Actual source code: sbaijfact4.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /*
6: Version for when blocks are 3 by 3 Using natural ordering
7: */
8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
9: {
10: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
11: PetscInt i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
12: PetscInt *ai, *aj, 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;
18: PetscFunctionBegin;
19: /* initialization */
20: allowzeropivot = PetscNot(A->erroriffailure);
21: PetscCall(PetscCalloc1(9 * mbs, &rtmp));
22: PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
23: il[0] = 0;
24: for (i = 0; i < mbs; i++) jl[i] = mbs;
26: PetscCall(PetscMalloc2(9, &dk, 9, &uik));
27: ai = a->i;
28: aj = a->j;
29: aa = a->a;
31: /* for each row k */
32: for (k = 0; k < mbs; k++) {
33: /*initialize k-th row with elements nonzero in row k of A */
34: jmin = ai[k];
35: jmax = ai[k + 1];
36: if (jmin < jmax) {
37: ap = aa + jmin * 9;
38: for (j = jmin; j < jmax; j++) {
39: vj = aj[j]; /* block col. index */
40: rtmp_ptr = rtmp + vj * 9;
41: for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
42: }
43: }
45: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
46: PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
47: i = jl[k]; /* first row to be added to k_th row */
49: while (i < mbs) {
50: nexti = jl[i]; /* next row to be added to k_th row */
52: /* compute multiplier */
53: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
55: /* uik = -inv(Di)*U_bar(i,k) */
56: diag = ba + i * 9;
57: u = ba + ili * 9;
59: uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
60: uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
61: uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);
63: uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
64: uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
65: uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);
67: uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
68: uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
69: uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);
71: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
72: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
73: dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
74: dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
76: dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
77: dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
78: dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
80: dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
81: dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
82: dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
84: PetscCall(PetscLogFlops(27.0 * 4.0));
86: /* update -U(i,k) */
87: PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));
89: /* add multiple of row i to k-th row ... */
90: jmin = ili + 1;
91: jmax = bi[i + 1];
92: if (jmin < jmax) {
93: for (j = jmin; j < jmax; j++) {
94: /* rtmp += -U(i,k)^T * U_bar(i,j) */
95: rtmp_ptr = rtmp + bj[j] * 9;
96: u = ba + j * 9;
97: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
98: rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
99: rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
101: rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
102: rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
103: rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
105: rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
106: rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
107: rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
108: }
109: PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin)));
111: /* ... add i to row list for next nonzero entry */
112: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
113: j = bj[jmin];
114: jl[i] = jl[j];
115: jl[j] = i; /* update jl */
116: }
117: i = nexti;
118: }
120: /* save nonzero entries in k-th row of U ... */
122: /* invert diagonal block */
123: diag = ba + k * 9;
124: PetscCall(PetscArraycpy(diag, dk, 9));
125: PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
126: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
128: jmin = bi[k];
129: jmax = bi[k + 1];
130: if (jmin < jmax) {
131: for (j = jmin; j < jmax; j++) {
132: vj = bj[j]; /* block col. index of U */
133: u = ba + j * 9;
134: rtmp_ptr = rtmp + vj * 9;
135: for (k1 = 0; k1 < 9; k1++) {
136: *u++ = *rtmp_ptr;
137: *rtmp_ptr++ = 0.0;
138: }
139: }
141: /* ... add k to row list for first nonzero entry in k-th row */
142: il[k] = jmin;
143: i = bj[jmin];
144: jl[k] = jl[i];
145: jl[i] = k;
146: }
147: }
149: PetscCall(PetscFree(rtmp));
150: PetscCall(PetscFree2(il, jl));
151: PetscCall(PetscFree2(dk, uik));
153: C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
154: C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
155: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
156: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
158: C->assembled = PETSC_TRUE;
159: C->preallocated = PETSC_TRUE;
161: PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
162: PetscFunctionReturn(PETSC_SUCCESS);
163: }