1 #include <../src/mat/impls/sbaij/seq/sbaij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
4 /*
5 Version for when blocks are 4 by 4 Using natural ordering
6 */
MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C,Mat A,const MatFactorInfo * info)7 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_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 PetscBool pivotinblocks = b->pivotinblocks;
15 PetscReal shift = info->shiftamount;
16 PetscBool allowzeropivot, zeropivotdetected = PETSC_FALSE;
17
18 PetscFunctionBegin;
19 /* initialization */
20 allowzeropivot = PetscNot(A->erroriffailure);
21 PetscCall(PetscCalloc1(16 * 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(16, &dk, 16, &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 * 16;
38 for (j = jmin; j < jmax; j++) {
39 vj = aj[j]; /* block col. index */
40 rtmp_ptr = rtmp + vj * 16;
41 for (i = 0; i < 16; 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 * 16, 16));
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 diag = ba + i * 16;
57 u = ba + ili * 16;
58
59 uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
60 uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
61 uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
62 uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);
63
64 uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
65 uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
66 uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
67 uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);
68
69 uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
70 uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
71 uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
72 uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);
73
74 uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
75 uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
76 uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
77 uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);
78
79 /* update D(k) += -U(i,k)^T * U_bar(i,k) */
80 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
81 dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
82 dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
83 dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
84
85 dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
86 dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
87 dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
88 dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
89
90 dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
91 dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
92 dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
93 dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
94
95 dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
96 dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
97 dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
98 dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
99
100 PetscCall(PetscLogFlops(64.0 * 4.0));
101
102 /* update -U(i,k) */
103 PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));
104
105 /* add multiple of row i to k-th row ... */
106 jmin = ili + 1;
107 jmax = bi[i + 1];
108 if (jmin < jmax) {
109 for (j = jmin; j < jmax; j++) {
110 /* rtmp += -U(i,k)^T * U_bar(i,j) */
111 rtmp_ptr = rtmp + bj[j] * 16;
112 u = ba + j * 16;
113 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
114 rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
115 rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
116 rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
117
118 rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
119 rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
120 rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
121 rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
122
123 rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
124 rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
125 rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
126 rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
127
128 rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
129 rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
130 rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
131 rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
132 }
133 PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));
134
135 /* ... add i to row list for next nonzero entry */
136 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
137 j = bj[jmin];
138 jl[i] = jl[j];
139 jl[j] = i; /* update jl */
140 }
141 i = nexti;
142 }
143
144 /* save nonzero entries in k-th row of U ... */
145
146 /* invert diagonal block */
147 diag = ba + k * 16;
148 PetscCall(PetscArraycpy(diag, dk, 16));
149 if (pivotinblocks) {
150 PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
151 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
152 } else {
153 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
154 }
155
156 jmin = bi[k];
157 jmax = bi[k + 1];
158 if (jmin < jmax) {
159 for (j = jmin; j < jmax; j++) {
160 vj = bj[j]; /* block col. index of U */
161 u = ba + j * 16;
162 rtmp_ptr = rtmp + vj * 16;
163 for (k1 = 0; k1 < 16; k1++) {
164 *u++ = *rtmp_ptr;
165 *rtmp_ptr++ = 0.0;
166 }
167 }
168
169 /* ... add k to row list for first nonzero entry in k-th row */
170 il[k] = jmin;
171 i = bj[jmin];
172 jl[k] = jl[i];
173 jl[i] = k;
174 }
175 }
176
177 PetscCall(PetscFree(rtmp));
178 PetscCall(PetscFree2(il, jl));
179 PetscCall(PetscFree2(dk, uik));
180
181 C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
182 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
183 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
184 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
185
186 C->assembled = PETSC_TRUE;
187 C->preallocated = PETSC_TRUE;
188
189 PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
190 PetscFunctionReturn(PETSC_SUCCESS);
191 }
192