1 2 /* 3 Inverts 5 by 5 matrix using 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 5. 10 11 */ 12 #include <petscsys.h> 13 14 #undef __FUNCT__ 15 #define __FUNCT__ "PetscKernel_A_gets_inverse_A_5" 16 PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_5(MatScalar *a,PetscInt *ipvt,MatScalar *work,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected) 17 { 18 PetscInt i__2,i__3,kp1,j,k,l,ll,i,kb,k3; 19 PetscInt k4,j3; 20 MatScalar *aa,*ax,*ay,stmp; 21 MatReal tmp,max; 22 23 /* gaussian elimination with partial pivoting */ 24 25 PetscFunctionBegin; 26 if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE; 27 28 shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[6]) + PetscAbsScalar(a[12]) + PetscAbsScalar(a[18]) + PetscAbsScalar(a[24])); 29 /* Parameter adjustments */ 30 a -= 6; 31 32 for (k = 1; k <= 4; ++k) { 33 kp1 = k + 1; 34 k3 = 5*k; 35 k4 = k3 + k; 36 /* find l = pivot index */ 37 38 i__2 = 6 - k; 39 aa = &a[k4]; 40 max = PetscAbsScalar(aa[0]); 41 l = 1; 42 for (ll=1; ll<i__2; ll++) { 43 tmp = PetscAbsScalar(aa[ll]); 44 if (tmp > max) { max = tmp; l = ll+1;} 45 } 46 l += k - 1; 47 ipvt[k-1] = l; 48 49 if (a[l + k3] == 0.0) { 50 if (shift == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 51 else { 52 /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */ 53 a[l + k3] = shift; 54 } 55 } 56 57 /* interchange if necessary */ 58 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 67 stmp = -1. / a[k4]; 68 i__2 = 5 - 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 74 ax = &a[k4+1]; 75 for (j = kp1; j <= 5; ++j) { 76 j3 = 5*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 = 5 - k; 84 ay = &a[1+k+j3]; 85 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 86 } 87 } 88 ipvt[4] = 5; 89 if (a[30] == 0.0) { 90 PetscErrorCode ierr; 91 if (allowzeropivot) { 92 ierr = PetscInfo1(NULL,"Zero pivot, row %D\n",4);CHKERRQ(ierr); 93 *zeropivotdetected = PETSC_TRUE; 94 } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",4); 95 } 96 97 /* 98 Now form the inverse 99 */ 100 101 /* compute inverse(u) */ 102 103 for (k = 1; k <= 5; ++k) { 104 k3 = 5*k; 105 k4 = k3 + k; 106 a[k4] = 1.0 / a[k4]; 107 stmp = -a[k4]; 108 i__2 = k - 1; 109 aa = &a[k3 + 1]; 110 for (ll=0; ll<i__2; ll++) aa[ll] *= stmp; 111 kp1 = k + 1; 112 if (5 < kp1) continue; 113 ax = aa; 114 for (j = kp1; j <= 5; ++j) { 115 j3 = 5*j; 116 stmp = a[k + j3]; 117 a[k + j3] = 0.0; 118 ay = &a[j3 + 1]; 119 for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll]; 120 } 121 } 122 123 /* form inverse(u)*inverse(l) */ 124 125 for (kb = 1; kb <= 4; ++kb) { 126 k = 5 - kb; 127 k3 = 5*k; 128 kp1 = k + 1; 129 aa = a + k3; 130 for (i = kp1; i <= 5; ++i) { 131 work[i-1] = aa[i]; 132 aa[i] = 0.0; 133 } 134 for (j = kp1; j <= 5; ++j) { 135 stmp = work[j-1]; 136 ax = &a[5*j + 1]; 137 ay = &a[k3 + 1]; 138 ay[0] += stmp*ax[0]; 139 ay[1] += stmp*ax[1]; 140 ay[2] += stmp*ax[2]; 141 ay[3] += stmp*ax[3]; 142 ay[4] += stmp*ax[4]; 143 } 144 l = ipvt[k-1]; 145 if (l != k) { 146 ax = &a[k3 + 1]; 147 ay = &a[5*l + 1]; 148 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 149 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 150 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 151 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 152 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 153 } 154 } 155 PetscFunctionReturn(0); 156 } 157 158