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
16: int Kernel_A_gets_inverse_A_2(MatScalar *a)
17: {
18: int i__2,i__3,kp1,j,k,l,ll,i,ipvt[2],k3;
19: int k4,j3;
20: MatScalar *aa,*ax,*ay,work[4],stmp;
21: MatReal tmp,max;
23: /* gaussian elimination with partial pivoting */
26: /* Parameter adjustments */
27: a -= 3;
29: /*for (k = 1; k <= 1; ++k) {*/
30: k = 1;
31: kp1 = k + 1;
32: k3 = 2*k;
33: k4 = k3 + k;
34: /* find l = pivot index */
36: i__2 = 2 - k;
37: aa = &a[k4];
38: max = PetscAbsScalar(aa[0]);
39: l = 1;
40: for (ll=1; ll<i__2; ll++) {
41: tmp = PetscAbsScalar(aa[ll]);
42: if (tmp > max) { max = tmp; l = ll+1;}
43: }
44: l += k - 1;
45: ipvt[k-1] = l;
47: if (a[l + k3] == 0.) {
48: SETERRQ(k,"Zero pivot");
49: }
51: /* interchange if necessary */
53: if (l != k) {
54: stmp = a[l + k3];
55: a[l + k3] = a[k4];
56: a[k4] = stmp;
57: }
59: /* compute multipliers */
61: stmp = -1. / a[k4];
62: i__2 = 2 - k;
63: aa = &a[1 + k4];
64: for (ll=0; ll<i__2; ll++) {
65: aa[ll] *= stmp;
66: }
68: /* row elimination with column indexing */
70: ax = &a[k4+1];
71: for (j = kp1; j <= 2; ++j) {
72: j3 = 2*j;
73: stmp = a[l + j3];
74: if (l != k) {
75: a[l + j3] = a[k + j3];
76: a[k + j3] = stmp;
77: }
79: i__3 = 2 - k;
80: ay = &a[1+k+j3];
81: for (ll=0; ll<i__3; ll++) {
82: ay[ll] += stmp*ax[ll];
83: }
84: }
85: /*}*/
86: ipvt[1] = 2;
87: if (a[6] == 0.) {
88: SETERRQ(3,"Zero pivot,final row");
89: }
91: /*
92: Now form the inverse
93: */
95: /* compute inverse(u) */
97: for (k = 1; k <= 2; ++k) {
98: k3 = 2*k;
99: k4 = k3 + k;
100: a[k4] = 1.0 / a[k4];
101: stmp = -a[k4];
102: i__2 = k - 1;
103: aa = &a[k3 + 1];
104: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
105: kp1 = k + 1;
106: if (2 < kp1) continue;
107: ax = aa;
108: for (j = kp1; j <= 2; ++j) {
109: j3 = 2*j;
110: stmp = a[k + j3];
111: a[k + j3] = 0.0;
112: ay = &a[j3 + 1];
113: for (ll=0; ll<k; ll++) {
114: ay[ll] += stmp*ax[ll];
115: }
116: }
117: }
119: /* form inverse(u)*inverse(l) */
121: /*for (kb = 1; kb <= 1; ++kb) {*/
122:
123: k = 1;
124: k3 = 2*k;
125: kp1 = k + 1;
126: aa = a + k3;
127: for (i = kp1; i <= 2; ++i) {
128: work[i-1] = aa[i];
129: aa[i] = 0.0;
130: }
131: for (j = kp1; j <= 2; ++j) {
132: stmp = work[j-1];
133: ax = &a[2*j + 1];
134: ay = &a[k3 + 1];
135: ay[0] += stmp*ax[0];
136: ay[1] += stmp*ax[1];
137: }
138: l = ipvt[k-1];
139: if (l != k) {
140: ax = &a[k3 + 1];
141: ay = &a[2*l + 1];
142: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
143: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
144: }
145:
146: return(0);
147: }