Actual source code: dgefa3.c
petsc-3.7.1 2016-05-15
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      2: /*
      3:      Inverts 3 by 3 matrix using gaussian elimination with partial pivoting.

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

      9:        This is a combination of the Linpack routines
     10:     dgefa() and dgedi() specialized for a size of 3.

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

     17: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
     18: {
     19:   PetscInt  i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
     20:   PetscInt  k4,j3;
     21:   MatScalar *aa,*ax,*ay,work[9],stmp;
     22:   MatReal   tmp,max;

     25:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
     26:   shift = .333*shift*(1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8]));

     28:   /* Parameter adjustments */
     29:   a -= 4;

     31:   for (k = 1; k <= 2; ++k) {
     32:     kp1 = k + 1;
     33:     k3  = 3*k;
     34:     k4  = k3 + k;

     36:     /* find l = pivot index */
     37:     i__2 = 4 - k;
     38:     aa   = &a[k4];
     39:     max  = PetscAbsScalar(aa[0]);
     40:     l    = 1;
     41:     for (ll=1; ll<i__2; ll++) {
     42:       tmp = PetscAbsScalar(aa[ll]);
     43:       if (tmp > max) { max = tmp; l = ll+1;}
     44:     }
     45:     l        += k - 1;
     46:     ipvt[k-1] = l;

     48:     if (a[l + k3] == 0.0) {
     49:       if (shift == 0.0) {
     50:         if (allowzeropivot) {
     52:           PetscInfo1(NULL,"Zero pivot, row %D\n",k-1);
     53:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
     54:         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
     55:       } else {
     56:         /* Shift is applied to single diagonal entry */
     57:         a[l + k3] = shift;
     58:       }
     59:     }

     61:     /* interchange if necessary */
     62:     if (l != k) {
     63:       stmp      = a[l + k3];
     64:       a[l + k3] = a[k4];
     65:       a[k4]     = stmp;
     66:     }

     68:     /* compute multipliers */
     69:     stmp = -1. / a[k4];
     70:     i__2 = 3 - k;
     71:     aa   = &a[1 + k4];
     72:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;

     74:     /* row elimination with column indexing */
     75:     ax = &a[k4+1];
     76:     for (j = kp1; j <= 3; ++j) {
     77:       j3   = 3*j;
     78:       stmp = a[l + j3];
     79:       if (l != k) {
     80:         a[l + j3] = a[k + j3];
     81:         a[k + j3] = stmp;
     82:       }

     84:       i__3 = 3 - k;
     85:       ay   = &a[1+k+j3];
     86:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
     87:     }
     88:   }
     89:   ipvt[2] = 3;
     90:   if (a[12] == 0.0) {
     91:     if (allowzeropivot) {
     93:       PetscInfo1(NULL,"Zero pivot, row %D\n",2);
     94:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
     95:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2);
     96:   }

     98:   /* Now form the inverse */
     99:   /* compute inverse(u) */
    100:   for (k = 1; k <= 3; ++k) {
    101:     k3    = 3*k;
    102:     k4    = k3 + k;
    103:     a[k4] = 1.0 / a[k4];
    104:     stmp  = -a[k4];
    105:     i__2  = k - 1;
    106:     aa    = &a[k3 + 1];
    107:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
    108:     kp1 = k + 1;
    109:     if (3 < kp1) continue;
    110:     ax = aa;
    111:     for (j = kp1; j <= 3; ++j) {
    112:       j3        = 3*j;
    113:       stmp      = a[k + j3];
    114:       a[k + j3] = 0.0;
    115:       ay        = &a[j3 + 1];
    116:       for (ll=0; ll<k; ll++) ay[ll] += stmp*ax[ll];
    117:     }
    118:   }

    120:   /* form inverse(u)*inverse(l) */
    121:   for (kb = 1; kb <= 2; ++kb) {
    122:     k   = 3 - kb;
    123:     k3  = 3*k;
    124:     kp1 = k + 1;
    125:     aa  = a + k3;
    126:     for (i = kp1; i <= 3; ++i) {
    127:       work[i-1] = aa[i];
    128:       aa[i]     = 0.0;
    129:     }
    130:     for (j = kp1; j <= 3; ++j) {
    131:       stmp   = work[j-1];
    132:       ax     = &a[3*j + 1];
    133:       ay     = &a[k3 + 1];
    134:       ay[0] += stmp*ax[0];
    135:       ay[1] += stmp*ax[1];
    136:       ay[2] += stmp*ax[2];
    137:     }
    138:     l = ipvt[k-1];
    139:     if (l != k) {
    140:       ax   = &a[k3 + 1];
    141:       ay   = &a[3*l + 1];
    142:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
    143:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
    144:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
    145:     }
    146:   }
    147:   return(0);
    148: }