Actual source code: sbaijfact3.c
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;
10: const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j;
11: PetscInt *a2anew, i, j, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
12: MatScalar *ba = b->a, *aa, *ap, *dk, *uik;
13: MatScalar *u, *diag, *rtmp, *rtmp_ptr;
14: PetscReal shift = info->shiftamount;
15: PetscBool allowzeropivot, zeropivotdetected;
17: PetscFunctionBegin;
18: /* initialization */
19: allowzeropivot = PetscNot(A->erroriffailure);
20: PetscCall(PetscCalloc1(9 * mbs, &rtmp));
21: PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
22: il[0] = 0;
23: for (i = 0; i < mbs; i++) jl[i] = mbs;
25: PetscCall(PetscMalloc2(9, &dk, 9, &uik));
26: PetscCall(ISGetIndices(perm, &perm_ptr));
28: /* check permutation */
29: if (!a->permute) {
30: ai = a->i;
31: aj = a->j;
32: aa = a->a;
33: } else {
34: ai = a->inew;
35: aj = a->jnew;
36: PetscCall(PetscMalloc1(9 * ai[mbs], &aa));
37: PetscCall(PetscArraycpy(aa, a->a, 9 * ai[mbs]));
38: PetscCall(PetscMalloc1(ai[mbs], &a2anew));
39: PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs]));
41: for (i = 0; i < mbs; i++) {
42: jmin = ai[i];
43: jmax = ai[i + 1];
44: for (j = jmin; j < jmax; j++) {
45: while (a2anew[j] != j) {
46: k = a2anew[j];
47: a2anew[j] = a2anew[k];
48: a2anew[k] = k;
49: for (k1 = 0; k1 < 9; k1++) {
50: dk[k1] = aa[k * 9 + k1];
51: aa[k * 9 + k1] = aa[j * 9 + k1];
52: aa[j * 9 + k1] = dk[k1];
53: }
54: }
55: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
56: if (i > aj[j]) {
57: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
58: ap = aa + j * 9; /* ptr to the beginning of j-th block of aa */
59: for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
60: for (k = 0; k < 3; k++) { /* j-th block of aa <- dk^T */
61: for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * k1];
62: }
63: }
64: }
65: }
66: PetscCall(PetscFree(a2anew));
67: }
69: /* for each row k */
70: 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]];
73: jmax = ai[perm_ptr[k] + 1];
74: if (jmin < jmax) {
75: ap = aa + jmin * 9;
76: for (j = jmin; j < jmax; j++) {
77: vj = perm_ptr[aj[j]]; /* block col. index */
78: rtmp_ptr = rtmp + vj * 9;
79: for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
80: }
81: }
83: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
84: PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
85: i = jl[k]; /* first row to be added to k_th row */
87: while (i < mbs) {
88: nexti = jl[i]; /* next row to be added to k_th row */
90: /* compute multiplier */
91: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
93: /* uik = -inv(Di)*U_bar(i,k) */
94: diag = ba + i * 9;
95: u = ba + ili * 9;
97: uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
98: uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
99: uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);
101: uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
102: uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
103: uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);
105: uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
106: uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
107: uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);
109: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
110: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
111: dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
112: dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
114: dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
115: dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
116: dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
118: dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
119: dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
120: dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
122: PetscCall(PetscLogFlops(27.0 * 4.0));
124: /* update -U(i,k) */
125: PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));
127: /* add multiple of row i to k-th row ... */
128: jmin = ili + 1;
129: jmax = bi[i + 1];
130: if (jmin < jmax) {
131: for (j = jmin; j < jmax; j++) {
132: /* rtmp += -U(i,k)^T * U_bar(i,j) */
133: rtmp_ptr = rtmp + bj[j] * 9;
134: u = ba + j * 9;
135: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
136: rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
137: rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
139: rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
140: rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
141: rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
143: rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
144: rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
145: rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
146: }
147: PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin)));
149: /* ... add i to row list for next nonzero entry */
150: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
151: j = bj[jmin];
152: jl[i] = jl[j];
153: jl[j] = i; /* update jl */
154: }
155: i = nexti;
156: }
158: /* save nonzero entries in k-th row of U ... */
160: /* invert diagonal block */
161: diag = ba + k * 9;
162: PetscCall(PetscArraycpy(diag, dk, 9));
163: PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
164: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
166: jmin = bi[k];
167: jmax = bi[k + 1];
168: if (jmin < jmax) {
169: for (j = jmin; j < jmax; j++) {
170: vj = bj[j]; /* block col. index of U */
171: u = ba + j * 9;
172: rtmp_ptr = rtmp + vj * 9;
173: for (k1 = 0; k1 < 9; k1++) {
174: *u++ = *rtmp_ptr;
175: *rtmp_ptr++ = 0.0;
176: }
177: }
179: /* ... add k to row list for first nonzero entry in k-th row */
180: il[k] = jmin;
181: i = bj[jmin];
182: jl[k] = jl[i];
183: jl[i] = k;
184: }
185: }
187: PetscCall(PetscFree(rtmp));
188: PetscCall(PetscFree2(il, jl));
189: PetscCall(PetscFree2(dk, uik));
190: if (a->permute) PetscCall(PetscFree(aa));
192: PetscCall(ISRestoreIndices(perm, &perm_ptr));
194: C->ops->solve = MatSolve_SeqSBAIJ_3_inplace;
195: C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
196: C->assembled = PETSC_TRUE;
197: C->preallocated = PETSC_TRUE;
199: PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
200: PetscFunctionReturn(PETSC_SUCCESS);
201: }