Actual source code: dgefa3.c


  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

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

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

 14: PETSC_EXTERN 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;

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

 24:   /* Parameter adjustments */
 25:   a -= 4;

 27:   for (k = 1; k <= 2; ++k) {
 28:     kp1 = k + 1;
 29:     k3  = 3*k;
 30:     k4  = k3 + k;

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

 44:     if (a[l + k3] == 0.0) {
 45:       if (shift == 0.0) {
 46:         if (allowzeropivot) {
 47:           PetscInfo(NULL,"Zero pivot, row %" PetscInt_FMT "\n",k-1);
 48:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 49:         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %" PetscInt_FMT,k-1);
 50:       } else {
 51:         /* Shift is applied to single diagonal entry */
 52:         a[l + k3] = shift;
 53:       }
 54:     }

 56:     /* 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 */
 64:     stmp = -1. / a[k4];
 65:     i__2 = 3 - k;
 66:     aa   = &a[1 + k4];
 67:     for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;

 69:     /* row elimination with column indexing */
 70:     ax = &a[k4+1];
 71:     for (j = kp1; j <= 3; ++j) {
 72:       j3   = 3*j;
 73:       stmp = a[l + j3];
 74:       if (l != k) {
 75:         a[l + j3] = a[k + j3];
 76:         a[k + j3] = stmp;
 77:       }

 79:       i__3 = 3 - k;
 80:       ay   = &a[1+k+j3];
 81:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
 82:     }
 83:   }
 84:   ipvt[2] = 3;
 85:   if (a[12] == 0.0) {
 86:     if (PetscLikely(allowzeropivot)) {
 87:       PetscInfo(NULL,"Zero pivot, row 2\n");
 88:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 89:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row 2");
 90:   }

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

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