1 #ifdef PETSC_RCS_HEADER 2 static char vcid[] = "$Id: dgefa7.c,v 1.7 1998/12/24 04:10:08 bsmith Exp bsmith $"; 3 #endif 4 /* 5 Inverts 7 by 7 matrix using partial pivoting. 6 7 Used by the sparse factorization routines in 8 src/mat/impls/baij/seq and src/mat/impls/bdiag/seq 9 10 See also src/inline/ilu.h 11 12 This is a combination of the Linpack routines 13 dgefa() and dgedi() specialized for a size of 7. 14 15 */ 16 #include "petsc.h" 17 18 #undef __FUNC__ 19 #define __FUNC__ "Kernel_A_gets_inverse_A_7" 20 int Kernel_A_gets_inverse_A_7(MatScalar *a) 21 { 22 int i__2, i__3, kp1, j, k, l,ll,i,ipvt_l[7],*ipvt = ipvt_l-1,kb,k3; 23 int k4,j3; 24 MatScalar *aa,*ax,*ay,work_l[49],*work = work_l-1,stmp; 25 MatFloat tmp,max; 26 27 /* gaussian elimination with partial pivoting */ 28 29 PetscFunctionBegin; 30 /* Parameter adjustments */ 31 a -= 8; 32 33 for (k = 1; k <= 6; ++k) { 34 kp1 = k + 1; 35 k3 = 7*k; 36 k4 = k3 + k; 37 /* find l = pivot index */ 38 39 i__2 = 7 - k; 40 aa = &a[k4]; 41 max = PetscAbsScalar(aa[0]); 42 l = 1; 43 for ( ll=1; ll<i__2; ll++ ) { 44 tmp = PetscAbsScalar(aa[ll]); 45 if (tmp > max) { max = tmp; l = ll+1;} 46 } 47 l += k - 1; 48 ipvt[k] = l; 49 50 if (a[l + k3] == 0.) { 51 SETERRQ(k,0,"Zero pivot"); 52 } 53 54 /* interchange if necessary */ 55 56 if (l != k) { 57 stmp = a[l + k3]; 58 a[l + k3] = a[k4]; 59 a[k4] = stmp; 60 } 61 62 /* compute multipliers */ 63 64 stmp = -1. / a[k4]; 65 i__2 = 7 - k; 66 aa = &a[1 + k4]; 67 for ( ll=0; ll<i__2; ll++ ) { 68 aa[ll] *= stmp; 69 } 70 71 /* row elimination with column indexing */ 72 73 ax = &a[k4+1]; 74 for (j = kp1; j <= 7; ++j) { 75 j3 = 7*j; 76 stmp = a[l + j3]; 77 if (l != k) { 78 a[l + j3] = a[k + j3]; 79 a[k + j3] = stmp; 80 } 81 82 i__3 = 7 - k; 83 ay = &a[1+k+j3]; 84 for ( ll=0; ll<i__3; ll++ ) { 85 ay[ll] += stmp*ax[ll]; 86 } 87 } 88 } 89 ipvt[7] = 7; 90 if (a[56] == 0.) { 91 SETERRQ(3,0,"Zero pivot,final row"); 92 } 93 94 /* 95 Now form the inverse 96 */ 97 98 /* compute inverse(u) */ 99 100 for (k = 1; k <= 7; ++k) { 101 k3 = 7*k; 102 k4 = k3 + k; 103 a[k4] = 1.0 / a[k4]; 104 stmp = -a[k4]; 105 i__2 = k - 1; 106 aa = &a[k3 + 1]; 107 for ( ll=0; ll<i__2; ll++ ) aa[ll] *= stmp; 108 kp1 = k + 1; 109 if (7 < kp1) continue; 110 ax = aa; 111 for (j = kp1; j <= 7; ++j) { 112 j3 = 7*j; 113 stmp = a[k + j3]; 114 a[k + j3] = 0.0; 115 ay = &a[j3 + 1]; 116 for ( ll=0; ll<k; ll++ ) { 117 ay[ll] += stmp*ax[ll]; 118 } 119 } 120 } 121 122 /* form inverse(u)*inverse(l) */ 123 124 for (kb = 1; kb <= 6; ++kb) { 125 k = 7 - kb; 126 k3 = 7*k; 127 kp1 = k + 1; 128 aa = a + k3; 129 for (i = kp1; i <= 7; ++i) { 130 work_l[i-1] = aa[i]; 131 /* work[i] = aa[i]; Fix for -O3 error on Origin 2000 */ 132 aa[i] = 0.0; 133 } 134 for (j = kp1; j <= 7; ++j) { 135 stmp = work[j]; 136 ax = &a[7*j + 1]; 137 ay = &a[k3 + 1]; 138 ay[0] += stmp*ax[0]; 139 ay[1] += stmp*ax[1]; 140 ay[2] += stmp*ax[2]; 141 ay[3] += stmp*ax[3]; 142 ay[4] += stmp*ax[4]; 143 ay[5] += stmp*ax[5]; 144 ay[6] += stmp*ax[6]; 145 } 146 l = ipvt[k]; 147 if (l != k) { 148 ax = &a[k3 + 1]; 149 ay = &a[7*l + 1]; 150 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 151 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 152 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 153 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 154 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 155 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 156 stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp; 157 } 158 } 159 PetscFunctionReturn(0); 160 } 161 162 163