1
2 /*
3 Inverts 5 by 5 matrix using gaussian elimination with partial pivoting.
4
5 Used by the sparse factorization routines in
6 src/mat/impls/baij/seq
7
8 This is a combination of the Linpack routines
9 dgefa() and dgedi() specialized for a size of 5.
10
11 */
12 #include <petscsys.h>
13
PetscKernel_A_gets_inverse_A_5(MatScalar * a,PetscInt * ipvt,MatScalar * work,PetscReal shift,PetscBool allowzeropivot,PetscBool * zeropivotdetected)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;
20
21 PetscFunctionBegin;
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]));
24
25 /* Parameter adjustments */
26 a -= 6;
27
28 for (k = 1; k <= 4; ++k) {
29 kp1 = k + 1;
30 k3 = 5*k;
31 k4 = k3 + k;
32
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;
44
45 if (a[l + k3] == 0.0) {
46 if (shift == 0.0) {
47 if (allowzeropivot) {
48 PetscErrorCode ierr;
49 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);CHKERRQ(ierr);
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 }
57
58 /* interchange if necessary */
59 if (l != k) {
60 stmp = a[l + k3];
61 a[l + k3] = a[k4];
62 a[k4] = stmp;
63 }
64
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;
70
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 }
80
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) {
89 PetscErrorCode ierr;
90 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",4);CHKERRQ(ierr);
91 *zeropivotdetected = PETSC_TRUE;
92 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",4);
93 }
94
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 }
116
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 PetscFunctionReturn(0);
149 }
150
151