Actual source code: dgefa3.c
2: /*
3: Inverts 3 by 3 matrix using gaussian elimination with partial pivoting.
5: Used by the sparse factorization routines in
6: src/mat/impls/baij/seq
8: This is a combination of the Linpack routines
9: dgefa() and dgedi() specialized for a size of 3.
11: */
12: #include <petscsys.h>
14: PETSC_EXTERN 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: if (allowzeropivot) {
51: PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
52: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
53: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
54: } else {
55: /* Shift is applied to single diagonal entry */
56: a[l + k3] = shift;
57: }
58: }
60: /* interchange if necessary */
61: if (l != k) {
62: stmp = a[l + k3];
63: a[l + k3] = a[k4];
64: a[k4] = stmp;
65: }
67: /* compute multipliers */
68: stmp = -1. / a[k4];
69: i__2 = 3 - k;
70: aa = &a[1 + k4];
71: for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
73: /* row elimination with column indexing */
74: ax = &a[k4 + 1];
75: for (j = kp1; j <= 3; ++j) {
76: j3 = 3 * j;
77: stmp = a[l + j3];
78: if (l != k) {
79: a[l + j3] = a[k + j3];
80: a[k + j3] = stmp;
81: }
83: i__3 = 3 - k;
84: ay = &a[1 + k + j3];
85: for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
86: }
87: }
88: ipvt[2] = 3;
89: if (a[12] == 0.0) {
90: if (PetscLikely(allowzeropivot)) {
91: PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n"));
92: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
93: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 2");
94: }
96: /* Now form the inverse */
97: /* compute inverse(u) */
98: for (k = 1; k <= 3; ++k) {
99: k3 = 3 * k;
100: k4 = k3 + k;
101: a[k4] = 1.0 / a[k4];
102: stmp = -a[k4];
103: i__2 = k - 1;
104: aa = &a[k3 + 1];
105: for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
106: kp1 = k + 1;
107: if (3 < kp1) continue;
108: ax = aa;
109: for (j = kp1; j <= 3; ++j) {
110: j3 = 3 * j;
111: stmp = a[k + j3];
112: a[k + j3] = 0.0;
113: ay = &a[j3 + 1];
114: for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
115: }
116: }
118: /* form inverse(u)*inverse(l) */
119: for (kb = 1; kb <= 2; ++kb) {
120: k = 3 - kb;
121: k3 = 3 * k;
122: kp1 = k + 1;
123: aa = a + k3;
124: for (i = kp1; i <= 3; ++i) {
125: work[i - 1] = aa[i];
126: aa[i] = 0.0;
127: }
128: for (j = kp1; j <= 3; ++j) {
129: stmp = work[j - 1];
130: ax = &a[3 * j + 1];
131: ay = &a[k3 + 1];
132: ay[0] += stmp * ax[0];
133: ay[1] += stmp * ax[1];
134: ay[2] += stmp * ax[2];
135: }
136: l = ipvt[k - 1];
137: if (l != k) {
138: ax = &a[k3 + 1];
139: ay = &a[3 * l + 1];
140: stmp = ax[0];
141: ax[0] = ay[0];
142: ay[0] = stmp;
143: stmp = ax[1];
144: ax[1] = ay[1];
145: ay[1] = stmp;
146: stmp = ax[2];
147: ax[2] = ay[2];
148: ay[2] = stmp;
149: }
150: }
151: PetscFunctionReturn(PETSC_SUCCESS);
152: }