Actual source code: dgefa5.c
petsc-3.14.6 2021-03-30
2: /*
3: Inverts 5 by 5 matrix using gaussian elimination with partial pivoting.
5: Used by the sparse factorization routines in
6: src/mat/impls/baij/seq
8: This is a combination of the Linpack routines
9: dgefa() and dgedi() specialized for a size of 5.
11: */
12: #include <petscsys.h>
14: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_5(MatScalar *a,PetscInt *ipvt,MatScalar *work,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
15: {
16: PetscInt i__2,i__3,kp1,j,k,l,ll,i,kb,k3;
17: PetscInt k4,j3;
18: MatScalar *aa,*ax,*ay,stmp;
19: MatReal tmp,max;
22: if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
23: shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[6]) + PetscAbsScalar(a[12]) + PetscAbsScalar(a[18]) + PetscAbsScalar(a[24]));
25: /* Parameter adjustments */
26: a -= 6;
28: for (k = 1; k <= 4; ++k) {
29: kp1 = k + 1;
30: k3 = 5*k;
31: k4 = k3 + k;
33: /* find l = pivot index */
34: i__2 = 6 - k;
35: aa = &a[k4];
36: max = PetscAbsScalar(aa[0]);
37: l = 1;
38: for (ll=1; ll<i__2; ll++) {
39: tmp = PetscAbsScalar(aa[ll]);
40: if (tmp > max) { max = tmp; l = ll+1;}
41: }
42: l += k - 1;
43: ipvt[k-1] = l;
45: if (a[l + k3] == 0.0) {
46: if (shift == 0.0) {
47: if (allowzeropivot) {
49: PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);
50: *zeropivotdetected = PETSC_TRUE;
51: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
52: } else {
53: /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
54: a[l + k3] = shift;
55: }
56: }
58: /* interchange if necessary */
59: if (l != k) {
60: stmp = a[l + k3];
61: a[l + k3] = a[k4];
62: a[k4] = stmp;
63: }
65: /* compute multipliers */
66: stmp = -1. / a[k4];
67: i__2 = 5 - k;
68: aa = &a[1 + k4];
69: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
71: /* row elimination with column indexing */
72: ax = &a[k4+1];
73: for (j = kp1; j <= 5; ++j) {
74: j3 = 5*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 = 5 - k;
82: ay = &a[1+k+j3];
83: for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
84: }
85: }
86: ipvt[4] = 5;
87: if (a[30] == 0.0) {
88: if (allowzeropivot) {
90: PetscInfo1(NULL,"Zero pivot, row %D\n",4);
91: *zeropivotdetected = PETSC_TRUE;
92: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",4);
93: }
95: /* Now form the inverse */
96: /* compute inverse(u) */
97: for (k = 1; k <= 5; ++k) {
98: k3 = 5*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 (5 < kp1) continue;
107: ax = aa;
108: for (j = kp1; j <= 5; ++j) {
109: j3 = 5*j;
110: stmp = a[k + j3];
111: a[k + j3] = 0.0;
112: ay = &a[j3 + 1];
113: for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
114: }
115: }
117: /* form inverse(u)*inverse(l) */
118: for (kb = 1; kb <= 4; ++kb) {
119: k = 5 - kb;
120: k3 = 5*k;
121: kp1 = k + 1;
122: aa = a + k3;
123: for (i = kp1; i <= 5; ++i) {
124: work[i-1] = aa[i];
125: aa[i] = 0.0;
126: }
127: for (j = kp1; j <= 5; ++j) {
128: stmp = work[j-1];
129: ax = &a[5*j + 1];
130: ay = &a[k3 + 1];
131: ay[0] += stmp*ax[0];
132: ay[1] += stmp*ax[1];
133: ay[2] += stmp*ax[2];
134: ay[3] += stmp*ax[3];
135: ay[4] += stmp*ax[4];
136: }
137: l = ipvt[k-1];
138: if (l != k) {
139: ax = &a[k3 + 1];
140: ay = &a[5*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: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
145: stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
146: }
147: }
148: return(0);
149: }