Date: 2013-07-02T14:42:36+00:00

Actual source code: dgefa6.c
petsc-3.4.2 2013-07-02

      2: /*
      3:       Inverts 6 by 6 matrix using partial pivoting.

      5:        Used by the sparse factorization routines in
      6:      src/mat/impls/baij/seq

      8:        This is a combination of the Linpack routines
      9:     dgefa() and dgedi() specialized for a size of 6.

     11: */
     12: #include <petscsys.h>

     16: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_6(MatScalar *a,PetscReal shift)
     17: {
     18:   PetscInt  i__2,i__3,kp1,j,k,l,ll,i,ipvt[6],kb,k3;
     19:   PetscInt  k4,j3;
     20:   MatScalar *aa,*ax,*ay,work[36],stmp;
     21:   MatReal   tmp,max;

     23: /*     gaussian elimination with partial pivoting */

     26:   shift = .25*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[7]) + PetscAbsScalar(a[14]) + PetscAbsScalar(a[21]) + PetscAbsScalar(a[28]) + PetscAbsScalar(a[35]));
     27:   /* Parameter adjustments */
     28:   a -= 7;

     30:   for (k = 1; k <= 5; ++k) {
     31:     kp1 = k + 1;
     32:     k3  = 6*k;
     33:     k4  = k3 + k;
     34: /*        find l = pivot index */

     36:     i__2 = 7 - 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;

     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:     }

     55: /*           interchange if necessary */

     57:     if (l != k) {
     58:       stmp      = a[l + k3];
     59:       a[l + k3] = a[k4];
     60:       a[k4]     = stmp;
     61:     }

     63: /*           compute multipliers */

     65:     stmp = -1. / a[k4];
     66:     i__2 = 6 - k;
     67:     aa   = &a[1 + k4];
     68:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;

     70: /*           row elimination with column indexing */

     72:     ax = &a[k4+1];
     73:     for (j = kp1; j <= 6; ++j) {
     74:       j3   = 6*j;
     75:       stmp = a[l + j3];
     76:       if (l != k) {
     77:         a[l + j3] = a[k + j3];
     78:         a[k + j3] = stmp;
     79:       }

     81:       i__3 = 6 - k;
     82:       ay   = &a[1+k+j3];
     83:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
     84:     }
     85:   }
     86:   ipvt[5] = 6;
     87:   if (a[42] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",5);

     89:   /*
     90:        Now form the inverse
     91:   */

     93:   /*     compute inverse(u) */

     95:   for (k = 1; k <= 6; ++k) {
     96:     k3    = 6*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 (6 < kp1) continue;
    105:     ax = aa;
    106:     for (j = kp1; j <= 6; ++j) {
    107:       j3        = 6*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:   }

    115:   /*    form inverse(u)*inverse(l) */

    117:   for (kb = 1; kb <= 5; ++kb) {
    118:     k   = 6 - kb;
    119:     k3  = 6*k;
    120:     kp1 = k + 1;
    121:     aa  = a + k3;
    122:     for (i = kp1; i <= 6; ++i) {
    123:       work[i-1] = aa[i];
    124:       aa[i]     = 0.0;
    125:     }
    126:     for (j = kp1; j <= 6; ++j) {
    127:       stmp   = work[j-1];
    128:       ax     = &a[6*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:       ay[5] += stmp*ax[5];
    136:     }
    137:     l = ipvt[k-1];
    138:     if (l != k) {
    139:       ax   = &a[k3 + 1];
    140:       ay   = &a[6*l + 1];
    141:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
    142:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
    143:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
    144:       stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
    145:       stmp = ax[4]; ax[4] = ay[4]; ay[4] = stmp;
    146:       stmp = ax[5]; ax[5] = ay[5]; ay[5] = stmp;
    147:     }
    148:   }
    149:   return(0);
    150: }