1 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 7 8 This is a combination of the Linpack routines 9 dgefa() and dgedi() specialized for a size of 7. 10 11 */ 12 #include <petscsys.h> 13 14 #undef __FUNCT__ 15 #define __FUNCT__ "PetscKernel_A_gets_inverse_A_7" 16 PetscErrorCode PetscKernel_A_gets_inverse_A_7(MatScalar *a,PetscReal shift) 17 { 18 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[7],kb,k3; 19 PetscInt k4,j3; 20 MatScalar *aa,*ax,*ay,work[49],stmp; 21 MatReal tmp,max; 22 23 /* gaussian elimination with partial pivoting */ 24 25 PetscFunctionBegin; 26 shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[8]) + PetscAbsScalar(a[16]) + PetscAbsScalar(a[24]) + PetscAbsScalar(a[32]) + PetscAbsScalar(a[40]) + PetscAbsScalar(a[48])); 27 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 = 8 - 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] == 0.0) { 49 if (shift == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 50 else { 51 /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */ 52 a[l + k3] = shift; 53 } 54 } 55 56 /* interchange if necessary */ 57 58 if (l != k) { 59 stmp = a[l + k3]; 60 a[l + k3] = a[k4]; 61 a[k4] = stmp; 62 } 63 64 /* compute multipliers */ 65 66 stmp = -1. / a[k4]; 67 i__2 = 7 - 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 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++) ay[ll] += stmp*ax[ll]; 85 } 86 } 87 ipvt[6] = 7; 88 if (a[56] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",6); 89 90 /* 91 Now form the inverse 92 */ 93 94 /* compute inverse(u) */ 95 96 for (k = 1; k <= 7; ++k) { 97 k3 = 7*k; 98 k4 = k3 + k; 99 a[k4] = 1.0 / a[k4]; 100 stmp = -a[k4]; 101 i__2 = k - 1; 102 aa = &a[k3 + 1]; 103 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 104 kp1 = k + 1; 105 if (7 < kp1) continue; 106 ax = aa; 107 for (j = kp1; j <= 7; ++j) { 108 j3 = 7*j; 109 stmp = a[k + j3]; 110 a[k + j3] = 0.0; 111 ay = &a[j3 + 1]; 112 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 113 } 114 } 115 116 /* form inverse(u)*inverse(l) */ 117 118 for (kb = 1; kb <= 6; ++kb) { 119 k = 7 - kb; 120 k3 = 7*k; 121 kp1 = k + 1; 122 aa = a + k3; 123 for (i = kp1; i <= 7; ++i) { 124 work[i-1] = aa[i]; 125 aa[i] = 0.0; 126 } 127 for (j = kp1; j <= 7; ++j) { 128 stmp = work[j-1]; 129 ax = &a[7*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 ay[5] += stmp*ax[5]; 137 ay[6] += stmp*ax[6]; 138 } 139 l = ipvt[k-1]; 140 if (l != k) { 141 ax = &a[k3 + 1]; 142 ay = &a[7*l + 1]; 143 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 144 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 145 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 146 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 147 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 148 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 149 stmp = ax[6]; ax[6] = ay[6]; ay[6] = stmp; 150 } 151 } 152 PetscFunctionReturn(0); 153 } 154 155 156