Actual source code: sbaijfact6.c
1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: /* Version for when blocks are 4 by 4 */
5: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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;
11: MatScalar *ba = b->a, *aa, *ap, *dk, *uik;
12: MatScalar *u, *diag, *rtmp, *rtmp_ptr;
13: PetscBool pivotinblocks = b->pivotinblocks;
14: PetscReal shift = info->shiftamount;
15: PetscBool allowzeropivot, zeropivotdetected = PETSC_FALSE;
17: PetscFunctionBegin;
18: /* initialization */
19: allowzeropivot = PetscNot(A->erroriffailure);
20: PetscCall(PetscCalloc1(16 * 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(16, &dk, 16, &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(16 * ai[mbs], &aa));
37: PetscCall(PetscArraycpy(aa, a->a, 16 * 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 < 16; k1++) {
50: dk[k1] = aa[k * 16 + k1];
51: aa[k * 16 + k1] = aa[j * 16 + k1];
52: aa[j * 16 + k1] = dk[k1];
53: }
54: }
55: /* transform column-oriented blocks that lie in the lower triangle to row-oriented blocks */
56: if (i > aj[j]) {
57: /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
58: ap = aa + j * 16; /* ptr to the beginning of j-th block of aa */
59: for (k = 0; k < 16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
60: for (k = 0; k < 4; k++) { /* j-th block of aa <- dk^T */
61: for (k1 = 0; k1 < 4; k1++) *ap++ = dk[k + 4 * 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 * 16;
76: for (j = jmin; j < jmax; j++) {
77: vj = perm_ptr[aj[j]]; /* block col. index */
78: rtmp_ptr = rtmp + vj * 16;
79: for (i = 0; i < 16; 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 * 16, 16));
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: diag = ba + i * 16;
95: u = ba + ili * 16;
97: uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
98: uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
99: uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
100: uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);
102: uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
103: uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
104: uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
105: uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);
107: uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
108: uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
109: uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
110: uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);
112: uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
113: uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
114: uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
115: uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);
117: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
118: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
119: dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
120: dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
121: dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
123: dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
124: dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
125: dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
126: dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
128: dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
129: dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
130: dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
131: dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
133: dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
134: dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
135: dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
136: dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
138: PetscCall(PetscLogFlops(64.0 * 4.0));
140: /* update -U(i,k) */
141: PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));
143: /* add multiple of row i to k-th row ... */
144: jmin = ili + 1;
145: jmax = bi[i + 1];
146: if (jmin < jmax) {
147: for (j = jmin; j < jmax; j++) {
148: /* rtmp += -U(i,k)^T * U_bar(i,j) */
149: rtmp_ptr = rtmp + bj[j] * 16;
150: u = ba + j * 16;
151: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
152: rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
153: rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
154: rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
156: rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
157: rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
158: rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
159: rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
161: rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
162: rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
163: rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
164: rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
166: rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
167: rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
168: rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
169: rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
170: }
171: PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));
173: /* ... add i to row list for next nonzero entry */
174: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
175: j = bj[jmin];
176: jl[i] = jl[j];
177: jl[j] = i; /* update jl */
178: }
179: i = nexti;
180: }
182: /* save nonzero entries in k-th row of U ... */
184: /* invert diagonal block */
185: diag = ba + k * 16;
186: PetscCall(PetscArraycpy(diag, dk, 16));
188: if (pivotinblocks) {
189: PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
190: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
191: } else {
192: PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
193: }
195: jmin = bi[k];
196: jmax = bi[k + 1];
197: if (jmin < jmax) {
198: for (j = jmin; j < jmax; j++) {
199: vj = bj[j]; /* block col. index of U */
200: u = ba + j * 16;
201: rtmp_ptr = rtmp + vj * 16;
202: for (k1 = 0; k1 < 16; k1++) {
203: *u++ = *rtmp_ptr;
204: *rtmp_ptr++ = 0.0;
205: }
206: }
208: /* ... add k to row list for first nonzero entry in k-th row */
209: il[k] = jmin;
210: i = bj[jmin];
211: jl[k] = jl[i];
212: jl[i] = k;
213: }
214: }
216: PetscCall(PetscFree(rtmp));
217: PetscCall(PetscFree2(il, jl));
218: PetscCall(PetscFree2(dk, uik));
219: if (a->permute) PetscCall(PetscFree(aa));
221: PetscCall(ISRestoreIndices(perm, &perm_ptr));
223: C->ops->solve = MatSolve_SeqSBAIJ_4_inplace;
224: C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
225: C->assembled = PETSC_TRUE;
226: C->preallocated = PETSC_TRUE;
228: PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
229: PetscFunctionReturn(PETSC_SUCCESS);
230: }