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: }