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>

 15: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a,PetscReal shift,PetscBool allowzeropivot,PetscBool *zeropivotdetected)
 16: {
 17:   PetscInt  i__2,i__3,kp1,j,k,l,ll,i,ipvt[3],kb,k3;
 18:   PetscInt  k4,j3;
 19:   MatScalar *aa,*ax,*ay,work[9],stmp;
 20:   MatReal   tmp,max;

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

 26:   /* Parameter adjustments */
 27:   a -= 4;

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

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

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

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

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

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

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

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

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