Actual source code: sbaijfact6.c
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: PetscErrorCode 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;
14: PetscInt *perm_ptr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
15: PetscInt *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
16: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
17: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
18: PetscTruth pivotinblocks = b->pivotinblocks;
21: /* initialization */
22: PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
23: PetscMemzero(rtmp,16*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(32*sizeof(MatScalar),&dk);
30: uik = dk + 16;
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(16*ai[mbs]*sizeof(MatScalar),&aa);
39: PetscMemcpy(aa,a->a,16*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<16; k1++){
49: dk[k1] = aa[k*16+k1];
50: aa[k*16+k1] = aa[j*16+k1];
51: aa[j*16+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*16; /* ptr to the beginning of j-th block of aa */
58: for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
59: for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */
60: for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*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*16;
75: for (j = jmin; j < jmax; j++){
76: vj = perm_ptr[aj[j]]; /* block col. index */
77: rtmp_ptr = rtmp + vj*16;
78: for (i=0; i<16; 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*16,16*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: diag = ba + i*16;
94: u = ba + ili*16;
96: uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
97: uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
98: uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
99: uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
101: uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
102: uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
103: uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
104: uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
106: uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
107: uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
108: uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
109: uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
111: uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
112: uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
113: uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
114: uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
116: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
117: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
118: dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
119: dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
120: dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
122: dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
123: dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
124: dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
125: dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
127: dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
128: dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
129: dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
130: dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
132: dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
133: dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
134: dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
135: dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
136:
137: /* update -U(i,k) */
138: PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));
140: /* add multiple of row i to k-th row ... */
141: jmin = ili + 1; jmax = bi[i+1];
142: if (jmin < jmax){
143: for (j=jmin; j<jmax; j++) {
144: /* rtmp += -U(i,k)^T * U_bar(i,j) */
145: rtmp_ptr = rtmp + bj[j]*16;
146: u = ba + j*16;
147: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
148: rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
149: rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
150: rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
152: rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
153: rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
154: rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
155: rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
157: rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
158: rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
159: rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
160: rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
162: rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
163: rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
164: rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
165: rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
166: }
167:
168: /* ... add i to row list for next nonzero entry */
169: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
170: j = bj[jmin];
171: jl[i] = jl[j]; jl[j] = i; /* update jl */
172: }
173: i = nexti;
174: }
176: /* save nonzero entries in k-th row of U ... */
178: /* invert diagonal block */
179: diag = ba+k*16;
180: PetscMemcpy(diag,dk,16*sizeof(MatScalar));
182: if (pivotinblocks) {
183: Kernel_A_gets_inverse_A_4(diag);
184: } else {
185: Kernel_A_gets_inverse_A_4_nopivot(diag);
186: }
188: jmin = bi[k]; jmax = bi[k+1];
189: if (jmin < jmax) {
190: for (j=jmin; j<jmax; j++){
191: vj = bj[j]; /* block col. index of U */
192: u = ba + j*16;
193: rtmp_ptr = rtmp + vj*16;
194: for (k1=0; k1<16; k1++){
195: *u++ = *rtmp_ptr;
196: *rtmp_ptr++ = 0.0;
197: }
198: }
199:
200: /* ... add k to row list for first nonzero entry in k-th row */
201: il[k] = jmin;
202: i = bj[jmin];
203: jl[k] = jl[i]; jl[i] = k;
204: }
205: }
207: PetscFree(rtmp);
208: PetscFree(il);
209: PetscFree(dk);
210: if (a->permute){
211: PetscFree(aa);
212: }
214: ISRestoreIndices(perm,&perm_ptr);
215: C->factor = FACTOR_CHOLESKY;
216: C->assembled = PETSC_TRUE;
217: C->preallocated = PETSC_TRUE;
218: PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
219: return(0);
220: }