Actual source code: sbaijfact4.c
1: #define PETSCMAT_DLL
3: #include src/mat/impls/sbaij/seq/sbaij.h
4: #include src/inline/ilu.h
6: /*
7: Version for when blocks are 3 by 3 Using natural ordering
8: */
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;
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;
22:
23: /* initialization */
24: PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
25: PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));
26: PetscMalloc(2*mbs*sizeof(PetscInt),&il);
27: jl = il + mbs;
28: for (i=0; i<mbs; i++) {
29: jl[i] = mbs; il[0] = 0;
30: }
31: PetscMalloc(18*sizeof(MatScalar),&dk);
32: uik = dk + 9;
34: ai = a->i; aj = a->j; aa = a->a;
36: /* for each row k */
37: for (k = 0; k<mbs; k++){
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: }
50: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
51: PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
52: i = jl[k]; /* first row to be added to k_th row */
54: while (i < mbs){
55: nexti = jl[i]; /* next row to be added to k_th row */
57: /* compute multiplier */
58: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
60: /* uik = -inv(Di)*U_bar(i,k) */
61: diag = ba + i*9;
62: u = ba + ili*9;
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]);
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]);
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]);
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];
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];
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];
89: /* update -U(i,k) */
90: PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));
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];
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];
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: }
120: /* save nonzero entries in k-th row of U ... */
122: /* invert diagonal block */
123: diag = ba+k*9;
124: PetscMemcpy(diag,dk,9*sizeof(MatScalar));
125: Kernel_A_gets_inverse_A_3(diag);
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: }
146: PetscFree(rtmp);
147: PetscFree(il);
148: PetscFree(dk);
150: C->factor = FACTOR_CHOLESKY;
151: C->assembled = PETSC_TRUE;
152: C->preallocated = PETSC_TRUE;
153: PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
154: return(0);
155: }