1 2 /* 3 Inverts 6 by 6 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 6. 10 11 */ 12 #include <petscsys.h> 13 14 #undef __FUNCT__ 15 #define __FUNCT__ "PetscKernel_A_gets_inverse_A_6" 16 PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_6(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected) 17 { 18 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[6],kb,k3; 19 PetscInt k4,j3; 20 MatScalar *aa,*ax,*ay,work[36],stmp; 21 MatReal tmp,max; 22 23 PetscFunctionBegin; 24 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 25 shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[7]) + PetscAbsScalar(a[14]) + PetscAbsScalar(a[21]) + PetscAbsScalar(a[28]) + PetscAbsScalar(a[35])); 26 27 /* Parameter adjustments */ 28 a -= 7; 29 30 for (k = 1; k <= 5; ++k) { 31 kp1 = k + 1; 32 k3 = 6*k; 33 k4 = k3 + k; 34 35 /* find l = pivot index */ 36 i__2 = 7 - k; 37 aa = &a[k4]; 38 max = PetscAbsScalar(aa[0]); 39 l = 1; 40 for (ll=1; ll<i__2; ll++) { 41 tmp = PetscAbsScalar(aa[ll]); 42 if (tmp > max) { max = tmp; l = ll+1;} 43 } 44 l += k - 1; 45 ipvt[k-1] = l; 46 47 if (a[l + k3] == 0.0) { 48 if (shift == 0.0) { 49 if (allowzeropivot) { 50 PetscErrorCode ierr; 51 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);CHKERRQ(ierr); 52 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 53 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 54 } else { 55 /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */ 56 a[l + k3] = shift; 57 } 58 } 59 60 /* interchange if necessary */ 61 if (l != k) { 62 stmp = a[l + k3]; 63 a[l + k3] = a[k4]; 64 a[k4] = stmp; 65 } 66 67 /* compute multipliers */ 68 stmp = -1. / a[k4]; 69 i__2 = 6 - k; 70 aa = &a[1 + k4]; 71 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 72 73 /* row elimination with column indexing */ 74 ax = &a[k4+1]; 75 for (j = kp1; j <= 6; ++j) { 76 j3 = 6*j; 77 stmp = a[l + j3]; 78 if (l != k) { 79 a[l + j3] = a[k + j3]; 80 a[k + j3] = stmp; 81 } 82 83 i__3 = 6 - k; 84 ay = &a[1+k+j3]; 85 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 86 } 87 } 88 ipvt[5] = 6; 89 if (a[42] == 0.0) { 90 if (allowzeropivot) { 91 PetscErrorCode ierr; 92 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",5);CHKERRQ(ierr); 93 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 94 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",5); 95 } 96 97 /* Now form the inverse */ 98 /* compute inverse(u) */ 99 for (k = 1; k <= 6; ++k) { 100 k3 = 6*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 (6 < kp1) continue; 109 ax = aa; 110 for (j = kp1; j <= 6; ++j) { 111 j3 = 6*j; 112 stmp = a[k + j3]; 113 a[k + j3] = 0.0; 114 ay = &a[j3 + 1]; 115 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 116 } 117 } 118 119 /* form inverse(u)*inverse(l) */ 120 for (kb = 1; kb <= 5; ++kb) { 121 k = 6 - kb; 122 k3 = 6*k; 123 kp1 = k + 1; 124 aa = a + k3; 125 for (i = kp1; i <= 6; ++i) { 126 work[i-1] = aa[i]; 127 aa[i] = 0.0; 128 } 129 for (j = kp1; j <= 6; ++j) { 130 stmp = work[j-1]; 131 ax = &a[6*j + 1]; 132 ay = &a[k3 + 1]; 133 ay[0] += stmp*ax[0]; 134 ay[1] += stmp*ax[1]; 135 ay[2] += stmp*ax[2]; 136 ay[3] += stmp*ax[3]; 137 ay[4] += stmp*ax[4]; 138 ay[5] += stmp*ax[5]; 139 } 140 l = ipvt[k-1]; 141 if (l != k) { 142 ax = &a[k3 + 1]; 143 ay = &a[6*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 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 147 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 148 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 149 stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp; 150 } 151 } 152 PetscFunctionReturn(0); 153 } 154 155