Actual source code: sbaijfact4.c
2: #include src/mat/impls/sbaij/seq/sbaij.h
3: #include src/inline/ilu.h
5: /*
6: Version for when blocks are 3 by 3 Using natural ordering
7: */
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;
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;
21:
22: /* initialization */
23: PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
24: PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));
25: PetscMalloc(2*mbs*sizeof(PetscInt),&il);
26: jl = il + mbs;
27: for (i=0; i<mbs; i++) {
28: jl[i] = mbs; il[0] = 0;
29: }
30: PetscMalloc(18*sizeof(MatScalar),&dk);
31: uik = dk + 9;
33: ai = a->i; aj = a->j; aa = a->a;
35: /* for each row k */
36: for (k = 0; k<mbs; k++){
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: }
49: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
50: PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
51: i = jl[k]; /* first row to be added to k_th row */
53: while (i < mbs){
54: nexti = jl[i]; /* next row to be added to k_th row */
56: /* compute multiplier */
57: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
59: /* uik = -inv(Di)*U_bar(i,k) */
60: diag = ba + i*9;
61: u = ba + ili*9;
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]);
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]);
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]);
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];
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];
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];
88: /* update -U(i,k) */
89: PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));
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];
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];
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: }
119: /* save nonzero entries in k-th row of U ... */
121: /* invert diagonal block */
122: diag = ba+k*9;
123: PetscMemcpy(diag,dk,9*sizeof(MatScalar));
124: Kernel_A_gets_inverse_A_3(diag);
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: }
145: PetscFree(rtmp);
146: PetscFree(il);
147: PetscFree(dk);
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: return(0);
154: }