Actual source code: dgefa3.c
petsc-3.8.4 2018-03-24
2: /*
3: Inverts 3 by 3 matrix using gaussian elimination with partial pivoting.
5: Used by the sparse factorization routines in
6: src/mat/impls/baij/seq
9: This is a combination of the Linpack routines
10: dgefa() and dgedi() specialized for a size of 3.
12: */
13: #include <petscsys.h>
15: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
16: {
17: PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
18: PetscInt k4,j3;
19: MatScalar *aa,*ax,*ay,work[9],stmp;
20: MatReal tmp,max;
23: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
24: shift = .333*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8]));
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;
34: /* 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] == 0.0) {
47: if (shift == 0.0) {
48: if (allowzeropivot) {
50: PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);
51: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
52: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
53: } else {
54: /* Shift is applied to single diagonal entry */
55: a[l + k3] = shift;
56: }
57: }
59: /* interchange if necessary */
60: if (l != k) {
61: stmp = a[l + k3];
62: a[l + k3] = a[k4];
63: a[k4] = stmp;
64: }
66: /* compute multipliers */
67: stmp = -1. / a[k4];
68: i__2 = 3 - k;
69: aa = &a[1 + k4];
70: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
72: /* row elimination with column indexing */
73: ax = &a[k4+1];
74: for (j = kp1; j <= 3; ++j) {
75: j3 = 3*j;
76: stmp = a[l + j3];
77: if (l != k) {
78: a[l + j3] = a[k + j3];
79: a[k + j3] = stmp;
80: }
82: i__3 = 3 - k;
83: ay = &a[1+k+j3];
84: for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
85: }
86: }
87: ipvt[2] = 3;
88: if (a[12] == 0.0) {
89: if (allowzeropivot) {
91: PetscInfo1(NULL,"Zero pivot, row %D\n",2);
92: if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
93: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2);
94: }
96: /* Now form the inverse */
97: /* 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++) ay[ll] += stmp*ax[ll];
115: }
116: }
118: /* form inverse(u)*inverse(l) */
119: for (kb = 1; kb <= 2; ++kb) {
120: k = 3 - kb;
121: k3 = 3*k;
122: kp1 = k + 1;
123: aa = a + k3;
124: for (i = kp1; i <= 3; ++i) {
125: work[i-1] = aa[i];
126: aa[i] = 0.0;
127: }
128: for (j = kp1; j <= 3; ++j) {
129: stmp = work[j-1];
130: ax = &a[3*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: }
136: l = ipvt[k-1];
137: if (l != k) {
138: ax = &a[k3 + 1];
139: ay = &a[3*l + 1];
140: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
141: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
142: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
143: }
144: }
145: return(0);
146: }