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: 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) {
 50:             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",k-1);
 51:           } else {
 52:             /* Shift is applied to single diagonal entry */
 53:             a[l + k3] = shift;
 54:           }
 55:         }
 56: /*           interchange if necessary */

 58:         if (l != k) {
 59:           stmp      = a[l + k3];
 60:           a[l + k3] = a[k4];
 61:           a[k4]     = stmp;
 62:         }

 64: /*           compute multipliers */

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

 73: /*           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++) {
 87:               ay[ll] += stmp*ax[ll];
 88:             }
 89:         }
 90:     }
 91:     ipvt[2] = 3;
 92:     if (a[12] == 0.0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D",2);

 94:     /*
 95:          Now form the inverse 
 96:     */

 98:    /*     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++) {
117:               ay[ll] += stmp*ax[ll];
118:             }
119:         }
120:     }

122:    /*    form inverse(u)*inverse(l) */

124:     for (kb = 1; kb <= 2; ++kb) {
125:         k   = 3 - kb;
126:         k3  = 3*k;
127:         kp1 = k + 1;
128:         aa  = a + k3;
129:         for (i = kp1; i <= 3; ++i) {
130:             work[i-1] = aa[i];
131:             aa[i]   = 0.0;
132:         }
133:         for (j = kp1; j <= 3; ++j) {
134:             stmp  = work[j-1];
135:             ax    = &a[3*j + 1];
136:             ay    = &a[k3 + 1];
137:             ay[0] += stmp*ax[0];
138:             ay[1] += stmp*ax[1];
139:             ay[2] += stmp*ax[2];
140:         }
141:         l = ipvt[k-1];
142:         if (l != k) {
143:             ax = &a[k3 + 1];
144:             ay = &a[3*l + 1];
145:             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
146:             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
147:             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
148:         }
149:     }
150:     return(0);
151: }