Actual source code: sbaijfact3.c
petsc-3.9.4 2018-09-11
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /* Version for when blocks are 3 by 3 */
6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C,Mat A,const MatFactorInfo *info)
7: {
8: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
9: IS perm = b->row;
11: const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
12: PetscInt *a2anew,i,j,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;
15: PetscReal shift = info->shiftamount;
16: PetscBool allowzeropivot,zeropivotdetected;
19: /* initialization */
20: allowzeropivot = PetscNot(A->erroriffailure);
21: PetscCalloc1(9*mbs,&rtmp);
22: PetscMalloc2(mbs,&il,mbs,&jl);
23: il[0] = 0;
24: for (i=0; i<mbs; i++) jl[i] = mbs;
25:
26: PetscMalloc2(9,&dk,9,&uik);
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: PetscMalloc1(9*ai[mbs],&aa);
35: PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));
36: PetscMalloc1(ai[mbs],&a2anew);
37: PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));
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<9; k1++) {
45: dk[k1] = aa[k*9+k1];
46: aa[k*9+k1] = aa[j*9+k1];
47: aa[j*9+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: %d\n",i,aj[j]); */
53: ap = aa + j*9; /* ptr to the beginning of j-th block of aa */
54: for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
55: for (k=0; k<3; k++) { /* j-th block of aa <- dk^T */
56: for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
57: }
58: }
59: }
60: }
61: PetscFree(a2anew);
62: }
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*9;
71: for (j = jmin; j < jmax; j++) {
72: vj = perm_ptr[aj[j]]; /* block col. index */
73: rtmp_ptr = rtmp + vj*9;
74: for (i=0; i<9; 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*9,9*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*9;
90: u = ba + ili*9;
92: uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
93: uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
94: uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
96: uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
97: uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
98: uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
100: uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
101: uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
102: uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
104: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
105: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
106: dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
107: dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
109: dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
110: dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
111: dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
113: dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
114: dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
115: dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
117: PetscLogFlops(27.0*4.0);
119: /* update -U(i,k) */
120: PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));
122: /* add multiple of row i to k-th row ... */
123: jmin = ili + 1; jmax = bi[i+1];
124: if (jmin < jmax) {
125: for (j=jmin; j<jmax; j++) {
126: /* rtmp += -U(i,k)^T * U_bar(i,j) */
127: rtmp_ptr = rtmp + bj[j]*9;
128: u = ba + j*9;
129: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
130: rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
131: rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
133: rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
134: rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
135: rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
137: rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
138: rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
139: rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
140: }
141: PetscLogFlops(2.0*27.0*(jmax-jmin));
143: /* ... add i to row list for next nonzero entry */
144: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
145: j = bj[jmin];
146: jl[i] = jl[j]; jl[j] = i; /* update jl */
147: }
148: i = nexti;
149: }
151: /* save nonzero entries in k-th row of U ... */
153: /* invert diagonal block */
154: diag = ba+k*9;
155: PetscMemcpy(diag,dk,9*sizeof(MatScalar));
156: PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);
157: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
159: jmin = bi[k]; jmax = bi[k+1];
160: if (jmin < jmax) {
161: for (j=jmin; j<jmax; j++) {
162: vj = bj[j]; /* block col. index of U */
163: u = ba + j*9;
164: rtmp_ptr = rtmp + vj*9;
165: for (k1=0; k1<9; k1++) {
166: *u++ = *rtmp_ptr;
167: *rtmp_ptr++ = 0.0;
168: }
169: }
171: /* ... add k to row list for first nonzero entry in k-th row */
172: il[k] = jmin;
173: i = bj[jmin];
174: jl[k] = jl[i]; jl[i] = k;
175: }
176: }
178: PetscFree(rtmp);
179: PetscFree2(il,jl);
180: PetscFree2(dk,uik);
181: if (a->permute) {
182: PetscFree(aa);
183: }
185: ISRestoreIndices(perm,&perm_ptr);
187: C->ops->solve = MatSolve_SeqSBAIJ_3_inplace;
188: C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
189: C->assembled = PETSC_TRUE;
190: C->preallocated = PETSC_TRUE;
192: PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
193: return(0);
194: }