1 #include <../src/mat/impls/sbaij/seq/sbaij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
4 /*
5 Version for when blocks are 5 by 5 Using natural ordering
6 */
MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat C,Mat A,const MatFactorInfo * info)7 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_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, ipvt[5];
12 MatScalar *ba = b->a, *aa, *ap, *dk, *uik;
13 MatScalar *u, *d, *rtmp, *rtmp_ptr, work[25];
14 PetscReal shift = info->shiftamount;
15 PetscBool allowzeropivot, zeropivotdetected;
16
17 PetscFunctionBegin;
18 /* initialization */
19 allowzeropivot = PetscNot(A->erroriffailure);
20 PetscCall(PetscCalloc1(25 * 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(25, &dk, 25, &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 * 25;
37 for (j = jmin; j < jmax; j++) {
38 vj = aj[j]; /* block col. index */
39 rtmp_ptr = rtmp + vj * 25;
40 for (i = 0; i < 25; 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 * 25, 25));
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 d = ba + i * 25;
56 u = ba + ili * 25;
57
58 uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]);
59 uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]);
60 uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]);
61 uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]);
62 uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]);
63
64 uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]);
65 uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]);
66 uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]);
67 uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]);
68 uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]);
69
70 uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]);
71 uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]);
72 uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]);
73 uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]);
74 uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]);
75
76 uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]);
77 uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]);
78 uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]);
79 uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]);
80 uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]);
81
82 uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]);
83 uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]);
84 uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]);
85 uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]);
86 uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]);
87
88 /* update D(k) += -U(i,k)^T * U_bar(i,k) */
89 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
90 dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
91 dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
92 dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
93 dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
94
95 dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
96 dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
97 dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
98 dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
99 dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
100
101 dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
102 dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
103 dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
104 dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
105 dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
106
107 dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
108 dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
109 dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
110 dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
111 dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
112
113 dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
114 dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
115 dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
116 dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
117 dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
118
119 PetscCall(PetscLogFlops(125.0 * 4.0));
120
121 /* update -U(i,k) */
122 PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
123
124 /* add multiple of row i to k-th row ... */
125 jmin = ili + 1;
126 jmax = bi[i + 1];
127 if (jmin < jmax) {
128 for (j = jmin; j < jmax; j++) {
129 /* rtmp += -U(i,k)^T * U_bar(i,j) */
130 rtmp_ptr = rtmp + bj[j] * 25;
131 u = ba + j * 25;
132 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
133 rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
134 rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
135 rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
136 rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
137
138 rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
139 rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
140 rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
141 rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
142 rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
143
144 rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
145 rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
146 rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
147 rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
148 rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
149
150 rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
151 rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
152 rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
153 rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
154 rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
155
156 rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
157 rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
158 rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
159 rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
160 rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
161 }
162 PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin)));
163
164 /* ... add i to row list for next nonzero entry */
165 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
166 j = bj[jmin];
167 jl[i] = jl[j];
168 jl[j] = i; /* update jl */
169 }
170 i = nexti;
171 }
172
173 /* save nonzero entries in k-th row of U ... */
174
175 /* invert diagonal block */
176 d = ba + k * 25;
177 PetscCall(PetscArraycpy(d, dk, 25));
178 PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
179 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
180
181 jmin = bi[k];
182 jmax = bi[k + 1];
183 if (jmin < jmax) {
184 for (j = jmin; j < jmax; j++) {
185 vj = bj[j]; /* block col. index of U */
186 u = ba + j * 25;
187 rtmp_ptr = rtmp + vj * 25;
188 for (k1 = 0; k1 < 25; k1++) {
189 *u++ = *rtmp_ptr;
190 *rtmp_ptr++ = 0.0;
191 }
192 }
193
194 /* ... add k to row list for first nonzero entry in k-th row */
195 il[k] = jmin;
196 i = bj[jmin];
197 jl[k] = jl[i];
198 jl[i] = k;
199 }
200 }
201
202 PetscCall(PetscFree(rtmp));
203 PetscCall(PetscFree2(il, jl));
204 PetscCall(PetscFree2(dk, uik));
205
206 C->ops->solve = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
207 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
208 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
209 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
210 C->assembled = PETSC_TRUE;
211 C->preallocated = PETSC_TRUE;
212
213 PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
214 PetscFunctionReturn(PETSC_SUCCESS);
215 }
216