xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact4.c (revision ccb4e88a40f0b86eaeca07ff64c64e4de2fae686)
1 
2 #include <../src/mat/impls/sbaij/seq/sbaij.h>
3 #include <petsc/private/kernels/blockinvert.h>
4 
5 /*
6       Version for when blocks are 3 by 3 Using natural ordering
7 */
8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
9 {
10   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
11   PetscErrorCode ierr;
12   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
13   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
14   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
15   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
16   PetscReal      shift = info->shiftamount;
17   PetscBool      allowzeropivot,zeropivotdetected;
18 
19   PetscFunctionBegin;
20   /* initialization */
21   allowzeropivot = PetscNot(A->erroriffailure);
22   ierr = PetscCalloc1(9*mbs,&rtmp);CHKERRQ(ierr);
23   ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
24   il[0] = 0;
25   for (i=0; i<mbs; i++) jl[i] = mbs;
26 
27   ierr = PetscMalloc2(9,&dk,9,&uik);CHKERRQ(ierr);
28   ai   = a->i; aj = a->j; aa = a->a;
29 
30   /* for each row k */
31   for (k = 0; k<mbs; k++) {
32 
33     /*initialize k-th row with elements nonzero in row k of A */
34     jmin = ai[k]; jmax = ai[k+1];
35     if (jmin < jmax) {
36       ap = aa + jmin*9;
37       for (j = jmin; j < jmax; j++) {
38         vj       = aj[j];   /* block col. index */
39         rtmp_ptr = rtmp + vj*9;
40         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
41       }
42     }
43 
44     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
45     ierr = PetscArraycpy(dk,rtmp+k*9,9);CHKERRQ(ierr);
46     i    = jl[k]; /* first row to be added to k_th row  */
47 
48     while (i < mbs) {
49       nexti = jl[i]; /* next row to be added to k_th row */
50 
51       /* compute multiplier */
52       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
53 
54       /* uik = -inv(Di)*U_bar(i,k) */
55       diag = ba + i*9;
56       u    = ba + ili*9;
57 
58       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
59       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
60       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
61 
62       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
63       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
64       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
65 
66       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
67       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
68       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
69 
70       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
71       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
72       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
73       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
74 
75       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
76       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
77       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
78 
79       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
80       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
81       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
82 
83       ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr);
84 
85       /* update -U(i,k) */
86       ierr = PetscArraycpy(ba+ili*9,uik,9);CHKERRQ(ierr);
87 
88       /* add multiple of row i to k-th row ... */
89       jmin = ili + 1; jmax = bi[i+1];
90       if (jmin < jmax) {
91         for (j=jmin; j<jmax; j++) {
92           /* rtmp += -U(i,k)^T * U_bar(i,j) */
93           rtmp_ptr     = rtmp + bj[j]*9;
94           u            = ba + j*9;
95           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
96           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
97           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
98 
99           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
100           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
101           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
102 
103           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
104           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
105           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
106         }
107         ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr);
108 
109         /* ... add i to row list for next nonzero entry */
110         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
111         j     = bj[jmin];
112         jl[i] = jl[j]; jl[j] = i; /* update jl */
113       }
114       i = nexti;
115     }
116 
117     /* save nonzero entries in k-th row of U ... */
118 
119     /* invert diagonal block */
120     diag = ba+k*9;
121     ierr = PetscArraycpy(diag,dk,9);CHKERRQ(ierr);
122     ierr = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
123     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
124 
125     jmin = bi[k]; jmax = bi[k+1];
126     if (jmin < jmax) {
127       for (j=jmin; j<jmax; j++) {
128         vj       = bj[j];      /* block col. index of U */
129         u        = ba + j*9;
130         rtmp_ptr = rtmp + vj*9;
131         for (k1=0; k1<9; k1++) {
132           *u++        = *rtmp_ptr;
133           *rtmp_ptr++ = 0.0;
134         }
135       }
136 
137       /* ... add k to row list for first nonzero entry in k-th row */
138       il[k] = jmin;
139       i     = bj[jmin];
140       jl[k] = jl[i]; jl[i] = k;
141     }
142   }
143 
144   ierr = PetscFree(rtmp);CHKERRQ(ierr);
145   ierr = PetscFree2(il,jl);CHKERRQ(ierr);
146   ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
147 
148   C->ops->solve          = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
149   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
150   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
151   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
152 
153   C->assembled    = PETSC_TRUE;
154   C->preallocated = PETSC_TRUE;
155 
156   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
157   PetscFunctionReturn(0);
158 }
159