2: /*
  3:      Inverts 3 by 3 matrix using 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)
 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;

 24: /*     gaussian elimination with partial pivoting */

 27:   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;
 35: /*        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) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
 50:       else {
 51:         /* Shift is applied to single diagonal entry */
 52:         a[l + k3] = shift;
 53:       }
 54:     }
 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 = 3 - 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 <= 3; ++j) {
 74:       j3   = 3*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 = 3 - k;
 82:       ay   = &a[1+k+j3];
 83:       for (ll=0; ll<i__3; ll++) ay[ll] += stmp*ax[ll];
 84:     }
 85:   }
 86:   ipvt[2] = 3;
 87:   if (a[12] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2);

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

 93:   /*     compute inverse(u) */

 95:   for (k = 1; k <= 3; ++k) {
 96:     k3    = 3*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 (3 < kp1) continue;
105:     ax = aa;
106:     for (j = kp1; j <= 3; ++j) {
107:       j3        = 3*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 <= 2; ++kb) {
118:     k   = 3 - kb;
119:     k3  = 3*k;
120:     kp1 = k + 1;
121:     aa  = a + k3;
122:     for (i = kp1; i <= 3; ++i) {
123:       work[i-1] = aa[i];
124:       aa[i]     = 0.0;
125:     }
126:     for (j = kp1; j <= 3; ++j) {
127:       stmp   = work[j-1];
128:       ax     = &a[3*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:     }
134:     l = ipvt[k-1];
135:     if (l != k) {
136:       ax   = &a[k3 + 1];
137:       ay   = &a[3*l + 1];
138:       stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
139:       stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
140:       stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
141:     }
142:   }
143:   return(0);
144: }