1 #include <../src/mat/impls/sbaij/seq/sbaij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
4 /* Version for when blocks are 5 by 5 */
MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C,Mat A,const MatFactorInfo * info)5 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C, Mat A, const MatFactorInfo *info)
6 {
7 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
8 IS perm = b->row;
9 const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j;
10 PetscInt i, j, *a2anew, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili, ipvt[5];
11 MatScalar *ba = b->a, *aa, *ap, *dk, *uik;
12 MatScalar *u, *d, *rtmp, *rtmp_ptr, work[25];
13 PetscReal shift = info->shiftamount;
14 PetscBool allowzeropivot, zeropivotdetected;
15
16 PetscFunctionBegin;
17 /* initialization */
18 allowzeropivot = PetscNot(A->erroriffailure);
19 PetscCall(PetscCalloc1(25 * mbs, &rtmp));
20 PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
21 il[0] = 0;
22 for (i = 0; i < mbs; i++) jl[i] = mbs;
23
24 PetscCall(PetscMalloc2(25, &dk, 25, &uik));
25 PetscCall(ISGetIndices(perm, &perm_ptr));
26
27 /* check permutation */
28 if (!a->permute) {
29 ai = a->i;
30 aj = a->j;
31 aa = a->a;
32 } else {
33 ai = a->inew;
34 aj = a->jnew;
35 PetscCall(PetscMalloc1(25 * ai[mbs], &aa));
36 PetscCall(PetscArraycpy(aa, a->a, 25 * ai[mbs]));
37 PetscCall(PetscMalloc1(ai[mbs], &a2anew));
38 PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs]));
39
40 for (i = 0; i < mbs; i++) {
41 jmin = ai[i];
42 jmax = ai[i + 1];
43 for (j = jmin; j < jmax; j++) {
44 while (a2anew[j] != j) {
45 k = a2anew[j];
46 a2anew[j] = a2anew[k];
47 a2anew[k] = k;
48 for (k1 = 0; k1 < 25; k1++) {
49 dk[k1] = aa[k * 25 + k1];
50 aa[k * 25 + k1] = aa[j * 25 + k1];
51 aa[j * 25 + k1] = dk[k1];
52 }
53 }
54 /* transform column-oriented blocks that lie in the lower triangle to row-oriented blocks */
55 if (i > aj[j]) {
56 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
57 ap = aa + j * 25; /* ptr to the beginning of j-th block of aa */
58 for (k = 0; k < 25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
59 for (k = 0; k < 5; k++) { /* j-th block of aa <- dk^T */
60 for (k1 = 0; k1 < 5; k1++) *ap++ = dk[k + 5 * k1];
61 }
62 }
63 }
64 }
65 PetscCall(PetscFree(a2anew));
66 }
67
68 /* for each row k */
69 for (k = 0; k < mbs; k++) {
70 /*initialize k-th row with elements nonzero in row perm(k) of A */
71 jmin = ai[perm_ptr[k]];
72 jmax = ai[perm_ptr[k] + 1];
73 if (jmin < jmax) {
74 ap = aa + jmin * 25;
75 for (j = jmin; j < jmax; j++) {
76 vj = perm_ptr[aj[j]]; /* block col. index */
77 rtmp_ptr = rtmp + vj * 25;
78 for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++;
79 }
80 }
81
82 /* modify k-th row by adding in those rows i with U(i,k) != 0 */
83 PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25));
84 i = jl[k]; /* first row to be added to k_th row */
85
86 while (i < mbs) {
87 nexti = jl[i]; /* next row to be added to k_th row */
88
89 /* compute multiplier */
90 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
91
92 /* uik = -inv(Di)*U_bar(i,k) */
93 d = ba + i * 25;
94 u = ba + ili * 25;
95
96 uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]);
97 uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]);
98 uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]);
99 uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]);
100 uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]);
101
102 uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]);
103 uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]);
104 uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]);
105 uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]);
106 uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]);
107
108 uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]);
109 uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]);
110 uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]);
111 uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]);
112 uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]);
113
114 uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]);
115 uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]);
116 uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]);
117 uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]);
118 uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]);
119
120 uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]);
121 uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]);
122 uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]);
123 uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]);
124 uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]);
125
126 /* update D(k) += -U(i,k)^T * U_bar(i,k) */
127 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
128 dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
129 dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
130 dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
131 dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
132
133 dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
134 dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
135 dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
136 dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
137 dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
138
139 dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
140 dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
141 dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
142 dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
143 dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
144
145 dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
146 dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
147 dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
148 dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
149 dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
150
151 dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
152 dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
153 dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
154 dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
155 dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
156
157 PetscCall(PetscLogFlops(125.0 * 4.0));
158
159 /* update -U(i,k) */
160 PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
161
162 /* add multiple of row i to k-th row ... */
163 jmin = ili + 1;
164 jmax = bi[i + 1];
165 if (jmin < jmax) {
166 for (j = jmin; j < jmax; j++) {
167 /* rtmp += -U(i,k)^T * U_bar(i,j) */
168 rtmp_ptr = rtmp + bj[j] * 25;
169 u = ba + j * 25;
170 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
171 rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
172 rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
173 rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
174 rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
175
176 rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
177 rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
178 rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
179 rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
180 rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
181
182 rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
183 rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
184 rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
185 rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
186 rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
187
188 rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
189 rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
190 rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
191 rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
192 rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
193
194 rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
195 rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
196 rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
197 rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
198 rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
199 }
200 PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin)));
201
202 /* ... add i to row list for next nonzero entry */
203 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
204 j = bj[jmin];
205 jl[i] = jl[j];
206 jl[j] = i; /* update jl */
207 }
208 i = nexti;
209 }
210
211 /* save nonzero entries in k-th row of U ... */
212
213 /* invert diagonal block */
214 d = ba + k * 25;
215 PetscCall(PetscArraycpy(d, dk, 25));
216 PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
217 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
218
219 jmin = bi[k];
220 jmax = bi[k + 1];
221 if (jmin < jmax) {
222 for (j = jmin; j < jmax; j++) {
223 vj = bj[j]; /* block col. index of U */
224 u = ba + j * 25;
225 rtmp_ptr = rtmp + vj * 25;
226 for (k1 = 0; k1 < 25; k1++) {
227 *u++ = *rtmp_ptr;
228 *rtmp_ptr++ = 0.0;
229 }
230 }
231
232 /* ... add k to row list for first nonzero entry in k-th row */
233 il[k] = jmin;
234 i = bj[jmin];
235 jl[k] = jl[i];
236 jl[i] = k;
237 }
238 }
239
240 PetscCall(PetscFree(rtmp));
241 PetscCall(PetscFree2(il, jl));
242 PetscCall(PetscFree2(dk, uik));
243 if (a->permute) PetscCall(PetscFree(aa));
244
245 PetscCall(ISRestoreIndices(perm, &perm_ptr));
246
247 C->ops->solve = MatSolve_SeqSBAIJ_5_inplace;
248 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace;
249 C->assembled = PETSC_TRUE;
250 C->preallocated = PETSC_TRUE;
251
252 PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
253 PetscFunctionReturn(PETSC_SUCCESS);
254 }
255