Actual source code: sbaijfact6.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /* Version for when blocks are 4 by 4 */
6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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;
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;
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;
26: PetscCall(PetscMalloc2(16, &dk, 16, &uik));
27: PetscCall(ISGetIndices(perm, &perm_ptr));
29: /* check permutation */
30: if (!a->permute) {
31: ai = a->i;
32: aj = a->j;
33: aa = a->a;
34: } else {
35: ai = a->inew;
36: aj = a->jnew;
37: PetscCall(PetscMalloc1(16 * ai[mbs], &aa));
38: PetscCall(PetscArraycpy(aa, a->a, 16 * ai[mbs]));
39: PetscCall(PetscMalloc1(ai[mbs], &a2anew));
40: PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs]));
42: for (i = 0; i < mbs; i++) {
43: jmin = ai[i];
44: jmax = ai[i + 1];
45: for (j = jmin; j < jmax; j++) {
46: while (a2anew[j] != j) {
47: k = a2anew[j];
48: a2anew[j] = a2anew[k];
49: a2anew[k] = k;
50: for (k1 = 0; k1 < 16; k1++) {
51: dk[k1] = aa[k * 16 + k1];
52: aa[k * 16 + k1] = aa[j * 16 + k1];
53: aa[j * 16 + k1] = dk[k1];
54: }
55: }
56: /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
57: if (i > aj[j]) {
58: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
59: ap = aa + j * 16; /* ptr to the beginning of j-th block of aa */
60: for (k = 0; k < 16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
61: for (k = 0; k < 4; k++) { /* j-th block of aa <- dk^T */
62: for (k1 = 0; k1 < 4; k1++) *ap++ = dk[k + 4 * k1];
63: }
64: }
65: }
66: }
67: PetscCall(PetscFree(a2anew));
68: }
70: /* for each row k */
71: for (k = 0; k < mbs; k++) {
72: /*initialize k-th row with elements nonzero in row perm(k) of A */
73: jmin = ai[perm_ptr[k]];
74: jmax = ai[perm_ptr[k] + 1];
75: if (jmin < jmax) {
76: ap = aa + jmin * 16;
77: for (j = jmin; j < jmax; j++) {
78: vj = perm_ptr[aj[j]]; /* block col. index */
79: rtmp_ptr = rtmp + vj * 16;
80: for (i = 0; i < 16; i++) *rtmp_ptr++ = *ap++;
81: }
82: }
84: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
85: PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16));
86: i = jl[k]; /* first row to be added to k_th row */
88: while (i < mbs) {
89: nexti = jl[i]; /* next row to be added to k_th row */
91: /* compute multiplier */
92: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
94: /* uik = -inv(Di)*U_bar(i,k) */
95: diag = ba + i * 16;
96: u = ba + ili * 16;
98: uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
99: uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
100: uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
101: uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);
103: uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
104: uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
105: uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
106: uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);
108: uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
109: uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
110: uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
111: uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);
113: uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
114: uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
115: uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
116: uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);
118: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
119: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
120: dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
121: dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
122: dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
124: dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
125: dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
126: dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
127: dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
129: dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
130: dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
131: dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
132: dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
134: dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
135: dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
136: dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
137: dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
139: PetscCall(PetscLogFlops(64.0 * 4.0));
141: /* update -U(i,k) */
142: PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));
144: /* add multiple of row i to k-th row ... */
145: jmin = ili + 1;
146: jmax = bi[i + 1];
147: if (jmin < jmax) {
148: for (j = jmin; j < jmax; j++) {
149: /* rtmp += -U(i,k)^T * U_bar(i,j) */
150: rtmp_ptr = rtmp + bj[j] * 16;
151: u = ba + j * 16;
152: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
153: rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
154: rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
155: rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
157: rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
158: rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
159: rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
160: rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
162: rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
163: rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
164: rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
165: rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
167: rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
168: rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
169: rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
170: rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
171: }
172: PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));
174: /* ... add i to row list for next nonzero entry */
175: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
176: j = bj[jmin];
177: jl[i] = jl[j];
178: jl[j] = i; /* update jl */
179: }
180: i = nexti;
181: }
183: /* save nonzero entries in k-th row of U ... */
185: /* invert diagonal block */
186: diag = ba + k * 16;
187: PetscCall(PetscArraycpy(diag, dk, 16));
189: if (pivotinblocks) {
190: PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
191: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
192: } else {
193: PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
194: }
196: jmin = bi[k];
197: jmax = bi[k + 1];
198: if (jmin < jmax) {
199: for (j = jmin; j < jmax; j++) {
200: vj = bj[j]; /* block col. index of U */
201: u = ba + j * 16;
202: rtmp_ptr = rtmp + vj * 16;
203: for (k1 = 0; k1 < 16; k1++) {
204: *u++ = *rtmp_ptr;
205: *rtmp_ptr++ = 0.0;
206: }
207: }
209: /* ... add k to row list for first nonzero entry in k-th row */
210: il[k] = jmin;
211: i = bj[jmin];
212: jl[k] = jl[i];
213: jl[i] = k;
214: }
215: }
217: PetscCall(PetscFree(rtmp));
218: PetscCall(PetscFree2(il, jl));
219: PetscCall(PetscFree2(dk, uik));
220: if (a->permute) PetscCall(PetscFree(aa));
222: PetscCall(ISRestoreIndices(perm, &perm_ptr));
224: C->ops->solve = MatSolve_SeqSBAIJ_4_inplace;
225: C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
226: C->assembled = PETSC_TRUE;
227: C->preallocated = PETSC_TRUE;
229: PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
230: PetscFunctionReturn(PETSC_SUCCESS);
231: }