Actual source code: sbaijfact5.c
1: #include <../src/mat/impls/sbaij/seq/sbaij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: /*
5: Version for when blocks are 4 by 4 Using natural ordering
6: */
7: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
8: {
9: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
10: PetscInt i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
11: PetscInt *ai, *aj, 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: 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 * 16;
38: for (j = jmin; j < jmax; j++) {
39: vj = aj[j]; /* block col. index */
40: rtmp_ptr = rtmp + vj * 16;
41: for (i = 0; i < 16; 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 * 16, 16));
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: diag = ba + i * 16;
57: u = ba + ili * 16;
59: uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
60: uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
61: uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
62: uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);
64: uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
65: uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
66: uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
67: uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);
69: uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
70: uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
71: uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
72: uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);
74: uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
75: uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
76: uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
77: uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);
79: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
80: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
81: dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
82: dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
83: dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
85: dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
86: dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
87: dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
88: dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
90: dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
91: dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
92: dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
93: dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
95: dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
96: dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
97: dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
98: dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
100: PetscCall(PetscLogFlops(64.0 * 4.0));
102: /* update -U(i,k) */
103: PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));
105: /* add multiple of row i to k-th row ... */
106: jmin = ili + 1;
107: jmax = bi[i + 1];
108: if (jmin < jmax) {
109: for (j = jmin; j < jmax; j++) {
110: /* rtmp += -U(i,k)^T * U_bar(i,j) */
111: rtmp_ptr = rtmp + bj[j] * 16;
112: u = ba + j * 16;
113: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
114: rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
115: rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
116: rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
118: rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
119: rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
120: rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
121: rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
123: rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
124: rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
125: rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
126: rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
128: rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
129: rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
130: rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
131: rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
132: }
133: PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));
135: /* ... add i to row list for next nonzero entry */
136: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
137: j = bj[jmin];
138: jl[i] = jl[j];
139: jl[j] = i; /* update jl */
140: }
141: i = nexti;
142: }
144: /* save nonzero entries in k-th row of U ... */
146: /* invert diagonal block */
147: diag = ba + k * 16;
148: PetscCall(PetscArraycpy(diag, dk, 16));
149: if (pivotinblocks) {
150: PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
151: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
152: } else {
153: PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
154: }
156: jmin = bi[k];
157: jmax = bi[k + 1];
158: if (jmin < jmax) {
159: for (j = jmin; j < jmax; j++) {
160: vj = bj[j]; /* block col. index of U */
161: u = ba + j * 16;
162: rtmp_ptr = rtmp + vj * 16;
163: for (k1 = 0; k1 < 16; k1++) {
164: *u++ = *rtmp_ptr;
165: *rtmp_ptr++ = 0.0;
166: }
167: }
169: /* ... add k to row list for first nonzero entry in k-th row */
170: il[k] = jmin;
171: i = bj[jmin];
172: jl[k] = jl[i];
173: jl[i] = k;
174: }
175: }
177: PetscCall(PetscFree(rtmp));
178: PetscCall(PetscFree2(il, jl));
179: PetscCall(PetscFree2(dk, uik));
181: C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
182: C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
183: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
184: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
186: C->assembled = PETSC_TRUE;
187: C->preallocated = PETSC_TRUE;
189: PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }