Actual source code: sbaijfact7.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /* Version for when blocks are 5 by 5 */
6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C, Mat A, const MatFactorInfo *info)
7: {
8: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
9: IS perm = b->row;
10: const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j;
11: PetscInt i, j, *a2anew, 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;
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;
25: PetscCall(PetscMalloc2(25, &dk, 25, &uik));
26: PetscCall(ISGetIndices(perm, &perm_ptr));
28: /* check permutation */
29: if (!a->permute) {
30: ai = a->i;
31: aj = a->j;
32: aa = a->a;
33: } else {
34: ai = a->inew;
35: aj = a->jnew;
36: PetscCall(PetscMalloc1(25 * ai[mbs], &aa));
37: PetscCall(PetscArraycpy(aa, a->a, 25 * ai[mbs]));
38: PetscCall(PetscMalloc1(ai[mbs], &a2anew));
39: PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs]));
41: for (i = 0; i < mbs; i++) {
42: jmin = ai[i];
43: jmax = ai[i + 1];
44: for (j = jmin; j < jmax; j++) {
45: while (a2anew[j] != j) {
46: k = a2anew[j];
47: a2anew[j] = a2anew[k];
48: a2anew[k] = k;
49: for (k1 = 0; k1 < 25; k1++) {
50: dk[k1] = aa[k * 25 + k1];
51: aa[k * 25 + k1] = aa[j * 25 + k1];
52: aa[j * 25 + k1] = dk[k1];
53: }
54: }
55: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
56: if (i > aj[j]) {
57: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
58: ap = aa + j * 25; /* ptr to the beginning of j-th block of aa */
59: for (k = 0; k < 25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
60: for (k = 0; k < 5; k++) { /* j-th block of aa <- dk^T */
61: for (k1 = 0; k1 < 5; k1++) *ap++ = dk[k + 5 * k1];
62: }
63: }
64: }
65: }
66: PetscCall(PetscFree(a2anew));
67: }
69: /* for each row k */
70: for (k = 0; k < mbs; k++) {
71: /*initialize k-th row with elements nonzero in row perm(k) of A */
72: jmin = ai[perm_ptr[k]];
73: jmax = ai[perm_ptr[k] + 1];
74: if (jmin < jmax) {
75: ap = aa + jmin * 25;
76: for (j = jmin; j < jmax; j++) {
77: vj = perm_ptr[aj[j]]; /* block col. index */
78: rtmp_ptr = rtmp + vj * 25;
79: for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++;
80: }
81: }
83: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
84: PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25));
85: i = jl[k]; /* first row to be added to k_th row */
87: while (i < mbs) {
88: nexti = jl[i]; /* next row to be added to k_th row */
90: /* compute multiplier */
91: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
93: /* uik = -inv(Di)*U_bar(i,k) */
94: d = ba + i * 25;
95: u = ba + ili * 25;
97: uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]);
98: uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]);
99: uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]);
100: uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]);
101: uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]);
103: uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]);
104: uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]);
105: uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]);
106: uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]);
107: uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]);
109: uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]);
110: uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]);
111: uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]);
112: uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]);
113: uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]);
115: uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]);
116: uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]);
117: uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]);
118: uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]);
119: uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]);
121: uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]);
122: uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]);
123: uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]);
124: uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]);
125: uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]);
127: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
128: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
129: dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
130: dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
131: dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
132: dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
134: dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
135: dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
136: dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
137: dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
138: dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
140: dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
141: dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
142: dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
143: dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
144: dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
146: dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
147: dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
148: dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
149: dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
150: dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
152: dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
153: dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
154: dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
155: dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
156: dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
158: PetscCall(PetscLogFlops(125.0 * 4.0));
160: /* update -U(i,k) */
161: PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
163: /* add multiple of row i to k-th row ... */
164: jmin = ili + 1;
165: jmax = bi[i + 1];
166: if (jmin < jmax) {
167: for (j = jmin; j < jmax; j++) {
168: /* rtmp += -U(i,k)^T * U_bar(i,j) */
169: rtmp_ptr = rtmp + bj[j] * 25;
170: u = ba + j * 25;
171: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
172: rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
173: rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
174: rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
175: rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];
177: rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
178: rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
179: rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
180: rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
181: rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];
183: rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
184: rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
185: rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
186: rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
187: rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];
189: rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
190: rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
191: rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
192: rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
193: rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];
195: rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
196: rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
197: rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
198: rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
199: rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
200: }
201: PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin)));
203: /* ... add i to row list for next nonzero entry */
204: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
205: j = bj[jmin];
206: jl[i] = jl[j];
207: jl[j] = i; /* update jl */
208: }
209: i = nexti;
210: }
212: /* save nonzero entries in k-th row of U ... */
214: /* invert diagonal block */
215: d = ba + k * 25;
216: PetscCall(PetscArraycpy(d, dk, 25));
217: PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
218: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
220: jmin = bi[k];
221: jmax = bi[k + 1];
222: if (jmin < jmax) {
223: for (j = jmin; j < jmax; j++) {
224: vj = bj[j]; /* block col. index of U */
225: u = ba + j * 25;
226: rtmp_ptr = rtmp + vj * 25;
227: for (k1 = 0; k1 < 25; k1++) {
228: *u++ = *rtmp_ptr;
229: *rtmp_ptr++ = 0.0;
230: }
231: }
233: /* ... add k to row list for first nonzero entry in k-th row */
234: il[k] = jmin;
235: i = bj[jmin];
236: jl[k] = jl[i];
237: jl[i] = k;
238: }
239: }
241: PetscCall(PetscFree(rtmp));
242: PetscCall(PetscFree2(il, jl));
243: PetscCall(PetscFree2(dk, uik));
244: if (a->permute) PetscCall(PetscFree(aa));
246: PetscCall(ISRestoreIndices(perm, &perm_ptr));
248: C->ops->solve = MatSolve_SeqSBAIJ_5_inplace;
249: C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace;
250: C->assembled = PETSC_TRUE;
251: C->preallocated = PETSC_TRUE;
253: PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
254: PetscFunctionReturn(PETSC_SUCCESS);
255: }