1 2 /* 3 Inverts 3 by 3 matrix using gaussian elimination with partial pivoting. 4 5 Used by the sparse factorization routines in 6 src/mat/impls/baij/seq 7 8 9 This is a combination of the Linpack routines 10 dgefa() and dgedi() specialized for a size of 3. 11 12 */ 13 #include <petscsys.h> 14 15 #undef __FUNCT__ 16 #define __FUNCT__ "PetscKernel_A_gets_inverse_A_3" 17 PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected) 18 { 19 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3; 20 PetscInt k4,j3; 21 MatScalar *aa,*ax,*ay,work[9],stmp; 22 MatReal tmp,max; 23 24 PetscFunctionBegin; 25 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 26 shift = .333*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8])); 27 28 /* Parameter adjustments */ 29 a -= 4; 30 31 for (k = 1; k <= 2; ++k) { 32 kp1 = k + 1; 33 k3 = 3*k; 34 k4 = k3 + k; 35 36 /* find l = pivot index */ 37 i__2 = 4 - 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) { 50 if (allowzeropivot) { 51 PetscErrorCode ierr; 52 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);CHKERRQ(ierr); 53 *zeropivotdetected = PETSC_TRUE; 54 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 55 } else { 56 /* Shift is applied to single diagonal entry */ 57 a[l + k3] = shift; 58 } 59 } 60 61 /* interchange if necessary */ 62 if (l != k) { 63 stmp = a[l + k3]; 64 a[l + k3] = a[k4]; 65 a[k4] = stmp; 66 } 67 68 /* compute multipliers */ 69 stmp = -1. / a[k4]; 70 i__2 = 3 - k; 71 aa = &a[1 + k4]; 72 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 73 74 /* row elimination with column indexing */ 75 ax = &a[k4+1]; 76 for (j = kp1; j <= 3; ++j) { 77 j3 = 3*j; 78 stmp = a[l + j3]; 79 if (l != k) { 80 a[l + j3] = a[k + j3]; 81 a[k + j3] = stmp; 82 } 83 84 i__3 = 3 - k; 85 ay = &a[1+k+j3]; 86 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 87 } 88 } 89 ipvt[2] = 3; 90 if (a[12] == 0.0) { 91 if (allowzeropivot) { 92 PetscErrorCode ierr; 93 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",2);CHKERRQ(ierr); 94 *zeropivotdetected = PETSC_TRUE; 95 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2); 96 } 97 98 /* Now form the inverse */ 99 /* compute inverse(u) */ 100 for (k = 1; k <= 3; ++k) { 101 k3 = 3*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 (3 < kp1) continue; 110 ax = aa; 111 for (j = kp1; j <= 3; ++j) { 112 j3 = 3*j; 113 stmp = a[k + j3]; 114 a[k + j3] = 0.0; 115 ay = &a[j3 + 1]; 116 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 117 } 118 } 119 120 /* form inverse(u)*inverse(l) */ 121 for (kb = 1; kb <= 2; ++kb) { 122 k = 3 - kb; 123 k3 = 3*k; 124 kp1 = k + 1; 125 aa = a + k3; 126 for (i = kp1; i <= 3; ++i) { 127 work[i-1] = aa[i]; 128 aa[i] = 0.0; 129 } 130 for (j = kp1; j <= 3; ++j) { 131 stmp = work[j-1]; 132 ax = &a[3*j + 1]; 133 ay = &a[k3 + 1]; 134 ay[0] += stmp*ax[0]; 135 ay[1] += stmp*ax[1]; 136 ay[2] += stmp*ax[2]; 137 } 138 l = ipvt[k-1]; 139 if (l != k) { 140 ax = &a[k3 + 1]; 141 ay = &a[3*l + 1]; 142 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 143 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 144 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 145 } 146 } 147 PetscFunctionReturn(0); 148 } 149 150 151