Actual source code: dgefa3.c
1: /*$Id: dgefa3.c,v 1.22 2001/04/07 15:45:14 bsmith Exp $*/
2: /*
3: Inverts 3 by 3 matrix using partial pivoting.
5: Used by the sparse factorization routines in
6: src/mat/impls/baij/seq and src/mat/impls/bdiag/seq
8: See also src/inline/ilu.h
10: This is a combination of the Linpack routines
11: dgefa() and dgedi() specialized for a size of 3.
13: */
14: #include petsc.h
16: int Kernel_A_gets_inverse_A_3(MatScalar *a)
17: {
18: int i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
19: int k4,j3;
20: MatScalar *aa,*ax,*ay,work[9],stmp;
21: MatReal tmp,max;
23: /* gaussian elimination with partial pivoting */
26: /* Parameter adjustments */
27: a -= 4;
29: for (k = 1; k <= 2; ++k) {
30: kp1 = k + 1;
31: k3 = 3*k;
32: k4 = k3 + k;
33: /* find l = pivot index */
35: i__2 = 4 - k;
36: aa = &a[k4];
37: max = PetscAbsScalar(aa[0]);
38: l = 1;
39: for (ll=1; ll<i__2; ll++) {
40: tmp = PetscAbsScalar(aa[ll]);
41: if (tmp > max) { max = tmp; l = ll+1;}
42: }
43: l += k - 1;
44: ipvt[k-1] = l;
46: if (a[l + k3] == 0.) {
47: SETERRQ(k,"Zero pivot");
48: }
50: /* interchange if necessary */
52: if (l != k) {
53: stmp = a[l + k3];
54: a[l + k3] = a[k4];
55: a[k4] = stmp;
56: }
58: /* compute multipliers */
60: stmp = -1. / a[k4];
61: i__2 = 3 - k;
62: aa = &a[1 + k4];
63: for (ll=0; ll<i__2; ll++) {
64: aa[ll] *= stmp;
65: }
67: /* row elimination with column indexing */
69: ax = &a[k4+1];
70: for (j = kp1; j <= 3; ++j) {
71: j3 = 3*j;
72: stmp = a[l + j3];
73: if (l != k) {
74: a[l + j3] = a[k + j3];
75: a[k + j3] = stmp;
76: }
78: i__3 = 3 - k;
79: ay = &a[1+k+j3];
80: for (ll=0; ll<i__3; ll++) {
81: ay[ll] += stmp*ax[ll];
82: }
83: }
84: }
85: ipvt[2] = 3;
86: if (a[12] == 0.) {
87: SETERRQ(3,"Zero pivot,final row");
88: }
90: /*
91: Now form the inverse
92: */
94: /* 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++) {
113: ay[ll] += stmp*ax[ll];
114: }
115: }
116: }
118: /* form inverse(u)*inverse(l) */
120: for (kb = 1; kb <= 2; ++kb) {
121: k = 3 - kb;
122: k3 = 3*k;
123: kp1 = k + 1;
124: aa = a + k3;
125: for (i = kp1; i <= 3; ++i) {
126: work[i-1] = aa[i];
127: aa[i] = 0.0;
128: }
129: for (j = kp1; j <= 3; ++j) {
130: stmp = work[j-1];
131: ax = &a[3*j + 1];
132: ay = &a[k3 + 1];
133: ay[0] += stmp*ax[0];
134: ay[1] += stmp*ax[1];
135: ay[2] += stmp*ax[2];
136: }
137: l = ipvt[k-1];
138: if (l != k) {
139: ax = &a[k3 + 1];
140: ay = &a[3*l + 1];
141: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
142: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
143: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
144: }
145: }
146: return(0);
147: }