xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact8.c (revision 6c2b77d522d8aa5c8b27f04fddd7150d0d6755fb)
1 
2 #include <../src/mat/impls/sbaij/seq/sbaij.h>
3 #include <petsc/private/kernels/blockinvert.h>
4 
5 /*
6       Version for when blocks are 5 by 5 Using natural ordering
7 */
8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_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, ipvt[5];
13   MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
14   MatScalar    *u, *d, *rtmp, *rtmp_ptr, work[25];
15   PetscReal     shift = info->shiftamount;
16   PetscBool     allowzeropivot, zeropivotdetected;
17 
18   PetscFunctionBegin;
19   /* initialization */
20   allowzeropivot = PetscNot(A->erroriffailure);
21   PetscCall(PetscCalloc1(25 * mbs, &rtmp));
22   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
23   il[0] = 0;
24   for (i = 0; i < mbs; i++) jl[i] = mbs;
25 
26   PetscCall(PetscMalloc2(25, &dk, 25, &uik));
27   ai = a->i;
28   aj = a->j;
29   aa = a->a;
30 
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 * 25;
38       for (j = jmin; j < jmax; j++) {
39         vj       = aj[j]; /* block col. index */
40         rtmp_ptr = rtmp + vj * 25;
41         for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++;
42       }
43     }
44 
45     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
46     PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25));
47     i = jl[k]; /* first row to be added to k_th row  */
48 
49     while (i < mbs) {
50       nexti = jl[i]; /* next row to be added to k_th row */
51 
52       /* compute multiplier */
53       ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
54 
55       /* uik = -inv(Di)*U_bar(i,k) */
56       d = ba + i * 25;
57       u = ba + ili * 25;
58 
59       uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]);
60       uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]);
61       uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]);
62       uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]);
63       uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]);
64 
65       uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]);
66       uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]);
67       uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]);
68       uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]);
69       uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]);
70 
71       uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]);
72       uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]);
73       uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]);
74       uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]);
75       uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]);
76 
77       uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]);
78       uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]);
79       uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]);
80       uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]);
81       uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]);
82 
83       uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]);
84       uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]);
85       uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]);
86       uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]);
87       uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]);
88 
89       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
90       dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
91       dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
92       dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
93       dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
94       dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
95 
96       dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
97       dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
98       dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
99       dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
100       dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
101 
102       dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
103       dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
104       dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
105       dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
106       dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
107 
108       dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
109       dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
110       dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
111       dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
112       dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
113 
114       dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
115       dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
116       dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
117       dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
118       dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
119 
120       PetscCall(PetscLogFlops(125.0 * 4.0));
121 
122       /* update -U(i,k) */
123       PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
124 
125       /* add multiple of row i to k-th row ... */
126       jmin = ili + 1;
127       jmax = bi[i + 1];
128       if (jmin < jmax) {
129         for (j = jmin; j < jmax; j++) {
130           /* rtmp += -U(i,k)^T * U_bar(i,j) */
131           rtmp_ptr = rtmp + bj[j] * 25;
132           u        = ba + j * 25;
133           rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
134           rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
135           rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
136           rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
137           rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
138 
139           rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
140           rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
141           rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
142           rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
143           rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
144 
145           rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
146           rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
147           rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
148           rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
149           rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
150 
151           rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
152           rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
153           rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
154           rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
155           rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
156 
157           rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
158           rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
159           rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
160           rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
161           rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
162         }
163         PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin)));
164 
165         /* ... add i to row list for next nonzero entry */
166         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
167         j     = bj[jmin];
168         jl[i] = jl[j];
169         jl[j] = i; /* update jl */
170       }
171       i = nexti;
172     }
173 
174     /* save nonzero entries in k-th row of U ... */
175 
176     /* invert diagonal block */
177     d = ba + k * 25;
178     PetscCall(PetscArraycpy(d, dk, 25));
179     PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
180     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
181 
182     jmin = bi[k];
183     jmax = bi[k + 1];
184     if (jmin < jmax) {
185       for (j = jmin; j < jmax; j++) {
186         vj       = bj[j]; /* block col. index of U */
187         u        = ba + j * 25;
188         rtmp_ptr = rtmp + vj * 25;
189         for (k1 = 0; k1 < 25; k1++) {
190           *u++        = *rtmp_ptr;
191           *rtmp_ptr++ = 0.0;
192         }
193       }
194 
195       /* ... add k to row list for first nonzero entry in k-th row */
196       il[k] = jmin;
197       i     = bj[jmin];
198       jl[k] = jl[i];
199       jl[i] = k;
200     }
201   }
202 
203   PetscCall(PetscFree(rtmp));
204   PetscCall(PetscFree2(il, jl));
205   PetscCall(PetscFree2(dk, uik));
206 
207   C->ops->solve          = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
208   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
209   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
210   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
211   C->assembled           = PETSC_TRUE;
212   C->preallocated        = PETSC_TRUE;
213 
214   PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
215   PetscFunctionReturn(0);
216 }
217