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 if (allowzeropivot) { 51 PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1)); 52 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 53 } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1); 54 } else { 55 /* Shift is applied to single diagonal entry */ 56 a[l + k3] = shift; 57 } 58 } 59 60 /* interchange if necessary */ 61 if (l != k) { 62 stmp = a[l + k3]; 63 a[l + k3] = a[k4]; 64 a[k4] = stmp; 65 } 66 67 /* compute multipliers */ 68 stmp = -1. / a[k4]; 69 i__2 = 3 - k; 70 aa = &a[1 + k4]; 71 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 72 73 /* row elimination with column indexing */ 74 ax = &a[k4 + 1]; 75 for (j = kp1; j <= 3; ++j) { 76 j3 = 3 * j; 77 stmp = a[l + j3]; 78 if (l != k) { 79 a[l + j3] = a[k + j3]; 80 a[k + j3] = stmp; 81 } 82 83 i__3 = 3 - k; 84 ay = &a[1 + k + j3]; 85 for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll]; 86 } 87 } 88 ipvt[2] = 3; 89 if (a[12] == 0.0) { 90 if (PetscLikely(allowzeropivot)) { 91 PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n")); 92 if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE; 93 } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 2"); 94 } 95 96 /* Now form the inverse */ 97 /* compute inverse(u) */ 98 for (k = 1; k <= 3; ++k) { 99 k3 = 3 * k; 100 k4 = k3 + k; 101 a[k4] = 1.0 / a[k4]; 102 stmp = -a[k4]; 103 i__2 = k - 1; 104 aa = &a[k3 + 1]; 105 for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp; 106 kp1 = k + 1; 107 if (3 < kp1) continue; 108 ax = aa; 109 for (j = kp1; j <= 3; ++j) { 110 j3 = 3 * j; 111 stmp = a[k + j3]; 112 a[k + j3] = 0.0; 113 ay = &a[j3 + 1]; 114 for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll]; 115 } 116 } 117 118 /* form inverse(u)*inverse(l) */ 119 for (kb = 1; kb <= 2; ++kb) { 120 k = 3 - kb; 121 k3 = 3 * k; 122 kp1 = k + 1; 123 aa = a + k3; 124 for (i = kp1; i <= 3; ++i) { 125 work[i - 1] = aa[i]; 126 aa[i] = 0.0; 127 } 128 for (j = kp1; j <= 3; ++j) { 129 stmp = work[j - 1]; 130 ax = &a[3 * j + 1]; 131 ay = &a[k3 + 1]; 132 ay[0] += stmp * ax[0]; 133 ay[1] += stmp * ax[1]; 134 ay[2] += stmp * ax[2]; 135 } 136 l = ipvt[k - 1]; 137 if (l != k) { 138 ax = &a[k3 + 1]; 139 ay = &a[3 * l + 1]; 140 stmp = ax[0]; 141 ax[0] = ay[0]; 142 ay[0] = stmp; 143 stmp = ax[1]; 144 ax[1] = ay[1]; 145 ay[1] = stmp; 146 stmp = ax[2]; 147 ax[2] = ay[2]; 148 ay[2] = stmp; 149 } 150 } 151 PetscFunctionReturn(PETSC_SUCCESS); 152 } 153