1 /*$Id: dgefa7.c,v 1.10 2001/04/07 15:51:54 bsmith Exp $*/ 2 /* 3 Inverts 7 by 7 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 7. 12 13 */ 14 #include "petsc.h" 15 16 #undef __FUNCT__ 17 #define __FUNCT__ "Kernel_A_gets_inverse_A_7" 18 int Kernel_A_gets_inverse_A_7(MatScalar *a) 19 { 20 int i__2,i__3,kp1,j,k,l,ll,i,ipvt[7],kb,k3; 21 int k4,j3; 22 MatScalar *aa,*ax,*ay,work[49],stmp; 23 MatReal tmp,max; 24 25 /* gaussian elimination with partial pivoting */ 26 27 PetscFunctionBegin; 28 /* Parameter adjustments */ 29 a -= 8; 30 31 for (k = 1; k <= 6; ++k) { 32 kp1 = k + 1; 33 k3 = 7*k; 34 k4 = k3 + k; 35 /* find l = pivot index */ 36 37 i__2 = 7 - k; 38 aa = &a[k4]; 39 max = PetscAbsScalar(aa[0]); 40 l = 1; 41 for (ll=1; ll<i__2; ll++) { 42 tmp = PetscAbsScalar(aa[ll]); 43 if (tmp > max) { max = tmp; l = ll+1;} 44 } 45 l += k - 1; 46 ipvt[k-1] = l; 47 48 if (a[l + k3] == 0.) { 49 SETERRQ(k,"Zero pivot"); 50 } 51 52 /* interchange if necessary */ 53 54 if (l != k) { 55 stmp = a[l + k3]; 56 a[l + k3] = a[k4]; 57 a[k4] = stmp; 58 } 59 60 /* compute multipliers */ 61 62 stmp = -1. / a[k4]; 63 i__2 = 7 - k; 64 aa = &a[1 + k4]; 65 for (ll=0; ll<i__2; ll++) { 66 aa[ll] *= stmp; 67 } 68 69 /* row elimination with column indexing */ 70 71 ax = &a[k4+1]; 72 for (j = kp1; j <= 7; ++j) { 73 j3 = 7*j; 74 stmp = a[l + j3]; 75 if (l != k) { 76 a[l + j3] = a[k + j3]; 77 a[k + j3] = stmp; 78 } 79 80 i__3 = 7 - k; 81 ay = &a[1+k+j3]; 82 for (ll=0; ll<i__3; ll++) { 83 ay[ll] += stmp*ax[ll]; 84 } 85 } 86 } 87 ipvt[6] = 7; 88 if (a[56] == 0.) { 89 SETERRQ(3,"Zero pivot,final row"); 90 } 91 92 /* 93 Now form the inverse 94 */ 95 96 /* compute inverse(u) */ 97 98 for (k = 1; k <= 7; ++k) { 99 k3 = 7*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 (7 < kp1) continue; 108 ax = aa; 109 for (j = kp1; j <= 7; ++j) { 110 j3 = 7*j; 111 stmp = a[k + j3]; 112 a[k + j3] = 0.0; 113 ay = &a[j3 + 1]; 114 for (ll=0; ll<k; ll++) { 115 ay[ll] += stmp*ax[ll]; 116 } 117 } 118 } 119 120 /* form inverse(u)*inverse(l) */ 121 122 for (kb = 1; kb <= 6; ++kb) { 123 k = 7 - kb; 124 k3 = 7*k; 125 kp1 = k + 1; 126 aa = a + k3; 127 for (i = kp1; i <= 7; ++i) { 128 work[i-1] = aa[i]; 129 aa[i] = 0.0; 130 } 131 for (j = kp1; j <= 7; ++j) { 132 stmp = work[j-1]; 133 ax = &a[7*j + 1]; 134 ay = &a[k3 + 1]; 135 ay[0] += stmp*ax[0]; 136 ay[1] += stmp*ax[1]; 137 ay[2] += stmp*ax[2]; 138 ay[3] += stmp*ax[3]; 139 ay[4] += stmp*ax[4]; 140 ay[5] += stmp*ax[5]; 141 ay[6] += stmp*ax[6]; 142 } 143 l = ipvt[k-1]; 144 if (l != k) { 145 ax = &a[k3 + 1]; 146 ay = &a[7*l + 1]; 147 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 148 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 149 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 150 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 151 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 152 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 153 stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp; 154 } 155 } 156 PetscFunctionReturn(0); 157 } 158 159 160