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. 4 5 Used by the sparse factorization routines in 6 src/mat/impls/baij/seq and src/mat/impls/bdiag/seq 7 8 See also src/inline/ilu.h 9 10 This is a combination of the Linpack routines 11 dgefa() and dgedi() specialized for a size of 2. 12 13 */ 14 #include "petsc.h" 15 16 #undef __FUNCT__ 17 #define __FUNCT__ "Kernel_A_gets_inverse_A_2" 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; 24 25 /* gaussian elimination with partial pivoting */ 26 27 PetscFunctionBegin; 28 /* Parameter adjustments */ 29 a -= 3; 30 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 */ 37 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; 48 49 if (a[l + k3] == 0.) { 50 SETERRQ(k,"Zero pivot"); 51 } 52 53 /* interchange if necessary */ 54 55 if (l != k) { 56 stmp = a[l + k3]; 57 a[l + k3] = a[k4]; 58 a[k4] = stmp; 59 } 60 61 /* compute multipliers */ 62 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 } 69 70 /* row elimination with column indexing */ 71 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 } 80 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 } 92 93 /* 94 Now form the inverse 95 */ 96 97 /* compute inverse(u) */ 98 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 } 120 121 /* form inverse(u)*inverse(l) */ 122 123 /*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 PetscFunctionReturn(0); 149 } 150 151 152