Actual source code: sbaijfact3.c
1: /*$Id: sbaijfact3.c,v 1.4 2001/06/21 21:17:00 bsmith Exp $*/
2: #include src/mat/impls/sbaij/seq/sbaij.h
3: #include src/inline/ilu.h
5: /* Version for when blocks are 3 by 3 */
8: int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
9: {
10: Mat C = *B;
11: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
12: IS perm = b->row;
13: int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
14: int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
15: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
16: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
19:
20: /* initialization */
21: PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
22: PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));
23: PetscMalloc(2*mbs*sizeof(int),&il);
24: jl = il + mbs;
25: for (i=0; i<mbs; i++) {
26: jl[i] = mbs; il[0] = 0;
27: }
28: PetscMalloc(18*sizeof(MatScalar),&dk);
29: uik = dk + 9;
30: ISGetIndices(perm,&perm_ptr);
32: /* check permutation */
33: if (!a->permute){
34: ai = a->i; aj = a->j; aa = a->a;
35: } else {
36: ai = a->inew; aj = a->jnew;
37: PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);
38: PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));
39: PetscMalloc(ai[mbs]*sizeof(int),&a2anew);
40: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));
42: for (i=0; i<mbs; i++){
43: jmin = ai[i]; jmax = ai[i+1];
44: for (j=jmin; j<jmax; j++){
45: while (a2anew[j] != j){
46: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
47: for (k1=0; k1<9; k1++){
48: dk[k1] = aa[k*9+k1];
49: aa[k*9+k1] = aa[j*9+k1];
50: aa[j*9+k1] = dk[k1];
51: }
52: }
53: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
54: if (i > aj[j]){
55: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
56: ap = aa + j*9; /* ptr to the beginning of j-th block of aa */
57: for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
58: for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */
59: for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
60: }
61: }
62: }
63: }
64: PetscFree(a2anew);
65: }
66:
67: /* for each row k */
68: for (k = 0; k<mbs; k++){
70: /*initialize k-th row with elements nonzero in row perm(k) of A */
71: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
72: if (jmin < jmax) {
73: ap = aa + jmin*9;
74: for (j = jmin; j < jmax; j++){
75: vj = perm_ptr[aj[j]]; /* block col. index */
76: rtmp_ptr = rtmp + vj*9;
77: for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
78: }
79: }
81: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
82: PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
83: i = jl[k]; /* first row to be added to k_th row */
85: while (i < mbs){
86: nexti = jl[i]; /* next row to be added to k_th row */
88: /* compute multiplier */
89: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
91: /* uik = -inv(Di)*U_bar(i,k) */
92: diag = ba + i*9;
93: u = ba + ili*9;
95: uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
96: uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
97: uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
99: uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
100: uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
101: uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
103: uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
104: uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
105: uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
107: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
108: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
109: dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
110: dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
112: dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
113: dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
114: dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
116: dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
117: dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
118: dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
120: /* update -U(i,k) */
121: PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));
123: /* add multiple of row i to k-th row ... */
124: jmin = ili + 1; jmax = bi[i+1];
125: if (jmin < jmax){
126: for (j=jmin; j<jmax; j++) {
127: /* rtmp += -U(i,k)^T * U_bar(i,j) */
128: rtmp_ptr = rtmp + bj[j]*9;
129: u = ba + j*9;
130: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
131: rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
132: rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
134: rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
135: rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
136: rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
138: rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
139: rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
140: rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
141: }
142:
143: /* ... add i to row list for next nonzero entry */
144: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
145: j = bj[jmin];
146: jl[i] = jl[j]; jl[j] = i; /* update jl */
147: }
148: i = nexti;
149: }
151: /* save nonzero entries in k-th row of U ... */
153: /* invert diagonal block */
154: diag = ba+k*9;
155: PetscMemcpy(diag,dk,9*sizeof(MatScalar));
156: Kernel_A_gets_inverse_A_3(diag);
157:
158: jmin = bi[k]; jmax = bi[k+1];
159: if (jmin < jmax) {
160: for (j=jmin; j<jmax; j++){
161: vj = bj[j]; /* block col. index of U */
162: u = ba + j*9;
163: rtmp_ptr = rtmp + vj*9;
164: for (k1=0; k1<9; k1++){
165: *u++ = *rtmp_ptr;
166: *rtmp_ptr++ = 0.0;
167: }
168: }
169:
170: /* ... add k to row list for first nonzero entry in k-th row */
171: il[k] = jmin;
172: i = bj[jmin];
173: jl[k] = jl[i]; jl[i] = k;
174: }
175: }
177: PetscFree(rtmp);
178: PetscFree(il);
179: PetscFree(dk);
180: if (a->permute){
181: PetscFree(aa);
182: }
184: ISRestoreIndices(perm,&perm_ptr);
185: C->factor = FACTOR_CHOLESKY;
186: C->assembled = PETSC_TRUE;
187: C->preallocated = PETSC_TRUE;
188: PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
189: return(0);
190: }