Actual source code: sbaijfact7.c
1: #define PETSCMAT_DLL
3: #include src/mat/impls/sbaij/seq/sbaij.h
4: #include src/inline/ilu.h
6: /* Version for when blocks are 5 by 5 */
9: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,MatFactorInfo *info,Mat *B)
10: {
11: Mat C = *B;
12: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
13: IS perm = b->row;
15: PetscInt *perm_ptr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
16: PetscInt *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
17: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
18: MatScalar *u,*d,*rtmp,*rtmp_ptr;
21: /* initialization */
22: PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);
23: PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));
24: PetscMalloc(2*mbs*sizeof(PetscInt),&il);
25: jl = il + mbs;
26: for (i=0; i<mbs; i++) {
27: jl[i] = mbs; il[0] = 0;
28: }
29: PetscMalloc(50*sizeof(MatScalar),&dk);
30: uik = dk + 25;
31: ISGetIndices(perm,&perm_ptr);
33: /* check permutation */
34: if (!a->permute){
35: ai = a->i; aj = a->j; aa = a->a;
36: } else {
37: ai = a->inew; aj = a->jnew;
38: PetscMalloc(25*ai[mbs]*sizeof(MatScalar),&aa);
39: PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));
40: PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);
41: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
43: for (i=0; i<mbs; i++){
44: jmin = ai[i]; jmax = ai[i+1];
45: for (j=jmin; j<jmax; j++){
46: while (a2anew[j] != j){
47: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
48: for (k1=0; k1<25; k1++){
49: dk[k1] = aa[k*25+k1];
50: aa[k*25+k1] = aa[j*25+k1];
51: aa[j*25+k1] = dk[k1];
52: }
53: }
54: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
55: if (i > aj[j]){
56: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
57: ap = aa + j*25; /* ptr to the beginning of j-th block of aa */
58: for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
59: for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */
60: for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
61: }
62: }
63: }
64: }
65: PetscFree(a2anew);
66: }
67:
68: /* for each row k */
69: for (k = 0; k<mbs; k++){
71: /*initialize k-th row with elements nonzero in row perm(k) of A */
72: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
73: if (jmin < jmax) {
74: ap = aa + jmin*25;
75: for (j = jmin; j < jmax; j++){
76: vj = perm_ptr[aj[j]]; /* block col. index */
77: rtmp_ptr = rtmp + vj*25;
78: for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
79: }
80: }
82: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
83: PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));
84: i = jl[k]; /* first row to be added to k_th row */
86: while (i < mbs){
87: nexti = jl[i]; /* next row to be added to k_th row */
89: /* compute multiplier */
90: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
92: /* uik = -inv(Di)*U_bar(i,k) */
93: d = ba + i*25;
94: u = ba + ili*25;
96: uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
97: uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
98: uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
99: uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
100: uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
102: uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
103: uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
104: uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
105: uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
106: uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
108: uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
109: uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
110: uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
111: uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
112: uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
114: uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
115: uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
116: uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
117: uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
118: uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
120: uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
121: uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
122: uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
123: uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
124: uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
127: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
128: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
129: dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
130: dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
131: dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
132: dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
134: dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
135: dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
136: dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
137: dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
138: dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
140: dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
141: dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
142: dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
143: dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
144: dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
146: dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
147: dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
148: dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
149: dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
150: dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
152: dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
153: dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
154: dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
155: dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
156: dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
158: PetscLogFlops(125*4);
160: /* update -U(i,k) */
161: PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));
163: /* add multiple of row i to k-th row ... */
164: jmin = ili + 1; jmax = bi[i+1];
165: if (jmin < jmax){
166: for (j=jmin; j<jmax; j++) {
167: /* rtmp += -U(i,k)^T * U_bar(i,j) */
168: rtmp_ptr = rtmp + bj[j]*25;
169: u = ba + j*25;
170: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
171: rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
172: rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
173: rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
174: rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
176: rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
177: rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
178: rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
179: rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
180: rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
182: rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
183: rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
184: rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
185: rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
186: rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
188: rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
189: rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
190: rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
191: rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
192: rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
194: rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
195: rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
196: rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
197: rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
198: rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
199: }
200: PetscLogFlops(2*125*(jmax-jmin));
201:
202: /* ... add i to row list for next nonzero entry */
203: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
204: j = bj[jmin];
205: jl[i] = jl[j]; jl[j] = i; /* update jl */
206: }
207: i = nexti;
208: }
210: /* save nonzero entries in k-th row of U ... */
212: /* invert diagonal block */
213: d = ba+k*25;
214: PetscMemcpy(d,dk,25*sizeof(MatScalar));
215: Kernel_A_gets_inverse_A_5(d);
216:
217: jmin = bi[k]; jmax = bi[k+1];
218: if (jmin < jmax) {
219: for (j=jmin; j<jmax; j++){
220: vj = bj[j]; /* block col. index of U */
221: u = ba + j*25;
222: rtmp_ptr = rtmp + vj*25;
223: for (k1=0; k1<25; k1++){
224: *u++ = *rtmp_ptr;
225: *rtmp_ptr++ = 0.0;
226: }
227: }
228:
229: /* ... add k to row list for first nonzero entry in k-th row */
230: il[k] = jmin;
231: i = bj[jmin];
232: jl[k] = jl[i]; jl[i] = k;
233: }
234: }
236: PetscFree(rtmp);
237: PetscFree(il);
238: PetscFree(dk);
239: if (a->permute){
240: PetscFree(aa);
241: }
243: ISRestoreIndices(perm,&perm_ptr);
244: C->factor = FACTOR_CHOLESKY;
245: C->assembled = PETSC_TRUE;
246: C->preallocated = PETSC_TRUE;
247: PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
248: return(0);
249: }