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 This is a combination of the Linpack routines 9 dgefa() and dgedi() specialized for a size of 3. 10 11 */ 12 #include <petscsys.h> 13 14 PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected) 15 { 16 PetscInt i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3; 17 PetscInt k4,j3; 18 MatScalar *aa,*ax,*ay,work[9],stmp; 19 MatReal tmp,max; 20 21 PetscFunctionBegin; 22 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 23 shift = .333*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8])); 24 25 /* Parameter adjustments */ 26 a -= 4; 27 28 for (k = 1; k <= 2; ++k) { 29 kp1 = k + 1; 30 k3 = 3*k; 31 k4 = k3 + k; 32 33 /* find l = pivot index */ 34 i__2 = 4 - k; 35 aa = &a[k4]; 36 max = PetscAbsScalar(aa[0]); 37 l = 1; 38 for (ll=1; ll<i__2; ll++) { 39 tmp = PetscAbsScalar(aa[ll]); 40 if (tmp > max) { max = tmp; l = ll+1;} 41 } 42 l += k - 1; 43 ipvt[k-1] = l; 44 45 if (a[l + k3] == 0.0) { 46 if (shift == 0.0) { 47 if (allowzeropivot) { 48 PetscErrorCode ierr; 49 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);CHKERRQ(ierr); 50 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 51 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 52 } else { 53 /* Shift is applied to single diagonal entry */ 54 a[l + k3] = shift; 55 } 56 } 57 58 /* interchange if necessary */ 59 if (l != k) { 60 stmp = a[l + k3]; 61 a[l + k3] = a[k4]; 62 a[k4] = stmp; 63 } 64 65 /* compute multipliers */ 66 stmp = -1. / a[k4]; 67 i__2 = 3 - 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 ax = &a[k4+1]; 73 for (j = kp1; j <= 3; ++j) { 74 j3 = 3*j; 75 stmp = a[l + j3]; 76 if (l != k) { 77 a[l + j3] = a[k + j3]; 78 a[k + j3] = stmp; 79 } 80 81 i__3 = 3 - k; 82 ay = &a[1+k+j3]; 83 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 84 } 85 } 86 ipvt[2] = 3; 87 if (a[12] == 0.0) { 88 if (allowzeropivot) { 89 PetscErrorCode ierr; 90 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",2);CHKERRQ(ierr); 91 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 92 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2); 93 } 94 95 /* Now form the inverse */ 96 /* compute inverse(u) */ 97 for (k = 1; k <= 3; ++k) { 98 k3 = 3*k; 99 k4 = k3 + k; 100 a[k4] = 1.0 / a[k4]; 101 stmp = -a[k4]; 102 i__2 = k - 1; 103 aa = &a[k3 + 1]; 104 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 105 kp1 = k + 1; 106 if (3 < kp1) continue; 107 ax = aa; 108 for (j = kp1; j <= 3; ++j) { 109 j3 = 3*j; 110 stmp = a[k + j3]; 111 a[k + j3] = 0.0; 112 ay = &a[j3 + 1]; 113 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 114 } 115 } 116 117 /* form inverse(u)*inverse(l) */ 118 for (kb = 1; kb <= 2; ++kb) { 119 k = 3 - kb; 120 k3 = 3*k; 121 kp1 = k + 1; 122 aa = a + k3; 123 for (i = kp1; i <= 3; ++i) { 124 work[i-1] = aa[i]; 125 aa[i] = 0.0; 126 } 127 for (j = kp1; j <= 3; ++j) { 128 stmp = work[j-1]; 129 ax = &a[3*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 } 135 l = ipvt[k-1]; 136 if (l != k) { 137 ax = &a[k3 + 1]; 138 ay = &a[3*l + 1]; 139 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 140 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 141 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 142 } 143 } 144 PetscFunctionReturn(0); 145 } 146 147