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) 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 shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[6]) + PetscAbsScalar(a[12]) + PetscAbsScalar(a[18]) + PetscAbsScalar(a[24])); 27 /* Parameter adjustments */ 28 a -= 6; 29 30 for (k = 1; k <= 4; ++k) { 31 kp1 = k + 1; 32 k3 = 5*k; 33 k4 = k3 + k; 34 /* find l = pivot index */ 35 36 i__2 = 6 - k; 37 aa = &a[k4]; 38 max = PetscAbsScalar(aa[0]); 39 l = 1; 40 for (ll=1; ll<i__2; ll++) { 41 tmp = PetscAbsScalar(aa[ll]); 42 if (tmp > max) { max = tmp; l = ll+1;} 43 } 44 l += k - 1; 45 ipvt[k-1] = l; 46 47 if (a[l + k3] == 0.0) { 48 if (shift == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1); 49 else { 50 /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */ 51 a[l + k3] = shift; 52 } 53 } 54 55 /* interchange if necessary */ 56 57 if (l != k) { 58 stmp = a[l + k3]; 59 a[l + k3] = a[k4]; 60 a[k4] = stmp; 61 } 62 63 /* compute multipliers */ 64 65 stmp = -1. / a[k4]; 66 i__2 = 5 - 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 72 ax = &a[k4+1]; 73 for (j = kp1; j <= 5; ++j) { 74 j3 = 5*j; 75 stmp = a[l + j3]; 76 if (l != k) { 77 a[l + j3] = a[k + j3]; 78 a[k + j3] = stmp; 79 } 80 81 i__3 = 5 - k; 82 ay = &a[1+k+j3]; 83 for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll]; 84 } 85 } 86 ipvt[4] = 5; 87 if (a[30] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",4); 88 89 /* 90 Now form the inverse 91 */ 92 93 /* compute inverse(u) */ 94 95 for (k = 1; k <= 5; ++k) { 96 k3 = 5*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 (5 < kp1) continue; 105 ax = aa; 106 for (j = kp1; j <= 5; ++j) { 107 j3 = 5*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) */ 116 117 for (kb = 1; kb <= 4; ++kb) { 118 k = 5 - kb; 119 k3 = 5*k; 120 kp1 = k + 1; 121 aa = a + k3; 122 for (i = kp1; i <= 5; ++i) { 123 work[i-1] = aa[i]; 124 aa[i] = 0.0; 125 } 126 for (j = kp1; j <= 5; ++j) { 127 stmp = work[j-1]; 128 ax = &a[5*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 ay[3] += stmp*ax[3]; 134 ay[4] += stmp*ax[4]; 135 } 136 l = ipvt[k-1]; 137 if (l != k) { 138 ax = &a[k3 + 1]; 139 ay = &a[5*l + 1]; 140 stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp; 141 stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp; 142 stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp; 143 stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp; 144 stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp; 145 } 146 } 147 PetscFunctionReturn(0); 148 } 149 150