         /* ... add i to row list for next nonzero entry */
112         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
113         j     = bj[jmin];
114         jl[i] = jl[j]; jl[j] = i; /* update jl */
115       }
116       i = nexti;
117     }
118 
119     /* save nonzero entries in k-th row of U ... */
120 
121     /* invert diagonal block */
122     diag = ba+k*9;
123     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
124     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
125 
126     jmin = bi[k]; jmax = bi[k+1];
127     if (jmin < jmax) {
128       for (j=jmin; j<jmax; j++){
129          vj = bj[j];           /* block col. index of U */
130          u   = ba + j*9;
131          rtmp_ptr = rtmp + vj*9;
132          for (k1=0; k1<9; k1++){
133            *u++        = *rtmp_ptr;
134            *rtmp_ptr++ = 0.0;
135          }
136       }
137 
138       /* ... add k to row list for first nonzero entry in k-th row */
139       il[k] = jmin;
140       i     = bj[jmin];
141       jl[k] = jl[i]; jl[i] = k;
142     }
143   }
144 
145   ierr = PetscFree(rtmp);CHKERRQ(ierr);
146   ierr = PetscFree(il);CHKERRQ(ierr);
147   ierr = PetscFree(dk);CHKERRQ(ierr);
148 
149   C->factor    = FACTOR_CHOLESKY;
150   C->assembled = PETSC_TRUE;
151   C->preallocated = PETSC_TRUE;
152   PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
153   PetscFunctionReturn(0);
154 }
155