Actual source code: dgefa2.c
1: /*$Id: dgefa2.c,v 1.10 2001/04/07 15:47:07 bsmith Exp $*/
2: /*
3: Inverts 2 by 2 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 2.
13: */
14: #include petsc.h
18: int Kernel_A_gets_inverse_A_2(MatScalar *a)
19: {
20: int i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3;
21: int k4,j3;
22: MatScalar *aa,*ax,*ay,work[4],stmp;
23: MatReal tmp,max;
25: /* gaussian elimination with partial pivoting */
28: /* Parameter adjustments */
29: a -= 3;
31: /*for (k = 1; k <= 1; ++k) {*/
32: k = 1;
33: kp1 = k + 1;
34: k3 = 2*k;
35: k4 = k3 + k;
36: /* find l = pivot index */
38: i__2 = 2 - k;
39: aa = &a[k4];
40: max = PetscAbsScalar(aa[0]);
41: l = 1;
42: for (ll=1; ll<i__2; ll++) {
43: tmp = PetscAbsScalar(aa[ll]);
44: if (tmp > max) { max = tmp; l = ll+1;}
45: }
46: l += k - 1;
47: ipvt[k-1] = l;
49: if (a[l + k3] == 0.) {
50: SETERRQ(k,"Zero pivot");
51: }
53: /* interchange if necessary */
55: if (l != k) {
56: stmp = a[l + k3];
57: a[l + k3] = a[k4];
58: a[k4] = stmp;
59: }
61: /* compute multipliers */
63: stmp = -1. / a[k4];
64: i__2 = 2 - k;
65: aa = &a[1 + k4];
66: for (ll=0; ll<i__2; ll++) {
67: aa[ll] *= stmp;
68: }
70: /* row elimination with column indexing */
72: ax = &a[k4+1];
73: for (j = kp1; j <= 2; ++j) {
74: j3 = 2*j;
75: stmp = a[l + j3];
76: if (l != k) {
77: a[l + j3] = a[k + j3];
78: a[k + j3] = stmp;
79: }
81: i__3 = 2 - k;
82: ay = &a[1+k+j3];
83: for (ll=0; ll<i__3; ll++) {
84: ay[ll] += stmp*ax[ll];
85: }
86: }
87: /*}*/
88: ipvt[1] = 2;
89: if (a[6] == 0.) {
90: SETERRQ(3,"Zero pivot,final row");
91: }
93: /*
94: Now form the inverse
95: */
97: /* compute inverse(u) */
99: for (k = 1; k <= 2; ++k) {
100: k3 = 2*k;
101: k4 = k3 + k;
102: a[k4] = 1.0 / a[k4];
103: stmp = -a[k4];
104: i__2 = k - 1;
105: aa = &a[k3 + 1];
106: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
107: kp1 = k + 1;
108: if (2 < kp1) continue;
109: ax = aa;
110: for (j = kp1; j <= 2; ++j) {
111: j3 = 2*j;
112: stmp = a[k + j3];
113: a[k + j3] = 0.0;
114: ay = &a[j3 + 1];
115: for (ll=0; ll<k; ll++) {
116: ay[ll] += stmp*ax[ll];
117: }
118: }
119: }
121: /* form inverse(u)*inverse(l) */
123: /*for (kb = 1; kb <= 1; ++kb) {*/
124:
125: k = 1;
126: k3 = 2*k;
127: kp1 = k + 1;
128: aa = a + k3;
129: for (i = kp1; i <= 2; ++i) {
130: work[i-1] = aa[i];
131: aa[i] = 0.0;
132: }
133: for (j = kp1; j <= 2; ++j) {
134: stmp = work[j-1];
135: ax = &a[2*j + 1];
136: ay = &a[k3 + 1];
137: ay[0] += stmp*ax[0];
138: ay[1] += stmp*ax[1];
139: }
140: l = ipvt[k-1];
141: if (l != k) {
142: ax = &a[k3 + 1];
143: ay = &a[2*l + 1];
144: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
145: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
146: }
147:
148: return(0);
149: }