1 /* 2 Inverts 3 by 3 matrix using gaussian elimination with partial pivoting. 3 4 Used by the sparse factorization routines in 5 src/mat/impls/baij/seq 6 7 This is a combination of the Linpack routines 8 dgefa() and dgedi() specialized for a size of 3. 9 10 */ 11 #include <petscsys.h> 12 13 PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected) 14 { 15 PetscInt i__2, i__3, kp1, j, k, l, ll, i, ipvt[3], kb, k3; 16 PetscInt k4, j3; 17 MatScalar *aa, *ax, *ay, work[9], stmp; 18 MatReal tmp, max; 19 20 PetscFunctionBegin; 21 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 22 shift = .333 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8])); 23 24 /* Parameter adjustments */ 25 a -= 4; 26 27 for (k = 1; k <= 2; ++k) { 28 kp1 = k + 1; 29 k3 = 3 * k; 30 k4 = k3 + k; 31 32 /* find l = pivot index */ 33 i__2 = 4 - k; 34 aa = &a[k4]; 35 max = PetscAbsScalar(aa[0]); 36 l = 1; 37 for (ll = 1; ll < i__2; ll++) { 38 tmp = PetscAbsScalar(aa[ll]); 39 if (tmp > max) { 40 max = tmp; 41 l = ll + 1; 42 } 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 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 51 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 52 } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 53 } else { 54 /* Shift is applied to single diagonal entry */ 55 a[l + k3] = shift; 56 } 57 } 58 59 /* interchange if necessary */ 60 if (l != k) { 61 stmp = a[l + k3]; 62 a[l + k3] = a[k4]; 63 a[k4] = stmp; 64 } 65 66 /* compute multipliers */ 67 stmp = -1. / a[k4]; 68 i__2 = 3 - k; 69 aa = &a[1 + k4]; 70 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 71 72 /* row elimination with column indexing */ 73 ax = &a[k4 + 1]; 74 for (j = kp1; j <= 3; ++j) { 75 j3 = 3 * 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 = 3 - k; 83 ay = &a[1 + k + j3]; 84 for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll]; 85 } 86 } 87 ipvt[2] = 3; 88 if (a[12] == 0.0) { 89 if (PetscLikely(allowzeropivot)) { 90 PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n")); 91 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 92 } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 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]; 140 ax[0] = ay[0]; 141 ay[0] = stmp; 142 stmp = ax[1]; 143 ax[1] = ay[1]; 144 ay[1] = stmp; 145 stmp = ax[2]; 146 ax[2] = ay[2]; 147 ay[2] = stmp; 148 } 149 } 150 PetscFunctionReturn(PETSC_SUCCESS); 151 } 152