1 #include <../src/mat/impls/sbaij/seq/sbaij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
4 /*
5 Version for when blocks are 3 by 3 Using natural ordering
6 */
MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo * info)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;
16
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;
24
25 PetscCall(PetscMalloc2(9, &dk, 9, &uik));
26 ai = a->i;
27 aj = a->j;
28 aa = a->a;
29
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 }
43
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 */
47
48 while (i < mbs) {
49 nexti = jl[i]; /* next row to be added to k_th row */
50
51 /* compute multiplier */
52 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
53
54 /* uik = -inv(Di)*U_bar(i,k) */
55 diag = ba + i * 9;
56 u = ba + ili * 9;
57
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]);
61
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]);
65
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]);
69
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];
74
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];
78
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];
82
83 PetscCall(PetscLogFlops(27.0 * 4.0));
84
85 /* update -U(i,k) */
86 PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));
87
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];
99
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];
103
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)));
109
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 }
118
119 /* save nonzero entries in k-th row of U ... */
120
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;
126
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 }
139
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 }
147
148 PetscCall(PetscFree(rtmp));
149 PetscCall(PetscFree2(il, jl));
150 PetscCall(PetscFree2(dk, uik));
151
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;
156
157 C->assembled = PETSC_TRUE;
158 C->preallocated = PETSC_TRUE;
159
160 PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
161 PetscFunctionReturn(PETSC_SUCCESS);
162 }
163