Actual source code: dgefa7.c
2: /*
3: Inverts 7 by 7 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 7.
11: */
12: #include <petscsys.h>
14: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_7(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
15: {
16: PetscInt i__2, i__3, kp1, j, k, l, ll, i, ipvt[7], kb, k3;
17: PetscInt k4, j3;
18: MatScalar *aa, *ax, *ay, work[49], stmp;
19: MatReal tmp, max;
21: PetscFunctionBegin;
22: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
23: shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[8]) + PetscAbsScalar(a[16]) + PetscAbsScalar(a[24]) + PetscAbsScalar(a[32]) + PetscAbsScalar(a[40]) + PetscAbsScalar(a[48]));
25: /* Parameter adjustments */
26: a -= 8;
28: for (k = 1; k <= 6; ++k) {
29: kp1 = k + 1;
30: k3 = 7 * k;
31: k4 = k3 + k;
33: /* find l = pivot index */
34: i__2 = 8 - 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; does this make any sense? */
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 = 7 - 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 <= 7; ++j) {
76: j3 = 7 * 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 = 7 - k;
84: ay = &a[1 + k + j3];
85: for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
86: }
87: }
88: ipvt[6] = 7;
89: if (a[56] == 0.0) {
90: if (PetscLikely(allowzeropivot)) {
91: PetscCall(PetscInfo(NULL, "Zero pivot, row 6\n"));
92: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
93: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 6");
94: }
96: /* Now form the inverse */
97: /* compute inverse(u) */
98: for (k = 1; k <= 7; ++k) {
99: k3 = 7 * 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 (7 < kp1) continue;
108: ax = aa;
109: for (j = kp1; j <= 7; ++j) {
110: j3 = 7 * 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 <= 6; ++kb) {
120: k = 7 - kb;
121: k3 = 7 * k;
122: kp1 = k + 1;
123: aa = a + k3;
124: for (i = kp1; i <= 7; ++i) {
125: work[i - 1] = aa[i];
126: aa[i] = 0.0;
127: }
128: for (j = kp1; j <= 7; ++j) {
129: stmp = work[j - 1];
130: ax = &a[7 * 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: ay[3] += stmp * ax[3];
136: ay[4] += stmp * ax[4];
137: ay[5] += stmp * ax[5];
138: ay[6] += stmp * ax[6];
139: }
140: l = ipvt[k - 1];
141: if (l != k) {
142: ax = &a[k3 + 1];
143: ay = &a[7 * l + 1];
144: stmp = ax[0];
145: ax[0] = ay[0];
146: ay[0] = stmp;
147: stmp = ax[1];
148: ax[1] = ay[1];
149: ay[1] = stmp;
150: stmp = ax[2];
151: ax[2] = ay[2];
152: ay[2] = stmp;
153: stmp = ax[3];
154: ax[3] = ay[3];
155: ay[3] = stmp;
156: stmp = ax[4];
157: ax[4] = ay[4];
158: ay[4] = stmp;
159: stmp = ax[5];
160: ax[5] = ay[5];
161: ay[5] = stmp;
162: stmp = ax[6];
163: ax[6] = ay[6];
164: ay[6] = stmp;
165: }
166: }
167: PetscFunctionReturn(PETSC_SUCCESS);
168: }