Actual source code: sbaijfact8.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
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;
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;
26: PetscCall(PetscMalloc2(25, &dk, 25, &uik));
27: ai = a->i;
28: aj = a->j;
29: aa = a->a;
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: }
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 */
49: while (i < mbs) {
50: nexti = jl[i]; /* next row to be added to k_th row */
52: /* compute multiplier */
53: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
55: /* uik = -inv(Di)*U_bar(i,k) */
56: d = ba + i * 25;
57: u = ba + ili * 25;
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]);
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]);
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]);
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]);
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]);
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];
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];
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];
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];
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];
120: PetscCall(PetscLogFlops(125.0 * 4.0));
122: /* update -U(i,k) */
123: PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
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];
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];
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];
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];
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)));
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: }
174: /* save nonzero entries in k-th row of U ... */
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;
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: }
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: }
203: PetscCall(PetscFree(rtmp));
204: PetscCall(PetscFree2(il, jl));
205: PetscCall(PetscFree2(dk, uik));
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;
214: PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
215: PetscFunctionReturn(PETSC_SUCCESS);
216: }