Actual source code: sbaijfact7.c
1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: /* Version for when blocks are 5 by 5 */
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;
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;
24: PetscCall(PetscMalloc2(25, &dk, 25, &uik));
25: PetscCall(ISGetIndices(perm, &perm_ptr));
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]));
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: }
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: }
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 */
86: while (i < mbs) {
87: nexti = jl[i]; /* next row to be added to k_th row */
89: /* compute multiplier */
90: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
92: /* uik = -inv(Di)*U_bar(i,k) */
93: d = ba + i * 25;
94: u = ba + ili * 25;
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]);
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]);
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]);
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]);
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]);
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];
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];
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];
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];
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];
157: PetscCall(PetscLogFlops(125.0 * 4.0));
159: /* update -U(i,k) */
160: PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));
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];
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];
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];
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];
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)));
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: }
211: /* save nonzero entries in k-th row of U ... */
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;
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: }
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: }
240: PetscCall(PetscFree(rtmp));
241: PetscCall(PetscFree2(il, jl));
242: PetscCall(PetscFree2(dk, uik));
243: if (a->permute) PetscCall(PetscFree(aa));
245: PetscCall(ISRestoreIndices(perm, &perm_ptr));
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;
252: PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
253: PetscFunctionReturn(PETSC_SUCCESS);
254: }