Actual source code: sbaijfact6.c
1: /*$Id: sbaijfact6.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 4 by 4 */
8: int MatCholeskyFactorNumeric_SeqSBAIJ_4(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;
17: PetscTruth pivotinblocks = b->pivotinblocks;
20: /* initialization */
21: PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
22: PetscMemzero(rtmp,16*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(32*sizeof(MatScalar),&dk);
29: uik = dk + 16;
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(16*ai[mbs]*sizeof(MatScalar),&aa);
38: PetscMemcpy(aa,a->a,16*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<16; k1++){
48: dk[k1] = aa[k*16+k1];
49: aa[k*16+k1] = aa[j*16+k1];
50: aa[j*16+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*16; /* ptr to the beginning of j-th block of aa */
57: for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
58: for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */
59: for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*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*16;
74: for (j = jmin; j < jmax; j++){
75: vj = perm_ptr[aj[j]]; /* block col. index */
76: rtmp_ptr = rtmp + vj*16;
77: for (i=0; i<16; 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*16,16*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*16;
93: u = ba + ili*16;
95: uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
96: uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
97: uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
98: uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
100: uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
101: uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
102: uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
103: uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
105: uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
106: uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
107: uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
108: uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
110: uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
111: uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
112: uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
113: uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
115: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
116: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
117: dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
118: dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
119: dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
121: dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
122: dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
123: dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
124: dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
126: dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
127: dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
128: dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
129: dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
131: dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
132: dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
133: dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
134: dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
135:
136: /* update -U(i,k) */
137: PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));
139: /* add multiple of row i to k-th row ... */
140: jmin = ili + 1; jmax = bi[i+1];
141: if (jmin < jmax){
142: for (j=jmin; j<jmax; j++) {
143: /* rtmp += -U(i,k)^T * U_bar(i,j) */
144: rtmp_ptr = rtmp + bj[j]*16;
145: u = ba + j*16;
146: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
147: rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
148: rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
149: rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
151: rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
152: rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
153: rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
154: rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
156: rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
157: rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
158: rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
159: rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
161: rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
162: rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
163: rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
164: rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
165: }
166:
167: /* ... add i to row list for next nonzero entry */
168: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
169: j = bj[jmin];
170: jl[i] = jl[j]; jl[j] = i; /* update jl */
171: }
172: i = nexti;
173: }
175: /* save nonzero entries in k-th row of U ... */
177: /* invert diagonal block */
178: diag = ba+k*16;
179: PetscMemcpy(diag,dk,16*sizeof(MatScalar));
181: if (pivotinblocks) {
182: Kernel_A_gets_inverse_A_4(diag);
183: } else {
184: Kernel_A_gets_inverse_A_4_nopivot(diag);
185: }
187: jmin = bi[k]; jmax = bi[k+1];
188: if (jmin < jmax) {
189: for (j=jmin; j<jmax; j++){
190: vj = bj[j]; /* block col. index of U */
191: u = ba + j*16;
192: rtmp_ptr = rtmp + vj*16;
193: for (k1=0; k1<16; k1++){
194: *u++ = *rtmp_ptr;
195: *rtmp_ptr++ = 0.0;
196: }
197: }
198:
199: /* ... add k to row list for first nonzero entry in k-th row */
200: il[k] = jmin;
201: i = bj[jmin];
202: jl[k] = jl[i]; jl[i] = k;
203: }
204: }
206: PetscFree(rtmp);
207: PetscFree(il);
208: PetscFree(dk);
209: if (a->permute){
210: PetscFree(aa);
211: }
213: ISRestoreIndices(perm,&perm_ptr);
214: C->factor = FACTOR_CHOLESKY;
215: C->assembled = PETSC_TRUE;
216: C->preallocated = PETSC_TRUE;
217: PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
218: return(0);
219: }