Actual source code: dgefa3.c
1: /*
2: Inverts 3 by 3 matrix using gaussian elimination with partial pivoting.
4: Used by the sparse factorization routines in
5: src/mat/impls/baij/seq
7: This is a combination of the Linpack routines
8: dgefa() and dgedi() specialized for a size of 3.
10: */
11: #include <petscsys.h>
12: #include <petsc/private/kernels/blockinvert.h>
14: PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
15: {
16: PetscInt i__2, i__3, kp1, j, k, l, ll, i, ipvt[3], kb, k3;
17: PetscInt k4, j3;
18: MatScalar *aa, *ax, *ay, work[9], stmp;
19: MatReal tmp, max;
21: PetscFunctionBegin;
22: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
23: shift = .333 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8]));
25: /* Parameter adjustments */
26: a -= 4;
28: for (k = 1; k <= 2; ++k) {
29: kp1 = k + 1;
30: k3 = 3 * k;
31: k4 = k3 + k;
33: /* find l = pivot index */
34: i__2 = 4 - k;
35: aa = &a[k4];
36: max = PetscAbsScalar(aa[0]);
37: l = 1;
38: for (ll = 1; ll < i__2; ll++) {
39: tmp = PetscAbsScalar(aa[ll]);
40: if (tmp > max) {
41: max = tmp;
42: l = ll + 1;
43: }
44: }
45: l += k - 1;
46: ipvt[k - 1] = l;
48: if (a[l + k3] == 0.0) {
49: if (shift == 0.0) {
50: PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
51: PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
52: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
53: } else {
54: /* Shift is applied to single diagonal entry */
55: a[l + k3] = shift;
56: }
57: }
59: /* interchange if necessary */
60: if (l != k) {
61: stmp = a[l + k3];
62: a[l + k3] = a[k4];
63: a[k4] = stmp;
64: }
66: /* compute multipliers */
67: stmp = -1. / a[k4];
68: i__2 = 3 - k;
69: aa = &a[1 + k4];
70: for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
72: /* row elimination with column indexing */
73: ax = &a[k4 + 1];
74: for (j = kp1; j <= 3; ++j) {
75: j3 = 3 * j;
76: stmp = a[l + j3];
77: if (l != k) {
78: a[l + j3] = a[k + j3];
79: a[k + j3] = stmp;
80: }
82: i__3 = 3 - k;
83: ay = &a[1 + k + j3];
84: for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
85: }
86: }
87: ipvt[2] = 3;
88: if (a[12] == 0.0) {
89: PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 2");
90: PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n"));
91: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
92: }
94: /* Now form the inverse */
95: /* compute inverse(u) */
96: for (k = 1; k <= 3; ++k) {
97: k3 = 3 * k;
98: k4 = k3 + k;
99: a[k4] = 1.0 / a[k4];
100: stmp = -a[k4];
101: i__2 = k - 1;
102: aa = &a[k3 + 1];
103: for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
104: kp1 = k + 1;
105: if (3 < kp1) continue;
106: ax = aa;
107: for (j = kp1; j <= 3; ++j) {
108: j3 = 3 * j;
109: stmp = a[k + j3];
110: a[k + j3] = 0.0;
111: ay = &a[j3 + 1];
112: for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
113: }
114: }
116: /* form inverse(u)*inverse(l) */
117: for (kb = 1; kb <= 2; ++kb) {
118: k = 3 - kb;
119: k3 = 3 * k;
120: kp1 = k + 1;
121: aa = a + k3;
122: for (i = kp1; i <= 3; ++i) {
123: work[i - 1] = aa[i];
124: aa[i] = 0.0;
125: }
126: for (j = kp1; j <= 3; ++j) {
127: stmp = work[j - 1];
128: ax = &a[3 * j + 1];
129: ay = &a[k3 + 1];
130: ay[0] += stmp * ax[0];
131: ay[1] += stmp * ax[1];
132: ay[2] += stmp * ax[2];
133: }
134: l = ipvt[k - 1];
135: if (l != k) {
136: ax = &a[k3 + 1];
137: ay = &a[3 * l + 1];
138: stmp = ax[0];
139: ax[0] = ay[0];
140: ay[0] = stmp;
141: stmp = ax[1];
142: ax[1] = ay[1];
143: ay[1] = stmp;
144: stmp = ax[2];
145: ax[2] = ay[2];
146: ay[2] = stmp;
147: }
148: }
149: PetscFunctionReturn(PETSC_SUCCESS);
150: }