Actual source code: sbaijfact6.c
1: /*$Id: sbaijfact6.c,v 1.3 2001/03/23 23:22:21 balay Exp $*/
2: #include "sbaij.h"
3: #include "src/inline/ilu.h"
5: /* Version for when blocks are 4 by 4 */
6: int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
7: {
8: Mat C = *B;
9: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
10: IS perm = b->row;
11: int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
12: int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
13: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
14: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
17: /* initialization */
18: PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
19: PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
20: PetscMalloc(2*mbs*sizeof(int),&il);
21: jl = il + mbs;
22: for (i=0; i<mbs; i++) {
23: jl[i] = mbs; il[0] = 0;
24: }
25: PetscMalloc(32*sizeof(MatScalar),&dk);
26: uik = dk + 16;
27: ISGetIndices(perm,&perm_ptr);
29: /* check permutation */
30: if (!a->permute){
31: ai = a->i; aj = a->j; aa = a->a;
32: } else {
33: ai = a->inew; aj = a->jnew;
34: PetscMalloc(16*ai[mbs]*sizeof(MatScalar),&aa);
35: PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));
36: PetscMalloc(ai[mbs]*sizeof(int),&a2anew);
37: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));
39: for (i=0; i<mbs; i++){
40: jmin = ai[i]; jmax = ai[i+1];
41: for (j=jmin; j<jmax; j++){
42: while (a2anew[j] != j){
43: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
44: for (k1=0; k1<16; k1++){
45: dk[k1] = aa[k*16+k1];
46: aa[k*16+k1] = aa[j*16+k1];
47: aa[j*16+k1] = dk[k1];
48: }
49: }
50: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
51: if (i > aj[j]){
52: /* printf("change orientation, row: %d, col: %dn",i,aj[j]); */
53: ap = aa + j*16; /* ptr to the beginning of j-th block of aa */
54: for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
55: for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */
56: for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
57: }
58: }
59: }
60: }
61: PetscFree(a2anew);
62: }
63:
64: /* for each row k */
65: for (k = 0; k<mbs; k++){
67: /*initialize k-th row with elements nonzero in row perm(k) of A */
68: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
69: if (jmin < jmax) {
70: ap = aa + jmin*16;
71: for (j = jmin; j < jmax; j++){
72: vj = perm_ptr[aj[j]]; /* block col. index */
73: rtmp_ptr = rtmp + vj*16;
74: for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
75: }
76: }
78: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
79: PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));
80: i = jl[k]; /* first row to be added to k_th row */
82: while (i < mbs){
83: nexti = jl[i]; /* next row to be added to k_th row */
85: /* compute multiplier */
86: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
88: /* uik = -inv(Di)*U_bar(i,k) */
89: diag = ba + i*16;
90: u = ba + ili*16;
92: uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
93: uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
94: uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
95: uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
97: uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
98: uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
99: uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
100: uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
102: uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
103: uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
104: uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
105: uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
107: uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
108: uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
109: uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
110: uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
112: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
113: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
114: dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
115: dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
116: dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
118: dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
119: dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
120: dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
121: dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
123: dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
124: dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
125: dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
126: dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
128: dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
129: dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
130: dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
131: dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
132:
133: /* update -U(i,k) */
134: PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));
136: /* add multiple of row i to k-th row ... */
137: jmin = ili + 1; jmax = bi[i+1];
138: if (jmin < jmax){
139: for (j=jmin; j<jmax; j++) {
140: /* rtmp += -U(i,k)^T * U_bar(i,j) */
141: rtmp_ptr = rtmp + bj[j]*16;
142: u = ba + j*16;
143: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
144: rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
145: rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
146: rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
148: rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
149: rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
150: rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
151: rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
153: rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
154: rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
155: rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
156: rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
158: rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
159: rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
160: rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
161: rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
162: }
163:
164: /* ... add i to row list for next nonzero entry */
165: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
166: j = bj[jmin];
167: jl[i] = jl[j]; jl[j] = i; /* update jl */
168: }
169: i = nexti;
170: }
172: /* save nonzero entries in k-th row of U ... */
174: /* invert diagonal block */
175: diag = ba+k*16;
176: PetscMemcpy(diag,dk,16*sizeof(MatScalar));
177: Kernel_A_gets_inverse_A_4(diag);
178:
179: jmin = bi[k]; jmax = bi[k+1];
180: if (jmin < jmax) {
181: for (j=jmin; j<jmax; j++){
182: vj = bj[j]; /* block col. index of U */
183: u = ba + j*16;
184: rtmp_ptr = rtmp + vj*16;
185: for (k1=0; k1<16; k1++){
186: *u++ = *rtmp_ptr;
187: *rtmp_ptr++ = 0.0;
188: }
189: }
190:
191: /* ... add k to row list for first nonzero entry in k-th row */
192: il[k] = jmin;
193: i = bj[jmin];
194: jl[k] = jl[i]; jl[i] = k;
195: }
196: }
198: PetscFree(rtmp);
199: PetscFree(il);
200: PetscFree(dk);
201: if (a->permute){
202: PetscFree(aa);
203: }
205: ISRestoreIndices(perm,&perm_ptr);
206: C->factor = FACTOR_CHOLESKY;
207: C->assembled = PETSC_TRUE;
208: C->preallocated = PETSC_TRUE;
209: PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
210: return(0);
211: }