Actual source code: sbaijfact5.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /*
6: Version for when blocks are 4 by 4 Using natural ordering
7: */
8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
9: {
10: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
11: PetscInt i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
12: PetscInt *ai, *aj, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
13: MatScalar *ba = b->a, *aa, *ap, *dk, *uik;
14: MatScalar *u, *diag, *rtmp, *rtmp_ptr;
15: PetscBool pivotinblocks = b->pivotinblocks;
16: PetscReal shift = info->shiftamount;
17: PetscBool allowzeropivot, zeropivotdetected = PETSC_FALSE;
19: PetscFunctionBegin;
20: /* initialization */
21: allowzeropivot = PetscNot(A->erroriffailure);
22: PetscCall(PetscCalloc1(16 * mbs, &rtmp));
23: PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
24: il[0] = 0;
25: for (i = 0; i < mbs; i++) jl[i] = mbs;
27: PetscCall(PetscMalloc2(16, &dk, 16, &uik));
28: ai = a->i;
29: aj = a->j;
30: aa = a->a;
32: /* for each row k */
33: for (k = 0; k < mbs; k++) {
34: /*initialize k-th row with elements nonzero in row k of A */
35: jmin = ai[k];
36: jmax = ai[k + 1];
37: if (jmin < jmax) {
38: ap = aa + jmin * 16;
39: for (j = jmin; j < jmax; j++) {
40: vj = aj[j]; /* block col. index */
41: rtmp_ptr = rtmp + vj * 16;
42: for (i = 0; i < 16; i++) *rtmp_ptr++ = *ap++;
43: }
44: }
46: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
47: PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16));
48: i = jl[k]; /* first row to be added to k_th row */
50: while (i < mbs) {
51: nexti = jl[i]; /* next row to be added to k_th row */
53: /* compute multiplier */
54: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
56: /* uik = -inv(Di)*U_bar(i,k) */
57: diag = ba + i * 16;
58: u = ba + ili * 16;
60: uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]);
61: uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]);
62: uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]);
63: uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]);
65: uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]);
66: uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]);
67: uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]);
68: uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]);
70: uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]);
71: uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]);
72: uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]);
73: uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]);
75: uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]);
76: uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]);
77: uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]);
78: uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]);
80: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
81: dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
82: dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
83: dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
84: dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
86: dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
87: dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
88: dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
89: dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
91: dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
92: dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
93: dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
94: dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
96: dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
97: dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
98: dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
99: dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
101: PetscCall(PetscLogFlops(64.0 * 4.0));
103: /* update -U(i,k) */
104: PetscCall(PetscArraycpy(ba + ili * 16, uik, 16));
106: /* add multiple of row i to k-th row ... */
107: jmin = ili + 1;
108: jmax = bi[i + 1];
109: if (jmin < jmax) {
110: for (j = jmin; j < jmax; j++) {
111: /* rtmp += -U(i,k)^T * U_bar(i,j) */
112: rtmp_ptr = rtmp + bj[j] * 16;
113: u = ba + j * 16;
114: rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3];
115: rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3];
116: rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3];
117: rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3];
119: rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7];
120: rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7];
121: rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7];
122: rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7];
124: rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11];
125: rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11];
126: rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11];
127: rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11];
129: rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15];
130: rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15];
131: rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15];
132: rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15];
133: }
134: PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin)));
136: /* ... add i to row list for next nonzero entry */
137: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
138: j = bj[jmin];
139: jl[i] = jl[j];
140: jl[j] = i; /* update jl */
141: }
142: i = nexti;
143: }
145: /* save nonzero entries in k-th row of U ... */
147: /* invert diagonal block */
148: diag = ba + k * 16;
149: PetscCall(PetscArraycpy(diag, dk, 16));
150: if (pivotinblocks) {
151: PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
152: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
153: } else {
154: PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag));
155: }
157: jmin = bi[k];
158: jmax = bi[k + 1];
159: if (jmin < jmax) {
160: for (j = jmin; j < jmax; j++) {
161: vj = bj[j]; /* block col. index of U */
162: u = ba + j * 16;
163: rtmp_ptr = rtmp + vj * 16;
164: for (k1 = 0; k1 < 16; k1++) {
165: *u++ = *rtmp_ptr;
166: *rtmp_ptr++ = 0.0;
167: }
168: }
170: /* ... add k to row list for first nonzero entry in k-th row */
171: il[k] = jmin;
172: i = bj[jmin];
173: jl[k] = jl[i];
174: jl[i] = k;
175: }
176: }
178: PetscCall(PetscFree(rtmp));
179: PetscCall(PetscFree2(il, jl));
180: PetscCall(PetscFree2(dk, uik));
182: C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
183: C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
184: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
185: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
187: C->assembled = PETSC_TRUE;
188: C->preallocated = PETSC_TRUE;
190: PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */
191: PetscFunctionReturn(PETSC_SUCCESS);
192: }