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 #include <petsc/private/kernels/blockinvert.h> 13 14 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) { 41 max = tmp; 42 l = ll + 1; 43 } 44 } 45 l += k - 1; 46 ipvt[k - 1] = l; 47 48 if (a[l + k3] == 0.0) { 49 if (shift == 0.0) { 50 PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 51 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 52 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 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 PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 2"); 90 PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n")); 91 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 92 } 93 94 /* Now form the inverse */ 95 /* compute inverse(u) */ 96 for (k = 1; k <= 3; ++k) { 97 k3 = 3 * k; 98 k4 = k3 + k; 99 a[k4] = 1.0 / a[k4]; 100 stmp = -a[k4]; 101 i__2 = k - 1; 102 aa = &a[k3 + 1]; 103 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 104 kp1 = k + 1; 105 if (3 < kp1) continue; 106 ax = aa; 107 for (j = kp1; j <= 3; ++j) { 108 j3 = 3 * j; 109 stmp = a[k + j3]; 110 a[k + j3] = 0.0; 111 ay = &a[j3 + 1]; 112 for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll]; 113 } 114 } 115 116 /* form inverse(u)*inverse(l) */ 117 for (kb = 1; kb <= 2; ++kb) { 118 k = 3 - kb; 119 k3 = 3 * k; 120 kp1 = k + 1; 121 aa = a + k3; 122 for (i = kp1; i <= 3; ++i) { 123 work[i - 1] = aa[i]; 124 aa[i] = 0.0; 125 } 126 for (j = kp1; j <= 3; ++j) { 127 stmp = work[j - 1]; 128 ax = &a[3 * j + 1]; 129 ay = &a[k3 + 1]; 130 ay[0] += stmp * ax[0]; 131 ay[1] += stmp * ax[1]; 132 ay[2] += stmp * ax[2]; 133 } 134 l = ipvt[k - 1]; 135 if (l != k) { 136 ax = &a[k3 + 1]; 137 ay = &a[3 * l + 1]; 138 stmp = ax[0]; 139 ax[0] = ay[0]; 140 ay[0] = stmp; 141 stmp = ax[1]; 142 ax[1] = ay[1]; 143 ay[1] = stmp; 144 stmp = ax[2]; 145 ax[2] = ay[2]; 146 ay[2] = stmp; 147 } 148 } 149 PetscFunctionReturn(PETSC_SUCCESS); 150 } 151