Actual source code: sbaijfact4.c
1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: /*
5: Version for when blocks are 3 by 3 Using natural ordering
6: */
7: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
8: {
9: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
10: PetscInt i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
11: PetscInt *ai, *aj, 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: ai = a->i;
27: aj = a->j;
28: aa = a->a;
30: /* for each row k */
31: for (k = 0; k < mbs; k++) {
32: /*initialize k-th row with elements nonzero in row k of A */
33: jmin = ai[k];
34: jmax = ai[k + 1];
35: if (jmin < jmax) {
36: ap = aa + jmin * 9;
37: for (j = jmin; j < jmax; j++) {
38: vj = aj[j]; /* block col. index */
39: rtmp_ptr = rtmp + vj * 9;
40: for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
41: }
42: }
44: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
45: PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
46: i = jl[k]; /* first row to be added to k_th row */
48: while (i < mbs) {
49: nexti = jl[i]; /* next row to be added to k_th row */
51: /* compute multiplier */
52: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
54: /* uik = -inv(Di)*U_bar(i,k) */
55: diag = ba + i * 9;
56: u = ba + ili * 9;
58: uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
59: uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
60: uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);
62: uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
63: uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
64: uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);
66: uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
67: uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
68: uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);
70: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
71: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
72: dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
73: dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
75: dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
76: dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
77: dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
79: dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
80: dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
81: dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
83: PetscCall(PetscLogFlops(27.0 * 4.0));
85: /* update -U(i,k) */
86: PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));
88: /* add multiple of row i to k-th row ... */
89: jmin = ili + 1;
90: jmax = bi[i + 1];
91: if (jmin < jmax) {
92: for (j = jmin; j < jmax; j++) {
93: /* rtmp += -U(i,k)^T * U_bar(i,j) */
94: rtmp_ptr = rtmp + bj[j] * 9;
95: u = ba + j * 9;
96: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
97: rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
98: rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];
100: rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
101: rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
102: rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];
104: rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
105: rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
106: rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
107: }
108: PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin)));
110: /* ... add i to row list for next nonzero entry */
111: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
112: j = bj[jmin];
113: jl[i] = jl[j];
114: jl[j] = i; /* update jl */
115: }
116: i = nexti;
117: }
119: /* save nonzero entries in k-th row of U ... */
121: /* invert diagonal block */
122: diag = ba + k * 9;
123: PetscCall(PetscArraycpy(diag, dk, 9));
124: PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
125: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
127: jmin = bi[k];
128: jmax = bi[k + 1];
129: if (jmin < jmax) {
130: for (j = jmin; j < jmax; j++) {
131: vj = bj[j]; /* block col. index of U */
132: u = ba + j * 9;
133: rtmp_ptr = rtmp + vj * 9;
134: for (k1 = 0; k1 < 9; k1++) {
135: *u++ = *rtmp_ptr;
136: *rtmp_ptr++ = 0.0;
137: }
138: }
140: /* ... add k to row list for first nonzero entry in k-th row */
141: il[k] = jmin;
142: i = bj[jmin];
143: jl[k] = jl[i];
144: jl[i] = k;
145: }
146: }
148: PetscCall(PetscFree(rtmp));
149: PetscCall(PetscFree2(il, jl));
150: PetscCall(PetscFree2(dk, uik));
152: C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
153: C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
154: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
155: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
157: C->assembled = PETSC_TRUE;
158: C->preallocated = PETSC_TRUE;
160: PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
161: PetscFunctionReturn(PETSC_SUCCESS);
162: }