Actual source code: sbaijfact6.c
petsc-3.3-p7 2013-05-11
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <../src/mat/blockinvert.h>
5: /* Version for when blocks are 4 by 4 */
8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat C,Mat A,const MatFactorInfo *info)
9: {
10: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
11: IS perm = b->row;
13: const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
14: PetscInt i,j,*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: PetscBool pivotinblocks = b->pivotinblocks;
18: PetscReal shift = info->shiftamount;
21: /* initialization */
22: PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
23: PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
24: PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);
25: for (i=0; i<mbs; i++) {
26: jl[i] = mbs; il[0] = 0;
27: }
28: PetscMalloc2(16,MatScalar,&dk,16,MatScalar,&uik);
29: ISGetIndices(perm,&perm_ptr);
31: /* check permutation */
32: if (!a->permute){
33: ai = a->i; aj = a->j; aa = a->a;
34: } else {
35: ai = a->inew; aj = a->jnew;
36: PetscMalloc(16*ai[mbs]*sizeof(MatScalar),&aa);
37: PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));
38: PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);
39: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
41: for (i=0; i<mbs; i++){
42: jmin = ai[i]; jmax = ai[i+1];
43: for (j=jmin; j<jmax; j++){
44: while (a2anew[j] != j){
45: k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
46: for (k1=0; k1<16; k1++){
47: dk[k1] = aa[k*16+k1];
48: aa[k*16+k1] = aa[j*16+k1];
49: aa[j*16+k1] = dk[k1];
50: }
51: }
52: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
53: if (i > aj[j]){
54: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
55: ap = aa + j*16; /* ptr to the beginning of j-th block of aa */
56: for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
57: for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */
58: for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
59: }
60: }
61: }
62: }
63: PetscFree(a2anew);
64: }
65:
66: /* for each row k */
67: for (k = 0; k<mbs; k++){
69: /*initialize k-th row with elements nonzero in row perm(k) of A */
70: jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
71: if (jmin < jmax) {
72: ap = aa + jmin*16;
73: for (j = jmin; j < jmax; j++){
74: vj = perm_ptr[aj[j]]; /* block col. index */
75: rtmp_ptr = rtmp + vj*16;
76: for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
77: }
78: }
80: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
81: PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));
82: i = jl[k]; /* first row to be added to k_th row */
84: while (i < mbs){
85: nexti = jl[i]; /* next row to be added to k_th row */
87: /* compute multiplier */
88: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
90: /* uik = -inv(Di)*U_bar(i,k) */
91: diag = ba + i*16;
92: u = ba + ili*16;
94: uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
95: uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
96: uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
97: uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
99: uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
100: uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
101: uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
102: uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
104: uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
105: uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
106: uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
107: uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
109: uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
110: uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
111: uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
112: uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
114: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
115: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
116: dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
117: dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
118: dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
120: dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
121: dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
122: dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
123: dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
125: dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
126: dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
127: dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
128: dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
130: dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
131: dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
132: dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
133: dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
135: PetscLogFlops(64.0*4.0);
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: PetscLogFlops(2.0*64.0*(jmax-jmin));
168:
169: /* ... add i to row list for next nonzero entry */
170: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
171: j = bj[jmin];
172: jl[i] = jl[j]; jl[j] = i; /* update jl */
173: }
174: i = nexti;
175: }
177: /* save nonzero entries in k-th row of U ... */
179: /* invert diagonal block */
180: diag = ba+k*16;
181: PetscMemcpy(diag,dk,16*sizeof(MatScalar));
183: if (pivotinblocks) {
184: PetscKernel_A_gets_inverse_A_4(diag,shift);
185: } else {
186: PetscKernel_A_gets_inverse_A_4_nopivot(diag);
187: }
189: jmin = bi[k]; jmax = bi[k+1];
190: if (jmin < jmax) {
191: for (j=jmin; j<jmax; j++){
192: vj = bj[j]; /* block col. index of U */
193: u = ba + j*16;
194: rtmp_ptr = rtmp + vj*16;
195: for (k1=0; k1<16; k1++){
196: *u++ = *rtmp_ptr;
197: *rtmp_ptr++ = 0.0;
198: }
199: }
200:
201: /* ... add k to row list for first nonzero entry in k-th row */
202: il[k] = jmin;
203: i = bj[jmin];
204: jl[k] = jl[i]; jl[i] = k;
205: }
206: }
208: PetscFree(rtmp);
209: PetscFree2(il,jl);
210: PetscFree2(dk,uik);
211: if (a->permute){
212: PetscFree(aa);
213: }
215: ISRestoreIndices(perm,&perm_ptr);
216: C->ops->solve = MatSolve_SeqSBAIJ_4_inplace;
217: C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
218: C->assembled = PETSC_TRUE;
219: C->preallocated = PETSC_TRUE;
220: PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
221: return(0);
222: }