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 PetscCall(PetscInfo(NULL,"Zero pivot, row %" PetscInt_FMT "\n",k-1)); 49 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 50 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %" PetscInt_FMT,k-1); 51 } else { 52 /* Shift is applied to single diagonal entry */ 53 a[l + k3] = shift; 54 } 55 } 56 57 /* interchange if necessary */ 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 stmp = -1. / a[k4]; 66 i__2 = 3 - k; 67 aa = &a[1 + k4]; 68 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 69 70 /* row elimination with column indexing */ 71 ax = &a[k4+1]; 72 for (j = kp1; j <= 3; ++j) { 73 j3 = 3*j; 74 stmp = a[l + j3]; 75 if (l != k) { 76 a[l + j3] = a[k + j3]; 77 a[k + j3] = stmp; 78 } 79 80 i__3 = 3 - k; 81 ay = &a[1+k+j3]; 82 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 83 } 84 } 85 ipvt[2] = 3; 86 if (a[12] == 0.0) { 87 if (PetscLikely(allowzeropivot)) { 88 PetscCall(PetscInfo(NULL,"Zero pivot, row 2\n")); 89 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 90 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row 2"); 91 } 92 93 /* Now form the inverse */ 94 /* compute inverse(u) */ 95 for (k = 1; k <= 3; ++k) { 96 k3 = 3*k; 97 k4 = k3 + k; 98 a[k4] = 1.0 / a[k4]; 99 stmp = -a[k4]; 100 i__2 = k - 1; 101 aa = &a[k3 + 1]; 102 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 103 kp1 = k + 1; 104 if (3 < kp1) continue; 105 ax = aa; 106 for (j = kp1; j <= 3; ++j) { 107 j3 = 3*j; 108 stmp = a[k + j3]; 109 a[k + j3] = 0.0; 110 ay = &a[j3 + 1]; 111 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 112 } 113 } 114 115 /* form inverse(u)*inverse(l) */ 116 for (kb = 1; kb <= 2; ++kb) { 117 k = 3 - kb; 118 k3 = 3*k; 119 kp1 = k + 1; 120 aa = a + k3; 121 for (i = kp1; i <= 3; ++i) { 122 work[i-1] = aa[i]; 123 aa[i] = 0.0; 124 } 125 for (j = kp1; j <= 3; ++j) { 126 stmp = work[j-1]; 127 ax = &a[3*j + 1]; 128 ay = &a[k3 + 1]; 129 ay[0] += stmp*ax[0]; 130 ay[1] += stmp*ax[1]; 131 ay[2] += stmp*ax[2]; 132 } 133 l = ipvt[k-1]; 134 if (l != k) { 135 ax = &a[k3 + 1]; 136 ay = &a[3*l + 1]; 137 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 138 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 139 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 140 } 141 } 142 PetscFunctionReturn(0); 143 } 144