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
18: int Kernel_A_gets_inverse_A_3(MatScalar *a)
19: {
20: int i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
21: int k4,j3;
22: MatScalar *aa,*ax,*ay,work[9],stmp;
23: MatReal tmp,max;
25: /* gaussian elimination with partial pivoting */
28: /* Parameter adjustments */
29: a -= 4;
31: for (k = 1; k <= 2; ++k) {
32: kp1 = k + 1;
33: k3 = 3*k;
34: k4 = k3 + k;
35: /* find l = pivot index */
37: i__2 = 4 - k;
38: aa = &a[k4];
39: max = PetscAbsScalar(aa[0]);
40: l = 1;
41: for (ll=1; ll<i__2; ll++) {
42: tmp = PetscAbsScalar(aa[ll]);
43: if (tmp > max) { max = tmp; l = ll+1;}
44: }
45: l += k - 1;
46: ipvt[k-1] = l;
48: if (a[l + k3] == 0.) {
49: SETERRQ(k,"Zero pivot");
50: }
52: /* interchange if necessary */
54: if (l != k) {
55: stmp = a[l + k3];
56: a[l + k3] = a[k4];
57: a[k4] = stmp;
58: }
60: /* compute multipliers */
62: stmp = -1. / a[k4];
63: i__2 = 3 - k;
64: aa = &a[1 + k4];
65: for (ll=0; ll<i__2; ll++) {
66: aa[ll] *= stmp;
67: }
69: /* row elimination with column indexing */
71: ax = &a[k4+1];
72: for (j = kp1; j <= 3; ++j) {
73: j3 = 3*j;
74: stmp = a[l + j3];
75: if (l != k) {
76: a[l + j3] = a[k + j3];
77: a[k + j3] = stmp;
78: }
80: i__3 = 3 - k;
81: ay = &a[1+k+j3];
82: for (ll=0; ll<i__3; ll++) {
83: ay[ll] += stmp*ax[ll];
84: }
85: }
86: }
87: ipvt[2] = 3;
88: if (a[12] == 0.) {
89: SETERRQ(3,"Zero pivot,final row");
90: }
92: /*
93: Now form the inverse
94: */
96: /* 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++) {
115: ay[ll] += stmp*ax[ll];
116: }
117: }
118: }
120: /* form inverse(u)*inverse(l) */
122: for (kb = 1; kb <= 2; ++kb) {
123: k = 3 - kb;
124: k3 = 3*k;
125: kp1 = k + 1;
126: aa = a + k3;
127: for (i = kp1; i <= 3; ++i) {
128: work[i-1] = aa[i];
129: aa[i] = 0.0;
130: }
131: for (j = kp1; j <= 3; ++j) {
132: stmp = work[j-1];
133: ax = &a[3*j + 1];
134: ay = &a[k3 + 1];
135: ay[0] += stmp*ax[0];
136: ay[1] += stmp*ax[1];
137: ay[2] += stmp*ax[2];
138: }
139: l = ipvt[k-1];
140: if (l != k) {
141: ax = &a[k3 + 1];
142: ay = &a[3*l + 1];
143: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
144: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
145: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
146: }
147: }
148: return(0);
149: }